Theoretical investigation on the impact of an oscillating time-dependent pressure gradient on Dean flow in a porous annulus

Abstract

In this article, a theoretical analysis on flow in a curvilinear horizontal coaxial cylinder with permeable walls has been proposed. Specifically, the transient impact of an oscillating pressure gradient has been taken into account. The non-linear time-dependent partial differential equation accountable for the flow has been transformed using the classical Laplace transform technique. Exact solution of the momentum equation has been obtained in Laplace domain. Due to the intricacy of the Laplace domain solutions, a numerical inversing technique which is established upon the Riemann-sum approximation (RSA) has been utilized to transform the Laplace domain solutions to time domain. Findings reveal that the outcome of suction on the porous walls and boosting the frequency of oscillation renders skin frictions on both walls of the cylinder less effective. The instability of the Dean vortices in the annular gap can be suppressed by amplifying the frequency of oscillating pressure gradient while time is maintained.

Keywords

• Annulus
• Dean flow
• Oscillating time-dependent pressure gradient
• Riemann-sum approximation (RSA)