Inverse Boundary Element/genetic Algorithm Method For Reconstruction O

A methodology is formulated for the solution of the inverse problem concerned with the reconstruction of multi-dimensional heat fluxes for film cooling applications. The motivation for this study is the characterization of complex thermal conditions in industrial applications such as those encountered in film cooled turbomachinery components. The heat conduction problem in the metal endwall/shroud is solved using the boundary element method (bem), and the inverse problem is solved using a genetic algorithm (ga). Thermal conditions are overspecified at exposed surfaces amenable to measurement, while the temperature and surface heat flux distributions are unknown at the film cooling hole/slot walls. The latter are determined in an iterative process by developing two approaches. The first approach, developed for 2d applications, solves an inverse problem whose objective is to adjust the film cooling hole/slot wall temperatures and heat fluxes until the temperature and heat flux at the measurement surfaces are matched in an overall heat conduction solution. The second approach, developed for 2d and 3d applications, is to distribute a set of singularities (sinks) at the vicinity of the cooling slots/holes surface inside a fictitious extension of the physical domain or along cooling hole centerline with a given initial strength distribution. The inverse problem iteratively alters the strength distribution of the singularities (sinks) until the measuring surfaces heat fluxes are matched. The heat flux distributions are determined in a post-processing stage after the inverse problem is solved. The second approach provides a tremendous advantage in solving the inverse problem, particularly in 3d applications, and it is recommended as the method of choice for this class of problems. It can be noted that the ga reconstructed heat flux distributions are robust, yielding accurate results to both exact and error-laden inputs. In all cases in this study, results from experiments are simulated using a full conjugate heat transfer (cht) finite volume models which incorporate the interactions of the external convection in the hot turbulent gas, internal convection within the cooling plena, and the heat conduction in the metal endwall/shroud region. Extensive numerical investigations are undertaken to demonstrate the significant importance of conjugate heat transfer in film cooling applications and to identify the implications of various turbulence models in the prediction of accurate and more realistic surface temperatures and heat fluxes in the cht simulations. These, in turn, are used to provide numerical inputs to the inverse problem. Single and multiple cooling slots, cylindrical cooling holes, and fan-shaped cooling holes are considered in this study. The turbulence closure is modeled using several two-equation approach, the four-equation turbulence model, as well as five and seven moment reynolds stress models. The predicted results, by the different turbulence models, for the cases of adiabatic and conjugate models, are compared to experimental data reported in the open literature. Results show the significant effects of conjugate heat transfer on the temperature field in the film cooling hole region, and the additional heating up of the cooling jet itself. Moreover, results from the detailed numerical studies presented in this study validate the inverse problem approaches and reveal good agreement between the bem/ga reconstructed heat fluxes and the cht simulated heat fluxes along the inaccessible cooling slot/hole wall

Singular Superposition/Boundary Element Method for Reconstruction of Multi-dimensional Heat Flux Distributions with Application to Film Cooling Holes

A hybrid singularity superposition/boundary element-based inverse problem method for the reconstruction of multi-dimensional heat flux distributions is developed. Cauchy conditions are imposed at exposed surfaces that are readily reached for measurements while convective boundary conditions are unknown at surfaces that are not amenable to measurements such as the walls of the cooling holes. The purpose of the inverse analysis is to determine the heat flux distribution along cooling hole surfaces. This is accomplished in an iterative process by distributing a set of singularities (sinks) inside the physical boundaries of the cooling hole (usually along cooling hole centerline) with a given initial strength distribution. A forward steady-state heat conduction problem is solved using the boundary element method (BEM), and an objective function is defined to measure the difference between the heat flux measured at the exposed surfaces and the heat flux predicted by the BEM under the current strength distribution of the singularities. A Genetic Algorithm (GA) iteratively alters the strength distribution of the singularities until the measuring surfaces heat fluxes are matched, thus satisfying Cauchy conditions. The distribution of the heat flux at the walls of the cooling hole is determined in a post-processing stage after the inverse problem is solved. The advantage of this technique is to eliminate the need of meshing the surfaces of the cooling holes, which requires a large amount of effort to achieve a high quality mesh. Moreover, the use of singularity distributions significantly reduces the number of parameters sought in the inverse problem, which constitutes a tremendous advantage in solving the inverse problem, particularly in the application of film cooling holes

