An iterative method for the computation of the response of linearised Navier–Stokes equations to harmonic forcing and application to forced cylinder wakes

Abstract

SUMMARYThe central aim of this paper is the development and application of an efficient, iterative methodology for the computation of the perturbation fields induced by harmonic forcing of the linearised Navier–Stokes equations. The problem is formulated directly in the frequency domain, and the resulting system of equations is solved iteratively until convergence. The method is easily implemented to any implicit code that can solve iteratively the steady‐state Navier–Stokes equations. In this paper, it is applied to investigate the flow around a static cylinder with pulsating approaching flow and a cylinder undergoing forced stream‐wise oscillations. All terms of the perturbation kinetic energy equation are computed, and it is shown that perturbations grow by extracting energy from two sources: the underlying base flow field and the externally provided energy that maintains the imposed oscillation. The periodic drag force acting on the cylinder is also computed, and it is demonstrated that Morrison's equation is a simple model that can estimate with good accuracy the amplitude and phase of this force with respect to the approaching flow. The perturbation fields induced by periodic inlet flow (static cylinder) and forced stream‐wise cylinder oscillation are closely related: the velocity fields are identical in the appropriate reference frames, and a simple expression is derived, which links the pressures in the two flow cases. Copyright © 2014 John Wiley & Sons, Ltd.