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.

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

2001 ◽  
Author(s):  
A. Azzi ◽  
D. Lakehal
Keyword(s):  
Film Cooling ◽  
Transport Coefficients ◽  
Turbine Blades ◽  
Turbulence Models ◽  
Outer Core ◽  
Equation Model ◽  
Wall Region ◽  
Non Linear ◽  
Stress Models ◽  
Near Wall

Abstract The paper exposes some recent new trends in modelling 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 flow physics. The study focuses on anisotropic eddyviscosity/diffusivity models and explicit algebraic stress models, up to cubic fragments of strain and vorticity tensors. The first class of models are DNS-based two-layer approaches transcending the conventional k–ε model by means of a non-isotropic 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 DNS statistics of channel flows and boundary layers. 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 non-linear 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, and are then extended to film cooling of a symmetrical turbine blade by a row of laterally 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 reduces the strength of the secondary vortices. The non-linear algebraic stress models were of a mixed quality in film cooling calculations.

Near-Wall Modeling of Turbulent Convective Heat Transport in Film Cooling of Turbine Blades With the Aid of Direct Numerical Simulation Data

2002 ◽  
Vol 124 (3) ◽  
pp. 485-498 ◽  
Author(s):  
Djamel Lakehal
Keyword(s):  
Prandtl Number ◽  
Film Cooling ◽  
Eddy Viscosity ◽  
Turbulent Transport ◽  
Transport Coefficients ◽  
Turbine Blades ◽  
Eddy Diffusivity ◽  
Equation Model ◽  
Turbulent Prandtl Number ◽  
Near Wall

The paper presents novel developments in the DNS-based, turbulence modeling strategy of Lakehal et al. developed for calculating jets in crossflow. The particular features of the model include: 1) dynamic coupling of the high-Re k−ε with a one-equation model resolving the near-wall viscosity-affected layer; 2) inclusion of the anisotropy of turbulent transport coefficients for all transport equations; 3) near-wall variation of the turbulent Prandtl number as a function of the local Reynolds number. Most of the important aspects of the proposed model are based on known DNS statistics of channel and boundary layer flows. The model is validated against experiments for the case of film cooling of a flat plate, where coolant air is injected from a row of streamwise inclined jets. Excellent results were obtained for this configuration as compared to earlier numerical investigations reported in the open literature. The model is then extended to calculate film cooling of a symmetrical turbine blade by a row of laterally injected jets for various blowing rates. Comparison of the calculated and measured wall-temperature distributions show that only with this anisotropy eddy-viscosity/diffusivity model can the spanwise spreading of the temperature field be well predicted and the strength of the secondary vortices reduced. Furthermore, results of additional calculations show that combining the anisotropy eddy viscosity model with the DNS-based relation for turbulent Prandtl number promotes the eddy diffusivity of heat vis-a`-vis that of momentum further, leading to an enhanced spanwise spreading of the jet. The performance of this new approach improves with increasing blowing rate.

Algebraic Anisotropic Eddy-Viscosity Modeling for Application to Turbulent Film Cooling Flows

2011 ◽  
Author(s):  
Xueying Li ◽  
Jing Ren ◽  
Hongde Jiang
Keyword(s):  
Flow Field ◽  
Film Cooling ◽  
Eddy Viscosity ◽  
Viscosity Ratio ◽  
Equation Model ◽  
Wall Region ◽  
Mean Flow ◽  
Film Cooling Effectiveness ◽  
Jet In Crossflow ◽  
Comparison Of The Results

Under-predicting the spanwise spreading of film cooling is a big problem in the film cooling computation. This is mainly due to the incorrect simulation of the spanwise transport of the jet in crossflow by conventional isotropic eddy viscosity turbulent models. An improved algebraic anisotropic eddy viscosity method including both the influence of the wall and the strain of the mean flow field to the anisotropic ratio has been raised by the authors in the paper, referred to as Algebraic Anisotropic Eddy Viscosity (AAEV) method. An equation derived from the algebraic Reynolds stress transport equations is applied to compute the anisotropic eddy-viscosity ratio. The variation of the anisotropic eddy-viscosity ratio is a function of both the dimensionless wall distance and the local mean flow field. This method is applied to the two layer k-ε model with a one-equation model in near-wall region to form a new turbulent model- AAEV k-ε model. The new model is tested for the computation of a flat plate film cooling flow with an inclined row of streamwise injected jets. Comparison of the results between the AAEV k-ε model and two-layer k-ε model with the measured adiabatic film-cooling effectiveness distributions indicates that the AAEV k-ε model can correctly predict the spanwise spreading of the film and reduce the strength of the secondary vortices.

