Effect of velocity ratio on plane mixing layer development: Influence of the splitter plate wake

An experimental study has been conducted to investigate the effect of velocity ratio on the approach of a plane mixing layer to self-similarity. Plane mixing layers with five different velocity ratios (0.5, 0.6, 0.7, 0.8 and 0.9) were generated in a newly designed mixing layer wind tunnel with both initial boundary layers tripped. For each velocity ratio, mean flow and turbulence measurements were obtained at eight streamwise locations with a single cross-wire probe. The results indicate that the splitter plate wake plays a very dominant and, in some cases, a lasting role in the development of the mixing layer. For velocity ratios between 0.5 and 0.7, self-similarity of the mixing layer was observed with the asymptotic states comparable. Mixing layers with the higher velocity ratios failed to achieve a self-similar state within the measurement domain, although a slow approach to it was apparent. The development distance decreased with increasing velocity ratio up to 0.7, after which it appeared to increase. Almost all of the observed effects may be attributed to the presence of the splitter plate wake and its complex interaction with the mixing layer.List of symbols C _f boundary layer skin friction coefficient - H boundary layer shape factor - r velocity ratio of the two streams, (=U ₂/U ₁) - Re _L Reynolds number, (=UL/v) - R correlation coefficient in least squares fit - U, V, W mean velocity in the X, Y, Z directions, respectively - U ^* velocity parameter, =(U–U ₂)/(U ₁–U ₂)] - U ₀ velocity difference, (=U ₁–U ₂) - U _e free-stream velocity in the wind tunnel - u, , w fluctuating velocity components in the X, Y, Z directions, respectively - u, , w instantaneous velocity in the X, Y, Z directions, respectively, e.g. u=U+u - X ₀ virtual origin of the mixing layer - X, Y, Z cartesian coordinates for streamwise, normal, and spanwise directions, respectively - Y ₀ centerline of mixing layer from error function fit - mixing layer width from error function fit - ₉₉ initial boundary layer thickness - similarity coordinate =(Y–Y ₀)/] - initial boundary layer momentum thickness - modified velocity ratio =(1–r)/(1+r)] - _n initial instability wavelength in the mixing layer - spreading parameter =1/(d/dX)] - ₀ spreading parameter for single-stream mixing layer - - (overbar) Time-averaged quantity - ( )_max maximum value at given X-station - ( )_min minimum value at given X-station - ( )₁ value for high-speed side - ( )₂ value for low-speed side