Innokentiy KURSAKOV,Egor KAZHAN,Roy GEBBINK

aCentral Aerohydrodynamic Institute Named After Professor N.E.Zhukovsky(TsAGI),Zhukovskiy 140180,Russia

bGerman-Dutch Wind Tunnels(DNW),Marknesse 8316 PR,The Netherlands

KEYWORDS Aerodynamic validation model;CFD;Sting interference;Transonic test;Wing deformation

Abstract A modern transonic computational fluid dynamics test case is described in this paper,which is the Aerodynamic Validation Model(AVM)from the Chinese Aeronautical Establishment(CAE).The CAE-AVM is a representation of a modern transonic business jet aircraft with a design Mach number of 0.85.Numerical simulations for the AVM are conducted for two geometries:one baseline geometry,and one geometry that includes the applied model support system of the wind tunnel as well as the deformed wing shape that occurred during wind tunnel testing.The combined influence of wing deformation and model support interference on local and integral aerodynamic features is presented.Comparisons between CFD and experimental results are made;reasons of discrepancy between results from considered cases are analyzed.

1.Introduction

The importance of validation test cases for CFD codes can be hardly overestimated.They allow for checking whether a considered CFD code satisfies the high demands of aircraft manufacturers on the accuracy of numerical simulations as a part of the design process.In the past,special test cases have been created for various validation purposes.Validation databases where various test cases could be found are described in Refs.1,2A classical test case is a problem about the 2D flow around an airfoil at the angle of attack,for which extensive experimental datasets are available.The most well-known examples are the NACA airfoils,in particular the NACA0012.3To validate numerical methods for 3D flows around wings,experimental data from the ONERA-M6(symmetric foil)wing is often used,which can be found in Ref.4,including the mathematical description of this wing model.Besides isolated wing studies,numerical methods are ultimately used for investigations of more complex aircraft configurations.The DLR-F65,6and the NASA Common Research Model(CRM)7,8are two publically available fuselage-wing-p ylon-nacelle-(tails)configurations for which extensive validation work has been conducted,even up to the present day.9,10Results obtained with the CRM11,12showed that to improve the correlation of CFD with experimental data,items such as sting interference and aeroelastic effects should be taken into account.To broaden the range of available test cases for commercial jet aircraft and determine and discuss the effects of wing deformation and sting interference,the Chinese Aeronautical Establishment(CAE)organized a workshop together with the German Dutch Wind Tunnels(DNW).This 1st CAE-DNW Workshop on CFD-Wind Tunnel Correlation Study was held in March 2016.The object of study in this workshop was the so-called CAE Aerodynamic Validation Model(AVM),which was tested in one of the DNW transonic wind tunnels.

This paper describes numerical simulations conducted at TsAGI using the CAE-AVM test case,as proposed for the CAE-DNW Workshop.After a brief introduction of the CAE-AVM,the numerical simulation approach is addressed.CFD results will be shown in comparison to wind tunnel results,while commenting on wing deformation and sting interference effects.

2.Validation model

The CAE-AVM represents a geometry for a small commercial jet aircraft.The aircraft consists of a narrow fuselage,a low wing configuration with a wing-fuselage fairing,aft-fuselage mounted engines,and a T-tail.It comprises a transonic supercritical swept wing of a high aspect ratio and is designed for a cruise Mach number 0.85 with a corresponding design lift coefficient CL=0.5.A detailed description of the aerodynamic design and an overview of the CAE-AVM development can be found in Refs.13,14

A wind tunnel model was designed for measurements of the overall aerodynamic loads and wing pressure distributions.Together the left and right wings comprised a total of 180 pressure orifices,located in six spanwise wing stations(η=0.20,0.35,0.45,0.55,0.65,and 0.75).The wing was specifically designed to allow for a measurement of wing pressure distributions,whilst maintaining appropriate stiffness to keep wing deformation at modest levels.The wing shape was measured throughout the test,using an optical technique.The overall forces and moments were measured by means of a sixcomponent internal strain gauge balance.The design of the model was such that this balance could be mounted on either a ventral z-sting support or a dorsal sting support.The latter allowed the model to be used for dedicated support interference investigations using a dummy sting.

