Laminar-turbulent boundary layer transition

Underlying Flow Regime 3-04 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

The modelling of transitional flows which are very common in turbomachinery applications is among the most difficult issues. In the case of simple configurations (usually shear stress and strain dominate in one direction) it is easier to calibrate the turbulence model even in the context of capturing transition. For complex cases linear eddy viscosity model fails if they are not combined with highly empirical transition correlations.

Low Reynolds number models developed for resolving boundary layer flows are calibrated to account for the effects of low turbulence intensity in the viscous sublayer and usually they use dumping functions for this purpose. However, the ability of low-Re models to capture transition seems to be coincidental, as the calibration of the damping functions is based on the viscous sublayer behaviour and not on transition phenomenon itself (Menter at al, 2002). These models themselves assume that diffusion of freestream turbulence leads to a built-up turbulence activity in the initial pseudo-laminar boundary layer and the transition is initiated when the local production of turbulence kinetic energy exceeds the local dissipation rate. Such models however, take no account of receptivity, development of secondary instability and turbulent spots.

Best practical advice

Application of experimental correlation to identify on-set of transition and then switching on or off the production term are helpful, but it could lead to numerical instabilities as the transition process influences also the neighbouring velocity profile and can have a feedback on the transition location. The most promising is the application of intermittency based approach. It should be noted, however that only in such a case where calculations are based on turbulent spots description the intermittency function could be identified as a discriminator between turbulent and non-turbulent flow regions (Savill, 2001). It means that intermittency models do attempt to account at least for spots formation and their growth rates. It is worth to mention, that because transition is sensitive to the free-stream turbulence, pressure gradient, as well as upstream conditions, it is necessary to take into account such influences in intermittency modelling. One of the approaches where these indications were taken into account was applied for numerical simulation of by-pass transition on turbine blade surface by PUIM method. As it was presented above the application of PUIM gave correct identification of not only onset of transition but also of a development of boundary layer to fully turbulent flow.

A new direction for modelling transitional flows is extension of turbulence models by intermittency transport equation which allows for a contamination of the blade flow with the turbulent side-wall boundary layer (Menter at al, 2002). There is also interesting possibility to extend eⁿ and parabolised stability equation (PSE) approaches to variable freestream turbulence in modelling of by-pass transition cases (Savill, 2001). For industrial applications where CPU time is important aspect application of simpler but less demanding methods seems to be reasonable.

Additional advice

The important issue in modelling the flow around blade profile is overprediction of turbulent kinetic energy in the stagnation point flows (Launder, Kato, 1993). It is caused by too small dissipation production due to a very large turbulent time scale in the stagnation region. It is suggested therefore to apply one of the remedies proposed by Durbin (1995) or Launder and Kato (1993), Menter (1992). The first solution is to bound the turbulent time-scale, while the second is to replace the rate of strain by vorticity in the production term, so that the kinetic energy would not grow in a potential flow.

Technical advice

For the proper modelling of the boundary layer general recommendations concerning computational grid should be fulfilled. The density of the mesh should be increased in the direction towards the wall. The wall adjacent grid node should be as close as y'⁺'<5

At least 5 – 10 nodes should be located between the wall and the relative y⁺=20.

Contributors: Andrzej Boguslawski - Technical University of Czestochowa