CFD-based optimization of hovering rotors using radial basis functions for shape parameterization and mesh deformation

Springer Science and Business Media LLC - Tập 14 - Trang 97-118 - 2011
Christian B. Allen1, Thomas C. S. Rendall1
1Department of Aerospace Engineering, University of Bristol, Bristol, UK

Tóm tắt

Aerodynamic shape optimization of a helicopter rotor in hover is presented, using compressible CFD as the aerodynamic model. An efficient domain element shape parameterization method is used as the surface control and deformation method, and is linked to a radial basis function global interpolation, to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh, and so both the geometry control and volume mesh deformation problems are solved simultaneously. This method is independent of mesh type (structured or unstructured) or size, and optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference, resulting in a flexible method of ‘wrap-around’ optimization. This paper presents results of the method applied to hovering rotors using local and global design parameters, allowing a large geometric design space. Results are presented for two transonic tip Mach numbers, with minimum torque as the objective, and strict constraints applied on thrust, internal volume and root moments. This is believed to be the first free form design optimization of a rotor blade using compressible CFD as the aerodynamic model, and large geometric deformations are demonstrated, resulting in significant torque reductions, with off-design performance also improved.

Tài liệu tham khảo

Allen CB (2001) Multigrid acceleration of an upwind Euler code for hovering rotor flows. Aeronaut J 105(1051):517–524 Allen CB (2004) An unsteady multiblock multigrid scheme for lifting forward flight rotor simulations. Int J Numer Methods Fluids 45(9):973–984 Allen CB (2007) Parallel universal approach to mesh motion and application to rotors in forward flight. Int J Numer Methods Eng 69(10):2126–2149 Allen CB (2008) Towards automatic structured multiblock mesh generation using improved transfinite interpolation. Int J Numer Methods Eng 74(5):697–733 Allen CB, Rendall TCS, Morris AM (2010) CFD-based twist optimisation of hovering rotors. J Aircr 47(6):2075–2085 Alonso JJ, Jameson A (1994) Fully implicit time-marching aeroelastic solutions. AIAA paper 1994-0056 Amoignon O (2010) AESOP—a numerical platform for aerodynamic shape optimization. Optim Eng 11:555–581 Anderson WK, Karman SL, Burdyshaw C (2009) Geometry parameterization method for multidisciplinary applications. AIAA J 17(6):1568–1578 Bloor MIG, Wilson MJ (1995) Efficient parameterization of generic aircraft geometry. J Aircr 32(6):1269–1275 Braibant V, Fleury C (1984) Shape optimal design using B-splines. Comput Methods Appl Mech Eng 44(3):247–267 Buhmann H (2005) Radial basis functions, 1st edn. Cambridge University Press, Cambridge Caradonna FX, Tung C (1981) Experimental and analytical studies of a model helicopter rotor in hover. NASA TM-81232 Celi R (1999) Recent applications of design optimization to rotorcraft—a survey. J Aircr 36(1):176–189 Choi S, Pottsdam M, Lee KH, Iaccarino G, Alonso JJ (2008) Helicopter rotor design using a time-spectral and adjoint-based method. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, Victoria, BC, Canada. AIAA paper 2008-5810 Chung HS, Alonso J (2004) Multiobjective optimization using approximati on model-based genetic algorithms. In: 10th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, Albany, NY. AIAA paper 2004-4325 Dulikravich SG (1992) Aerodynamic shape design and optimization: status and trends. J Aircr 29(6):1020–1025 Dumont A, Pape AL, Peter J, Huberson S (2009) Aerodynamic shape optimization of hovering rotors using a discrete adjoint of the RANS equations. In: AHS 65th annual forum, Grapevine, TX Fasshauer GE (2007) Meshfree approximation methods with Matlab. Interdisciplinary Mathematical Sciences, vol 6. World Scientific, Singapore Gumbert CR, Hou G, Newman PA (2001a) Simultaneous aerodynamic analysis and design optimization (SAADO) for a 3-D flexible wing. In: Aerospace sciences meeting and exhibit, Reno, NV. AIAA paper 2001-1107 Hicks RM, Henne PA (1978) Wing design by numerical optimization. J Aircr 15(1):407–412 Jakobsson S, Patriksson M, Rudholm J, Wojciechowski A (2009b) A method for simulation