Film Cooling Effectiveness From A Single Scaled-Up Fan-Shaped Hole A Cfd Simulation Of Adiabatic And Conjugate Heat Transfer Models

This paper documents a computational investigation of the film cooling effectiveness of a 3-D gas turbine endwall with one fan-shaped cooling hole. The simulations were performed for adiabatic and conjugate heat transfer models. Turbulence closure was investigated using three different turbulence models; the realizable k-ε model, the SST k-ω model, as well as the v 2 - f turbulence model. Results were obtained for a blowing ratio of one, and a coolant-to-mainflow temperature ratio of 0.54. The simulations used a dense, high quality, O-type, hexahedral grid with three different schemes of meshing for the cooling hole: hexahedral-, hybrid-, and tetrahedral-topology grid. The computed flow/temperature fields are presented, in addition to local, two-dimensional distribution of film cooling effectiveness for the adiabatic and conjugate cases. Results are compared to experimental data in terms of centerline film cooling effectiveness downstream cooling-hole, the predictions with realizable k-ε turbulence model exhibited the best agreement especially in the region for (2 ≤ x/D ≤ 6). Also, the results show the effect of the conjugate heat transfer on the temperature (effectiveness) field in the film cooling hole region and, thus, the additional heating up of the cooling jet itself. Copyright © 2005 by ASME

Film Cooling Effectiveness: Comparison Of Adiabatic And Conjugate Heat Transfer Cfd Models

This paper documents a computational investigation of the film cooling effectiveness of a 3-D gas turbine endwall with one fan-shaped cooling hole. The simulations were performed for adiabatic and conjugate heat transfer models. Turbulence closure was investigated using three different turbulence models: the realizable k-ε{lunate} model, the SST k-ω model, as well as the v2-f turbulence model. Results were obtained for a blowing ratio of one, and a coolant-to-mainflow temperature ratio of 0.54. The simulations used a dense, high quality, O-type, hexahedral grid with three different schemes of meshing for the cooling hole: hexahedral-, hybrid-, and tetrahedral-topology grid. The computed flow/temperature fields are presented, in addition to local, two-dimensional distribution of film cooling effectiveness for the adiabatic and conjugate cases. Results are compared to experimental data in terms of centerline film cooling effectiveness downstream cooling-hole, the predictions with realizable k-ε{lunate} turbulence model exhibited the best agreement especially in the region for (2 ≤ x/D ≤ 6). Also, the results show the effect of the conjugate heat transfer on the temperature (effectiveness) field in the film cooling hole region and, thus, the additional heating up of the cooling jet itself. © 2009 Elsevier Masson SAS. All rights reserved

NUMERICAL INVESTIGATION OF ADIABATIC AND CONJUGATE FILM COOLING EFFECTIVENESS ON A SINGLE CYLINDRICAL FILM-COOLING HOLE Introduction and Literature Review

Abstract This paper documents a computational investigation of the film-cooling effectiveness of a 3-D gas turbine endwall with one cylindrical cooling hole. The simulations were performed for an adiabatic and conjugate heat transfer models. Turbulence closure was investigated using five different turbulence models; the standard -model, the RNG -model, the realizable -5 5 5 % % % model, the standard -model, as well as the SST -model 5 5 = = . Results were obtained for a blowing ratio of 2.0, and a coolantto-mainflow temperature ratio of 0.54. The simulations used a dense, high quality, O-type, hexahedral grid. The computed flow/temperature fields are presented, in addition to local, twodimensional distribution of film cooling effectiveness for the adiabatic and conjugate cases. Results are compared to experimental data in terms of centerline film cooling effectiveness downstream cooling-hole, the predictions with realizable -turbulence model exhibited the best agreement 5 % especially in the region for . All turbulence models ÐBÎH Ÿ 'Ñ predicted the jet lift-off. Also, the results show the effect of the conjugate heat transfer on the temperature (effectiveness) field in the film-cooling hole region and, thus, the additional heating up of the cooling jet itself

Singular Superposition/Bem Inverse Technique For Reconstruction Of Multi-Dimensional Heat Flux Distributions With Application To Film-Cooling Slots

