Principle And Practice Of Hotwire Constant Temperature ...

11 th Israeli Symposium on 

Jet Engines and Gas 

Turbines, October 2012 

Technion, Israel 

Principle And Practice Of Hotwire Anemometry In 

Turbomachinery Applications 

Beni Cukurel 

Technion - Israel Institute of Technology 

Aerospace Engineering 

Haifa, Israel





Introduction 

Advantages of Hot wire Anemometry 

Ideal tool for Measurement of Perturbation Quantities in Time Domain 

• High Frequency Response (~ 10 2 kHz) Accurately follow transients 

• Wide Velocity Range 

• High Accuracy / High Signal to Noise Ratio 

• Signal Analysis: Output is continuous analogue signal 

Both Time and Frequency Domain analysis is possible 

Challenges of Hot-wire in Turbomachinery Flows: 

• Transonic Multi-Dimensional Flow with Large Independent Fluctuating Components 

– HW Data Reduction for Compressible Subsonic / Transonic Flow (0.4





Objectives 

Development and Validation of X-Hotwire Methodology for Turbomachinery flows: 

Experimental Technique Development Requirements: 

• Practical : Absent of Closed Loop Wind Tunnels Varying Each Flow Quantity Independently 

• Reliable / Repeatable Precise & Accurate Results 

• Applicable in Wide range of Flow Conditions (from Subsonic to Transonic) 

• Intuitive: Based on Scientific Concepts, not Empirical Collapse of Data 

Limitations and Capabilities Well Known 

Validation and Exemplary Implementation 

• 2-D Fluctuation Measurements in Compressible Subsonic / Transonic Flow regimes 

Downstream of a Gas Turbine Fan 

• Instantaneous Mass Flow, Velocity, Density, Pressure are Measured





Constant Temperature 

Hotwire Anemometry 

Wheatstone Bridge 

Keeps Bridge in Balance via 

Controlling current to the wire 

∴ R wire ( T wire ) is constant 

E b 

ρ, U, T 

Represents Heat Transfer 

∴ Measure of Flow Properties 

• Low Sensor Thermal Inertia 

• High Servo Loop Amplifier Gain 

High Frequency Response





Hotwire Voltage Dependency 

Bridge Voltage is Sensitive to Variations in Velocity, but also: 

a. Total Temperature 

b. Density 

c. Flow angle 

E f( , U , T , ) 

0





Sensitivity analysis: 

e' ρ' u' 

0 

=S 

ρ 

+S 

u 

+S 

T 

+S ' 

0 

0 

E ρ U T 

Conventional Methodology 

T' 

 

In supersonic flow S =S u ; 

 

e' 

ρu' 

T' 

0 

=S 

ρ 

+ S 

T 

+S ' 

0 

0 

E ρU T 

 

logE 

S(ρ,U,T 

ρ 0 

, ) = 

log 

logE 

S(ρ,U,T 

u 0, ) = 

logU 

logE 

S 

T 

(ρ,U,T 

0 0, )= 

logT 

S(ρ,U,T , ) = 

 

0 

logE 

 

U=const., T =const., 

0 

0 

const. 

=const., T =const., const. 

0 =const., U=const., const. 

=const., U=const., T const. 

0 

Not True for 

Subsonic & Transonic 

• Parameterizing one parameter at a time while others remain constant 

Impractical Non-Physical (Purely Empirical) Not Reliable





Dimensional Analysis 

Dimensional Analysis of Thin Heated Wires: 

Nu = f(Re, Pr, M, Gr, 

l 

, , ) 

d 

 

T -T 

w 

T 

0 

0 

= f(Re, M, ) 

(η = Recovery factor) 

High speed air flow for a given probe at constant overheating: 

Pr , l / d and τ are constant and negligible natural convection (if Gr< Re 3 ) 

Nu = f(Re, M, ) 

U d w 

Re 

h d 

Nu = w 

U 

M= 

k γRT 

s 

q" 

 

h = and q" = 

T -T 

E 

AR 

2 

w 

w r w 

=





Non-Dimensional Methodology 

Nu = f(Re, M, ) 

Where; 

Nu (Re) = 

corr 

Nu (Re, M) 

(Re, M) 

1.109 

 

Re 

φ(Re, M) = 1+ A(M) 1.834 -1.634 

 

2.765+ Re 

1.109 

 

 

 

0.0650 Re 

x 1+ 0.3 - M 

1.670 4+Re 

 

 

1.222 

1.569 

0.6039 

M 

A(M)= +0.5701 

-1 

1.222 

M 1+M 

 

 

All Mach numbers 

Nu 

corr 

= f(Re, )





Required Calibration Facility 

The calibration setup schematic view:





Wire Temperature Calculation 

h d w 

q" 

For Ma





Mass Flux Calibration 

Nu 

corr 

= f(Re, ) 

Nu (Re) = 

corr 

Nu (Re, M) 

(Re, M) 

Ma independent! 

