Transition Prediction in Low Reynolds Airfoil Flows using Finite Element/Difference Solvers Coupled with the e n Method: a Comparative Study

The Institute for Aerospace Research (IAR), of the National Research council (NRC) of Canada, and the Technical University of Braunschweig (TUBS), in Germany, have been collaborating, over the past three years, on low Reynolds airfoil flows research using computational flow dynamics and wind tunnel experiments. The present paper addresses one of the research aspects which focused mainly on the development of a finite element algorithm at IAR, FEAT2D, for transition prediction in two-dimensional incompressible laminar flows. The FEAT2D code performance was accessed by conducting comparisons with the available COAST3 code results that was used by TUBS for the prediction of the transition location. The numerical solutions of flows past an experimental airfoil, HGR-01, were considered for stability analysis. The solutions were obtained using RANS simulations with different turbulence models. A coupling technique between the RANS solvers and the transition modules was performed. The finite element algorithm was based on the high precision Hermite quintic element using a non-uniform grid distribution. Temporal and spatial stability theories were considered and the e n method was implemented to compute the global amplification rate in the streamwise direction. Validations were conducted for the Blasius boundary layer and for the HGR-01 airfoil flows at various angles of attack. The present finite element results for transition location prediction were found to be in excellent agreement with those predicted by the COAST3 code. The FEAT2D code was also validated with an LES solution of low Reynolds incompressible flows past the SD7003 airfoil by comparing the n-factor with the amplitude of the Reynolds shear stress. The transition location was determined by FEAT2D code using the time-averaged LES solution as input data. For the LES solution the transition location was assumed to be where the magnitude of the Reynolds shear stress reaches 0.1%.

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