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半正交曲线坐标系下三维不可压边界层的一种差分解法

FINITE DIFFERENCE METHOD FOR CALCUL ATING THREE- DIMENSIONAL INCOMPRESSIBLE BOUNDARY LAYER IN CURVILINEAR SEMI- ORTHOGONAL COORDINATES
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摘要 本文提出一种三维不可压边界层的差分解法。此法中采用了半正交曲线坐标系和涡粘性各向异性的湍流模型,数值分析中采用了变换域和Keller分块差分格式。用本法计算了一个三维边界层实例,计算结果同实验数据吻合得很好。 After nearly a centry development of boundary layer theory and calculation, research work has now mainly been focused on two subjects, three-dimensional boundary layer and its separation. On the firsts object many researchers, for example, J.F. Nash, T. Cebeci, V. N. Vatsa and O. L. Anderson calculated three-dimensional boundary layer by using the implicit difference scheme. In the present computation of three-dimensional incompressible laminar and turbulent boundary layers a finite difference method is presented. In the calculation the curvilinear semi-orthogonal coordinate system, in which the x-coordinate is along the mainflow direction, the z-coordinate along the crossflow direction and the y-coordinate perpendicular to the x-z surface, is used to express three-dimensional boundary layer equations. Meanwhile it is not necessary for the angle θ between x and z coordinate axes to be right for simulating the real flow condition. In order to set up this coordinate system methods in numerical fitting of twisted blade surfaces and an automatic generation system are applied.For the laminar boundary layer Reynolds' stresses are assumed to be zero. And for the turbulent one the Reynolds' stresses are expressed through an algebraic turbulence model considering non-isotropic eddy viscosity based on Cebeci-Smith turbulence model and Rottta' s turbulent stress formulas. In the model a coefficint T is a constant reflecting the ratio of velocities along x- and z-directions, i. e., the anisotropy of Reynolds' stresses.The numerical solution for three-dimensional boundary layers was carried out in the following procedures. First, the convenient useful transformation for three-dimensional boundary layers presented by T. Cebeci et al. was used with a two-component vector potential. Then the box method of Keller was applied, which had second order acuracy. It involves four steps: simplifing the governing equations to a system of first order ones; writing difference equations with central difference, schemes; linearizing the resulting algebraic equations and solving the linear system by using a block tridiangonal elimination method.The Calculation was carried out for a three-dimensinal boundary layer of a wing measured by L. F. East and R. P. Hoxey. Calculated results indicate the distributions of friction coefficient, pressure coefficient, momentum thinknesses and displacement thicknesses in the mainflow and crossflow directions along the blade surface at the position of z=0.152m. Calculated results are found to be in good agreement with measured data by East and Hoxey, and are compared with computed results by M. Formery. In fact, the present method and computer programme has the advantages of high accuracy, less storage in computer, fast computation speed and flexibility in use.
机构地区 清华大学
出处 《空气动力学学报》 CSCD 北大核心 1991年第2期233-242,共10页 Acta Aerodynamica Sinica
关键词 三维边界层 数值分析 湍流模型 three-dimensional boundary layer, numerical calculation, turbulence model.
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