Cold calibration 

is possible!!





Angular Calibration 

Re 

eff1 

= Re f1( ) Reeff1 f1( ) 

 

Re 

eff2 

= Re f2( ) Reeff2 f2( ) 

Re 

Re eff : Same Nu if the probe 

was aligned at the reference 

position 

Ma and Re 

independent!!





Procedure Steps 

• Mass flux uncertainty is 1.8 % (95% confidence level) 

• Flow angle uncertainty is 1.1 degrees (95% confidence level)





Sensitivity Analysis 

Logarithmic differentiation of Nu gives: 

Re f ( , U , T 0 

) M f( U , T 0 

) 

 

(Re, M, ) 

1 logNu 1 log 

 

S 

 

2logRe logRe 

1 logNu 1 log 

 

Su 

S 

+ 

2 

logM logM 

 

K 1 1 

S K1n mS S S 

 

T0 

t t u 

Aw 

2 2 

11log 

logNu 

S 

 

2 

 

K logRw 

logTw 

 

A logR logI 

w 

e' ρ' u' 

= S 

ρ 

+ S 

u 

+ S ' 

E ρ U 

w 

nt logk logT0 

m log 

logT 

 

t 0 

 

 

e' 

1 ρ' 

E 

 

1 S1 Sρ1 

Su1 ρ 

- '= 

e' S 

 

S 

2 

ρ2 

S 

 

u2 

u' 

E 

 

 

 

2 

U 

 

∆ [S ρ /S u ] with ∆ is limited to 8 % [ ] ill-conditioned 

∆ [S ρ /S u ] with ∆d wire = 5μm to 9 μm up to 20 % 

Instantaneous Density AND Velocity Fluctuations can be Computed





Why Should You Care 

RTD 

5-Hole Probe 

X-wire 

X-wire 

5μm wire (~60kHz @M=0.8)





Exemplary Analysis 

Mass Flux [kg/m 2 -s] 

This is not CFD!!!! 

Interpolation 

in Direction 

Of Cross- 

Correlation 

Possible to Calculate: 

■ Mass flux Independent Fluctuation 

■ Angle of Each Component 

■ Velocity 

+ 

■ Density Blade to Blade Variation 

■ P o 

of Each Component 

Data Useful in: 

■ Time/Frequency Domain Analysis 

▫ CFD Validation ▫ Test-Aided Design 

▫ Performance Characterization 

▫ Length/Time Scale Identification 

▫ Effects of Manufacturing Tolerance 

▫ Noise Spectra





Separation of ρ and U 

The Perturbation Quantities in a Real Gas Turbine Fan 

Perturbation Quantities 

For The First Time: Instantaneous Velocity & Density in Compressible Flows





Summary & Conclusions 

Demonstrated Novel High Speed Cross-Hotwire Operation Scheme: 

‣ Practical 

• Nondimensional Parameters (Re, Nu, Ma) and widely accepted 

correlations are used 

• No need for closed loop wind tunnels 

• Effort equivalent to that of operation in isothermal low speed flows 

‣ Accurate 

• Instantaneous mass flux and flow angle can be determined within 1.8% and 

1.1° uncertainty (95% confidence level) 

‣ Valid over a wide range of Reynolds and Mach numbers (Subsonic + Transonic) 

• Calibrations obtained in cold jet (e.g. T 0 =290K) are valid at measurement 

environments (e.g. Gas turbine fan where T 0 =335K). 

‣ Instantaneous density and velocity fluctuations can be independently computed 

‣ Application is demonstrated by measurements conducted in gas turbine fan





Associated Publication 

Cukurel, B., Acarer, S., Arts T., “A Novel Perspective to High Speed Cross-Hotwire 

Calibration Methodology”, Experiments in Fluids, Vol. 53, pp. 1073-1085, 2012.

Principle And Practice Of Hotwire Constant Temperature ...

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