Integrating CFD and Experiment in Aerodynamics - CFD4Aircraft

Integrating CFD and Experiment in 

Aerodynamics 

An international symposium to celebrate the 

career of Prof. Bryan E. Richards 

8 th /9 th September, 2003 

Kelvin Gallery, University of Glasgow 

http://www.aero.gla.ac.uk/integration

Background 

Bryan Richards retires in September, 2003 following forty years of research and 

teaching in aerodynamics. 

His career has involved both experimental work at Imperial College and Von 

Karman Institute and CFD at University of Glasgow. The symposium is 

dedicated to the important topic of how to use CFD and experiments towards the 

goal of improved understanding of aerodynamics. It is intended to bring together 

international experts in these fields to look forward to new ways of integrating 

the two disciplines, and in the process celebrate the varied contributions of Bryan 

Richards to aerodynamics. 

Scientific Rationale 

CFD practitioners and experimentalists have a common goal of understanding aerodynamics. It is therefore 

surprising that the disciplines often only interact for the validation of CFD. This provides a very limited 

form of integration but often there is no interaction between the experimentalist and the CFD practitioners. 

This situation is unsatisfactory from many points of view including (a) the need to have an appreciation of 

the flow before deciding what should be measured, (b) the desirability of having checks in place on the 

experimental measurements as they are taken, (c) the difficulty in making certain important measurements, 

(d) the need to assess the influence of the experimental techniques on the measurements, (e) the ability of 

CFD to provide detailed flow information and sensitivity at a reasonable cost for some cases, (f) the large 

cost of CFD calculations for other cases, and (g)the lack of credibility for the CFD results for some flow 

categories. 

It could be argued that the process of aerodynamic investigation would be significantly enhanced if the 

integration of CFD and experiments was much stronger. In particular, the design and reliability of 

experiments could be significantly enhanced by CFD, the scope of experimental measurements extended 

through CFD and the credibility of the simulation results enhanced by the availability of suitable 

measurements from experiments. This sort of closer integration is however rare. The aim of the symposium 

is to bring together leading researchers from both fields to initiate more careful consideration of these 

issues and to stimulate new ways of approaching aerodynamic studies. 

Local Organisers 

Ken Badcock 

Department of Aerospace Engineering 

University of Glasgow 

Glasgow G12 8QQ 

United Kingdom 

Phone: +44(0)141 3304106 

Fax: +44(0)141 3305560 

gnaa36@aero.gla.ac.uk 

http://www.gla.ac.uk/Research/CFD 

George Barakos, 

Department of Aerospace Engineering 

University of Glasgow 

Glasgow G12 8QQ 


Phone: +44(0)141 3304106 

Fax: +44(0)141 3305560 

gbarakos@aero.gla.ac.uk 

http://www.gla.ac.uk/Research/CFD 

Scientific Committee 

Prof. Ning Qin 

Department of Mechanical Eng. 

University of Sheffield 

UK 

Prof. Daniel Favier 

LABM 

University of Marseilles 

France 

Prof. Richard Hillier 

Department of Aeronautics 

Imperial College 

UK

Experimentalist’s requirements for a safe methodology in 

CFD code validation 

Jean Délery 

ONERA – Centre de Meudon, France, delery@onera.fr 

Keywords: experimental techniques, code 

validation, database 

Abstract 

In spite of the spectacular progress in CFD there is 

still a strong need to validate the computer codes by 

comparison with experiments. The first validation step 

is the assessment of the code numerical safety and 

the physical models accuracy. This validation step 

requires carefully made building block experiments. 

To be calculable, such experiments must satisfy 

conditions such as the precise definition of the test 

set-up geometry, the absence of uncontrolled 

parasitic effects, a complete information on the flow 

conditions and indication on the uncertainty margins. 

Under these conditions, the experiment can be put 

into a database which will be precious to help in the 

development of reliable and accurate codes. The 

paper provides also an overview of modern 

measurement techniques allowing a precise and 

thorough description of complex separated flows. 

Recommendation for the constitution of experimental 

databases are provided as a conclusion. 

Introduction 

Methods for verifying the capability of a code to solve 

given equations have been the object of close 

examinations. Identification and elimination of various 

types of errors and use of precision criteria, methods 

for convergence testing, rules for establishing grid 

convergence, are all required when one has to assess 

the quality of the numerical tool. The various stages of 

the general process of verification that will give to the 

code a confidence label permitting to use it for testing 

theoretical models have been summed up by Roache 

with references to many authors 1 . The ERCOFTAC 

association has issued Best Practice Guidelines 

giving strict recommendations to asses code quality 

for industrial computational fluid dynamics 2 . The code 

verification process constitutes by itself a complex 

program often partially carried out but that should be 

completely satisfied in the ideal cases. A second step 

is devoted to the validation of models aimed at 

predicting flows that cannot be presentable as clearly 

identified solutions of well known mathematical 

problems. At this stage, comparison with experimental 

data is mandatory. 

In the past, predictive methods were validated by 

comparison of the computed results with some 

measured global quantities, such as forces and 

moments, and with wall properties, namely the 

pressure and the heat-transfer for hypersonic 

applications. The skin friction was more rarely 

available, this quantity being difficult to measure 

(even now) in compressible flows. However, the flow 

prediction landscape has completely changed over 

the past 40 years with the advent of numerical 

methods solving the Navier-Stokes equations or 

approaches such as DSMC to predict rarefied flows. 

However, in their present state the CFD codes are still 

far from being free of critics, since many difficulties 

persist both on the numerical and physical sides. 

There is thus a strong need to validate CFD codes, 

more particularly from the physical point of view 

before their routine use for design purposes 3 . 

A comparison restricted to the wall properties is in 

general insufficient to validate the most advanced 

predictive methods. In particular, information on the 

Mach number, temperature, density fields is essential 

to elucidate the cause of discrepancies affecting, for 

example, the wall quantities distribution. Such a 

requirement is still more demanding in hypersonic 

flows where one has to represent complex thermochemical 

processes and/or strongly interacting and 

shock-separated turbulent flows. In this case, 

information on turbulence quantities is also needed, 

which is a formidable challenge in high Mach number 

flows! The prediction of shock/shock interferences 

which can have destructive effects on a nearby 

structure necessitates an accurate prediction of the 

complex structures resulting from shock intersection. 

The problem of code validation is crucial in threedimensional 

applications where the Navier-Stokes 

approach becomes mandatory. Due to the complexity 

of such flows, it is clear that the consideration of the 

surface pressure alone is inadequate, this information 

giving a very partial view of the flow (in threedimensional 

flows, it is no longer possible to infer 

separation from an inspection of the wall pressure 

distributions). 

1

In these conditions, the validation of computer codes 

requires well documented experiments providing not 

only wall quantities but also flow field measurements. 

It is remarkable that the breakthrough in our predictive 

capacity has been paralleled by spectacular 

developments in measurement techniques over 

approximately the same period, mainly with the 

advent of laser based optical methods, optical 

techniques having operated a true revolution in our 

capacity to investigate flows containing shock waves, 

concentrated expansions, thin shear-layers and 

recirculating regions 4 . 

The validation methodology 

Code requirements : reliability or accuracy? 

Before considering a validation action, the aim of the 

calculation must be clearly stated. 

If calculation is used to predict the performance 

of a system or a sub-system, accuracy is 

mandatory. 

In the design of devices involving complex flows 

whose experimental simulation is not possible a 

calculation showing the flow field topology is of 

great help. In this case, accuracy is not essential, 

but reliability is crucial since one must be 

confident on the physical features of the 

computed field. 

The physical understanding of complex flows 

must be based on a theoretical analysis whose 

aim is to help in the interpretation of the 

phenomena and in the establishment of a 

consistent topological description. In this case, 

accuracy is not needed since theoretical 

analyses are most often derived from simplifying 

assumptions rendering quantitative results 

questionable. 

In the last issue, a code is used as a tool to test a 

new physical model. Then, numerical accuracy is 

mandatory since it would be vain to implement a 

good model in an inaccurate code. 

The methodology different steps 

The verification/ validation procedure has to be 

submitted to a four step methodology. 

First step: Assessment of the code numerical 

accuracy. A conclusive assessment of this point is not 

a straightforward issue in the sense that the numerics 

involves many aspects. When possible, a first firm 

answer can be obtained from comparison with 

analytical solutions in laminar flow or well established 

empirical results. In turbulent flow, the question is not 

so clear since numerical and physical modelling 

problems are closely linked. Verification by 

confrontation with other codes is not always 

conclusive since the codes may use different 

numerical techniques, discretization schemes and 

solution algorithms. A further step is to run the code 

on a configuration for which reliable experimental 

results are available. This point is far less obvious that 

it would appear at first sight, since the experimental 

data should allow to draw clear conclusions. 

Second step: Validation of the physics implemented in 

the code on elementary configurations. This is the 

most important point for the specialist in flow physics, 

the first step being only a preliminary step simply 

aiming at verifying the tool. In the second step, the 

code is used to compute what can be considered as 

the elementary components of an aerodynamic flow: 

attached boundary layer, laminar-turbulent transition 

on a flat plate, separation induced by an obstacle, 

flow past a base, shock wave/boundary layer 

interaction, start and development of a vortex 

structure, vortex breakdown, shock/shock interference 

or shock crossing, etc. Two-dimensional - preferably 

axisymmetric - as well as three-dimensional basic 

situations have to be considered. For this first 

validation step, the numerical results are compared 

with building block experiments focusing on a specific 

elementary phenomenon. 

Third step: Validation on more complex sub-systems. 

Once the code and its physical model(s) have been 

validated on basic cases, a more complete 

configuration must be considered consisting in a subsystem 

of a complete vehicle, where several 

elementary phenomena are combined. This is the 

case of a profile on which one encounters laminarturbulent 

transition, attached boundary layers, 

transonic shock wave/boundary layer interaction, 

separation, wake development, etc. The wing 

constitutes a three-dimensional extension with the 

additional problems of the vortices emanating from 

the wing and control surfaces extremities. The 

supersonic air-intake involves shock/shock 

interference, shock wave/boundary layer interactions, 

corner flows with vortex development. After-bodies 

combine supersonic jets with complex shock patterns 

(Mach disc formation), shock induced separation, 

either inside the nozzle (overexpanded nozzle) or on 

the fuselage (jet pluming at the exit of an 

underexpanded nozzle). Many other examples can be 

cited: propulsive nacelle, compressor/turbine 

cascade, helicopter rotor, etc. 

Fourth step: Validation on the complete vehicle or 

object. This is the ultimate target in which the code is 

applied to a complete vehicle. 

Each of the above steps implies an iterative 

procedure between computation and experiment to 

adapt or correct the code from inspection and 

interpretation of the discrepancies between the 

computed and experimental results. This exercise is 

not entirely safe for the experimentalist, since a 

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persistent discrepancy may be due to measurement 

errors or ill defined experimental conditions. 

Requirements for good test cases constitution 

Definition of the geometry. A first condition for an 

experiment aiming at code verification/validation is to 

focus on a configuration whose geometry is 

representative of a typical situation, precisely defined 

and as simple as possible while avoiding singularities 

leading to meshing difficulties. When possible, an 

analytical definition of the contour should be provided. 

It is preferable to give the dimensions in metric units 

to avoid risk of confusion in the reference length used 

to compute a Reynolds number. When possible, a 

two-dimensional geometry should be adopted - even 

for three-dimensional problems - since it offers many 

advantages to visualise the phenomena and to 

execute measurements, in addition of the lower cost 

of the test-set up fabrication. Furthermore, the original 

set-up must frequently be modified before arriving at a 

fully satisfactory flow; such modifications are far 

easier on a two-dimensional/ axisymmetric 

arrangement. Two typical models are shown in Fig. 1. 

a – double cone model for hypersonic separation 

study 

b – Axisymmetric model for powered base flow 

Investigation 

Fig. 1: Two typical simple models for code 

validation purposes 

The first one is a double cone configuration used to 

produced shock-induced separation at high Mach 

number, the second one is a model used to validate 

codes predicting the flow past an axisymmetric 

afterbody equipped with a propulsive jet. 

Boundary conditions. The boundary conditions must 

be well identified and accurately known. This 

concerns the upstream flow conditions (Mach 

number, velocity, pressure, density) when a uniform 

incoming flow exists. In transonic experiments 

executed in a channel type arrangement, one often 

considers phenomena taking place on the channel 

walls, the test section itself being the model. In this 

case, a well defined origin with a uniform state at 

upstream infinity does not exist. Then, the data should 

provide all the flow conditions in a section located 

sufficiently far upstream of the region of interest, 

including the boundary layer properties (mean velocity 

profile, turbulent quantities). If LDV measurements 

now permit to know with a good approximation the 

Reynolds stress profiles in moderate supersonic 

flows, a method must be conceived for deducing from 

these data the dissipation rate of two-equation 

turbulence models. 

In all cases the stagnation conditions (pressure, 

temperature) and the incoming stream 

thermodynamic properties must be given. 

Downstream boundary conditions leading to a well 

posed problem must be provided. If the flow leaving 

the zone of interest is supersonic, then no-conditions 

have to be imposed to perform the calculation. The 

question of the downstream conditions is more 

delicate if the configuration is such that the flow 

leaving the test region is subsonic. When the outgoing 

flow is again uniform, most often a downstream 

pressure is given, since this quantity is easily 

obtained. It is far more difficult to provide the pressure 

field in a complete plane, as some theoreticians 

sometimes ask for. In transonic channel experiments 

where a shock is produced by the choking effect of a 

second throat, the best way is to provide the 

geometry of the second throat and, in the calculation, 

to impose downstream conditions insuring the 

choking of this throat. The photograph in Fig. 2 shows 

a test set-up which has been extensively used to 

analyse shock wave/boundary layer interaction in a 

transonic channel 5 . The entrance of the test section 

has a converging-diverging upper wall constituting a 

first sonic throat. At this location, the flow conditions, 

including the boundary layer profiles, are provided. In 

the present arrangement, an oscillating shock is 

produced by a rotating shaft placed in the 

downstream part of the channel. The shaft has also a 

choking effect, thus providing well defined 

downstream conditions. 

3

model shown in Fig. 4, which has been much used to 

validate both laminar and turbulent shock 

wave/boundary layer interactions 6 . Even in this case, 

the flow adopts a three-dimensional structure at a 

“microscopic” scale, as it can be seen in the surface 

flow pattern in Fig. 5. 

Fig. 2: Test set up arrangement for transonic 

interaction studies 

Parasitic effects. Side effects or uncontrolled 

perturbations must be avoided, except if they can be 

taken into account by the calculation. The side effects 

due to the finite span of any experimental 

arrangement strongly affect the flow when separation 

occurs. Then, the experimented flow can be very 

different from the assumed ideal two-dimensional flow 

which would correspond to the infinite span condition. 

Fig. 4 : Hollow cylinder-plus-flare model for 

axisymmetric flow investigation 

Fig. 3: Surface flow pattern in a nominally 2D 

transonic channel (IMP/PAM document) 

As an illustration Fig. 3, shows a surface flow 

visualisation realised in a nominally two-dimensional 

transonic channel. In the vicinity of the side-walls, two 

foci which are the traces of two tornado-like vortices 

are clearly visible. Confrontation of such an 

experiment with a planar two-dimensional calculation 

can be deprived of any signification and lead to 

erroneous conclusions. When the boundary layer is 

attached or weakly separated this effect is small and 

2D calculations remain acceptable. If one desires to 

keep the mathematical simplicity of two space 

dimensions, the best is to compute an axisymmetric 

flow, as the one past the hollow cylinder-plus-flare 

Fig. 5 : 3D micro structures in an axisymmetric 

reattachment region 

When the goal of an experiment is to reproduce 

closely the behaviour of an aircraft, the coincidence of 

the wind tunnel's Reynolds number with that of real 

flight tests is a condition often hard to satisfy. Even if 

this condition is fulfilled, premature transition can 

occur on the model. The boundary layers on the walls 

of classical wind tunnels are generally turbulent and 

unsteady perturbations radiate from the wall to the 

whole test channel. Such perturbations lead to 

transition of the flow around the model at Reynolds 

4

numbers significantly lower than those where it occurs 

in real flying tests. The conception of quiet wind 

tunnels, at NASA, ONERA and Purdue University 7 , 

has been undertaken to overcome this difficulty. 

Inversely, when a plainly turbulent regime is searched 

for code validations, it is preferable that the wind 

tunnel be naturally turbulent without the help of 

auxiliary means like transition strips. The transition in 

general is indeed far from being treated satisfactorily 

by the methods of calculation presently at our 

disposal and transitional effects are often present 

when turbulence is set up artificially. 

Experimental needs. The description of the flow must 

be as complete as possible to provide all the 

information useful to understand its physics and to 

help in the elucidation of disagreements. Flow 

visualisations are desirable to give a precise idea of 

the flow topology. Surface flow visualisations are 

mandatory in three-dimensional flows to indicate the 

location of separation/attachment lines. 

Measurements reliability and accuracy. The 

experimental data must be reliable, which means that 

the experiment is not "polluted" by an extraneous 

phenomenon due to a bad definition of the test 

arrangement or an ill functioning of the facility. The 

risk is at its maximum when such an influence has not 

been identified and is interpreted as a proper basic 

feature of the flow under investigation. Measurements 

must be safe, as for the calculations, this aspect 

being distinct from the problem of accuracy which 

must also be carefully assessed. Measurement 

accuracy must be in proportion with the calculation 

purposes and the modelling present status. Precision 

has a very high cost; in most circumstances what is 

important is to be confident in the experimental results 

and to known (even approximately) the uncertainty 

margins. 

The physical interpretation. Constitution of safe data 

base is not restricted to the execution of hopefully 

good experiments in relation with code development. 

The experimentalist must also be a physicist able to 

interpret its findings and to understand the physics of 

the investigated flow field. This interpretation, which 

must be based on theoretical arguments, is essential 

to insure the safety of the results. It must precede any 

numerical exploitation. 

The above conditions lead to reject of a large quantity 

of existing experiments for validation purposes. In 

particular, nearly all the two-dimensional ramp flow 

experiments have to be considered with suspicion 

when separation occurs. Also, in a large number of 

published experiments some information is missing to 

execute the calculation or the boundary conditions are 

not clean in the sense that the conditions on the 

frontiers of the zone of interest affect the 

phenomenon in a complicated and unclear manner. In 

the present context, any experiment should satisfy a 

calculability criterion meaning that the experiment is 

not useful if it cannot be calculated. 

Validation of experiment by calculation. Calculation is 

also used by the experimentalist to control his results. 

There are simple situations where theory can be 

considered as safe and accurate, so that a good way 

to check a new experimental method is to compare its 

results with the theoretical ones. In situations where 

the calculation cannot be considered as entirely safe, 

an important, persistent and unexplained discrepancy 

should provoke a reconsideration of the experimental 

results. In hypersonic flows, measurements executed 

with optical techniques like Laser Doppler Velocimetry 

(LDV), Coherent Anti-Stokes Raman Scattering 

(CARS), Electron Beam Fluorescence (EBF) have 

been in great part validated by comparison with 

theoretical results, no other techniques being 

available to perform such measurements. 

An overview of modern measurement 

techniques 

The purpose of this section is to briefly present 

modern measurement techniques which are used (or 

could be used) to investigate complex flows, mare 

particularly at high Mach number. The classical and 

well proven methods will not be mentioned, even if 

they are still routinely used! 

Flow visualisations 

Fortunately, most flow phenomena can been 

visualised, which is a great help for their physical 

understanding and modelling 8 . Flow visualisations 

must be attempted in all circumstances where they 

are possible, specially on three-dimensional 

configurations for which they are nearly mandatory. 

The first step consists in making a visualisation of the 

surface flow pattern in order to localise the critical 

points that it contains and the accompanying 

separation/ attachment lines 9 . The photograph in Fig. 

6a shows the complex surface flow pattern produced 

by the impingement on the central body of the 24 

primary jets of a plug nozzle. Flow field visualisation 

can be achieved by several techniques, including the 

laser sheet method (both in low and high speed 

streams, see Fig. 6b), shlieren, shadowgraph of 

interferometry in compressible flows (see Fig. 6c), 

electron beam fluorescence (EBF) in low pressure 

high Mach number flows (see Fig 6d). Particle Image 

velocimetry (PIV, see below) can also be considered 

as a sophisticated visualisation method for separated 

flows. 

5

a – surface flow on the central body of an aerospike 

nozzle 

d - EBF visualisation of the flow past a double code 

model at Mach 10 

Fig. 6: Different techniques of flow visualisation 

Wall measurements 

b – laser sheet visualisation of the vortices past an 

elongated body 

c – interferogram of a transonic shock wave 

Pressure Sensitive Paint. This method (known as 

PSP) which allows to determine the complete 

pressure distribution over a model, is based on the 

fact that some compounds emit light (luminescence) 

when excited by a suitable source, the emitted light 

having a longer wave-length than the excitation 

light 10,11 . The quantity of light emitted depends on the 

oxygen diffused into the paint because oxygen 

quenches and deactivates the excited molecules. The 

internal concentration of oxygen being a linear 

function of the external pressure of the same gas, one 

can measure the pressure acting on the paint by 

detecting some of its luminescent parameters. A 

difficulty with PSP’s is their simultaneous response to 

change in temperature, which could restricts their use 

in hypersonic flows. The difficulty can be 

circumvented either by using a paint nearly insensitive 

to temperature or by making a correction from 

measurement of the wall temperature. Convincing 

PSP measurements have been performed at high 

Mach number on a plug nozzle with a PSP 

component having a low sensitivity to temperature 12 

(see Fig. 7). 

