球面间流体流动考虑流动惯性的近似解
An Approximate Solution Considered Flow Inertia between Spherical Surfaces
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摘要: 本文利用球坐标下的Navier-Stokes方程式,采用迭代近似解法,求出了考虑流动惯性时的球面间流动的压力分布、速度分布以及流量的解析式。并利用此式可直接导出平行圆板间径向层流的相应解析表达式,它与文献[3],[4]中所提供的相应结果是完全一致的。Abstract: In this paper, the analytical expressions of the pressure distribution, velocity distribution and volume flue of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms in Navier-Stokes equation of the spherical coordinates are taken into consideration, Furthermore, using these egpressions, we may directly obtain the corresponding analytical expressions of the radial laminar flow between parallel disks, which are fully unified with corresponding results presented from references [3.4].
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[1] 川崎义人,空气轴受に就て,精密机械,Ⅻ5,6,7(昭和22年,5, 6.7,No.152, 153, 154,p39-44. [2] Goldstein, S,Modern Developments in Fluid Dynamics, Oxford University Press,Amen House, London, Vol, I,(1938),105. [3] Savage, S, D,Laminar radial flow between parallel plates, Trans, of the ASME,1. Appl, Mech,86, Ser, c-4 (Dec,1964). 594-596. [4] 郭金基,平行平板间径向气流的Navier-Stokes方程的近似解,力学学报,3(1980). 306-310. [5] 平克斯,O.,B,斯德因李希,(英),《流体动力学润滑理论》,机械工业出版社(1980). [6] Moller, P, S,Radial Flow without Swirl between Parallel Disks, M, Sc, Thesis,Department of Mechanical Engineering, Megill University, Montreal, Canada (1961). -
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