Zhoujie Lyu

Aerodynamic Design Optimization Studies of a Blended-Wing-Body Aircraft

The blended wing body is an aircraft configuration that has the potential to be more efficient than conventional large transport aircraft configurations with the same capability. However, the design of the blended wing is challenging due to the tight coupling between aerodynamic performance, trim, and stability. Other design challenges include the nature and number of the design variables involved, and the transonic flow conditions. To address these issues, a series of aerodynamic shape optimization studies using Reynolds-averaged Navier–Stokes computational fluid dynamics with a Spalart–Allmaras turbulence model is performed. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. A total of 273 design variables—twist, airfoil shape, sweep, chord, and span—are considered. The drag coefficient at the cruise condition is minimized subject to lift, trim, static margin, and center plane bending moment constraints. ...

Aerodynamic Shape Optimization Investigations of the Common Research Model Wing Benchmark

Despite considerable research on aerodynamic shape optimization, there is no standard benchmark problem allowing researchers to compare results. This work addresses this issue by solving a series of aerodynamic shape optimization problems based on the Common Research Model wing benchmark case defined by the Aerodynamic Design Optimization Discussion Group. The aerodynamic model solves the Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the required derivatives. The drag coefficient is minimized subject to lift, pitching moment, and geometric constraints. A multilevel technique is used to reduce the computational cost of the optimization. A single-point optimization is solved with 720 shape variables using a 28.8-million-cell mesh, reducing the drag by 8.5%. A more realistic design is achieved through a multipoint optimization. Multiple local minima are found when starting...

Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model

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.

Aerodynamic Shape Optimization of Common Research Model Wing-Body-Tail Configuration

Wing shape is one of the main drivers of aircraft aerodynamic performance, so most aerodynamic shape optimization efforts have focused solely on the wing. However, the performance of the full aircraft configuration must account for the fact that the aircraft needs to be trimmed. Thus, to realize the full benefit of aerodynamic shape optimization, one should optimize the wing shape while including the full configuration and a trim constraint. To evaluate the benefit of this approach, we perform the aerodynamic shape optimization of the Common Research Model wing–body–tail configuration using gradient-based optimization with a Reynolds-averaged Navier–Stokes model that includes a discrete adjoint implementation. We investigate the aerodynamic shape optimization of the wing with a trim constraint that is satisfied by rotating the horizontal tail. We then optimize the same wing–body configuration without the tail but with an added trim drag penalty based on a surrogate model we created before the optimization...

Aerodynamic Shape Optimization of an Adaptive Morphing Trailing-Edge Wing

Adaptive morphing trailing-edge wings have the potential to reduce the fuel burn of transport aircraft. However, to take full advantage of this technology and to quantify its benefits, design studies are required. To address this need, the aerodynamic performance benefits of a morphing trailing-edge wing are quantified using aerodynamic design optimization. The aerodynamic model solves the Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the required derivatives. The baseline geometry is optimized using a multipoint formulation and 192 shape design variables. The average drag coefficient is minimized subject to lift, pitching moment, geometric constraints, and a 2.5g maneuver bending moment constraint. The trailing edge of the wing is optimized based on the multipoint optimized wing. The trailing-edge morphing is parameterized using 90 design variables that are optimized i...

Aerodynamic Shape Optimization of a Blended-Wing-Body Aircraft

A series of RANS-based aerodynamic shape optimization for an 800-passenger blended-wing-body aircraft is performed. A gradient-based optimization algorithm and a parallel structured multiblock RANS solver with Spalart–Allmaras turbulence model are used. The derivatives are computed using a discrete adjoint method considering both frozen-turbulence and full-turbulence assumptions. A total of 274 shape and planform design variables are considered. The objective function is the drag coefficient at nominal cruise condition. Lift, trim and root bending moment are constrained. Control surfaces at the rear centerbody are used to trim the aircraft via a nested free-form deformation volume approach. The optimized design is trimmed and stable in both onand off-design conditions. The drag coefficient of the optimized design is reduced by 37 counts with trim and bending moment constraints satisfied. The addition of planform design variables provide an additional 2 drag count reduction.

RANS-based aerodynamic shape optimization investigations of the common research modelwing

The aerodynamic shape optimization of transonic wings requires Reynolds-averaged Navier–Stokes (RANS) modeling due to the strong nonlinear coupling between airfoil shape, wave drag, and viscous effects. While there has been some research dedicated to RANS-based aerodynamic shape optimization, there has not been an benchmark case for researchers to compare their results. In this investigations, a series of aerodynamic shape optimizations of the Common Research Model wing defined for the Aerodynamic Design Optimization Workshop are presented. The computational fluid dynamics solves Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. The drag coefficient at the nominal flight condition is minimized subject to lift, pitching moment and geometric constraints. A multilevel acceleration technique is used to reduce the computational cost. A total of 768 shape design variables are considered, together with a grid with 28.8 million cells. The drag coefficient of the optimized wing is reduced by 8.5% relative to the baseline. The single-point design has a sharp leading edge that is prone to flow separation at off-design conditions. A more robust design is achieved through a multipoint optimization, which achieves more reliable performance when lift coefficient and Mach number are varied about the nominal flight condition. To test the design space for local minima, randomly generated initial geometries are optimized, and a flat design space with multiple local minima was observed.

