A NEW LOW-REYNOLDS VERSION OF AN EXPLICIT ALGEBRAIC STRESS MODEL FOR TURBULENT CONVECTIVE HEAT TRANSFER IN DUCTS

This investigation concerns performance of a new low-Reynolds version of an explicit algebraic stress model (EASM) for numerical calculation of turbulent forced-convective heat transfer and fluid flow in straight ducts with fully developed conditions. The turbulent heat fluxes are modeled by a SED concept, the GGDH, and the WET methods. New versions of GGDH, WET, and EASM are presented for low Reynolds numbers. However, at high Reynolds numbers, two wall functions are used, one for velocity fields and one for the temperature field. All the models are computed in a general three-dimensional channel. The low-Reynolds version of the models presented is very stable and has been used for Reynolds numbers up to 70,000 with least demanded number of grid points, and without any convergence problem or stability problem.     

TURBULENCE MODELING EXPERIENCE IN DUCTS WITH FORCED CONVECTION FLOW

This study presents a general computational method for calculating turbulent quantities in arbitrary three-dimensional ducts. Four different turbulence models for the turbulent Reynolds stresses are compared, namely, a standard K-epsilon model, a nonlinear K- epsilon model, an explicit algebraic stress model (EASM), and a full Reynolds stress model (RSM). The turbulent heat fluxes are modeled by the simple eddy diffusivity concept, the generalized gradient diffusion hypothesis, and the wealth alpha earnings time methods. A finite volume technique for nonstaggered grids combined with the SIMPLEC algorithm is applied. A modified strongly implicit procedure is implemented for solving the equations. The van Leer scheme is applied for the convective terms except for the K and epsilon equations, where the hybrid scheme is used.     

A FOUR-EQUATION MODEL FOR PREDICTION OF GAS-SOLID TURBULENT FLOWS

A four-equation model is proposed for prediction of dilute turbulent gas-solid flows where the ratio of the particle and the gas densities is large. The model is based on explicit algebraic relations for Reynolds stresses and turbulent fluxes of the void fraction, which were derived in an earlier work within the context of Reynolds-averaged Navier-Stokes (RANS) methodology. These relations are manipulated here to derive nonlinear eddy-viscosity-type models for thin-shear flows. Further, new models are proposed for third-order correlations which are also simplified for thin-shear flows. These models are used to propose four transport equations for the turbulence kinetic energy of the carrier phase and its rate of dissipation, the turbulence kinetic energy of the dispersed phase, and the velocity covariance of the two phases. The final four-equation model is implemented for prediction of a particle-laden turbulent jet, and encouraging agreements with available laboratory data are observed.     

Direct numerical simulation of turbulent flow and combined convective heat transfer in a square duct with axial rotation

Direct numerical simulations (DNS) of turbulent flow and convective heat transfer in a square duct with axial rotation were carried out. The pressure-driven flow is assumed to be hydrodynamically and thermally fully developed, for which the Reynolds number based on the friction velocity and hydraulic diameter is kept at constant (Re_τ = 400). In the finite length duct, two opposite walls are perfectly insulated and another two opposite walls are kept at constant but different temperatures. Four thermal boundary conditions were chosen in combination with axial rotation to study the effects of rotation and Grashof number on mean flow, turbulent quantities and momentum budget. The results show that thermal boundary conditions have significant effects on the topology of secondary flows, profiles of streamwise velocity, distribution of temperature and other turbulent statistic quantities but have marginal effects on the bulk-averaged quantities; Coriolis force affects the statistical results very slightly because it exerts on the plane normal to main flow direction and the rotation rate is low; Buoyancy effects on the turbulent flow and heat transfer increase with the increase of Grashof number (Gr), and become the major mechanism of the development of secondary flow, turbulence increase, and momentum and energy transport at high Grashof number.     

