Immersed boundary method for the problem of interaction between elliptic body and viscous fluid flow

Kutateladze Institute of Thermophysics, Siberian Branch of the RAS, 630090, Ac. Lavrentiev ave., 1, Novosibirsk, Russia

^* Corresponding author: d.kuranakov@g.nsu.ru

Abstract

Immersed boundary method is developed for the problem of interaction between elliptic body and viscous fluid flow. The method consists in independent considering fluid flow on the Euler grid and immersed body movement using the Lagrangian grid. Special force of fluid-particle interaction is introduced to fulfill the no-slip boundary condition. The model has been used to investigate the influence of the shape and orientation of immersed body on the fluid flow in case of moderately high Reynolds number. Two problem statements have been considered: flow past the fixed immersed body in rectangular channel and particle sedimentation in rectangular vessel. Sedimentation of the elliptical particle tends to the quasistationary oscillation regime regardless of initial orientation of the body. The elliptical particle tends to rotate to the equilibrium orientation in such a way that its semi-major axis is orthogonal to the flow direction. This fact has been approved by analyzing the value of the torque acting on the fixed elliptical particle turned at asymmetrical angles relative to the fluid flow. Asymmetrical orientation of the fixed elliptical body leads to non-zero value of average lift force and torque, and causes non-sinusoidal oscillations of the drag force and torque. The values of force and torque oscillations are the largest in case of particle orientation across the fluid flow streamlines.