An analytic solution of Navier–Stokes flow past a sphere in the region of intermediate Reynolds number

IF 1.3 4区工程技术 Q3 MECHANICS Fluid Dynamics Research Pub Date : 2023-07-18 DOI:10.1088/1873-7005/ace846

Yuki Yagi, K. Yabushita, Hiroyoshi Suzuki

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Abstract

We study an analytical solution of steady, laminar, and incompressible flow past a sphere in the region of intermediate Reynolds number. The flow is governed by the Navier–Stokes (N–S) equation and the continuity equation. By applying a simple perturbation method to solve the equations, a second-order approximation cannot be obtained, as well-known (Whitehead’s paradox). Many analytical studies, such as Oseen approximation, matching technique, the homotopy analysis method, etc, have been conducted to resolve the paradox. The drag coefficients of these solutions are valid in the region of Reynolds number Rd<30 (R d is the diameter-based Reynolds number) However, the solution cannot express the flow separation behind a sphere observed in experiments. We also develop a perturbation technique to construct a solution of the N–S equation asymptotically to solve the paradox. The solution consists of power series of Rdh , where h is an arbitrary constant (0

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中等雷诺数区域内Navier-Stokes流通过球体的解析解

本文研究了在中间雷诺数区域内通过球体的稳定、层流和不可压缩流的解析解。流动由Navier-Stokes (N-S)方程和连续性方程控制。用简单的微扰法求解方程，不能得到二阶近似，这是众所周知的(Whitehead悖论)。为了解决这一悖论，人们进行了许多分析研究，如Oseen近似、匹配技术、同伦分析法等。这些解的阻力系数在雷诺数Rd<30 (Rd为基于直径的雷诺数)范围内有效，但不能表达实验中观察到的球后流动分离。我们还开发了一种微扰技术来构造N-S方程的渐近解来解决悖论。解由Rdh的幂级数组成，其中h是任意常数(0

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来源期刊

Fluid Dynamics Research 物理-力学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

5 months

期刊介绍： Fluid Dynamics Research publishes original and creative works in all fields of fluid dynamics. The scope includes theoretical, numerical and experimental studies that contribute to the fundamental understanding and/or application of fluid phenomena.