Numerical Benchmark of Non-Conventional RANS Turbulence Models for Film and Effusion Cooling

2012 ◽  
Author(s):  
L. Andrei ◽  
A. Andreini ◽  
C. Bianchini ◽  
B. Facchini
Keyword(s):  
Film Cooling ◽  
Eddy Viscosity ◽  
Isotropic Turbulence ◽  
Turbulence Models ◽  
Lateral Spreading ◽  
Algebraic Expression ◽  
Test Plate ◽  
Single Row ◽  
Turbulent Reynolds Number ◽  
Wide Range

In the course of the years several turbulence models specifically developed to improve the predicting capabilities of conventional two-equations RANS models have been proposed. However they have been mainly tested against experiments only comparing with standard isotropic models, in single hole configuration and for very low blowing ratio. A systematic benchmark of the various non-conventional models exploring a wider range of application is hence missing. This paper performs a comparison of 3 recently proposed models over three different test cases of increasing computational complexity. The chosen test matrix covers a wide range of blowing ratios (0.5–3.0)including both single row and multi-row cases for which experimental data of reference are available. In particular the well known test by Sinha and Bogard [1] at BR = 0.5 is used in conjuction with two in-house carried out experiments: a single row film-cooling test at BR = 1.5 and a 15 rows test plate designed to study the interaction between slot and effusion cooling at BR = 3.0. The first two considered models are based on a tensorial definition of the eddy viscosity in which the stream-span position is augmented to overcome the main drawback connected with standard isotropic turbulence models that is the lower lateral spreading of the jet downwards the injection. An anisotropic factor to multiply the off-diagonal position is indeed calculated from an algebraic expression of the turbulent Reynolds number developed by Bergeles [2] from DNS statistics over a flat plate. This correction could be potentially implemented in the framework of any eddy viscosity model. It was chosen to compare the predictions of such modification applied to two among the most common two-equation turbulence models for film-cooling tests, namely the Two-Layer (TL) model and the k–ω Shear Stress Transport (SST), firstly proposed and tested in the past respectively by Azzi and Lakeal [3] and Cottin at al. [4]. The third model, proposed by Holloway et al. [5], involves the unsteady solution of the flow and thermal field to include the short-time response of the stress tensor to rapid strain rates. This model takes advantage of the solution of an additional transport equation for the local effective total stress to trace the strain rate history. The results are presented in terms of adiabatic effectiveness distribution over the plate as well as spanwise averaged profiles.

Numerical Benchmark of Nonconventional RANS Turbulence Models for Film and Effusion Cooling

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Cosimo Bianchini ◽  
Luca Andrei ◽  
Antonio Andreini ◽  
Bruno Facchini
Keyword(s):  
Film Cooling ◽  
Eddy Viscosity ◽  
Computational Study ◽  
Turbine Blades ◽  
Density Ratio ◽  
Turbulence Models ◽  
Single Row ◽  
Turbulent Reynolds Number ◽  
Wide Range ◽  
Asme Turbo Expo

