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.

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.

Numerical Investigation of Gas Turbine Combustor Liner Film Cooling Slots

2018 ◽  
Author(s):  
Firat Kiyici ◽  
Ahmet Topal ◽  
Ender Hepkaya ◽  
Sinan Inanli
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Temperature ◽  
Gas Turbine ◽  
Film Cooling ◽  
Turbulent Prandtl Number ◽  
Surface Cooling ◽  
Gas Turbine Combustor ◽  
Cooling Effectiveness ◽  
Combustor Liner

A numerical study, based on experimental work of Inanli et al. [1] is conducted to understand the heat transfer characteristics of film cooled test plates that represent the gas turbine combustor liner cooling system. Film cooling tests are conducted by six different slot geometries and they are scaled-up model of real combustor liner. Three different blowing ratios are applied to six different geometries and surface cooling effectiveness is determined for each test condition by measuring the surface temperature distribution. Effects of geometrical and flow parameters on cooling effectiveness are investigated. In this study, Conjugate Heat Transfer (CHT) simulations are performed with different turbulence models. Effect of the turbulent Prandtl Number is also investigated in terms of heat transfer distribution along the measurement surface. For this purpose, turbulent Prandtl number is calculated with a correlation as a function of local surface temperature gradient and its effect also compared with the constant turbulent Prandtl numbers. Good agreement is obtained with two-layered k–ϵ with modified Turbulent Prandtl number.

Particle Collision Effect on Turbulent Prandtl Number in Gas-Solid Flows

2006 ◽  
Author(s):  
Zohreh Mansoori ◽  
Majid Saffar-Avval ◽  
Hasan Basirat-Tabrizi ◽  
Goodarz Ahmadi ◽  
Payam Ramezani
Keyword(s):  
Prandtl Number ◽  
Turbulent Flow ◽  
Time Scale ◽  
Turbulence Models ◽  
Flow Region ◽  
Eddy Diffusivity ◽  
Particle Collision ◽  
Turbulent Prandtl Number ◽  
Particle Collisions ◽  
Particle Properties

Traditional gas-solid turbulence models using constant or the single-phase gas turbulent Prandtl number cause error in the thermal eddy diffusivity and thermal turbulent intensity fields calculation. The thermo-mechanical turbulence model is based on solving the hydrodynamic transport equations of the turbulent kinetic energy and turbulent time scale, beside the thermal turbulent equations of temperature variance and thermal turbulence time scale. This model has the ability to calculate the turbulent Prandtl number directly by computing the eddy viscosity and the thermal eddy diffusivity through the values of turbulence fluctuation velocity and thermal variances and time scales. A four way Eulerian/Lagrangian formulation was used to study the effect of particle properties on the turbulent flow and thermal fields, as well as on turbulent Prandtl number in a gas-solid developing pipe flow. Inter-particle collisions were included and the Lagrangian trajectory analysis was used. The earlier results showed that turbulent Prandtl number is influenced by the variations of gas and particle properties and also inter-particle collisions in a fully-developed riser. In the current study, the developing gas-solid flow region in a pipe was considered and the variation of turbulent flow field due to inter-particle collision was evaluated.

Simulation of Scalar Mixing in Co-Axial Jet Flows Using an LES Method

2005 ◽  
Author(s):  
M. Dianat ◽  
D. Jiang ◽  
Z. Yang ◽  
J. J. McGuirk
Keyword(s):  
Prandtl Number ◽  
Turbulent Transport ◽  
Scalar Fields ◽  
Scale Model ◽  
Jet Flows ◽  
Turbulent Prandtl Number ◽  
Time Resolved ◽  
Jet Mixing ◽  
Cfd Models ◽  
Mixing Problem

The present paper describes a study that is aimed at establishing and quantifying the benefits of the Large Eddy Simulation (LES) method for predicting scalar turbulent transport in a combustor relevant jet-mixing problem. A non-reacting co-annular jet mixing configuration is considered for which comprehensive experimental data for both velocity and scalar fields have recently been obtained. Detailed comparisons are presented for the development of the axial velocity field in terms of both mean and turbulence intensity. Similarly, the mixing between the jets is examined by comparison with measurements for the mean concentration and the variance of concentration fluctuations. Agreement with these statistically averaged fields is demonstrated to be very good, and a considerable improvement over the standard eddy viscosity RANS approach. Illustrations are presented of the time-resolved information that LES provides such as time histories, and also conserved scalar pdf predictions. The LES results are shown, even using a simple Smagorinsky sub-grid-scale model, to predict correctly lower values of the turbulent Prandtl number (∼ 0.6) in the free shear regions of the flow, as well as higher values (∼ 1.0) in the wall-affected regions. The ability to predict turbulent Prandtl number variations (rather than input these as commonly done in most combustor RANS CFD models) is an important and promising feature of the LES approach for combustor simulation since it is known to be important in determining combustor exit temperature traverse.