Skin-friction measurement. In a recent technique, the 

skin-friction is determined by measuring the rate of 

deformation of a thin oil film deposited on the model 

surface 13-15 . If the film of oil is thin compared to its 

length, its surface takes the shape of a small wedge 

whose thickness y at any time t can be accurately 

measured by an interferometric technique (see Fig. 

8). Knowing the location x of the measurement point 

and the time t, the determination of the wall shear 

stress is in principle straightforward. 

6

Heat flux measurements. Over the past 20 years, 

quantitative infrared thermography has experienced a 

strong development in a large number of 

laboratories 16-18 . As it is well known, a body emits a 

radiative signal whose intensity is a strong function of 

its temperature. In infrared thermography, the model 

is observed by an infrared camera containing a 

detector element sensitive to infrared radiations at a 

certain wave-length. By processing a series of 

pictures taken at known time intervals, it is possible to 

construct the time history of the model temperature 

and to deduce the surface heat flux distribution by 

means of the heat equation. The example of infrared 

image (in false colour) in Fig. 9 shows the heat flux 

distribution on a hemisphere in a Mach 5 flow. 

Infrared pictures also provide a convenient way to 

detect laminar-turbulent transition. 

Fig. 7: PSP measurements on a plug nozzle 

central body 

t = 0 m n 

2 m n 

4 m n 

Fig. 9: Infrared measurements of the heat flux 

distribution over an hemisphere in a Mach 5 

flow. 

Field measurements 

6 m n 

Measurement of field quantities such as velocity, 

temperature, density, gas species concentration,etc is 

a difficult task. However, the advent of laser sources 

in the early 60s has given a dramatic impetus to the 

development of non intrusive methods allowing an insitu 

determination of the properties of a gas, including 

its velocity 

Laser Doppler Velocimetry 

Fig. 8 : Skin friction measurement by the thin oil 

film technique 

The basic idea underlying LDV, which is now a well 

known technique, is to measure the velocity of tiny 

particles transported by the flow 19-21 . If these particles 

are small enough, their velocity is assumed to be that 

7

of the stream and LDV provides a measure of the 

local instantaneous velocity. A statistical treatment of 

a sample acquired at one point permits to determine 

the mean velocity as well as the turbulent quantities. 

The basic postulate of LDV is not always true in highly 

decelerating or accelerating flows in which the 

particles do not instantaneously adjust their velocity to 

that of the fluid. The problem of particle lag is at the 

heart of LDV and one should be cautious in the use of 

results obtained in regions where the velocity 

undergoes a large variation over a short distance, 

situations frequently met in hypersonic flows. Reliable 

LDV measurements have been obtained in shockseparated 

flows up to Mach number 5; above 

measurements become hazardous. 

Developed since 1991, Doppler global velocimetry 

(DGV) - also called planar Doppler velocimetry (PDV) 

- is a particle based velocity measurement system 

giving the velocity of particles injected in the flow, as 

LDV. The difference is that LDV determines the 

velocity at one point in space, whereas DGV has the 

capacity to give the velocity at a multitude of points in 

a given region of space 22-24 . The basic principle 

consists in determining the Doppler shift of the light 

scattered by a moving particle. 

Particle Image Velocimetry 

The principle of PIV is to illuminate particles injected 

in the flow by a laser sheet and to observe the 

scattered light 24-26 . In order to perform velocity 

measurements, two laser pulses, separated by a 

short and known time interval ∆t, are emitted to 

provide two images recorded on the same 

photographic plate (in practice, the photographic plate 

is replaced by a CCD camera providing the image in a 

numerical form). During the interval ∆t, each particle 

has moved over a distance proportional to its velocity 

(assumed to be that of the flow) giving two images on 

the plate. The velocity components contained in the 

plane of the image are deduced by measuring the 

displacement of the particles which is done by 

automated procedures using sophisticated algorithms. 

Particle image velocimetry is a very powerful 

technique since it provides a complete velocity field in 

a large number of points for a whole region of space, 

whereas LDV is restricted to measurements at one 

point. PIV is very precious for the study of unsteady 

phenomena since it allows to freeze the velocity field 

at a given instant. On the other hand, the access to 

the averaged field quantities (mean velocity) 

necessitates to operate an averaging procedure over 

a large quantities of pictures. This can become 

problematic for the Reynolds tensor components 

whose determination requires averaging several 

thousands of instantaneous values. In this case LDV 

if still more effective (see in Fig. 10a an average LDV 

velocity field in the vicinity of the bleed system of a 

supersonic air-intake and in Fig. 10b, the instant PIV 

velocity field in a rotating jet). 

0 50 100 

X (mm) 

a – LDV measurement in the bleed region of a 

supersonic air intake (average Mach number) 

b – PIV velocity field in a rotating jet 

Fig. 10: Velocity measurements by laser 

techniques with flow seeding 

Laser Spectroscopic Flow Diagnostic 

These methods are based on fundamental physical 

processes related to the interaction between light and 

matter an do not need seeding by heavy particles of 

relatively big size. Laser spectroscopic measurements 

are based on the radiative interaction of a laser beam 

with spectroscopic properties of the investigated flow. 

Depending on the interaction process, the laser light 

is either absorbed or scattered by those species 

which are radiatively active at wave-length used. 

8

The measurements are made on selected populations 

from which it is possible to deduce the local gas 

properties. The intensity of the radiative signal gives a 

measure of the species concentration (or 

atom/molecule number density). The temperature is 

most often deduced from the broadening of a spectral 

line due to the Doppler effect induced by the motion of 

the atoms or molecules (the energy contained in this 

motion being proportional to the square root of the 

translational temperature). The velocity of the flow is 

deduced from the shift of the central frequency of the 

signal coming from the Doppler effect produced by 

the bulk motion of the gas. Rotational and vibrational 

temperatures can also be deduced from an analysis 

of the reactive signal. 

Laser absorption. In this technique, the laser beam is 

tuned to a wave-length which is resonant with an 

absorbing transition of a selected species. The 

attenuation of the beam passing through the test 

region is measured, the absorption of two or more 

wave-lengths being used to determine both the gas 

temperature and the density of the absorbing species. 

This technique is simple to implement since it requires 

an optical access which is just sufficient to allow the 

laser beam to pass through the test region. 

Production of a detectable and usable signal does not 

depend on the laser power, so that small power lasers 

can be used. 

analysis of the emitted spectrum constitutes a way to 

measure the vibrational and rotational temperatures in 

this particular state. Species concentration is 

determined from the amount of light contained in a 

certain narrow spectral band. 

If the photon emerges from the interaction at a shorter 

wave-length, hence higher energy, the process is 

called Raman Anti-Stokes scattering. This scattering 

process takes place with molecules of a higher 

energy level whose relative number is small; thus the 

Raman Anti-Stokes signal is naturally fainter than the 

Stokes signal. Raman signals are at a wave-length 

different from that of the laser and consequently are 

affected very little by background scattering. In 

addition, the Raman effect is an interaction driven by 

the radiation field and, for this reason, is not affected 

by collisional quenching (see below). The 

disadvantage of the technique is that the signal is 

very weak and that the laser beam is scattered in all 

directions of space. In order to eliminate this serious 

disadvantage, stimulated Raman spectroscopy has 

been developed. 

Among these methods, the diode laser absorption 

technique consists of illuminating a transverse section 

of the gas to be studied by an infrared light beam 27,28 . 

Doppler broadening and shift in wave-length of the 

species absorption lines is used to obtain a measure 

of translational temperature and flow velocity 

Rayleigh scattering. In Rayleigh scattering the light 

from a laser beam is scattered at nearly the same 

frequency as that of the incident light. By measuring 

the intensity of the scattered light and its spectral 

properties, it is possible to determine the density, 

pressure and velocity of the gas. Rayleigh scattering 

is probably the simplest method giving a local 

measurement of flow properties, since it does not rely 

on any spectral resonance of a seed material (see LIF 

below). On the debit side, the method lacks spectral 

difference between the light scattered by the gas and 

the background light so that it is difficult to distinguish 

the useful signal from parasitic light. 

Raman scattering. When a photon strikes a molecule, 

it leaves a fraction of its energy to the molecule which 

is then raised to a higher energy state. When deexcitation 

occurs, a photon is released which has a 

longer wave-length, or lower energy, than the incident 

photon. This process is called Raman Stokes 

scattering. The scattered light has a spectrum whose 

frequencies are characteristic of the molecule. Thus, 

Fig. 11: CARS measurements in a hypersonic 

wind tunnel 

Stimulated Raman scattering. This technique is 

analogous to spontaneous Raman scattering, the 

scattering being produced by a first laser called the 

pump laser. The system now includes a second laser, 

the probe laser, whose frequency is shifted so that the 

differences in wave-length with the pump laser 

matches a resonant frequency of the molecule. This 

arrangement is used in Coherent Anti-Stokes Raman 

Scattering (CARS) in which measurements are made 

with the Anti-Stokes radiation 29 (see Fig. 11). The 

main advantage of CARS is that the scattering cross 

section is much higher than that of the spontaneous 

Raman effect by several orders of magnitude. In 

addition, the emitted light leaves in a preferred 

direction defined by the directions of the incident 

beams. Thus, the useful light is collected more 

efficiently than in ordinary Raman scattering. Analysis 

9

of the CARS signal allows the determination of the 

nature of the species, of their concentration, 

temperature, etc. Also, the gas velocity can be 

determined from Doppler shift. There are several 

variants of CARS, for example in Dual Line CARS 

(DLCARS) four beams are used to excite two energy 

levels of the studied molecule which allows a more 

direct determination of the density and temperature of 

the gas 30 . 

y 

O 

x 

a – EBF visualisation of the flow 

1000 

500 

T( K) 

ρ × 10 

3 

2 

1 

3 

x( mm) 

− 4 − 3 − 2 − 1 0 

3 

( kg / m ) 

temperature 

CARS measurements 

N.S. calculation 

cylinder 

density 

x( mm) 

0 

− 4 − 3 − 2 − 1 0 

b – density and temperature distributions 

Fig. 12: DLCARS measurements in front of a 

cylinder at Mach 10 

Density and temperature measurements by DLCARS 

in front of a cylinder placed in a Mach 10 flow are 

shown in Fig. 12, along with a comparison with a 

Navier-Stokes calculation which was used here to 

validate the measurements. 

Laser induced fluorescence. In Laser Induced 

Fluorescence (LIF) the measured signal is obtained 

from the subsequent spontaneous emission of 

absorbed energy or fluorescence 31 . In this process, 

the emission takes place after a relatively long time, 

several seconds in some cases, whereas in other 

types of interaction emission occurs after 10 -8 s for 

most molecules. Due to this long relaxation time, the 

signal analysis must consider the effect on some 

species of non-radiative energy transfers taking place 

through collisions between molecules (quenching). 

Quenching depends on temperature and species 

concentration. Proper operation of LIF requires the 

presence of species For aerodynamic research in non 

reacting fluids, the flow is seeded with a small 

concentration of sodium, iodine, nitric oxide, acetone, 

etc. 

Fluorescence properties are also used to obtain a 

picture of an entire flow region by using planar laser 

induced fluorescence (PLIF) 32 . In this technique, the 

zone of interest is illuminated by a laser sheet and the 

fluorescence picture recorded by a camera containing 

a two-dimensional array of photo-detectors. 

Electron beam fluorescence 

Electron Beam Fluorescence (EBF) is a wellestablished 

technique to perform local and non 

intrusive measurements of density, vibrational and 

rotational temperatures in a low density flow of 

nitrogen or air 33 . The technique is based on the 

formation of N 2 + excited ions by an energetic electron 

beam (typically 25keV energy) traversing the flow. 

The almost immediate drop to a lower energy state 

gives rise to fluorescence whose intensity is 

proportional to the density. At high densities, 

quenching destroys the linearity of the response. 

Tomographic imaging with a sweeping electron beam 

creating a visualisation plane is a classical application 

of EBF (several examples are shown in this paper). 

The photograph in Fig. 6d is an EBF visualisation of 

the flow past a double-cone model. In this case, the 

electron beam is fixed, the visualisation being 

obtained by post-luminescence. 

Density measurements using electron-beam-excited 

X-ray detection. In order to obtain quantitative density 

results, even when quenching occurs, a variant based 

on the detection of brehmstrahlung and characteristic 

X-rays can be employed 34-36 . These X-rays are 

emitted by electrons which are decelerated when 

passing close to an atom. The method has the 

10

advantage that the signal is emitted instantly and 

shows no collisional quenching. The X-ray radiation at 

the point of measurement is collimated and detected 

with X-ray counters equipped with preamplifiers. The 

photograph in Fig. 13a shows the electron beam used 

to perform X-rays measurements on a cylinder-flare 

configuration (see below). The beam traverses the 

model (though a small tube) to avoid the intense X- 

rays production which would result from the impact of 

the beam on the surface. Density profiles obtained in 

the interaction region are compared to Navier-Stokes 

and DSMC calculations in Fig. 13b. 

principle. The miniature pseudo-spark developed at 

Onera generates an intense pulsed electron beam, 

emitted by an electron gun 27,37 which penetrates 

within the flow from a hole across the surface of the 

model and traces the path of a high voltage glow 

discharge in some 10ns. At a precise delay time (5µs) 

after the electron gun actuation, a CCD camera is 

opened briefly (250ns) to image the position of the 

luminous column convected by the flow. The local 

velocity of the stream is deduced from the horizontal 

displacement of a given point during the selected 

delay time. 

Unsteady flow qualification 

A greater attention is now paid to flow unsteady 

aspects, since unsteadiness is intrinsically linked to 

any phenomenon (the steady state is as illusory as 

2D assumption!) and since flow fluctuations can 

generate vibrations, noise and other disagreements. 

The discovery of flow fluctuations is not new, but now 

there exist CFD methods in measure to compute 

unsteady flows with increasing accuracy. One can cite 

the URANS (Unsteady Reynolds Averaged Navier- 

Stokes), LES (Large Eddy Simulation), DES 

(Detached Eddy Simulation), DNS (Direct Numerical 

Simulation) approaches In parallel to this progress, 

there is a need for more complete and more accurate 

descriptions of typical unsteady flows to validate the 

codes. 

a – EBF visualisation of the flow and electron beam 

25 

20 

15 

10 

5 

Y (mm) 

EXP 

DSM C 

FLOW 

NASCA 

0 

0 0.5 1 1.5 2 2.5 

ρ/ρ 0 

b – comparison between computed and measured 

density profiles 

Fig. 13: Measurements by X-rays detection in a 

laminar shock-separated boudary layer 

Velocity measurements using an electron-beamassisted 

glow discharge. This technique uses a 

miniature pseudo-spark type electron gun to perform 

velocity measurements through a time of flight 

Instant visualisations (schlieren, shadowgraphy) 

coupled with high speed cinematography are precious 

to “follow” the fluctuating phenomenon. The local 

velocity fluctuations (in particular turbulence) are 

classically measured with hot-wire anemometry in 

conjunction with unsteady pressure measurement at 

the wall with appropriate transducers. PIV is a 

precious tool to obtain an instant picture of the flow 

field showing the large structures generated by 

separation (see Fig. 10b). A sequence of such 

pictures allow to follow the structures in space and 

time (in fact, the time interval between two 

consecutive pictures is still too long for rapid 

phenomena but rapid progress is made in the field). 

As we know, LDV gives the instant velocity at one 

point which provides the Reynolds tensor components 

by suitable averaging. If the unsteadiness is driven by 

a periodic mechanism (like in transonic shock 

oscillation, cavity flow or air-intake buzz), conditional 

sampling and appropriate processing permits to 

establish the organised motion from local instant 

measurements (hot-wire, LDV). 

Database constitution 

Constitution of a database is not a straightforward 

operation. In addition of technical skill to fabricate a 

test set up, to operate the wind tunnel and execute 

11

the experiment, to perform the measurements, it 

requires a solid background in fundamental fluid 

mechanics. The database constitution is not limited to 

the acquisition of a vast amount of results, but must 

be accompanied by an in depth analysis of the flow 

physics. Because of the investment needed by such 

operations and their strategic importance for the 

development of predictive methods, the question of 

the database test cases dissemination inevitably 

arises. It is now realised that a good database can be 

as precious as a code and cannot be freely 

transmitted. Even basic experiments have now an 

economic weight and cannot be put on the market 

without something in exchange. Thus, dissemination 

rules have to be more precisely defined according to 

the more or less precious nature of the database 

contents. 

In addition of the permanent scientific concern about 

more accurate, safer and less expansive predictive 

methods, the problem of the constitution of valuable, 

safe, well identified and permanent databases is now 

considered as a strategic issue and addressed 

seriously. In this perspective, the ONERA Fluid 

Mechanics and Energetic Branch has started the 

constitution of a database containing the most 

prominent experimental results obtained in its 

research wind tunnels of the Meudon-Centre over the 

last 30 years 38 . This task will be actively pursued and 

the database contents fed with new experiments 

satisfying the quality criteria here above defined. At 

the European level, the ERCOFTAC association has 

constituted a database containing 82 test cases, 

stored by the University of Surrey, which can be 

obtained through the ERCOFTAC website 39 . In the 

framework of the FLOWNET European-Union project 

a database has been constituted which can be 

accessed through the INRIA website 40 . Thus, several 

national and international initiated have been initiated 

in the past years to build complete, well documented 

and safe databases in order to help in the 

development of accurate predictive methods both for 

research end industry. 

Concluding Remarks 

The confidence in code predictions is still limited 

because of the uncertainties in the numerical handling 

of the equations and of the lack of accuracy of the 

physical models implemented in the codes. This is 

particularly true in separated high Mach number flows 

which contain both intense shock waves, thin shear 

layers, separated regions (laminar, transitional and 

turbulent) and are affected by real gas effects. A 

consequence of the intense development of the CFD 

activity has been to urge experimentalists to execute 

more complete experiments, including the definition of 

all the flow properties. This demand has motivated an 

important effort to develop advanced and non 

intrusive methods for detailed flow investigation, such 

as PSP, infrared thermography, LDV, DGV, laser 

spectroscopic diagnostic techniques, etc. 

Thus, during the past years a strategy has emerged 

to organise more efficiently the dialectics between 

computation and experiment. To validate their codes, 

numericians need an as complete as possible 

information on some representative test cases. This 

information constitutes what is called a database 

which must respect certain rules to be useful. Thus, 

the database must contain a precise description of the 

configuration, along with all the necessary flow and 

boundary conditions. The measurements must be 

considered as safe, and if possible accurate, these 

objectives being difficult to reach in hypersonic 

facilities because of the extreme flow conditions and 

the short useful test duration. Uncertainty margins 

must be provided in order to allow meaningful 

conclusion on the accuracy of physical models. 

Bibliography 

1. Roache, P.J., Verification of Codes and Calculations, 

AIAA Journal, Vol. 36, N°5, May 1998, pp. 696-702 

2. The ERCOFTAC Best Practice Guidelines for 

Industrial Computational Fluid Dynamics. Contact 

ahhutton@qinetic.com 

3. Benay, R., Chanetz, B. and Délery, J., Code 

Verification/Validation with Respect to Experimental 

Data Banks, Aerospace Science and Technology, 7 

(2003), pp. 239-362 

4. Délery, J. and Chanetz, B., Experimental Aspects 

of Code Verification/Validation: Application to Internal 

Aerodynamics, VKI Lecture Series 2000-08, 5-8 June, 

2000 

5 Bur,R., Corbel, B. and Délery, J., Study of Passive 

Control in a Transonic Shock Wave/Boundary Layer 

Interaction. AIAA Journal, Vol. 36, N°3, 1998, pp. 394- 

400 

6 Chanetz, B., Benay, R., Bousquet, J.-M., Bur, R., Pot, 

T., Grasso, F. and Moss, J., Experimental And 

Numerical Study of the Laminar Separation in 

Hypersonic Flow, Aerospace Science and Technology, 

No. 3, 1998, pp. 205-218 

7 Schneider, S.P.,Rufer, S.J., Randall, L. and Skoch, 

C., Shakedown of the Purdue Mach-6 Quiet-Flow 

Ludwieg Tube, AIAA Paper 2001-0457, Jan. 2001 

8 Van Dyke, M., An Album of Fluid Motion, The 

Parabolic Press, Stanford, CA,1982 

9. Délery, J., Robert Legendre and Henri Werlé: 

Toward the Elucidation of Three-Dimensional 

Separation, Ann. Rev. Fluid Mech.,2001-33, pp. 129- 

154 

10. Crites, R. C., Pressure Sensitive Paint Technique, 

VKI Lecture Series 1993-05 on Measurement 

Techniques, April 1993 

11. Mébarki, Y., Peintures sensibles à la pression : 

application en soufflerie aérodynamique (Pressure 

Sensitive Paints: Application in wind tunnels). Ph. D. 

Dissertation, University of Lille 1, March 1998 

12

12. Mébarki, Y. and Mérienne, M. C., PSP Application 

on a Supersonic Aerospike Nozzle, PSP Workshop, 

Seattle, USA, Oct. 6-8, 1998 

13 Settles, G. S., Recent Skin-Friction Techniques for 

Compressible Flows, AIAA Paper 86-1099, May 1986 

14 Seto, J. and Hornung, H., Two-Directional Skin 

Frictions Measurement Utilizing a Compact Internally- 

Mounted Thin-Liquid Skin-Friction Meter; AIAA Paper 

93-0180, Jan. 1993 

15 Desse, J. M., Oil-Film Interferometry Skin-Friction 

Measurements under White Light. AIAA Journal, Vol. 

