Constrained Aerodynamic Optimization of Three-Dimensional Wings Driven by Navier-Stokes Computations

Chapter 4 - Massive Parallelization as Prinicipal Technology for Constrained Optimization of Aerodynamic Shapes

Robust optimization of 2D airfoils driven by full Navier–Stokes computations

The proper orthogonal decomposition method has been shown to produce accurate reduced-order models for the aeroelastic analysis of complete aircraft configurations at fixed flight conditions. However, changes in the Mach number or angle of attack often necessitate the reconstruction of the reduced-order model to maintain accuracy, which destroys the sought-after computational efficiency. Straightforward approaches for reduced-order model adaptation-such as the global proper orthogonal decomposition method and the direct interpolation of the proper orthogonal decomposition basis vectors-that have been attempted in the past have been shown to lead to inaccurate proper orthogonal decomposition bases in the transonic flight regime. Alternatively, a new reduced-order model adaptation scheme is described in this paper and evaluated for changes in the freestream Mach number and angle of attack. This scheme interpolates the subspace angles between two proper orthogonal decomposition subspaces, then generates a new proper orthogonal decomposition basis through an orthogonal transformation based on the interpolated subspace angles. The resulting computational methodology is applied to a complete F-16 configuration in various airstreams. The predicted aeroelastic frequencies and damping coefficients are compared with counterparts obtained from full-order nonlinear aeroelastic simulations and flight test data. Good correlations are observed, including in the transonic regime. The obtained computational results reveal a significant potential of the adapted reduced-order model computational technology for accurate, near-real-time, aeroelastic predictions.

Euler's equations, the shock wave relations, and the surface boundary condition are used to derive a hypersonic slender body theory applicable to angles of attack from zero to 90 degrees. The theory is not based on small disturbances, but it gives Van Dyke's theory for small angles of attack, Sychev's similarity for moderate angles of attack, and strip theory for large angles of attack. The new similarity parameters are Meo~, 0 cos a/~, and y (where ~=o cos a + sin a). They are shown to be a combination of Sychev's parameters and can be used to modify equations for pressure and force coefficients at small angles of attack for moderate and large angle of attack applications. B(X,y,Z) CA CA CD CD CN CN Cp Cp d D Db A n p,p S(x,y,Z) T Nomenclature scaled function for body geometry axial force coefficient, based on ref. area ::: 2Ld scaled axial force coefficient given by eq. (50) drag coefficient, based on ref. area ::: 2Ld scaled drag coefficient given by eq. (51) normal force coefficient based on ref. area ::: 2Ld scaled normal force coefficient given by eq. (19) pressure coefficient, eq. (47) ... scaled pressure coefficient given by eq. (47) base height of lower surface, see Fig. 1 parameter defined by eq. (2) parameter defmed by eq. (44) unit vectors in x, y, z directions, respectively similarity parameter, 0 cos a~ similarity parameter, Moo~ body length freestream Mach number unit vector normal (inner) to surface static pressure and scaled static pressure, eq. (25) scaled function for shock surface temperature * Professor of Mechanical and Aerospace Engineering, Associate Fellow AlAA. Copyright© 1992 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 542 u,v,w u,v,w ~ Veo,VOQ x,y,z x,y,z a ~ y o ~ Cartesian velocity components in x,y,z directions, respectively scaled (nondimensional) velocity components freestream velocity vector and magnitude Cartesian coordinates, see Fig. 1 x/L, y/d, z/d, respectively angle of attack shockwave angle ratio of specific heats, 1.4 for air lower surface thickness ratio, d/L, see Fig. 1 --'> lower surface thickness ratio relative to V 00' see Fig. 1 and eq. (15) p,p density and scaled density, eq. (22) circumferential angle, =0 in windward plane SUbscripts c Cone b body s shock wave 00 freestream value Introduction Analysis of inviscid, hypersonic flow past slender bodies has been developed by Van Dyke l for small angles of attack and by Sychev2 for large angles of attack. The small angle of attack analysis is based on small disturbance theory and the similarity parameters are Moo 0, a/o, and y. At large angles of attack the Sychev similarity parameters are Moo sin a, 0 cot a, and y. Hemsch3 showed that the large angle of attack similarity parameters can be combined to yield the small angle of attack parameters when a is small, i.e. (MOQ sin a) (0 cot a) --'> Moo 0 and 0 cot a --'> o/a. Cox and Crabtree4 and Hayes and Probstein5 discuss hypersonic small disturbance theory and Sychev similarity. BarnweU6 showed that Sychev's analysis is applicable to all slender-body flows with crossflow Mach numbers greater than sonic and hence is not restricted to hypersonic values of the cross flow Mach number. In addition, he showed that Sychev similarity applied to a number of slender-body flows with subsonic crossflow Mach numbers, including incompressible flow. Hemsch3 demonstrated empirically that Sychev similarity holds for any value of the cross-flow Mach number if the axial flow component is 4

