A kinetic approach to studying low-frequency molecular fluctuations in a one-dimensional shock

Abstract

Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterized for the first time in a kinetic collisional framework in the Mach number range 2 ≤ M ≤ 10. Our analysis draws upon the well-known bimodal nature of the probability density function (PDF) of gas particles in the shock, as opposed to their Maxwellian distribution in the freestream, the latter exhibiting two orders of magnitude higher dominant frequencies than the former. Inside the (finite-thickness) shock region, the strong correlation between perturbations in the bimodal PDF and fluctuations in the normal stress suggests introducing a novel two-bin model to describe the reduced-order dynamics of a large number of collision interactions of gas particles. Our model correctly predicts two orders of magnitude differences in fluctuation frequencies in the shock vs those in the freestream and is consistent with the small-amplitude fluctuations obtained from the highly resolved direct simulation Monte Carlo computations of the same configuration. The variation of low-frequency fluctuations with changes in the conditions upstream of the shock revealed that these fluctuations can be described by a Strouhal number, based on the bulk velocity upstream of the shock and the shock-thickness based on the maximum density gradient inside the shock, that remains practically independent of Mach number in the range examined.