An Analytical and Experimental Study of the Plane, Incompressible, Turbulent Free-Shear Layer With Arbitrary Velocity Ratio and Pressure Gradient

Abstract

A first-order approximation is derived in similarity coordinates for the velocity variation across a mixing zone between two streams of different velocities in an arbitrary pressure grudient. The velocity profiles obtained are functions of a single parameter, the ratio of the velocity of the slow stream to that of the fast stream. The first-order velocity profiles are compared to those obtained from the complete solution to the zero-pressure-gradient case obtained by Go¨rtler and good agreement is found when the velocity ratio is greater than 0.5. The form of the eddy diffusivity appropriate to the first-order theory is determined from analysis and experimental data. This form leads to an explicit transformation for the similarity coordinate requiring only a single empirical constant for all cases.

Effect of shear on Rayleigh-Taylor mixing at small Atwood number

“…A summation of the first two terms in this solution, and neglecting all other terms, is considered by many researchers to be accurate enough for all practical purposes. Using a similar approach, Sabin [17] derived a first order approximate solution with a pressure gradient for the plane mixing layer problem that compared well with the zero pressure gradient solution of Goertler [16] at lower velocity ratios. He suggested the use of the same eddy viscosity for all pressure gradients from his experimental work, and he quantified the dependence of mixing layer spreading rate on the velocity ratio (velocity of slow moving stream/velocity of fast moving stream) between the two streams.…”

Turbulent Free Shear Layer Mixing and Combustion

“…9 as a local relation. The argument, which was suggested by M. Koochesfahani and is akin to some of the ideas put forth by Sabin (1965), is summarized below.…”

“…The effects of pressure gradient on shear layer growth were discussed by Sabin (1965) and have been investigated in non-reacting shear layers (Rebollo 1973), and in reacting shear layers (Keller andDaily 1985, Hermanson andDimotakis 1989) for incompressible flow conditions. In the case of a favorable pressure gradient (dp/dx < 0) and equal free stream densities (s = P2/PI = 1), it was found (Hermanson and Dimotakis 1989) that the decrease in the growth could be accounted by interpreting Eq.…”

“…2.1 Dependence on the velocity and density ratio Abramowich (1963) and Sabin (1965) proposed an expression for the shear-layer growth rate given by 6 ; C6 -i (9) x l+r where Cb is taken as a constant. This is an expression that can be argued for on similarity grounds,* and is found to be in reasonable accord with experimental data of incompressible shear layers with equal freestream densities.…”

Flow physics of a hypervelocity mixing wake with oxygen enrichment

“…One of the major differences between the mixing layer and other free shear flows is that the velocity difference remains constant as the flow travels down-stream. The velocity difference, in combination with a length scale, is a standard mixing layer normalisation parameter (Sabin, 1965):…”