NUMBER THE AERONAUTICAL JOURNAL OCTOBER 2004model, a change in dynamic pressure about the model due to solidand wake blockage, and in the buoyancy effect due to the axial pressuregradient al<strong>on</strong>g the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> test secti<strong>on</strong>. The magnitude of these<str<strong>on</strong>g>effects</str<strong>on</strong>g> increases with model size (increasing solid blockage).Weinberg (4) c<strong>on</strong>ducted an experimental investigati<strong>on</strong> into wall<str<strong>on</strong>g>effects</str<strong>on</strong>g>. He tested two sets of three <strong>wing</strong>s (<strong>on</strong>e set with 60° sweep, and<strong>on</strong>e set with <strong>70°</strong> sweep), each <strong>wing</strong> with a different span size. Theexperiment was performed in a square water <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> at a c<strong>on</strong>stant flowvelocity of 11ms –1 . The <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> size was 45cm × 45cm. He found thatfor the three <strong>wing</strong>s with <strong>70°</strong> sweep, as the <strong>wing</strong> size was increased(kept at a c<strong>on</strong>stant angle-of-attack), vortex breakdown moved downstream.For the three <strong>wing</strong>s with 60° sweep, he found that as the <strong>wing</strong>span-to-<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> width ratio increased from 0⋅175 to 0⋅35, the wall<str<strong>on</strong>g>effects</str<strong>on</strong>g> followed the computed trends (i.e. vortex breakdown wasshifted downstream with increasing <strong>wing</strong> size). However, when the<strong>wing</strong> span-to-<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> width ratio was increased from 0⋅35 to 0⋅7, nosignificant change was observed. This suggested that effective camberwas not the <strong>on</strong>ly influence. For both the 60° and the <strong>70°</strong> <strong>wing</strong>s, thedifference in breakdown locati<strong>on</strong> observed from the smallest model tothe largest model, was of the order 25% c r .Thomps<strong>on</strong> and Nels<strong>on</strong> (5) investigated experimentally the influenceof <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> walls <strong>on</strong> a <strong>70°</strong> <strong>delta</strong> <strong>wing</strong> by testing full, two thirds, andhalf scale models in a square <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> (the largest model gave theratios S/H = S/W = 0⋅364). Due to a steady hysteresis effect the <strong>wing</strong>was tested for a quasi-steady upward and downward stroke. It wasfound that for the smallest model tested (S/H = S/W = 0⋅124) thebreakdown locati<strong>on</strong> shifted downstream by as much as 15%c r <strong>on</strong>both the quasi-steady upstroke and downstroke. For the half scalemodel and the full scale model, there appeared to be little differencein the breakdown locati<strong>on</strong>s. As stated by Thomps<strong>on</strong> and Nels<strong>on</strong>, thisshift downstream as model size is decreased is in c<strong>on</strong>trast to theresults of Weinberg (4) . It was noted that Weinberg used a Reynoldsnumber an order of magnitude lower, and a c<strong>on</strong>stant velocity, asopposed to keeping the Reynolds number c<strong>on</strong>stant (as in the experimentsof Thomps<strong>on</strong> and Nels<strong>on</strong>). It was observed that the vortexsucti<strong>on</strong> <strong>on</strong> the model surface increased with model size.More recently Pelletier and Nels<strong>on</strong> (6) studied the effect of <str<strong>on</strong>g>tunnel</str<strong>on</strong>g><str<strong>on</strong>g>interference</str<strong>on</strong>g> <strong>on</strong> <strong>70°</strong> <strong>delta</strong> <strong>wing</strong>s. Experiments were c<strong>on</strong>ducted in awater <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> with three different sized <strong>wing</strong>s. These low Reynoldsnumber tests agreed with the previous findings of Thomps<strong>on</strong> andNels<strong>on</strong> (5) who tested at higher Reynolds number, in that breakdownmoved towards the apex with increasing <strong>wing</strong> size. Pelletier andNels<strong>on</strong> used the method of images to explain this effect, c<strong>on</strong>cludingthat the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> walls increased the mean incidence of the <strong>wing</strong>, thuspromoting breakdown.Verhaagen et al (7) performed Euler calculati<strong>on</strong>s of the flow over a76° <strong>delta</strong> <strong>wing</strong> inside wind-<str<strong>on</strong>g>tunnel</str<strong>on</strong>g>s of increasing size. The <strong>wing</strong>span-to-<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> width ratios c<strong>on</strong>sidered were 0⋅292, 0⋅389, and 0⋅584and the test secti<strong>on</strong> was octag<strong>on</strong>al. To model the effect of asec<strong>on</strong>dary separati<strong>on</strong>, a small ‘fence’ was placed where sec<strong>on</strong>daryseparati<strong>on</strong> would