In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopts time-averaged aerodynamic coefficients as objective functions is presented. The time-accurate continuous adjoint equation and its boundary conditions are derived. The flow field and the adjoint equation are simulated numerically by the finite volume method (FVM). Feasibility and accuracy of the approach are perfectly validated by the design optimization results of the plunging NACA0012 airfoil.
Liang FANG, Xiaowei LI
. Design optimization of unsteady airfoils with continuous adjoint method[J]. Applied Mathematics and Mechanics, 2015
, 36(10)
: 1329
-1336
.
DOI: 10.1007/s10483-015-2010-9
[1] Raymond, M. H. and Preston, A. H. Wing design by numerical optimization. Journal of Aircraft, 15(7), 407-412(1978)
[2] Jameson, A. Aerodynamic design via control theory. Journal of Scientific Computing, 3(3), 233-260(1988)
[3] Jameson, A. Computational aerodynamics for aircraft design. Science (Washington), 245(4916), 361-371(1989)
[4] Reuther, J. and Jameson, A. Control theory based airfoil design using the Euler equations. 5th Symposium on Multidisciplinary Analysis and Optimization, American Institute of Aeronautics and Astronautics, Reston, 206-222(1994)
[5] Jameson, A., Martinelli, L., and Pierce, N. A. Optimum aerodynamic design using the Navier-Stokes equations. Theoretical and Computational Fluid Dynamics, 10(1-4), 213-237(1998)
[6] Reuther, J., Jameson, A., Alonso, J. J., Rimlinger, M. J., and Saunders, D. Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers, part 1. Journal of Aircraft, 36(1), 51-60(1999)
[7] Reuther, J., Alonso, J. J., Rimlinger, M. J., and Jameson, A. Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers. Computers and Fluids, 28(4), 675-700(1999)
[8] Anderson, W. K. and Venkatakrishnan, V. Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation. Computers and Fluids, 28(4), 443-480(1999)
[9] Bueno-Orovio, A., Castro, C., Palacios, F., and Zuazua, E. Continuous adjoint approach for the Spalart-Allmaras model in aerodynamic optimization. AIAA Journal, 50(3), 631-646(2012)
[10] Nadarajah, S. and Jameson, A. Optimal control of unsteady flows using a time accurate method. 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization Conference, American Institute of Aeronautics and Astronautics, Atlanta (2002)
[11] Nadarajah, S. and Jameson, A. Optimum shape design for unsteady flows with time-accurate continuous and discrete adjoint method. AIAA Journal, 45(7), 1478-1491(2007)
[12] Srinath, D. N. and Mittal, S. Optimal aerodynamic design of airfoils in unsteady viscous flows. Computer Methods in Applied Mechanics and Engineering, 199(29), 1976-1991(2010)
[13] Allaneau, Y. and Jameson, A. Direct numerical simulations of plunging airfoils. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and Astronautics, Florida (2010)
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