Forced turbulent heat convection in a square duct with non-uniform wall temperature

In the present work, the numerical simulation to calculate the problem of the turbulent convection with non-uniform wall temperature in a square cross-section duct was adopted. To solve this problem some assumptions for the flow, such as: the condition of fully developed turbulence and incompressible flow have been assumed. The methodology of the dimensionless energy equation was used to calculate the fluid temperature field in the square cross-section in function of the non-uniform wall temperatures prescribed. Numerical simulations were done using two different turbulent models to resolve the momentum equations and two more models to resolve the energy equation. The models of turbulence k-ε Nonlinear Eddy Viscosity Model (NLEVM) and the Reynolds Stress Model (RSM) were used to determine the turbulent intensities as well as the profiles of axial and secondary mean velocities. The turbulence model RSM was simulated using a commercial software. The thermal field was determined from other two models: Simple Eddy Diffusivity (SED), based in the hypothesis of the constant turbulent Prandtl number; and Generalized Gradient Diffusion Hypothesis (GGDH). In this last model, as the turbulent heat transfer depends on the shear tensions, the anisotropy is considered. These two last equation models of the energy equation of the fluid have been implemented in FORTRAN, a code of programming. The performances of the models were evaluated by validating them based in the experimental and numerical results published in the literature. Two important parameters of great interest in engineering are presented: the friction factor and the Nusselt number. The results of this investigation allow the evaluation of the behavior of the turbulent flow and convective heat fluxes for different square cross-sectional sections throughout the direction of the main flow, which is mainly influenced by the temperature distribution in the wall.     

COMPUTATIONAL ANALYSIS OF TURBULENT FLUID FLOW AND HEAT TRANSFER OVER AN ARRAY OF HEATED MODULES USING TURBULENCE MODELS

A computational analysis is carried out using the standard k - l model and two low Reynolds number turbulence models as applied to developing turbulent fluid flow and heat transfer in a channel with surface-mounted heat-generating modules. The channel is assumed to be formed between two adjacent circuit boards with surface-mounted heat-generating modules mounted on a single side of each board. A detailed discussion of the computational model and the solution algorithm is given. Numerical experimentation is carried out with respect to mesh size and other mesh parameters. Calculation is performed for a Reynolds number range 2,000-7,000, and a Prandtl number of 0.7. The predictions of both pressure drop and heat transfer coefficient over the modules are compared with selected experimental data. The comparison showed that the low Reynolds number model based on Jones and Launder gives good predictions in a Reynolds number range of 2,000-5,000. At higher Reynolds numbers such as at Re=7,000, the standard k - l results in better predictions.     

Laser doppler velocimetry investigation of the turbulence structure of axisymmetric diffusion flames

Measurements of mean velocity components, turbulent intensities, velocity probability density functions, power spectra and autocorrelation functions of axial velocity fluctuation, and spatial turbulence macroscale, are reported in a turbulent round jet flow, issuing vertically into stagnant air, in non-combusting and combusting situations. The fuel density (a mixture of methane and argon) is chosen to be equal to the cold flow gas density (a mixture of air and helium) in order to minimize cold fuel/cold gas mixture density difference effects on measured turbulence properties. The objectives are to study the influence of the combustion process on the turbulence structure of the combustible jet flows considered, and to provide data against which results of numerical prediction methods for such flows embodying various turbulence and combustion models can be compared, with a view to improving our understanding of relevant transport processes and on guiding modelling and prediction efforts of such flows. A one-dimensional laser velocimeter operating in forward scatter differential Doppler mode was used to obtain the measurements. Gas temperatures were measured by thermocouples. A visual study by schlieren photography has also been conducted. It is found that the existence of the flame suppresses turbulence in the upstream region of the jet flow and enhances it in the downstream region, where turbulence intensities are substantially higher than in the corresponding cold jet flow. However, the relative intensities, i.e. the ratio of the local turbulent intensity to the local mean velocity, are smaller in the jet diffusion flame and become comparable to relative turbulent intensities found in the cold jet flow in the downstream region of the flow. Turbulence in the jet diffusion flame is appreciably more anisotropic than in the corresponding cold jet in all regions of the flow, suggesting the eventual desirability of multi-stress models of turbulence for the prediction of such flames. The combustion process has been found to have also a marked influence on the turbulence macroscale. It is significantly smaller than in the cold jet flow in the upstream region and increases appreciably at downstream distances, the rate of this increase closely following the rate of temperature increase. The experimental results obtained will guide the development of an improved prediction method for such combusting systems.     

