Modeling the amplitude growth of Richtmyer–Meshkov instability in shock–flame interactions

Abstract

This paper discusses the shock–flame interactions and the aspects associated with it, including the types of interactions, role of interactions in turbulent flames, high pressure generation during interactions, initial pressure effects on interactions, equivalence ratio effects on turbulent interactions, and the Richtmyer–Meshkov instability (RMI). In particular, the theory of RMI and the models associated with its amplitude growth with time have been discussed. Then, a new analytical model, Al-Thehabey model, is presented based on the impulsive acceleration of Richtmyer, not the gravitational acceleration. This model predicts the amplitude growth of the interface perturbation in terms of Atwood number (A), wave number of the perturbation (k), interface velocity (uc), and time (t). This new model’s prediction of the amplitude growth of the RMI is tested on six different combinations of fluids at different interface velocities. The results of the new model are compared with the results of four other existing analytical models and the new model’s performance fared very well. In addition, the new model’s performance has been compared with the experimental results from a shock wave incident on CO2–air, at Mach number, M = 3.08, interface velocity, u = 699.1 m/s, Atwood number, A = 0.206, and wavelength, λ = 990.0 × 10−6 m. The new model showed much closer results with the experimental ones than all other models used in the evaluation. The advantage of this new model is that it is capable of predicting the amplitude growth for both linear, at the early stages of the instability, and non-linear later regimes of the instability. In addition, it covers a larger time-domain than both the Alon et al. and the Sadot et al. models.