On the turbulence structure in inert and reacting compressible mixing layers

Abstract

Direct numerical simulation is used to investigate effects of heat release and compressibility on mixing-layer turbulence during a period of self-similarity. Temporally evolving mixing layers are analysed at convective Mach numbers between 0.15 and 1.1 and in a Reynolds number range of 15000 to 35000 based on vorticity thickness. The turbulence inhibiting effects of heat release are traced back to mean density variations using an analysis of the fluctuating pressure field based on a Green's function.

Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow

“…Sénéchal (2009) used data from coarse-grid DNS computations to calculate the budgets of the transport equations for the variances of thermodynamic fluctuations (ρ 2 , ρT 2 , p 2 ), and observed that the coefficient of variation of density [ρ −1 ρ ] rms at constant friction Reynolds number (3.1b) Re τw 230 and M CL ∈ {1.5, 0.34} , plotted against the outer-scaled wall-distance δ −1 (y − y w ) (δ is the channel half-height) varied asM in compressible turbulent plane channel flow, using the compressible analogue (Gerolymos et al 2013, (A 1e), p. 46) of the incompressible flow Poisson equation for ∇ 2 p (Chou 1945), and found that the observed reduction with increasing Mach number of the absolute magnitude of pressure-strain correlations could be satisfactorily accounted for by mean-density stratificationρ(y), in line with Morkovin's hypothesis (Morkovin 1962), the terms associated with ρ in (Foysi et al 2004, (4.1), p. 213) having marginal influence. This contrasts with the free shear-layer case, where acoustic propagation of ρ effects (Pantano & Sarkar 2002, (4.7), p. 347) were found to be important (Mahle, Foysi, Sarkar & Friedrich 2007). Ghosh, Foysi & Friedrich (2010) also studied the case of compressible turbulent pipe flow and found again that Morkovin's hypothesis (Morkovin 1962) was applicable.…”

Wall effects on pressure fluctuations in turbulent channel flow

“…Pantano & Sarkar (2002) used the inviscid form of (A 1a), considering only acoustic pressure (dp a = a 2 dρ where a is the speed of sound), to study compressibility effects in high-speed shear-layers. Foysi et al (2004) further developed (A 1a) using the Garrick operator (Garrick 1957) [D ct ] 2 of theoretical compressible unsteady aerodynamics and aeroacoustics (Miles 1959;Bisplinghoff & Ashley 1962), which highlights a wavelike influence of the fluctuating density, and Mahle et al (2007) applied it to high-speed compressible mixing-layers All these high-Mach-number studies used Favre decomposition (Favre 1965a,b), and the form ∂ 2 xixj (u i u j − u i u j ) for the slow terms. Since we are interested here in establishing the order-of-magnitude of compressibility effects in comparison with the incompressible flow equation (1.1), we recast the fluctuating part of (A 1a) in a form containing (1.1) plus compressible terms.…”

Direct Numerical Simulation of Inert Droplet Effects on Scalar Dissipation Rate in Turbulent Reacting and Non-Reacting Shear Layers

“…To prevent the numerical errors from accumulating in the computational domain and contaminating the physical phenomena, a common practise is to apply a numerical filter to the numerically-resolved flow fields [37,[51][52][53]. The 4th-order compact filter [39] employed in the present study can be written as…”