41, N°4, April 2003 

16 Bouchardy, A. M, Durand, G. and Gauffre, G., 

Processing of Infrared Thermal Images for 

Aerodynamics Research, 1983 SPIE Int. Technical 

Conference, Geneve, April 18-22, 1983 

17 Gartenberg, E. and Roberst, S. Jr., Twenty-Five 

Years of Aerodynamics Research with Infrared Imaging, 

Thermosense XIII, SPIE Proc. Vol. 1467, 1991, pp. 338- 

353 

18 Le Sant, Y. and Fontaine, J., Application of Infrared 

Measurements in the ONERA's Wind Tunnels, Wind 

Tunnels and Wind Tunnel Test Techniques, Cambridge, 

U.K., April 14-16, 1997 

19 Yanta, W.-J., Turbulence Measurements with a 

Laser Doppler Velocimeter, NOLTR 73-94, 1973. 

20 Boutier, A., Caractérisation de la turbulence par 

vélocimétrie laser (Turbulence Characterization with 

Laser Velocimetry) 35 ème Colloque d'Aérodynamique 

Appliquée de l'AAAF, Lille, France, March 22-24, 1999 

21 Boutier, A. and Micheli, F., Laser Anemometry for 

Aerodynamics flow Characterization, La Recherche 

Aérospatiale, N°3, 1996, pp. 217-226 

22 Meyers, J. F., Development of Doppler Global 

Velocimetry for Wind Tunnel Testing, 18 th Aerospace 

Ground Testing Conference, Colorado Springs, CO, 

June 1994, AIAA Paper 94-2582 

23 Lempereur, C., Barricau, P., Mathe, J. M. and A. 

Mignosi, Doppler Global Velocimetry: Accuracy Test in 

a Wind Tunnel, ICIASF 99, Toulouse, France, June 14- 

17, 1999 

24 Samimy, M. and Wernet, M. P., Review of Planar 

Multiple-Component Velocimetry in High Speed Flows, 

AIAA Journal, Vol. 38, N°4, April 2000 

25 Riethmuller, M. L., Vélocimétrie par images de 

particules ou PIV. Summer school of the Association 

Francophone de Vélocimétrie Laser, Saint-Pierre 

d'Oléron, Sept. 22-26, 1997 

26 Raffel, M., Willert, C. and Kompenhans, J., Particle 

image velocimetry. A practical guide. Springer-Verlag, 

1998 

27 Beck, W. H., Trinks, O. and Mohamed, A., Diode 

Laser Absorption Measurements in High Enthalpy 

Flows: HEG Free Stream Conditions and Driver Gas 

Arrival, 22 nd International Symposium on Shock Waves, 

Imperial College, London, U.K., July 18-23, 1999 

28 Chanetz, B., Bur, R., Dussillols, Joly, V., Larigaldie, 

S., Lefèbvre, M., Marmignon, C., Mohamed, A. K., 

Oswald, J., Pot, T., Sagnier, P., Vérant, J. L. and 

William, J., High Enthalpy Hypersonic Project at 

ONERA, Aerospace Science and Technology, Vol. 4, 

N°5, July 2000, pp. 347-361 

29 Lefebvre, M., Chanetz, B., Pot, T., Bouchardy, P. 

and Varghese, Ph., Measurement by Coherent Anti- 

Sokes Raman Scattering in the R5Ch Hypersonic 

Wind Tunnel, Aerospace Research, No. 1994-4, 

1994, pp. 295-298. 

30 Grisch, F., Bouchardy, P., Péalat, M., Chanetz, B., 

Pot, T. and Cöet, M.-C., “Rotational Temperature and 

Density Measurements in a Hypersonic Flow by Dualline 

CARS”, Applied Physics B 56, 1993, pp. 14-20 

31 Gross, K.-P., McKenzie, R.-L. and Logan, P., 

Measurements of Temperature, Density, Pressure, and 

Their Fluctuations in Supersonic Turbulence Using 

Laser-Induced Fluorescence, Experiments In Fluids 5, 

1987, pp. 372-380 

32 Hiller, B. and Hanson, R.-K., Simultaneous Planar 

Measurements of Velocity and Pressure Fields in Gas 

Flows using Laser-Induced Fluorescence, Applied 

Optics, Vol. 27, N°1, Jan. 1988, pp. 33-48 

33 Mohamed, A.K., Pot, T. and Chanetz, B., 

Diagnostics by Electron Beam Florescence in 

Hypersonics, 16 th International Congress on 

Instrumentation in Aerospace Facilities, Dayton, OH, 

July 18-21, 1995 

34 Kuznetsov, L., Rebrov, A. and Yarigin, V., 

Diagnostics of Ionized Gas by Electron Beam in X-Ray 

Spectrum Range, 11 th Int. Conference on Phenomena 

in Ionized Gases, Prague, 1973 

35 Gorchakova, N., Kuznetsov, L., Rebrov, A. and 

Yarigin, V., Electron Beam Diagnostics of High 

Temperature Rarefied Gas, 13 th Int. Symposium on 

Rarefied Gas Dynamics - Vol. 2, Plenum Press Eds., 

1985, pp. 825-832 

36 Gorchakova, N., Chanetz, B., Kuznetsov, L., 

Pigache, D., Pot, T., Taran, J.-P. and Yarigin, V., 

Electron Beam Excited X-Ray Method for Density 

Measurements of Rarefied Gas Flows Near Models. 

21 st Int. Symposium on Rarefied Gas Dynamics - Vol. 2, 

Cepadues Eds., Toulouse, France, July 1999, pp. 617- 

624 

37 Larigaldie, S., Bize, D., Mohamed, A. K., Ory, M., 

Soutadé, J. and Taran, J. P., Velocity Measurement in 

High Enthalpy, Hypersonic Flows using an Electron 

Beam Assisted Glow Discharge, AIAA Journal, Vol. 36, 

N°6, June 1998 

38 Benay, R., La base de données du DAFE. Mise à 

jour 2001 (The Data Bank of the Fundamental/ 

Experimental Aerodynamics Department. Update 2001), 

ONERA Technical Report N° RT 3/03589 DAFE, July 

2001 

39 ERCOFTAC Database at University of Surrey at 

www.ercoftac.org 

40 FLOWNET Database at INRIA at www.inria.fr 

13

The Synergy of CFD and Experiments in Aerodynamics Research 

at Cranfield University, Shrivenham 

A. J. Saddington, K. Knowles and N. J. Lawson 

Aeromechanical Systems Group, 

Department of Aerospace, Power and Sensors, 

Cranfield University, RMCS, Shrivenham, 

Swindon, Wiltshire, SN6 8LA, UK 

k.knowles@rmcs.cranfield.ac.uk 

Keywords: LDV, PIV, CFD, supersonic, jet, transonic, cavity, racecar 

Abstract 

This paper discusses how the combined use of computational fluid dynamics and experimentation has been applied to 

three particular fluid dynamics problems: high-speed turbulent jet flow, transonic cavity flows and open-wheeled race car 

aerodynamics. In each case knowledge gathered from one analysis technique has been used to assist in the application 

of the second technique thereby enabling greater understanding of the flow physics being studied than would have been 

possible through the isolated use of one or other methodology. 

1 Introduction 

For some time now, aerodynamics research carried out at Cranfield University’s Shrivenham Campus has made use of 

both experimental and numerical methods. The combination of these two disciplines has enabled greater understanding 

of the flow physics being studied than would have been possible through either a purely experimental or purely 

numerical approach. Using examples of recent research projects, this paper will discuss the synergistic role that CFD 

and experiments have had in our aerodynamics research programme. 

Early combined CFD and experimental research was primarily driven by the need for CFD validation e.g. [1]. With 

computational resources limited, the experimental results were primarily used to validate the CFD models. The main 

objective was to give globally similar results to those measured in the experiments. The CFD was then used to reveal 

limited extra information on the flowfield. 

More recently, improved computational resources have enabled refinements to the CFD models. Whilst CFD validation 

is still important, these models have provided additional insight into the physical processes involved, which were not 

discernable from the experimental measurements. 

2 High-speed jet research 

The rate at which a supersonic jet mixes with the surrounding ambient fluid is important for many aerospace applications, 

notably in jet aircraft and rocket propulsion. For supersonic jets the generation of streamwise vortices appears 

to be beneficial in improving mixing [2] and schemes have been investigated using vortex generators, tabs [3] and other 

intrusive devices. This work [4,5] presents a numerical and experimental study of mixing in underexpanded, supersonic 

turbulent jets issuing from axisymmetric and castellated nozzles into quiescent conditions. 

Experimental measurements using laser doppler velocimetry (LDV) and pitot probe measurements [6] along the jet 

centreline at a nozzle pressure ratio (NPR = nozzle total to ambient static pressure ratio) of 4 indicated that the 

1

castellated nozzles entrained more mass flow into the jet than a simple convergent nozzle. The CFD models verified 

that this was the case but crucially also provided a physical explanation of the entrainment mechanism that would 

have been very difficult to deduce from the available experimental data. 

2.1 Nozzle design 

Three castellated nozzles with convergent profiles and an exit diameter, D of 29.4 mm were investigated (Fig. 1). Each 

nozzle had four regularly spaced castellations. The difference between the three nozzles was confined to the geometry 

of the gap between each castellation. The first nozzle (regular) had castellations cut by a radial line from the centre of 

the nozzle, as shown by the inner region of Fig. 2. The ‘outer region’ of Fig. 2 indicates alternative tooth designs (for 

all four teeth); radial position is as the ‘inner region’. The second nozzle (divergent chamfered) had castellations cut 

such that the gap between each nozzle was divergent in profile, as indicated by the ‘*’ on the outer region of Fig. 2. 

The third nozzle (convergent chamfered) had castellations cut such that the gap between each profile was convergent 

in profile, as indicated by the ‘**’ on the outer region of Fig. 2. The plain axisymmetric nozzle was of the same overall 

geometry as the castellated ones but with the gaps between the teeth ‘filled in’ [7]. The mixing enhancement obtained 

from the three castellated nozzle geometries was to be compared with the axisymmetric convergent nozzle [7]. 

Figure 1: Nozzle geometry showing the internal profile. 

Figure 2: Nozzle castellation configurations. Hatched 

boxes indicate locations of teeth in nozzle lip: (*) alternative 

profile for divergent chamfered castellations; 

(**) alternative profile for convergent chamfered castellations. 

2.2 Experiments 

Experiments were conducted in a nozzle test cell at Shrivenham (Fig. 3). Data were collected for a NPR of 4. Threedimensional 

LDV measurements were taken of the flow from the castellated nozzles. Seeding of the jet was by direct 

injection from a TSI six-jet seeder into the nozzle plenum chamber using JEM Hydrosonic seeding fluid. 

Measurement traverses were made along the nozzle centreline, x. Probe access limited data collection to the first 10D 

from the nozzle exit plane. The LDV measurements were estimated to be accurate to ±1% of velocity based on the 

sample time and frequency. Additional comparative data were taken from centreline LDV measurements of the plain 

axisymmetric nozzle [4] and pitot probe measurements of the convergent chamfered castellated nozzle [6, 8] made 

previously under the same test conditions. 

2

2.3 Numerical Model 

The CFD model was developed using the Fluent commercial code (Version 5.5). The computational domain consisted 

of a three dimensional hexahedral mesh with approximately 250,000 to 450,000 cells depending on the test conditions. 

Only one quarter of the geometry was modelled since each nozzle has two axes of symmetry. The inlet plane was 

approximately 1D upstream of the nozzle exit, the outlet plane was at about 50D downstream and the radial boundary 

diverged from 2D at the upstream end to more than 10D downstream. 

Figure 3: LDV measurements in the nozzle test cell. 

The boundary condition for the nozzle inlet was set as a pressure inlet with a prescribed total pressure, static pressure, 

total temperature and turbulence intensity. The turbulence intensity, T i at nozzle inlet in the CFD model was adjusted 

to give the same nozzle exit turbulence intensity as the experiments (approximately 4%). The experimental T i was 

derived from the rms velocity data measured by the LDV technique. The turbulence length scale was set as 7.5% 

of nozzle radius [9]. The farfield boundary was set as a pressure outlet with a prescribed static pressure and static 

temperature. 

Turbulent calculations were performed using the RNG k-ε turbulence model [10], which has been shown to be suitable 

for modelling under-expanded jets [11]. Initial axisymmetric calculations were conducted on a mesh of 14700 cells. 

Three stages of mesh adaption, based on density gradients greater than 1 × 10 −5 (to capture the shear layer) and 

Mach numbers greater than 1.0 (to capture the shock core), were then performed. This reduced the grid spacing in the 

shock cell regions from 2 mm to 0.25 mm. Three stages of mesh adaption were sufficient to ensure a grid-independent 

solution [7]. 

2.4 Mixing Enhancement 

Both the experimental measurements and the CFD model indicated that the castellated nozzles produce jets with 

shorter shock cells than the axisymmetric jet (Table 1), however, it was still to be determined if this translated into 

enhanced jet mixing. For the purposes of the study, jet mixing was determined by a numerical integration of the mass 

flow rate passing through planes normal to the jet axis at various streamwise positions (x/D = 2.5, 5, 7.5, 10, 15, 20). 

The edge of the integration plane was chosen to be where M = 0.06. 

At x/D = 2.5 all three castellated nozzles showed an increased mass flow rate in the jet of between 6% and 9% when 

compared with the axisymmetric jet. At x/D = 5 this has increased to approximately 13% for the regular and divergent 

chamfered castellated nozzles. The convergent chamfered castellated nozzle showed a reduced mixing enhancement 

of only 2%. At x/D = 7.5 the level of mixing enhancement started to deteriorate in the other nozzles as well, the 

divergent chamfered castellated nozzle offering the best enhancement with a 10% increase in mass flow rate. The 

mixing enhancement continued to reduce as downstream distance was increased until, beyond x/D = 15, the mass 

flow rate in the axisymmetric jet exceeds that in the jets from the castellated nozzles. 

In order to gain some insight into the mechanism responsible for the mixing enhancement, contour plots of the Mach 

3

Axisymmetric Regular Convergent Divergent 

x/D ṁ ( kgs −1) ṁ ( kgs −1) % change ṁ ( kgs −1) % change ṁ ( kgs −1) % change 

0.0 0.638 0.642 0.6 0.643 0.8 0.640 0.3 

2.5 0.745 0.811 8.9 0.796 6.8 0.790 6.0 

5.0 0.867 0.975 12.5 0.884 2.0 0.982 13.3 

7.5 1.012 1.080 6.7 1.011 -0.1 1.110 9.7 

10.0 1.172 1.192 1.7 1.166 -0.5 1.220 4.1 

12.5 1.377 1.361 -1.2 1.325 -3.8 1.417 2.9 

15.0 1.582 1.547 -2.2 1.557 -1.6 1.541 -2.6 

17.5 1.795 1.770 -1.4 1.749 -2.6 1.794 -0.1 

20.0 2.025 1.982 -2.1 1.961 -3.2 2.016 -0.4 

25.0 2.476 2.458 -0.7 2.440 -1.5 2.483 0.3 

30.0 2.953 2.916 -1.3 2.897 -1.9 2.937 -0.5 

Table 1: CFD prediction of the mass flow rate of the four nozzles at various streamwise planes. 

Divergent 

Chamfered 

y/D 

2 

Axisymmetric 

Divergent 

Chamfered 

y/D 

2 

Axisymmetric 

1 

Nozzle lip 

1 

0 

-2 -1 0 1 2 

z/D 

0 

-2 -1 0 1 2 

z/D 

-1 

Tooth 

Gap 

-1 

Convergent 

Chamfered 

-2 

Regular 

Convergent 

Chamfered 

-2 

Regular 

a). 

Mach Number: 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 

b). 

Mach Number: 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 

Divergent 

Chamfered 

y/D 

2 

Axisymmetric 

Divergent 

Chamfered 

y/D 

2 

Axisymmetric 

1 

1 

0 

-2 -1 0 1 2 

z/D 

0 

-2 -1 0 1 2 

z/D 

-1 

-1 

Convergent 

Chamfered 

-2 

Regular 

Convergent 

Chamfered 

-2 

Regular 

c). 

Mach Number: 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 

d). 

Mach Number: 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 

Figure 4: CFD-predicted Mach number contours at various distances downstream of the nozzle exit: a). x/D = 2.5; 

b). x/D = 5; c). x/D = 7.5; d). x/D = 10. 

4

number at each streamwise plane were examined for the CFD data (Fig. 4). At x/D = 2.5, the cross-sectional shapes 

of the jets are very different. The divergent chamfered nozzle produces a jet with a lobe of high velocity fluid, which 

has been ejected radially through the gap in the castellations. Similar fluid ejections, but of slightly different shapes 

were observed for the other two castellated nozzle designs. 

The CFD model showed that the increased jet mixing produced by the castellated nozzles appeared to be due to 

differential expansion of the jet fluid in the gap and tooth regions as it leaves the nozzle exit. This differential 

expansion created a distorted jet cross section which presented a larger surface area to the ambient air, thus enabling 

more rapid entrainment. The mixing enhancement was, however, confined to the nearfield flow (x/D < 10). At greater 

streamwise distances viscous dissipation appeared to cause the entrainment mechanism to decay resulting in mixing 

rates lower than an axisymmetric jet with final mass flow rates similar in each case. Although the mixing enhancement 

could be determined experimentally, the entrainment mechanism responsible could only be determined from the CFD. 

3 Transonic cavity flow 

Transonic cavity flows over rectangular cavities are of particular relevance to aircraft weapons bays. For cavity length 

to depth ratios less than about 10 the flow is characterised by intense acoustic tones and flow unsteadiness. We present 

here numerical modelling and particle image velocimetry (PIV) measurements of a transonic cavity (M ∞ = 0.85) with 

a length to depth ratio, L/D of 5 [12]. Here the numerical model is used to aid optimisation of the PIV set-up. 

3.1 Numerical model 

The CFD model was completed using commercial software GAMBIT + Fluent 6. The computational grid was created 

from 86000 uniform quadrilateral cells with a distribution of 320 × 65 cells within the cavity. The domain was designed 

to be geometrically similar to the wind tunnel test section. Thus, the upper and lower surface of the tunnel were 

modelled with wall boundary conditions whilst the inlet and outlet conditions were modelled as the pressure far-field 

or free air condition. The flow problem was solved using the unsteady coupled solver and realisable k-ε turbulence 

model. The k-ε family of turbulence models was selected as a number of previous studies have shown it to perform 

well for flows with high shear and regions of recirculation. 

3.2 Experimental Model 

PIV data were taken from inside an all glass cavity of 160 mm length, 80 mm width and 32 mm depth. The cavity 

is made from 5 mm thick glass and is mounted in a modified tunnel wall. Due to the design of the transonic wind 

tunnel test section it was not possible to image the entire cavity and into the freestream and the top 3 mm inside the 

cavity could not be mapped due to the presence of a metal flat plate. Details of the experimental set up are given in 

Ritchie [12]. 

An in-house designed seeder injected a 5% glycerol and water solution into the contraction section of the wind tunnel 

for the PIV measurements. The seeder consisted of an atomiser with 25 selectable jets and was supplied from the 

main tunnel air supply. 

PIV images were recorded using a Kodak ES1.0 CCD with a 105 mm Micro-Nikor lens and a New Wave Gemini 

double pulsed Nd:YAG laser. Sets of 70 images were taken for each run. Figure 5 shows a typical PIV image. Data 

processing of the sets of 70 images was carried out using the TSI software UltraPIV with the Hart algorithm [13]. The 

performance of the UltraPIV algorithm, however, was found to be poor in regions of low seeding density. Therefore an 

in-house algorithm was also developed based on correlation averaging as proposed by Meinhart [14]. This was used to 

process the same 70 image set. 

3.3 Experimental Optimisation 

Lawson et. al. [15] have described an optimisation method for a double pulsed PIV experiment which can be applied 

to autocorrelation or cross correlation analysis. They have shown that in order to retrieve a valid velocity vector from 

an interrogation region there exists a strong interdependence between the dynamic range, D r of the flow defined by: 

5

Figure 5: Typical instantaneous PIV particle image. 

∣ D r = 

V max ∣∣∣ 

∣ 

(1) 

V min 

where V max and V min are the maximum and minimum velocities measured in the flow plane and the velocity gradient 

strength, ϕ defined by: 

ϕ = 

V2 − V1 

V max 

(2) 

Here, V 2 − V 1 is the velocity change across the interrogation region. A high dynamic range requirement necessarily 

restricts the strength of the velocity gradient in a chosen region and vice versa. The latter condition is crucial to 

the design of a PIV experiment for use in transonic and supersonic flows. In any given experiment, other parameters 

critical to the PIV system’s performance include the seeding density and corresponding particle image density, N i 

and the interrogation region size relative to particle image size, D/d. All these parameters must be considered when 

optimising the correlation performance whether using conventional correlation or the Hart correlation. In the latter 

case, an equivalent number of particle images must be used by considering the surrounding interrogation regions. 

With a-priori knowledge of D r, ϕ and V max, D/d and N i, it is possible to use the method to determine a laser pulse 

separation, ∆t for a PIV experiment which will ensure that, on average, from a series of experiments at least 50% of 

valid vectors will be obtained from a ‘worst case’ interrogation region in the flow. The experiments are then defined 

as being optimised. 

The CFD predictions provide the a-priori knowledge of D r, ϕ, V max and V min, where the spatial resolution requirement 

will determine the parameters D/d and N i from the PIV experiment. The optimisation method will then yield a 

recommended magnification, M and pulse separation, ∆t. 

The system magnification is defined in terms of the ratio of object and image distances and is that which is required 

to capture the flow area. The spatial resolution, L of the system is defined by: 

L = D/M (3) 

where D is the interrogation region length and the particle image size, d is dependent on the depth of field and laser 

power of the system. 

