Controlling critical Reynolds number of parallel plate flow by boundary input

Abstract

Purpose

The aim of this study is to modify the critical Reynolds number (Re_cr) which is the critical parameter of the transition from laminar to turbulence regime. The transition to turbulence is delayed by increasing the critical Reynolds number.

Design/methodology/approach

A method to control the critical Reynolds number of viscous flow between parallel plates with an imposed pressure gradient to infinitesimal harmonic disturbances is introduced. The method consists of introducing harmonic perturbations to the lower plate based on skin friction measurements at the upper plate. The size of the introduced harmonic perturbation is chosen to be proportional to the measured skin friction. The proportionality constant is the control parameter for the manipulation of the critical Reynolds number. The resulting eigenvalue problem, similar to the Orr‐Sommerfeld problem, is solved for various values of the control parameter.

Findings

Solution of the eigenvalue problem shows that the critical Reynolds number for the instability with respect to infinitesimal disturbances can be increased from 5,772.22 to 37,900.

Originality/value

The paper demonstrates that it is theoretically possible to increase the critical Reynolds number of parallel plate flow from 5,772.22 to 37,900 by applying a small motion to the bottom plate, the amplitude of the motion being proportional to the skin friction measured at the upper plate.

Citation

Kucur, M. and Uzal, E. (2007), "Controlling critical Reynolds number of parallel plate flow by boundary input", Aircraft Engineering and Aerospace Technology, Vol. 79 No. 5, pp. 507-510. https://doi.org/10.1108/00022660710780632