The Effect of Rough-Wall Boundary Conditions on RANS-Based Transition Prediction

A study on the prediction of transition-based ReynoldsAveraged Navier-Stokes (RANS)-equations of rough-wall boundary conditions is presented at various pressure gradients. This work focuses on the interaction of turbulence and transition models implemented in the flow solver TRACE in order to a rough-wall boundary condition. An annular wind tunnel test case is used to study the quality of transition prediction of the model combinations when simulating surface roughness under different pressure gradients. The numerical results are compared with experimental data generated with sand paper roughness. Subsequently, the interdependencies of the investigated model combinations are analyzed by focusing on the model equations. The results show that the transition process is already affected by rough walls, even if the transition model has no sensitivity to surface roughness implemented. Moreover, none of the model combinations can precisely predict the experimental results. As an outlook, ideas to further improve the modeling of the rough wall effect on the transition onset are described. INTRODUCTION In recent years, a substantial progress in transition modeling for turbomachinery applications has been made. Mayle (1991) emphasized the significance of laminar-turbulent tran∗Address all correspondence to this author. sition in gas turbines and stated the different transition modes, i.e. natural and bypass-transition, separation-induced transition, and wake-induced transition. To account for the different modes of transition, different approaches for modeling the transition evolved in the past decades (Suzen et al., 2002; Menter et al., 2006; Koz̆ulović, 2007; Stripf et al., 2008; Langtry and Menter, 2009; Menter et al., 2015). Most of the transition models are based on the correlations of Abu-Ghannam and Shaw (1980) and, thus, are designed to trigger the turbulence model and not to predict the physical effect in detail (Langtry and Menter, 2009). In contrast, laminar kinetic energy models present a more physically-based approach for transition modeling (Walters and Leylek, 2004; Walters and Cokljat, 2008). However, to achieve an increase in gas turbine efficiency and consequently a more accurate prediction of deterioration-based performance losses, extensions of the transition models by second order effects, i.e. surface roughness, are needed (Boyle and Senyitko, 2003; Hohenstein et al., 2013a; Gilge et al., 2017). Extensions for other secondary flow effects, such as injection-induced transition or crossflow-induced transition, are proposed by Herbst et al. (2014) and Müller and Herbst (2014). Several approaches exist for the turbulence models to incorporate second-order flow effects. Wilcox (1988) adjusts the dissipation rate ω at the wall depending on the surface roughness. This is not suitable for surface structures such as riblets due to their drag-decreasing effects. Thus, Koepplin et al. (2017) applied a damping function to the destruction term of the dissipation rate ω. This work is licensed under Attribution 4.0 International (CC BY 4.0) See: https://creativecommons.org/licenses/by/4.0/legalcode As described by Schlichting (1936) and Feindt (1956), surface roughness (compared to a smooth surface) generally moves the laminar-turbulent transition upstream and increases the turbulent fluctuations in the turbulent boundary layer. At high Reynolds number with an almost turbulent boundary layer for a hydraulically smooth surface, Hummel et al. (2005) found that the total pressure loss of turbine blades is increased up to 40% by surface roughness. In contrast, at low Reynolds numbers, surface roughness can lower the aerodynamic losses by eliminating a laminar separation (Boyle and Senyitko, 2003). A correct prediction of the roughness-induced transition is also important for the heat transfer design of turbine blades which show an increase in heat transfer coefficients by up to 50% in the turbulent boundary layer caused by surface roughness (Stripf et al., 2005). Bons (2010) presents a detailed overview of the effect of surface roughness in gas turbines. Based on the different use cases, i.e. prediction of heat transfer or aerodynamic losses, different approaches considering surface roughness in transition modeling have been developed (Stripf et al., 2008; Dassler, 2013). In this paper, the prediction quality of the effect of surface roughness on skin friction and velocity profile will be analyzed. Most of the correlations for modeling the skin friction across rough surfaces are correlated with the equivalent sand-grain roughness ks, in both laminar and turbulent boundary layers (Bons, 2010; Dassler, 2013; Wilcox, 1988). The equivalent sand-grain roughness ks assumes that the effect of each technical roughness can be equally achieved by a uniform layer of sand-grains with a diameter ks with an equivalent effect based on skin friction losses (Nikuradse, 1933; Schlichting, 1936). To model the effect of surface roughness in the transition model, Dassler (2013) used the transition model formulation of Langtry and Menter (2009) and added a third transport equation. The third transport equation allows transporting the flow disturbances induced by the surface roughness into the complete flow field via the variable Ar. However, Hohenstein et al. (2013b) and Alldieck (2019) show still existing deficits in transition modeling of rough surfaces, especially of complex surface structures. So far, little attention has been paid to the interaction of transition and turbulence models considering a rough-wall boundary condition. Based on the transition model formulations, the authors assume that the interaction, in particular the effect of the rough-wall boundary condition of the turbulence model on the transition model, has a significant effect on the transition prediction. This leads to the question: which parameters of the turbulence model are used by the transition model, and how significant is the effect of each parameter on the roughness-induced transition? Answering this question is essential, when improving or extending existing models by second order transition modes due to surface roughness. To this end, this paper focuses on the interaction of existing transition and turbulence models implemented in the non-commercial flow solver TRACE considering rough-wall boundary condition. First, the prediction quality of the roughness transition model in combination with the k-ω turbulence model is validated with experiments conducted in an annular wind tunnel under different pressure gradients and a variation of surface roughness heights (Feindt, 1956). Secondly, the transition onset prediction of model combinations which do not feature a rough-wall boundary condition in transition modeling is studied. FUNDAMENTALS This section describes the incorporation of the roughwall boundary condition in the turbulence and transition models. First, the model formulations of the k-ω model (Wilcox, 1988) and SST model (Menter, 1994) implemented in the noncommercial flow solver TRACE are described. Secondly, the γ-Reθ model (Langtry and Menter, 2009) and the roughness extension (Dassler et al., 2012; Dassler, 2013) are introduced. Turbulence Model The turbulence models used in this study are based on the eddy viscosity μT. In the k-ω turbulence model by Wilcox (1988), the eddy viscosity μT