Further development of an algebraic intermittency model for separation-induced transition under elevated free-stream turbulence

Abstract

An algebraic transition model (Kubacki S., Dick, E., 2016, “An algebraic intermittency model for bypass, separation induced and wake-induced transition” Int. J. Heat Fluid Flow, 62: 344-361) has been modified using an experimental data base on boundary layer flows along a flat plate (Simoni D., Lengani D., Dellacasagrande M., Kubacki S., Dick, E., 2019, “An accurate data base on laminar-to-turbulent transition in variable pressure gradient flows”, Int. J. Heat Fluid Flow, 77: 84-97) and results by large eddy simulation (LES) of transition in a separated boundary layer on a flat plate (Li H.J., Yang Z., 2019, “Separated boundary layer transition under pressure gradient in the presence of free-stream turbulence” Phys. Fluids, 31 104106). The transition model for use with RANS equations functions by an algebraic expression of an intermittency factor and a supplementary term added to the production term of the equation for turbulent kinetic energy of a k-omega turbulence model. For modelling transition in separated state under an elevated free-stream turbulence level, a sensor is made for detection of the front part of a separated boundary layer. The sensor activates the intermittency factor and the supplementary source term. The added model ingredients express the effect of Klebanoff streaks generated upstream of separation on the splitting in the separated part of the layer of full-span Kelvin-Helmholtz instability rolls into part-span structures, which accelerates the breakdown and the direct effect of the Klebanoff streaks on the breakdown of the separated layer. By the Klebanoff streaks, the breakdown is faster and occurs under the combined effects of a large adverse pressure gradient and a large free-stream turbulence level. The extended algebraic intermittency model produces improved predictions, compared to the originating model, for separation-induced transition at moderate and elevated free-stream turbulence levels combined with moderate or strong adverse pressure gradients. The algebraic intermittency model is a simple alternative for commonly used transition models with transport equations for simulation of turbomachinery flows.