Balance of Kinetic Energy in a Supersonic Mixing Layer Compared to Subsonic Mixing Layer and Subsonic Jets with Variable Density

Abstract

In recent years, a lot of experimental and computational work was done to study the effect of compressibility on turbulent free flows. In particular, the supersonic mixing layer was extensively studied (see (Lele, 1994) for a review). Despite all these efforts it seems that, at this time, nobody knows yet what is the real mechanism which creates the compressiblity effects observed on supersonic free flows like mixing layers or jets. It has been observed by many experimentalists that the turbulent intensity is decreased while increasing compressibility. Different authors tried to explain this fact in order to be able to take in account these effects in modelling such flows. For example Zeman (1990) and Sarkar et al. (1989) both proposed a model based on an extra dissipation due to dilatation to explain the observed decrease of turbulent activity in high speed flows. Applications of such models to mixing layer computations described qualitatively the flow but the results are not accurate enough to make these models available for practical applications (Sarkar & Balakrishnan, 1990). Trying to understand what the real differences are between compressible and incompressible turbulence seems to be an interesting first step to increase our knowledge. So, we decided to measure with 2D Laser Doppler Velocimetry, a preliminary turbulent kinetic energy budget in a highly compressible mixing layer (convective Mach number close to 1) with assumptions derived from the work of different authors ((Panchapakesan & Lumley, 1993), (Wygnanski & Fiedler, 1970) and (Gruber et al., 1993)). Then we compare it to the balance obtained in subsonic jets or mixing layers with and without density gradients.