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.

[1]  D. B. Spalding,et al.  An Improved Version of the k-W Model of Turbulence , 1983 .

[2]  S. Wittig,et al.  Free-Stream Turbulence and Pressure Gradient Effects on Heat Transfer and Boundary Layer Development on Highly Cooled Surfaces , 1985 .

[3]  D. Wilcox.  A model for transitional flows , 1977 .

[4]  Suhas V. Patankar,et al.  Prediction of transition on a flat plate under the influence of free-stream turbulence using low-Reynolds-number two-equation turbulence models , 1987 .

[5]  J. Kestin,et al.  INFLUENCE OF TURBULENCE ON THE TRANSFER OF HEAT FROM PLATES WITH AND WITHOUT A PRESSURE GRADIENT , 1961 .

[6]  P. Saffman,et al.  A model for inhomogeneous turbulent flow , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  Terrence W. Simon,et al.  Heat transfer and fluid mechanics measurements in transitional boundary layers on convex-curved surfaces , 1985 .

[8]  Moshe Israeli,et al.  Numerical calculation of transitional boundary layers , 1982 .

[9]  G. Mellor,et al.  Experiment on convex curvature effects in turbulent boundary layers , 1973, Journal of Fluid Mechanics.

[10]  W. D. Baines,et al.  An Investigation of Flow Through Screens , 1951, Journal of Fluids Engineering.

[11]  A. Townsend.  The Structure of Turbulent Shear Flow , 1975 .

[12]  R. Zerkle,et al.  The influence of freestream turbulence and pressure gradient on heattransfer to gas turbine airfoils , 1987 .

[13]  M. F. Blair,et al.  The influence of free-stream turbulence on the zero pressure gradient fully turbulent boundary layer , 1980 .

[14]  Alexander J. Smits,et al.  The recovery of a turbulent boundary layer from longitudinal curvature , 1986 .

[15]  Mark Malin.  The calculation of two-dimensional buoyant surface jets with the k-W model of turbulence , 1984 .

[16]  M F Blair,et al.  Combined Influence of Free-Stream Turbulence and Favorable Pressure Gradients on Boundary Layer Transition and Heat Transfer , 1981 .

[17]  R. J. Moffat,et al.  A review of turbulent-boundary-layer heat transfer research at Stanford, 1958-1983 , 1984 .

[18]  Klaus Bremhorst,et al.  A Modified Form of the k-ε Model for Predicting Wall Turbulence , 1981 .

[19]  P. Libby,et al.  Analysis of Turbulent Boundary Layers , 1974 .

[20]  D. B. Spalding,et al.  PAPER 2 – A Two-Parameter Model of Turbulence, and its Application to Free Jets , 1983 .

[21]  D. C. Wilcox,et al.  Turbulence-Model Predictions for Turbulent Boundary Layers , 1974 .

[22]  T. Simon,et al.  Heat Transfer and Fluid Mechanics Measurements in Transitional Boundary Layer Flows , 1985 .

[23]  R. Grundmann,et al.  Berechnung von zweidimensionalen, inkompressiblen, transitionellen Grenzschichten an gekrümmten Oberflächen , 1984 .

[24]  P. Bernard,et al.  Limitations of the near-wall k-epsilon turbulence model , 1986 .

[25]  G. H. Junkhan,et al.  Effects of Free-Stream Turbulence and Pressure Gradient on Flat-Plate Boundary-Layer Velocity Profiles and on Heat Transfer , 1967 .

[26]  S. A. Maslowe,et al.  Shear flow instabilities and transition , 1981 .

[27]  E. Epik,et al.  Characteristics of the laminar boundary layer in the presence of elevated free-stream turbulence , 1976 .

[28]  Alair Townsend,et al.  The structure of turbulent shear flow /2nd edition/ , 1976 .

[29]  Wolfgang Rodi,et al.  Scrutinizing the k-ε Turbulence Model Under Adverse Pressure Gradient Conditions , 1986 .

[30]  J. Gillis,et al.  Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall , 1983, Journal of Fluid Mechanics.

[31]  R. T. Wood,et al.  THE MECHANISM WHICH CAUSES FREE-STREAM TURBULENCE TO ENHANCE STAGNATION-LINE HEAT AND MASS TRANSFER , 1970 .

[32]  M. F. Blair.  Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat Transfer and Mean Profile Development, Part I—Experimental Data , 1983 .

[33]  David C. Wilcox,et al.  Turbulence-Model Transition Predictions , 1975 .

[34]  Francis H. Harlow,et al.  TRANSPORT OF TURBULENCE ENERGY DECAY RATE. , 1968 .

[35]  R. W. Fish,et al.  Practical calculations of transitional boundary layers , 1973 .

[36]  A. E. Forest.  Engineering predictions of transitional boundary layers , 1977 .

