Turbulence modeling using a lagged eddy viscosity model for subsonic separated flows over wind turbine airfoils

The objective of this research work is to assess the capability of the lagged eddy viscosity model in predicting separated flows over wind turbine airfoils at subsonic flow conditions. Pressure driven flow separation is an important category of flows and many aerodynamic devices are required to operate on the verge of boundary layer separation to maximize efficiency. Current one- and two-equation turbulence models do not capture all the relevant physics associated with flow separation and, hence, result in erroneous predictions. The lagged eddy viscosity turbulence model is a new model proposed as an improvement over existing two-equation based models. In this model an additional transport equation is solved to account for history effects, which become predominant for non-equilibrium flows, such as separated flows. This model was implemented in the NASA CFD code, OVERFLOW, and has shown promising results in predicting separated flows under high speed or supersonic flow conditions. In the current study, the lagged eddy viscosity turbulence model is implemented in the commercial CFD software FLUENT and CFX. An additional transport equation for the non-equilibrium eddy viscosity is solved using user defined functions in FLUENT and through expressions in CFX. Compared to FLUENT, CFX has the option of an additional turbulence model (EARSM) and also allows the option of simulating natural transition flows by lagging the eddy viscosity of the four-equation SST transition model. Hence, CFX was used for all the flow computations. To ensure proper implementation of the lagged eddy viscosity model, zero pressure gradient flow over a flat plate and flow inside an asymmetric diffuser are computed using the standard k– ω, SST k– ω and EARSM models and compared to computations using the lagged eddy viscosity model and results from experiments. Airfoils with thickness to chord ratios of 18% (DU96-W-180) and 25% (DU91-W2-250) were considered for this study. The standard k– ω and SST k– ω models predicted a delayed separation and stall. EARSM, although it performed better than SST k– ω, did not predict stall to the desired level of accuracy. The lagged eddy viscosity model with the original parameters for σ kA and a0 as recommended by Olsen behaved similarly to SST k- ω; however, the lag model showed significantly improved separated flow prediction capability for modified parameter values for σ kA and a0