The CFD provided the a-priori information from inside the cavity listed in Table 2. The PIV requires a spacial resolution 

of 1.5 mm. This leads to the experimental PIV values listed in Table 3. 

Therefore if the particle image displacement is restricted to 20% of D and applying the optimisation method [15], 

yields a maximum allowable value of ϕD r = 1.5, which corresponds to ϕ = 21% given D r = 7. Also, a magnification 

of M = 1/16 must be used and a pulse separation ∆t = 30 ms. Since the maximum allowable value of ϕ = 21% is 

greater than the CFD predicted value of ϕ = 15%, this means the PIV experiment will have sufficient performance to 

ensure a minimum of 50% of valid vectors, on average, inside this region where the velocity gradients and dynamic 

range are highest. 

6

Parameter 

Value 

( 

V ) min ms 

−1 

( 

-5 

V ) max ms 

−1 

( 

35 

V 2 − V ) 1 ms 

−1 

5 

D r 7 

ϕ (%) 15 

Table 2: CFD a-priori values. 

Parameter 

Value 

L (mm) 1.5 

CCD size (pixels) 1000 2 

Particle image size (pixels) 3 

D/d 10 

N i 5 

Table 3: Experimental parameter values. 

3.4 Results 

Figures 6 and 7 show time-averaged vector maps output from the PIV data processing from the Hart and the correlation 

averaging algorithms. The results from the Hart algorithm do not show any substantial recirculation regions contrary 

to predictions by the CFD model. In contrast the results from the in-house correlation averaging algorithm show a 

distinct large scale recirculation inside the cavity. The poor performance of the Hart algorithm is attributed to locally 

low levels of seeding inside the cavity as can be seen in the PIV image of Figure 5. Lower than expected seeding levels 

would not provide the performance predicted by the optimisation method which assumed a minimum of 5 particle 

images per interrogation region. The correlation averaging algorithm, however, ensures greater than 5 particles images 

per interrogation region as the 70 images set on average accumulates more than 5 particle images in each interrogation 

region. 

Figure 6: TSI code processed time averaged PIV vector map (70 Image average). 

Figure 7: In House code processed time averaged PIV vector map (70 Image average). 

The improved performance of the correlation averaging method is further illustrated in a U component centreline 

plot of velocity shown in Figure 8. In this case the TSI data has a greater deviation than the correlation averaged 

results when compared to the CFD prediction. Therefore optimisation of a given PIV system requires not just a-priori 

knowledge of the flow to specify variables such as M and ∆t, but also careful control of variables such as seeding and 

judicious choice of the data processing algorithms for a given flow. 

4 Open-wheeled racecars 

Ground simulation and wheel rotation are known to be essential for accurate automotive testing [16], particularly for 

open-wheeled racecars. With this type of vehicle, ground effects and large unfaired wheels dominate their aerodynamic 

characteristics. Every care must be taken to ensure that the wheels are modelled correctly both in experimental testing 

7

Figure 8: Streamwise Velocity Profile - y/d=0.5. 

and computational simulation. Previous evaluations of the capability of CFD to model wheel flows [17–19] used the 

surface pressure and force data published by Fackrell [20, 21] as their main validation criteria. 

CFD models enable researchers to investigate physical processes that may be impossible to reproduce experimentally. 

In our work the investigation concentrated on the effect of using external wheel support struts during racecar wind 

tunnel testing [22]. The struts are used to mechanically decouple the car body from the ground whilst still allowing the 

wheels to rotate. Ideally the support struts should be aerodynamically neutral, however, this is not always the case. 

An experimentally validated CFD model of an isolated racecar wheel and strut was used to quantify the aerodynamic 

interference effects between the two. The virtual environment of the CFD model enabled the support strut to be easily 

removed, something that could not have been carried out experimentally. 

4.1 Experiments 

A 40% scale (263 mm diameter), non-deformable Champ Car front wheel assembly was chosen along with its associated 

support sting. The experimentally tested sting was of aluminium beam section with a symmetrical aerofoil profile. It 

supported a 50 N load cell, oriented to measure drag force, to which the wheel was attached. The aerofoil profile was 

extended to the wheel by shrouding the load cell with carbon fibre. The instrumentation cabling was shielded from the 

freestream air by routing it inside the sting. No vertical force, other than that due to the weight of the components, 

was applied during testing and no problems were encountered with wheel lift. The experimental set-up is shown in 

Figure 9. 

The LDV measurements were made using a two-component and a single-component, 1m focal length, Dantec FibreFlow 

probes mounted to a three-component traverse. Data acquisition was carried out by three BSA enhanced signal 

processors, with all equipment centrally controlled by Dantec Burstware software. 

The experimental set-up was tested at 20 ms −1 , corresponding to a Reynolds number (based on wheel diameter) 

of 3.69 × 10 5 . LDV measurements were made in four vertical planes oriented perpendicular to the freestream flow. 

Traverse access confined each plane to being a 250 mm square, centred about the longitudinal centreline of the wheel. 

The planes were located at 10, 25, 50 and 100 mm downstream of the rearmost part of the wheel and contained 

identical grids of 441 equally-spaced data points. All three velocity components were simultaneously sampled over a 

15 second period yielding 2500 samples for each component at each point. When processed, these data subsequently 

provided time-averaged three-dimensional velocity results. 

8

4.2 Numerical model 

The wheel and sting assembly was placed in a rectangular domain with the inlet 5 wheel diameters upstream, outlet 

16 wheel diameters downstream, a width of 10 and a height of 5 wheel diameters. The interior of the sting was also 

meshed to allow it to be removed from the solution domain by allowing fluid to flow through it, thus eliminating the 

need to generate an entirely new mesh for that section of the study. 

The only significant deviation from the experimental geometry was made at the tyre contact patch. Difficulty was 

encountered in maintaining high cell quality when modelling the near line-contact between the rolling road and nondeformable 

tyre. Therefore, the wheel was slightly truncated by raising the ground plane by 0.8mm. This increased 

the size of the contact patch and greatly improved the cell skewness in this area. The final mesh was of the order of 

0.93 million cells. Figure 10 shows the surface mesh on the wheel and sting assembly. 

Figure 9: Experimental Set-up 

Figure 10: CFD Surface Mesh of Wheel Assembly and 

Support Sting 

The boundary conditions of the CFD simulation were chosen to be representative of those of the experiment. A 

uniform flow with a velocity of 20 ms −1 was specified at the inlet and standard atmospheric pressure specified at the 

outlet. The rolling road and wheel components were modelled as translating and rotating walls respectively, all with 

a linear velocity of 20 ms −1 . When simulating the wheel and sting, the sting surface was specified as a wall with the 

no-slip condition applied. When testing the wheel without the sting, the latter’s surface was represented by an interior 

condition, which did not impede flow. The mesh inside the sting was solved as a fluid, effectively removing the sting 

from the domain. Symmetry planes represented the remaining domain boundaries. Simulations were run with the k-ω 

turbulence model. 

4.3 Validation 

The mean drag force calculated from the experimental data was non-dimensionalised by the frontal area of the wheel. 

The drag coefficient, C D predicted by the CFD simulation was 0.638, which was 6.2% lower than the measured value 

of 0.680. 

Care should be exercised when using force data as the sole accuracy measure [23] but the good experimental velocity 

correlation supported the validity of this prediction. This was further reinforced by inspection of the circumferential 

static pressure coefficient, C p on the centreline of the tyre surface, Figure 11. Although surface C p was not measured 

experimentally, comparison can be made with the work of Hinson [24]. This presented the pressure coefficients on 

the surface of a Formula One wheel, measured using transducers mounted within. Comparison was made with results 

taken from tests at the same Reynolds number as, and using a geometrically similar wheel to, this investigation. The 

results show good correlation and illustrate several important features. CFD predicted the separation 22 ◦ late at 244 ◦ 

as opposed to 266 ◦ measured by Hinson. Also, the base pressure was under-predicted just downstream of separation. 

Both factors would lead to an under-prediction of drag coefficient and are believed to be responsible, along with 

experimental errors, for the discrepancy seen in this study. 

9

1.25 

CFD (SKW PRESTO) 

Experimental (Hinson[10]) 

1 

0 o θ 

0.75 

Pressure Coefficient 

0.5 

0.25 

0 

-0.25 

-0.5 

-0.75 

-1 

0 90 180 270 360 

θ° 

Figure 11: Circumferential Pressure Distribution on the Tyre Centreline 

4.4 Support Sting Effects 

Once the CFD model had been validated, it could be used to determine the effect of the support sting on the flow 

in proximity to the wheel. Figure 12 shows velocity vector plots from the CFD investigations with and without the 

support sting. The model used throughout the study enabled the sting to be removed without modification to the 

mesh. The solver settings could, therefore, remain constant, thus improving comparison. 

The main difference (seen in the 10 mm and 25 mm planes) is the presence of a contra-rotating upper vortex pair in 

the no-sting results, as opposed to the single structure with the sting present. This would suggest that the presence of 

the sting suppresses the formation of the upper left vortex. The upper structures appear to breakdown quicker when 

the sting is not present and are absent in the 100 mm plane. 

With regard to the two vortices close to the ground (known as ‘jetting’ vortices), the left structure is the larger of the 

two and is located higher and closer to the wheel centreline in the no-sting results. This is in contrast to the results 

noted in the presence of the sting. 

Inspection of the remaining data showed that removal of the support sting resulted in: 

• A wheel drag reduction of 2%; 

• An increase in wheel lift of 16%; 

• A reduction in mass flow-rate through the wheel of 83%; 

• A delay of separation by 4 ◦ , on the wheel centreline. 

The slight drag reduction appears to correlate with the later separation, whilst the additional upper vortex agrees with 

the increase in lift. Flow through the wheel is from right to left, therefore the results suggest that the sting forces 

more flow to pass through the wheel than would otherwise occur. 

This study has shown how an experimentally validated CFD model of an isolated racecar wheel and strut can be used 

to quantify the aerodynamic interference effects between the two. The virtual environment of the CFD model enabled 

the support strut to be removed easily, something that could not have been carried out experimentally. 

10

10mm Plane - Sting - CFD (SKW 2nd. Order) 

250 

10mm Plane - No Sting - CFD (SKW 2nd Ord.) 

250 

200 

200 

Z (mm) 

150 

100 

Z (mm) 

150 

100 

50 

50 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 


250 


250 

200 

200 

Z (mm) 

150 

100 

Z (mm) 

150 

100 

50 

50 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 


250 


250 

200 

200 

Z (mm) 

150 

100 

Z (mm) 

150 

100 

50 

50 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 


250 


250 

200 

200 

Z (mm) 

150 

100 

Z (mm) 

150 

100 

50 

50 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 

0 

-600 -500 -400 

Y (mm) 

= 5 ms -1 

Figure 12: In-Plane Velocity Vectors (Sting - No Sting CFD Comparison) 

11

5 Conclusions 

In this paper we have illustrated how the combined use of computational fluid dynamics and experimentation has 

been applied to three particular fluid dynamics problems: high-speed turbulent jet flow, transonic cavity flows and 

open-wheeled race car aerodynamics. In each case knowledge gathered from one analysis technique has been used 

to assist in the application of the second technique thereby enabling greater understanding of the flow physics being 

studied than would have been possible through the isolated use of one or other methodology. The authors would like 

to acknowledge the work of Simon Ritchie and Robin Knowles in support of this paper. 

References 

[1] Knowles, K. and Bray, D., “Computation of Normal Impinging Jets in Cross-flow and Comparison with Experiment,” 

International Journal of Numerical Methods in Fluids, Vol. 13, No. 10, December 1991, pp. 1225–1233. 

[2] Samimy, M., Reeder, M. F., and Zaman, K., “Supersonic Jet Mixing Enhancement by Vortex Generators,” 

AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, Sacramento, CA, USA, 24-26 June 1991, No. 91-2263. 

[3] Samimy, M., Zaman, K. B. M. Q., and Reeder, M. F., “Effect of Tabs on the Flow and Noise Field of an Axisymmetric 

Jet,” AIAA Journal, Vol. 31, No. 4, April 1993, pp. 609–619. 

[4] Saddington, A. J., Lawson, N. J., and Knowles, K., “Numerical Predictions and Experiments on Supersonic Jet Mixing 

from Castellated Nozzles,” 23rd Congress of the International Council of the Aeronautical Sciences, Toronto, Canada, 8-13 

September 2002. 

[5] Saddington, A. J., Knowles, K., and Wong, R. Y. T., “Numerical Modelling of Mixing in Jets from Castellated Nozzles,” 

The Aeronautical Journal of the RAeS, Vol. 106, No. 1066, December 2002, pp. 643–652. 

[6] Knowles, K. and Wong, R. Y. T., “Passive Control of Entrainment in Supersonic Jets,” RAeS Aerodynamics Research 

Conference, London, 17-18 April 2000, pp. 9.1–9.14. 

[7] Saddington, A. J., Lawson, N. J., and Knowles, K., “Simulation and Experiments on Under-expanded Turbulent Jets,” 

CEAS Aerospace Aerodynamics Research Conference, Cambridge, UK, 10-13 June 2002. 

[8] Wong, R. Y. T., Enhancement of Supersonic Jet Mixing, Ph.D. thesis, Department of Aerospace, Power and Sensors, 

Cranfield University, July 2000. 

[9] Rodi, W., Turbulence Models and their Application in Hydraulics - A State of the Art Review, International Association for 

Hydraulic Research, Rotterdamseweg 185 - P.O. Box 177, 2600 MH Delft, The Netherlands, 2nd ed., 1984. 

[10] Yakhot, A. and Orszag, S. A., “Renormalisation Group Analysis of Turbulence: I. Basic Theory,” Journal of Scientific 

Computing, Vol. 1, No. 1, 1986, pp. 1–51. 

[11] Knowles, K. and Saddington, A. J., “Modelling and Experiments on Underexpanded Turbulent Jet Mixing,” 5th International 

Symposium on Engineering Turbulence Modelling and Measurement, Mallorca, Spain, 16-18 September 2002. 

[12] Ritchie, S. A., Lawson, N. J., and Knowles, K., “An Experimental and Numerical Investigation of an Open Transonic 

Cavity,” 21st AIAA Applied Aerodynamics Conference, Orlando, Florida, USA, 23-26 June 2003, Paper No. 2003-4221. 

[13] Hart, D. P., “PIV error correction,” Experiments in fluids, Vol. 29, No. 1, 2000, pp. 13–22. 

[14] Meinhart, C., Wereley, S., and Santiago, J., “A PIV Algorithm for Estimating Time-Averaged Velocity Fields,” Journal of 

Fluids Engineering, Vol. 122, No. 2, June 2000, pp. 285–289. 

[15] Lawson, N. J., Coupland, J. M., and Halliwell, N. A., “A Generalised Optimisation Method for Double Pulsed Particle Image 

Velocimetry,” Optics and Lasers in Engineering, Vol. 27, No. 6, August 1997, pp. 637–656. 

[16] Hackett, J. E., Baker, J. B., Williams, J. E., and Wallis, S. B., “On the influence of ground movement and wheel rotation 

in tests on modern car shapes,” Paper 870245, Society of Automotive Engineers, 1987. 

[17] Skea, A. F., Bullen, P. R., and Qiao, J., “The Use of CFD to Predict the Air Flow Around a Rotating Wheel,” 2 nd MIRA 

Int. Vehicle Aerodynamics Conf , UK, 1998. 

[18] Basara, B., Beader, D., and Przulj, V. P., “Numerical Simulation of the Airflow around a Rotating Wheel,” 3rd MIRA Int. 

Vehicle Aerodynamics Conf , UK, 2000. 

[19] Axon, L., Garry, K., and Howell, J., “An Evaluation of CFD for Modelling the Flow Around Stationary and Rotating Isolated 

Wheels,” Paper 980032, Society of Automotive Engineers, 1998. 

[20] Fackrell, J. E., The Aerodynamic Characteristics of an Isolated Wheel Rotating in Contact with the Ground, Ph.D. thesis, 

Imperial College of Science and Technology, London, 1972. 

[21] Fackrell, J. E. and Harvey, J. K., “The Flow Field and Pressure Distribution of an Isolated Road Wheel,” Advances in Road 

Vehicle Aerodynamics, Paper 10, BHRA, London, 1973, pp. 155–165. 

[22] Knowles, R. D., Saddington, A. J., and Knowles, K., “Simulation and Experiments on an Isolated Road Wheel Rotating in 

Ground Contact,” 4th MIRA International Vehicle Aerodynamics Conference, Warwick, UK, 16-17 October 2002. 

[23] Makowski, F. T. and Kim, S.-E., “Advances in External-Aero Simulation of Ground Vehicles Using the Steady RANS 

Equations.” Vehicle Aerodynamics SP-1524, Paper 2000-01-0484, Society of Automotive Engineers, 2000. 

[24] Hinson, M., Measurement of the Lift Produced by an Isolated, Rotating Formula One Wheel Using a New Pressure Measurement 

System, MSc thesis, Cranfield University, 1999. 

12

OPPORTUNITIES FOR THE INTEGRATED USE OF 

MEASUREMENTS AND COMPUTATIONS FOR THE 

UNDERSTANDING OF DELTA WING 

AERODYNAMICS 

I.A.Gursul 

Department of Mechanical Engineering, 

University of Bath, 

Bath, BA2 7AY, 


M.R.Allan and K.J.Badcock 

Computational Fluid Dynamics Laboratory, 

Department of Aerospace Engineering, 

University of Glasgow, 

Glasgow, G12 8QQ, 


Paper for the Conference on Integration of CFD and experiments at University of 

Glasgow, September, 2003 

Abstract 

This paper considers the current status of delta wing research from the point of view of the potential 

for using joint experimental and computational studies to advance the subject. After a brief review 

of the available measurement and numerical methods, delta wing phenomena are considered in the 

following categories: shear layer instabilities, vortex breakdown, vortex interactions, nonslender vortices, 

multiple vortices, manoevring wing vortices and vortex/flexible wing interaction. It is concluded 

that CFD can be very valuable to guide the type amd location of experimental data collected and to 

enhance the understanding of the data but adding information. Currently CFD requires more datasets 

1

2 

which include boundary layer and field information and which ideally combine different types of data. 


The flow over a delta wing at moderate angles of attack is dominated by two large, counter-rotating 

leading-edge vortices that are formed by the roll-up of vortex sheets. The flow separates from the 

leading edge of the wing to form a curved free shear layer above the suction side of the wing, which 

rolls up into a core. The time-averaged axial velocity is roughly axisymmetric and its maximum can 

be as large as four or five times the free stream velocity. These large axial velocities are due to very 

low pressures in the vortex core, which generate additional suction and lift force on the delta wings. A 

great deal of effort has been focused on the study of these vortices and aerodynamics of delta wings, 

as summarised in a review article by Lee and Ho [1]. 

The opportunities for gaining a deep understanding of the behaviour of the vortical flow has been 

greatly enhanced in recent years due to a revolution in the methods which can provide raw data. 

These methods can involve experiments using an expanding range of field and surface techniques 

or Computational Fluid Dynamics (CFD). It has been traditionally the case that these have been 

used with only very limited interaction, often only involving validation of the computational results 

using legacy experimental data which might not even be very suitable for the task. However, it is 

becoming increasingly recognised that if the goal is to improve the understanding of aerodynamics 

then these methods must be used in a deeper and coordinated way. The purpose of this paper is to 

give suggestions for how this statement can be realised for delta wings. 

2 Tools Available for Aerodynamic Studies 

2.1 Experimental Techniques 

There are several experimental techniques available for experimental research in delta wing aerodynamics: 

1. Steady and unsteady pressure measurements including pressure sensitive paints. These are 

limited to wing surface measurements and so do not provide information on off-surface flow 

and the nature of the vortices.

3 

2. Surface flow visualisation. Oil flow visualisation gives an indication of surface streamlines, but 

only in a time averaged sense. Tufts also give an indication of surface streamlines and can reveal 

flow separation and reattachment, but are limited with the response time in unsteady flows and 

can also be intrusive. 

3. Off surface flow visualisation (smoke/dye). This can provide useful information on shear layer 

structures and vortex breakdown, but extra care should be taken in interpreting the streakline 

patterns in unsteady flows. 

4. Multi-hole velocity probes. These can measure three-components of mean velocity, but are 

intrusive and can cause premature breakdown. 

5. Hot-wire anemometry. This can provide unsteady velocity components but can be intrusive. 

6. LDV and PIV. These are non-intrusive point and field measurements respectively of velocity 

vectors in a plane. Seeding of vortical flow near the axis becomes problematic with increasing 

speed in air flows. 

2.2 CFD Techniques 

It has been well documented that CFD has developed at a rapid pace over the past 30 years. With 

developments in algorithms and computers it is possible to simulate complex flows on real aircraft 

using cheap computers. A recent NATO technical organisation (RTO) working group has examined 

the predictive capability for vortical flows on generic delta wing configurations (AVT 80) [2]. 

1. Euler simulations can predict vortex breakdown and vortical interactions when a sharp leading 

edge is used, fixing the separation point. No secondary separation can be predicted since this is 

due to boundary layer separation having the effect of shifting the primary vortex closer to the 

wing leading edge. In addition the strength of the leading edge vortex is strongly dependent on 

the grid used. However, for sharp leading edges this level of modelling is useful for evaluating 

qualitative behaviour at a low cost. 

2. Unsteady RANS simulations can give good prediction for the secondary separation although 

the prediction of primary separation and vortex formation for rounded leading edge wings has

4 

not received much attention in the literature. A major problem with URANS is the prediction 

of the levels of turbulence in the vortex itself which can strongly influence the development of 

breakdown. Ad-hoc treatments [3] can be used to limit production in regions of high vorticity 

but the turbulence levels after breakdown are still too high, making the simulation of the helical 

instability questionable. 

