Marking function of Stokes number on airfoils’ aerodynamic penalties in a gas–solid flow

Abstract

This paper aims to employ the Stokes number to mark aerodynamic penalties of airfoils caused by particles, which is crucial to implement their scaling experiments in a gas-solid flow. Each Stokes number is associated with a series of approximate aerodynamic penalties which are obtained at the same Reynolds number with different chord lengths. In the process, two phenomena which go against the mark are discussed and their mechanisms are revealed. The results show they occur at smaller and larger ranges of Stokes number, respectively. The effect of gravity is the leading cause and a larger chord length or diameter particle can strength its effect. The application scope of the mark, meanwhile, is ascertained. A chord length smaller than 1.5 m is advised at Re = 1.00 × 106 and those at other Reynolds numbers are also presented. As Stokes number decreases from 3, the aerodynamic penalty increases exponentially first at the advised chord length and reaches up to their peak values at the Stokes number of 0.050. In addition, the change of the aerodynamic penalty with Stokes number is dominated by the momentum exchange in the direction of gravity in the region between the particle injection plane and the airfoil.