AIAA 2002–2808VALIDATION OF THE SIMULATIONOF FLOW IN AN S-DUCTR. D. D. Menzies, K. J. Badcock, G. N. Barakos, andB. E. RichardsCFD Group, Department of Aerospace Engineering,University of Glasgow, Scotland G12 8QQ, UnitedKingdom.

20th Applied Aerodynamics ConferenceJune 24–27, 2002/St. Louis, Missouri

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VALIDATION OF THE SIMULATIONOF FLOW IN AN S-DUCT

R. D. D. Menzies∗, K. J. Badcock†, G. N. Barakos‡, and B. E. Richards§

CFD Group, Department of Aerospace Engineering,University of Glasgow, Scotland G12 8QQ, United Kingdom.

Flow in a diffusing s-shaped intake has been ex-amined using computational fluid dynamics sim-ulations. This paper discusses the effects of dif-ferent modelling techniques for such flows. Invis-cid modelling gave a qualitatively good descrip-tion of the flow for a simple low mass flow case.However it was seen that at high mass flow ratesthe inviscid solution is unsteady unless a modi-fication is made to the duct geometry. Navier-Stokes calculations were performed for the samehigh and low mass flow cases using a varietyof turbulence models. Results were much morefavourable for both cases. It was found that dif-ferent closure techniques and convergence levelshad major differences in terms of the flow fea-tures predicted.

IntroductionBackground

SINCE the invention of the first jet engine,intake aerodynamics has been an important

field with most improvements arising from windtunnel tests. Problems such as intake structuraldamage due to engine surge tended to only be de-tected after prototype testing and flying. Windtunnel testing methods have improved drasti-cally over this period and the understanding ofsome important characteristics of flows in com-plex integrated intake ducts has followed as aconsequence. Over the same period computa-tional methods of tackling such problems havealso evolved considerably and, coupled with arapid performance increase in computing power,increasingly more complex investigations havebeen attempted, adding to the understanding ofintake flow physics.

Intakes are a crucial sub-component of an air-craft. The efficiency is crucial as it makes contri-butions to the performance and handling charac-teristics of the aircraft. The primary purpose of

∗Research Student, corresponding author.†Senior Lecturer.‡Lecturer.§Mechan Professor, AIAA Associate Fellow.

the device is to offer the compressor face a uni-form stream of air at specific conditions requiredby the engine whilst maximising efficiency andminimising total pressure loss.

Integrating an intake into an aircraft structurecan often be challenging. Undercarriage wellsand intake store bays often have to be negoti-ated leading to offset intake ducts. Intakes arealso offset to provide low observability character-istics and reduce the radar cross section (RCS)of the aircraft as a large contribution to the RCSof an aircraft comes from the reflections of radarsignals off the engine compressor face.

The flow in the RAE intake model 2129(M2129) is complex. The flow accelerates intothe intake from a stagnation point on the outercowl surface. There is further acceleration ofthe flow around the starboard side first bend ofthe intake - Fig. 1 - where separation occurs.The faster moving core stream is acted upon bycentrifugal and pressure forces which cause it tomove towards the outside of the bend (port side).Here the flow meets an adverse pressure gradi-ent. Energy deficient near wall fluid approachesthis adverse pressure gradient but cannot passthrough it. Instead the flow moves around theoutside curve of the wall towards the lower staticpressure on starboard side. This action of the lowenergy region towards the inside bend combinedwith the movement of the core flow towards theoutside bend sets up two cells of contra-rotatingsecondary flow.

A consequence of the rotating flow can be anincrease or decrease in the flow angle of attack onthe compressor blades which can then lead on tostall. If a sufficient number of compressor bladesstall then it is possible that an engine may surgewhich is an undesirable occurrence. Variationsin flow angle of attack at the compressor facealso cause a maldistribution of pressure which isquantified by a parameter called distortion. Thisparameter is usually given for a 60◦ sector thatis worst effected.

1American Institute of Aeronautics and Astronautics

Fig. 1 M2129 intake geometry showing sur-face grid and intake definitions.

Test Case M PR MFR CR1 0.21 0.9897 1.457 0.9311462 0.21 0.9280 2.173 0.931146

Table 1 Summary of Test Case Conditions

Test Case

The two test cases that are examined here havebeen examined previously.1 Test case 1 featuresa low mass flow rate and is relatively straight-forward. The second case is more complex as itis for a high mass flow rate which is sufficient todevelop supersonic flow within the intake.

