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.Copyright © 2004 by ASME

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

Corrugated ducts are commonly used in compact heat exchangers because of their efficient heat exchange capabilities. Here, the numerical prediction of transitional characteristics of fluid flow and heat transfer in periodic fully developed corrugated duct is carried out by using a Lam-Bremhorst low Reynolds number turbulence model. Computations were performed for Prandtl number of 0.7, in the Reynolds number range of 100 to 2500, for corrugation angles of {theta} = 15 and 30{degree}, and for three interwall spacings. The predicted transitional Reynolds number is lower than the value for the parallel plate duct and it decreases with increasing corrugation angle. Experiments were also performed for pressure drop measurements and for flow visualization and the results were compared with the numerical predictions.

Numerical prediction of transitional characteristics of flow and heat transfer in a corrugated duct

Assessment of various CFD models for predicting airflow and pressure drop through pleated filter system

A model has been developed to incorporate more of the physics offree-stream turbulence effects into boundary layer calculations. The transport in the boundary layer is modeled using three terms: (1) the molecular viscosity, ν (2) the turbulent eddy viscosity, ∈ T , as used in existing turbulence models; and (3) a new free-stream-induced eddy viscosity, ∈ f . The three terms are added to give an effective total viscosity. The free-stream-induced viscosity is modeled algebraically with guidance from experimental data. It scales on the rms fluctuating velocity in the free stream, the distance from the wall, and the boundary layer thickness. The model assumes a direct tie between boundary layer and free-stream fluctuations, and a distinctly different mechanism than the diffusion of turbulence from the free-stream to the boundary layer assumed in existing higher order turbulence models. The new model can be used in combination with any existing turbulence model. It is tested here in conjunction with a simple mixing length model and a parabolic boundary layer solver. Comparisons to experimental data are presented for flows with free-stream turbulence intensities ranging from I to 8 percent and for both zero and nonzero streamwise pressure gradient cases. Comparisons are good. Enhanced heat transfer in higher turbulence cases is correctly predicted. The effect of the free-stream turbulence on mean velocity and temperature profiles is also well predicted. In turbulent flow, the log region in the inner part of the boundary layer is preserved, while the wake is suppressed. The new model provides a simple and effective improvement for boundary layer prediction.

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A New Model for Free-Stream Turbulence Effects on Boundary Layers

Progress towards understanding and predicting heat transfer in the turbine gas path

The use of low Reynolds number (LRN) forms of the k-epsilon turbulence model in predicting transitional boundary layer flow characteristic of gas turbine blades is developed. The research presented consists of: (1) an evaluation of two existing models; (2) the development of a modification to current LRN models; and (3) the extensive testing of the proposed model against experimental data. The prediction characteristics and capabilities of the Jones-Launder (1972) and Lam-Bremhorst (1981) LRN k-epsilon models are evaluated with respect to the prediction of transition on flat plates. Next, the mechanism by which the models simulate transition is considered and the need for additional constraints is discussed. Finally, the transition predictions of a new model are compared with a wide range of different experiments, including transitional flows with free-stream turbulence under conditions of flat plate constant velocity, flat plate constant acceleration, flat plate but strongly variable acceleration, and flow around turbine blade test cascades. In general, calculational procedure yields good agreement with most of the experiments.

Two-Equation Low-Reynolds-Number Turbulence Modeling of Transitional Boundary Layer Flows Characteristic of Gas Turbine Blades. Ph.D. Thesis. Final Contractor Report

The use of low Reynolds number (LRN) forms of the k-epsilon turbulence model in predicting transitional boundary layer flow characteristic of gas turbine blades is developed The research presented consists of: (1) an evaluation of two existing models; (2) the development of a modification to current LRN models; and (3) the extensive testing of the proposed model against experimental data The prediction characteristics and capabilities of the Jones-Launder (1972) and Lam-Bremhorst (1981) LRN k-epsilon models are evaluated with respect to the prediction of transition on flat plates Next, the mechanism by which the models simulate transition is considered and the need for additional constraints is discussed Finally, the transition predictions of a new model are compared with a wide range of different experiments, including transitional flows with free-stream turbulence under conditions of flat plate constant velocity, flat plate constant acceleration, flat plate but strongly variable acceleration, and flow around turbine blade test cascades In general, calculational procedure yields good agreement with most of the experiments

Two-Equation Low-Reynolds-Number Turbulence Modeling of Transitional Boundary Layer Flows Characteristic of Gas Turbine Blades

The prediction characteristics and capabilities of two popular two-equation low-Reynolds-number turbulence models (Jones, Launder 1972; Lam, Bremhorst 1981) have been evaluated with respect to the prediction of transition of a flat plate under the influence of free-stream turbulence. The sensitivity of the predictions to free-stream turbulence intensity, initial starting location of the calculation, and the assumed initial starting profiles for k and epsilon has been determined and presented. Although both models predict the correct qualitative characteristics of transition, they also exhibit significant quantitative deficiencies with regard to both the predicted location and the length of transition. A modification to the production term in the turbulent kinetic energy equation is proposed which is based on a simple stability criterion and correlated to the free-stream turbulence level. The modification becomes inactive in the fully turbulent regime, but is shown to improve both the qualitative and quantitative characteristics of the transition predictions.

Prediction of transition on a flat plate under the influence of free-stream turbulence using low-Reynolds-number two-equation turbulence models

A research effort was underway to study the use of two equation low Reynolds number turbulence models in predicting gas side heat transfer on turbine blades. The major objectives of this work are basicly threefold: study the predictive capabilities of two equation low Reynolds number turbulence models under the conditions characteristic of modern gas turbine blades; explore potential improvements to the models themselves as well as to the specification of initial conditions; and provide a comparison of the predictions of these models with the experimental data from a broad range of recently available turbine cascade experiments. The problems associated with predicting the boundary layer transition from laminar to turbulent flow are emphasized, as this may be the most serious deficiency of current modeling techniques. The results and conclusions of the first two phases are briefly described.

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Development of low Reynolds number two equation turbulence models for predicting external heat transfer on turbine blades

A modified form of the Lam-Bremhorst low-Reynolds number kappa-epsilon turbulence model was developed for predicting transitional boundary layer flows under conditions characteristic of gas turbine blades. The application of the model to flows with pressure gradients is described. Tests against a number of turbine blade cascade data sets are included. Some additional refinements of the model that were made in recent months are explained.

Rodney C. Schmidt

Papers

Two-Equation Low-Reynolds-Number Turbulence Modeling of Transitional Boundary Layer Flows Characteristic of Gas Turbine Blades. Ph.D. Thesis. Final Contractor Report

Two-Equation Low-Reynolds-Number Turbulence Modeling of Transitional Boundary Layer Flows Characteristic of Gas Turbine Blades

Prediction of transition on a flat plate under the influence of free-stream turbulence using low-Reynolds-number two-equation turbulence models

Development of low Reynolds number two equation turbulence models for predicting external heat transfer on turbine blades

A low-Reynolds-number two-equation turbulence model for predicting heat transfer on turbine blades