[American Institute of Aeronautics and Astronautics 18th Applied Aerodynamics Conference -...

(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

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AIAA 2000-4223Predicting Air Loads With SteadyAeroelastic Effects On The Wing Of ABusiness Jet ConfigurationElias BounajemCessna Aircraft Co.Wichita, KS

18th AIAA Applied AerodynamicsConference

14-17 August 2000 / Denver, COFor permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,

1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.


AIAA-2000-4223

Predicting Air Loads With Steady Aeroelastic Effects OnThe Wing Of A Business Jet Configuration

Elias Bounajem *Cessna Aircraft Co.Wichita, KS67215

Abstract

A loosely-coupled fluid-structure interactionapproach, primarily geared toward thepreliminary design phase, is being used forthe estimation of steady aeroelastic effect onwing air loads of a business jet configuration.This iterative approach combines wingstructural model stiffness characteristics andComputational Fluid Dynamics (CFD)predicted air loads to estimate the CFD griddeformation. The CFD solution is carriedthrough on the deformed grid and theprocess is repeated until convergence. Thestructural model consists of a set of beamelements representing the wing and the CFDmodel is a wing-body-pylon-nacelleconfiguration. The Euler solver capability ofthe unstructured, cell based code USM3Dwith Integral Boundary Layer (IBL) is used inthis analysis. The present approach isvalidated by comparing predicted surfacepressure on the wing to those measured inflight and in the wind tunnel at differentMACH numbers and angle of attacks

Introduction

As aircraft manufacturers strive to reduceproduct development time, a thoroughunderstanding of the interaction between thevarious disciplines in the early stages of thedesign process is of great value. Potentialproblems can be addressed before the first

* Member, AIAACopyright © 2000 by the American Institute of Aeronautics andAstronautics, Inc. All rights reserved.

prototype is built. Interaction between thesurrounding air and the aircraft structure,steady as well as unsteady, has obviouslydirect impact on requirements for an optimalweight and flutter speeds etc.. Therefore,there is a need to establish a process toquantify this interaction in a timely manner soas to impact the design in the early stages.Steady state aeroelastic effects will beaddressed in the present work.

Aeroelastic analysis can be carried out byeither a closely or a loosely coupledapproach of Computational Fluid Dynamics(CFD) and Computational StructuralDynamics disciplines. In a closely coupledapproach [1,2], aerodynamics and structureequations are rewritten into one set ofequations which then can be solved toprovide a simultaneous update of the CFDand CSD variables. Here the advantageresides in the fact that only one analysis isneeded. However, this often requiresmassive changes to the CFD and CSDcodes. Also, numerical instabilities are oftenencountered because of the differentcharacteristics of the governing equations. Ina loosely coupled approach [3,4], thecomputed aerodynamic loads are transferredto the structural model to computedisplacements. These displacements arethen applied to the CFD grid. A new set ofaerodynamic loads are computed and theprocess is repeated until convergence.Although this approach is less rigorous thanthe previous one, it provides the flexibility ofusing different CFD or CSD codes if a

1American Institute of Aeronautics and Astronautics


AIAA-2000-4223

modular approach is adopted. This approachwill be used here.

The degree of complexity of the CFDanalysis can vary from a simple method tothe fully viscous formulation. Likewise, thestructural analysis can either be a FiniteElement Model (FEM) solution, a modalanalysis or a beam representation. Thechoice of the level of sophistication dependson the stage of the design. Early in thedesign process, the wing is fairly welldefined from an aerodynamic standpoint,while structural characteristics are assumedfrom a similar aircraft model. Therefore, adetailed structural representation of a wing(FEM or Modal approach) that is yet to bedesigned may not be necessary noraccurate. As for the source of aerodynamicloads, this depends on the desired accuracyand the time requirements because the winggeometry is already available.

A modular implementation of USM3D withinteractive boundary layers, CDISC andaeroelastic interaction has been madeavailable by Frink et. al [5] at the NASALangley Research Center. This setup iscoupled with the structural code ELAPS tocompute deformations. The modularimplementation allows for an alternativeapproach to integrate aerodynamic loads anddifferent structural modeling approach tocompute structural deformations. Thisprocess will be used here with theappropriate modifications to accommodatethe structural analysis.

