Prediction of Bypass and Separation-Induced Transition With an Algebraic Intermittency Model

The paper discusses applications of an algebraic intermittency model for prediction of bypass and separationinduced boundary layer transition. The transition model is coupled with a k−ω turbulence model. The transition model uses only local variables and is tuned for turbomachinery flows. For bypass transition, two effects in an attached pre-transitional boundary layer are modelled: damping of small-scale disturbances induced by the free stream and breakdown of the near-wall perturbed flow with generation of fine-scale turbulence. For separated flow, the model describes breakdown of a laminar free shear layer. We refer to [1] for a complete discussion of the modelling assumptions and the model validation. 1 Transition mechanisms Transition mechanisms in an attached laminar boundary layer subjected to a high free-stream turbulence level (above 0.5-1%) are discussed by Hack and Zaki [2]. Streamwise elongated disturbances are generated. These are zones of forward and backward jet-like perturbations, alternating in spanwise direction. They are called streaks or Klebanoff disturbances. Streaks grow downstream both in length and amplitude and finally some streaks cause turbulent spots. Transition is then called of bypass type, which means that instability by Tollmien-Schlichting waves is bypassed. Breakdown is then earlier and much faster. Klebanoff modes are initiated by deep penetration into a laminar boundary layer of large-scale perturbations from the free stream. The strong damping of small-scale components is called shear sheltering. There are at least two instability mechanisms in a boundary layer perturbed by streaks. One is instability by inflection of the velocity profile in wall-normal direction between the boundary layer edge and a lowspeed streak. The other is instability of the velocity profile in wall-normal direction in the overlap zone of the leading edge of a high-speed streak and the trailing edge of a low-speed streak. Both instabilities are triggered by small-scale perturbations, although these are damped in the boundary layer Transition mechanisms in a separated laminar boundary layer are discussed by McAuliffe and Yaras [3]. Under low free-stream turbulence, transition is initiated by inviscid Kelvin-Helmholtz instability, with formation of spanwise vortices. They group at selective streamwise wavelengths, analogous to Tollmien-Schlichting waves in an attached boundary layer. The roll-up vortices break down as they travel downstream. The breakdown process is rather slow with low free-stream turbulence, but, under high free-stream turbulence, bypass transition with formation of streaks in the attached boundary layer prior to separation can co-exist with the Kelvin-Helmholtz generated spanwise vortices in the separated layer. The breakdown of the vortex rolls is then strongly accelerated by perturbations due to the Klebanoff modes. For sufficiently strong free-stream turbulence, the Kelvin-Helmholtz instability may even be bypassed by the breakdown of the streaks. So, a bypass mechanism is possible in a separated shear layer, similar as in an attached boundary layer.