James H. Leylek

A New Model for Boundary Layer Transition Using a Single-Point RANS Approach

This paper presents the development and implementation of a new model for bypass and natural transition prediction using Reynolds-averaged Navier-Stokes computational fluid dynamics (CFD), based on modification of two-equation, linear eddy-viscosity turbulence models. The new model is developed herein based on considerations of the universal character of transitional boundary layers that have recently been documented in the open literature, and implemented into a popular commercial CFD code (FLUENT) in order to assess its performance. Two transitional test cases are presented: (1) a boundary layer developing on a flat heated wall, with free-stream turbulence intensity (Tu∞) ranging from 0.2 to 6%; and (2) flow over a turbine stator vane, with chord Reynolds number 2.3 × 10 5 , and Tu∞ from 0.6 to 20%. Results are presented in terms of Stanton number, and compared to experimental data for both cases. Results show good agreement with the test cases and suggest that the new approach has potential as a predictive tool.

A Systematic Computational Methodology Applied to a Three-Dimensional Film-Cooling Flowfield

Numerical results are presented for a three-dimensional discrete-jet in crossflow problem typical of a realistic film-cooling application in gas turbines. Key aspects of the study include: (1) application of a systematic computational methodology that stresses accurate computational model of the physical problem, including simultaneous, fully elliptic solution of the crossflow, film-hole, and plenum regions; high-quality three-dimensional unstructured grid generation techniques, which have yet to be documented for this class of problems ; the use ofa high-order discretization scheme to reduce numerical errors significantly; and effective turbulence modeling; (2) a three-way comparison of results to both code validation quality experimental data and a previously documented structured grid simulation; and (3) identification of sources of discrepancy between predicted and measured results, as well as recommendations to alleviate these discrepancies. Solutions were obtained with a multiblock, unstructured/adaptive grid, fully explicit, time-marching, Reynolds-averaged Navier-Stokes code with multigrid, local time stepping, and residual smoothing type acceleration techniques. The computational methodology was applied to the validation test case of a row of discrete jets on a flat plate with a streamwise injection angle of 35 deg, and two film-hole length-to-diameter ratios of 3.5 and 1.75. The density ratio for all cases was 2.0, blowing ratio was varied from 0.5 to 2.0, and free-stream turbulence intensity was 2 percent. The results demonstrate that the prescribed computational methodology yields consistently more accurate solutions for this class of problems than previous attempts published in the open literature. Sources of disagreement between measured and computed results have been identified, and recommendations made for future prediction of film-cooling problems.

Computational Fluid Dynamics Study of Wake-Induced Transition on a Compressor-Like Flat Plate

Recent experimental work has documented the importance of wake passing on the behavior of transitional boundary layers on the suction surface of axial compressor blades. This paper documents computational fluid dynamics (CFD) simulations using a commercially available general-purpose CFD solver, performed on a representative case with unsteady transitional behavior. The study implements an advanced version of a three-equation eddy-viscosity model previously developed and documented by the authors, which is capable of resolving boundary layer transition. It is applied to the test cases of steady and unsteady boundary layer transition on a two-dimensional flat plate geometry with a freestream velocity distribution representative of the suction side of a compressor airfoil. The CFD results are analyzed and compared to a similar experimental test case from the open literature. Results with the model show a dramatic improvement over more typical Reynolds-averaged Navier-Stokes (RANS)-based modeling approaches, and highlight the importance of resolving transition in both steady and unsteady compressor aerosimulations.

Three-Dimensional Conjugate Heat Transfer Simulation of an Internally-Cooled Gas Turbine Vane

A conjugate numerical methodology was employed to predict the metal temperature of a three-dimensional gas turbine vane at two different engine-realistic operating conditions. The vane was cooled internally by air flowing through ten round, radially-oriented channels. The conjugate heat transfer approach allows the simultaneous solution of the external flow, internal convection, and conduction within the metal vane, eliminating the need for multiple, decoupled solutions, which are time-consuming and inherently less accurate when combined. Boundary conditions were specified only for the inlet and exit of the vane passage and the coolant channels, while the solid and fluid zones were coupled by energy conservation at the interfaces, a condition that was maintained throughout the iterative solution process. Validation of the methodology was accomplished through the comparison of the predicted aerodynamic loading curves and the midspan temperature distribution on the vane external surface with data from a linear cascade experiment in the literature. The superblock, unstructured numerical grid consisted of nearly seven million finite-volumes to allow accurate resolution of flowfield features and temperature gradients within the metal. Two models for turbulence closure were used for comparison: the standard k-e model and a realizable version of the k-e model. The predictions with the realizable k-e model exhibited the best agreement with the experimental data, with maximum differences in normalized temperature of less than ten percent in each case. The present study shows that the conjugate heat transfer simulation is a viable tool in gas turbine design, and it serves as a platform on which to base future work with more complex geometries and cooling schemes.© 2003 ASME