3. Detached Eddy Simulation (DES) [4] has been used to overcome this problem by simulating 

the large scale turbulence in the vortex by Large Eddy Simulation (LES). In the wing boundary 

layer, where the cost of LES would be prohibitive at realistic Reynolds numbers, the RANS 

model is used. Some promising results for the prediction of vortex breakdown have been published, 

indicating the promise of the approach. The disadvantage is that the simulations are 

more costly in terms of the finer grids needed in the vortex and the small time steps that are 

required. In addition, the DES gives no improvement over URANS in terms of the vortex 

formation from rounded leading edges and predicting the influence of transition. 

4. Finally, LES and Direct Numerical Simulation (DNS) [5] have been used at low Reynolds 

numbers to indicate fundamental physics. The cost of these calculations is prohibitive at flight 

Reynolds numbers because of the grid and temporal resolution required. 

CFD predictions have progressed to the point where a current RTO working group (AVT-113) 

is evaluating the predictions of the flow on the F-16XL aircraft through comparison with in-flight 

measurements. There are clearly a number of useful tools in the CFD bag with varying cost and 

predictive capability. 

3 Delta Wing Phenomena 

3.1 Shear Layer Instabilities 

The separated shear layers on a delta wing roll up periodically into discrete vortical substructures 

as visualised by Gad-el-Hak and Blackwelder [6]. This phenomenon was attributed to a Kelvin- 

Helmholtz type instability of the shear layer. The origin of these structures has been the subject of 

controversy as several researchers [7] [8] revealed the existence of stationary small-scale vortices

5 

around the primary vortex. The spatially fixed substructures were measured by velocity probes at 

fixed locations, and were identified as a result of time-averaging the flow. However,such small scale 

structures are difficult to measure experimentally. PIV and Global Doppler techniques are spatially 

and temporally limited, whilst LDA and HWA techniques are spatially limited (sampling at a point). 

Therefore it is not feasible to provide a complete unsteady data set of the flowfield which would be 

necessary to characterise these structures. 

Small scale substructures also require more advanced turbulence modelling than the common 

Boussinesq-type models. However the relationship of the spatially fixed substructures to observed 

temporal substructures was recently demonstrated by direct numerical simulation (DNS) [5]. Instantaneous 

flow visualisation shows the temporal substructures and the transition process with increasing 

Reynolds number (see figure 1). More interestingly the time-averaged flow visualisation shows isosurfaces 

of time-averaged axial vorticity, and mean vortical substructures. These results indicate that 

the steady and unsteady substructures are not necessarily two separate phenomena. Details of the 

shear layer structure and transition process need to be investigated further. 

In this example the use of DNS has suggested the flow structure and the challenge for experimentalists 

is to apply their techniques to examine these explanations, especially at high Reynolds number 

where satisfactory computations become more difficult, 

3.2 Vortex Breakdown 

At a sufficiently high angle of attack leading edge vortices undergo a sudden expansion known as 

vortex breakdown (see Figure 2), which was first observed by Werlé in 1954 in a water tunnel facility. 

Different explanations of the vortex breakdown phenomenon based on hydrodynamic instability, wave 

propagation, and flow stagnation are summarized in several review articles [9] [10] [11]. It is now 

generally agreed that this is a wave propagation phenomenon, and there is a strong analogy to shocks 

in gas dynamics. Concepts of supercritical and subcritical flows based on the wave propagation 

characteristics seem to play an important role in the understanding of vortex breakdown. 

Vortex breakdown has adverse effects on time-averaged performance. For example, the magnitude 

of the lift and nose down pitching moment decreases after vortex breakdown for slender wings. 

However, the effects of vortex breakdown are more modest for low sweep angle delta wings [12].

6 

Although a great deal of effort has been focused on the study of the vortex breakdown phenomenon, 

accurate prediction at high Reynolds numbers remains challenging [13]. Despite higher fidelity modelling 

and increasing resolution of simulations, core properties (believed to be fundamental in the 

development of vortex breakdown) are still difficult to predict. In particular the axial velocities in 

vortex cores tend to be predicted considerably lower than those found in experiment [2] . Prediction 

of time accurate vortex breakdown is also costly (especially for manoeuvring aircraft where the 

manoeuvring frequencies are several orders of magnitude lower than frequencies associated with the 

helical mode instability - see figure 3). The quality of the predictions is also heavily dependent on the 

realism of the modelling applied with DES showing promise but requiring further detailed scutiny. 

In order to be able to further understand the difficulties associated with predicting core properties 

there are still questions remaining with regard to the structure of the core flow. It is widely assumed 

that due to viscous effects the core rotates as a rigid body rotation. However it remains unclear 

whether at high Reynolds number the core is turbulent or laminar and further experimental evidence 

is needed on this point. 

Experimental investigations show that large scatter appears in the vortex breakdown location (see 

Figure 4, taken from Reference [14]). Geometric variations, tunnel wall effects, support interference, 

model deformations, Reynolds number, and measurement technique are all possible sources of the 

large scatter. A further difficulty is that the vortex breakdown location is highly unsteady, exhibiting 

oscillations in the streamwise direction [15]. These factors significantly affect the usefulness of the 

experimental data for aerodynamic analysis and design. 

It is generally accepted that for a large range of values, breakdown is little affected by Reynolds’ 

number. Tunnel wall influences have been shown by CFD to have an influence on breakdown location 

[16] [17]. It has also been shown that support structures can promote [18] or even delay [19] 

breakdown, though the actual influence is likely to be Reynolds number dependent. As such it is 

recommended that an experimental study be conducted in conjunction with a CFD study. The experimental 

study should provide accurate flowfield information for realistic upstream and downstream 

boundary conditions (velocity and pressure profiles), as well as tunnel boundary layer growth data. 

Useful measurements would include (but are not limited to) wing surface and tunnel wall pressure

7 

distributions, and load and moment data for dynamic cases. Flowfield measurements of the vortices 

would also be required to compare core properties and locations. To obtain results with various 

model to tunnel ratios, ideally the tunnel geometry should be altered (with artificial walls), as opposed 

to changing model size. In this way support structure interference would be consistent. If this is not 

possible and the wing size must vary, the size of the support structure should be adjusted accordingly 

(for example sting diameter). A useful experimental study would be as follows: 

• Select for example a square cross section tunnel. 

• Perform measurements for various angles of attack (upstream and downstream pressure and 

velocity profiles, tunnel boundary layers, wall pressures at selected locations, surface pressure 

data and flowfield measurements). 

• Measure loads and moments for dynamic cases (for example pitching motion). 

• Add artificial walls to bring side walls closer. 

• Repeat measurements for static and dynamic cases. 

• Add artificial walls to bring roof and floor closer 

• Repeat measurements for static and dynamic cases. 

Such experimental results could be used to validate a similar CFD study. These tests could also 

be conducted with and without supports for further validation. 

There has been less emphasis on the unsteady aspects of vortex breakdown which have an impact 

on aircraft stability and control, and wing/fin buffeting. The flow downstream of vortex breakdown 

exhibits a well-documented hydrodynamic instability, called the helical mode instability [20]. Experimentally 

observed periodic velocity/pressure oscillations correspond to the most unstable normal 

modes of the time-averaged velocity profiles of the vortex (downstream of breakdown) based on the 

linearised, inviscid stability analysis. Unsteady flow phenomena relevant to vortical flows over delta 

wings have been studied in several previous investigations [20] [21] [22] However current knowledge 

of the unsteady aspects of breakdown is limited to slender wings [23].

8 

Computational simulations can contribute to understanding these flows better. Time-accurate CFD 

simulations of the helical mode instability can predict buffet frequencies for a range of static and manoeuvring 

cases. Coupled CFD and structural modelling could also be used to predict whether new 

aircraft designs would undergo wing / tail buffet, and any possible coupling of fluid / structural instabilities. 

The prediction of core properties is likely to be crucial however and detailed experimental 

data is needed to improve the simulations in this respect. 

3.3 Vortex Interactions 

It was observed in several experiments that the vortex breakdown location over stationary delta wings 

is not steady and exhibits fluctuations along the axis of the vortices. Subsequently it was discovered 

that these oscillations are in the form of an asymmetric motion of breakdown locations for left and 

right vortices [15]. This is demonstrated by plotting the difference and average of left and right breakdowns 

in Figure 5. The two breakdowns, which are almost mirror images, oscillate in an asymmetric 

motion. The amplitude of these fluctuations can be a significant fraction of the chord length. These 

oscillations may be very important for the stability and control of highly manoeuvrable aircraft, and 

also have important consequences for wing and tail buffeting. 

It was also reported [15] that the oscillations of breakdown locations are quasi-periodic. Both 

flow visualization and pressure measurements at high Reynolds numbers confirmed the existence of 

vortex interactions. The exact mechanism of this interaction and whether vortex breakdown is an 

essential part of it remains little understood due to the difficulties of temporal resolution using PIV 

or spatial resolution with LDA. It was found that the oscillations become larger and more coherent 

as the time-averaged breakdown locations get closer to each other when the angle of attack or sweep 

angle is increased. 

Asymmetric oscillations of breakdown location have been observed computationally with symmetric 

computational domains. Oscillations have been seen both with Euler simulations [2] and higher 

fidelity DES simulations [2] and potentially such simulations can provide a great deal of understanding 

of these interactions. For example, studying cases without vortex breakdown may highlight if 

breakdown plays an important role in vortex interactions. Careful examination of the apex region and 

the mid plane of the computational domain may also provide insight into where the interactions start

9 

to occur and how they could proceed into asymmetric motions of breakdown location. Such studies 

are impossible to achieve experimentally. Experiments have a crucial role to play in validating the 

predictions in the sense of breakdown movement (from visualization), core properties and frequencies 

(from surface measurements or LDA). 

Although this kind of interaction is more of a concern for slender wings, evidence of such interactions 

at a relatively low sweep angle of Λ = 60 o was reported recently [24]. Wing tip accelerations 

occurred in an asymmetric structural mode for a slightly flexible delta wing when vortex breakdown 

occurred on the wing. Time-accurate CFD simulations could provide evidence of the underlying 

reasons for the instability and guide detailed flowfield measurements to further the understanding. 

3.4 Nonslender Vortices 

Much of our knowledge of vortex flows is related to slender vortices. There is very little known about 

the structure of vortices over nonslender delta wings (Λ ≤ 55 o ) and unsteady flow phenomena. Figure 

7 shows an example of flow visualisation for a Λ = 50 o delta wing, where a dual vortex structure is 

identified. Both PIV measurements [25] and DNS calculations [26] confirmed that both vortices have 

the same sign of vorticity. 

It has been found that nonslender wings (with sweep angles as low as 40 o ) at angles of attack as 

low as a few degrees can produce strong vortical flows. An example of surface flow visualization 

for α = 2.5 o is shown in Figure 8 for a Λ = 50 o delta wing, where the secondary separation and 

reattachment lines are visible. For α = 15 o , there is a change in the curvature of the secondary 

separation line around the midchord, which is presumably due to the vortex breakdown. Figure 9 

shows root mean square values of fluctuating velocity together with the surface streamline pattern 

obtained from velocity measurements close to the wing surface. 

For α = 15 o , the signature of 

vortex breakdown starting around 40% of the chord length is visible. However, for α = 20 o , it is 

not the breakdown, but the reattachment of the shear layer which produces unsteadiness near the 

wing surface. Reattachment of shear layer, vortex breakdown, and stall over wings with rounded 

leading-edges are very complex and can benefit from numerical simulations for better understanding 

of the general flow topology which can then guide detailed measurements. Such numerical studies are 

problematic due to the difficulty in accurately predicting the (non-fixed Reynolds number dependent)

10 

separation location over rounded leading edges. However, it is unknown to what extent the vortical 

structures are dependent on the accurate prediction of the separation location. Again experiments 

focussing on the leading edge region to provide detailed velocity and turbulence data for separation 

onset would provide valuable validating data for the predictions. Also, there is a need to understand 

separated and vortical flows at nonzero roll angles for nonslender wings. Recently, it was discovered 

that nonslender delta wings can exhibit wing rock phenomenon [27]. 

3.5 Multiple Vortices 

Another area that has received little attention is the interaction of multiple vortices such as those 

found on double delta wings (see Figure 10). Interactions of multiple vortices, complex vortex patterns, 

coiling-up and merging, vortex breakdown, and unsteady interactions are highly challenging 

vortical flows. These aspects are even more complex and challenging for manoeuvring aircraft. This 

is a particularly interesting area in which CFD can provide much needed understanding since the entire 

unsteady flowfield can be visualised and studied. Experimental flow visualisation techniques can 

be applied for static cases though this is harder for manoeuvring cases. As such time accurate CFD 

simulations would be able to track core motions, examine vortex interactions, highlight interaction 

induced vortex breakdown, as other phenomena currently poorly understood. Location of interesting 

phenomena with CFD would also have the advantage of guiding experimentalists in finding measurement 

locations of interest. 

3.6 Manoeuvring wing vortices 

The spectrum of unsteady flow phenomena over stationary delta wings is shown in Figure 3 as a function 

of dimensionless frequency [15]. Also shown is the frequency range of aerodynamic manoeuvres 

for current fighter aircraft. Future unmanned aircraft could be highly manoeuvrable and flexible, with 

the capability of performing extreme manoeuvres at high g (with a 30g vehicle envisioned). At such 

high reduced frequencies, there is the possibility of a coupling of aerodynamic manoeuvres with vortex 

instabilities. For highly manoeuvrable aircraft configurations, nonlinear unsteady aerodynamics 

presents major challenges for the development of flight control laws. 

The dynamic response of leading edge vortices and breakdown is important for flight of unmanned

11 

aircraft. For a pitching delta wing, both the formation of leading-edge vortices [28] and vortex breakdown 

[29] [30] show hysteresis and time lag compared with respect the quasi-steady case. This time 

lag, which is important for the stability and control of aircraft, has also been observed for other types 

of wing motion, such as plunging and rolling. The time lag of vortex breakdown is much larger than 

that of vortex formation. Although it is common to all unsteady flows regardless of the type of unsteady 

motion [31], the mechanism of hysteresis and time lag is not well understood. The dynamic 

response of vortex breakdown is strongly linked to the adverse pressure gradient along the vortex axis 

[30], which cannot be measured experimentally and which as previously mentioned, is hard to obtain 

with CFD. 

As CFD simulations has become more realistic the opportunity to couple CFD and flight mechanics 

has been exploited. A great deal of experimental data is available for 1 Degree of Freedom (DOF) 

motion around the roll axis of a delta wing, when a highly swept delta wing exhibits wing rock (see for 

example figure 11). CFD has been able to predict the wing rock phenomenon of highly swept wings 

with Euler, laminar, and RANS models of the flow. For a Λ = 65 o delta wing rolling about its x- 

(body)axis, RANS simulations have been performed [32]. In this case the experimental results were 

contaminated by mechanical friction between the sting and the support structure. As such, instead of 

the experimental results exhibiting an aerodynamically damped oscillation, the model stopped at nonzero 

roll angles for various initial roll angles. CFD simulations were able to reproduce such behaviour 

if mechanical friction was added, though the choice of mechanical friction model was governed by 

comparison with experiment. 

As an extension to the 1 DOF roll cases discussed it is also currently feasible to perform multiple 

degree-of-freedom (rigid body motion) simulations with CFD. Multiple degree of freedom experimental 

studies are uncommon and problematic due to the support structures required to move freely 

(though as discussed mechanical friction remains a problem) and in any direction. Coupling CFD 

and flight mechanics in such a way will allow virtual studies of new aircraft configurations in regimes 

which are usually avoided due to highly non-linear aerodynamics. However, experiments with simplified 

free response cases are required to allow evaluation of the influence of modelling induced effects 

on the rigid body dynamics.

12 

3.7 Vortex / flexible wing interaction 

Because of unusual designs and high rate motions for future aircraft, wing flexibility could become 

an issue. Coupling of unsteady, separated and vortical flows with flexible wings may result in limitcycle-oscillations 

or control problems. For flexible delta wings, vortex/wing interaction (see Figure 6) 

may lead to limit cycle oscillations, where the vortex acts like an aerodynamic spring [33]. Unsteady 

flow phenomena may interact and couple with structural vibrations. As it is very difficult to simulate 

aeroelastic phenomena experimentally due to model scaling requirements, validated computational 

simulations may be very useful for this kind of multidisciplinary and challenging engineering problem. 

CFD simulations have the advantage of being able make predictions at real flight conditions with 

structural models representing the full aircraft behaviour. 

4 Conclusions 

For experimentalists, with the current capabilities of CFD and the assumptions it employs, CFD 

should be primarily used as a tool to build on measurement opportunities. Ideally an iterative process 

should be used, using CFD to highlight areas of interest either before or after experiments. As 

a greater understanding is gained of the flowfield, further experiments or CFD simulations could be 

done which would provide a much more detailed picture of the flowfield. Due to the temporal limitations 

of PIV and the spatial restrictions of LDA, using CFD to focus (and also understand) the 

measurements is seen as particularly advantageous. Since delta wing flows are particularly susceptible 

to facility interference an accurate tool for predicting tunnel interference is required. A suitably 

validated CFD method would be able to provide details of combined tunnel wall, tunnel boundary 

layer, and support structure interference effects. The tool would also be applicable to all facilities and 

all tests. 

For the CFD practitioners more detailed high quality data is required, especially in boundary 

layers. There is little insight to be gained from validating an expensive DES simulation with force 

and moment data. Instead to validate models high quality flowfield data is required, especially in 

vortical flows where the understanding of off surface flow features is of vital importance. Similarly 

as the effects of facility interference often contaminate experimental results, modelling the entire

13 

experiment is required for fair comparisons. As such details of freestream flow properties, supports, 

tunnel boundary layers etc are required to provide better boundary conditions for the simulations. 

Ideally, combinations of different types of data is required. For example in delta wing flows vortex 

behaviour is of importance in predicting the response of an aircraft to manoeuvres. Given the time 

lags associated with vortex breakdown and its effect on the loads and moments experienced by the 

aircraft, it is vital to know the off surface flow as well as the loads and moments and surface pressure 

distributions for validation purposes. Such combinations of data are rare or non-existent! 

References 

[1] Lee, M. and Ho, C.-M., 1990, ”Lift Force of Delta Wings”, Applied Mechanics Reviews, vol. 

43, pp. 209-221. 

[2] Publication of RTO AVT-080 Task group on “Vortex breakdown over slender wings”, To be 

published October 2004. 

[3] Brandsma, F. J., Kok, J. C., Dol, H. S., and Elsenaar, A., ”Leading edge vortex flow computations 

and comparison with DNW-HST wind tunnel data”, RTO / AVT Vortex Flow Symposium, 

Loen, Norway, 2001. 

[4] Spalart, P. R., Jou, W. H., Streles, M., and Allmaras, S. R.,“Comments on feasibility of LES for 

wings and on a hybrid RANS / LES approach”, Proceedings of the first AFSOR International 

Conference on DNS/LES, Greyden Press, Columbus, OH, Ruston, LA, August 4-8 1997. 

[5] Visbal, M. R. and Gordnier, R. E., “On the structure of the shear layer emanating from a swept 

leading edge at angle of attack”, AIAA 2003-4016, June 2003. 

[6] Gad-el-Hak, M. and Blackwelder, R.F. The discrete vortices from a delta wing, AIAA Journal, 

vol. 23, 1985, pp. 961-962. 

[7] Riley, A.J. and Lowson, M.V., Development of a Three-Dimensional Free Shear Layer, Journal 

of Fluid Mechanics, vol. 369, 1998, pp. 49-89.

14 

[8] Mitchell, A.M. and Molton, P., Vortical Substructures in the Shear Layers Forming Leading- 

Edge Vortices, AIAA Journal, vol. 40, no. 8, 2002, pp. 1689-1692. 

[9] Hall, M.G., Vortex Breakdown, Annual Review of Fluid Mechanics, vol. 4, 1972, pp. 195-218. 

[10] Leibovich, S., Vortex Stability and Breakdown: Survey and Extension, AIAA Journal, vol. 22, 

no. 9, 1984, pp. 1192-1206. 

[11] Delery, J.M. Aspects of vortex breakdown, Progress in Aerospace Sciences, vol. 30, 1994, pp. 

1-59. 

[12] Earnshaw, P.B. and Lawford, J.A., Low speed wind tunnel experiments on a series of sharpedged 

delta wings, R&M 3424, August 1964. 

[13] Morton, S., High Resolution Computational Unsteady Aerodynamic Techniques Applied to Maneuvering 

Unmanned Combat Aircraft, Workshop on Aerodynamic Issues of Unmanned Air 

Vehicles, 4-5 November 2002, University of Bath, UK. 

[14] Gursul, I., Criteria for Location of Vortex Breakdown over Delta Wings, The Aeronautical Journal, 

May 1995, pp. 194-196. 

[15] Menke, M., Yang, H., and Gursul, I., Experiments on the Unsteady Nature of Vortex Breakdown 

over Delta Wings, Experiments in Fluids, vol. 27, no. 3, 1999, pp. 262-272. 

[16] Allan, M. R., Badcock, K. J., and Richards, B. E., A CFD investigation of wind tunnel wall 

influences on pitching delta wings, AIAA Paper 2002-2938, June 2002. 

[17] Allan, M. R., Badcock, K. J., Barakos, G. N. and Richards, B. E., A RANS investigation of wind 

tunnel interference effects on delta wing aerodynamics, AIAA Paper 2003-4214, June 2003. 

[18] Taylor G., Gursul, I., and Greenwell, D. I., An investigation of support interference in high angle 

of attack testing, AIAA Paper 2003-1105, January 2003. 

