Applied Mathematics and Mechanics >
Airfoil design optimization based on lattice Boltzmann method and adjoint approach
Received date: 2017-09-18
Revised date: 2017-11-23
Online published: 2018-06-01
Supported by
Project supported by the National Basic Research Program of China (No. 2014CB744100), the National Natural Science Foundation of China (Nos. 61403245 and 91648119), and the Shanghai Municipal Science and Technology Commision (No. 14500500400)
We present a new aerodynamic design method based on the lattice Boltzmann method (LBM) and the adjoint approach. The flow field and the adjoint equation are numerically simulated by the GILBM (generalized form of interpolation supplemented LBM) on non-uniform meshes. The first-order approximation for the equilibrium distribution function on the boundary is proposed to diminish the singularity of boundary conditions. Further, a new treatment of the solid boundary in the LBM is described particularly for the airfoil optimization design problem. For a given objective function, the adjoint equation and its boundary conditions are derived analytically. The feasibility and accuracy of the new approach have been perfectly validated by the design optimization of NACA0012 airfoil.
Xiaowei LI, Liang FANG, Yan PENG . Airfoil design optimization based on lattice Boltzmann method and adjoint approach[J]. Applied Mathematics and Mechanics, 2018 , 39(6) : 891 -904 . DOI: 10.1007/s10483-018-2333-9
[1] Inamuro, T., Ogata, T., and Ogino, F. Numerical simulation of bubble flows by the lattice Boltzmann method. Future Generation Computer Systems, 20(6), 959-964(2004)
[2] Chen, S., Dawson, S. P., Doolen, G. D., Janecky, D. R., and Lawniczak, A. Lattice methods and their applications to reacting systems. Computers and Chemical Engineering, 19(6), 617-646(1995)
[3] Li, B. and Kwok, D. Y. A lattice Boltzmann model for electrokinetic microchannel flow of electrolyte solution in the presence of external forces with the Poisson-Boltzmann equation. International Journal of Heat and Mass Transfer, 46(22), 4235-4244(2003)
[4] Guo, Z. and Zhao, T. S. Lattice Boltzmann model for incompressible flows through porous media. Physical Review E, 66(3), 036304(2002)
[5] Jameson, A. Aerodynamic design via control theory. Journal of Scientific Computing, 3(3), 233-260(1988)
[6] 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 (1984)
[7] Jameson, A. and Baker, T. J. Multigrid solution of the Euler equations for aircraft configurations. 22nd Aerospace Sciences Meeting, Aerospace Sciences Meetings, American Institute of Aeronautics and Astronautics, Reston (1984)
[8] Jameson, A., Martinelli, L., and Pierce, N. A. Optimum aerodynamic design using the NavierStokes equations. Theoretical and Computational Fluid Dynamics, 10(1-4), 213-237(1998)
[9] Kim, S., Alonso, J. J., and Jameson, A. A gradient accuracy study for the adjoint-based NavierStokes design method. 37th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, Reston (1999)
[10] 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)
[11] Pingen, G., Evgrafov, A., and Maute, K. Topology optimization of flow domains using the lattice Boltzmann method. Structural and Multidisciplinary Optimization, 34(6), 507-524(2007)
[12] Evgrafov, A., Pingen, G., and Maute, K. Topology optimization of fluid problems by the lattice Boltzmann method. IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, Springer, the Netherlands, 559-568(2006)
[13] Pingen, G., Waidmann, M., Evgrafov, A., and Maute, K. A parametric level-set approach for topology optimization of flow domains. Structural and Multidisciplinary Optimization, 41(1), 117-131(2010)
[14] Pingen, G., Evgrafov, A., and Maute, K. Adjoint parameter sensitivity analysis for the hydrodynamic lattice Boltzmann method with applications to design optimization. Computers and Fluids, 38(4), 910-923(2009)
[15] Yaji, K., Yamada, T., Yoshino, M., Mausumoto, T., Izui, K., and Nishiwaki, S. Topology optimization using the lattice Boltzmann method incorporating level set boundary expressions. Journal of Computational Physics, 274, 158-181(2014)
[16] Ngnotchouye, J. M. T., Herty, M., Steffensen, S., and Banda, M. K. Relaxation approaches to the optimal control of the Euler equations. Computational and Applied Mathematics, 30(2), 399-425(2011)
[17] Qian, Y. H., d'Humières, D., and Lallemand, P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 17(6), 479-484(1992)
[18] Guo, Z. L., Zheng, C. G., and Shi, B. C. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chinese Physics, 11(4), 366-374(2002)
[19] Imamura, T., Suzuki, K., Nakamura, T., and Yoshida, M. Flow simulation around an airfoil by lattice Boltzmann method on generalized coordinates. AIAA Journal, 43(9), 1968-1973(2005)
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