No abstract

This paper investigates the influence of different broadband perturbations on the evolution of a Richtmyer-Meshkov turbulent mixing layer initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3:1. Both the bandwidth of modes in the interface perturbation, as well as their relative amplitudes, are varied in a series of carefully designed numerical simulations at grid resolutions up to 3.2×10 9 cells. Three different perturbations are considered, characterised by a power spectrum of the form P (k) ∝ k m where m = −1, −2 and −3. The growth of the mixing layer is shown to strongly depend on the initial conditions, with the growth rate exponent θ found to be 0.5, 0.63 and 0.75 for each value of m at the highest grid resolution. The asymptotic values of the molecular mixing fraction Θ are also shown to vary significantly with m; at the latest time considered Θ is 0.56, 0.39 and 0.20 respectively. Turbulent kinetic energy (TKE) is also analysed in both the temporal and spectral domains. The temporal decay rate of TKE is found not to match the predicted value of n = 2 − 3θ, which is shown to be due to a time-varying normalised dissipation rate C . In spectral space, the data follow the theoretical scaling of k (m+2)/2 at low wavenumbers and tend towards k −3/2 and k −5/3 scalings at high wavenumbers for the spectra of transverse and normal velocity components respectively. The results represent a significant extension of previous work on the Richtmyer-Meshkov instability evolving from broadband initial perturbations and provide useful benchmarks for future research.

Early to intermediate time behaviour of the planar Richtmyer-Meshkov instability (RMI) is investigated through direct numerical simulation (DNS) of the evolution of a deterministic interfacial perturbation initiated by a Ma = 1.84 shock. The model problem is the well studied initial condition from the recent θ-group collaboration [Phys. Fluids. 29 (2017) 105107]. A grid convergence study demonstrates that the Kolmogorov microscales are resolved by the finest grid for the entire duration of the simulation, and that both integral and spectral quantities of interest are converged. Compar-isons are made with implicit large eddy simulation (ILES) results from the θ-group collaboration, generated using the same numerical algorithm. The total amount of turbulent kinetic energy (TKE) is shown to be decreased in the DNS compared to the ILES, particularly in the transverse directions, giving rise to a greater level of anisotropy in the flow (70% vs. 40% more TKE in the shock parallel direction at the latest time considered). This decrease in transfer of TKE to the transverse components is shown to be due to the viscous suppression of secondary instabilities. Overall the agreement in the * large scales between the DNS and ILES is very good and hence the mixing width and growth rate exponent θ are very similar. There are substantial differences in the small scale behaviour however, with a 38% difference observed in the minimum values obtained for the mixing fractions Θ and Ξ.Differences in the late time decay of TKE are also observed, with decay rates calculated to be τ −1.41 and τ −1.25 for the DNS and ILES respectively.

Abstract

Typical multispecies compressible Navier-Stokes computations employ conservative equations for mass fraction transport. Upwind discretisations of these governing equations produce spurious pressure oscillations at diffuse contact surfaces between gases of differing ratio of specific heat capacities which degrade the convergence rate of the algorithm. Adding quasi-conservative equations for volume fraction can solve this error, however this approach has been derived only for immiscible fluids.Here, a five-equation quasi-conservative model is proposed that includes the effects of species diffusion, viscosity and thermal conductivity. The derivation of the model is presented, along with a numerical method to solve the governing equations at second order accuracy in space and time. Formal convergence studies demonstrate the expected order of accuracy is achieved for three benchmark problems, crossvalidated against two standard mass fraction models. In these test cases, the new model has between 2 and 10 times lower error for a given grid size. Simulations of a two-dimensional air-SF 6 Richtmyer-Meshkov instability demonstrate that the new model converges to the solution with four times fewer points in each direction when compared to the mass fraction model in an identical numerical framework. This represents an ≈ 40 times lower computational cost for an equivalent error in two-dimensional computations. The proposed model is thus very suitable for Direct Numerical Simulation and Large Eddy Simulation of compressible mixing.