Motion of particles with inertia in a compressible free shear layer

Abstract

The effects of inertia of a particle on its flow tracking accuracy and particle dispersion are studied using direct numerical simulations of two-dimensional compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6. The results show that particle response is well characterized by τ, the ratio of particle response time to the flow time scale (Stokes’ number). The slip between particle and fluid imposes a fundamental limit on the accuracy of optical measurements such as LDV and PIV. The error is found to grow like τ up to τ=1 and taper off at higher τ. For τ=0.2 the error is about 2%. In the flow visualizations based on Mie scattering, particles with τ>0.05 are found to grossly misrepresent the flow features. These errors are quantified by calculating the dispersion of particles relative to the fluid. The trend in lateral dispersion of particles is similar to that of incompressible flows reported by previous investigators. Overall, the effect of compressibility does not seem to be significant on the motion of particles in the range of Mc considered here.