In the present investigation, a looselycoupled approach will be used to assess theaeroelastic effects on a swept wing of abusiness jet. The CFD model is a tail-offmodel with a powered nacelle configuration.The unstructured CFD code USM3D will beused to generate the aerodynamic loads. Thewing will be assumed cantilevered at the sideof body and will be represented by a series ofbeam elements along the elastic axis. Therest of the model is considered rigid.Aerodynamic and inertia loads are applied atthe beam endpoints. The computeddisplacements are then applied to the CFDgrid. Since the deformations are small, thestiffness properties of the wing are assumed

to be unchanged because of deformation.Therefore, for the next cycle, theaerodynamic loads are applied to the originalstructural model and the deformations areapplied to the original CFD grid.

CFD Approach

CFD Solver:USM3D, is a cell centered, finite-volume,upwind flow solver for solving the Euler andNavier-Stokes equations on tetrahedral grids[6]. Inviscid flux quantities are computedacross each cell face using the Roe [7] fluxdifference splitting approach. The implicittime integration scheme [8] uses thelinearized backward Euler time differencingapproach to update the solution at each timestep. Since the inviscid solver capability isused in this analysis, viscous effects areaccounted for through an Integral BoundaryLayer (IBL) method applied to the wing. Thisapproach takes flow information at severalwing stations from a partially convergedsolution. This data is used to calculatetranspiration velocities at these stations tosimulate boundary layer thickness effect.When the solution is restarted, thisinformation is read into the flow solver andthe boundary conditions are then modifiedon the wing to take into account theadditional normal velocity component. TheIBL step is repeated after a number ofinviscid iterations. This entire process isrepeated until convergence.

Grid Generation:The grid (Figure 1) is generated usingGridTools and Vgrid, both are components ofthe NASA Tetrahedral Unstructured SoftwareSystem (TetrUSS) [9]. The CAD geometry isimported into GridTools in the form of anIGES file format where the model surface isrepresented by 4 and 3-sided patches. Cellsize and density are controlled through pointand line sources which are located nearareas where grid control is desired. Surfacemesh generation is accomplished in Vgrid.After the surface mesh has been projected tothe CAD surface, the volume grid is thengenerated using the Advancing FrontMethod. After a post-processing step, wherethe grid quality is checked and local

American Institute of Aeronautics and Astronautics


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remeshing is done where needed, the flowsolution can be started.

One of the attractive features of this softwaresystem is the capability of allowing cellstretching to reduce the overall grid sizewhile allowing a better resolution of thesurface in highly curved areas.

Structural Approach:

A beam model is used to represent thestructural characteristics of the wing. Thismodel consists of a set of n beam elementsalong the wing elastic axis, which areconnected end to end from wing root to wingtip (Figure 2). The end of each element isallowed to have six degrees of freedom: threetranslations and three rotations, except forthe node at butt line zero. This node isconstrained to avoid having a singular matrix.Once stiffness characteristics have beenassigned to the individual elements, astiffness coefficient matrix [K] for the entirewing can be assembled. This is an m by msymmetric matrix, where m is equal to 6 x n.The stiffness matrix K relates theaerodynamic and inertia forces [F] applied tothe structure to the resulting displacement [X]in the following manner:

(1)

Let us define the matrix [A] as the inverse of[K] or [A]=[K]"\ Equation (1) can be rewrittenas

[X] = [A] [F] (2)

[A] is also known as the influence coefficientmatrix of the structure.

Equation (2) implies that if the influencecoefficient matrix and the applied forces tothe structure are known, then thedisplacements of the structure can be easilycomputed.

The stiffness data has been validated bymatching the beam model frequencies andmode shapes to those observed in GroundVibration Test (GVT). Therefore it representsthe wing structural characteristics.

Fluid-Structure Coupling Procedure

As indicated previously, a CFD code(USM30) is being loosely coupled with awing structural model to predict theaerodynamic load on the wing in thepresence of aeroelastic effect. The followinghighlights the mechanics of the couplingprocess.

1. Generate an intermediate inviscidUSM3D (about 100 iterations).

2. Integrate wing pressures to getaerodynamic forces and moments.

3. Apply loads to structural model andcompute displacements.

4. Displace surface and volume grid usingspring analogy method

5. Run Integral Boundary Layer module toget normal velocities.

6. Run USM3D for 20 iterations.7. Repeat steps 2 through 6 until

convergence criteria are met.

