Heat and mass transfer study of impinging turbulent premixed flames

 Impinging jet combusting flows on granite plates are studied. A mathematical model for calculating heat release in turbulent impinging premixed flames is developed. The combustion including radiative heat transfer and local extinction effects, and flow characteristics are modeled using a finite volume computational approach. Two different eddy viscosity turbulence models, namely the standard k–ɛ and the RNG k–ɛ model with and without radiation (discrete transfer model) are assessed. The heat released predictions are compared with experimental data and the agreement is satisfactory only when both radiative heat transfer and local extinction modeling are taken into account. The results indicate that the main effect of radiation is the decrease of temperature values near the jet stagnation point and along the plate surface. Radiation increases temperature gradients and affects predicted turbulence levels independently of the closure model used. Also, the RNG k–ɛ predicts higher temperatures close the solid plate, with and without radiative heat transfer. Received on 13 November 2000 / Published online: 29 November 2001     

Suitability of the k–ω turbulence model for scramjet flowfield simulations

The suitability of Wilcox's 2006 k– ω turbulence model for scramjet flowfield simulations is demonstrated by validation against five test cases that have flowfields representative of those to be expected in scramjets. The five test cases include a 2D flat plate, an axisymmetric cylinder, a backward‐facing step, the mixing of a pair of coaxial jets and the interaction between a shock wave and turbulent boundary layer. A generally good agreement between the numerical and experimental results is obtained for all test cases. These tests reveal that despite the turbulence model's sensitivity to freestream turbulence properties, the numerically predicted skin friction agrees with experimental data and theoretical correlations to their degree of uncertainty. The tests also confirm the importance of using a y⁺ value of less than 1 in getting accurate surface heat transfer distributions. In the coaxial jets case, the importance of matching the turbulence intensities at the inflow plane in improving the predictions of the turbulent mixing phenomena is also shown. A review of guidelines with regard to the setting up of grids and specification of freestream turbulence properties for turbulent Reynolds‐averaged Navier–Stokes CFD simulations is also included in this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k _s), thermal conductivity of flush-mounted discrete heat source (k _c), Reynolds number of fluid flow (Re _s), modified Richardson number (Ri ⁺) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T ^*) using the asymptotic computational fluid dynamics (ACFD) technique.     

Numerical simulation of fully developed turbulent flow and heat transfer in annular-sector ducts

 The mixing length theory is employed to simulate the fully developed turbulent heat transfer in annular-sector ducts with five apex angles (θ₀=18,20,24,30,40^∘) and four radius ratios (R _o/R _i=2,3,4,5). The Reynolds number range is 10⁴10⁵. The numerical results agree well with an available correlation which was obtained in following parameter range: θ₀=18,20,24,30,40^∘, R _o/R _i=4 and Re=10⁴5×10⁴. The present work demonstrates that the application range of the correlation can be much extended. Apart from the mixing length theory, the kɛ model with wall function and the Reynolds stress model are also employed. None of the friction factor results predicted by the three models agrees well with the test data. For the heat transfer prediction the mixing length theory seems the best for the cases studied. Received on 17 July 2000 / Published online: 29 November 2001     

Large eddy simulation using a dynamic mixing length subgrid‐scale model

A novel dynamic mixing length (DML) subgrid‐scale model for large eddy simulations is proposed in this work to improve the cutoff length of the Smagorinsky model. The characteristic mixing length (or the characteristic wave number) is dynamically estimated for the subgrid‐scale fluctuation of turbulence by the cutoff wave‐number, k_c, and the dissipation wave‐number, k_d. The dissipation wave number is derived from the kinetic energy spectrum equation and the dissipation spectrum equation. To prove the promise of the DML model, this model is used to simulate the lid‐driven cubical cavity with max‐velocity‐based Reynolds numbers 8850 and 12,000, the channel flows with friction‐velocity‐based Reynolds numbers 180, 395, 590, and 950, and the turbulent flow past a square cylinder at the higher Reynolds number 21,400, respectively, compared with the Smagorinsky model and Germano et al.'s dynamic Smagorinsky model. Different numerical experiments with different Reynolds numbers show that the DML model can be used in simulations of flows with a wide range of Reynolds numbers without the occurrence of singular values. The DML model can alleviate the dissipation of the Smagorinsky model without the loss of its robustness. The DML model shows some advantages over Germano et al.'s dynamic Smagorinsky model in its high stability and simplicity of calculation because the coefficient of the DML model always stays positive. The characteristic mixing length in the DML model reflects the subgrid‐scale fluctuation of turbulence in nature and thus the characteristic mixing length has a spatial and temporal distribution in turbulent flow. Copyright © 2011 John Wiley & Sons, Ltd.     