A hybrid singularity superposition/boundary element-based inverse problem method for the reconstruction of multi-dimensional heat flux distributions is developed. Cauchy conditions are imposed at exposed surfaces that are readily reached for measurements while convective boundary conditions are unknown at surfaces that are not amenable to measurements such as the edges of cooling slots. The purpose of the inverse analysis is to determine the heat flux distribution along cooling slot surfaces. This is accomplished in an iterative process by distributing a set of singularities at the vicinity of the cooling slot surface inside a fictitious extension of the physical domain with a given initial strength distribution. A forward steady-state heat conduction problem is solved using the boundary element method (BEM), and an objective function is defined to measure the difference between the heat flux measured at the exposed surfaces and the heat flux predicted by the BEM under the current strength distribution of the singularities. A genetic algorithm iteratively alters the strength distribution of the singularities until the measuring surfaces heat fluxes are matched, thus, satisfying Cauchy conditions. Subsequent to the solution of the inverse problem, the heat flux at the inaccessible surface is computed using the BEM. The hybrid singularity superposition/BEM approach thus eliminates the need to mesh the surface of the film cooling slot and the need to parametrize the heat flux over that surface. Rather, the heat flux is determined in a post-processing stage after the inverse problem is solved. This constitutes a tremendous advantage in solving the inverse problem, particularly in three-dimensional applications. Copyright © 2004 by ASME

Numerical Investigation Of Adiabatic And Conjugate Film Cooling Effectiveness On A Single Cylindrical Film-Cooling Hole

This paper documents a computational investigation of the film-cooling effectiveness of a 3-D gas turbine endwall with one cylindrical cooling hole. The simulations were performed for an adiabatic and conjugate heat transfer models. Turbulence closure was investigated using five different turbulence models; the standard k-ε model, the RNG k-ε model, the realizable k-ε model, the standard k-ω model, as well as the SST k-ω model. Results were obtained for a blowing ratio of 2.0, and a coolant-to-mainflow temperature ratio of 0.54. The simulations used a dense, high quality, O-type, hexahedral grid. The computed flow/temperature fields are presented, in addition to local, two-dimensional distribution of film cooling effectiveness for the adiabatic and conjugate cases. Results are compared to experimental data in terms of centerline film cooling effectiveness downstream cooling-hole, the predictions with realizable k-ε turbulence model exhibited the best agreement especially in the region for (x / D ≤ 6). All turbulence models predicted the jet lift-off. Also, the results show the effect of the conjugate heat transfer on the temperature (effectiveness) field in the film-cooling hole region and, thus, the additional heating up of the cooling jet itself. Copyright © 2004 by ASME

The Effect Of Conjugate Heat Transfer On Film Cooling Effectiveness

The film cooling effectiveness of a two-dimensional gas turbine endwall is compared for the cases of conjugate heat transfer and an adiabatic wall condition using five common turbulence models. The turbulence models employed in this study are: the RNG k- model, the realizable k- model, the standard k- model, the SST k- model, and the RSM model. The computed flow field and surface temperature profiles along with the film effectiveness for one and two cooling slots at different injection angles are presented. The results show the strong effect of conjugate heat transfer on the film effectiveness compared to the adiabatic case and also compared to the effectiveness values obtained from analytically solvable models

The Effect Of Conjugate Heat Transfer On Film Cooling Effectiveness

We investigate the numerical prediction of film cooling effectiveness of a two-dimensional gas turbine endwall for the cases of conjugate and adiabatic heat transfer models. Further, the consequence of various turbulence models employed in the computation are investigated by considering various turbulence models: \u27RNG1 k-ε. model, Realizable k-ε model, Standard k-ω model, \u27SST\u27 k-ω model, and \u27RSM\u27 model. The computed flow field and surface temperature profiles along with the film effectiveness for one and two cooling slots at different injection angles and blowing ratio of one are presented. The results show the strong effect of the conjugate heat transfer on the film effectiveness compared to the adiabatic and analytically derived formulae and show that turbulence model used significantly affects the film effectiveness prediction when separation occurs in the film hole and some level of jet lift-off is present. Copyright © 2004 by ASME