Momentum and heat flux events in compressible turbulent channel flows

In the present study, the momentum and heat fluxes (MF & HF) in subsonic/supersonic channel flows are studied and compared via resorting to the established analysis tools developed for incompressible flows, such as the conditional sampling and the spectral linear stochastic estimation, by leveraging the newly built database. Particular attention is paid to clarifying the effects of the inner-outer scale interactions on the statistical characteristics of MF and HF in the near-wall and logarithmic regions. To this end, by employing the spectral linear stochastic estimation, the near-wall fluxes are decomposed into large and small-scale components, and the logarithmic-region fluxes are decomposed into active and inactive parts, respectively. For the near-wall region, the large-scale component is found to be the footprints of large-scale eddies and rather uniform in physical space, whereas the remaining small-scale component is uneven in space, and includes the strong transports of momentum and heat in the near-wall region. For the logarithmic region, both the inactive and active components of MF and HF are found to contribute to their mean flux. In the outer region, the ejections of HF are remarkably stronger than those of the MF, and the former is more sparse in the physical space. Reynolds number is shown to have a minor effect on the statistical characteristics of the two fluxes, and the enlargement of the Mach number only appears to lessen the linkages between the inner and outer region fluxes, adjust the proportions of the inactive and active components in the logarithmic region, and rarely alter the overall properties of them. The findings of the present study may contribute to the development of the modeling approach in compressible wall turbulence.

High-order low-dissipation shock-resolving TENO-THINC schemes for hyperbolic conservation laws

While the recently proposed TENO (targeted essentially non-oscillatory) schemes [Fu et al., Journal of Computational Physics 305 (2016): 333-359] exhibit better performance than the classical WENO (weighted essentially non-oscillatory) schemes with the same accuracy order, there is still a room for further improvement, e.g., the physical discontinuities may be significantly smeared by the excessive numerical dissipation due to the enforcement of the ENO property after a long-time advection. More recently, a new fifth-order TENO5-THINC scheme is proposed by coupling the TENO5 scheme with a non-polynomial THINC (tangent of hyperbola for interface capturing) scheme based on a parameter-free discontinuity indicator. The novelty originates from the fact that the new strategy locates the discontinuities accurately and deploys the jump-like THINC reconstruction scheme for resolving the discontinuities with a sub-cell resolution, instead of enforcing the ENO property. The new scheme successfully leverages the excellent wave-resolution property of standard TENO schemes for smooth and under-resolved continuous scales and the discontinuity-resolving capability of THINC for reconstructing genuine discontinuities. In this work, we further develop the low-dissipation discontinuity-resolving very-high-order TENO-THINC reconstruction schemes for hyperbolic conservation laws by proposing tailored coupling strategies. Without loss of generality, the six- and eight-point TENO-THINC schemes are developed, and the explicit formulas are given as well as the built-in parameters. Based on a set of critical benchmark simulations, the newly proposed schemes show significantly lower numerical dissipation when compared to the counterpart TENO schemes without sacrificing numerical robustness. The presented numerical results represent the state-of-the-art in the literature and can serve as references for future algorithm development.

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation [Griffin, Fu, & Moin, PNAS, 118:34, 2021] and an algebraic temperature-velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows, and boundary layers (48 cases with edge Mach numbers in the range of 0.77–11 and semi-local friction Reynolds numbers in the range of 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range of 0.7–4 and friction Reynolds numbers in the range of 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two and has a similar computational cost and implementation complexity as the commonly used ODE model.