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

流体力学与飞行力学

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一种改进的计算压力分布的格林函数方法

刘千刚, 周洲

西北工业大学无人机特种技术重点实验室, 西安 710065

收稿日期:2014-07-06 修回日期:2014-08-07 出版日期:2015-06-15 发布日期:2014-09-17
通讯作者: 刘千刚 Tel.: 029-88493371 E-mail: liuqg@163.com E-mail:liuqg@163.com
作者简介:刘千刚男, 教授, 博士生导师。主要研究方向: 空气动力学和飞行力学。 Tel: 029-88493371 E-mail: Liuqg0419@163.com;周洲女, 博士, 教授, 博士生导师。主要研究方向: 无人机总体、气动布局设计等。 Tel: 029-88453368 E-mail: zhouzhou@mail.nwpu.edu.cn
基金资助:
总装预研基金 (9140A25010312HK03295)

An improved Green's function method for pressure distribution calculations

LIU Qiangang, ZHOU Zhou

Science and Technology on UAV Laboratory, Northwestern Polytechnical University, Xi'an 710065, China

Received:2014-07-06 Revised:2014-08-07 Online:2015-06-15 Published:2014-09-17
Supported by:
National Defence Pre-research Foundation of China (9140A25010312HK03295)

摘要/Abstract

摘要：

对计算压力分布的格林函数方法作了一定的改进,虽然格林函数方法能给出比较准确的速势分布计算,但在压力分布的计算方面却比较欠缺,只给出了一个根据离散点上的速势值进行有限差分计算的简单的公式,采用这个公式无法算出物面准确的压力分布。鉴于此,通过对速势积分方程离散化后所得到的扰动速势的解析表达式进行微分运算,得到一组计算扰动速势导数的解析公式,并由此计算了物面上各离散点上的压力系数,其结果相当准确,与Navier-Stokes方程算法及实验结果相比,均吻合较好。另外,还对库塔条件在数值求解速势积分方程中的应用作了一定的改进,使计算结果更加准确。

关键词: 格林函数, 势流, 唯一性, 压力系数, 库塔条件

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

中图分类号:

V211.3

刘千刚, 周洲. 一种改进的计算压力分布的格林函数方法[J]. 航空学报, 2015, 36(6): 1744-1751.

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

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E-mail：hkxb@buaa.edu.cn

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一种改进的计算压力分布的格林函数方法

An improved Green's function method for pressure distribution calculations

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