一种改进的计算压力分布的格林函数方法
收稿日期: 2014-07-06
修回日期: 2014-08-07
网络出版日期: 2014-09-17
基金资助
总装预研基金 (9140A25010312HK03295)
An improved Green's function method for pressure distribution calculations
Received date: 2014-07-06
Revised date: 2014-08-07
Online published: 2014-09-17
Supported by
National Defence Pre-research Foundation of China (9140A25010312HK03295)
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。
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. DOI: 10.7527/S1000-6893.2014.0209
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
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