At what point in the process the couplingshould start is subject to engineeringjudgement. The minimum requirement is apartially converged CFD solution beforestarting to generate wing deformation. Apreliminary analysis showed that whether thecoupling is started after 100 iterations ofinviscid CFD solution or if the solution iscarried out another 100 iterations withviscous effect, the resulting lift coefficientswere identical. In fact, invoking the IBL optionwith the deformation tend to dampen theoscillations in the solution (Figure 3).

The aerodynamic loads are computed bysubdividing the wing, spanwise, intoaerodynamic bays. The bay boundaries aremidway between the structural beams endpoints. The pressures on each bay areintegrated into forces and moments and areapplied at the node inside the bay.

Inertia loads are computed in a similarfashion. The wing structure, including fuel, isbroken up into structural bays (Figure 2). Theresulting weights are lumped at the nodes. Allthe cases examined in this study were cruisepoints at a load factor equal to one. For otherconditions, the load factor should be taken


(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

AIAA-2000-4223

into account and the inertia loads updatedaccordingly.

Once aerodynamic and inertia loads havebeen found, then using equation (2) one cancompute the three displacements and threerotations at each bean end point along theelastic axis. These are presented as afunction of y in the spanwise direction andvarying linearly between beam end points. Ofparticular interest are the verticaldisplacement and twist at these points. Onlythese two components will be used inupdating the vertical displacement of thewing surface grid points. The displacement ofa point on the wing surface at a fuselagestation x and buttline y is made up of twocomponents: one is due to verticaldisplacement of the elastic axis, the other isdue to the twist component. Therefore, DZ(y)is computed as follows:

ee.*(x-xe.)

whereDZ(y)ea and 0 „ are the vertical

displacement and the angle of twist of theelastic axis at buttline y, and

x.. is the fuselage station of theaeroelastic axis at buttline y.

Once the wing surface mesh has beendeformed, the points in the volume grid areredistributed using "spring analogy" approach[5]. In this method, the edge of a tetrahedronis modeled as a spring whose stiffness isinversely proportional to the distancebetween the two nodes. As the farfield nodesare held fixed, the equations of motion areused to compute the node displacementsusing a predictor corrector method. Asindicated above, one of the TetrUSS softwaresystem features that was used to reduce gridsize was anisotopic stretching. However,deforming the grid resulted in some highlyskewed cells or cells with negative volumedespite using an under-relaxation factor tointroduce deformation gradually. The solutionwas to reduce the amount of stretching andslightly coarsen up the cells on the wing,especially near the leading edge.

At this point, the process continues byrestarting the CFD solution with the updatedgrid since grid connectivity did not change.After 20 USM3D iterations, steps 2 through 6were repeated until convergence. This canbe evaluated both on the CFD side and thestructural model side. The CFD solutionconvergence is monitored through reductionin the residuals and the how the lift coefficientstabilized (Figure 4). On the structural modelside, the convergence is evaluated throughexamination of the behavior of verticaldisplacement and twist at three points alongthe wing: 50%, 75% span and at the wing tip(Figures 5). Typically these were 0.01" invertical displacement and 0.01 (deg) in twist.

Processing Requirements

The grid for this configuration has a total of540,000 cells. Solutions were generated onan SGI origin 200 with four processors and3.3 GB of memory. Each case required 350MB of memory and 13 hours to converge ona single processor. All cases were run at CFLnumber of 100.

Results and Method Validation

A total of three cases are presented in thisstudy. These cases correspond to cruiseangle of attack at MACH numbers rangingfrom 0.5 to 0.82 between 30,000 and 40,000feet altitude. Surface pressure coefficientsare presented on the wing at two stations,one close to mid-span, the other is closer tothe wingtip.

Two sets of experimental data are used tovalidate the computational results. One setcomes from flight test data at MACH numbers0.5-0.6 and cruise angle of attack. TheMACH 0.82 validation data comes from ahigh speed wind tunnel test. The wind tunnelmodel is rigid and is built with a twistdistributions that the airplane's wing willdeform to at MACH number 0.82 and cruiseangle of attack. It is necessary to keep inmind that flight test data may be affected bynon-zero deflection of control surfaces andeffect of turning rates even for well trimmedconditions.



