Non-equilibrium wall functions for large Eddy simulations of complex turbulent flows and heat transfer

Highlights: • Novel wall function for large eddy simulation of complex turbulent heated flows. • Valid over the whole range of dimensionless wall distance y⁺. • Applicable to complex flow situations that include local non-equilibrium effects. • Suitable for a wide range of molecular Prandtl numbers. • Thermodynamically consistent with the second law of thermodynamics. In this paper novel unified wall function formulations for large eddy simulation of complex turbulent flows and heat transfer are presented. In contrast to existing wall functions, the proposed analytical expressions for velocity and temperature are: (1) valid over the whole range of dimensionless wall distance $y^{+}$, (2) applicable to complex flow situations that include local non-equilibrium effects, (3) suitable for a wide range of molecular Prandtl numbers, (4) thermodynamically consistent with the second law of thermodynamics, and (5) easily extendable to account for contributions of additional source term e.g. gravity, radiation, chemical reactions. Such an universal and consistent wall function formulation is particularly useful for computational fluid dynamics applications in providing appropriate wall boundary conditions for complex high Reynolds number flows. The accuracy and thermodynamic consistency of the proposed wall treatment is first testified by comparison with experimental and direct numerical simulation data. Second, in order to highlight the applicability and performance of the proposed wall functions for computational fluid dynamics, results of large eddy simulations of various complex turbulent flows including heat transfer relevant to internal combustion engine applications are presented and evaluated. It turns out that the suggested wall function approach features a superior physics modeling accuracy in terms of well-known key parameters in near-wall bounded flows in comparison to state-of-the-art wall functions.