Clyde R. Gumbert, Gene J.-W. Hou*, and Perry A. Newman

Multidisciplinary Optimization Branch, NASA Langley Research Center

*Department of Mechanical Engineering, Old Dominion University

October 2000

TA 714-05-10-13

Research Objective. The objective of this research is to develop design optimization procedures, incorporating advanced CFD and FEM analysis codes, which are easily implemented, computationally efficient, and applicable to practical 3-D aerospace vehicle designs.

Approach. Simultaneous Aerodynamic Analysis & Design Optimization (SAADO) is a procedure that incorporates design improvement within iterative CFD aerodynamic analyses so as to achieve fully converged flow solutions only near optimal design, thereby gaining computational efficiency in the entire design process. Our previous SAADO feasibility demonstrations used consistent, discrete, analytical sensitivity derivatives for a quasi 1-D Euler nozzle study; a 2-D Navier-Stokes turbulent, transonic, airfoil study; and a 3-D Euler, transonic, rigid wing study. When SAADO is applied to a flexible wing rather than a rigid wing, the linear FEM solution is iteratively coupled with the nonlinear CFD solution for both analysis and sensitivity analysis. This flexible SAADO procedure therefore exhibits dual simultaneity; that is, not only with respect to analysis and design, but also with respect to the aero-structural coupling. The present study is for a simple, trapezoidal planform wing; changes in eight design variables are sought to maximize the wing lift-to-drag ratio subject to solution-dependent constraints on the difference between lift and weight, the pitching moment coefficient and the compliance, a measure of the work required to deflect the wing. These eight design variables are tip chord, tip setback, semispan, twist, root thickness, tip thickness, root camber, and location of maximum root camber.

Accomplishment Description. These flexible wing optimization results demonstrate the feasibility of SAADO under dual simultaneity; and, as shown on the figure, SAADO finds essentially the same local minimum as a conventional technique. The flexible wing results are contrasted with rigid wing results that were previously obtained for constraints not dependent on structural code output; that is, only the CFD code output: lift, and moment coefficients for pitch and roll. The results for wing shapes are different, but so are the optimization problems. Wing upper surface pressure contour plots indicate a substantially weakened shock wave (less drag) for all of these optimized shapes. The relative computational efficiency of SAADO with respect to conventional optimization, as observed in prior applications, including the rigid wing results shown here, was not seen in this eight design-variable flexible wing problem. However, two-design-variable SAADO results, not shown here, did exhibit the expected gains in computational efficiency.

Significance. The feasibility of SAADO for a flexible wing application has been demonstrated by these initial results.

Future Plans. Current work is a Simultaneous Aerodynamic & Structural Design Optimization (SASDO) demonstration incorporating both aerodynamic and structural design variables.

Figure: SAADO Optimization Results: Flexible and Rigid Wing

Related Presentations:

Related Publications:

Hou, G. J.-W., Korivi, V. M., Taylor, III, A. C., Maroju, V., and Newman, P. A.: "Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) of a Turbulent Transonic Airfoil Using a Navier-Stokes Code With Automatic Differentiation (ADIFOR)," Computational Aerosciences Workshop 95, edited by W. J. Feiereisen, and A. K. Lacer, NASA CD CP-20010, Jan. 1996, pp. 82-85.

Gumbert, C. R., Hou, G. J.-W., and Newman, P. A.: "Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) of a 3-D Rigid Wing", AIAA Paper 99-3296, Proceedings, 14^th AIAA Computational Fluid Dynamics Conference, Norfolk, June 1999, pp. 402-418.

Gumbert, C. R., Hou, G. J.-W., and Newman, P. A.: "Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) of a 3-D Flexible Wing", AIAA Paper 2001-1107, January 2001.