Non-linear eddy-viscosity modelling of transitional boundary layers pertinent to turbomachine aerodynamics

The predictive performance of three low-Reynolds-number turbulence models, one based on the linear (Boussinesq) stress-strain relationship and two adopting cubic forms, is examined by reference to transitional flat-plate boundary layers subjected to streamwise pressure gradient and moderate free-stream turbulence, the latter causing bypass transition. One of the cubic models involves the solution of two transport equations, while the other involves three equations, one of which relates to the second invariant of turbulence anisotropy. The investigation demonstrates that, for the conditions examined, the non-linear models return a more credible representation of transition than the linear variant, although none of the models may be said to be entirely satisfactory. Thus, while non-linear modelling shows promise and offers inherent advantages through the use of a more general stress-strain linkage and elaborate calibration, further refinement is needed in the present cubic variants for transitional flows.