Impact of Structure-Preserving Discretizations on Compressible Wall-Bounded Turbulence of Thermally Perfect Gases

Abstract

Direct numerical simulations of compressible turbulent channel flow at supersonic and hypersonic Mach numbers are performed using a thermally perfect gas model for CO$_2$. The objective is to assess the role of structure-preserving discretizations of the convective terms in high-enthalpy regimes, with particular emphasis on entropy conservation, kinetic-energy preservation, and consistency with the thermodynamic closure. The comparative analysis of various formulations examines their impact on robustness, thermodynamic fluctuations, and turbulence statistics across a range of Mach numbers. Differences among formulations are found to originate primarily in the treatment of thermodynamic variables and progressively influence the dynamical fields as compressibility effects intensify. In particular, the coupling between entropy consistency and pressure discretization is shown to affect Reynolds stresses and mean flow properties in high-speed regimes. Overall, the results indicate that consistency between the numerical formulation and the thermodynamic model contributes significantly to the reliable simulation of high-enthalpy compressible turbulence. The study systematically assesses entropy-conservative discretizations for thermally perfect gases in wall-bounded flows and examines their impact on thermodynamic-dynamic coupling at high Mach numbers.

Figures (3)

• Figure 1: Wall-normal distributions of inner-scaled, Trettel--Larsson transformed, Favre-averaged streamwise velocity component $\tilde{u}^+_{TL}$ (panels (a)--(c)) and temperature $\tilde{T}$ (panels (d)--(f)) profiles, in semi-local scaling $y^*$. Solid black lines: EC-TP; dashed blue lines: KEEP; dotted green lines: Gouasmi et al.; dash-dotted red lines: Ranocha. In panels (a)--(c), solid gray curves represent standard law-of-the-wall trends in the viscous sublayer $u^+=y^+$ and the log-law $u^+=6.0+1/0.41\log{ y^+}$.
• Figure 2: Wall-normal distributions of the density-scaled turbulent stresses $\tau_{ij}^+ = \langle\rho\rangle \widetilde{u"_{i} u"_{j}}/\tau_w$ in semi-local units $y^*$. Colors are set as in Fig. \ref{['fig:velprofiles']}. Panels (a)--(c) display the orthogonal components of the turbulent stresses at various Mach numbers, whereas panels (d)--(f) display turbulent shear stress $\tau_{12}^+$.
• Figure 3: Wall-normal distributions of normalized thermodynamic variable root-mean-squares in semi-local units $y^*$. Colors are set as in Fig. \ref{['fig:velprofiles']}. Panels (a)--(c) display normalized temperature fluctuations, panels (d)--(f) report normalized density fluctuations, panels (g)--(i) depict inner-scaled pressure fluctuation for various Mach numbers and numerical schemes.