Predicting Transition in Turbomachinery: Part I — A Review and New Model Development

Here we report on an effort to include an empirically based transition modeling capability in a RANS solver. Testing of well-known empirical models from literature for both attached- and separated-flow transition against cascade data revealed that the models did not provide enough fidelity for implementation in an airfoil design system. Consequently, a program was launched to develop models that would provide sufficient accuracy for use in an airfoil design system. As a first step in the effort, accurate modeling of freestream turbulence development was identified as a need for any form of transition modeling capability. Additionally, capturing the effects of freestream turbulence on pre-transitional boundary layers was found to have a significant effect on the accuracy of transition modeling. A CFD-supplemented database of experimental cascade cases (57 with attached-flow transition and 47 with separation and turbulent reattachment) was constructed to explore the development of new correlations. Dimensional analyses were performed to guide the work and appropriate non-dimensional parameters were then extracted from CFD predictions of the laminar boundary layers existing on the airfoil surfaces prior to either transition onset or incipient separation. For attached-flow transition, exploration of the database revealed a distinct correlation between local levels of freestream turbulence intensity, turbulence length scale, and momentum-thickness Reynolds number at transition onset. It was found that the correlation could be recast as a ratio of the boundary-layer diffusion time to a time-scale associated with the energy-bearing turbulent eddies. In the case of separated-flow transition, it was found that the length of a separation bubble prior to turbulent re-attachment was a simple function of the local momentum thickness at separation and the overall surface length traversed by a fluid element prior to separation. Both the attached- and separated-flow transition models were implemented into the design system as point-like trips.