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Weak inertial effects on arbitrarily shaped objects in the presence of a wall
Physical Review Fluids ( IF 2.7 ) Pub Date : 
Forest O. Mannan and Karin Leiderman

The Navier-Stokes equations are greatly simplified when the Reynolds number, Re, tends to zero and inertial effects become negligible. A plethora of relevant, real-world flows occur at small but non-zero Re and these flows are generally well approximated by the simplified Stokes equations. However, the simplification to Stokes equations means important qualitative features that are inertial in origin may be lost. One approach to capture inertial effects such as lift, for small Re, without wholly having to consider the full Navier-Stokes equations, is to consider a complimentary problem using an asymptotic expansion in Re; here inertial corrections are represented by the O(Re) terms. Research in this direction has mainly employed analytic approaches and thus relied on simple, symmetric shapes of any objects in the fluid, such as spheres. Here, we extend this work and present a numerical approach to compute the analytic expressions for weak, inertial lift on arbitrarily shaped objects moving in a fluid near a wall. Specifically, we use the Method of Regularized Stokeslets to solve two, distinct Stokes equations systems that arise in the complimentary problem. We compute the lift on these objects due to pure translation, pure rotation, and coupled translation and rotation, for various orientations and distances from the wall. The method is validated by comparing to previous analytical results for a sphere and then used to compute inertial lift on two adjacent spheres (dimer), as well as prolate and oblate spheroids.

中文翻译:

有墙时对任意形状物体的惯性作用弱

当雷诺数时,Navier-Stokes方程被大大简化, [RË趋于零,惯性效应可忽略不计。大量相关的,真实的流量发生在很小但非零的情况下[RË这些流量通常可以通过简化的斯托克斯方程很好地近似。但是,简化到斯托克斯方程意味着可能失去原点惯性的重要定性特征。捕获惯性效应(例如升力)的一种方法[RË,而不必完全考虑完整的Navier-Stokes方程,而是考虑使用一个渐近展开式 [RË; 这里惯性校正由Ø[RË条款。在这个方向上的研究主要采用分析方法,因此依赖于流体中任何物体(例如球体)的简单,对称形状。在这里,我们扩展了这项工作,并提出了一种数值方法来计算在壁附近的流体中运动的任意形状物体上的弱惯性升力的解析表达式。具体来说,我们使用正则Stokeslets方法来求解互补问题中出现的两个不同的Stokes方程组。由于壁的各种方向和距离,我们通过纯平移,纯旋转以及耦合的平移和旋转计算这些对象的升力。通过与一个球体的先前分析结果进行比较来验证该方法,然后将该方法用于计算两个相邻球体(二聚体)以及扁球和扁球体的惯性升力。
更新日期:2020-03-05
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