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.

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.

On Near-Wall Dynamic Coupling of LES With RANS Turbulence Models

2006 ◽  
Author(s):  
Goe´ric Daeninck ◽  
Gorazd Medic ◽  
Jeremy A. Templeton ◽  
Georgi Kalitzin
Keyword(s):  
Channel Flow ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Wall Region ◽  
Subgrid Scale ◽  
Turbulent Stress ◽  
Dynamic Coupling ◽  
Rans Turbulence Models ◽  
Model Equations ◽  
Near Wall

In this paper, the RANS/LES coupling formulation proposed in [1–3] is adapted for various RANS turbulence models. In that formulation, the LES subgrid-scale eddy-viscosity is replaced in the near-wall region with a RANS eddy-viscosity dynamically corrected with the resolved turbulent stress. The RANS eddy-viscosity is first obtained from precomputed tables. To further generalize the approach, RANS turbulence model equations (for Spalart-Allmaras and k-ω) are then solved simultaneously with the LES. Detailed results are presented for channel flow at Reτ = 395 and compared to traditional LES. The method is then applied to a serpentine passage and compared with DNS computations [4] at Reτ = 180.

scholarly journals Comparison of Two-Equation Turbulence Models for Prediction of Heat Transfer on Film-Cooled Turbine Blades

1997 ◽  
Author(s):  
Vijay K. Garg ◽  
Ali A. Ameri
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Computer Time ◽  
Suction Surface ◽  
The Heat Transfer Coefficient

A three-dimensional Navier-Stokes code has been used to compute the heat transfer coefficient on two film-cooled turbine blades, namely the VKI rotor with six rows of cooling holes including three rows on the shower head, and the C3X vane with nine rows of holes including five rows on the shower head. Predictions of heat transfer coefficient at the blade surface using three two-equation turbulence models, specifically, Coakley’s q-ω model, Chien’s k-ε model and Wilcox’s k-ω model with Menter’s modifications, have been compared with the experimental data of Camci and Arts (1990) for the VKI rotor, and of Hylton et al. (1988) for the C3X vane along with predictions using the Baldwin-Lomax (B-L) model taken from Garg and Gaugler (1995). It is found that for the cases considered here the two-equation models predict the blade heat transfer somewhat better than the B-L model except immediately downstream of the film-cooling holes on the suction surface of the VKI rotor, and over most of the suction surface of the C3X vane. However, all two-equation models require 40% more computer core than the B-L model for solution, and while the q-ω and k-ε models need 40% more computer time than the B-L model, the k-ω model requires at least 65% more time due to slower rate of convergence. It is found that the heat transfer coefficient exhibits a strong spanwise as well as streamwise variation for both blades and all turbulence models.

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

1998 ◽  
Author(s):  
Jeffrey D. Ferguson ◽  
Dibbon K. Walters ◽  
James H. Leylek
Keyword(s):  
Experimental Data ◽  
Film Cooling ◽  
Turbulence Models ◽  
Viscous Sublayer ◽  
Reynolds Stress Model ◽  
Quality Data ◽  
Wall Functions ◽  
First Time ◽  
Near Wall ◽  
Non Equilibrium

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-ε model with generalized wall functions; 2) standard k-ε model with non-equilibrium wall functions: 3) Renormalization Group k-ε (RNG) model with generalized wall functions; 4) RNG model with non-equilibrium wall functions: 51 standard k-ε 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-ε turbulence model with the two-layer near-wall treatment, which resolves the viscous sublayer, produces results that are more consistent with experimental data.