Over the course of the years, several turbulence models specifically developed to improve the predicting capabilities of conventional two-equations Reynolds-averaged Navier–Stokes (RANS) models have been proposed. They have, however, been mainly tested against experiments only comparing with standard isotropic models, in single hole configuration and for very low blowing ratio. A systematic benchmark of the various nonconventional models exploring a wider range of application is hence missing. This paper performs a comparison of three recently proposed models over three different test cases of increasing computational complexity. The chosen test matrix covers a wide range of blowing ratios (0.5–3.0) including both single row and multi-row cases for which experimental data of reference are available. In particular the well-known test by Sinha et al. (1991, “Film-Cooling Effectiveness Downstream of a Single Row of Holes with Variable Density Ratio,” J. Turbomach., 113, pp. 442–449) at BR = 0.5 is used in conjunction with two in-house carried out experiments: a single row film-cooling test at BR = 1.5 and a 15 rows test plate designed to study the interaction between slot and effusion cooling at BR = 3.0. The first two considered models are based on a tensorial definition of the eddy viscosity in which the stream-span position is augmented to overcome the main drawback connected with standard isotropic turbulence models that is the lower lateral spreading of the jet downwards the injection. An anisotropic factor to multiply the off diagonal position is indeed calculated from an algebraic expression of the turbulent Reynolds number developed by Bergeles et al. (1978, “The Turbulent Jet in a Cross Stream at Low Injection Rates: A Three-Dimensional Numerical Treatment,” Numer. Heat Transfer, 1, pp. 217–242) from DNS statistics over a flat plate. This correction could be potentially implemented in the framework of any eddy viscosity model. It was chosen to compare the predictions of such modification applied to two among the most common two-equation turbulence models for film-cooling tests, namely the two-layer (TL) model and the k–ω shear stress transport (SST), firstly proposed and tested in the past respectively by Azzi and Lakeal (2002, “Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models,” J. Turbomach., 124, pp. 472–484) and Cottin et al. (2011, “Modeling of the Heat Flux For Multi-Hole Cooling Applications,” Proceedings of the ASME Turbo Expo, Paper No. GT2011-46330). The third model, proposed by Holloway et al. (2005, “Computational Study of Jet-in-Crossflow and Film Cooling Using a New Unsteady-Based Turbulence Model,” Proceedings of the ASME Turbo Expo, Paper No. GT2005-68155), involves the unsteady solution of the flow and thermal field to include the short-time response of the stress tensor to rapid strain rates. This model takes advantage of the solution of an additional transport equation for the local effective total stress to trace the strain rate history. The results are presented in terms of adiabatic effectiveness distribution over the plate as well as spanwise averaged profiles.

Application of Advanced RANS Turbulence Models for the Prediction of Turbomachinery Flows

2020 ◽  
Author(s):  
Ernesto Casartelli ◽  
Luca Mangani ◽  
David Roos ◽  
Armando Del Rio
Keyword(s):  
Boundary Layer ◽  
Isotropic Turbulence ◽  
Flow Direction ◽  
Stress Component ◽  
Turbulence Models ◽  
Tip Clearance ◽  
Algebraic Expression ◽  
Reynolds Stresses ◽  
Mixing Processes ◽  
Near Wall

Abstract The simulation models used in the design process of modern turbo-machines are becoming increasingly complex. Nevertheless, the steady-state RANS approach is still the mostly used method for CFD computations. However, detailed flow information is more and more required for further improving the performance and extend the operating range. Turbulence modeling has becoming therefore a key issue in this context. The increased computer power already available would enable the use of more sophisticated turbulence models than standard two equation ones, such as SST k-omega and k-epsilon. These, despite their shortcomings, are still predominant in the field, since more advanced models often lead to numerical instabilities in the simulations. The most important shortcomings can be related to either boundary layer effects or mixing process in the channels. In order to improve the predictions considering boundary layer effects, like impingement or large pressure gradients in flow direction, various derivations of four equations models were investigated. Using an additional transport equation for the wall normal Reynolds-stress component and an elliptic equation for near-wall effects, they improve the results for this kind of flows. Considering the accurate prediction of mixing processes, like (1) the interaction of tip-clearance vortices with the main flow or (2) off-design conditions, the focus was oriented to the anisotropy present in the turbulent structures. Standard models are often not sufficient to predict accurately vortices, which can have a huge impact on the performance, since based on the assumption of isotropic turbulence. Accordingly, they tend to dissipate and diffuse the vortices too quickly. Improved models, which take the anisotropic nature of the Reynolds-stresses into account, can help in this context. The models can thereby introduce the additional anisotropy via an explicit algebraic expression, or model directly the transport equations for the Reynolds-stresses. In order to improve the predictions using advanced turbulence models a particularly robust framework based on a pressure-based fully coupled approach was used. The goal of this work is the development and testing of improved models for the application in turbo-machinery. The focus lies thereby on near-wall behavior and mixing / vortex dissipation. The assessment of the models is exemplarily used on the centrifugal compressor open-case Radiver with vaned diffuser.