NUMERICAL PREDICTION OF SEMI-CONFINED JET IMPINGEMENT AND COMPARISON WITH EXPERIMENTAL DATA

The standard k–ε eddy viscosity model of turbulence in conjunction with the logarithmic law of the wall has been applied to the prediction of a fully developed turbulent axisymmetric jet impinging within a semi-confined space. A single geometry with a Reynolds number of 20,000 and a nozzle-to-plate spacing of two diameters has been considered with inlet boundary conditions based on measured profiles of velocity and turbulence. Velocity, turbulence and heat transfer data have been obtained using laser–Doppler anemometry and liquid crystal thermography respectively. In the developing wall jet, numerical results of heat transfer compare to within 20% of experiment where isotropy prevails and the trends in turbulent kinetic energy are predicted. However, stagnation point heat transfer is overpredicted by about 300%, which is attributed directly to the turbulence model and inapplicability of the wall function.     

Influence of turbulence model parameter settings on conjugate heat transfer simulation

Rationality of the parameter settings in turbulence model is an important factor affecting the accuracy of conjugate heat transfer (CHT) prediction. On the basis of a developed CHT methodology and the experimental data of Mark// cooling turbine blade, influences of the turbulence model parameter settings and the selection of turbulence models on CHT simulation are investigated. Results and comparisons with experimental data indicate that the inlet setting of the $\tilde{v}$ in Spalart–Allmaras model has nearly no influence on flow and heat transfer in blade surface. The inlet turbulence length scale l _T in the low-Reynolds number Chien k-ε turbulence model and the blade surface roughness in shear stress transport (SST) k-ω SST model have relatively obvious effects on the blade surface temperature which increases with the increase of them. Both of the laminar Prandtl number and turbulent Prandtl number have slight influences on the prediction, and they only need to be constant in CHT simulation. The k-ω SST model has the best accuracy in the turbine blade CHT simulation compared with the other two models.     

Advanced near-wall modeling for engine heat transfer

Recent developments in the engine heat transfer modeling tend to improve existing wall heat transfer models (temperature wall functions) which mostly rely on the standard or low-Re variants of k-ε turbulence model. Presently applied mesh resolutions already allow for first near-wall computational cells reaching the buffer or locally even viscous/conductive sub-layer, thus increasing the importance of more sophisticated modeling approach. As temperature gradient-induced density and fluid property variations become significant, wall heat transfer is strongly influenced by property variations (viscous/conductive sub-layer) and predictive capability of the turbulence model (buffer region), standard wall laws being inadequate anymore, even for attached boundary layers. The present approach relies on the k-ζ-f turbulence model and formulates a compressible wall function of Han and Reitz in the framework of hybrid wall treatment. The model is validated against spark ignition (SI) engine heat transfer measurements. Predicted wall heat flux evolutions on the cylinder head exhibit very good agreement with the experimental data, being superior to similar numerical predictions available in the published literature.     

