A new modeling strategy adapted to Reynolds-Averaged Navier-Stokes (RANS) turbulence models is proposed to predict combined effects of roughness and blowing boundary conditions. First, an analysis of experimental data is presented, leading to a specific description of the velocity profile in the logarithmic region of transpired turbulent boundary layers over rough walls. This analysis points out the deficiencies of existing roughness corrections to predict the effect of blowing in the presence of surface roughness. Indeed, these corrections tend to underestimate skin friction coefficients and Stanton numbers with addition of blowing. The failure of existing models derives from an inaccurate estimation of the velocity shift of the logarithmic law given by roughness corrections. Concretely, roughness corrections underestimate the apparent velocity shift of the logarithmic law with blowing. To recover the expected law of the wall, an additional contribution on the velocity shift, characterizing blowing/roughness interactions, is integrated to standard roughness corrections. To that end, a modification of the equivalent sand grain height, adapted to k − ω based turbulence models, is proposed to take blowing effects into account. Furthermore, an extension of Aupoix's thermal correction [B. Aupoix, International Journal of Heat and Fluid Flow 56, 160 (2015)] to blowing is presented to predict combined thermal effects of roughness and blowing. The assessment of the proposed corrections is performed using k − ω Shear Stress Transport (SST) model on a large set of experimental data and proves the relevance of the strategy for incompressible and compressible turbulent boundary layers.
Transpired boundary layers are of major interest for many industrial applications. Although well described, there is no turbulence model specifically dedicated to the prediction of boundary layers for both blowing and suction configurations. Revisiting closure relations of turbulence models, a general strategy was established to recover Stevenson's law of the wall that described the behavior of transpired boundary layers in the wall region. The methodology is applied to the k − ω SST turbulence model and compared to Wilcox's correction, only applicable to blowing cases. A version of the proposed correction, more suited to RANS solvers, was also derived. Several experimental boundary layer configurations with blowing or suction were computed using both versions of the correction. The good agreements observed on all cases prove the relevance and the efficiency of the present strategy. w subscript for quantities at the wall Reynolds average
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