The test case conditions can be seen in table 1.The contraction ratio (CR) is defined as the ratioof the area of the highlight plane to the area ofthe engine face plane, where the highlight planeis defined as the plane that cuts the leading edgeof the cowl. The mass flow rate (MFR) can bethought of as being related to the engine demand.In physical terms, it is defined by the dividingstreamline, the streamline that borders flow thatenters the intake with flow that does not. It is theratio of the dividing streamline in the freestreamto the area of the highlight. For subsonic intakesthe MFR is greater than 1. However, when con-sidering supersonic flows, the MFR is less thanone as the intake draws air from an area less thanit’s highlight area. The pressure recovery (PR) isa value estimated from experimental experience.Clearly a value as close to unity as possible isdesirable.

These values can be used to determine a staticpressure that is applied across the downstreamplane. A constant static pressure boundary con-dition has been found to be suitable for strictlysubsonic flows.2 The boundary condition doesnot model the fan in any way, but only the en-gine demand. Setting the correct engine demand

(applying the correct static pressure) is sufficientto model the upstream effects. This is a simplifi-cation in that the fan may impose a small amountof bulk swirl into the main flow but this has beenfound to be negligible. The downstream bound-ary has been placed far enough from the engineface to make all approximations valid.

Previous Work

Experimental and computational work havebeen published previously.1,3–7 The first two ref-erences also consider the inviscid case. It wasfound from experiments that considerable sec-ondary flow is a feature of the high mass flowcase and so it is much more challenging. Thereare greater variations in results between exper-iment and computation for the high mass flowcase. Inviscid results require an addition to thegeometry to account for any displacement (sepa-ration) of the flow from the starboard side of theduct at the first bend.

Turbulent computational results in previousworks did not require any modifications to the ge-ometry. However there is also little informationon convergence for the turbulent results. IndeedMay4 describes a failure to reach fully convergedresults. A reasonable qualitative comparison be-tween experiment and computation for the lowmass flow case was found for all previous com-putational works. Quantitatively, however, thecomparison is not so good. Inviscid results over-predict key features and turbulent results fail tocapture secondary flow satisfactorily. Overall itcan be said that the variations in results betweenexperiment and computation is considerable forthe Euler calculations, even with modificationsto the geometry. Turbulent results improve thepredictions although convergence details are lim-ited and secondary flow prediction is challenging.This paper aims to clarify the various problemsassociated with predicting inviscid and turbulentflows for these cases.

Simulation Method

The problem was modelled including the in-take cowl and a large far field freestream re-gion. This enabled the flow to be simulated fromfreestream into the duct and eliminated the needfor complicated inflow boundary conditions tobe developed. A further advantage is that a di-rect comparison between flow solvers is possible.For Navier-Stokes calculations, the flow was as-sumed to be turbulent in all but the freestreamblocks and a symmetry boundary condition wasimplemented through the x − z plane to reducecomputational costs.

2American Institute of Aeronautics and Astronautics

PMB,8 Glasgow University’s three-dimensional and two-dimensional flow solver,was applied to the problem. A cell centred finitevolume technique is used to solve the Eulerand Reynolds averaged Navier-Stokes (RANS)equations. The diffusive terms are discretisedusing a central differencing scheme and theconvective terms use Roe’s scheme with MUSCLinterpolation offering third order accuracy.Steady flow calculations proceed in two parts,initially running an explicit scheme to smoothout the flow then switching to an implicitalgorithm to obtain rapid convergence. Thepre-conditioning is based on Block IncompleteLower-Upper (BILU) factorisation and is alsodecoupled between blocks to improve parallelperformance. The linear system arising ateach implicit step is solved using a GeneralisedConjugate Gradient (GCG) method.

The flow solvers have previously been appliedto a wide range of problems including:

• Hypersonic spiked body flows9

• Rolling, pitching and more recently yawingdelta wings10

• Two and three-dimensional cavity flows11

• Other complex three dimensional geometries

To study complex, inviscid, and more espe-cially turbulent, 3D intake flows requires con-siderable computing power. The ComputationalFluid Dynamics group at the University of Glas-gow owns a clusters of PC’s consisting of 32nodes of 750MHz AMD Athlon Thunderbirduni-processor machines with 768Mb of 100MHzDRAM. A typical grid size of 500,000 points re-quires around 4 hours to complete 2000 implicitsteady state steps at a CFL of 30 in order for thelog of the residuals to drop 8 orders, at whichpoint it is considered fully converged.

