William D. York

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

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 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, ...

Leading-Edge Film-Cooling Physics—Part III: Diffused Hole Effectiveness

A proven computational methodology was applied to investigate film cooling from diffused holes on the simulated leading edge of a turbine airfoil. The short film-hole diffuser section was conical in shape with a shallow half-angle, and was joined to a plenum by a cylindrical metering section. The diffusion resulted in a film-hole breakout area of 2.5 times that of a cylindrical hole. In the present paper, predictions of adiabatic effectiveness for the cases with diffused holes are compared to results for standard cylindrical holes, and performance is analyzed in the context of extensive flowfield data. The leading edge surface was elliptic in shape to accurately model a turbine airfoil. The geometry consisted of one row of holes centered on the stagnation line and nvo additional rows located 3.5 hole (metering section) diameters downstream on either side of the stagnation line. Film holes in the downstream rows were centered laterally between holes in the stagnation row. All holes were angled at 20 deg with the leading edge surface, and were turned 90 deg with respect to the streamwise direction (radial injection). The average blowing ratio was varied from 1.0 to 2.5, and the coolant-to-mainstream density ratio was equal to 1.8. The steady Reynolds-averaged Navier-Stokes equations were solved with a pressure-correction algorithm on an unstructured, multi-block grid containing 4.6 million finite-volumes. A realizable k-e turbulence model was employed to close the equations. Convergence and grid-independence was verified using strict criteria. Based on the laterally averaged effectiveness over the leading edge. the diffused holes showed a marked advantage over standard holes through the range of blowing ratios. However, ingestion of hot crossflow and thermal diffusion into the second row of film holes was observed to cause significant, and potentially detrimental, heating of the film-hole walls.

Leading-Edge Film-Cooling Physics: Part II — Heat Transfer Coefficient

A comprehensive study of film cooling on a turbine airfoil leading edge was performed with a documented, well-tested computational methodology. In this paper, numerically predicted heat transfer coefficients on the film-cooled leading edge are compared with experimental data from the open literature. The results are presented as the ratio of heat transfer coefficient with film cooling to that without film cooling, and the physics behind the surface results are discussed. The leading edge model was a half-cylinder in shape with a bluff afterbody to match the validation experiment, and other geometric parameters matched those of Part I of this study. Coolant at a density equal to that of the mainstream flow was injected through three rows of cylindrical film-cooling holes. One row of holes was centered on the stagnation line of the cylinder, and the other two rows were located ±3.5 hole diameters off stagnation. The downstream rows were staggered such that they were centered laterally between holes in the stagnation row. The holes were inclined at 20° with the surface, and made a 90° angle with the streamwise direction (radial injection). Four average blowing ratios were simulated in the range of 0.75 to 1.9, corresponding to the same momentum flux ratios as in Part I of this work. The multi-block, unstructured numerical grid was characterized by high quality and density, especially in the near wall region, in order to minimize error in predictions of the heat transfer. A fully-implicit scheme was used to solve the steady Reynolds-averaged Navier-Stokes equations, and a realizable k-e model provided turbulence closure. A two-layer near-wall treatment allowed the resolution of the viscous sublayer for maximum accuracy in the prediction of the wall heat transfer coefficient. The numerical predictions exhibited generally good agreement with experimental data. The heat transfer coefficient was observed to increase sharply aft of the holes in the downstream rows. When coupled with the adiabatic effectiveness results of the first paper in this series, it is evident that a systematic computational methodology may be effectively applied to investigate and understand the complicated leading edge film-cooling problem.Copyright

Prediction of Heat Transfer in a Ribbed Channel: Evaluation of Unsteady RANS Methodology