Experimental and numerical simulations of turbulent ventilation in aircraft cabins

Airflow in a generic airplane cabin has been investigated numerically by means of Reynolds averaged Navier–Stokes computations and experimentally by particle image velocimetry (PIV). High and low Reynolds number as well as two layer turbulence models were tested for their ability to describe turbulent velocity fields. Special attention was given to the flow of the incoming air jet along the luggage compartment. Comparison with PIV measurements reveals that for reliable prediction of isothermal cabin flow, low Reynolds number turbulence models have to be used.     

Reynolds analogy in combustor modeling

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS (Reynolds-averaged Navier–Stokes) simulations, where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer. This concept, applied to a diffusion flame model combustor, is assessed in this paper. Some of the numerical results, obtained from a flamelet combustion model with the turbulent Prandtl/Schmidt number varying from 0.25 to 0.85, are presented and compared with a benchmark experimental database. It is found that the turbulent Prandtl/Schmidt number has significant effects on the predicted temperature and species fields in the combustor. This is also true for the temperature profile along the combustor wall. In contrast, its effect on the velocity field is insignificant in the range considered. With an optimized turbulent Prandtl/Schmidt number, both velocity and scalar fields can be reasonably and quantitatively predicted. For the present configuration and operating conditions, the optimal Prandtl/Schmidt number is 0.5, lower than the traditionally used value of ～0.85. This study suggests that for accurate prediction of turbulence scalar transfers in practical reacting flows, the Reynolds analogy concept should be improved and new approaches should be developed.     

Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method

A numerical study of a turbulent natural convection in a rectangular cavity with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural-convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds-averaged Navier-Stokes equation (RANS) method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction method to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.     

Computation of a turbulent natural convection in a rectangular cavity with the elliptic-blending second-moment closure

A numerical study of a turbulent natural convection in an enclosure with the elliptic-blending second-moment closure (EBM) is presented. The primary emphasis of the study is placed on an investigation of the accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent natural convection flow. The turbulent heat fluxes in this model are treated by the general gradient diffusion hypothesis (GGDH). The model is applied to the prediction of a natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for a validation of the turbulence models. The results are also compared with those by the two-layer model, the SST model, the V2-f model and the second-moment differential stress and flux model. It is shown that the elliptic blending model predicts as good as or better than the existing models for the mean velocity and turbulent quantities although this model employs a simpler GGDH for treating the turbulent heat fluxes.     

Radiation Effects on Turbulent Mixed Convection in an Asymmetrically Heated Vertical Channel

The purpose of present study is to numerically investigate the radiation effects on turbulent mixed convection flow between two differentially heated vertical parallel plates. Two flow situations known as aiding and opposing flow are considered. Frictional Reynolds number and Grashof number are assumed to be 150 and 1.6 × 10⁶, respectively. Both hydrodynamically and thermally developing and fully developed regions in the channel are investigated. Three Reynolds-averaged Navier–Stokes-based low Reynolds turbulence models are evaluated and the model with better overall performance is applied to the simulations. The radiative transfer equation for the gray and participating fluid is solved using the discrete-ordinates method, adopting its eighth-order quadrature scheme. The effects of two radiative parameters, namely, wall emissivity and optical thickness, on the flow and thermal fields, Nusselt number, and friction factor are addressed. Present results indicate that the presence of thermal radiation has a significant influence on flow and thermal fields. With an increase in wall emissivity and optical thickness, influence of radiation on the mean velocity, mean temperature, and turbulence kinetic energy profiles grows in both aiding and opposing regions. This results in an increase in bulk temperature, centerline velocity, and Nusselt number and a decrease in friction factor on both sides.     

SIMULATION OF SWIRLING TURBULENT FLOWS AND HEAT TRANSFER IN AN ANNULAR DUCT

The article presents a numerical simulation of swirling turbulent flows and heat transfer in an annular duct. The time-averaged governing equations are solved, which are closed by a new algebraic Reynolds stress model (ASM). The simulation is performed under different flow conditions. The calculated results of gas axial and tangential velocities, turbulent kinetic energy, temperature, and local heat transfer coefficients on the inner and outer walls of the annulus are provided. They illustrate the effect of swirl number, inlet axial velocity, and ratio of inner to outer radius on the mean flow and turbulence properties, as well as on enhancing heat transfer in the annular duct.     