Aerostructural Design Optimization of an Adaptive Morphing Trailing Edge Wing

Adaptive morphing trailing edge technology offers the potential to decrease the fuel burn of transonic transport aircraft by allowing wings to dynamically adjust to changing flight conditions. Current aircraft use flap and aileron droop to adjust the wing during flight. However, this approach offers only a limited number of degrees of freedom, and the gaps in the wing created when using these devices introduce unnecessary drag. Morphing trailing edge technology offers more degrees of freedom, with a seamless interface between the wing and control surfaces. In this paper we seek to quantify the extent to which this technology can improve the fuel burn of transonic commercial transport sized aircraft. Starting from the undeformed Common Research Model (uCRM) geometry, we perform fixed-planform aerostructural optimizations of a standard wing, a wing retrofitted with a morphing trailing edge, and a clean sheet wing designed with the morphing trailing edge. The wing retrofitted with the morphing trailing edge improved the fuel burn as effectively as the full wing redesign without morphing. Additional fuel burn reductions were observed for the clean sheet design. The morphing trailing edge decreased the fuel burn by performing load alleviation at the maneuver condition, weakening the trade-off between cruise performance and maneuver structural constraints, resulting in lighter wingboxes and more aerodynamically efficient cruise configurations.

High-fidelity hydrodynamic shape optimization of a 3-D hydrofoil

With recent advances in high-performance computing, computational fluid dynamics (CFD) modeling has become an integral part in the engineering analysis and even in the design process of marine vessels and propulsors. In aircraft wing design, CFD has been integrated with numerical optimization and adjoint methods to enable high-fidelity aerodynamic shape optimization with respect to large numbers of design variables. There is a potential to use some of these techniques for maritime applications, but there are new challenges that need to be addressed to realize that potential. This work presents a solution to some of those challenges by developing a CFD-based hydrodynamic shape optimization tool that considers cavitation and a wide range of operating conditions. A previously developed three-dimensional compressible Reynolds-averaged Navier‐Stokes (RANS) solver is extended to solve for nearly incompressible flows, using a low-speed preconditioner. An efficient gradient-based optimizer and the adjoint method are used to carry out the optimization. The modified CFD solver is validated and verified for a tapered NACA 0009 hydrofoil. The need for a large number of design variables is demonstrated by comparing the optimized solution obtained using different number of shape design variables. The results showed that at least 200 design variables are needed to get a converged optimal solution for the hydrofoil considered. The need for a high-fidelity hydrodynamic optimization tool is also demonstrated by comparing RANS-based optimization with Euler-based optimization. The results show that at high lift coefficient (C L) values, the Euler-based optimization leads to a geometry that cannot meet the required lift at the same angle of attack as the original foil due to inability of the Euler solver to predict viscous effects. Single-point optimization studies are conducted for various target C L values and compared with the geometry and performance of the original NACA 0009 hydrofoil, as well as with the results from a multipoint optimization study. A total of 210 design variables are used in the optimization studies. The optimized foil is found to have a much lower negative suction peak, and hence delayed cavitation inception, in addition to higher efficiency, compared to the original foil at the design C L value. The results show significantly different optimal geometry for each C L, which means an active morphing capability was needed to achieve the best possible performance for all conditions. For the single-point optimization, using the highest C L as the design point, the optimized foil yielded the best performance at the design point, but the performance degraded at the off-design C L points compared to the multipoint design. In particular, the foil optimized for the highest C L showed inferior performance even compared to the original foil at the lowest C L condition. On the other hand, the multipoint optimized hydrofoil was found to perform better than the original NACA 0009 hydrofoil over the entire operation profile, where the overall efficiency weighted by the probability of operation at each C L, is improved by 14.4%. For the multipoint optimized foil, the geometry remains fixed throughout the operation profile and the overall efficiency was only 1.5% lower than the hypothetical actively morphed foil with the optimal geometry at each C L. The new methodology presented herein has the potential to improve the design of hydrodynamic lifting surfaces such as propulsors, hydrofoils, and hulls.

Comparison of inexact- and quasi-Newton algorithms for aerodynamic shape optimization

Large-scale aerodynamic and multidisciplinary design problems challenge conventional optimization algorithms, because these problems typically involve thousands of design variables and constraints. Alternative algorithms must be developed that produce solutions to large-scale design problems in a reasonable time. To this end, we investigate a scalable reduced-space Newton–Krylov optimization algorithm. This inexact-Newton algorithm uses a novel matrix-free Krylov solver that requires only KKT-matrix-vector products; these products are formed by solving two linear PDEs. We present preliminary results that benchmark the inexact-Newton algorithm against a conventional quasi-Newton algorithm on the Euler-based drag minimization of the Common-Research-Model wing benchmark. For this problem, the preliminary results indicate that the inexact-Newton algorithm scales well and outperforms the conventional algorithm for problems with more than 500 design variables.