A Simplified Model Predicting the Kelvin–Helmholtz Instability Frequency for Laminar Separated Flows

Abstract

A semi-empirical model for the estimation of the Kelvin–Helmholtz (KH) instability frequency, in the case of short laminar separation bubbles over airfoils, has been developed. To this end, the Thwaites's pressure gradient parameter has been adopted to account for the effects induced by the aerodynamic loading distribution as well as by the Reynolds number on the separated shear layer thickness at separation. The most amplified frequency predicted by linear stability theory (LST) for a piecewise linear profile, which can be considered as the KH instability frequency, has been related to the shear layer thickness at separation, hence to the Reynolds number and the aerodynamic loading distribution through the Thwaites's pressure gradient parameter. This procedure allows the formulation of a functional dependency between the Strouhal number of the shedding frequency based on exit conditions and the dimensionless parameters. Experimental results obtained in different test cases, characterized by different Reynolds numbers and aerodynamic loading distributions, have been used to validate the model, as well as to identify the regression curve best fitting the data. The semi-empirical correlation here derived can be useful to set the activation frequency of active flow control devices for the optimization of boundary layer separation control strategies.