Pressure-Side Bleed Film Cooling: Part I — Steady Framework for Experimental and Computational Results

This study examines the unsteady transonic pressure-side bleed film cooling on the trailing edge of a turbine blade and resolves the key mechanism responsible for the unusual relationship between film cooling effectiveness and increasing blowing ratio. This study is meant to show that unsteadiness is the key mechanism causing the unexpected results seen in the experiments. It is believed that this unsteadiness is highly dependent on the ratio of the lip thickness to slot height and the shedding frequencies of the passage and coolant vortices, which depend on blowing ratio. For low blowing ratio, hot passage flow has the dominant vortices. For high blowing ratio, coolant flow has the dominant vortices. For intermediate blowing ratio, the vortices have the potential to interact and cause the unusual behavior seen in pressure-side bleed film cooling. On the basis of these observations, experiments were repeated with pressure probes used to acquire the shedding frequencies at the effectiveness measurement location, which showed that unsteadiness was indeed present. Realistic engine conditions are considered with lip thickness to slot height ratio of 0.9 and mainstream Mach numbers of 0.7 at the coolant injection point and expanding to sonic conditions at the exit plane of the test section. Numerical results are from a 2-D mid-plane cut of the original geometry and a full-pitch 3-D model. Computations use high quality grids, high order discretization schemes, and an advanced turbulence model. The 3-D grid consists of 4.4 million cells and a high quality, unstructured, multi-topology mesh with resolution of the viscous sublayer and y+ < 1 on all surfaces. The simulations are fully converged, time accurate, and grid-independent. A novel methodology is used to introduce unsteadiness into the simulations. Effects of blowing ratio are examined, where blowing ratio is equal to 1.0 for 3-D and ranges from 0.3 to 1.5 for 2-D with a density ratio of 1.52. By performing an unsteady simulation, the unusual relationship between the effectiveness and blowing ratio is demonstrated in an unsteady framework.Copyright

Performance of Turbulence Models and Near-Wall Treatments in Discrete Jet Film Cooling Simulations

For the first time in the open literature, code validation quality data and a well-tested, highly reliable computational methodology are employed to isolate the true performance of seven turbulence treatments in discrete jet film cooling. The present research examines both computational and high quality experimental data for two length-to-diameter ratios of a row of streamwise injected, cylindrical film holes. These two cases are used to document the performance of the following turbulence treatments: 1) standard k-e model with generalized wall functions; 2) standard k-e model with non-equilibrium wall functions: 3) Renormalization Group k-e (RNG) model with generalized wall functions; 4) RNG model with non-equilibrium wall functions: 51 standard k-e model with two-layer turbulence wall treatment; 6) Reynolds Stress Model (RSM) with generalized wall functions; and 7) RSM with non-equilibrium wall functions. Overall, the standard k-e turbulence model with the two-layer near-wall treatment, which resolves the viscous sublayer, produces results that are more consistent with experimental data.Copyright

Impact of Film-Cooling Jets on Turbine Aerodynamic Losses

This paper documents a computational investigation of the aerodynamic impact of film cooling on a linear turbine airfoil cascade. The simulations were for single row injection on both the pressure and suction surfaces, downstream of the leading edge region. The cases match experimental efforts previously documented in the open literature. Results were obtained for density ratio equal to 1.0 and 2.0, and a blowing ratio range from 0.91 to 6.6. The domain included the passage flow as well as the film hole and blade interior. The simulation used a dense, high-quality, unstructured hybrid-topology grid, comprised of hexahedra, tetrahedra, prisms, and pyramids. The processing was performed with a pressure-correction solution procedure and a second-order discretization scheme. Turbulence closure was obtained using standard, RNG, and realizable k-e models, as well as a Reynolds stress model. Results were compared to experimental data in terms of total pressure loss downstream of the blade row. Flow mechanisms responsible for the variation of aerodynamic losses due to suction and pressure surface coolant injection are documented. The results demonstrate that computational methods can be used to predict losses accurately on film-cooled airfoils.