Prediction of turbulent flow structure in a fully developed rib-roughened narrow rectangular channel

Fully developed turbulent water-flow structure over one-side repeated-ribs in narrow two-dimensional rectangular channels was investigated experimentally by Particle Image Velocimetry (PIV) and analytically by the standard κ-ɛ and nonlinear κ-ɛ turbulent models. Two rib-pitch to height ratios (p/k) of 10 and 20 were investigated while the rib height was held constant at 4 mm. The rib height-to-channel equivalent diameter ratio (k/De) was 0.1. The streamwise mean velocity and turbulent kinetic energy distributions at six selected axial stations from the center rib for the two Reynolds number (Re) of 7,000 and 20,000 were obtained and compared with the predicted one. The performance ability in predicting separating and reattaching turbulent water-flow between the standard κ-ɛ and nonlinear κ-ɛ models had yielded no clear conclusion. A large-scale turbulent eddy was generated by the rib promoter and then propagated into the mainstream flow, which led to the deformation of the velocity profile. The turbulent kinetic energy was increased about two times higher at p/k = 20 than that at p/k =10 under the two Reynolds numbers. The effect of the p/k value and the Reynolds number (Re) on reattachment length (XR) was investigated and showed that the p/k and Re had no significant effect on the reattachment length beyond a critical value of Re = 15,000 where XR was found to be approximately 4 times of the rib height under water-flow condition.     

Effects of turbulence model and interfacial shear on heat transfer in turbulent falling liquid films

An improved method is presented for the prediction of heat transfer coefficients in turbulent falling liquid films with or without interfacial shear for both heating or condensation. A modified Mudawwar and El-Masr's semi-empirical turbulence model, particularly to extend its use for the turbulent falling film with high interfacial shear, is used to replace the eddy viscosity model incorporated in the unified approach proposed by Yih and Liu. The liquid film thickness and asymptotic heat transfer coefficients against the film Reynolds number for wide range of interfacial shear predicted by both present and existing methods are compared with experimental data. The results show that, in general, predictions of the modified model agree more closely with experimental data than that of existing models.     

Investigation of local heat transfer coefficients in plate heat exchangers with temperature oscillation IR thermography and CFD

A method for the measurement of local convective heat transfer coefficients from the outside of a heat-transferring wall has been developed. This method is contact-free and fluid independent, employing radiant heating by laser or halogen spotlights and an IR camera for surface temperature measurements; it allows for the rapid evaluation of the heat transfer coefficient distribution of sizable heat exchanger areas. The technique relies first on experimental data of the phase lag of the outer surface temperature response to periodic heating, and second on a simplified numerical model of the heat exchanger wall to compute the local heat transfer coefficients from the processed data. The IR temperature data processing includes an algorithm for temperature drift compensation, phase synchronization between the periodic heat flux and the measured temperatures, and Single Frequency Discrete Fourier Transformations. The ill-posed inverse heat conduction problem of deriving a surface map of heat transfer coefficients from the phase-lag data is solved with a complex number finite-difference method applied to the heat exchanger wall. The relation between the local and the mean heat transfer coefficients is illuminated, calculation procedures based on the thermal boundary conditions are given. The results from measurements on a plate heat exchanger are presented, along with measurements conducted on pipe flow for validation. The results show high-resolution surface maps of the heat transfer coefficients for a chevron-type plate for three turbulent Reynolds numbers, including a promising approach of visualizing the flow field of the entire plate. The area-integrated values agree well with literature data. CFD calculations with an SST and an EASM–RSM were carried out on a section of a PHE channel. A comparison with the measured data indicates the shortcomings of even advanced turbulence models for the prediction of heat transfer coefficients but confirms the advantages of EASM–RSM in complex flows.     

Influence of Turbulence Schmidt Number on Exit Temperature Distribution of an Annular Gas Turbine Combustor using Flamelet Generated Manifold