Merging Near-Wall RANS Models With LES for Separating and Reattaching Flows

2006 ◽  
Author(s):  
Suad Jakirlic´ ◽  
Bjo¨rn Kniesner ◽  
Sanjin Sˇaric´ ◽  
Kemal Hanjalic´
Keyword(s):  
Reynolds Number ◽  
Equation Model ◽  
Navier Stokes ◽  
Model Parameters ◽  
Wall Region ◽  
Detached Eddy Simulation ◽  
Rans Model ◽  
Eddy Simulation ◽  
Moderate Reynolds Number ◽  
Near Wall

A method of coupling a low-Reynolds-number k–ε RANS (Reynolds-Averaged Navier-Stokes) model with Large-Eddy Simulation (LES) in a two-layer Hybrid LES/RANS (HLR) scheme is proposed in the present work. The RANS model covers the near-wall region and the LES model the remainder of the flow domain. Two different subgrid-scale (SGS) models in LES were considered, the Smagorinsky model and the one-equation model for the residual kinetic energy (Yoshizawa and Horiuti, 1985), combined with two versions of the RANS ε equation, one governing the “isotropic” (ε˜; Chien, 1982) and the other the “homogeneous” dissipation rate (εh; Jakirlic and Hanjalic, 2002). Both fixed and self-adjusting interface locations were considered. The exchange of the variables across the interface was adjusted by smoothing the turbulence viscosity either by adjusting the RANS model parameters, such as Cμ (Temmerman et al., 2005), or by applying an additional forcing at the interface using a method of digital-filter-based generation of inflow data for spatially developing DNS and LES due to Klein et al. (2003). The feasibility of the method was illustrated against the available DNS, fine- and coarse grid LES, DES (Detached Eddy Simulation) and experiments in turbulent flow over a backward-facing step at a low (Yoshioka et al., 2001) and a high Re number (Vogel and Eaton, 1985), periodic flow over a series of 2-D hills (Fro¨hlich et al., 2005) and in a high-Re flow over a 2-D, wall-mounted hump (Greenblat et al, 2004). Prior to these computations, the method was validated in a fully-developed channel flow at a moderate Reynolds number Rem ≈ 24000 (Abe et al., 2004).

Applications of EARSM Turbulence Models to Internal Flows

2012 ◽  
Author(s):  
O. Z. Mehdizadeh ◽  
L. Temmerman ◽  
B. Tartinville ◽  
Ch. Hirsch
Keyword(s):  
Reynolds Stress ◽  
High Performance ◽  
Eddy Viscosity ◽  
Computational Cost ◽  
Turbulence Models ◽  
Industrial Applications ◽  
Mean Flow ◽  
Viscosity Models ◽  
Stress Models ◽  
Corner Flows

Turbulence modeling remains an active CFD development front for turbomachinery as well as for general industrial applications. While DNS and even LES still seem out of reach within the typical industrial design cycle due to their high computational cost, RANS-based models remain the workhorse of CFD. Currently, the most widely used models are Linear Eddy-Viscosity Models (LEVM), despite their known limitations for certain flow complexities. Therefore, extending the reliability of eddy-viscosity models to more complex flows without significantly increasing the computational cost can immediately contribute to more reliable CFD results for wider range of applications. This, in turn, can further reduce the need for costly tests and consequently can reduce the product development cost. A promising approach to achieve this goal is using Explicit Algebraic Reynolds Stress Models (EARSM), obtained through a simplification of the full Differential Reynolds Stress Models (DRSM), and can be perceived as an extension of LEVMs by including the non-linear relation between the turbulence stress tensor, the mean-flow gradient and the turbulence scales. These models are thus less demanding than DRSM, yet capable of capturing more complex turbulence features, compared to LEVM, such as anisotropy in the normal stresses. This may be particularly important in corner flows, for instance, in the hub-blade regions or in diffusers. This work explores the application of EARSM models to a double diffuser and a high-performance centrifugal compressor stage (HPCC). The results are compared to available experimental data [1,2] showing the importance of including the anisotropy of turbulence in the model, particularly in presence of turbulent corner flows in a diffuser. Furthermore, the EARSM results are also compared to results from the commonly used SST turbulence model. The CFD comparison includes details of the flow structure in the diffuser, where the most noticeable impact from the use of EARSM turbulence models is expected.

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