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 Reynolds Averaged Navier-Stokes solver. Well known empirical models for both attached- and separated-flow transition were tested against cascade data and found unsuitable for use in turbomachinery design. Consequently, a program was launched to develop models with sufficient accuracy for use in design. As a first step, accurate prediction of free stream turbulence development was identified as a prerequisite for accurate modeling. Additionally, a demonstrated capability to capture the effects of free stream turbulence on pre-transitional boundary layers became an impetus for the work. A computational fluid dynamics (CFD)-supplemented database of 104 experimental cascade cases 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, onset was found to occur at a critical 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 reattachment 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.