| Abstract | A three equation transition/turbulence model has been applied to the prediction of low-Reynolds number flows, characterized by separation-induced transition, in high-lift airfoil cascades for aeronautical low pressure turbine applications. Classical linear two equation turbulence models fail to predict accurately laminar separation and turbulent reattachment, and usually over-predict the separation length. The main reason for this is the slow rise of the turbulent kinetic energy in the shear layer during the early stage of the separation process.
In order to overcome this limit, the proposed approach is based on solving an additional transport equation for the so-called laminar kinetic energy, which allows the increase
of the non-turbulent fluctuations in the pre-transitional and transitional regions of the boundary layer. The model is derived from that proposed by Lardeau et al., which was originally formulated to predict bypass transition for attached flows, subject to a wide range of free-stream turbulence intensity. In this work a new production term for the laminar kinetic energy is proposed, based on the mean shear and a laminar eddy-viscosity concept (Pacciani et al.).
The laminar kinetic energy transport equation has been coupled with the RQEVM (Realizable Quadratic Eddy Viscosity Model) turbulence model proposed by Rung et al. The result is a non-linear transition-sensitive three equation model which gives an explicit algebraic formulation for the Reynolds stresses (EARSM).
The study described in this work is part of the activities carried out in the framework of the European research projects UTAT (Unsteady Transitional flows in Axial Turbomachines) and TATMo (Turbulence and Transition Modelling for Special Turbomachinery Applications). Several flow configurations of particular interest in the field of aeronautical low pressure turbines have been analyzed both experimentally and numerically during these projects. In this paper, after a validation of the model for a flat plate boundary layer, subjected to an adverse pressure gradient, the results obtained for the T106C, T108 and T2 high-lift cascades, recently tested at the von Karman Institute during the aforementioned research projects, are presented and discussed. These cascades have different loading distributions and suction side diffusion rates which, give rise to different boundary layer separations and lapse rates. The analyzed Reynolds number values span the whole range typically encountered in aeroengines low-pressure turbines operations.
Several expansion ratios for steady inflow conditions characterized by different freestream turbulence intensities were considered. Some examples of these comparisons are presented in the following figures. Results obtained with the proposed model show its ability to predict the evolution of the separated flow region, including bubble bursting phenomenon and the formation of open separations.
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