2021/01/03 by Saurabh S. Sawant, Sawant, Saurabh S., Deborah A. Levin +3
Engineering · Mathematics · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.2101.00664
openalex publication_date 2021/01/03 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28
Linear instability of high-speed boundary layers is routinely examined\nassuming quiescent edge conditions, without reference to the internal structure\nof shocks or to instabilities potentially generated in them. Our recent work\nhas shown that the kinetically modeled internal nonequilibrium zone of straight\nshocks away from solid boundaries exhibits low-frequency molecular\nfluctuations. The presence of the dominant low frequencies observed using the\nDirect Simulation Monte Carlo (DSMC) method has been explained as a consequence\nof the well-known bimodal probability density function (PDF) of the energy of\nparticles inside a shock. Here, PDFs of particle energies are derived in the\nupstream and downstream equilibrium regions, as well as inside shocks, and it\nis shown for the first time that they have the form of the non-central\nchi-squared (NCCS) distributions. A linear correlation is proposed to relate\nthe change in the shape of the analytical PDFs as a function of Mach number,\nwithin the range 3 \≤ M \≤ 10, with the DSMC-derived average characteristic\nlow-frequency of shocks, as computed in our earlier work. At a given Mach\nnumber M=7.2, varying the input translational temperature in the range 89\n\≤ Ttr,1/(K) \≤ 1420, it is shown that the variation in DSMC-derived\nlow-frequencies is correlated with the change in most-probable-speed inside\nshocks at the location of maximum bulk velocity gradient. Using the proposed\nlinear functions, average low-frequencies are estimated within the examined\nranges of Mach number and input temperature and a semi-empirical relationship\nis derived to predict low-frequency oscillations in shocks. Our model can be\nused to provide realistic physics-based boundary conditions in receptivity and\nlinear stability analysis studies of laminar-turbulent transition in high-speed\nflows.\n