Reconstruction of Nusselt number in RANS computations with wall function approach

Abstract

Two novel methods for reconstruction of Nusselt number (Nu) are proposed when the wall function approach is used in the RANS framework for defining wall boundary conditions for high Reynolds number flows. The work is motivated by the observation that the velocity and temperature fields are often well predicted when the wall function formulations are used, while at the same time Nu is not. The reason for discrepancy in predictions of flow fields and temperature, and prediction of Nu, is because Nu estimation is solely dependent on the wall function, while the variables obtained from the transport equations are determined also by the convection and pressure force in the momentum transport. The method based on the correction factor Ψ∗ originates from the simplified analytical wall function approach of Popovac and Hanjalić (2007) and modifies the formulation of so-called wall viscosity. The method based on a wall shape function of exponential type approximates temperature variation in the near-wall region. Once the shape function’s coefficients are calculated using values of temperature in three near-wall consecutive cells, the wall values of temperature or temperature gradient, needed for calculation of Nu, can be determined. The methods are tested for four standard benchmark cases, backward-facing step, impinging jet, differentially heated square cavity, and Rayleigh-Bénard convection. The method based on the correction factor significantly improved Nu predictions for the cases where the velocity field is strongly impacted by pressure force. The method based on the wall shape function improves predictions of Nu in all tested cases, with somewhat less accurate predictions of the maximum value of Nu compared to the correction factor method.