Numerical simulation and experimental validation of heat transfer within rotating flows for three‐dimensional non‐axisymmetric,turbulent conditions

A control volume type numerical methodology for the analysis of steady three‐dimensional rotating flows with heat transfer, in both laminar and turbulent conditions, is implemented and experimentally tested. Non‐axisymmetric momentum and heat transfer phenomena are allowed for. Turbulent transport is alternatively represented through three existing versions of the k–ε model that were adjusted to take into account the turbulence anisotropy promoted by rotation, streamline curvature and thermal buoyancy. Their relative performance is evaluated by comparison of calculated local and global heat balances with those obtained through measurements in a laboratory device. A modified version of the Lam and Bremhorst, low Reynolds number model is seen to give the best results. A preliminary analysis focused on the flow structure and the transfer of heat is reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Turbulent forced convection in a helically coiled square duct with one uniform temperature and three adiabatic walls

In this study, effects of geometrical parameters on the average convection heat transfer characteristics in helical square ducts were investigated both experimentally and numerically. The inner wall of the helical square duct was uniformly temperatured, and the top, bottom, and outer walls were adiabatic. The Renormalization Group (RNG) k–ε turbulence model was used to simulate turbulent flow and heat transfer. The governing equations were solved by a finite volume method. Numerical results were found to be in good agreement with the presented experimental data. The new correlation was proposed for the average heat transfer coefficient on the inner wall of the helical square duct. The results showed that the ratio of pitch to coil radius b/R has no obvious effect on the inner wall convective heat transfer coefficient but the ratio of hydraulic radius to coil radius a/R has considerable effect.     

NUMERICAL STUDY OF TURBULENT FORCED CONVECTION IN A PERIODICALLY RIBBED CHANNEL WITH OSCILLATORY THROUGHFLOW

Numerical computations are performed on the fully developed flow and heat transfer in a periodically ribbed channel with oscillatory throughflow. A uniform heat flux is imposed at the lower plate of the channel. An externally sustained pressure gradient varies sinusoidally in time. A low-turbulent-Reynolds-number version of the k–ϵ two-equation model of turbulence is invoked, together with a preferential dissipation modification, to predict the complex turbulent flow field. Computed results indicate that much heat transfer enhancement is expected by increasing the Womersley number, which measures the relative strength of the oscillatory motion to the viscous effects.     

Prediction of a Turbulent Non-Premixed Natural Gas Flame in a Semi-Industrial Scale Furnace using a Radiative Flamelet Combustion Model

A mixedness-reactedness flamelet combustion model coupled with a comprehensive radiation heat transfer model based on the discrete transfer method of solution of the radiative transport equation is applied for the simulation of a 3 MW non-swirling turbulent non-premixed natural gas flame in the experimental furnace at the International Flame Research Foundation. In the calculation, turbulence is represented by the standard k − ε and a differential Reynolds-stress model. Predictions are compared with measurements of mean gas velocity, temperature, major species concentrations and incident radiation wall flux. The radiative mixedness-reactedness flamelet combustion model, irrespective of the model for turbulence, is able to reproduce the basic structure of the experimental flame, which is stabilised downstream of the burner nozzle. In the near burner region, encompassing the non-reacting lift-off zone, good quality predictions are obtained using both the turbulence models, whereas further downstream, within the combusting zone of the jet, the Reynolds-stress turbulence model generates better predictions at and about the furnace axis. The nitric oxide (NO) formation via the thermal- and prompt-NO routes was also calculated and compared with in-flame and flue-gas NO data. The measured NO level at the furnace exit is well reproduced in the calculation, however discrepancies exist near the burner where NO concentrations around the furnace axis are overpredicted.     

Effect of cavity aspect ratio on flow and heat transfer characteristics in pipes: a numerical study

Using the standard k–ε turbulence model, a two-dimensional turbulent pipe flow was simulated with and without square cavities. Effect of cavity aspect ratio on flow and heat transfer characteristics was investigated. Uncertainty was approximated through experimental validation and grid independence. The simulation revealed circulation inside the cavities. Cavity boundaries were shown to contribute significantly toward turbulence production. Cavity presence was shown to enhance overall heat transfer through the wall, while increasing pressure drop significantly across the pipe. It was predicted that cavities with higher aspect ratio enhance heat transfer more while increasing pressure drop.     