A multi-objective aerodynamic optimization of supercritical wing of a wide-body aircraft based on genetic algorithm and CST parameterization method is presented in this paper. Favorable pressure distributions of a “supercritical type” wing are considered as a lot of constraints in the optimization process. Geometry constraints and aerodynamic constraints are also employed. A full potential solver is adopted as a low fidelity aerodynamic analysis tool for preliminary optimization. A Reynolds Averaged NavierStokes solver is used as high fidelity tool for detailed optimization, and design validation. With more than 150 constraints, the optimized design has a typical supercritical pressure distribution. The CFD results also show that the design has a superior aerodynamic performance.

This paper presents the effect of wing elasticity on the efficiency of a nonintrusive reduced order model using a three-dimensional sweptback wing. For this purpose, a computationally low-cost but highly accurate nonintrusive reduced order method is constructed utilizing proper orthogonal decomposition (POD) coupled with radial basis function (RBF) interpolation. The results are evaluated in terms of order reduction and prediction capability of rigid and aeroelastic ROMs. Our results show that compared to the rigid wing, reduced order modeling is more effectively applied to the aeroelastic sweptback wing due to the postponement of flow separation caused by bending–torsion coupling, when the pressure coefficient (Cp) is considered as the output. We further show that for flexible wings, utilizing rigid nodes is not sufficient for presenting the Cp distribution accurately; hence, separate ROMs must be generated for the deformed positions of the nodes. Moreover, the RBF method is also exploited for prediction of the results with direct interpolation of the data ensemble by generating a surrogate model. Finally, the proposed methods are compared in terms of accuracy, computational cost and practicality.

In this study, we computed the lift force of the aircraft with ONERA OA206 airfoil type. It was positioned at 0%, 25%, 50%, 75%, and 100% of the wingspan for Angle of Attack (AoA) variations of 0o, 4o, 8o, 12o, and 16o. The research was to determine the effect of AoA on pressure, pressure coefficient (Cp), and lift coefficient (CL) on the ONERA OA206 aircraft wing. It shows that the greater AoA on the result of the pressure contour causes the increase in the difference of span at AoA 0o to 16o t these are 0.25%; 0.26%; 0.43%; 0.52%; and 0.53%. Through the graph of the pressure coefficient (Cp) against x/c, it can be seen that the greater AoA, the expansion point, and the stagnation point will shift to the right with the direction of x/c. In addition, the Cp at the lower is greater than the upper of the airfoil. Based on the research results, it was found that CL at the position of 0% to 50% increased when given AoA from 0o to 12o (CL max) and decreased at AoA = 16o (stall). Meanwhile, CL at 75% to 100% increased when given AoA from 0o to 8o (CL max) and decreased at AoA = 12o (stall). With these results, it can be concluded that the maximum AoA that can be applied to the wing of the ONERA OA206 aircraft is 8o. The closer to the end position of the airfoil, the higher the CL measured.

Navier-Stokes computations of heat transfer at high speeds have been a source of considerable dificulty. , Problems arise not only due to the particular iiuinerical scheme employed but also due to the resolution of the computational mesh. A comparative study of some of the important numerical schemes is presented herein, with regards to their ability to accurately predict the heating loads along the surface of the body. The grid dependency effects of these schemes are investigated. A parametric study is carried out and it is shown that the grid resolution for the accurate prediction of wall flux quantities is dependent on the free stream Mach and Reynolds numbers. Expressions are developed, for the generic class of blunt configurations studied herein, for predicting the grid requirements based on the free stream Mach and Reynolds numbers. * Graduate Research Assistant, Department of Acrospace Engineering, Member AlAA + Associate Professor, Department, of Aerospicr Enginecring, Associate Fellow AIAA t Research Associate, lnstitute for Advanced Technology. Member AIAA 1 Member Technical Staff, Senior Member AIAA Copyright