Heat transfer in a straight channel with rib turbulators on one wall is predicted numerically with an unsteady Reynolds-averaged Navier-Stokes (URANS) methodology and compared to code-validation quality experimental data from the literature. Additionally, for comparison, steady simulations of the problem are conducted using two popular turbulence closure models, a Realizable k-e model and a differential Reynolds-stress model. Closure in the URANS simulation is provided by a new eddy-viscosity-based model that was developed in the Advanced Computational Research Laboratory at Clemson University. This new model consists of three transport equations, and it is designed specifically to promote natural unsteadiness in the flow without the need for artificial forcing. In all cases, the Reynolds number, based on hydraulic diameter, is equal to 24,000. Eight square ribs, orthogonal to the flow direction, are equally spaced on the bottom wall of the channel. For the URANS simulation, after the flow becomes fully-developed in the streamwise direction, the predicted Nusselt number on the ribbed wall follows the trend of measured data from the modeled experimental study. However, the unsteady simulation slightly overpredicts the distance to the peak heat transfer aft of each rib. Also, the heat transfer prediction is very dependent on the grid resolution aft of the ribs. Therefore, efficient refinement of the unstructured mesh and grid-independence issues are discussed. Results of both steady simulations show a significant underprediction of Nusselt number over the entire ribbed wall, with the Reynolds-stress model giving the better result of the two steady closure models. The results of this study clearly show that unsteady vortex shedding off of the ribs is important in the physics of this problem, and a systematic, unsteady methodology is necessary to accurately predict ribbed-channel heat transfer.Copyright

A Novel Transition-Sensitive Conjugate Methodology Applied to Turbine Vane Heat Transfer

A documented numerical methodology for conjugate heat transfer was employed to predict the metal temperature of an internally-cooled gas turbine vane at realistic operating conditions. The conjugate heat transfer approach involves the simultaneous solution of the flow field (convection) and the conduction within the metal vane, allowing a solution of the complete heat transfer problem in a single simulation. This technique means better accuracy and faster turn-around time than the typical industry practice of multiple, decoupled solutions. In the present simulations, the solid and fluid zones were coupled by energy conservation at the interfaces. In the fluid zones, the Reynoldsaveraged Navier-Stokes equations were closed with a three-equation, eddy-viscosity model, developed in-house and previously documented, with the capability to predict laminar-to-turbulent boundary-layer transition. The single-point model is fully-predictive for transition and requires no problem-dependent user inputs. For comparison, a simulation was also run with a commercially available Realizable k-e turbulence model. A high-quality, unstructured gird was employed in both cases. Numerical predictions for midspan temperature on the airfoil surface are compared to data from an open-literature experiment with the same geometry and operating conditions. The new model captured transition of the initially laminar boundary layer to a turbulent boundary layer on the suction surface. The results with the new model show excellent agreement with measured data for surface temperature over the majority of the airfoil surface. The new model showed a marked improvement over the Realizable k-e model in all regions where laminar boundary layers exist, highlighting the importance of accurately modeling transition in turbomachinery heat transfer simulations.Copyright

Numerical Prediction of Mainstream Pressure Gradient Effects in Film Cooling

A documented, systematic, computational methodology is applied to singularly investigate the effects of mainstream pressure gradients on film cooling over a flat surface for realistic gas turbine parameters. Key aspects of the study include: (1) validation of the ability of computational fluid dynamics to simulate film cooling in regions of mainstream pressure gradients, accomplished through the isolation of this parameter and the careful modeling of a published experimental study; (2) documentation of the effects of the applied pressure gradient on film cooling adiabatic effectiveness, as compared to the zero-pressure gradient case; and (3) detailed discussion of the pertinent physical mechanisms involved, with appropriate flowfield results. The imposed pressure gradient is typical of the suction surface of a gas turbine airfoil, with a strong favorable pressure gradient (the acceleration parameter was K = 1.5×10−6 at injection) transitioning to a mild adverse pressure gradient region beyond 30 diameters downstream. A single row of cylindrical film-cooling holes had an injection angle of 35°, with hole length-to-diameter ratio of 4.0 and a lateral spacing of 3.0 diameters. The simulated mass flux ratios were M = 0.6, 1.0, and 1.5, and the density ratio was held constant at 1.6. Solutions were obtained using a multi-block, multi-topology grid and a pressure-correction based, fully-implicit Navier-Stokes solver. A “realizeable” k-e turbulence model, which eliminates the documented unrealistic turbulence production of the standard k-e model in regions of large flow strain, was employed to obtain practical results economically. The applied pressure gradient resulted in a small advantage in center-line effectiveness, while laterally averaged effectiveness was slightly lower as compared to the zero-pressure gradient reference case. The results of this study demonstrate the ability of the applied computational methodology to accurately model film cooling in the presence of mainstream pressure gradients and resolve one of the key fundamental issues in turbine airfoil film cooling.Copyright