Two main model configurations were tested in the wind tunnel:the full-aircraft model and the wing-fuselage combination(i.e.,the full aircraft without the T-tail and engines).For the full-aircraft model configuration,the engines were represented by through flow nacelles,as shown in Fig.1(a).The model mechanical design and manufacturing were done by the Netherlands Aerospace Centre,the NLR.The wind tunnel test was conducted in the DNW High-Speed Tunnel(HST)in the Netherlands(Fig.1(b)).

After completion of the wind tunnel test,two variants of the aircraft geometry were created(Fig.2):

AVM Full aircraft configuration with a nominal design shape.

AVM-DZ Full aircraft configuration with a representation of the z-sting support and a deformed wing shape as acquired at the test status:Ma=0.85,Re=4.7 million,and CL=0.515,where Re is the Reynolds number based on the model mean aerodynamic chord.

Fig.1 AVM model.

3.Numerical simulation approach

3.1.Flow solver

The flow solver used in the present work is the EWT-TsAGI code that has been in use at TsAGI since 1996.The method has been well described in Refs.15,16It permits to solve stationary Reynolds-Averaging Navier-Stokes(RANS)equations and Non-stationary RANS(URANS)equations.Results presented in the present paper are all based on RANS.An implicit smoother method was developed to accelerate the Godunovtype TVD scheme for approximation of convective fluxes(MUSCL).17,18The method used is based on the delayed correction procedure19and applies the Gauss–Seidel block method with cell renumbering to solve a system of linear equations.For approximation of Shear Stress Transport(SST)turbulence model20source terms,a method based on the analysis of eigenvalues of the Jacobi matrix was used.The local choice of an explicit or implicit scheme and the manner of time step implementation(global or local),depending on the relationship between the specified global time step and the local stability condition of the explicit scheme,are the main specific features of the numerical method.

3.2.Test cases

As part of the CAE-DNW Workshop,four test cases were defined,based on the two geometric variants,AVM and AVM-DZ.The four cases are listed in Table 1.All calculations,as well as experiments,were performed at Ma=0.85 and Re=4.7 million.For Cases 2 and 4,experimental data is available for comparison.

3.3.Computational grids

For each of the two geometric variants,multi-block structured computational grids were made available by the organizers of the CAE-DNW Workshop.The characteristics of these socalled standard meshes are presented in Table 2.The boundary layer mesh contains 45 levels.The average y+of the grids is approximately 1.0.

To improve and accelerate the convergence process of numerical simulations,the authors of the current work modified the workshop-supplied standard mesh of the AVM.The modified mesh is referred to as AVM_mod.This adapted calculation grid has become more uniform,degeneration of some cells has been corrected,and the topology of the fuselage-wing joint has been changed from H-to O-type.In the end,the resulting mesh characteristics are marginally different from those of the standard AVM mesh.In case of the AVM-DZ,the workshop-supplied standard mesh was used for the simulations.

4.Results

4.1.Grid convergence

Fig.3 Convergence improvement due to modification of the AVM baseline grid.

Table 1 Overview of test cases.

Table 2 Overview of computational grids.

The convergence improvement due to modification of the basic computational grid is illustrated in Fig.3,where the logarithm of the L2-norm of the density residual L2(Δρ)through iterations is depicted.The grid modification was found to improve the iteration convergence.Block dimensions of the grids allowed using a series of nested grids to perform a grid convergence check according to Ref.21Three grids were under consideration;for simplicity,they are here referred to as:(A)medium,(B) fine,and(C)x- fine.The fine grid was the Workshop standard grid.Parameters of the fine grid are listed in Table 2.The medium grid was produced from the fine one by removing every second node in each index direction.To produce the x- fine grid,the number of cells in each index direction was doubled.As a result,the x- fine grid consisted of 317579264 cells.A grid convergence check was performed for the AVM-DZ configuration at a fixed lift coefficient CL=0.515.Drag(pressure and friction components separately)and pitching moment coefficient curves for the nested grids are shown in Fig.4.On the x-axis,the grid spacing Ncellsis shown.The results do not show good grid convergence.In case of applying the method of second order of accuracy,the curves should look like straight lines.The orders of convergence evaluated according to Ref.21are 2.71 for the pressure drag coefficient,1.47 for the friction drag coefficient,and 2.17 for the pitching moment coefficient.These values are consistent with the 2nd order of the numerical scheme used.On the other hand,if comparing the total 4 drag counts difference for the full aircraft with the support system between the fine and x- fine grids,the later has a mesh size of one more order,but the fine mesh is already good enough for engineering application of aircraft design.