Numerical Simulations of the Sandia Flame D Using the Eddy Dissipation Concept

A turbulent piloted methane/air diffusion flame (Sandia Flame D) is calculated using both compressible Reynolds-averaged and large-eddy simulations (RAS and LES, respectively). The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction, which assumes that molecular mixing and the subsequent combustion occur in the fine structures (smaller dissipative eddies, which are close to the Kolmogorov length scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the fine structures are evaluated using a standard k- ?? turbulence model for RAS and a one-equation eddy-viscosity sub-grid scale model for LES. Finite-rate chemical kinetics are taken into account by treating the fine structures as constant pressure and adiabatic homogeneous reactors (calculated as a system of ordinary-differential equations (ODEs)) described by a Perfectly Stirred Reactor (PSR) concept. A robust implicit Runge-Kutta method (RADAU5) is used for integrating stiff ODEs to evaluate reaction rates. The radiation heat transfer is treated by the P1-approximation. The assumed β-PDF approach is applied to assess the influence of modeling of the turbulence-chemistry interaction. Numerical results are compared with available experimental data. In general, there is good agreement between present simulations and measurements both for RAS and LES, which gives a good indication on the adequacy and accuracy of the method and its further application for turbulent combustion simulations.     

Buoyancy effects on turbulent swirling flows

A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′². Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.     

Unsteady flow and heat transfer analysis of an impinging synthetic jet

The present paper focuses on the analysis of unsteady flow and heat transfer regarding an axisymmetric impinging synthetic jet on a constant heat flux disc. Synthetic jet is a zero net mass flux jet that provides an unsteady flow without any external source of fluid. Present results are validated against the available experimental data showing that the SST/k − ω turbulence model is more accurate and reliable than the standard and low-Re k − ε models for predicting heat transfer from an impinging synthetic jet. It is found that the time-averaged Nusselt number enhances as the nozzle-to-plate distance is increased. As the oscillation frequency in the range of 16–400 Hz is increased, the heat transfer is enhanced. It is shown that the instantaneous Nu distribution along the wall is influenced mainly by the interaction of produced vortex ring and wall boundary layer. Also, the fluctuation level of Nu decreases as the frequency is raised.     

Reynolds-Averaged,Scale-Adaptive and Large-Eddy Simulations of Premixed Bluff-Body Combustion Using the Eddy Dissipation Concept

A lean premixed propane/air bluff-body stabilized flame (Volvo test rig) is calculated using the Scale-Adaptive Simulation turbulence model (SAS) and Large-Eddy simulations (LES) as well as the conventional Reynolds-averaged approach (RAS). RAS and SAS are closed by the standard k-?? and the k-ω Shear Stress Transport (SST) turbulence models, respectively. The conventional Smagorinsky and the k-equation sub-grid scales models are used for the LES closure. Effects of the sub-grid scalar flux modeling using the classical gradient hypothesis and Clark’s tensor diffusivity closures both for the inert and reactive LES flows are discussed. The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction. It assumes that molecular mixing and the subsequent combustion occur in the ’fine structures’ (smaller dissipative eddies, which are close to the Kolmogorov scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the ’fine structures’ are evaluated using different turbulence models (RAS, SAS and LES). The finite-rate chemical kinetics is taken into account by treating the ’fine structures’ as constant pressure and adiabatic homogeneous reactors, calculated as a system of ordinary-differential equations (ODEs) described by a Perfectly Stirred Reactor (PSR) concept. Several further enhancements to model the PSRs are proposed, including a new Livermore Solver (LSODA) for integrating stiff ODEs and a new correction to calculate the PSR time scales. All models have been implemented as a stand-alone application \(\text {edcPisoFoam}\) based on the OpenFOAM technology. Additionally, several RAS calculations were performed using the Turbulence Flame Speed Closure model in Ansys Fluent to assess effects of the heat losses by modeling the conjugate heat transfer between the bluff-body and the reactive flow. Effects of the turbulence Schmidt number on RAS results are discussed as well. Numerical results are compared with available experimental data. Reasonable consistency between experimental data and numerical results provided by RAS, SAS and LES is observed. In general, there is satisfactory agreement between present LES-EDC simulations, numerical results by other authors and measurements without any major modification to the EDC closure constants, which gives a quite reasonable indication on the adequacy and accuracy of the method and its further application for turbulent premixed combustion simulations.     

