Correlation-based Transition Modeling for External Aerodynamic Flows
Baeder, James D
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Conventional turbulence models calibrated for fully turbulent boundary layers often over-predict drag and heat transfer on aerodynamic surfaces with partially laminar boundary layers. A robust correlation-based model is developed for use in Reynolds-Averaged Navier-Stokes simulations to predict laminar-to-turbulent transition onset of boundary layers on external aerodynamic surfaces. The new model is derived from an existing transition model for the two-equation k-omega Shear Stress Transport (SST) turbulence model, and is coupled with the one-equation Spalart-Allmaras (SA) turbulence model. The transition model solves two transport equations for intermittency and transition momentum thickness Reynolds number. Experimental correlations and local mean flow quantities are used in the model to account for effects of freestream turbulence level and pressure gradients on transition onset location. Transition onset is triggered by activating intermittency production using a vorticity Reynolds number criterion. In the new model, production and destruction terms of the intermittency equation are modified to improve consistency in the fully turbulent boundary layer post-transition onset, as well as ensure insensitivity to freestream eddy viscosity value specified in the SA model. In the original model, intermittency was used to control production and destruction of turbulent kinetic energy. Whereas, in the new model, only the production of eddy viscosity in SA model is controlled, and the destruction term is not altered. Unlike the original model, the new model does not use an additional correction to intermittency for separation-induced transition. Accuracy of drag predictions are improved significantly with the use of the transition model for several two-dimensional single- and multi-element airfoil cases over a wide range of Reynolds numbers. The new model is able to predict the formation of stable and long laminar separation bubbles on low-Reynolds number airfoils that is not captured with conventional turbulence models. The validated transition model is successfully applied to rotating blade configurations in axial flow conditions to study the effects of transitional boundary layers on rotor thrust and torque. In helicopter rotors, inclusion of transition effects increased thrust prediction by 2% and decreased torque by as much as 8% at lower collective angles, due to reduced airfoil profile drag. In wind turbine rotors, transition model predicted a 7%--70% increase in generated shaft torque at lower wind speeds, due to lower viscous drag. This has important implications for CFD analysis of small wind turbines operating at low values of rated power. Transition onset locations along upper and lower surfaces of rotor blades are analyzed in detail. A new crossflow transition onset criterion is developed to account for crossflow instability effects in three-dimensional boundary layers. Preliminary results for swept wing and rotating blade flows demonstrate the need to account for crossflow transition in three-dimensional simulations of wings, rotating blades, and airframes. Inclusion of crossflow effects resulted in accelerated transition in the presence of favorable pressure gradients and yawed flow. Finally, a new correction to the wall damping function in the Spalart-Allmaras turbulence model is proposed to improve sensitivity of the model to strong adverse pressure gradients (APG). The correction reduces turbulence production in the boundary layer when the ratio of magnitudes of local turbulent stress to the wall shear stress exceeds a threshold value, therefore enabling earlier separation of boundary layer. Improved prediction of static and dynamic stall on two-dimensional airfoils is demonstrated with the APG correction.