4.2.Cases 1 and 2: fixed lift study

Comparisons of the grid effect as well as z-sting and deformations effects at the fixed lift cases are presented in Table 3.The differences between the calculated results for the same geometry at the baseline and modified calculation grids are ΔCD=0.0001(for the drag coefficient)and ΔCm=0.002(for the pitching moment coefficient).These values could be treated as the estimation of the errors caused by the grid modification.It is supposed that the combined effect of the sting interference and wing deformation will be kept in calculations if they generate a difference of higher magnitude in aerodynamic coefficients.The discrepancies of aerodynamic performances for different configurations are ΔCD=0.0005 and ΔCm=0.004.In terms of the drag coefficient,experimental and computational results seem very close to each other.The CFD-WT(wind tunnel)discrepancy at the cruise lift is within 3 drag counts.At the same time,the difference between CFD and WT values of the pitching moment coefficient looks significant.The maximal discrepancy is observed for the AVM-DZ configuration which is supposed to be compared with uncorrected experimental results.The reasons that the comparison between AVM-DZ and experiments in the pitching moment is not as good as those of the lift and drag could be:

Table 3 Integral characteristics for Cases 1 and 2 and for calculations on modified grid.

(1)The aeroelastic deformation of the horizontal tail is not measured and taken into account in CFD simulation,even though deformation could be very small under the cruise condition.

(2)The local Mach number reduction in the tail region due to sting and boom support which will be discussed in Section 4.4.

(3)The force in the cavity of the connection area of the zsting to the rear fuselage is not simulated in CFD.Further investigations in more detail would be of interest.

A comparison of the wing pressure coefficient Cpdistributions between the two CFD cases is shown in Fig.5,along with experimental data.Pressure distributions are only compared till 75%spanwise length because there are no pressure orifices at further wing sections.This is due to design restrictions of the wind-tunnel model.It should be noticed that z-sting surfaces are excluded from integration when integral characteristics are determined.Numerical and experimental data are obtained at the same lift coefficient CL=0.515.Because of the wing deformation and interference of the z-sting,the given lift coefficient value is reached at a higher angle of attack with the AVM-DZ simulation compared to the AVM simulation result.According to the figure,the numerical result for AVM-DZ is considerably closer to the experimental data than the AVM simulation result.The same observation could be done according to the data in Table 3.This confirms the statement that taking into account the combined effects due to the sting support interference and wing deformation improves the agreement with experimental results.The AVM-DZ simulation result follows the experimental data points in every wing section with the exception of η=0.65.At this wing section,the computed leading edge suction zone is notably higher than the experimental values.The same observation was found in Ref.14,where the experimental data was compared with simulation results from a different flow solver.It is suspected that this is caused by a local imperfection of the wind tunnel model’s leading edge contour(near η =0.65),and as for all other stations,the CFD-WT correspondence is better in terms of suction zones.

Fig.4 Dependence of the model aerodynamic performance upon the calculation grid dimension capability.

Fig.5 Combined influence of wing deformation and sting interference on pressure coefficient distribution along wingspan(Results at a fixed lift coefficient CL=0.515).

4.3.Cases 3 and 4:Polar study

The coefficients of the aerodynamic loads as computed in Cases 3 and 4 are plotted for different angles of attack α in Fig.6,along with the experimental results.The experimental results are uncorrected data(i.e.,no correction for the interference of the sting support is applied).The CFD case with a deformed wing and sting yields a lower lift coefficient and drag coefficient at the same angle of attack,as compared to those from the AVM simulation.The difference between these two configurations increases with an increase of the incidence angle.The dependency of the lift coefficient on the angle of attack deviates from being linear for α-values higher than 4°(i.e.,when buffeting occurs).Within the linear part,the AVM-DZ configuration results are closer to the experimental data points than the AVM simulation results.Outside of the linear part,the correlation with the experiment results becomes rather poor,in particular in terms of the pitching moment coefficient.In these regimes,CFD methods in the stationary formulation appear to be unreliable.