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS(Reynoldsaveraged Navier–Stokes)simulations,where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer.This concept,applied to a lean premixed combustion system,was assessed in this paper in terms of exit temperature distribution.Because of the isotropic assumption involved in this analogy,the prediction in some flow condition,such as jet cross flow mixing,would be inaccurate.In this study,using Flamelet Generated Manifold as reaction model,some of the numerical results,obtained from an annular combustor configuration with the turbulent Schmidt number varying from 0.85 to 0.2,were presented and compared with a benchmark atmospheric test results.It was found that the Schmidt numberσt in mean mass fraction f transport equation had significant effect on dilution air mixing process.The mixing between dilution air and reaction products from the primary zone obviously improved asσt decreased on the combustor exit surface.Meanwhile,the sensitivity ofσt in three turbulence models including Realizable k-ε,SST(Shear Stress Transport)and RSM(Reynolds Stress Model)has been compared as well.Since the calculation method of eddy viscosity was different within these three models,RSM was proved to be less sensitive than another two models and can guarantee the best prediction of mixing process condition.On the other hand,the results of dilution air mixing were almost independent of Schmidt number Sct in progress variable c transport equation.This study suggested that for accurate prediction of combustor exit temperature distribution in steady state reacting flow simulation,the turbulent Schmidt number in steady state simulation should be modified to cater to dilution air mixing process.     

Large Eddy Simulation of low Reynolds number turbulent hydrogen jets - Modelling considerations and comparison with detailed experiments

The main objective of this work is to apply Large Eddy Simulation (LES) on hydrogen subsonic round jets in order to evaluate modelling strategies and to provide guidelines for similar applications. The ADREA-HF code and the experiments conducted by Sandia National Laboratories are used for that purpose. These experiments are very suitable for LES studies because turbulent fluctuations have been measured which is something rare in hydrogen experiments. Hydrogen is released vertically from a small orifice of 1.91 mm diameter into stagnant environment. Three experimental cases are simulated with different Reynolds number at the release area, namely 885, 1360 and 2384. Hydrogen mass fraction and velocity mean values and fluctuations are compared against the experimental data. Several grid resolutions are used to assess the effect on the results, using mainly the Smagorinsky subgrid scale model. In the lowest Reynolds number case, an Implicit LES code, used independently from a different scientific group, is also tested. In this case, the performance of the RNG-LES subgrid scale model of the ADREA-HF code is also examined. Additionally, the effect of Smagorinsky constant and of the Van Driest correction is evaluated. The amount of the resolved turbulence and of the velocity spectra are presented. Finally, the effect of the release modelling is discussed. The analysis shows that even a coarse discretization of the release area can give acceptable results for hydrogen safety engineering applications. However, dense grids are required for the more accurate prediction of the turbulent characteristics. The two LES codes gave similar results and the overall agreement with the experiment was satisfactory.     

Direct numerical simulation of turbulent flow in a vertical channel with buoyancy orthogonal to mean flow

The effect of buoyancy on turbulent air flowing horizontally between two differentially heated vertical plates has been investigated using direct numerical simulation. Grashof number ranges between zero and 4.0 × 10⁶ and the Boussinesq approximation is used in the buoyant term. In this particular configuration, the buoyancy forces result in skewed mean velocity profiles with non-zero anti-symmetric spanwise component W. The resulting flow has the features of three-dimensional turbulent boundary layer flows. In particular, suppression of the primary Reynolds stress in near-wall region is observed. Titled streaks with significant destruction of the associated vortical structures are highlighted. The induced mean spanwise strain enhances the turbulence intensities in the channel core. The effect of buoyancy on mean quantities and second-order statistics including Reynolds stress components and turbulent heat fluxes are presented and analyzed with detailed budgets of their transport equations which are believed to be helpful to testify and improve turbulence models incorporating buoyancy effect.     

Modelling of turbulent molten pool convection in laser welding of a copper–nickel dissimilar couple

The effects of turbulence on momentum, heat, and mass transfer during laser welding of a copper–nickel dissimilar couple are studied by carrying out three-dimensional unsteady Reynolds Averaged Navier Stokes (RANS) simulations. The turbulent transport is modelled by a suitably modified high Reynolds number k–ε model. The solid–liquid phase change is accounted for by a modified enthalpy porosity technique. In order to demonstrate the effects of turbulence, two sets of simulations are carried out for the same set of processing parameters: one with the turbulence model, and the other without activating the turbulence model. The enhanced diffusive transport associated with turbulence is shown to decrease the maximum values of temperature, velocity magnitude, and copper mass fraction in the molten pool. The effects of turbulence are found to be most prominent on the species transport in the molten pool. The composition distribution in turbulent simulation is found to be more uniform than that obtained in the simulation without turbulent transport. The nickel composition distribution predictions, as obtained from the present turbulence model based simulations, are also found to be in good agreement with the corresponding experimental results.