Turbulent energy flux generated by shock/homogeneous-turbulence interaction

Abstract

High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modelling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the postshock turbulent energy flux is predicted to be strongly dependent on the angle of incidence of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available data from direct numerical simulations. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.

Numerical prediction of shock/boundary-layer interactions at high Mach numbers using a modified Spalart–Allmaras model

“…The numerical scheme (WENO) as implemented by Zhang et al (2017) can further improve the heat flux distribution in the separation region from 2.3 to 2.36 m as observed in Figure 11. Also, the scheme is better able to resolve the pressure distribution in the plateau region In a recent work, the turbulent-energy heat flux for isotropic homogeneous shock-turbulence interaction was modeled in terms of varying Prandtl number and the results matched the DNS data accurately Quadros, Sinha & Larsson, 2016). This model when implemented on oblique shock/boundarylayer interaction flows at Mach 5 improved the heattransfer predictions in the reattachment region (Roy, Pathak, & Sinha, 2018).…”

Effect of equivalence ratio fluctuations on planar detonation discontinuities

“…Note that near-field profiles are computed for purely inviscid flows. Depending on the particular conditions, there may exist another contribution coming from viscous dissipation that may not be neglected, as noted in Quadros et al (2016) and Sethuraman et al (2018).…”

Interaction of two-dimensional spots with a heat releasing/absorbing shock wave: linear interaction approximation results

“…This decomposition has been extended by splitting the vorticity mode as the sum of a poloidal and a toroidal components , and also considering a binary mixture of perfect gas (Griffond 2005(Griffond , 2006. Several cases have been succesfully investigated using LIA, among which the case of an upstream entropy spot (Fabre et al 2001), upstream vortical isotropic turbulent field (Lee et al 1993(Lee et al , 1997Quadros et al 2016), upstream isotropic acoustic turbulent field (Mahesh et al 1995), upstream isotropic mixed vortical-entropy turbulent field (Mahesh et al 1997).…”

“…It is worth noting that in the case of an upstream turbulent field, LIA can be rewritten in terms of turbulent fluxes, leading to a linear problem for the jump of these quantities across the shock. These relations can be used to derive RANS models well suited for the simulation of the shock-turbulence interaction (Sinha et al 2003;Griffond et al 2010;Soulard et al 2012;Sinha 2012;Quadros et al 2016).…”