A study of initial conditions' effects on thermal properties of compressible homogeneous sheared non-isentropic turbulence using rapid distortion theory (RDT)

Abstract

The paper investigates the effect of initial conditions characterized by compressibility of turbulence on the changes in scalar such as density, temperature and pressure within the framework of rapid distortion theory (RDT) in the case of non-isentropic turbulence. This study is a follow-up of the basic work from the J. Fluid Mech. article 330, 307 (1997) carried out by A. Simone, G.N. Coleman and C. Cambon in the case of quasi-isentropic turbulence and the previous work of M. Riahi and T. Lili from Fluid Dyn. Res. article 52, 025501 (2020) in the case of non-isentropic turbulence. RDT is used to examine the behavior of the root mean square (rms) fluctuations of density, temperature and pressure. The coupling between these rms quantities, the partition factor and the polytropic coefficient are also studied. RDT equations are solved numerically using a code which solves directly evolution equations of two-point spectral correlations for compressible homogeneous sheared non-isentropic turbulence. The RDT analysis is carried out for various initial turbulent Mach number <i>M</i><sub><i>t</i>0</sub> ranging from 0.1 to 0.4, and the initial compressible turbulence is to be one of the three states concerning the fraction of kinetic energy <i>χ</i><sub>0</sub>: solenoidal (<i>χ</i><sub>0</sub>=0), mixed (<i>χ</i><sub>0</sub>=0.6) and dilatational (<i>χ</i><sub>0</sub>=1) (<i>χ</i><sub>0</sub> is the ratio of the initial dilatational kinetic energy to the initial total kinetic energy). It is shown from this study that the changes in scalars are strongly dependent on the initial conditions. Magnitudes and asymptotic values of rms thermodynamics fluctuations and correlations between these thermodynamics fluctuations depend of <i>M</i><sub><i>t</i>0</sub>. For large times, the isentropic state of the flow is well observed whatever <i>M</i><sub><i>t</i>0</sub> and <i>χ</i><sub>0</sub>.