Turbulent Transport Equations and Kubo Formulae for Eddy Transport Coefficients

1971 ◽  
Vol 26 (11) ◽  
pp. 1782-1791
Author(s):  
S. Grossmann
Keyword(s):  
Eddy Viscosity ◽  
Turbulent Transport ◽  
Transport Coefficients ◽  
Time Integration ◽  
Time Correlation ◽  
Heat Conducting ◽  
Eddy Transport ◽  
Cascade Method ◽  
Factor C ◽  
Heat Conducting Fluids

Kubo type time correlation formulae for turbulent transport coefficients in incompressible but heat conducting fluids are derived, especially for eddy viscosity, eddy heat conductivity, and pressure. The connection to the cascade method as well as its equivalence to the methods of closure of hierarchy are established. Lagrangean time integration is used. If the retarded Green’s function has exponential time behaviour the damping constant Γq can be calculated explicitely. In this approximation in the inertial range one finds the Kolmogoroff k-5/3 spectrum including its numerical factor (C=1.53). This induces a frequency spectrum ∼ ω -2.

scholarly journals Analysis of Turbulent Scalar Flux Models for a Discrete Hole Film Cooling Flow

2015 ◽  
Author(s):  
Julia Ling ◽  
Kevin J. Ryan ◽  
Julien Bodart ◽  
John K. Eaton
Keyword(s):  
Temperature Distribution ◽  
Prandtl Number ◽  
Film Cooling ◽  
Turbulent Viscosity ◽  
Fluid Temperature ◽  
Turbulent Prandtl Number ◽  
Generalized Gradient ◽  
Reynolds Analogy ◽  
Scalar Fluxes ◽  
Gradient Diffusion

Algebraic closures for the turbulent scalar fluxes were evaluated for a discrete hole film cooling geometry using the results from the high-fidelity Large Eddy Simulation (LES) of Bodart et al. [1]. Several models for the turbulent scalar fluxes exist, including the widely used Gradient Diffusion Hypothesis, the Generalized Gradient Diffusion Hypothesis [2], and the Higher Order Generalized Gradient Diffusion Hypothesis [3]. By analyzing the results from the LES, it was possible to isolate the error due to these turbulent mixing models. Distributions of the turbulent diffusivity, turbulent viscosity, and turbulent Prandtl number were extracted from the LES results. It was shown that the turbulent Prandtl number varies significantly spatially, undermining the applicability of the Reynolds analogy for this flow. The LES velocity field and Reynolds stresses were fed into a RANS solver to calculate the fluid temperature distribution. This analysis revealed in which regions of the flow various modeling assumptions were invalid and what effect those assumptions had on the predicted temperature distribution.

A Two-Equation Model for Heat Transport in Wall Turbulent Shear Flows

1988 ◽  
Vol 110 (3) ◽  
pp. 583-589 ◽  
Author(s):  
Y. Nagano ◽  
C. Kim
Keyword(s):  
Prandtl Number ◽  
Turbulence Modeling ◽  
Plate Boundary ◽  
Eddy Diffusivity ◽  
Equation Model ◽  
Wall Turbulence ◽  
Turbulent Heat Transfer ◽  
Turbulent Shear ◽  
Turbulent Heat ◽  
Wide Range

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modeling. The eddy diffusivity concept is used in modeling. However, just as the eddy viscosity is determined from solutions of the k and ε equations, so the eddy diffusivity for heat is given as functions of temperature variance t2, and the dissipation rate of temperature fluctuations εt, together with k and ε. Thus, the proposed model does not require any questionable assumptions for the “turbulent Prandtl number.” Modeled forms of the t2 and εt equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat-plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with the experiment is generally very satisfactory.

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