[37]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[38]  R. A. Delaney.  Time-Marching Analysis of Steady Transonic Flow in Turbomachinery Cascades Using the Hopscotch Method , 1983 .

[39]  J. C. Gibbings,et al.  Influence of Stream Turbulence and Pressure Gradient upon Boundary Layer Transition , 1972 .

[40]  David C Wilcox.  Development of an Alternative to the E9 Procedure for Predicting Boundary-Layer Transition. , 1979 .

[41]  R. Graham.  Fundamental mechanisms that influence the estimate of heat transfer to gas turbine blades , 1980 .

[42]  B. Launder,et al.  Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc , 1974 .

[43]  Kam Hong Ng,et al.  Predictions of turbulent boundary-layer developments using a two-equation model of turbulence , 1972 .

[44]  Michael Poreh,et al.  A Turbulent Energy Model for Flows With Drag Reduction , 1975 .

[45]  B. J. Abu-Ghannam,et al.  Natural Transition of Boundary Layers—The Effects of Turbulence, Pressure Gradient, and Flow History , 1980 .

[46]  E. R. V. Driest,et al.  BOUNDARY LAYER TRANSITION--FREE-STREAM TURBULENCE AND PRESSURE GRADIENT EFFECTS, , 1963 .

[47]  Ting Wang.  An experimental investigation of curvature and freestream turbulence effects on heat transfer and fluid mechanics in transitional boundary layer flows , 1984 .

[48]  F. Brown,et al.  BOUNDARY LAYER TRANSITION , 1963 .

[49]  Dudley Brian Spalding,et al.  PREDICTIONS OF TWO-DIMENSIONAL BOUNDARY LAYERS ON SMOOTH WALLS WITH A TWO-EQUATION MODEL OF TURBULENCE , 1976 .

[50]  N. W. Foster.  Film cooling of gas turbine blades , 1976 .

[51]  P. Bradshaw,et al.  Effect of Free-Stream Turbulence on Heat Transfer through a Turbulent Boundary Layer , 1978 .

[52]  Walter Tollmien,et al.  Über ein neues Formelsystem für die ausgebildete Turbulenz , 1961 .

[53]  P. Bradshaw.  Calculation of boundary-layer development using the turbulent energy equation , 1967, Journal of Fluid Mechanics.

[54]  M. S. Mihelc,et al.  Analytical and Experimental Evaluation of the Heat Transfer Distribution over the Surfaces of Turbine Vanes , 1983 .

[55]  P. Bradshaw.  Effects of Streamline Curvature on Turbulent Flow. , 1973 .

[56]  J. Whitelaw,et al.  Convective heat and mass transfer , 1966 .

[57]  W. Rodi,et al.  Calculation of Heat Transfer to Convection-Cooled Gas Turbine Blades , 1984 .

[58]  Roddam Narasimha,et al.  Some properties of boundary layer flow during the transition from laminar to turbulent motion , 1958, Journal of Fluid Mechanics.

[59]  B. W. Martin,et al.  Flow Transition Phenomena and Heat Transfer Over the Pressure Surfaces of Gas Turbine Blades , 1981 .

[60]  Joseph Kestin,et al.  The influence of turbulence on the transfer of heat to cylinders near the stagnation point , 1961 .

[61]  Robert S. Barlow,et al.  Structure of a turbulent boundary layer on a concave surface , 1988, Journal of Fluid Mechanics.

[62]  Wolfgang Rodi,et al.  Second-moment closure : methodology and practice . Physical and analytical foundations, concepts, and new directions in turburlence modeling and simulation . Examples of turbulence-model applications , 1984 .

[63]  M. F. Blair.  Influence of free-stream turbulence on boundary layer transition in favorable pressure gradients , 1982 .

[64]  W. Jones,et al.  The prediction of laminarization with a two-equation model of turbulence , 1972 .

[65]  B. W. Martin,et al.  Factors influencing heat transfer to the pressure surfaces of gas turbine blades , 1979 .

[66]  Christopher Hornby Priddin.  Behaviour of the turbulent boundary layer on curved, porous walls , 1975 .

[67]  Peter Bradshaw,et al.  The Effect of Free-Stream Turbulence on Turbulent Boundary Layers , 1983 .

[68]  L. D. Daniels,et al.  Calculation of heat transfer rates to gas turbine blades , 1981 .

[69]  M. F. Blair.  Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat Transfer and Mean Profile Development, Part II—Analysis of Results , 1983 .

[70]  W. Jones,et al.  The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence , 1973 .

[71]  Ephraim M Sparrow,et al.  Analysis of Effects of Free-Stream Turbulence on Heat Transfer and Skin Friction , 1977 .

[72]  A. B. Turner,et al.  Local Heat Transfer Measurements on a Gas Turbine Blade , 1971 .

[73]  S. Wittig,et al.  Laminar and Transitional Boundary Layer Structures in Accelerating Flow With Heat Transfer , 1986 .