CFD Predictions of Single Row Film Cooling With Inclined Holes: Influence of Hole Outlet Geometry

2010 ◽  
Author(s):  
Habeeb Idowu Oguntade ◽  
Gordon E. Andrews ◽  
Alan Burns ◽  
Derek Ingham ◽  
Mohammed Pourkashanian
Keyword(s):  
Film Cooling ◽  
Turbulence Models ◽  
Experimental Results ◽  
Hexahedral Mesh ◽  
Mesh Structure ◽  
Film Cooling Effectiveness ◽  
Single Row ◽  
Narrow Angle ◽  
Hexahedral Meshes ◽  
Outlet Hole

A CFD investigation of a single row of round inclined film cooling holes in a crossflow has been carried out with the view of investigating the discrepancies in the literature between predicted and measured results. The experimental results of Sinha et al. [1], Kohli et al. [40], Pedersen et al. [3] and others form the data base for validation of the CFD prediction of film cooling. Previous work in the literature is reviewed to show that CFD has had difficulty in obtaining agreement with these basic experimental film cooling results. However, most previous work has used tetrahedral meshes which gave poor agreement with experiments in the near hole region. In the present work it is shown by direct comparison of tetrahedral and hexahedral meshes, using the FLUENT code, with the same turbulence models, that only hexahedral meshes give good agreement with the experimental results in the near hole region. It is postulated that the reason is that the mesh structure is aligned with the flow and has more computational nodes in the important film cooling boundary layer. The hexahedral mesh was used with five turbulence models, which showed the standard k-epsilon model consistently gave the best agreement with experimental data for narrow angle film cooling. This CFD methodology was shown to be capable of predicting the influence on film cooling effectiveness of trench hole and larger diameter outlet hole geometries.

scholarly journals EVALUATION OF THE RANS TURBULENCE MODEL PREDICTIVE CAPABILITY OF FLAT PLATE FILM COOLING

2021 ◽  
Vol 850 (1) ◽  
pp. 012020
Author(s):  
F Ferdaus ◽  
N Raghukiran
Keyword(s):  
Turbulence Model ◽  
Film Cooling ◽  
Turbulence Models ◽  
Lateral Spreading ◽  
Test Surface ◽  
Ansys Fluent ◽  
Cooling Hole ◽  
Cooling Behavior ◽  
Mass Flow Rates ◽  
Theoretical Results

Abstract The two-equation turbulence models used for the present study are the commonly used standard k-ॉ model and k-ω model. In order to achieve this target, numerical simulation was initiated in Ansys Fluent to simulate a flow over a flat test surface with a diameter of 4mm straight, circular film cooling hole at angled injections of 25°, 30°, 35°and 40°. The comparison between the numerical calculations and the theoretical results showed the standard k-ω turbulence model gave better predictions against those with the standard k-ω turbulence models. The ability of k-ω model in closely predicting the cooling behavior is due to the precise modeling of the lateral spreading of the film. The isotropic two-equation turbulence models exhibited a huge dissent. The results also indicated that increasing the mass flow rates in the mainstream channels reduces the temperature distribution along the stream-wise direction.

Numerical Study on Flat Plate and Leading Edge Film Cooling

2009 ◽  
Author(s):  
Eiji Sakai ◽  
Toshihiko Takahashi ◽  
Ken-ichi Funazaki ◽  
Hamidon Bin Salleh ◽  
Kazunori Watanabe
Keyword(s):  
Flat Plate ◽  
Film Cooling ◽  
Numerical Study ◽  
Turbulence Models ◽  
Leading Edge ◽  
Lateral Spreading ◽  
Strong Impact ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Rans Simulation

This study describes a 3-D computation for film cooling effectiveness investigation using Fluent commercial code, version 6.2. Two configurations are examined: (1) Flat plate, and (2) Semi-cylindrical leading edge with a flat after-body. Three different RANS turbulence models and DES based on Spalart-Allmaras model are utilized to see the difference in accuracy between DES and RANS approaches. Similar to the previous RANS simulation, lateral spreading of film cooling is under-estimated in the RANS simulation, while in the DES, lateral spreading of film cooling is enhanced and shows adequate agreement with the previous experiments. The effects of velocity magnitude and orientation of plenum flow on film cooling effectiveness are also studied in the flat plate configuration. The plenum flow is eventually found to have a strong impact on the flow structure in the cooling pipe, and the distorted velocity profile in the pipe consequently lowers film cooling effectiveness, in particularly at high blowing ratio.

scholarly journals An assessment of k–ε and k–l turbulence models for a wide range of oscillatory rough bed flows