An aim of this paper is to assess the perfor-mance of various turbulence closures in modellingcomplex internal flows. The flow is challengingwith complex secondary flows and strong ad-verse pressure gradients, generated by localisedaccelerating flows, placing high demands on tur-bulence models. Turbulence modelling is one ofthe central problems and remains a huge chal-lenge in CFD.

The non-linearity of the Navier-Stokes equa-tions has the effect of developing momentumfluxes (unknown a priori) that act as apparentstresses in the flow. Equations are developed forthese stresses and include additional unknowns.It can be said that the function of turbulence

modelling is to devise approximations for the un-known correlations in terms of flow propertiesthat are known so that a sufficient number ofequations exist. In making such approximations,we close the system.

Past research in relation to steady and un-steady turbulent flow simulations in the contextof Reynolds Averaged Navier-Stokes (RANS),has shown that the realism of numerical predic-tions is significantly affected by the accuracy ofthe turbulence model employed. Experience us-ing zero-equation turbulence models (e.g. Bald-win and Lomax12) has shown that these mod-els do not provide satisfactory results, especiallyin separated flows and their predictions dependupon empirical constants and topographic pa-rameters which are case specific.

Linear eddy-viscosity models (LEVM) as-sume an explicit algebraic relationship betweenReynolds stresses and mean strain, known asBoussinesq approximation (the principal axes ofthe Reynolds stress tensor (τij) is computed asthe product of the eddy viscosity (µT ) and themean strain rate-rate tensor (Sij)). These mod-els provide satisfactory results for attached, fullydeveloped turbulent boundary layers with weakpressure gradients and are also relatively easyto implement into computational fluid dynamics(CFD) codes. However, the predictions deterio-rate when all components of the Reynolds-stresstensor become dynamically significant.

Linear low-Re two-equation models seem tooffer the best balance between accuracy andcomputational cost, but since they employthe Boussinesq approximation for the Reynoldsstress tensor, are not able to capture effectsarising from normal-stress anisotropy. Second-moment closures offer a more exact representa-tion of the Reynolds stresses but require longercomputing times and careful numerical imple-mentation for obtaining stable numerical solu-tions. Reynolds-stress models have been usedin the past to investigate shock/boundary layerinteraction (see Davidson 1995;13 Batten etal,14 amongst others). These studies showedthat in certain cases second-moment closuresmay provide better results than linear mod-els, but in other cases the results are incon-clusive. Other approaches in turbulence mod-elling include the non-linear eddy viscosity mod-els (NLEVM) (Speziale;15 Craft et al16) and ex-plicit algebraic stress models (see Gatski;17 Abidet al18,19).

NLEVM’s is one of the approaches employedin this study. The objective of this approach isto introduce closures that incorporate key fea-

3American Institute of Aeronautics and Astronautics

tures of the Reynolds-stress models, but which,however, require computational effort compara-ble to linear two-equation eddy-viscosity mod-els. The idea behind non-linear eddy-viscositymodels can be found in the paper of Pope,20

while later on Speziale15 and Speziale and Ngo21

demonstrated the ability of non-linear modelsto capture secondary flows in ducts and flowsover backward-facing steps, respectively. Fur-thermore, Rubinstein and Barton22 developed anon-linear model based on the re-normalisationgroup theory (Yakhot and Orszag;23 Orszag24),while Shih et al25 developed a realisable non-linear algebraic-stress model.