The combined influence of wing deformation and the sting is also visible in the six sectional pressure distributions along the wingspan.Fig.7 presents the two CFD simulations at an identical angle of attack, α =2.45°.The wing deformation,primarily twist,results in the diminishing of the local angle of attack.This leads to a weaker rarefaction at the leading edge of the AVM-DZ configuration,compared to that of the AVM.The magnitude of the nose-down twist grows towards the wing tip(see Fig.8),and the difference in the leading edge rarefaction shows the same tendency.The baseline AVM configuration,in comparison,shows a shock that is considerably stronger and located in a more downstream position.Besides the twist effect that causes a more upstream shock position,one may also expect that the effective Mach number is locally lower as the flow becomes partially stagnated due to the blockage of the z-sting support.

4.4.Relative attributions

The comparison between the AVM and AVM-DZ simulations has thus far allowed for inspection of the combined effect due to wing deformation and support interference effects.In an attempt to discriminate between individual attributions,the airfoil silhouettes from the AVM and AVM-DZ geometries are compared in Fig.8(a),which shows silhouettes that correspond to the six wing sections considered before.The twist angle differences are in a range from-0.13°to-0.75°,for the most inboard and outboard sections respectively.Based on this visualization,one may expect the deformed wing to generate a lower overall lift and hence a lower lift-induced drag.Due to the lift losses on the outboard sections of the backsweptwing,theoverallnose-up pitching moment increases.

Fig.6 Dependence of the model aerodynamic performance upon the angle of attack.

Fig.7 Combined influence of wing deformation and sting interference on pressure coefficient distribution along wingspan(Results at a fixed incidence angle α =2.45°).

Fig.8 Two effects on the local angle of attack of the wing.

To estimate the support interference effect,two additional calculations are conducted with the isolated model support system.The simulations are based on meshes that include solely the main boom support,either with or without the vertical z-blade(i.e.,the sting),but not the actual aircraft.Computed results show that the support causes an increase of the local angle of attack in the virtual position of the wing.The support-induced upwash along the virtual wing quarter chord line is in a range from 0.02°to 0.045°as is visualized in Fig.8(b).Numerical simulation results further show a progressive decrease of the Mach number towards the sting support(Fig.9).Computed disturbances generated by the configuration boom support only are weaker as compared to those by the boom support with z-blade variant.A similar supportinduced Mach number gradient is established via measurements along the test section’s centreline,as is visualized in Fig.9 too.Both the calculation and experiment for boom support only follow the same trend and are in agreement that the Mach number decrease at the model reference point is about ΔMa=-0.004.Besides this local Mach number reduction due to the main boom support,further interferences on the aft-fuselage and pylon-nacelles can be expected due to the additionalgradientimposed by thez-blade.Itshould be noticed that the procedure of sting effect estimation without taking into account the wind tunnel walls is not fully correct,but this task is of minor complexity and supply,but gives very useful results even in limited formulation.The work in Ref.22is a good example of such kind of investigation.

Fig.9 Centreline effect of isolated model support.

These two basic assessments illustrate the fact that wing deformation has an opposite effect on the local angle of attack near the wing,compared to the upwash generated by the sting support.The sting-generated upwash is one order of magnitude lower than the local incidence changes caused by the deformation of the wing.In terms of support interference,the support-induced flow deceleration and the corresponding Mach number gradient are deemed substantial.

5.Conclusions

(1)The first application of the EWT-TsAGI software for simulations of AVM and AVM-DZ configurations showed that the combined effect of wing deformation and model support interference could be determined by means of CFD.

(2)The inclusion of the deformed wing shape and the model support geometry in CFD yields simulation results which are in significantly better agreement with experimental data for wing pressure distributions,compared to CFD simulation results for the baseline free- flying AVM.Similarly,obtained overall loads coefficients are found to be in agreement with test data,though only in the linear region below buffeting.

(3)Wing deformation and model support interference impose local incidence angle changes that are of an opposite sign.For a better understanding of the individual effects,the sources should be separated.

(4)A comparison between the computational assessment and the experimental measurements of the supportinduced flow deceleration was performed for the first time.According to this comparison,the corresponding Mach number gradient is deemed substantial and could be estimated as ΔMa=-0.004 at a reference point.

Acknowledgement

This study was financially supported by the Grant Agreement(No.4.628.21.0004)with the Ministry of Education and Science of the Russian Federation(project unique identifier RFMEFI62815X0004)onthetheme ‘‘Developmentand implementation of the optimization of the aircraft power plant aerodynamics as a part of a 3rd generation multidisciplinary optimization and its application to optimization of promising new types of aircraft”.