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

[+] Author and Article Information
T. J. Praisner

 Turbine Aerodynamics, United Technologies Pratt & Whitney, 400 Main St., M/S 169-29, East Hartford, CT 06108

J. P. Clark

Turbine Branch, Turbine Engine Division, Propulsion Directorate, Air Force Research Laboratory, Building 18, Room 136D, 1950 5th St., WPAFB, OH 45433john.clark3@wpafb.af.mil

J. Turbomach 129(1), 1-13 (Mar 01, 2004) (13 pages) doi:10.1115/1.2366513 History: Received October 01, 2003; Revised March 01, 2004

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.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Measured and predicted distributions of free stream turbulence around the C3X airfoil. Data are from Ames (8).

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Figure 2

Comparison of measured and predicted turbulence dissipation around the C3X airfoil. Data are from Ames (8).

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Figure 3

Measured convective heat transfer coefficient distributions from Arts (22) and CFD predictions run with fully laminar boundary layers

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Figure 4

Results from CFD simulations run with the QL model for capturing pre-transitional quasi-laminar boundary layers

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Figure 5

Non-dimensional momentum and thermal boundary layer profiles in a quasi-laminar boundary layer just prior to transition. Data are from Blair (25).

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Figure 6

A comparison between the “universal” curve of Narasimha (43) and both experimental data and simulations from Clark (49)

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Figure 7

A comparison between the current database for attached-flow transition onset and the correlation of Mayle (1)

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Figure 8

A comparison between the transition onset criteria of Liepmann (54), Sharma (48), and Mayle and Schulz (57) and the current attached-flow database

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Figure 9

A comparison of the efficacy of the current transition-onset model for attached flow with that of Abu-Ghannam and Shaw (11)

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Figure 10

The current model for the onset of attached-flow transition compared to the database

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Figure 11

Schematic representation of suction-side, laminar-separation characteristics showing both reattached (a) and stalled (b) conditions

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Figure 12

Measured and predicted separation and reattachment locations. Transition was specified in the simulations based on data.

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Figure 13

A comparison between the separated-flow transition model of Roberts (71) and the separated-flow transition database

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Figure 14

A comparison between the separated-flow transition models of Mayle (1) and the separated-flow transition database

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Figure 15

The current model and database for separated-flow transition. The model with a conservative shift is also shown.




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