Linear-Stability-Based Transition Modeling for Aerodynamic Flow Simulations with a Near-Wall Reynolds-Stress Model

An extended e(N)-based modeling approach. for Tollmien-Schlichting-type transition in aerodynamic flow simulations with the low-Re epsilon(h)-Reynolds-stress model is presented. Instead of simply activating the turbulence production terms at the transition location (point-transition approach), the method incorporates the otherwise neglected Reynolds-stress contributions by the fluctuations of the Tollmien-Schlichting waves and provides them as local input for the turbulence model at the transition point. The shapes of the Reynolds-stress profiles are derived from linear stability analysis within the e(N) method, whereas their absolute magnitudes are calibrated with the aid of direct numerical simulation data of a transitional boundary layer with adverse-pressure gradient. The dissipation-rate input is adjusted to theoretically match the amplification rate of the fluctuations but requires a correction to account for the low-Re damping in the epsilon(h)-Reynolds-stress model. The paper describes the general modeling ideas and the implementation in the flow solver. Aspects of the numerical discretization and a verification for three-dimensional flows are addressed as well. Besides a basic validation for the adverse-pressure-gradient boundary layer, simulations of the SD7003 airfoil flow comprising a laminar separation bubble are presented, which yield very good agreement with measurements. Results of a transitional flat-plate flow are, however, impaired by the lack of intermittency modeling. Finally, the method is applied to a flowthrough nacelle near stall conditions in order to prove its ability to compute consistent transitional behavior in complex three-dimensional flows.