A different approach was taken by Apsley andLeschziner26 who developed a low-Re NLEVMby simplifying a second-moment closure. Otherattempts to use advanced turbulence models inaerodynamic flows can be found in the works byGatski,17 Jiang et al,27 amongst others. Theexperience from steady flows has shown thatNLEVM’s offer some promising capabilities interms of accuracy and, additionally, are moreeconomic in terms of computing resources com-pared to the Reynolds-stress transport models.Non-linear models have been and are still be-ing refined and validated for steady flows, mainlytwo-dimensional and incompressible (see Craft etal16,28), while limited experience has been ac-quired from applications to compressible flows(e.g. Gatski17 and Barakos and Drikakis29). Al-though most of the NLEVM’s have emerged fromthe k − ε EVM, efforts have also been made todevelop a k − ω NLEVM.30

This paper has employed the S-A model,31

k−ω,32 and it’s hybrid, the SST model.33 Thesemodels are eddy viscosity models. One-equationmodels have perhaps been the least successfuland used of all the models devised. The S-Afalls into this category and has been used for thiswork. It was chosen as it gives improved pre-diction of flows with adverse pressure gradientscompared with the k − ω or k − ε models.

The k − ω turbulence model is a two-equationmodel and is also based on the Boussinesq eddyviscosity hypothesis. The eddy viscosity coeffi-cient is determined from the solution to two par-tial differential equations - one for the turbulentkinetic energy (k) and one for the specific dissi-pation rate (ω). The rate of dissipation of energyin unit volume and time is related to the externalscale of turbulence, l. Consequently such 2 equa-tion models are termed as complete as they canbe used to predict turbulent flow without initialknowledge of the turbulent flow structure.

The SST turbulence closure technique is a two-

equation model that is a hybrid of the k − ωand k − ε models. Closures that are Boussinesq-like are notoriously unreliable for flows with sec-ondary motions. The eddy viscosity formulationis modified to account for transport effects of theprincipal turbulent shear stress by forcing theturbulent shear stress to be bounded by a con-stant times the turbulent kinetic energy insidethe boundary layer (a realisability constraint).By doing this, the modification improves the pre-diction for flows that have separation and aredominated by strong adverse pressure gradients.To this end, it was expected that SST predic-tions would show improvements over standardk − ω and one-equation S − A predictions forflows in diffusing offset internal ducts.

Examination of ResultsLow Mass Flow Rate

As mentioned, the low mass flow rate case isconsidered the easier of the two test cases. Flowacceleration into the intake duct is subsonic atall times and secondary flow generation is notso intense relative to the high mass flow case.This brings problems in terms of turbulence mod-elling as it has been proven difficult1,5 to predictsecondary flow satisfactorily using computationaltechniques.

Inviscid

Fully converged results were obtained for theEuler calculation. Figure 2 shows the ratio of thelocal static pressure to freestream total pressurefrom the starboard surface of the duct. There isa significant over-prediction in the flow accelera-tion into the intake. This has knock-on effects asthe pressure does not recover and drops again atthe first intake bend (X/D = 1) on the starboardside by around 10% more than witnessed in theexperiments. There is no inviscid separation offof the first bend and secondary flow is, of course,not predicted.

Turbulent

Various closure techniques were used for theturbulent calculations. Fully converged solutionswere reached in all cases, fully converged meaningthe residuals had dropped 8 orders of magnitude.Figure 2 shows the pressure trace from the star-board side of the duct for all models comparedagainst previous computation and experiment.1

Flow acceleration around the cowl is well pre-dicted for all models. The subsequent pressurerecovery is over-predicted for the SST and SA.The k − ω model shows a very close match withexperiment upstream of the first bend.

4American Institute of Aeronautics and Astronautics

X/D, V1, V19

P/P

t0,V

2,V

18

0 1 2 3 4

0.8

0.825

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AGARD ComputationExperimentPMB3D-KWPMB3D-SAPMB3D-SST

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AGARD ComputationExperimentPMB3D-KWPMB3D-SAPMB3D-SSTPMB3D-Inviscid

Fig. 2 LMFR, turbulent. Pressure extrac-tion’s from the starboard side of the intake.

It has been documented previously1,3,4 thatthe prediction of secondary flow for this case hasbeen challenging. Secondary flow can be detectedby a dip in the static pressure trace downstreamof the first bend as witnessed for the experimen-tal data. Close examination of the figure suggeststhat all models fail to predict any significant sec-ondary flow.

However the graph shows that the SST modeldoes show signs of dipping. The magnitude ofthis drop is not sufficient to match experimentaldata. However it can be seen that the pressurerecovery in the cowl region is greater than wit-nessed in experiment and this leads to a higherpressure from the first bend downstream. Fig-ure 3 shows a contour plot of the ratio of local tofreestream total pressure at the engine face planeon one half, with velocity vectors plotted in thesecond half. Lower total pressures are seen dueto the secondary flow and this is highlighted bythe vector plot showing a small swirling vortex.