occur. It was found that decreasing the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> size(increasing the <strong>wing</strong> span-to-<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> width ratio) increased thesucti<strong>on</strong> in the vortices and increased the velocities in the vortex core,due to an increase in circulati<strong>on</strong> with decreasing <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> size.Allan et al (8) performed Euler simulati<strong>on</strong>s of <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> <str<strong>on</strong>g>interference</str<strong>on</strong>g><str<strong>on</strong>g>effects</str<strong>on</strong>g> <strong>on</strong> a 65° <strong>delta</strong> <strong>wing</strong> in various <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>s for static and pitchingcases. It was observed that <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> side walls were the most influentialfactor <strong>on</strong> breakdown locati<strong>on</strong>, with roof and floor having littleeffect. This is due to the fact that the roof and floor of the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> areunlikely to have any influence <strong>on</strong> the effective angle-of-attack of the<strong>wing</strong>, or <strong>on</strong> the development of the vortices. It was also noted that inpitching simulati<strong>on</strong>s, the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> <str<strong>on</strong>g>interference</str<strong>on</strong>g> <str<strong>on</strong>g>effects</str<strong>on</strong>g> were str<strong>on</strong>gest<strong>on</strong> the downstroke, during the vortex reformati<strong>on</strong>.When c<strong>on</strong>sidering support <str<strong>on</strong>g>interference</str<strong>on</strong>g> <str<strong>on</strong>g>effects</str<strong>on</strong>g> Hummel (9)observed that the presence of an obstacle <strong>on</strong>e chord length downstreamof the trailing edge of a <strong>delta</strong> <strong>wing</strong> caused vortex breakdownto shift towards the apex by up to 40%c r . The obstacle c<strong>on</strong>sideredwas unrealistically large (wider than the span of the <strong>delta</strong> <strong>wing</strong>),however, this early observati<strong>on</strong> highlighted the possible <str<strong>on</strong>g>effects</str<strong>on</strong>g> thatsupport structures can have. Recently Taylor et al (10) varied the positi<strong>on</strong>of various obstacles behind the <strong>wing</strong>’s trailing edge to find theeffect support proximity had <strong>on</strong> vortex breakdown. It was c<strong>on</strong>cludedthat when an obstacle was placed in the vortex core, breakdown waspromoted due to the adverse pressure gradient, which formed infr<strong>on</strong>t of the obstacle. As the obstacle was moved away from thevortex core, breakdown was observed to move downstream. It canbe expected that the degree of support <str<strong>on</strong>g>interference</str<strong>on</strong>g> will be dependent<strong>on</strong> support size, vortex strength and trajectory. Although possiblynot c<strong>on</strong>sidered as support <str<strong>on</strong>g>interference</str<strong>on</strong>g>, fuselages <strong>on</strong> <strong>delta</strong> <strong>wing</strong>models can effect the breakdown locati<strong>on</strong>. Some sting mounted<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> models have upper surface fuselages to c<strong>on</strong>nect the model tothe sting. The effect of such fuselages has been c<strong>on</strong>sidered in anumber of investigati<strong>on</strong>s, each of which have shown significant variati<strong>on</strong>sin breakdown locati<strong>on</strong> for a given sweep angle and incidence.See for example Refs (11-13). A possible reas<strong>on</strong> for the variati<strong>on</strong> inthe breakdown locati<strong>on</strong>s was given by Ericss<strong>on</strong> (12) in which theeffect of the fuselage was described as an induced camber effect.The induced camber effect alters the locati<strong>on</strong> of vortex breakdown,either delaying or promoting breakdown depending <strong>on</strong> the fuselage.It is the aim of the current work to evaluate the influence of <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>walls and downstream structures <strong>on</strong> <strong>delta</strong> <strong>wing</strong> aerodynamics. Inorder to include the influence of the sec<strong>on</strong>dary separati<strong>on</strong> a 3DRANS model of the flow is assumed. A particular advantage of CFDfor such an investigati<strong>on</strong> is that the various influences can be examinedseparately, thus the qualitative effect of each comp<strong>on</strong>ent of testfacility <str<strong>on</strong>g>interference</str<strong>on</strong>g> can be evaluated and c<strong>on</strong>clusi<strong>on</strong>s drawn.2.0 COMPUTATIONAL METHODAll simulati<strong>on</strong>s described in this paper were performed using theUniversity of Glasgow PMB3D (Parallel Multi-Block 3D) RANS(Reynolds Averaged Navier-Stokes) solver. A full