[19] Allan, M. R., Badcock, K. J., Barakos, G. N. and Richards, B. E., Wind tunnel interference 

effects on a 70 o delta wing, Proceedings of the CEAS Aerospace Aerodynamics Research Conference, 

London, UK, 10-12 June 2003.

15 

[20] Gursul, I., Unsteady Flow Phenomena over Delta Wings at High Angle of Attack, AIAA Journal, 

vol. 32, no. 2, February 1994, pp. 225-231. 

[21] Gursul, I. and Xie, W., Buffeting Flows over Delta Wings, AIAA Journal, vol. 37, no. 1, 1999, 

pp. 58-65. 

[22] Menke, M. and Gursul, I., Unsteady nature of leading edge vortices, Physics of Fluids, vol. 9, 

no. 10, 1997, pp. 1-7. 

[23] Gursul, I., Review of Unsteady Vortex Flows over Delta Wings, AIAA-2003-3942, AIAA Applied 

Aerodynamics Conference, 23-26 June, 2003, Orlando, FL. 

[24] Gray, J.M., Gursul, I., and Butler, R., Aeroelastic Response of a Flexible Delta Wing due to 

Unsteady Vortex Flows, AIAA-2003-1106, 41st Aerospace Sciences Meeting and Exhibit, 6-9 

January, 2003, Reno, Nevada. 

[25] Taylor, G., Schnorbus, T. and Gursul, I., An Investigation of Vortex Flows over Low Sweep Delta 

Wings, AIAA-2003-4021, AIAA Fluid Dynamics Conference, 23-26 June, 2003, Orlando, FL. 

[26] Gordnier, R.E. and Visbal, M.R., Higher-Order Compact Difference Scheme Applied to the Simulation 

of a Low Sweep Delta Wing Flow, AIAA-2003-0620, 41st Aerospace Sciences Meeting 

and Exhibit, 6-9 January, 2003, Reno, Nevada. 

[27] Matsuno, T. and Nakamura, Y., Self-Induced Roll Oscillation of 45-Degree Delta Wing, AIAA- 

2000-0655, 38th AIAA Aerospace Sciences Meeting and Exhibit, 10-13 January, 2000, Reno, 

NV. 

[28] Gad-el-Hak, M. and Ho, C.M., The Pitching Delta Wing, AIAA Journal, vol. 23, no. 11, 1985, 

pp. 1660-1665. 

[29] Rockwell, D., Three-Dimensional Flow Structure on Delta Wings at High Angle-of-Attack: 

Experimental Concepts and Issues, AIAA Paper 93-0550, January, 1993. 

[30] Visbal, M.R., Computational and Physical Aspects of Vortex Breakdown on Delta Wings, AIAA 

Paper 95-0585, January, 1995.

16 

[31] Gursul, I., Proposed Mechanism for Time Lag of Vortex Breakdown Location in Unsteady 

Flows, Journal of Aircraft, vol. 37, no. 4, 2000, pp. 733-736. 

[32] Arthur, M., “The impact of vortical flow on the free rolling motion of a delta wing aircraft”, 

Proceedings of conference on Integrating CFD and Experiments, Glasgow, UK, September 8-9, 

2003. 

[33] Gordnier, R., High-Fidelity Computational Simulation of Nonlinear Fluid-Structure Interaction 

Problems, Workshop on Aerodynamic Issues of Unmanned Air Vehicles, 4-5 November 2002, 

University of Bath, UK.

17 

Figure 1: Instantaneous flow showing the transition process with increasing Reynolds number (left); 

and time-averaged flow showing mean vortical substructures (right) [5] 

Figure 2: Magnitude of velocity measured by PIV over a slender delta wing showing the timeaveraged 

structured of vortex breakdown.

18 

Figure 3: Spectrum of unsteady flow phenomena over delta wings as a function of dimensionless 

frequency [15] 

Figure 4: Scatter of vortex breakdown location in different facilities (from [14])

19 

Figure 5: Time history of average and difference of breakdown locations showing asymmetric oscillations. 

Figure 6: Asymmetric structural mode for a slightly flexible delta wing when vortex breakdown 

occurred on the wing.

20 

Figure 7: Flow visualisation of vortices over a nonslender delta wing with a sweep angle of Λ = 50 o 

(left). Dual vortex structure (of the sane sign of vorticity) in a cross-flow plane exists upstream of 

vortex breakdown (right), alpha = 15 o . 

Figure 8: Surface flow visualisation for Λ = 50 o for α = 2.5 o (left) and α = 15 o (right).

21 

Figure 9: RMS value of fluctuating velocity together with the surface streamline pattern obtained 

from velocity measurements close to the wing surface. 

Figure 10: Interaction of multiple vortices originating from strake and wing, showing coiling-up and 

vortex breakdown.

Figure 11: Upper surface pressure distribution and roll history from Euler simulations of the wing 

rock phenomenon 

22

Computational and Experimental Studies of Pressure Relief Doors in Ventilated 

Nacelle Compartments 

Mr Peter Pratt, Dr. John Watterson, Dr. Emmanuel Benard 

School of Aeronautical Engineering 

The Queen's University of Belfast, Belfast, Northern Ireland, BT9 5AG 

Email: p.pratt@qub.ac.uk; j.watterson@qub.ac.uk; e.benard@qub.ac.uk 

Keywords: discharge flow, transonic, flapped outlet, vortices, oblique jets, shear layers 

Abstract: 

A computational study of the performance of a flapped exhaust outlet is carried out. The outlet duct is 

curved, turning exhaust gases through 90 o to the stream-wise direction before passing to the free-stream, 

and is of a rectangular cross section. A flap is fixed at the upstream edge. The resulting flow is a complex 

mixture of a jet emerging into a transonic flow, longitudinal vortices, free shear layers and normal 

shockwaves. The effect of varying flap angle, pressure ratio and free-stream Mach number is considered 

and force and discharge characteristics predicted. Information obtained is used to aid the design of a 

transonic wind tunnel test rig for gathering experimental data useful in the design of Pressure Relief Doors 

for ventilating engine nacelle compartments. 

Introduction 

Performance and reliability of modern aircraft engines is affected by many factors, among which is the requirement 

for dedicated auxiliary air systems necessary for the safe and successful operation of the engine. An important set of 

auxiliary outlets are related to the relief of under cowl pressure in the event of a leak from, or burst of, high pressure 

supply lines to engine subsystems. These outlets are known as Pressure Relief Doors (PRDs) and are important to 

regulate excess internal pressure so as to prevent structural damage or failure. 

One design for a PRD is a flap hinged at the downstream edge of the outlet. This flap will automatically open before 

the under cowl pressure reaches a structurally unsafe level, venting excess air to the free-stream. When the slender 

bodied flap enters the free-stream it creates a complex three dimensional (3D) flow structure which is a combination 

of longitudinal vortices, shear layers, an oblique jet and in some cases normal shockwaves. The exact combination 

and development of these structures is dependent on flap geometry, flap angle, free-stream Mach number and the 

ratio of under cowl to free-stream total pressures. 

The design of such a system requires reliable information on force and discharge characteristics across a range of 

parameters. Very little research has been done on this subject, especially in recent years. Consequently a 

conservative approach to design has been adopted by the aerospace industry and more detailed information is now 

required to achieve an efficient design that satisfies both customers and certification authorities. 

It is proposed that, through the use of a systematic process of computational investigations and experimental studies, 

a design database can be developed to help improve aerodynamic and structural performance of PRDs. 

Literature 

Current PRD designs are based on literature regarding the discharge of auxiliary outlets to transonic free-stream 

flows. There are a number of passing mentions of experimental studies 1,2 specifically related to flapped outlets in 

papers concerning more generalised auxiliary air systems. However the most comprehensive set of experimental 

data is presented by Vick 3 in NACA TN4007. This deals with force and discharge characteristics of flapped, curved 

duct outlets in transonic flows and has particular relevance and influence on current PRD designs. Information on the 

performance of inclined auxiliary outlets is found in studies by Dewey 4 and Vick 5 , with these showing that the 

discharge performance for given flow conditions is better for outlets with flaps than without.

While the information presented in NACA TN4007 is of great importance, it raises a number of questions and covers 

only a small range of parameters. There is no consideration of the flow structures formed around or downstream of 

the outlet and therefore no satisfactory explanation of the effect of flap angle, geometry, pressure ratio or free-stream 

Mach number on the discharge performance of the outlet. 

For an efficient design of a PRD it is important however to understand how the above-mentioned parameters effect 

the flow field and therefore the discharge and force characteristics. 

Methodology 

The expensive nature of high-speed wind tunnel experiments means that to cover a wide range of design parameters 

a computational model is preferable. However experimental data is still required to validate any numerical solutions. 

A flapped outlet above a plenum chamber should be used to simulate the PRD system rather than the ducted outlets 

found in the literature. A lack of description of, or explanation for, the flow physics of flapped outlets within previous 

literature raises questions with regard to the scale lengths and properties of any flow structures. This leads therefore 

to uncertainties when considering the design of a suitable test rig and its related instrumentation. A numerical study 

of the experiment described in NACA TN4007 was therefore proposed, with the predictions of the computational 

model being compared to the published data to provide a greater understanding of the physics of the flow field. This 

in turn allowed for a validation of a numerical model, which can be used to help design the experimental test rig. The 

commercial CFD package, Fluent 6 TM , was used for the calculations. 

The computational domain was based on the geometry of the wind tunnel and flapped outlet used in the NACA 

experimental study, as shown in figure 1 and figure 2. The outlet consists of a rectangular duct 1 wide by 1.865 in 

length, which turns the exhaust flow through 90 about a radius of curvature of 2 into the streamwise direction. The 

upstream edge of the orifice is extended 0.375 so that the orifice length is 1.49. A flat, rectangular flap 1 wide by 1 

long and 0.032” thick is attached to the upstream edge of the duct orifice. The orifice leading edge was placed 8 

downstream of the inflow boundary. With the computational domain being symmetric, only one half, measuring 17 

long by 3.125 wide by 4.5 tall was modelled. 

Figure 1 : Outlet geometry (adapted from NACA TN4007)

Flap angle is assumed to be fixed rather than freely hinged with flap weight considered negligible. By studying force 

data across a range of fixed angles it is possible to deduce hinge moments and therefore the steady state angle at 

which the flap will balance for a given pressure ratio and Mach number. The discharge characteristics for this flap 

angle can then be determined and therefore the performance of the outlet for given conditions. Meshes were created 

for flap angles from 15 to 45, in 5 increments. The free-stream Mach number was varied from 0.4 to 0.85 in 

increments of 0.15. As a result, the ratio of leading edge boundary layer thickness to orifice length varied between 

0.095 and 0.110. 

Figure 2: Computational domain 

The performance of the duct is measured in terms of Discharge flow ratio (DFR) which is defined as the ratio of mass 

flow through the effective area of the orifice to the mass flow in the free stream through the same effective area as 

the orifice. The pressure ratio, defined as the ratio of duct total pressure to free stream total pressure, was varied 

between 0.64 and 0.97 in order to obtain the range of flow ratios required. Pressure inlet and outlet boundary 

conditions were applied and the realisable k- turbulence model was used because of its known accuracy when 

dealing with flows involving jets, separations and secondary flows. 

A mesh dependence study was performed to ensure that converged solutions were mesh independent. 

Results 

Mass flow through the effective outlet area was extracted from the data files and discharge flow rates were calculated 

for each case, doubled to account for the symmetry plane. These values were plotted against angle for each pressure 

ratio and Mach number, as shown in figure 3. In each case the value of DFR increases with flap angle up to a 

maximum before falling off. The angle at which this maximum occurs decreases with increasing pressure ratio. 

Increasing Mach number also reduces the angle at which maximum discharge occurs. The maximum value of DFR 

increases with increasing pressure ratio but decreases with increasing Mach number. 

Next the force on the flap, and load centre were extracted and used to calculate the moment about the hinge point for 

each case. These were converted to pitching moment coefficients by normalising with free-stream dynamic head, 

effective outlet area and flap length, with positive moment defined to be closing the flap. These values are then 

plotted against flap angle, shown in figure 4. Extrapolation of the data shows that for the majority of combinations of 

pressure ratio and Mach number, the zero pitching moment coefficients occurred in the range of 10 o to 15 o . At lower 

pressure ratios and Mach numbers this point is lowered below 10 o .

Figure 3 : DFR against Flap angle for a range of pressure ratios (legend) and angles 

Figure 4 : Hinge moment coefficient against flap angle for a range of pressure ratios (legend) and Mach numbers

Increasing Mach number increases the hinge moments and curve gradients considerably. However for every 

pressure ratio and Mach number the curves intersect at a flap angle of 25 o . For angles above this, increasing 

pressure ratio increases the pitching moment. Angles under 25 o show the opposite trend. There appears to be a 

maximum value for the moment as the curves begin to flatten at 45 0 , however more data at higher angles is required 

to verify this prediction. 

To investigate the accuracy and validity of the CFD model, DFR and pressure ratio data were extracted from the plots 

in figure 3 for a single angle and plotted in figure 5 (dashed line) with the corresponding data from the NACA paper 

(solid line) across a range of Mach numbers. The curves through the CFD data points match the trend of the curves 

for the experimental data. However for a given pressure ratio the CFD result appears to under predict the DFR. This 

discrepancy increases with increasing pressure ratio with the effect becoming more severe with increasing freestream 

Mach number. The maximum error at each Mach number increases from 5% at M=0.4 to 20% at M=0.85. 

Figure 5 : DFR against pressure ratio, for flap angle=25 o , comparing NACA TN4007 and CFD results 

The thrust generated by the outlet, defined positive in the stream-wise direction, was measured in the NACA paper 

through the use of a force gauge (see figure 1) and non-dimensionalised with free-stream dynamic head and effective 

outlet area. For comparison, the same thrust coefficient was calculated using the CFD results and taking into account 

the force on both the curved duct and flap. The envelope of thrust data from the NACA experiments is plotted in 

figure 6, along with the corresponding CFD data points, for a given flap angle. At lower values of DFR the predicted 

values of thrust fall within the envelope from the experimental data. At the larger values of DFR the CFD results over 

predict the generated thrust with the points lying just outside the envelope, with an error between 5% and 10%. 

Discussion 

From the plots in figure 3 it can be clearly seen that flap angle has a pronounced effect on the discharge performance 

of the outlet. Previous studies 1,2 had indicated that flaps, or other protrusions, generated areas of low pressure over 

the outlet which increased discharge through suction. The mechanism behind this is the formation of a pair of 

longitudinal vortices, shed from the edges of the flap (c.f. a delta wing). As the flap angle increases the strength of the 

vortices increases until a maximum angle is reached. Beyond that angle the flap could be said to “stall” and behaves 

like a bluff body.

Figure 7 shows a series of plots of total pressure contours in the Y-Z plane of the computational domain, downstream 

of the outlet, for a flap angle of 15 0 , free-stream Mach number of 0.7 and pressure ratio of 0.8. Note that the 

symmetry plane has been plotted to illustrate the pair of vortices. The structure of the flow can be seen to develop 

downstream of the outlet as the vortices interact with the exhaust jet and shear layer shed from the trailing edge of 

the flap. 

Figure 6 : Coefficient of thrust against DFR, for flap angle=25 o , comparing NACA TN4007 and CFD results 

Figure 7 : Contours of total pressure, flap angle = 15 o , M=0.7, pressure ratio = 0.8

Figure 8 shows a similar plot for a flap angle of 40 o but with the same pressure ratio and free-stream Mach number, 

as shown in figure 8. A marked difference in the flow field can be seen, with a much stronger initial vortex pair 

leading to a larger flow structure further downstream. For the smaller flap angle, the flow structure impinges on the 

surface downstream which appears to have a thinning effect on the boundary layer in the downstream area outboard 

of the vortices. 

Figure 8 however shows that for a large flap angle the structure is lifted away from the surface with the result that the 

boundary layer thinning does not occur, in fact, between the vortices the boundary layer is substantially thickened. 

Variations in pressure ratio will change the nature of the discharge jet from the outlet, which will then in turn effect the 

manner in which the vortices, jet and shear layer interact. Free-stream Mach number will also determine the 

properties of the shed vortices and therefore the resulting flow structure. In cases of high Mach number and pressure 

ratio, flow in the outlet becomes choked as flow velocity exceeds sonic conditions and a normal shock is formed, as 

illustrated in figure 9. The position of this shock moves forward as the flap angle decreases, due to a repositioning of 

the throat of the outlet as effective area decreases. 

Figure 8 : Contours of total pressure, flap angle = 40 o , M=0.7, pressure ratio = 0.8 

Conclusions 

Generally good agreement was achieved between the previously published data and the CFD prediction of integral 

properties such as DFR and thrust coefficient. Confidence has been gained that the numerical model, to a degree of 

accuracy, predicts the flow physics involved. A large amount of information is now available to be studied in an 

attempt to understand fluid mechanics involved. The numerical model can also be adapted to aid the design of a new 

experimental test rig, including the sizing of the required plenum chamber. 

It is also noted that the information obtained may be of use in areas other than PRD design. A large number of 

engineering applications involve longitudinal vortices impinging on a surface, either from vortex generators or jets 

emerging into a cross flow. Such applications include boundary layer control, prevention of shock induced separation, 

cooling and chemical mixing. Through studying the flow structures around PRDs some insight into the interaction of 

longitudinal vortices and boundary layers may be obtained and applied to the applications mentioned above.

Figure 9 : Contours of Mach number, flap angle = 40 o , free-stream M=0.85, pressure ratio = 0.85 

Bibliography 

1. Rogallo, F.M., Internal-flow systems for Aircraft, NACA, Report 713, 1941. 

2. Drag of Auxiliary Inlets and Outlets, AGARD, 264. 

3. Vick, A.R., An Investigation of Discharge and Thrust Characteristics of Flapped Outlets for Stream Mach Numbers 

from 0.4 to 1.3, NACA TN 4007, 1957. 

4. Dewey, P., A Preliminary Investigation of Aerodynamic Characteristics of Small Inclined Air Outlets at Transonic 

Mach Numbers, NACA TN 3442, 1955. 

5. Dewey, P. and Vick, A.R., An Investigation of the Discharge and Drag Characteristics of Auxiliary Air Outlets 

Discharging into a Transonic Stream, NACA TN 3466, 1955.

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Turbulent Wind Flow over a High Speed Train 

R K Cooper 

School of Aeronautical Engineering 

Queen’s University Belfast 

r.cooper@qub.ac.uk 

Keywords: train aerodynamics, cross-wind effects 

Abstract: 

The flow of a turbulent cross-wind over a stationary train, including the effect of an embankment, has been 

simulated by CFD. The coefficient of rolling moment about the lee rail have been compared with 

experimental data. Agreement is satisfactory for flat ground and a low (4m) embankment. The level of 

turbulence intensity was an important parameter for obtaining a correct simulation. 

Acknowledgement: 

Permission from Network Rail WCML, to use aerodynamic data obtained by BMT Fluid Mechanics Ltd., is gratefully 

acknowledged. 

Introduction 

Strong cross-winds may overturn trains, so an understanding of the fluid mechanics is important. To facilitate the 

proper estimation of the probability of a train overturning, accurate data for the aerodynamic rolling moment about the 

lee rail is essential. (Of course, many other parameters are required.) The flow of a turbulent cross-wind over a train 

moving across an embankment is complex, and difficult to model experimentally. Many experiments have been done 

with stationary model trains; some including turbulent flows. The aim of this work is to use such data to verify a CFD 

simulation with a stationary model train on an embankment. Clearly, even the ‘best’ such experiment is an 

approximation. However, CFD provides the ability to model the motion of the train with respect to the ground, with a 

turbulent cross wind, and this is the ultimate aim. 

Experimental Data 

It has been surprisingly difficult to obtain accurate aerodynamic data for trains in cross winds. The close proximity of 

train to ground implies that under-body flow must be carefully modelled, including the effect of rails. The effect of free 

stream turbulence has been found to be significant, and apparently contradictory results have been observed: e.g. for 

an APT leading vehicle, Fig. 1 [1]. To model turbulence with a sufficiently large integral length scale has proved to be 

difficult. Simulation of the motion of the train may be less significant than providing the correct turbulence scale [2]. 

This hypothesis may be tested using CFD simulation, provided the CFD method can be verified for a stationary train. 

Electric locomotive hauled Mark 3 passenger coaches (Fig. 2), and the diesel powered High Speed Train (HST, or 

Intercity 125, Fig. 3), have been in use on Britain’s railways for more than 30 years, without an overturning event, so 

provide a reference case. Recent experiments at BMT Fluid Mechanics in an atmospheric boundary layer (ABL) 

simulation [4] have provided aerodynamic data for the Mark 3 passenger coach. Models of a train (Class 87 

locomotive and two coaches) of 1/7 scale and 1/30 scale were tested. Only the latter, shown in Fig. 4, is relevant to 

the present study. The ABL wind tunnel provided a good simulation at 1/30 scale, of the mean velocity profile, 

turbulence intensity profile, and turbulence length scale, compared with the ESDU model. The ‘wind’ was used to 

simulate the resultant flow with respect to a moving train. (Clearly, this was an approximation, but the effect of the 

degree of approximation is not considered here.) The side force, lift and rolling moment about the lee rail were 

obtained from a high frequency balance. Mean force and moment coefficients were obtained as a function of resultant

yaw angle. Also, extreme value coefficients normalised with respect to an extreme resultant speed were obtained. 

Only the mean coefficients are considered in this report. The effect of Reynolds number was examined by comparing 

data for two model scales, over a range of tunnel speeds. For Reynolds number (based on body height and relative 

speed) exceeding 2*10 5 , no significant changes in surface pressure distribution or mean forces were observed. This 

proprietary data is considered to be amongst the most reliable, as a simulation of the full-scale case. The experiment 

was an approximation of reality, since the model train was stationary. But the flow turbulence was close to reality, so 

the effect of turbulence at least, should be representative. 

