James Reuther

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet

This paper focuses on the demonstration of an integrated aerostructural method for the design of aerospace vehicles. Both aerodynamics and structures are represented using high-fidelity models such as the Euler equations for the aerodynamics and a detailed finite element model for the primary structure. The aerodynamic outer-mold line and a structure of fixed topology are parameterized using a large number of design variables. The aerostructural sensitivities of aerodynamic and structural cost functions with respect to both outer-mold line shape and structural variables are computed using an accurate and efficient coupled-adjoint procedure. Kreisselmeier‐ Steinhauser functions are used to reduce the number of structural constraints in the problem. Results of the aerodynamic shape and structural optimization of a natural laminar-flow supersonic business jet are presented together with an assessment of the accuracy of the sensitivity information obtained using the coupled-adjoint procedure.

Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design

This paper presents an adjoint method for sensitivity analysis that is used in an aero-structural aircraft design framework. The aero-structural analysis uses high-fidelity models of both the aerodynamics and the structures. Aero-structural sensitivities are computed using a coupled-adjoint approach that is based on previously developed single discipline sensitivity analysis. Alternative strategies for coupled sensitivity analysis are also discussed. The aircraft geometry and a structure of fixed topology are parameterized using a large number of design variables. The aero-structural sensitivities of aerodynamic and structural functions with respect to these design variables are computed and compared with results given by the complex-step derivative approximation. The coupled-adjoint procedure is shown to yield very accurate sensitivities and to be computationally efficient, making high-fidelity aero-structural design feasible for problems with thousands of design variables.

Control theory based airfoil design using the Euler equations

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

Aerodynamic shape optimization of wing and wing-body configurations using control theory

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. Recently, the method has been implemented for both potential flows and flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can more easily be extended to treat general configurations. Here results are presented both for the optimization of a swept wing using an analytic mapping, and for the optimization of wing and wing-body configurations using a general mesh.

Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

Abstract This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. A high fidelity computational fluid dynamics (CFD) algorithm modelling the Euler equations is used to calculate the aerodynamic properties of complex three-dimensional aircraft configurations. The design process is greatly accelerated through the use of both control theory and parallel computing. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented in parallel using a domain decomposition approach, an optimized communication schedule, and the Message Passing Interface (MPI) Standard for portability and efficiency. In our earlier studies, the serial implementation of this design method, was shown to be effective for the optimization of airfoils, wings, wing–bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In this work, our concern will be to extend the methodologies such that the combined capabilities of these new technologies can be used routinely and efficiently in an industrial design environment. The aerodynamic optimization of a supersonic transport configuration is presented as a demonstration test case of the capability. A particular difficulty of this test case is posed by the close coupling of the propulsion/airframe integration.

A coupled aero-structural optimization method for complete aircraft configurations

This paper presents a new framework for the coupled optimization of aero-structural systems. The framework permits the use of high-fidelity modeling of both the aerodynamics and the structures and represents our first step in an effort towards the development of a high-fidelity multidisciplinary optimization capability. The approach is based on efficient analysis methodologies for the solution of the aerodynamics and structures subproblems, an adjoint solver to obtain aerodynamic sensitivities, and a multiprocessor parallel implementation. We have placed a geometry database representing the outer mold line (OML) of the configuration of interest at the core of our framework. Using this geometry description, the information exchange between aerodynamics and structures is accomplished through an independent coupling of each discipline with the OML database. The framework permits the later inclusion of other disciplines, such as heat transfer and radar signatures, with relative ease. Specific results from the coupling of a finite volume flow solver for the Euler and Reynolds Averaged Navier-Stokes

Single-Point and Multipoint Aerodynamic Shape Optimization of High-Speed Civil Transport

Single-point and multipoint aerodynamicshapeoptimization methods weredeveloped and demonstrated forthe designofanadvancedsupersonictransportsubjecttomanygeometricconstraints.Thestartingpointcone guration baseline was developed in support of the NASA High-Speed Research program using linear-theory-based methods and multidisciplinary system analyses. The single-point design method simulated the presence of nacelles and diverters at supersonic cruise by superimposing nacelles-on/nacelles-off pressure differences, from complete cone gurationanalyses,ontosingle-block-gridwing/bodycalculations.Themultipointdesignmethodusedamultiblock gridto treatthecompletecone guration,including nacelles/diverters, canard,empennage,and wing e aps/slats.Two forms of multipoint optimization were performed at Mach 2.4, 1.1, and 0.9: sequential (design at cruise followed by e ap and canard/tail incidence angle optimization at the two transonic conditions ) and multipoint (simultaneous design at the three e ight conditions via a composite objective function ). Euler-based optimization using a combination of the two methods achieved signie cant performance gains derived from the nonlinear effects. The single-point approach produced much of the improvement, lowering the appropriately weighted thrust coefe cient by 4.28 counts after trimming the full cone guration at the three design points. (A seven count drag reduction was achieved at cruise for the untrimmed vehicle. ) The sequential and multipoint methods achieved 6.03 and 7.55 counts of composite thrust reduction, respectively.

High-Fidelity Aero-Structural Design Using a Parametric CAD-Based Model

This paper presents two major additions to our high-fidelity aero-structural design environment. Our framework uses high-fidelity descriptions for both the flow around the aircraft (Euler and Navier-Stokes) and for the structural displacements and stresses (a full finite-element model) and relies on a coupled-adjoint sensitivity analysis procedure to enable the simultaneous design of the shape of the aircraft and its underlying structure to satisfy the measure of performance of interest. The first of these additions is a direct interface to a parametric CAD model that we call AEROSURF and that is based on the CAPRI Application Programming Interface (API). This CAD interface is meant to facilitate designs involving complex geometries where multiple surface intersections change as the design proceeds and are complicated to compute. In addition, the surface geometry information provided by this CAD-based parametric solid model is used as the common geometry description from which both the aerodynamic model and the structural representation are derived. The second portion of this work involves the use of the Finite Element Analysis Program (FEAP) for the structural analyses and optimizations. FEAP is a full-purpose finite element solver for structural models which has been adapted to work within our aero-structural framework. In addition, it is meant to represent the state-of-the-art in finite element modeling and it is used in this work to provide realistic aero-structural optimization costs for structural models of sizes typical in aircraft design applications. The capabilities of these two major additions are presented and discussed. The parametric CAD-based geometry engine, AEROSURF, is used in aerodynamic shape optimization and its performance is compared with our standard, in-house, geometry model. The FEAP structural model is used in optimizations using our previous version of AEROSURF (developed in-house) and is shown to provide realistic results with detailed structural models.