The application of adjoint methods to three-dimensional aerodynamic shape optimization has increased in popularity due to their speed in handling large numbers of design variables. However, they have a known tendency to converge on local minima in the design space, which can result in a solution that may not be the global minimum [1]. This paper presents the application of our optimization methodology Jetstream, to a set of problems in exploratory wing design for fully turbulent, transonic flow.
The Reynolds-averaged Navier-Stokes equations are solved on multi-block structured grids with the Spalart-Allmaras turbulence model. Spatial discretization of the equations is performed using summation-by-parts operators with simultaneous approximation terms at boundaries and block interfaces. The governing equations are then solved iteratively using a parallel Newton-Krylov-Schur algorithm [2]. The grids are fitted with B-spline volumes, and the resulting control mesh is deformed using a linear elastic model. The discrete adjoint method is used to calculate gradients, which are then supplied to SNOPT, a sequential quadratic programming optimization algorithm [4].
The optimizer is first applied to investigate multimodality in the case of lift-constrained drag minimization of the NASA Common Research Model (CRM) wing, one of the benchmark cases defined by the Aerodynamic Design Optimization Discussion Group [3]. The z-coordinates of the B-spline control points on the wing surface are design variables, giving the optimizer freedom to design the section and twist of the wing. The Mach number is 0.85 and the Reynolds number is 5 million. The optimizer is required minimize drag while maintaining a CL of 0.50, a CM greater than -0.17, and an internal volume greater than or equal to its initial volume. To investigate multimodality, a number of optimizations are performed with different initial starting sections for the CRM planform. These results are then compared to the drag optimized geometry for the original wing [3].
Jetstream is also used to study the various solutions to the design of wingtip devices. While non-planar wingtip devices have been proven to reduce induced drag in theory and in Euler optimizations [4], their overall benefit is not as clear once turbulence and skin friction are accounted for. The initial geometry is based on a Boeing 737-900 wing with RAE2822 airfoil sections. For greater geometric flexibility, the B-spline surface points are embedded into a Free- Form Deformation (FFD) volume controlled by axial curves [5]. The points on FFD lattice are allowed to move vertically to control section and twist throughout the wing. The span of the overall wing is kept constant. The control points on the axial curve on the outboard wing section are allowed to move vertically and in the streamwise direction, controlling the wingtip height and sweep. Finally, the taper of the wingtip section is allowed to change. The optimization is performed at a Reynolds number of 20 million and a Mach number of 0.74. The optimizer is required to minimize drag while maintaining a lift equivalent to the original projected area at a CL of 0.50. The optimizer is able to reduce the overall drag using several configurations shown in Figure 1: winglet up, raked wingtip, and winglet down.
References
[1] Chernukhin O. and Zingg, D.W., “An investigation of multi-modality in aerodynamic shape optimization.” 20th AIAA Computational Fluid Dynamics Conference, No. AIAA-2011-3070, Honolulu, Hawaii, U.S.A., June 2011.
[2] Osusky, M. and Zingg, D.W., “A Parallel Newton-Krylov-Schur Flow Solver for the Reynolds- averaged Navier-Stokes Equations.” 50th AIAA Aerospace Meeting including the New Horizons Forum and Aerospace Exposition, No. AIAA-2012-0442, Nashville, Tennessee, U.S.A., January 2012.
[3] Lee, C., Koo, D., Telidetzki, K., Buckley, H., Gagnon, H., and Zingg, D.W., “Aerodynamic Shape Optimization of Benchmark Problems Using Jetstream,” AIAA Science and Technology Forum and Exposition 2015: 53rd Aerospace Science Meeting, Florida, January 2015
[4] Hicken, J.E., and Zingg, D.W., “Induced Drag Minimization of Nonplanar Geometry Based on the Euler Equations,” 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, No. AIAA-2008-5807, Victoria, British Columbia, Canada, September 2008.
[5] Gagnon, H., and Zingg, D.W., “High-fidelity Aerodynamic Shape Optimization of Unconventional Aircraft through Axial Deformation,” AIAA Science and Technology Forum and Exposition: 52nd Aerospace Science Meeting, No. AIAA 2014-0908, National Harbor, Maryland.
Topics: Aerodynamics of airfoils, wings, wing/fuselage interactions, nacelles, etc., inclu , Topics: Aerodynamic design of fixed and rotary wing aircraft, propellers, future aircraft , Topics: Aerodynamic optimization and uncertainty analysis methods; Multidisciplinary Analy , Topics: Computational Fluid Dynamics as applied to any of the above, including surface mod
