Analytical and Experimental Investigation of a Turbulent Mixing Layer of Different Gases in a Pressure Gradient

Abstract

An analytical and experimental study has been made of the turbulent mixing layer in a pressure gradient. Theory predicts the possible existence of equilibrium flows, and this was confirmed experimentally for turbulent shear layers between streams of helium and nitrogen. The only case for which similarity is possible is for ρ_2U_2%2 = ρ_1U1^2, since then P_2(x) = P_1(x). These equilibrium flows are of the form U_1 ~ x^α and δ ~ x where α = u/U-1 dU_1/dx is a non-dimensional pressure gradient parameter. The experimental investigation was conducted in the facility designed by Brown to produce turbulent flows at pressures up to 10 atmospheres. The adjustable walls of the test section of the apparatus were modified in order to set the pressure gradient. Shadowgraphs of the mixing zone for α = 0 and α = - 0.. 18, at different Reynolds numbers, revealed a large scale structure noticeably different for each α. The similarity properties of the shear layer were established from mean profiles of total head and density. In addition, the rms density fluctuations were found to be self-preserving. From the mean profiles, the spreading rate, turbulent mass diffusion, Reynolds stress and Schmidt number distributions were calculated from the equations of motion. The experimental results show that the spreading rate for the adverse pressure gradient is 60% greater than for the α = 0 case. The maximum shearing stress is 70% larger and the maximum value of the turbulent mass diffusion is 20% larger than their α = 0 counterparts. The maximum rms density fluctuations are approximately O.2 in both flows. Surprisingly low values of turbulent Schmidt numbers were found; e.g. , at the dividing streamline Sc_t ~ 0.16 for α = 0 and Sc_t = 0.33 for α = -0.18.

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