Performance Prediction of a Novel Design for Turbine Vane Film Cooling With Low Aerodynamic Loss and High Effectiveness

A new film-cooling scheme for the suction surface of a gas turbine vane in a transonic cascade is studied numerically. The concept of the present design is to inject a substantial amount of coolant at a very small angle, approaching a “wall-jet,” through a single row of relatively few, large holes near the vane leading edge. The near-match of the coolant stream and mainstream momentums, coupled with the low coolant trajectory, theoretically results in low aerodynamic losses due to mixing. A minimal effect of the film cooling on the vane loading is also important to realize, as well as good coolant coverage and high adiabatic effectiveness. A systematic computational methodology, developed in the Advanced Computational Research Laboratory (ACRL) and tested numerous times on film-cooling applications, is applied in the present work. For validation purposes, predictions from two previous turbine airfoil film-cooling studies, both employing this same numerical method, are presented and compared to experimental data. Simulations of the new film-cooling configuration are performed for two blowing ratios, M=0.90 and M=1.04, and the density ratio of the coolant to the mainstream flow is unity in both cases. A solid vane with no film cooling is also studied as a reference case in the evaluation of losses. The unstructured numerical mesh contains about 5.5 million finite-volumes, after solution-based adaption. Grid resolution is such that the full boundary layer and all passage shocks are resolved. The Renormalization Group (RNG) k-e turbulence model is used to close the Reynolds-averaged Navier-Stokes equations. Predictions indicate that the new film-cooling scheme meets design intent and has negligible impact on the total pressure losses through the vane cascade. Additionally, excellent coolant coverage is observed all the way to the trailing edge, resulting in high far-field effectiveness. Keeping the design environment in mind, this work represents the power of validated computational methods to provide a rapid and reasonably cost-effective analysis of innovative turbine airfoil cooling.© 2004 ASME

Leading-Edge Film-Cooling Physics: Part III — Diffused Hole Effectiveness

holes on the simulated leading edge of a turbine airfoil. The short film-hole diffuser section was conical in shape with a shallow half-angle, and was joined to a plenum by a cylindrical metering section. The diffusion resulted in a film-hole breakout area of 2.5 times that of a cylindrical hole. In the present paper, predictions of adiabatic effectiveness for the cases with diffused holes are compared to results for standard cylindrical holes, and performance is analyzed in the context of extensive flowfield data. The leading edge surface was elliptic in shape to accurately model a turbine airfoil. The geometry consisted of one row of holes centered on the stagnation line, and two additional rows located 3.5 hole (metering section) diameters downstream on either side of the stagnation line. Film holes in the downstream rows were centered laterally between holes in the stagnation row. All holes were angled at 20 deg with the leading edge surface, and were turned 90 deg with respect to the streamwise direction (radial injection). The average blowing ratio was varied from 1.0 to 2.5, and the coolant-to-mainstream density ratio was equal to 1.8. The steady Reynolds-averaged Navier-Stokes equations were solved with a pressurecorrection algorithm on an unstructured, multi-block grid containing 4.6 million finitevolumes. A realizable k-« turbulence model was employed to close the equations. Convergence and grid-independence was verified using strict criteria. Based on the laterally averaged effectiveness over the leading edge, the diffused holes showed a marked advantage over standard holes through the range of blowing ratios. However, ingestion of hot crossflow and thermal diffusion into the second row of film holes was observed to cause significant, and potentially detrimental, heating of the film-hole walls. @DOI: 10.1115/1.1559899#