Modeling of combined effects of surface roughness and blowing for Reynolds-Averaged Navier-Stokes turbulence models

International audienceA 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

Roughness corrections applied to the simulation of turbulent hypersonic flows

International audienceThis work is dedicated to the application of roughness corrections [B. Aupoix, J. Fluids Engineering 137/021202, 2015; B. Aupoix, Int. J. Heat and Fluid Flow 56, 160-171, 2015] to hypersonic turbulent flows. Simulations of configurations are performed using different RANS solvers for the k-ω SST model including both dynamic and thermal turbulent contributions. The experiments deal with conic and biconic models at Mach number for which friction coefficients and Stanton numbers are available

A propos du rôle de la correction d'Hanratty dans la réponse linéaire d'un écoulement turbulent contraint par une paroi ondulée

International audienceScallop patterns forming on erodible surfaces were studied historically using a linear analysis of the inner region of a turbulent boundary layer growing on a corrugated wall. Experimental observations show a phase shift between the shear stress at the wall and the wall oscillation that depends on the wavenumber. An ad hoc correction applied to the turbulent closure and due to Hanratty et al. (Thorsness et al. , Chem. Engng Sci. , vol. 33, issue 5, 1978, pp. 579–592; Abrams & Hanratty, J. Fluid Mech. , vol. 151, issue 1, 1985, p. 443; Frederick & Hanratty, Exp. Fluids , vol. 6, issue 7, 1988, pp. 477–486) was systematically used to recover the reference experimental results. In this study, Reynolds-averaged Navier–Stokes (RANS) and direct numerical simulations (DNS) were performed and revealed the role of the Boussinesq assumption in the results obtained. We show that the Hanratty correction acts as a palliative to the misrepresentation of Reynolds stresses due to the use of the Boussinesq hypothesis. The RANS calculations based on a turbulence model using a second-order moment closure recovered the expected results obtained in the reference DNS calculations, in particular with respect to wall heat transfer. The analysis of these results highlights the critical importance of the anisotropy of the diagonal Reynolds stresses on the prediction of wall transfer under these conditions and their implication in the occurrence of scalloping.Les motifs de coups de gouges se formant sur des surfaces érodables ont été étudiés historiquement à l'aide d'une analyse linéaire de la région interne d'une couche limite turbulente se développant sur une paroi ondulée. Les observations expérimentales montrent un déphasage entre la contrainte de cisaillement à la paroi et l'oscillation de la paroi qui dépend du nombre d'ondes. Une correction ad hoc appliquée à la fermeture turbulente et due à Hanratty et al. (Thorsness et al., Chem. Engng Sci., vol. 33, numéro 5, 1978, pp. 579-592 ; Abrams & Hanratty, J. Fluid Mech., vol. 151, numéro 1, 1985, p. 443 ; Frederick & Hanratty, Exp. Fluids, vol. 6, numéro 7, 1988, p. 477-486) a toujours dû être utilisée pour récupérer les résultats expérimentaux de référence. Dans cette étude, des simulations Navier-Stokes à moyenne de Reynolds (RANS) et des simulations numériques directes (DNS) ont été réalisées et ont révélé le rôle de l'hypothèse de Boussinesq dans les résultats obtenus. Nous montrons que la correction de Hanratty agit comme un palliatif à la mauvaise représentation des contraintes de Reynolds due à l'utilisation de l'hypothèse de Boussinesq. Les calculs RANS basés sur un modèle de turbulence utilisant une fermeture au second ordre ont retrouvé les résultats attendus obtenus dans les calculs DNS de référence, en particulier en ce qui concerne le transfert de chaleur à la paroi. L'analyse de ces résultats met en évidence le rôle critique de l'anisotropie des contraintes de Reynolds diagonales sur la prévision du transfert à la paroi dans ces conditions et leur implication dans l'apparition des coups de gouges