A 1/50th scale wind tunnel model representing the Class 87 and Mark 3 coach has been tested at Queen’s University 

Belfast. The side force and rolling moment about the lee rail were obtained for steady and unsteady flow cases. 

Computational Domain 

The CFD software used was Fluent 6. The Gambit meshing package was used to create the computational grid. A 

basic HST geometry was defined using a solid modeller, at full scale. The simplified train shape had no bogies or 

inter-vehicle gaps. Nose shape approximated the HST diesel locomotive, Fig. 3, with a solid under-body 

approximating the bogies. The cross-section was a close approximation of the Mark 3 coach, as a cylindrical body. 

Details, such as the roof ribs, were omitted. Note that this is not the same as the wind tunnel model, but the most 

significant difference is the nose shape. 

The aim was to create as much as possible of the computational domain using structured grid. This involved 

considerable time and effort by two students [5, 6]. The regions around the nose and tail were unstructured. A box 

with a semicircular top was created around the train. The nose and tail were partitioned from the cylindrical centre 

section and the cylindrical volumes were further partitioned into parallelepiped boxes, as shown in Fig. 5. The train on 

an embankment was placed in an enclosing box, with a round top. This was extended by further regular volumes, as 

required. A typical mesh section is shown in Fig. 6. The mesh density in the structured region was easy to control and 

modify. This apparently simple grid evolved gradually, with much trial and error. The final grid had about 430,000 

nodes. 

The aim was to model wind tunnel cases, so the parameters were chosen to model incompressible flow at the 

Reynolds number of the experiment. The realisable k-e turbulence model was used. Wall functions were used to 

determine the boundary turbulence quantities. The cell sizes near the train surface and ground plane were chosen to 

give a satisfactory resolution of the wall boundary condition. The value of y + was maintained in the desirable range, 

viz. 30-60, over most of the embankment and train surface, with the exception of the lower train surface, which gave 

values 150-250. Probably, the grid in the gap region should be refined. The flow velocities in this region were small, 

so small changes would not necessarily have much effect of the forces. 

The inflow velocity profile was defined to match the experimental profile. For the ABL simulation this closely matched 

the logarithmic profile with a surface roughness length of z 0=0.03m (full scale), corresponding to typical rural terrain, 

using the ESDU model. The inflow turbulence intensity and length scale were set, initially, to 3% and 3m, 

respectively. 

Results 

Train on flat ground 

Flow streamlines around the train are shown in Fig. 7-9. For yaw angles less than about 70 0 a strong vortex is formed 

on the lee side. The vortex structure becomes unsteady at about 50 0 . The computed coefficient of side force is 

compared with the QUB experimental data for a uniform inflow profile [1], in Fig. 10. The Reynolds number was 

1.6*10 5 for the experiment and 10% less for the CFD. There is a significant difference in the range 60 0 to 80 0 . The 

CFD was able to replicate observed flow features on the windward side of the train. The attachment line moved down 

with increasing Reynolds number. This was associated with movement of a separation line on the ground plane 

upstream of the train, Fig. 9. This observation is significant, since the separation and attachment lines would be 

sensitive to flow turbulence as well as Reynolds number. 

The computed side force coefficient is compared with the BMT experimental data for a logarithmic inflow profile, with 

Reynolds number of about 2.5*10 5 , in Fig. 11. Results for the coefficient of rolling moment about the lee rail are 

shown in Fig. 12. The experimental values of turbulence intensity at 3m height, were about 20% and 24m (referred to 

full scale), respectively. The CFD inflow turbulence intensity was 3%, with a length scale of 3m. The CFD did not

simulate the flow correctly, as shown by the large difference in the results. The turbulence intensity was increased to 

10%, and a much closer agreement with experiment was obtained. Visualisation of the flow streamlines showed that 

the separation on the ground upstream of the train was probably eliminated. Clearly, the turbulence parameters 

significantly affect the CFD modelling of this flow. (The investigation is still in progress, so the results are incomplete. 

In particular, the effects of turbulence length scale or ground surface roughness have not been investigated.) The 

results suggest that some of the observed variations between different wind tunnel experiments may be due to this 

effect. The highly turbulent inflow of the ABL experiment seems to eliminate the upstream separation. It also makes 

the flow over the train less susceptible to Reynolds number effects. 

Train on an embankment 

For a train on a 4m high embankment, experimental and CDF results are shown in Figs. 13 and 14. The inflow 

turbulence intensity was 3%. The CFD and experimental results are similar for the rolling moment, but not side force. 

This appears to contradict the result for the flat ground case above. The flow streamlines around the embankment 

and train are shown in Fig. 15. The flow is attached to the embankment slope and separates cleanly at the edge, 

reattaching upstream of the rail. It is surmised that the well-defined separation causes the flow to be less sensitive to 

inflow turbulence. 

Train motion over the ground 

It was easy to simulate the effect of the train moving over the ground with the CFD. Preliminary runs indicated only a 

small change from the corresponding steady flow case, but the inflow profile was not correctly skewed with height. 

The prospects for examining the effect of train motion and unsteady cross-wind gusts is encouraging. 

Conclusions 

CFD has been applied to the case of a train in a turbulent flow. The boundary layer behaviour, particularly on the 

ground just upstream of the train, was affected by the inflow turbulence intensity and scale, which thus had a strong 

influence on the forces and rolling moment. With appropriate turbulence intensity, the side force coefficient was 

predicted to good accuracy. 

Bibliography 

1. Ahmed, K., Development of wind tunnel techniques for unsteady train aerodynamics, MPhil Thesis, QUB 

Aeronautical Engineering, 2003. 

2. Baker, C J, Ground vehicles in high cross winds. Part 1: Steady aerodynamic forces. J. Fluids and Structures, 

1991, 5, 69-90. 

3. Baker, C J, Ground vehicles in high cross winds. Part 2: Unsteady aerodynamic forces. J. Fluids and Structures, 

1991, 5, 91-111. 

4. WCRM Wind Loading Studies, Atmospheric Boundary Layer Studies. BMT Fluid Mechanics Ltd. Report 

43309rep4v3, Final, 16 January 2003. 

5. Fanning, C., CFD investigation of aerodynamics of a high speed train, QUB Aeronautical Engineering, MEng 

project report, May 2003. 

6. Chraibi, H., Turbulent flow over a high speed train on an embankment, QUB Aeronautical Engineering, summer 

project report, Aug. 2003.

0.9 

Cs vs yaw angle 

Side force coefficient (Cs) 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 10 20 30 40 50 60 70 80 90 100 

Yaw angle (deg) 

QUB 1/50 scale (M-III) 

MIRA 1/5 scale (APT) 

Cranfield 1/50 (APT) Turbulence simulation 

AEA 1/50 (AEA) Turbulence simulation 

Fig. 1. Coefficient of side force vs. yaw angle: APT (various) and Mark 3 coach (QUB) 

Fig 2. Class 87 locomotive and Mark 3 coaches: prototype for wind tunnel model

Fig 3. High Speed Train with Mark 3 coaches: prototype for CFD model 

Fig.4. Model train (Class 87 locomotive + 2 Mark 3 coaches) in ABL wind tunnel (©BMT Fluid Mechanics Ltd.)

Fig. 5. Grid block structure around train. 

Fig. 6. Mesh section for train on embankment of height 4m.

Fig. 7. Flow on flat ground at yaw angles of 30 0 and 75 0 

Fig. 8. Flow on flat ground at yaw angle of 60 0 

Fig. 9. Flow on flat ground at yaw angle of 60 0

Cs comparison at V=0.6 m/s 

Fig. 10. Side force coefficient vs. yaw angle: QUB experiment, Re=1.6*10 5 , flat ground. 

Cs flat ground 

Side force coefficient Cs 

Side Force Coefficient (Cs) 

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Cm Flat ground 

Rolling Moment Coef. ( Cm) 


Exp 

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Yaw angle(deg) 

Fig. 12. Coefficient of rolling moment about lee rail vs. yaw angle: 

BMT experiment, Re=2.5*10 5 , flat ground. CFD turbulence intensity 3%.

Cs 4m Embankment 

Side Force Coefficient ( 

Cs) 


Exp 

0 20 40 60 80 100 


Fig. 13. Side force coefficient vs. yaw angle: BMT experiment, Re=2.5*10 5 , 4m embankment. 

Cm 4m Embankment 

Rolling Moment 

Coefficient ( Cm) 


Exp 

0 20 40 60 80 100 


Fig. 14. Coefficient of rolling moment about lee rail vs. yaw angle: 

BMT experiment, Re=2.5*10 5 , 4m embankment. CFD turbulence intensity 3%. 

Fig. 15. Flow over train on 4m embankment.

Investigation of Flow Turning in a Natural Blockage Thrust Reverser 

S. Hall, R.K. Cooper, E. Benard, S. Raghunathan 

School of Aeronautical Engineering, Queen's University Belfast 

David Keir Building, Stranmillis Rd, Belfast BT9 5AG, UK 

s.l.hall@qub.ac.uk, r.cooper@qub.ac.uk, e.benard@qub.ac.uk, s.raghunathan@qub.ac.uk 

Keywords: Thrust Reverser, Internal Flow 

Abstract: 

Experimental and computational low speed tests have been conducted on a 50% scale model of a twodimensional 

natural blockage fan flow cascade thrust reverser. The aim of the work is to provide a 

reference database for future work investigating innovative flow control in fan flow thrust reversers. 

Results are presented for a reverser with cascade solidity = 1.3. The experimental nozzle pressure ratio 

must be increased to obtain relevant quantitative data. In addition the 2D computational results highlight 

problems of simulating a flow with 3D effects. 

Introduction 

Virtually all modern jet transport aircraft incorporate thrust reverser systems which are primarily used to provide 

an extra safety margin during landings and aborted take offs 1 . Thrust reversers operate by redirecting the engine 

exhaust flow forwards to produce a braking force. Unlike wheel braking systems their performance is not 

degraded by wet/icy runway conditions. Several types of thrust reverser are in operation today however this 

paper considers only the natural blockage cascade type fan flow thrust reverser which is used on the CF-34-8C 

powerplant of the Bombardier Aerospace CRJ-700/900 Regional Jet aircraft. The nacelle fan duct of the CF-34- 

8C engine is S-shaped. When the thrust reverser is deployed the rear section of the nacelle cowling translates aft 

to naturally block the fan duct whilst simultaneously exposing the reverser cascade opening in the side of the 

nacelle 2 . The fan flow is blocked and diverted outwards through the cascade opening where the cascade vanes 

deflect it forwards to produce the reverse thrust efflux (see figure 1). 

It may be possible to use partial-cascade or cascadeless flow turning to achieve similar levels of reverse thrust. 

In the long term it may even be possible to design a thrust reverser with no moving parts which is essentially 

blockerless and cascadeless. Such a design would yield advantages in terms of reduced weight, reduced 

activation time and reduced leakage and pressure losses in the nacelle. The removal of the cascade from the 

system will necessitate its replacement with innovative fluidic flow control to ensure that flow turning through the 

reverser is maintained. Before investigating this possibility it is important to first understand the flow in the 

conventional natural blockage thrust reverser. This paper presents results from recent experimental and 

numerical studies of flow through a conventional natural blockage thrust reverser conducted at Queen's 

University Belfast. These studies form the basis to ongoing research within the school into innovative flow control 

in thrust reversers. 

Methodology 

The wind tunnel has a constant speed fan motor and the flow velocity can be set by partially blanking the fan inlet 

duct. Downstream of the fan there are four gauze screens for flow smoothing and a two-dimensional contraction 

section of contraction ratio 0.24. Following the contraction is the test section which measures 380mm by 89mm in 

cross-section. The maximum velocity in the test section is approximately 20m/s. The experimental model is a 

50% scale two-dimensional simplified geometry representing the CF-34-8C thrust reverser in its deployed state. 

The cascade vanes are of constant thickness with blunt leading and trailing edges and have a design discharge 

angle of 45 0 . The blocker surface is modelled as a simple flat plate (see figure 2). In a cross-sectional plane 

located at 125mm from the duct entrance six static pressure tappings are arranged in the duct walls with even 

spacing (two per wall). A total pressure rake consisting of thirteen probes is mounted in a sliding traverse in the 

duct roof. The rake vertically spans the duct and can be moved manually across the duct by means of the 

traverse. The constant cross-section duct is connected to the thrust reverser model by a set of bellows so that 

force measurements may be made on the reverser model at a later date. An exit pressure rake consisting of 26 

probes (6 static probes, 19 total pressure probes and 1 directional alignment probe) 3 is mounted spanwise above 

the exit plane of the cascade. It can be manually rotated about its main centreline and using the alignment probe 

can be set to the local exit flow direction. The rake attachment consists of two slotted bars mounted on a

spanwise axle. This allows the spanwise rake to be moved longitudinally relative to the model duct exit plane and 

also to be moved vertically to various heights above the exit plane. 

Within the model duct several series of static pressure tappings are placed on the upper and lower surfaces. On 

the upper surface 16 tappings are placed along the centreline of the model. The positions of these tappings are 

shown in figure 3. On the lower surface a series of 15 tappings is placed along the centreline and an additional 

series of 15 tappings span the surface. In the spanwise series the tappings are located at 25mm intervals with 

the end tappings each being 15.5mm from the duct wall. The spanwise set of tappings will help to ascertain the 

degree of two-dimensionality of the flow and the effects of the sidewalls on the lower surface flow. In the 

longitudinal series the tappings are placed in denser concentrations in areas where flow separation is predicted 

to occur i.e. close to the blocker door on the lower surface and around the sharp corner at the inlet ramp. The 

pressure values from the various tappings and rakes are recorded manually from an inclined multi-tube 

manometer. 

A CFD simulation of the experimental test is carried out using the commercial flow solver, FLUENT 6 TM . The CFD 

code is based on first order upwind difference operators on a two-dimensional, steady, implicit solution of the full 

Reynolds averaged Navier-Stokes (RANS) equations. The viscous turbulence model used is the RNG 

(renormalization group) k-ε model. Because of the low velocities involved in the case to be modelled the flow is 

assumed to be incompressible with the flow density set to the experimental atmospheric air density. 

The computational grid is unstructured and is composed of 46726 cells. The farfield limits of the domain are set 

20 model lengths upstream from the model, 10 model lengths downstream from the model and 20 model lengths 

vertically above the model. Figure 9 shows details of the computational thrust reverser model geometry. The 

main thrust reverser inflow is set as a velocity inlet boundary condition corresponding to the experimental 

velocity. The farfield boundaries are all set with pressure outlet boundary conditions equal to the experimental 

atmospheric pressure. In initial test runs it was found that the reverser efflux from the cascade was turned and 

attached to the wall upstream of the cascade exit. This effect does not occur in reality because the reverser efflux 

entrains flow into the low pressure region beneath the efflux. In the present 2D computational model this is 

simulated by creating an inflow of 5% of the experimental velocity on the upstream wall which injects flow 

vertically into the domain (see figure 9). The scheme converges after 1500 iterations. 

It should be noted that the CFD analysis is still in early development. At the time of publication grid independence 

studies have yet to be carried out. However the CFD results to date are presented to show general trends and 

comparisons with the experimental data. 

Results and Discussion 

Results are presented for the case of cascade solidity (σ) of 1.3 at six different mean inlet velocities: 8.5m/s, 

9.5m/s, 10.8m/s, 12m/s, 12.4m/s, 13.3m/s. For each case the nozzle pressure ratio, defined as the ratio of inlet 

total pressure to atmospheric pressure is calculated. Static pressure is measured longitudinally on the upper and 

lower surfaces along the model centreline and also on the lower surface a spanwise static pressure distribution is 

measured. At a plane above the cascade exit a spanwise survey of total pressure is taken for the case of inlet 

velocity 13.3m/s. In addition the two-dimensional direction of the exit flow streamlines are determined at the 

centre span. The pressure data is presented in terms of pressure coefficients:- 

C 

p 

= 

P − P 

1 ρU 

2 

a 

2 

ref 

Where P a is the atmospheric pressure datum and U ref is a notional isentropic nozzle velocity. This is obtained 

from an assumed isentropic expansion through the nozzle for the velocity 13.3m/s case. Based on this 

assumption U ref =1.76 U m where U m is the measured mean inlet velocity. The use of pressure coefficients should 

collapse the data for various flow rates to a single curve because of the low Mach number of the experiment and, 

hopefully, a small effect due to Reynolds number. The Reynolds number is defined in terms of the duct hydraulic 

diameter and inlet velocity. 

For the tunnel velocity variation the nozzle pressure ratio was found to vary from 1.0013-1.0033. The low nozzle 

pressure ratio is due to the low velocities of the tests. Literature on other experimental test programs typically 

quote nozzle pressure ratio ranges of 1.1-2.0 to be comparable with full-scale flow conditions. 

Figures 4 and 5 show the surface static pressure distributions on the centreline of the top and bottom surfaces of 

the internal duct. On the bottom surface the initial decrease of pressure coefficient suggests that the flow 

accelerates around the curvature of the bottom surface. The pressure coefficient then increases suggesting that 

the flow slows as it travels along the following straight duct section . Figure 5 shows the static pressure levelling 

off at the position of static port number 12. This may imply flow separation away from the bottom surface of the

duct as it approaches the blocker corner. On the top surface of the duct (figure 4) the increasing pressure 

coefficient indicates that the flow slows as it moves around the initial curvature and following straight duct section. 

As it approaches the inlet ramp the flow accelerates rapidly as shown by the rapid decrease in pressure 

coefficient here. There is an adverse pressure gradient around the inlet ramp and separation occurs at 

approximately the position of port number 10 after which the pressure is approximately constant. 

Figure 6 shows the spanwise static pressure distribution across the bottom surface of the duct. There are small 

variations in the static pressure which may be due to the beginnings of corner vortices and/or surface 

irregularities at the duct inlet due to the bellows. 

At the front and rear of the cascade exit the flow is degraded as shown by the lower spanwise total pressure 

coefficient distributions (traverse position x=170mm and x=80mm respectively, figure 7). Over the middle of the 

cascade (x=90mm to x=150mm) the flow rate is higher and there is little change in the flow with longitudinal 

position. In similar experiments Thompson 6 noted that the cascade vanes at the aft of the cascade have relatively 

little effect as the flow here is being turned internally by the flow blocker surface. Similarly the flow at the front of 

the cascade is relatively unaffected by the foremost cascade vane. The degraded flow at the front and rear of the 

cascade is supported by the measurement of centre-span flow direction at the traverse plane (figure 8). At 

x=170mm the flow is overturned to deflection angle 26 0 whilst over the middle section of the cascade the flow is 

deflected to approximately 40-45 0 which is very close to the design discharge angle of the vanes. Flow 

overturning is caused by the flow adhering to the convex trailing edge of the cascade vanes as observed by 

Poland 4 . Romine and Johnson 5 also noted that losses in the thrust reverser are a function of the cascade 

effective area. As deflection angle decreases the cascade effective area decreases leading to increased flow 

blockage and a drop in flow discharge. This could account for the degraded flow at the first exit rake traverse 

position in figure 7. The pressure coefficient data shows that over the middle of the cascade pressure losses are 

less than 20%. 

A CFD simulation of the experimental test with inlet velocity 13.3 m/s (NPR=1.0033) has been conducted. Figure 

10 shows velocity vectors of the flow through and leaving the thrust reverser geometry. The regions of increased 

flow around the curvatures and the region of reduced flow velocity at the junction of the bottom wall and flow 

blocker surface are clearly visible as is the efflux jet exiting the cascade at approximately 45 0 . Figures 11 and 12 

show a comparison of the experimental and computational results for static pressure distribution on the bottom 

and top walls of the reverser duct. In figure 11 the static pressure is given at positions along the bottom wall 

corresponding to the horizontal distance relative to the inlet (x). There is a problem with the same scheme for the 

upper wall since at the inlet ramp the wall doubles back on itself. Therefore in figure 12 the positions located after 

the inlet ramp apex are presented in terms of a modified horizontal distance. The apex of the inlet ramp on the 

upper surface is defined as x max = 0.174m as shown in figure 12. The modified horizontal distance is expressed 

as the apex distance plus the modulus of the distance from the apex to the post-apex position in question. 

From figure 11 and 12 it can be seen that on the duct walls the experimental static pressure coefficients are 

higher than those predicted by the computational scheme. The fact that the difference in pressure coefficient 

between experimental and computational results is approximately 0.15 on the bottom wall but only 0.1 on the top 

wall is as yet unexplained. The computational scheme appears to capture the variation of static pressure with 

wall position very well except for the flow separation occurring at the inlet ramp and bottom wall/flow blocker 

junction. The difference in static pressure coefficient between the experimental and computational results 

indicates that in the experiments more pressure is required to drive the flow. This may be due to a combination of 

three-dimensional factors which are not present in the two-dimensional model. Such factors may include the 

affect of corner vortices on the bottom surface and reduced flow turning through the duct. Reduced flow turning 

would give a less uniform flow at the cascade resulting in a reduction of cascade efficiency. Hence a larger 

pressure difference would be required to maintain the mass flow rate through the duct. 

It is also suggested that the flow separation on the inlet ramp contributes to the higher driving pressure in the 

experiments. The relationship between this separation and the aforementioned three-dimensional effects is still 

not fully understood. In an attempt to deliberately make the 2D computational model simulate the separation the 

flow from the inlet ramp the ramp surface was made notionally porous. The variation in static pressure 

distribution for this deliberate porous alteration is also shown in figures 11 and 12. The region of separation on 

the inlet ramp is more accurately captured and as a result of the separation the pressure coefficient over the main 

duct is increased. This appears to corroborate the earlier suggestion that the ramp separation is a factor leading 

to the increased pressure required to drive the experimental flow. From figure 11 the additional porosity has 

virtually no affect on the static pressure coefficient on the bottom wall. 