The accuracy and the computational e!ciency of a Point-Collocation Non-Intrusive Polynomial Chaos (NIPC) method applied to stochastic problems with multiple uncertain input variables has been investigated. Two stochastic model problems with multiple uniform random variables were studied to determine the eect of dierent sampling methods (Random, Latin Hypercube, and Hammersley) for the selection of the collocation points. The e ect of the number of collocation points on the accuracy of polynomial chaos expansions were also investigated. The results of the stochastic model problems show that all three sampling methods exhibit a similar performance in terms of the the accuracy and the computational e!ciency of the chaos expansions. It has been observed that using a number of collocation points that is twice more than the minimum number required gives a better approximation to the statistics at each polynomial degree. This improvement can be related to the increase of the accuracy of the polynomial coe!cients due to the use of more information in their calculation. The results of the stochastic model problems also indicate that for problems with multiple random variables, improving the accuracy of polynomial chaos coe!cients in NIPC approaches may reduce the computational expense by achieving the same accuracy level with a lower order polynomial expansion. To demonstrate the application of Point-Collocation NIPC to an aerospace problem with multiple uncertain input variables, a stochastic computational aerodynamics problem which includes the numerical simulation of steady, inviscid, transonic flow over a three-dimensional wing with an uncertain free-stream Mach number and angle of attack has been studied. For this study, a 5 th degree Point-Collocation NIPC expansion obtained with Hammersley sampling was capable of estimating the statistics at an accuracy level of 1000 Latin Hypercube Monte Carlo simulations with a significantly lower computational cost.

Computation of transonic flow around a 654egree sharp-edged, cropped delta wing undergoing a forced pitching oscillating is carried out using the unsteady, compressible, full Navier-Stokes equations. The implicit, upwind, flux-difference splitting, finite-volume scheme is used with time-accurate stepping. A fine, 0 H grid of 125x 85 x 84 points in the wrap-around, normal and axial directions, respectively, is used. The wing mean angle of attack is 20 and the freestream Mach number and Reynolds number are 0.85 and 3 . 2 3 ~ lo6, respectively. The wing is forced to oscillate in pitch around an axis at the 0.25 root-chord station with an amplitude of 4 and a reduced frequency of a. The results for the initial conditions show a system of shock waves consisting of a ray shock under the primary vortex and a transverse terminating shock through which the primary vortex core experiences a breakdown. During the pitching oscillation, the terminating shock and vortex breakdown behind it oscillate. Moreover, the lift coefficient decreases as the angle of attack approaches its maximum value (shock moves upstream) and increases as the angle of attack approaches its minimum value (shock moves downstream).

Dynamics and spectral character of unsteady pressure field on afterbody of generic space launcher: Transonic flows

Surrogate models are used to dramatically improve the design efficiency of numerical aerodynamic shape optimization, where high-fidelity, expensive computational fluid dynamics (CFD) is often employed. Traditionally, in adaptation, only one single sample point is chosen to update the surrogate model during each updating cycle, after the initial surrogate model is built. To enable the selection of multiple new samples at each updating cycle, a few parallel infilling strategies have been developed in recent years, in order to reduce the optimization wall clock time. In this article, an alternative parallel infilling strategy for surrogate-based constrained optimization is presented and demonstrated by the aerodynamic shape optimization of transonic wings. Different from existing methods in which multiple sample points are chosen by a single infill criterion, this article uses a combination of multiple infill criteria, with each criterion choosing a different sample point. Constrained drag minimizations of the ONERA-M6 and DLR-F4 wings are exercised to demonstrate the proposed method, including low-dimensional (6 design variables) and higher-dimensional problems (up to 48 design variables). The results show that, for surrogate-based optimization of transonic wings, the proposed method is more effective than the existing parallel infilling strategies, when the number of initial sample points are in the range from Nv to 8Nv (Nv here denotes the number of design variables). Each case is repeated 50 times to eliminate the effect of randomness in our results.

In this study, a transonic flow past NACA0012 profile at angle of attack α=00 whose aspect ratio AR is 1.0 with non-equilibrium condensation is analyzed by numerical analysis using a TVD scheme and is investigated using an intermittent indraft type supersonic wind tunnel. Transonic flows of 0.78–0.90 in free stream Mach number with the variations of the stagnation relative humidity(Φ0) are tested. For the same free stream Mach number, the increase in Φ0 causes decrease in the drag coefficient of profile which is composed of the drag components of form, viscous and wave. In the case of the same M∞ and T0, for more than Φ0=30%, despite the irreversibility of process in non-equilibrium condensation, the drag by shock wave decreases considerably with the increase of Φ0. On the other hand, it shows that the effect of condensation on the drag coefficients of form and viscous is negligible. As an example, the decreasing rate in the drag coefficient of profile caused by the influence of non-equilibrium condensation for the case of M∞=0.9 and Φ0 =50% amounts to 34%. Also, it were turned out that the size of supersonic bubble (that is, the maximum height of supersonic zone) and the deviation of pressure coefficient from the value for M=1 decrease with the increase of Φ0 for the same M∞.

This paper presents an approach for the rapid implementation of an adjoint solver for the ReynoldsAveraged Navier–Stokes equations with a Spalart–Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each partial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complex-step method using a flow over a bump case. The RANS-based aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coefficient is reduced by 19% when subject to a lift coefficient constraint. The results are compared with Euler-based aerodynamic shape optimization and previous work. Finally, the effects of the frozenturbulence assumption on the accuracy and computational cost are assessed.

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.