Hybrid RANS/LES of flow and heat transfer in round impinging jets

Fluid flow and convective heat transfer predictions are presented of round impinging jets for several combinations of nozzle-plate distances H/D = 2, 6 and 13.5 (where D is the nozzle diameter) and Reynolds numbers Re = 5000, 23,000 and 70,000 with the newest version of the k-ω model of Wilcox (2008) and three hybrid RANS/LES models. In the RANS mode of the hybrid RANS/LES models, the k-ω model is recovered. Three formulations are considered to activate the LES mode. The first model is similar to the hybrid models of Davidson and Peng (2003) and Kok et al. (2004). The turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the definition of the RANS eddy viscosity. As grid size, a maximum measure of the hexahedral grid cell is used. The second model has the same k-equation, but the eddy viscosity is the minimum of the k-ω eddy viscosity and the Smagorinsky eddy viscosity, following a proposal by Batten et al. (2004). The Smagorinsky eddy viscosity is formed with the cube root of the cell volume. The third model has, again, the same k-equation, but has an eddy viscosity which is an intermediate between the eddy viscosities of the first and second models. This is reached by using the cube root of the cell volume in the eddy viscosity formula of the first model.The simulation results are compared with experimental data for the high Reynolds number cases Re = 23,000 and Re = 70,000 and LES data for the low-Reynolds number case Re = 5000. The Reynolds numbers are defined with the nozzle diameter and the bulk velocity at nozzle outlet. At low nozzle-plate distance (the impingement plate is in the core of the jet), turbulent kinetic energy is overpredicted by RANS in the stagnation flow region. This leads to overprediction of the heat transfer rate along the impingement plate in the impact zone. At high nozzle-plate distance (the impingement plate is in the mixed-out region of the jet), the turbulence mixing is underpredicted by RANS in the shear layer of the jet which gives a too high length of the jet core. This also results in overprediction of the heat transfer rate in the impingement zone caused by too big temperature gradients at impingement.All hybrid RANS/LES models are able to correct the heat transfer overprediction of the RANS model. For good predictions at low nozzle-plate distance, it is necessary to sufficiently resolve the formation and development of the near-wall vortices in the jet impingement region. At high nozzle-plate distance, the essence is to capture the evolution and breakup of the flow unsteadiness in the shear layer of the jet, so that accurate mean and fluctuating velocity profiles are obtained in the impingement region. Although the models have a quite different theoretical justification and generate a quite different eddy viscosity in some flow regions, their overall results are very comparable. The reason is that in zones that are crucial for the results, the models behave similarly.     

Numerical investigation of fully developed turbulent fluid flow and heat transfer in a square duct

Three-dimensional fully developed turbulent fluid flow and heat transfer in a square duct are numerically investigated with the author's anisotropic low-Reynolds-number k-ε turbulence model. Special attenton has been given to the regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, instead of the common wall function approach, the no-slip boundary condition at the wall is directly used. Velocity and temperature profiles are predicted for fully developed turbulent flows with constant wall temperature. The predicted variations of both local wall shear stress and local wall heat flux are shown to be in close agreement with available experimental data. The present paper also presents the budget of turbulent kinetic energy equation and the systematic evaluation for existing wall function forms. The commonly adopted wall function forms that are valid for two-dimensional flows are found to be inadequate for three-dimensional turbulent flows in a square duct.     

The influence of rotation on turbulent flow and heat transfer in an annulus between independently rotating tubes

Experimental and numerical investigations of turbulent flow and heat transfer have been performed in a concentric annulus between independently rotating tubes. Numerical predictions, applying a Reynolds stress turbulence model, are compared with experimental fluid flow and heat transfer results for the case of a heated outer tube and an adiabatic inner tube. Compared to the above mentioned boundary conditions for the conservation equation of energy, differences in heat transfer in case of a heated inner tube and an adiabatic outer one, are examined by analysis, applying a mixing length turbulence model. Numerical investigations with both kinds of models about the influence of annulus radius ratio make evident that due to different superimpositions of centrifugal force and additional shear stress there is a wide variation of effects on fluid flow and heat transfer caused by the rotation of the inner and the outer tube.