AIAA-2000-4223

Figure 6 shows a comparison of wing surfacepressure distribution at the three buttlinelocations. The match is good overall. Atbuttline one, the pressure port at 10% is atthe trailing edge of the slat element. This maybe the cause for the increased suction peakat this location. At buttline two, no flight testdata is available beyond 70% chord becauseof the presence of the aileron, which was notinstrumented. In the MACH 0.6 case (Figure7), the same discrepancy is evident atbuttline one as in the previous case, althoughit is a little more pronounced. At buttline twoand three, and because of the wing twist, thelower surface is carrying more negativepressure near the leading edge, therefore off-loading the wing. The CFD captures thispattern reasonably well.

Figure 8 shows the pressure comparison towind tunnel data at MACH 0.82. At thebuttline locations, the pressure is wellpredicted. The pattern in the wind tunnel dataon the lower surface at buttline two andbeyond 60% percent chord is present at otherMACH and is considered a data anomaly.

To evaluate the wing sensitivity to istructuralcharacteristics, several solutions weregenerated with stiffness constants increasedor decreased by as much as 20%. The tablebelow shows that a ±10% change in bendingcharacteristics would result in about 1%change in wing normal coefficient androughly the same variation can be expectedwith 20% change in wing torsional stiffness.This indicates that an approximate structuralmodel can be used to carry this type ofanalysis early in the early stages of thedesign.

Wing CZ Sensitivity to Changes in El and GJ

BendingTorsion

-20%N/A

-1.05

-10%-1.22N/A

+10%1.13N/A

-20%2.180.81

Conclusions and recommendations

A loosely coupled approach for theestimation of steady aeroelastic effect onwing air loads of a business jet configurationhas been established. The approach allowsusing different sources for the CFD data

without major changes to the interface. Theresults match fairly well with the experimentaldata.For cases at MACH number above 0.9, it isrecommended that a Navier-Stokes code beused to provide the aerodynamic data. Thatis due to the increased interaction betweenthe shock wave and the boundary layer.

References

1- Guruswamy, G. P., "Coupled Finite-Difference/Finite-Element Approach forWing-Body Aeroelasticity," AIAA Paper92-4680, Sept. 1992.

2- Bauchau, O. O. And Ahmad, J. U.,"Advanced CFD and CSD Methods forMultidisciplinary Applications inRotorcraft Problems," AIAA Paper 96-4151, July 1996.

3- Guruswamy, G. P., Reichnbach, E.,Bhardwaj, M. K. And Kapania, R. K.,"Computational Fluid Dynamics/Computational Structural DynamicsMethodlogy for Aircraft Wings," AIAAJournal, Vol. 36, No. 12, Dec. 1998.

4- Chen, H. H., Chang, K. C., Tsong, T. AndCebeci, T. "Aeroelastic Analysis of Wingand Wing/Fuselage Configurations,"AIAA Paper 98-0907, 1997.

5- Frink, NT., Pirzadeh, S., and Parikh,P.,"An Unstructured-Grid SoftwareSystem for Solving ComplexAerodynamic Problems." NASA CP-3291, pp 289-308, May 9-11, 1995.

6- Frink, N.T. "Recent Progress Toward aThree Dimensional Unstructured Navier-Stokes Flow Solver." AIAA Paper 94-0061, January, 1994.

7- Roe, P.L. "Characteristic BasedSchemes for the Euler Equations."Annual Review of Fluid Mechanics, Vol.18, pp 337-365, 1986.

8- Anderson, W.K. "Grid Generation andFlow Solution Method for the EulerEquations on Unstructured Grids." NASATM 4295, April 1992.

9- Batina, J.T. "Unsteady Euler Algorithmwith Unstructured Dynamic Mesh forComplex-Aircraft Aerodynamic Analysis."AIAA Journal, vol. 29, pp 329-333,March, 1991.



AIAA-2000-4223

Figure 1: Business Jet Tail Off CFD Surface Grid

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350

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AIAA-2000-4223

o

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Figure 3: Solution History for different approaches to implementing WingDeformation

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Figure 4: CFD Convergence - Solution History for MACH=0.5 case



AIAA-2000-4223

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AIAA-2000-4223

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AIAA-2000-4223

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AIAA-2000-4223

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