2000 ◽  
Vol 2 (4) ◽  
pp. 221-234 ◽  
Author(s):  
S. B. Letherman ◽  
M. A. Cotton ◽  
P. K. Stansby ◽  
C. Chen ◽  
D. Chen
Keyword(s):  
Eddy Viscosity ◽  
Reynolds Shear Stress ◽  
Laboratory Data ◽  
Turbulence Models ◽  
Field Measurements ◽  
Mean Flow ◽  
Wide Range ◽  
Rough Bed ◽  
Experimental Resolution ◽  
First Time

The k–ε and k–l eddy viscosity turbulence models are now used extensively in environmental flow modelling. In the present work computations for oscillatory flows are examined over a broader range of experimental parameters than considered previously. Comparisons are made with field measurements and laboratory data, including new measurements reported here for the first time. It is confirmed that the bed friction velocity and mean flow profiles are, in general, adequately predicted by both models (the k–ε model is, however, somewhat more accurate than the k–l formulation). Reynolds shear stress, turbulent kinetic energy, and eddy viscosity are less well predicted, although the k–ε model again gives more accurate results than the k–l model. An attempt has been made to assess the uncertainty in the experimental data for Reynolds stress and eddy viscosity: it is found that the k–ε model computations for both quantities more frequently lie within the estimated uncertainty bounds. Those bounds are nonetheless wide, emphasizing the need for improved experimental resolution of rough bed flows. Such an improvement would assist in the evaluation of proposed refinements to commonly used turbulence models such as those under investigation here and, indeed, to greater reliability in the development and assessment of more sophisticated schemes.

Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models

2002 ◽  
Vol 124 (3) ◽  
pp. 472-484 ◽  
Author(s):  
A. Azzi ◽  
D. Lakehal
Keyword(s):  
Film Cooling ◽  
Eddy Viscosity ◽  
Transport Coefficients ◽  
Turbine Blades ◽  
Turbulence Models ◽  
Outer Core ◽  
Equation Model ◽  
Wall Region ◽  
Stress Models ◽  
Near Wall

The paper presents recent trends in modeling jets in crossflow with relevance to film cooling of turbine blades. The aim is to compare two classes of turbulence models with respect to their predictive performance in reproducing near-wall flow physics and heat transfer. The study focuses on anisotropic eddy-viscosity/diffusivity models and explicit algebraic stress models, up to cubic fragments of strain and vorticity tensors. The first class of models are direct numerical simulation (DNS) based two-layer approaches transcending the conventional k−ε model by means of a nonisotropic representation of the turbulent transport coefficients; this is employed in connection with a near-wall one-equation model resolving the semi-viscous sublayer. The aspects of this new strategy are based on known channel-flow and boundary layer DNS statistics. The other class of models are quadratic and cubic explicit algebraic stress formulations rigorously derived from second-moment closures. The stress-strain relations are solved in the context of a two-layer strategy resolving the near-wall region by means of a nonlinear one-equation model; the outer core flow is treated by use of the two-equation model. The models are tested for the film cooling of a flat plate by a row of streamwise injected jets. Comparison of the calculated and measured wall-temperature distributions shows that only the anisotropic eddy-viscosity/diffusivity model can correctly predict the spanwise spreading of the temperature field and reduce the strength of the secondary vortices. The wall-cooling effectiveness was found to essentially depend on these two particular flow features. The non-linear algebraic stress models were of a mixed quality in film-cooling calculations.

Evaluation of Film Cooling Superposition Predictions Using Shaped Holes on the Suction Side of a Blade Model

2019 ◽  
Author(s):  
Christopher Yoon ◽  
Jacob Moore ◽  
David Bogard
Keyword(s):  
Film Cooling ◽  
Suction Side ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Single Row ◽  
Blowing Ratio ◽  
Actual Application ◽  
Wide Range ◽  
Cylindrical Holes ◽  
Blade Model