Y

Z

X

Pt/PT

1.007711.002360.9970170.9916710.9863250.9809790.9756330.9702860.964940.9595940.9542480.9489020.9435560.9382090.9328630.9275170.922171

Fig. 3 LMFR, SST model. Secondary flowat the engine face.

The k − ω predictions match the previousAGARD computation and experimental dataclosely throughout the cowl and to the firstbend. Following the first bend the result de-

viates with the computations remaining closelymatched and deviating from the experimentaldata which shows stronger secondary flow. TheSA results are closer matched to the SST resultsin the cowl region. Following the first bend theseparation predicted is less leading to a poorersimulation of secondary flow.

High Mass Flow Rate

The high mass flow case is known to be chal-lenging. The engine demand is such that super-sonic flow is generated at the cowl as the flowaccelerates into the duct, but also on the star-board side at the first bend. Again inviscid andturbulent calculations have been performed.

Inviscid

A converged solution for the Euler calculationwas not found. The issue of the convergenceproblem is likely to be from one of two sources:the problem as modelled is not steady, or the do-main boundary conditions are unrealistic. Theunsteady flow solver was run. The pressure his-tory is plotted in Fig. 4 from a point on thecentreline at the first bend. It is evident that thepressure is fluctuating by around ±15% aboutthe mean value and is periodic. Further analysisrevealed that the problem exhibits inviscid sepa-ration off of the starboard side first bend, thisbeing the contributing source of the unsteadi-ness. The literature is limited with regard to thehigh mass flow inviscid case. However there is adescription of a case where a modification refer-ence is made to the geometry that accounts forany ’displacement’ of the flow.3 It is thoughtthat such a modification would solve the prob-lem of unsteadiness experienced although timeconstraints did not allow this to be verified.The more salient problem was that of turbulencemodelling and so attention focused on that.

6

7

8

9

10

11

12

13

14

0 10 20 30 40 50 60

p[1]

t(real)

’4_probe.0013’ u 1:2

Fig. 4 HMFR, inviscid. Pressure time his-tory from a probe on the centreline at the firstbend.

5American Institute of Aeronautics and Astronautics

Turbulent

Figure 5 shows pressure extraction from thestarboard side from all models examined. Onceagain the results are compared against experi-ment and previous computational solutions (us-ing the k − ω model). It is clear that there aremajor problems with the results for the SA andk − ω models from PMB. Flow acceleration intothe duct is over-predicted. This appears to leadto a complex shock reflection system in the cowlregion, more especially for the k−ω results. TheSA results recover somewhat prior to the firstbend.

X/D, V1, V19

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Frame 002 15 Oct 2001 No Dataset

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Fig. 5 HMFR, turbulent. Pressure extrac-tion’s from the starboard side of the intake.

All models predict significant secondary flow.The k−ω results give the closest match with ex-periment but this is primarily due to the pressurerecovery problems in the cowl. Consequentlyit is the SST results that are again the mostsatisfactory. Figures 6 and 7 show contours oftotal pressure and velocity vectors at the engineface, and total pressure at locations through theduct. The extent of the maldistribution of pres-sure across the engine face is evident.

Y

Z

X

Pt/PT

1.005270.9880610.9708570.9536530.9364490.9192450.9020410.8848370.8676330.8504290.8332240.816020.7988160.7816120.7644080.7472040.73

Fig. 6 HMFR, SST. Secondary flow at theengine face.

XY

Z

Pt/PT

0.9895730.9617770.933980.9061840.8783870.8505910.8227940.7949980.7672010.7394050.7116080.6838110.6560150.6282180.6004220.5726250.5448290.5170320.4892360.4614390.4336430.4058460.378050.3502530.322457

Fig. 7 HMFR, SST. Secondary flow at loca-tions through the intake.

Figure 8 shows the interior surface of the in-take with streamlines of shear stress. As the flowapproaches the first intake bend flow on the up-per port side is swept round the curvature of thebend by the mechanisms described in the intro-duction. As one moves round the surface of theintake from the port to the starboard sides, apoint is reached where the flow spirals to a sad-dle point.

