Analysis of two-dimensional viscous flow over cylinders in unsteady motion

Abstract

The two-dimensional, viscous flow around elliptic cylinders undergoing prescribed rotary and translational motions is analyzed. The fluid is taken to be incompressible and initially at rest. Departing from conventional numerical formulations, the body is replaced by fluid which has a rigid motion exactly the same as the actual solid body. This is achieved by placing a uniform vorticity field within the body (equal to twice the instantaneous angular velocity), and bound vorticity on the body surface in the form of a vortex sheet. The latter distribution is governed by an integral equation. The solution is made unique by the principle of conservation of total vorticity. This depends on the instantaneous angular velocity of the body, the new ingredient to this analysis. The free vorticity in the outer flowfield is governed by the usual vorticity transport equation, which is solved numerically. The velocity field is determined by the velocity induction law. Transient flow results are presented for 1) an elliptic cylinder started impulsively from rest with constant angular velocity, and 2) a pitching elliptic cylinder moving with constant translational velocity. Results for case 1 are compared with those from a previous numerical analysis. Previous results for case 2 are not known. Predictions for the drag, lift, and moment coefficients are given over two complete cycles of oscillation.