The laminar and turbulent mixing of jets of compressible fluid. Part I Flow far from the orifice

Abstract

For flows of jet type, the assumption of a coefficient of eddy kinematic viscosity in turbulent flow leads to the possibility of combining in one the equations for laminar and turbulent motion. An approximation to the solution of these equations is found for the flow of compressible fluid issuing from a narrow slit, far from the slit. The stream function is expanded in a power series in squares of the Mach number. Bickley's solution (1937) for the corresponding problem in incompressible flow is used to start the iterative process by which successive terms of the power series are obtained. In order to find an analytical form for the second term of the series, it has been assumed that the Prandtl number is unity, that the viscosity varies as the nth power of the absolute temperature, and that the stagnation temperature of the jet is the same as that of the surrounding gas. The solution found differs only slightly from that of Howarth (1948) and Illingworth (1949) when laminar flow is considered; only the ‘change of scale’ effect (arising from a distortion of the coordinates in Bickley's solution) is of importance. In turbulent flow the effect of the second term of the series is as important as the ‘change of scale’ effect. The effect of compressibility on the width of the mixing region is discussed for both laminar and turbulent jet flow far from the orifice.