Similarity solutions of compressible flow over a rotating cone with surface suction

P.D Towers,S.J Garrett

doi:10.2298/tsci130408032t

Abstract

We present solutions of the laminar compressible boundary-layer flows over the family of rotating cones subject to surface mass flux. The work is a generalization of previous studies of the compressible rotating-disk flow and incompressible rotating-cone flow without surface mass flux. Transformations are used which lead to a system of generalized von Karman equations with boundary conditions parameterized by half-angle and a mass-flux parameter. Results are discussed in terms of wall temperature and local Mach number in the particular case of air, although the formulation is readily extended to other fluids. It is suggested that suction acts a stabilizing mechanism, whereas increased wall temperature and local Mach number have destabilizing influences.

Highlights

There have been many experimental and theoretical studies seeking to identify and understand the various instability mechanisms found in rotating 3-D boundary-layer flows
Experimental work by Kreith et al [5] as well as Tien and Campbell [6] has led to the recent theoretical studies of Garrett [7, 10], Garrett and Peake [8], Garrett et al [9, 11], and Hussain et al [12] wich are made progress in understanding the stability characteristics of the incompressible boundary-layer flow over rotating cones
We begin by considering the simple case of zero surface mass flux and set a = 0

Summary

Introduction

There have been many experimental and theoretical studies seeking to identify and understand the various instability mechanisms found in rotating 3-D boundary-layer flows. The motivation for this particular study is to generalize this body of previous work to examine the effect of compressibility on the boundary-layer flow over a rotating cone with general half-angle, ψ. Work into the stability of the incompressible boundary-layer flows over rotating cones [7,8,9] has shown that the normal component has only a marginal qualitative effect on the stability properties.

Results

Conclusion