Interaction of isotropic turbulence with shock waves: effect of shock strength

Abstract

As an extension of the authors' work on isotropic vortical turbulence interacting with a shock wave (Lee, Lele & Moin 1993), direct numerical simulation and linear analysis are performed for stronger shock waves to investigate the effects of the upstream shock-normal Mach number (M1). A shock-capturing scheme is developed to accurately simulate the unsteady interaction of turbulence with shock waves. Turbulence kinetic energy is amplified across the shock wave, and this amplification tends to saturate beyond M1 = 3.0. An existing controversy between experiments and theoretical predictions on length scale change is thoroughly investigated through the shock-capturing simulation: most turbulence length scales decrease across the shock, while the dissipation length scale (ρq3/ε) increases slightly for shock waves with M1<1.65. Fluctuations in thermodynamic variables behind the shock wave are nearly isentropic for M1<1.2, and deviate significantly from isentropy for the stronger shock waves, due to the entropy fluctuation generated through the interaction.

Numerical investigation of the compressible flow past an aerofoil

“…As shown in figures 12(a)-12(c), the turbulence intensities in region II, such as at x/c = 0.6 and 0.7, are significantly enhanced compared with those at x/c = 0.2 and 0.4, consistent with the experimental measurements (Marvin et al 1980) and theoretical predictions by LIA (Ribner 1953(Ribner , 1954(Ribner , 1987Lee et al 1997). Here, we introduce the turbulence Mach number defined as M t = {u i u i } 1/2 /a loc (Lele 1992) and have identified that M t reaches as high as approximately 0.5 in region II.…”

“…Since the 1950s, linear interaction analyses (LIA) on turbulence modification by the shock wave have been performed with an emphasis on the acoustic wave generation behind the shock wave (e.g. Ribner 1953Ribner , 1954Ribner , 1987Lee, Lele & Moin 1997). Through the linear analyses, it is found that turbulent fluctuations are amplified across the shock wave, and significant acoustic noise is also generated because of the interaction of vortical turbulence with the shock wave.…”

High resolution conjugate filters for the simulation of flows

“…Many high order shock-capturing schemes are found to be too dissipative to be applicable for the long-time integration of such flows [14,15]. In the framework of free decaying turbulence, the effect of a subgrid-scale model was masked by some highorder shock-capturing schemes.…”

Hybrid LES of Detonations in Reacting Multi-Phase Mixtures

“…In the case of shock / isotropic turbulence interactions, linear analysis shows that the stream-wise component of the stress is the most amplified for a mean flow Mach number of M < 2, and that the trend is reversed afterward. As the mean flow Mach number is further increased, the amplification factors saturate at M « 3 (Lee et al [1997]). …”

“…Such interactions can have a strong impact on the flow evolution, increasing turbulent mixing, but also increasing losses and surface drag and/or heat transfer depending upon the strength of the shock. Many studies of shock / turbulence interactions have been conducted, both numerically and experimentally (see Andreopoulos et al [2000] for a review), and physical insights have been gained from the studies of simple test cases, such as the interaction of shocks with isotropic and/or homogeneous turbulence, studied experimentally (e.g., Jacquin et al [1993], Honkan and Andreopoulos [1992], Barre et al [1996], Agui et al [2005]) and numerically using high-order shock capturing methods (e.g., Lee et al [1993], Hannappel and Friedrich [1995], Lee et al [1997], Mahesh et al [1997], Jamme et al [2002Jamme et al [ , 2005) and, more recently, using a shock-fitting method (Sesterhenn et al [2005]). …”