.

Conclusion 

The experiment successfully models the qualitative aspects of the flow through the reverser in terms of efflux 

deflection angle and pressure distributions. However the nozzle pressure ratio range for the experiments is set 

too low for quantitative data collection. It is suggested that the tunnel velocity is increased to rectify the problem. 

The preliminary CFD results highlight the problems of attempting to computationally model in 2D a flow which is 

highly 3D in nature. Generating a 3D computational model would reduce the need to make artificial alterations to 

correctly simulate the three-dimensional effects in the thrust reverser. This could potentially offset the inherent 

added complexity and computation time of such a model. 

Bibliography 

1. Yetter, J.A., Why do airlines want and use thrust reversers? - A compilation of airline industry responses to a 

survey regarding the use of thrust reversers on commercial transport airplanes, NASA TM-109158, January 

1995 

2. Short Brothers PLC (GB), Aircraft Propulsive Power Unit Thrust Reverser with Separation Delay Means, UK 

patent no. GB231481, November 2000. 

3. Ower, E. and Pankhurst, R.C., The Measurement of Air Flow, Pergamon Press, Oxford, 1966. 

4. Poland, D.T., Aerodynamics of Thrust Reversers for High Bypass Turbofans, AIAA paper 67-418, July 1967. 

5. Romine, B.M. and Johnson, W.A., Performance Investigation of a Fan Thrust Reverser for a High Bypass 

Turbofan Engine, AIAA-84-1178, AIAA/SAE/ASME 20 th Joint Propulsion Conference, Cincinnati, OH., June 11- 

13, 1984. 

6. Thompson, J.D., Thrust Reverser Effectiveness on High Bypass Ratio Fan Powerplant Installations, SAE 

Paper, Ref. 660736, October 1966.

Figure 1. Natural Blockage Thrust Reverser 

Figure 2. The Experimental Model 

Figure 3. Positions of Static Ports and the Traverse of the External Pressure Rake.

Figure 4. Top Wall Static Pressure Distribution. 

Figure 5. Bottom Wall Static Pressure Distribution. 

Figure 6. Bottom Wall Spanwise Static Pressure Distribution.

Figure 7. Post-Exit rake Total Spanwise Pressure Distribution. 

Figure 8. Post-Exit Rake Flow Direction at Centre-Span.

Figure 9. Detail of CFD Model Geometry 

Figure 10. Velocity Vectors in the Thrust Reverser.

Figure 11. Comparison of Static Pressure Distribution on Bottom Wall. 

Figure 12. Comparison of Static Pressure Distribution on Top Wall.

Detailed Evaluation of CFD Predictions against LDA measurements for flow on an 

aerofoil 

A. Benyahia 1 , E. Berton 1 , D. Favier 1 , C. Maresca 1 , K. J. Badcock 2 , G.N.Barakos 2 

1 LABM, 163, Avenue de Luminy, Case Postale 918 13288 MARSEILLE Cedex 09, FRANCE, 

benyahia@morille.univ-mrs.fr 

2 University of Glasgow, Glasgow G12 8QQ, U.K, gnaa36@aero.gla.ac.uk 

Keywords: boundary layer, Embedded LDA, RANS 

Abstract: 

The current work is the validation of the Glasgow flow solver PMB for static and moving aerofoils against 

data measured at LABM. The treatment of turbulence and transition is considered. Measurements made at 

LABM using an Embedded Laser Doppler Velocimetry (ELDV technique) provide detailed boundary layer 

measurements on a pitching NACA0012 aerofoil. Flow laser sheet visualisation was used to characterize the 

transition behaviour. Finally, balance measurements of the lift and drag were made.After the measurements 

had been collected some RANS calculations were carried out. The detailed comparisons with the measured 

boundary layer profiles highlighted some difficulties, particularly with regard to the influence of the methods 

used for applying transition. Once fixed the agreement was much improved. 


The prediction of boundary layer behaviour on moving aerofoil sections is a necessary step towards the 

representation of dynamic stall which is experienced on the reatreating blade of a helicopter rotor in forward flight. 

Blades in motion can benefit from a delay in the static angle of stall due to the re-energising influence of the motion 

on the boundary layer. However, the eventual stall is abrupt. Prediction of dynamic stall is difficult because it requires 

the resolution of smooth body separation which in turn is influenced by turbulence. In addition, since the crucial 

separation is close to the leading edge, transition plays an important role, even at high Reynolds' number. The 

prediction of dynamic stall using CFD is a key unsolved problem of rotor aerodynamics. RANS predictions give the 

time averaged boundary layer behaviour. However, the validation of RANS codes is usually done using pressure or 

force data, since this is what is most commonly available. More recently, with advances in laser based measurement 

techniques, velocity measurements are becoming available. This creates opportunities for a more direct validation of 

the RANS predictions relevant to dynamic stall, namely the boundary layer behaviour. The current report documents 

the validation of the Glasgow flow solver pmb for static and moving aerofoils against boundary layer data measured 

at LABM. The treatment of turbulence and transition is considered. 

2 Experimental Setup 

2.1 Test Cases 

The cases considered here are for a NACA0012 aerofoil with a root chord of 0.3m. The wing used in the experiments 

spans the tunnel which has a test section of 1m by 0.5m and a length of 3m. The freestream velocity can be varied 

between 5 and 25 m/s and the natural turbulence intensity is less than 0.5%. The velocity used for the cases in this 

paper was 5 m/s. Since the RANS solver is formulated for compressible flows the computations have all been done 

for a freestream Mach number of 0.2, which is not expected to introduce compressible effects and so influence the 

solution behaviour. Three cases are considered. The first two are for flow around the fixed section, first at six degrees 

incidence and the secondly at fifteen degrees. Finally, a forced motion case is considered, with a sinuisoidal motion 

applied about the quarter chord at a frequency of 1 Hz, which gives a reduced frequency (based on the chord and 

freestream velocity) of 0.188.

2.2 Data Aquired 

The Embedded Laser Doppler Velocimeter (ELDV) has an optical head mounted on a supporting turntable linked to 

the oscillating frame as sketched in figures 1 and 2. The optical head is equipped with a beam-expander in order to 

increase the focal distance up to 400 mm. The laser beams focus through a 45 deg mirror at a given position in chord 

and span. The supporting turntable is linked with the oscillating frame, so that U and V velocity components can be 

directly measured in the same reference frame of the motion. Due to the periodicity of the motion, each period is 

considered as a specific sample of the same phenomenon. So, each velocity component is recorded at each phase 

angle ωt between 0 deg and 360 deg by steps of 0.703 deg over a large number of periods. Data are then statistically 

analyzed at prescribed values of the period, e.g. the instantaneous incidence, with an uncertainty of: 

δα=4∆α/360=24/360=0.066deg (1) 

Data acquisitions are made on a microcomputer from two Burst Spectrum Analyzer (BSA) delivering the values of the 

two components U and V together with the arrival validation time for each frequency measurement. The software used for 

acquisition and data reduction (COMBSA) was developed at LABM under the Apple LABVIEW system. 

The unsteady data reduction is performed using an ensemble average procedure suited for periodic flows investigation 

as described below. During a boundary-layer survey (s/C fixed) and for each normal distance y above the wall, 38 blocks of 

512 values are acquired which correspond to 19456 measurements of U and t u (arrival validation time of U) and the same 

number for V and t v. The two BSA work in a master-master mode : the (U,V) acquisition is independently performed with the 

same time origin. Moreover, this particular acquisition mode is coupled with a «dead time» function which makes sure that 

only one particle can be validated during a fixed time interval (here ∆t = 10 -4 s). This function avoids the simultaneous 

validation of a burst of particles. Based on such options, the oscillation cycle number varies in a range between 150 and 300 

depending on the flow configuration (with or without separation). Finally, one data file containing the 19456 data lines (t U, U, 

t V, V) is created for each normal distance y and the analysis software, provides the phase averaged (,) velocity 

components and their associated RMS quantities 1 . Indeed, due to the periodicity of the flow, each period is considered as a 

specific sample of the same phenomenon, so that each velocity component can be obtained at each phase angle t as the 

averaged value of the velocity samples recorded at the same given phase angle and over a large number of oscillation cycles 

(greater than 150). 

The negative arrival times due to the internal clock reset of the BSA are cut out in the first step. In the second step, the 

oscillation cycles are counted to keep only the common Nc cycles corresponding to the U and V simultaneous 

measurements. In the third step, the Nc cycles are pooled to obtain only one fictitious cycle. This cycle is split up into different 

divisions (512 in the present study) where velocities are averaged in order to provide discrete equidistributed representations 

of U and V velocities, written as and . The discrete representation obtained (512 points) results for each division, 

from an average of measurements from one or different cycles. Indeed, the division length (which represents 2.10 -3 second 

for a typical frequency of 1Hz), appears to be larger than the «dead time» interval fixed to ∆t = 10 -4 s. 

The next step is to produce a Fourier series (256 harmonics) representing the two mean functions of velocity 

components (written as U ~ and V ~ ) in pitching motion case. The fluctuating quantities u’ and v’ can be then calculated by : 

u' n (t) = U n (t) -U(ωt), v' n (t) = V n (t) -V(ωt) . 

Then the RMS intensities are defined by: 

σ u( 

t) 

= 

σ v( 

t) 

= 

1 

Nu 

1 

Nv 

Nu 

[ un' ( t) 

] 

n= 

1 

Nv 

[ vn' ( t) 

] 

n= 

1 

2 

2 

(2a) 

(2b) 

Where Nu and Nv are respectively the number of U and V velocity component values included in one division. 

All these fluctuating quantities are presented according to the phase averaged procedure, by representing the , , 

, , , and < 

u 'v' 

> quantities as a function of the normal distance y to the surface.

Finally, A particular attention has been paid to the process used for the turbulence determination from the velocity signal. 

Thus, the new procedure of data acquisition involves only a given phase that can be repeated along the oscillation cycle. This 

acquisition procedure “phase by phase” makes sure that velocity components are measured by the ELDV method, along the 

same cycle and at the same time. This condition secures the validity of the velocity fluctuation measurements required for the 

Reynolds stress consideration. 

3 Numerical Setup 

3.1 Method 

Ken to add details of numerical method. 

3.2 Grids 

A structured grid was generated using the commercial code ICEMHEXA. This has a C-topology and has 89 points 

normal and 309 points wrapped around the NACA0012 section. There are 33 points in the wake and the first normal 

mesh spacing adjacent to the aerofoil is 5 10 5 . A coarser grid for convergence studies was created with half the 

number of points in each direction (i.e. 45 points normal and 155 points around the section). 

3.3 Calculation Details 

All calculations were run on a PC with a 750 MHz processor. It was found important to drive the residual down for 

both the fixed and pitching cases to ensure that the turbulence had developed fully and an equilibrium had been 

achieved. 

For the fixed steady state case at six degrees incidence the solution converged in about 1600 implicit steps at a 

CFL number of 50. This required 1200 seconds of CPU time. The comparison of the boundary layer profiles for the 

KW and SA models on the different grids at x/c=0.67 for the case with an incidence of six degrees is shown in figure 

4. The agreement between the two sets of results is close. 

For the fixed unsteady case at fifteen degrees incidence a reduced real time step of 0.07 was used to give 20 

time steps per shedding cycle. The pseudo residual was dropped two orders of magnitude, typically requiring about 

25 pseudo steps at each real time step. The total time for the calculation on the fine grid to reach a periodic state 

(after about 7 shedding cycles) was 10500 CPU seconds. The results obtained when halving the time step are very 

similar. 

Finally, for the forced pitching case, at six degrees mean incidence and six degrees amplitude, 19 real time steps 

per cycle were used. It was found necessary to drive the pseudo residual down 3-4 orders in this case to obtain 

converged results. This required 300 pseudo steps per real time step for the first cycle and a half, and then, by 

restarting the pseudo convergence from the corresponding time on the previous cycle, this was reduced to less than 

ten pseudo steps per real time step thereafter. The influence of too lax a criteria is shown in figure 5 which shows that 

the loops thin as the tolerance is relaxed. The complete calculation on the fine grid took 25000 CPU seconds. 

4 Fixed Cases Below Stall 

The Spalart-Allmaras, k-ω and baseline SST turbulence models were evaluated for the flow at a fixed incidence of six 

degrees. In addition, the influence of the location of transition and the level of freestream turbulent kinetic energy was 

assessed. The last two factors turned out to influence the behaviour of the predictions much more than the model 

used and these are discussed in this section using the baseline SST model. 

4.1 Lift Curve 

The comparison between the measured and computed lift curves is shown in figure 6. At lower incidence the 

predictions and measurements are close to linear theory and are in good agreement. The predicted stall is earlier 

than in the experiments. The level of freestream turbulence has an influence as the stall angle is approached. 

4.2 Six Degrees 

In the experiments transition was observed between 0.1 and 0.3 of the chord. The behaviour of the predictions has 

been assessed for varying transition locations and freestream levels of turbulence.

First, plots of the turbulent Reynolds' number are shown in figure 7. All of these plots use the same scale and so 

comparison can be made between the plots. The major difference is introduced when using fully turbulent flow with a 

higher level of freestream turbulence. Large generation of turbulence is observed around the aerofoil nose and is 

then convected over the upper surface of the aerofoil. This is a well known artefact of linear eddy viscosity models [2]. 

Looking to the comparison of the boundary layer profiles at x/c=0.67 as shown in figure 8, the influence of this 

behaviour, which is to thicken the boundary layer and make the profile more turbulent, is clear. 

Applying transition away from the leading edge (in the middle of the observed transition region at x/c=0.2), 

removes the problem of spurious generation of turbulence at the leading edge and improves the comparison with the 

measured profile for the larger value of freestream turbulence. Reducing the level of freestream turbulence for the 

fully turbulent flow has a similar effect on the profile obtained. For dynamic stall cases the state of the boundary layer 

at the leading edge is important and this behaviour of the turbulence model around the stagnation point may be very 

significant. 

5 Fixed Case Above Stall 

The case at 15 degrees incidence is observed in experiment to feature trailing edge shedding at a frequency of the 

order of 10 Hz, and hence a RANS solution should be unsteady. In experiment transition was observed to be very 

close to the leading edge at this incidence. For this more demanding case the turbulence model was found to have a 

significant influence of the flow topology predicted. Variants of the k-ω model were used throughout this section. A 

low level of freestream turbulence has been applied to avoid excessive generation of turbulence at the leading edge. 

Using the standard k-ωmodel the solution is steady, with no shedding at the trailing edge. Relatively high levels 

of turbulence are predicted in the centre of the separated region, which arise from the turbulence model source terms 

reacting to velocity gradients which are not attributable to shear. 

This is a common problem for Boussinesq based turbulence models and has been observed, for example, for 

delta wing flows [3]. A fix is to either reduce the production of turbulent kinetic energy or to enhance the production of 

the turbulent dissipation term according to the ratio of the magnitudes of the vorticity and strain rate tensors. When 

the vorticity is high, as in the region of separation, the scaling acts to reduce the turbulence, and when the strain rate 

is high, as in a boundary or shear layer, then the original model is recovered. The influence of this scaling is shown in 

figure 9 and indicates that the turbulence levels are reduced as expected. This flow field now allows vortex shedding 

to start at the trailing edge through separation of the recirculating flow to form a secondary separation. This was 

surpressed when the high levels of turbulence were present for the unscaled model. 

An unsteady calculation was run using the scaled model for fully turbulent flow. The evolution of the lift coefficient 

to a periodic state is shown in figure 10. The reduced period is 1.6, indicated a reduced frequency of 0.51. A 

sequence of frames, shown in figure 11 shows a vortex being shed from the trailing edge. Time averaged boundary 

layer measurements at x/c=0.3 and 0.67 are available for comparison. It was observed in the computations that the 

boundary layer profiles at these locations change very little in time and the profile from one instant is shown in figure 

12. The comparison shows that the extent of the separated region is over-predicted when compared with experiment. 

6 Pitching Aerofoil Case 

Finally, a case in forced pitch is considered. The mean incidence and amplitude of the sinusoidal motion is six 

degrees and the frequency is 1Hz, leading to a reduced frequency of 0.188. Dynamic stall is not expected for this 

motion. From the static results the main influence of the transition is herefore expected to be from the production of 

turbulence around the stagnation point. For this case the baseline SST model has been used, with little difference 

being observed between these and the k-ω results. 

First, the lift loop is shown in figure 13, with reasonable agreement obtained. All cases generated negative values for 

the turbulent kinetic energy at some stage throughout the cycle and this was reset to freestream values to allow the 

calculation to continue. However, for very low values of freestream turbulence this ad-hoc treatment triggered 

massive separation and the results thereafter were unrealistic. These results are omitted. The influence of transition 

and freestream values of turbulence, with the exception of the case with high freestream turbulence and fully 

turbulent, on the solutions is seen to be limited. For this case it was seen for the static case that high levels of 

turbulence are created around the leading edge. 

The comparison of boundary layer profiles, shown in figure 14, is very close throughout the pitching cycle. 

7 Conclusions

Bibliography 

1. Berton, E. Favier, D., and Maresca., C, “Embedded L.V. Methodology for Boundary-Layer Measurements on 

Oscillating Models”, Proceedings of the Twenty-Eight Fluid Dynamics Conference, AIAA, AIAA paper 97/1832, 

Snowmass, June 1997. 

2. Barakos, G.N., ''Study of Unsteady Aerodynamics Phenomena using advanced turbulence closures'', PhD thesis, 

UMIST, 1999. 

3. Brandsma, F.J., Kok, J.C., Dol, H.S. and Elsenaar, A., ''Leading edge vortex flow computations and comparison 

with DNW-HST wind tunnel data''. RTO/AVT Vortex Flow Symposium, Loen, Norway, 2001.

Particles 

seeding tube 

3 m 

1 m 

model 

pitching 

Fore-and-aft 

U ∞ 

0,5 

m 

oscillating 

devices 

Laser source 

optical fibers 

Figure 1: S2L low speed wind-tunnel, Experimental set-up

Oscillating model 

α 0 

U ∞ 

Optical 

head 

t 

u 

v 

Measuring 

volume 

n 

y min = 0,2 mm 

Optical 

fibres 

Beamexpander 

turntable 

y max = 145 mm 

45deg mirror 

Figure 2: ELDV measurements linked with the oscillating frame model

000000000 

MEASUREM ENT 

S 

MEASUREM ENTS 

CH 1 

CH 2 

465 B 

OSCIL LOSCOP 

VOLT E S:DIV 

VOLT S:DIV 

SETU 

P 

SETU 

P 

A and B 

TIME/D IV 

and D EL AY TIM E 

SETT INGS 

BSA enhan ced 

SETT ING 

S 

BSA enhan ced 

TRIGGER 

POW ER 

A TR IGGER 

SHIFT 

ENTER 

SHIFT 

ENTER 

Laser 

source 

000000000 

Transmitin 

g block 

Optical 

head 

U 

V 

positio 

nsensor 

PM1 

Optical 

fibers 

PM2 

Oscillosco 

p 

1 

3.95 

3.00 

4.00 

64 

10.67 

7 8 9 

4 5 6 

1 2 3 

0 . +/- 

Color 

separator 

DANTEC 

9.318 

1.00 

1560 

8 

0 

1 

3.9 

5 

3.00 

4.00 

10.6 

7 

64 

7 8 9 

4 5 6 

1 2 3 

0 

. 

+/- 

Postprocessing: 

Macintos 

hLabview 

IEE 

E 

DANTE 

C 

9.31 

8 

1.0 

0 

1560 

8 

0 

BSA 

(Burst Spectrum Analyser) 

Figure 3: ELDV Acquisition chain

Figure 4: Comparison of predicted boundary layer profiles at x/c=0.67 on the coarse and 

refined grids for the case with fully turbulent flow, k=0.001 and a fixed incidence of six 

degrees.

Figure 5: Influence of the pseudo time tolerance on the lift coefficient loop for the 

pitching case at six degrees mean incidence and an amplitude of six degrees.

Figure 6: Comparison of lift curve with experiment for two levels of freestream 

turbulence.

Figure 7: Turbulent Reynolds' number for aerofoil at fixed incidence of six degrees for 

various locations of transition and freestream turbulence.

Figure 8: Comparison of boundary layer profiles for aerofoil at at fixed incidence of six degrees for various 

locations of transition and freestream turbulence.

Figure 9: Turbulent Reynolds' number for aerofoil at fixed incidence of fifteen degrees 

using k-ω model with enhaced destruction of turbulence and fully turbulent.

Figure 10: Time evolution of the lift coefficient for an aerofoil at a fixed incidence of 

fifteen degrees using k-ω model with enhanced destruction of turbulence and fully 

turbulent.

Figure 11: Vortex Shedding cycle for aerofoil at fixed incidence of fifteen degrees using 

k-ω model with enhanced destruction of turbulence and fully turbulent.

Figure 12: Comparison of Boundary Layer profiles for aerofoil fixed at fifteen degrees 

incidence using k-ω model with enhanced destruction of turbulence and fully turbulent.

Figure 13: Comparison with experiment for the lift coefficient loop for the pitching case 

at six degrees mean incidence and an amplitude of six degrees.

Figure 14: Comparison of boundary layer profiles for pitching aerofoil using SST model 

with fully turbulent flow.

Integrating CFD and Experiment in Aerodynamics - CFD4Aircraft

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