气动力学基本方程中的粘性项在非正交曲线坐标系内展开式的简化
Simplification of the Expansions of Viscous Terms in Basic Aerodynamic Equations in Non-Orthogonal Curvilinear Coordinate System
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摘要: 采用任意曲线坐标系可使具有复杂边界的流场计算大大地简化,并且可提高计算精度。所以,将气体动力学基本方程中的粘性项(粘性力、粘性应力作功率和消散函数)在该座标系中展开显得十分必要。然而,适用于变粘性系数可压流体的粘性项展开式由几十项甚至上百项组成。本文经过量阶分析将粘性项展开式进行了大大地简化。Abstract: The application of non-orthogonal curvilinear coordinate system to the calculation of the flow field inside the channel,with complex boundary geometry,can effectively simplify the work of designing the calculation program and improve the accuracy of calculation[1].Therefore,it is obviously necessary to expand the viscous terms,i.e.viscous force,rate of work done by viscous stress and dissipation,in basic aerodynamic equations in the non-orthogonal curvilinear system[2].However,each of these expansions consistes of tens or even hundreds of algebraic terms.The expansions of these three viscous terms discribed in this paper are considerably simplified by analysing their order of magnitude.
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[1] 吴仲华,使用非正交曲线坐标系和非正交速度分量的叶轮机械三元流动基本方程及其解法,机械工程学报,15.1(1979),1-23. [2] 王仲奇、康顺,气动力学基本方程中的粘性项在非正交曲线坐标系中的展开式及其数值微分方法,工程热物理学报,8,2(1985),142-144. [3] 陈乃兴,叶轮机械粘性气体气动热力学的若干问题-粘性项、传热项及基本方程的求解途径,中国科学,A辑,第10期(1983),958-988. -
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