Leading Edge Film-Cooling Physics: Part I — Adiabatic Effectiveness

A systematic, computational methodology was employed to study film cooling on a turbine airfoil leading edge. In this paper, numerical predictions are compared with surface effectiveness measurements from a code-validation quality experiment in the open literature, and a detailed discussion of the physical mechanisms involved in leading edge film cooling is presented. The leading edge model was elliptic in shape to accurately simulate a rotor airfoil, and other geometric parameters were in the range of current design practice for aviation gas turbines. Three laterally-staggered rows of cylindrical film-cooling holes were investigated. One row of holes was centered on the stagnation line, and the other rows were located 3.5 hole-diameters downstream, mirrored about the stagnation line. All holes had an injection angle of 20° with the surface, and a 90° compound angle (radial injection). The average blowing ratio was varied from 1.0 to 2.5, and the coolant-to-mainstream density ratio was 1.8 in all simulations. Converged and grid independent solutions were obtained using a high-quality, multi-topology grid with 3.6 million cells and a fully-implicit, pressure correction-based Navier-Stokes solver. Turbulence closure was obtained with a realizable k-e model, which has been demonstrated to be especially effective in controlling spurious production of turbulent kinetic energy in regions of rapid, irrotational strain. The predictions of laterally averaged effectiveness agreed well with the experimental data, especially at low-range blowing ratios. Highly nonuniform coolant coverage was seen to exist downstream of the second row of holes, caused mainly by interaction between the two rows of jets and by a strong vortex that reduced the spread of coolant from the downstream row. The results of the present study demonstrate that computational methods can accurately model the highly-complex film-cooling flowfield in the stagnation region.Copyright

A Detailed Analysis of Film–Cooling Physics: Part I — Streamwise Injection With Cylindrical Holes

A previously documented systematic computational methodology is implemented and applied to a jet–in–crossflow problem in order to document all of the pertinent flow physics associated with a film–cooling flowfield. Numerical results are compared to experimental data for the case of a row of three–dimensional, inclined jets with length–to–diameter ratios similar to a realistic film–cooling application. A novel vorticity based approach is included in the analysis of the flow physics. Particular attention has been paid to the downstream coolant structures and to the source and influence of counter–rotating vortices in the crossflow region. It is shown that the vorticity in the boundary layers within the film hole is primarily responsible for this secondary motion. Important aspects of the study include: (1) a systematic treatment of the key numerical issues, including accurate computational modeling of the physical problem, exact geometry and high quality grid generation techniques, higher–order numerical discretization, and accurate evaluation of turbulence model performance; (2) vorticity–based analysis and documentation of the physical mechanisms of jet–crossflow interaction and their influence on film–cooling performance; (3) a comparison of computational results to experimental data; and (4) comparison of results using a two–layer model near–wall treatment versus generalized wall functions. Solution of the steady, time–averaged Navier–Stokes equations were obtained for all cases using an unstructured/adaptive grid, fully explicit, time–marching code with multi–grid, local time stepping, and residual smoothing acceleration techniques. For the case using the two–layer model, the solution was obtained with an implicit, pressure–correction solver with multi–grid. The three–dimensional test case was examined for two different film–hole length–to–diameter ratios of 1.75 and 3.5, and three different blowing ratios, from 0.5 to 2.0. All of the simulations had a density ratio of 2.0, and an injection angle of 35°. An improved understanding of the flow physics has provided insight into future advances to film–cooling configuration design. In addition, the advantages and disadvantages of the two–layer turbulence model are highlighted for this class of problems.Copyright

A simple and robust linear eddy‐viscosity formulation for curved and rotating flows

Purpose – The purpose of this paper is to present a new eddy‐viscosity formulation designed to exhibit a correct response to streamline curvature and flow rotation. The formulation is implemented into a linear k‐ e turbulence model with a two‐layer near‐wall treatment in a commercial computational fluid dynamics (CFD) solver.Design/methodology/approach – A simple, robust formula is developed for the eddy‐viscosity that is curvature/rotation sensitive and also satisfies realizability and invariance principles. The new model is tested on several two‐ and three‐dimensional problems, including rotating channel flow, U‐bend flow and internally cooled turbine airfoil conjugate heat transfer. Predictions are compared to those with popular eddy‐viscosity models.Findings – Converged solutions to a variety of turbulent flow problems are obtained with no additional computational expense over existing two‐equation models. In all cases, results with the new model are superior to two other popular k‐ e model variants, ...