一种改进的计算压力分布的格林函数方法

doi:10.7527/S1000-6893.2014.0209

Abstract

Abstract:

An improvement on the pressure distribution calculations in the Green's function method is presented. Although the Green's function method can give some very accurate results in velocity potential calculations, in pressure distribution calculations, the accuracy of the results is not good becaused in this method a very simple formula evaluated by finite difference method is used to get the pressure distributions on the surface of the body. In the present paper we use a different method to calculate the pressure distributions. We differentiate both side of the algebraical velocity potential equation and get the analytic expressions of the derivatives of the velocity potential along the x,y,z directions respectively, then we use these formulas to calculate the pressure coefficients and get the pressure distributions on the body. The results are very accurate and in good agreement with the results of Navier-Stokes solver and the experimental data.Moreover we have also made some improvements on the numerical applications of the Kutta conditions and render the results of the calculation more accurate.

Key words: Green's function, potential flow, unigueness, pressure coefficient, Kutta condition

CLC Number:

V211.3

LIU Qiangang, ZHOU Zhou. An improved Green's function method for pressure distribution calculations[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(6): 1744-1751.

References

[1] Morino L, Kuo C C. Subsonic potential aerodynamics for complex configurations: A general theory[J]. AIAA Journal, 1974, 12(2): 191-197.
[2] Liu Q G. The uniqueness of the solution of the velocity potential integral equation established by using Green's theorem[J]. Journal of Northwestern Polytechnical University, 1978(1): 139-145 (in Chinese). 刘千刚.关于用格林定理建立的物面速势积分方程解的唯一性问题[J].西北工业大学学报, 1978(1): 139-145.
[3] Liu Q G. Review of the Green's function method for steady and unsteady, subsonic, transonic and supersonic aerodynamics around complex configuration[J]. Acta Aeronautica et Astronautica Sinica, 1996, 17(2): 137-143 (in Chinese). 刘千刚. 复杂构形的亚、跨、超音速定常及非定常气动力的Green函数算法综述[J]. 航空学报, 1996, 17(2): 137-143.
[4] Hess J L. Review of integral equation techniques for solving potential flow problems with emphasis on the surface-source method[J]. Computer Methods in Applied Mechanics and Engineering, 1975, 5: 145-196.
[5] Chmitt V S, Charpin F. Pressure distributions on the ONERA-M6-wing at transonic Mach numbers, AGARD AR-138[R]. [S.l.]: AGARD, 1979.
[6] Gao Z L, Zou Z J.A three-dimensional desingularized high order panel method based on NURBS[J].Journal of Hydrodynamics, 2008, 20(2): 137-146.
[7] Chen Z M.A vortex based panel method for potential flow simulation around a hydrofoil[J]. Journal of Fluid and Structures, 2012(28): 379-391.
[8] Richard L F. Airfoil aerodynamics using panel method[J]. The Mathematical Journal, 2008, 10(4): 725-739.
[9] Cheng B L, Cranfill C W, Axford R. Using the Green's function method to calculate pressure fluctuations in compressible multifluid[C]//Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing. Cambridge: [s.n.], 2004: 1-14.
[10] Tan J F, Wang H W. Panel/full-span free wake coupled method for unsteady aerodynamic of a helicopter rotor blade[J]. Chinese Journal of Aeronautics, 2013, 26(3): 535-543.
[11] Markus D, Manuel K, Ewald K, et al. Tip vortex conservation on a helicopter main rotor using vortex-adapted chimera grids[J]. AIAA Journal, 2007, 45(8): 2062-2074.
[12] Liang H, Zong Z, Zou L, et al. Vortex shedding from a two-dimensional cylinder beneath a rigid wall and a free surface according to the discrete vortex method[J]. European Journal of Mechanics B/Fluids, 2014, 43: 110-119.
[13] Ji J C, Bai L, Huang X. A state observer based algorithm for aeroacoustic beamforming[J]. Acta Aeronautica et Astronautic Sinica, 2011, 25(1): 35-40 (in Chinese). 季建朝, 白龙, 黄迅. 基于状态观测器的波束行成算法及其航空应用[J]. 航空学报, 2011, 25(1): 35-40.
[14] Xu J H, Song W P, Han Z H. Prediction of aeroacoustic noise for helicopter rotors based on vorticity confinement method[J]. Acta Aeronautica et Astronautic Sinica, 2011, 25(12): 2204-2212 (in Chinese). 徐建华, 宋文萍, 韩忠华. 基于涡限制法的旋翼气动噪声计算[J]. 航空学报, 2011, 25(12): 2204-2212.
[15] Francescantonio P D, Casalino D. Green's function discretization scheme for sound propagation in nonuniform flows[J]. AIAA Journal, 1999, 37(10): 1161-1172.

An improved Green's function method for pressure distribution calculations

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[3]	Yang Yong;Yu Shouqin. INTEGRAL SOLUTION OF THE FULL POTENTIAL EQUATION FOR TRANSONIC FLOW AROUND WIND-BODY COMBINATIONS [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1996, 17(4): 448-451.
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[5]	Zhu Ziqiang;Bai Xuesong. DISCUSSION OF IMPROVED TRANSONIC POTENTIAL METHOD [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1991, 12(7): 337-344.
[6]	Chen Hongquan;Huang Mingke. AN AF3 ALGORITHM FOR THE CALCULATION OF TRANSONIC NONCONSERVATIVE FULL POTENTIAL FLOWS OVER WINGS OR WING/BODY COMBINATIONS [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1991, 12(5): 234-240.
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