Y

Z

X

Fig. 8 HMFR, SST. Surface shear stressshowing spiral node and saddle point.

The boundary layer profile through the star-board side following the flows acceleration intothe duct is shown in Fig. 9. The graph shows theu-velocity non-dimensionalised with freestreamvelocity plotted against distance from the wall.The k − ω and S − A models have very similarprofiles and vary from the profile obtained withthe S − A model. The S − A model shows amuch lower velocity as you move away from the

6American Institute of Aeronautics and Astronautics

wall surface. There is also a small pocket of sepa-ration that can be seen in the graph as a negativecomponent of u-velocity. Both the k−ω and S−Amodels do not predict this small separated regionin the cowl flow. It can also be seen that peakvelocities actually occur closer to the wall, notin the core as may be thought, due to the largeacceleration of the flow around the cowl and intothe duct.

U

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Fig. 9 HMFR, turbulent. Extraction of theu-velocity through the boundary layer.

In studying the literature on previous com-putational work on this problem, it is hard tofind clear information on the level of convergenceachieved in other calculations. As mentioned, allcalculations here are considered fully convergedwhen the log of the residuals reduces 8 orders ofmagnitude. However there is previous work thatstates that some computations are consideredfully converged when the residuals are reduced4 orders.1 For comparison, all turbulence clo-sure techniques were re-run and stopped whenthe residuals had dropped 4 orders.

Figure 10 shows the pressure history throughthe duct from the starboard side for this re-duced convergence case. Comparison with fullyconverged results in Fig. 5 shows some major dif-ferences. Initial flow acceleration into the duct isnow better predicted for all models. The sub-sequent pressure recovery is over-predicted foralthough the k−ω model is promising. Howeverthis model greatly over-predicts the starboard ac-celeration around the first bend. There follows astrong local shock which leads to a good agree-ment with the other models downstream of thefirst bend. The S−A and SST models predict agreater pressure recovery in the cowl region thanwas seen in experiment. However these modelsbetter predict the starboard side acceleration atthe first bend. Secondary flow is predicted withall the models but the characteristic dip or sad-dle in the pressures trace between the two bends

is not evident.

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Fig. 10 HMFR, turbulent. Pressure extrac-tion’s from the starboard side of the intake forsolutions converged 4 orders of magnitude.

ConclusionsEuler and Reynolds-averaged Navier-Stokes

equations (using various closure techniques) hasbeen applied to the problem of predicting flow inthe RAE intake model 2129, an offset diffusings-shaped aircraft intake. The aim was to clarifythe effects of different modelling techniques for astandard low and high mass flow case.

Euler calculations for the low mass flow casewere qualitatively good. However flow acceler-ation into the duct was over-predicted and sec-ondary flow was obviously not captured leadingto a poorer comparison of the pressure levelsthrough the duct. The high mass flow case wasfound to be unsteady with the origins of this com-ing from flow separation off the starboard sidefirst bend. The literature revealed that this casehad not been as widely studied and that previouswork had made modifications to the geometry toaccount for any displacement of the flow from thestarboard side first bend.

Turbulent calculations for the low mass flowcase were much more promising. Comparisonwith experiment and previous computation wasbetter. The prediction of secondary flow for thiscase is known to be challenging. It was foundthat all models predicted limited secondary flow,the SST model showing the strongest effects,although the pressure levels were around 6%higher.

The turbulent high mass flow case is complex.Secondary flow is better predicted for all mod-els with the SST model again performing thebest and comparing well with previous compu-tation and experiment. The main problem wasthe prediction of the flow in the cowl region. Thek − ω and SA models predicted complex shock

7American Institute of Aeronautics and Astronautics

reflection in this region that was no found in ex-perimental data. Previous computational workfor this case does not discuss convergence in anydetail although one reference mentions a drop inthe residuals of 4 orders being fully converged.As this work considers fully converged to be adrop of 8 orders, calculations were re-run stop-ping at 4 orders. It was found that the solutionsvaried remarkably. The problem of shock reflec-tion in the cowl is no longer present for the k−ωand SA simulations and the results show a muchcloser match for those models.

AcknowledgementsThis work is supported by a Scholarship from

the Defence Evaluation and Research Agency(DERA), Bedford.

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8American Institute of Aeronautics and Astronautics