discussi<strong>on</strong> of thecode and turbulence models implemented is given in Ref. 14.PMB3D uses a cell centred finite volume technique to solve theEuler and RANS equati<strong>on</strong>s. The diffusive terms are discretised usinga central differencing scheme and the c<strong>on</strong>vective terms use Roe’sscheme with MUSCL interpolati<strong>on</strong> offering third order accuracy.Steady flow calculati<strong>on</strong>s proceed in two parts, initially running anexplicit scheme to smooth the flow soluti<strong>on</strong>, followed by switchingto an implicit scheme to obtain faster c<strong>on</strong>vergence. The pre-c<strong>on</strong>diti<strong>on</strong>ingis based <strong>on</strong> block incomplete lower-upper (BILU) factorisati<strong>on</strong>and is also decoupled between blocks to help reduce the computati<strong>on</strong>altime. The linear system arising at each implicit step is solvedusing a generalised c<strong>on</strong>jugate gradient (GCG) method. For timeaccuratesimulati<strong>on</strong>s, James<strong>on</strong>’s pseudo-time (dual-time stepping)formulati<strong>on</strong> is applied, with the steady state solver used to calculatethe flow steady states <strong>on</strong> each physical time step (discussed fully inRef. 14).Since the RANS equati<strong>on</strong>s are solved the two equati<strong>on</strong> k-ω turbulencemodel is used for closure. It is well known that most linear twoequati<strong>on</strong> turbulence models over-predict the eddy viscosity withinvortex cores, thus causing too much diffusi<strong>on</strong> of vorticity (15) . Thisweakens the strength of the vortices and can eliminate sec<strong>on</strong>daryvortices, especially at low angles of attack where the vortices arealready relatively weak. The follo<strong>wing</strong> modificati<strong>on</strong> suggested byBrandsma et al (16) was therefore applied to the standard k-ω model ofWilcox (17) to reduce the eddy-viscosity in vortex cores.P k = min{P ku,(2⋅0 + 2⋅0min{0, r – 1})ρβ * kω}. . . (1)Here P ku is the unlimited producti<strong>on</strong> of k and r is the ratio of themagnitude of the rate-of-strain and vorticity tensors. When k is overpredicted in the vortex core, it will be limited to a value relative tothe dissipati<strong>on</strong> in that regi<strong>on</strong>. This modificati<strong>on</strong> was found improvepredicti<strong>on</strong>s compared with the standard k-ω turbulence model (18) .
ALLAN ET AL WIND-TUNNEL INTERFERENCE EFFECTS ON A <strong>70°</strong> DELTA WING NUMBERTable 1ONERA <strong>70°</strong> <strong>wing</strong> test cases — fully turbulent flowTunnel S/W S/H M ∞ ReFarfield – – 0⋅2 1⋅56 × 10 6ONERA F2 0⋅49 0⋅38 0⋅2 1⋅56 × 10 6S/W = 0⋅63 0⋅63 0⋅38 0⋅2 1⋅56 × 10 63.0 TEST CASESThe subs<strong>on</strong>ic case of a <strong>70°</strong> <strong>delta</strong> <strong>wing</strong> is c<strong>on</strong>sidered at 27° angle-ofattack.At this incidence vortex breakdown occurs over the <strong>wing</strong>.The <strong>wing</strong> has a root chord length of 950mm, a trailing edge length of691⋅5mm, flat upper and lower surfaces, and a leading edge bevel of15°. The wind-<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> model had a blunt trailing edge 20mm thickwhich has been bevelled (15° bevel) in the computati<strong>on</strong>al model tosimplify the grid generati<strong>on</strong>. Experimental data for this case wasobtained by Mitchell (19) . The <strong>wing</strong> was tested in the ONERA F2<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> (situated at Le Fauga-Mauzac Centre, near Toulouse, France)which has a working secti<strong>on</strong> of height 1⋅8m, width 1⋅4m, and length5m. It is a subs<strong>on</strong>ic, c<strong>on</strong>tinuous, closed-return <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>. The <strong>wing</strong> wasalso tested in the ONERA S2Ch <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> situated at the Chalais-Meud<strong>on</strong> Centre (ONERA), which is of quasi-circular cross-secti<strong>on</strong>with a diameter of 3m and a test secti<strong>on</strong> length of 4⋅93m. Themodel/<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> ratios are S/W = 0⋅49 and S/H = 0⋅38 for the ONERAF2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>, and S/W = 0⋅23 and S/H = 0⋅55 (taking into account theoff <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> centreline locati<strong>on</strong> of <strong>wing</strong>) for the ONERA S2Ch <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>.Despite the flow c<strong>on</strong>diti<strong>on</strong>s being similar in both <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>s, the meanbreakdown locati<strong>on</strong>s were closer to the apex in the ONERA F2<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> (the smaller of the two) when compared with those measuredin the ONERA S2Ch <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>. This suggests some test facility <str<strong>on</strong>g>interference</str<strong>on</strong>g>which could be due to either the support