based optimization using radial basis functions. Optim Eng 11:1–32 Jameson A (1988) Aerodynamic design via control theory. J Sci Comput 3(3):233–260 Jameson A (2003) CFD for aerodynamic design and optimization: its evolution over the last three decades. In: 16th AIAA CFD conference, June 23–26, Orlando, FL. AIAA 2003-3438 Jameson A, Leoviriyakit K, Shankaran S (2007) Multi-point aero-structural optimization of wings including variations. In: Aerospace sciences meeting and exhibit, Reno, NV Kulfan BM (2007) A universal parametric geometry representation method—CST. In: 45th AIAA aerospace sciences meeting and exibit, 8–11 Jan 2007, Reno, NV Li W, Huyse L, Padula S (2002) Robust airfoil optimization to achieve drag reduction over a range of Mach numbers. Struct Multidiscip Optim 24(1):38–50 Morris AM, Allen CB, Rendall TCS (2008) CFD-based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation. Int J Numer Methods Fluids 58(8):827–860 Morris AM, Allen CB, Rendall TCS (2009) Domain element method for aerodynamic shape optimization applied to modern transport wing. AIAA J 47(7):1647–1659 Nadarajah S, Castonguay P, Mousavi A (2007) Survey of shape parameterization techniques and its effect on three-dimensional aerodynamic shape optimization. In: 18th AIAA computational fluid dynamics conference, Miami, FL. AIAA paper 2007-3837 Nadarajah S, Soucy O, Tatossian C (2008) Aerodynamic shape optimisation of hovering rotor blades using a NLFD approach. In: 46th AIAA aerospace sciences meeting and exibit, Reno, NV. AIAA paper 2008-0322 Nielsen EJ, Lee-Rausch EM, Jones WT (2009) Adjoint-based design of rotors using the Navier-Stokes equations in a noninertial frame. In: AHS 65th annual forum, Grapevine, TX Pape AL, Beaumier P (2005) Numerical optimization of helicopter rotor aerodynamic performance in hover. Aerosp Sci Technol 9(3):111–201 Parpia IH (1988) Van-Leer flux vector splitting in moving coordinates. AIAA J 26:113–115 Perry FJ (1987) Aerodynamics of the helicopter world speed record. In: 43rd annual national forum of the American helicopter society Pickett RM, Rubinstein MF, Nelson RB (1973) Automated structural synthesis using a reduced number of design coordinates. AIAA J 11(4):494–498 Rendall TCS, Allen CB (2008a) Multi-dimensional aircraft surface pressure interpolation using radial basis functions. Proc Inst Mech Eng, G J Aerosp Eng 222:483–495 Rendall TCS, Allen CB (2008b) Unified fluid-structure interpolation and mesh motion using radial basis functions. Int J Numer Methods Eng 74(10):1519–1559 Rendall TCS, Allen CB (2009) Efficient mesh motion using radial basis functions with data reduction algorithms. J Comput Phys 228(17):6231–6249 Renzoni P, DAlascio A, Kroll N, Peshkin D, Hounjet MH, Boniface J, Vigevano L, Allen CB, Badcock KJ, Mottura L, Scholl E, Kokkalis A (2000) EROS—a common European Euler code for the analysis of the helicopter rotor flowfield. Prog Aerosp Sci 36(5):437–485 Reuther J, Jameson A, Farmer J, Martinelli L, Saunders D (1996) Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation. In: 34th aerospace sciences meeting and exhibit, Reno, NV. AIAA paper 96-0094 Samareh JA (2001) Survey of shape parameterization techniques for high-fidelity multidisciplinary shape optimization. AIAA J 39(5):877–884 Smith RE, Bloor MIG, Wilson MJ, Thomas AT (1995) Rapid airplane parametric input design (rapid). In: Proceedings of 12th AIAA computational fluid dynamics conference. AIAA, Washington van Leer B (1982) Flux vector splitting for the Euler equations. In: Lecture notes in physics, vol 170, pp 507–512 Watt A, Watt M (1992) Advanced animation and rendering techniques. Addison-Wesley, New York Wendland H (2005) Scattered data approximation, 1st edn. Cambridge University Press, Cambridge Wong WS, Moigne AL, Qin N (2007) Parallel adjoint-based optimization of a blended wing body aircraft with shock control bumps. Aeronaut J 111(1117):165–174 Zhou JL, Tits AL (1993) Nonmonotone line search for minimax problems. J Optim Theory Appl 76(3):455–476 Zhou JL, Tits AL, Lawrence CT (1997) Users guide for ffsqp version 3.7: a Fortran code for solving optimization programs, possibly minimax, with general inequality constraints and linear equality constraints, generating feasible iterates. Technical report SRC-TR-92-107r5, Institute for Systems Research, University of Maryland, College Park