Abstract Film cooling is often used for turbine airfoil cooling, and there are numerous studies of the performance of a single row of holes. In actual application there will typically be multiple rows of holes which interact. Consequently there is a need to develop techniques to predict film cooling performance with multiple rows of coolant holes using superposition of single row cooling effectiveness. Although there have been many studies of superposition techniques for predicting film cooling effectiveness with multiple rows of cylindrical holes, there have been very few in which shaped holes were used with a typical turbine airfoil model. In this study, film effectiveness was measured on the suction side of a turbine blade model using two rows of shaped coolant holes. Measurements were made with each row independently and with both rows combined. This provided the experimental data for superposition predictions and to evaluate these predictions. Each row had 7-7-7 shaped holes with pitch to diameter ratio of 6, and the two rows were more than 40 diameters apart. The experiments were run using two different upstream blowing ratios, and a wide range of downstream blowing ratios. The superposition predictions of film effectiveness were reasonably accurate when the upstream row of holes were operated at a high blowing ratio with a corresponding smaller film effectiveness (due to jet separation). However, when the upstream coolant holes were operated at the optimum blowing ratio, and hence maximum film effectiveness downstream, the superposition analysis predicted film effectiveness levels slightly lower than actual levels. These results show that there was an interaction between jets that resulted in higher film effectiveness than was accounted for with a superposition prediction.

Full Field Algebraic Anisotropic Eddy Viscosity Model for the Film Cooling Flows

2012 ◽  
Author(s):  
Xueying Li ◽  
Jing Ren ◽  
Hongde Jiang
Keyword(s):  
Flow Field ◽  
Film Cooling ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Viscosity Model ◽  
Wall Region ◽  
Mean Flow ◽  
Experiment Data ◽  
Anisotropic Models ◽  
Eddy Viscosity Model

The algebraic anisotropic eddy viscosity model proposed by the authors is further developed to make it suitable to the full flow field in order to focus not only in the near wall region but also in the main flow field. The three anisotropic eddy viscosity ratios for u′v′, u′w′, v′w′ are determined from the eddy viscosity hypothesis and algebraic Reynolds stress transport equations and expressed in Cartesian coordinate system. This model is applied to four isotropic two-equation turbulence models to make them anisotropic. These anisotropic models are validated with the experiment data from Sinha et al.[1]. Thorough tests are performed with all these isotropic and anisotropic turbulence models for film cooling on a flatplate with different blowing ratios. Detailed analyses of computational simulations are presented. The predicted adiabatic film cooling effectiveness and mean flow field show that the algebraic anisotropic eddy-viscosity turbulence models agree better with the experiment data. Among the four anisotropic models, the anisotropic models based on the realizable k-ε and RNG k-ε models stand out as the most promising models for flatplate film cooling predictions. It’s a big advantage of this model that it deals with the whole flow field and can be combined with different turbulence models.

Turbulence Modeling for the Numerical Simulation of Film and Effusion Cooling Flows

2007 ◽  
Author(s):  
Alessandro Bacci ◽  
Bruno Facchini
Keyword(s):  
Numerical Simulation ◽  
Film Cooling ◽  
Eddy Viscosity ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Cooling Flows ◽  
Eddy Simulation ◽  
Viscosity Models ◽  
Rans Turbulence Models ◽  
Computationally Intensive

RANS simulations are known to suffer from serious deficiencies in the prediction of jet in a crossflow (JCF) because of the high complexity of this kind of flow. Particularly, the coherent structures resulting from the interaction of the two flow streams are characterized by a highly unsteady and anisotropic behavior which hardly stresses the hypotheses underling common eddy viscosity models (EVMs). Direct numerical simulation (DNS) and large eddy simulation (LES) methodologies are still excessively computationally intensive to be used as ordinary design tools. Therefore, the development of reliable RANS turbulence models for film cooling flows deserved a great deal of attention from the gas turbine community. Computations presented in this work were carried out using a modified k-ε turbulence model specifically designed for film cooling flows. The model, due to Lakehal et al., is based on the usage of an anisotropic eddy viscosity. The model has been implemented in the framework of a CFD commercial package through the user subroutine features. Computational model is developed following the suggestions of Walters and Leylek concerning the correct representation of the problem geometry and the location of the boundary conditions. The predictive capabilities of the model concerning the ability to capture the main flow structures as well as heat transfer features are investigated. Comparison of computed adiabatic effectiveness profiles with experimental measurements is provided in order to quantitatively validate the model. Results obtained with standard EVMs, particularly a two layer standard k-ε model, are also shown in order to reveal the improvements in the predictive capabilities resulting from the modified models.

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