structure or <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>wall <str<strong>on</strong>g>interference</str<strong>on</strong>g>.The flow c<strong>on</strong>diti<strong>on</strong>s for which extensive experimental data fromthe ONERA F2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> are available, are an incidence of 27°,Reynolds number of 1⋅56×10 6 , and a freestream velocity of 24ms –1(M ∞ = 0⋅069). For these flow c<strong>on</strong>diti<strong>on</strong>s, flow visualisati<strong>on</strong> ofvelocity comp<strong>on</strong>ents, vorticity comp<strong>on</strong>ents, turbulent kinetic energycomp<strong>on</strong>ents and local static pressure are available in various planes.Vortex breakdown locati<strong>on</strong>s were also obtained based <strong>on</strong> where theaxial comp<strong>on</strong>ent of velocity becomes negative. In the current worksteady state simulati<strong>on</strong>s are performed in all cases, with theReynolds number being matched, however the Mach number is 0⋅2,compared with the lower Mach number of 0⋅069 in the experiment.Since the current work is based <strong>on</strong> a high speed flow solver, afreestream Mach number of 0⋅2 was used to avoid any possiblec<strong>on</strong>vergence issues. Transiti<strong>on</strong> was observed to occur at around40%c r in experiment, however the CFD simulati<strong>on</strong>s assume a fullyturbulent flow. As will be described the fully turbulent flow assumpti<strong>on</strong>will influence the validati<strong>on</strong> of the results. However, the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g><str<strong>on</strong>g>interference</str<strong>on</strong>g> will mainly be dependent <strong>on</strong> vortex strength, thus thefully turbulent assumpti<strong>on</strong> is unlikely to influence the trendsobserved (the leading edge separati<strong>on</strong> locati<strong>on</strong> is fixed due to thesharp leading edge and breakdown is known to be independent ofReynolds number (20) ).Three boundaries have been chosen. The first has the <strong>wing</strong> in freeair (farfield c<strong>on</strong>diti<strong>on</strong>s), the sec<strong>on</strong>d represents the ONERA F2<str<strong>on</strong>g>tunnel</str<strong>on</strong>g>, and the third the ONERA F2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> side walls brought closerto the <strong>wing</strong> (increasing the S/W ratio). Full details of these c<strong>on</strong>figurati<strong>on</strong>sas well as flow parameters can be found in Table 1.To assess the <str<strong>on</strong>g>effects</str<strong>on</strong>g> of downstream structures in the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> avertical (generic) structure was placed in the centre of the ONERAF2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>, downstream of the <strong>wing</strong>. Since supports in dynamictesting tend to be fairly large (driving mechanisms must also behoused) a thick cross-secti<strong>on</strong>al area for the support was chosen. Thegeneric structure c<strong>on</strong>sidered is a cylinder with a straight taper in theFigure 1. ONERA F2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> setup with downstream structure.Figure 2. Geometry of downstream support structure (plan view).downstream directi<strong>on</strong>. Figure 1 shows the support structure and itsplacement within the ONERA F2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>. To avoid grid generati<strong>on</strong>complicati<strong>on</strong>s the mounting attaching the <strong>wing</strong> to the vertical structureis omitted (it may be expected that there is further <str<strong>on</strong>g>interference</str<strong>on</strong>g>from this mounting). The downstream structure (shown in Fig. 2with dimensi<strong>on</strong>s) gives a fr<strong>on</strong>tal area blockage of around 12%.The support structure was placed at two downstream locati<strong>on</strong>s inthe ONERA F2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g>, at 0⋅5c r and 1c r from the trailing edge of the<strong>wing</strong>. The mesh over the <strong>wing</strong> is identical to that for the ONERA F2<str<strong>on</strong>g>tunnel</str<strong>on</strong>g> without downstream structures. Therefore there is no changein grid resoluti<strong>on</strong> in the vortical regi<strong>on</strong> above the <strong>wing</strong>. The ONERAF2 <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> mesh was altered downstream of the <strong>wing</strong> to allow thepresence of the structure.In all cases c<strong>on</strong>sidered the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> walls and downstream supportstructures have been modelled with inviscid wall boundary c<strong>on</strong>diti<strong>on</strong>s.Eliminating the <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> wall boundary layers reduces grid sizes,however, a c<strong>on</strong>sequence of this is that the favourable pressuregradient within the test secti<strong>on</strong> (due to <str<strong>on</strong>g>tunnel</str<strong>on</strong>g> wall boundary-layer