arXiv subjects

Youjie Xu

Publications and source records attributed to Youjie Xu.

2 recordsLinked to original sources

arXiv2026

Temperature transformation recovering the compressible law of the wall for turbulent channel flow

Velocity and temperature distributions are both crucial for modeling compressible wall-bounded turbulent flows. The compressible law of the wall for velocity has been extensively examined through velocity transformations. However, a well-established temperature transformation remains an open issue. We propose new Van Driest type (VD-type) and semi-local type (SL-type) temperature transformation for compressible turbulent channel flow. Our approach is based on an analysis of the momentum and energy balance equations in the overlap layer. It accounts for the influences of mixing length model, the work of the body force, and the turbulent kinetic energy (TKE) flux. The proposed transformations are evaluated using data from direct numerical simulations and wall-resolved large eddy simulations of compressible turbulent channel flow. The SL-type transformation provides better data collapse than the VD-type in the viscous sublayer and buffer layer. With a suitable mixing length model, the SL-type transformed temperature agrees well with the incompressible temperature profile or the extended law of the wall. For the isothermal wall, the integral mean error over the entire boundary layer remains below 2% for most cases, with root mean square value of about 1.7%. The results highlight the importance of mitigating the energy imbalance in the transformation. This work identifies the multi-layer structure of the turbulent TKE flux, which in turn enables approximate models and corresponding simplified yet effective temperature transformations. Applications of the proposed approach in near-wall modeling and inverse transformation, as well as its potential extension to more general configurations, are also discussed.

physics.flu-dyn↗

arXiv2025

Flux-controlled wall model for large eddy simulation integrating the compressible law of the wall

Recent advances in velocity and temperature transformations have enabled recovery of the law of the wall in compressible wall-bounded turbulent flows. Building on this foundation, a flux-controlled wall model (FCWM) for Large Eddy Simulation (LES) is proposed. Unlike conventional wall-stress models that solve the turbulent boundary layer equations, FCWM formulates the near-wall modeling as a control problem applied directly to the outer LES solution. It consists of three components: (1) the compressible law of the wall, (2) a feedback flux-control strategy, and (3) a shifted boundary condition. The model adjusts the wall shear stress and heat flux based on discrepancies between the computed and target transformed velocity and temperature, respectively, at the matching location. The proposed wall model is evaluated using LES of turbulent channel flows across a broad range of conditions, including quasi-incompressible cases with bulk Mach number \(M_b = 0.1\) and friction Reynolds number \(Re_τ= 180 \sim 10{,}000\), and compressible cases with \(M_b = 0.74 \sim 4.0\) and bulk Reynolds number \(Re_b = 7667 \sim 34{,}000\). The wall-modelled LES reproduce mean velocity and temperature profiles in agreement with direct numerical simulation data. For all tested cases with \(M_b \leq 3\), the wall model achieves relative errors of \(|ε_{C_f}| < 4.1\%\), \(|ε_{B_q}| < 2.7\%\), and \(|ε_{T_c}| < 2.7\%\) in friction coefficient, non-dimensional heat flux, and centerline temperature, respectively. In the quasi-incompressible regime, the wall model achieves \(|ε_{C_f}| < 1\%\). Compared to the conventional equilibrium wall model, the proposed FCWM achieves higher accuracy in compressible turbulent channel flows without solving the boundary layer equations, thereby reducing computational cost.

physics.flu-dyn↗