Heated transcritical and unheated non-transcritical turbulent boundary layers at supercritical pressures

Abstract

Nominally zero-pressure-gradient fully developed flat-plate turbulent boundary layers with heated and unheated isothermal walls at supercritical pressures are studied by solving the full compressible Navier–Stokes equations using direct numerical simulation. With a heated isothermal wall, the wall temperature sets such that the flow temperature varies through the pseudo-critical temperature, and thus pseudo-boiling phenomena occur within the boundary layers. The pseudo-boiling process induces strongly nonlinear real-fluid effects in the flow and interacts with near-wall turbulence. The peculiar abrupt density variations through the pseudo-boiling process induce significant near-wall density fluctuations $\sqrt{\overline{\unicode[STIX]{x1D70C}^{\prime }\unicode[STIX]{x1D70C}^{\prime }}}/\overline{\unicode[STIX]{x1D70C}}\approx 0.4{-}1.0$ within the heated transcritical turbulent boundary layers. The large near-wall density fluctuations induce a turbulent mass flux $\unicode[STIX]{x1D70C}^{\prime }u_{i}^{\prime }$, and the turbulent mass flux amplifies the Favre-averaged velocity fluctuations $u_{i}^{\prime \prime }$ in the near-wall predominant structures of streamwise low-speed streaks that are associated with the ejection (where $u^{\prime \prime }<0$ and $v^{\prime \prime }>0$), while reducing the velocity fluctuations in the high-speed streaks associated with the sweep ($u^{\prime \prime }>0$ and $v^{\prime \prime }<0$). Although the near-wall low-speed and high-speed streak structures dominate the Reynolds-shear-stress generation, the energized Favre-averaged velocity fluctuations in the low-speed streaks enhance both the mean-density- and density-fluctuation-related Reynolds shear stresses ($-\overline{\unicode[STIX]{x1D70C}}\overline{u^{\prime \prime }v^{\prime \prime }}$ and $-\overline{\unicode[STIX]{x1D70C}^{\prime }u^{\prime \prime }v^{\prime \prime }}$) in the ejection event and, as a result, alter the Reynolds-shear-stress profile. The large density fluctuations also alter the near-wall viscous-stress profile and induce a near-wall convective flux $-\overline{\unicode[STIX]{x1D70C}}\widetilde{u}\widetilde{v}$ (due to non-zero $\widetilde{v}$). The changes in the contributions in the stress-balance equation result in a failure of existing velocity transformations to collapse to the universal law of the wall. The large density fluctuations also greatly contribute to the turbulent kinetic energy budget, and especially the mass flux contribution term becomes noticeable as one of the main positive terms. The unheated non-transcritical turbulent boundary layers show a negligible contribution of the real-fluid effects, and the turbulence statistics agree well with the statistics of an incompressible constant-property turbulent boundary layer with a perfect-gas law.