Turbulence modelling for wall-bounded particle-laden flow with separation

The performance of different turbulence models and source-term models for the turbulent separated particle-laden flow is investigated. The accuracy of various turbulence models is firstly evaluated without any modification by the source-term model. The considered models are the k–ω SST model; the standard, the RNG and the realizable k–ε models with the standard, the non-equilibrium and the enhanced wall functions. The accuracy of various source-term models is then compared. The results are investigated and analyzed to find the best combination of the turbulence model and the source-term model in predicting the combined effects of turbulence, particles, viscous wall and flow separation. It is found that the RNG k–ε turbulence model with the non-equilibrium wall function using the source-term model of Tu and Fletcher is the most suitable combination for this type of flow.     

Optimization of high-pressure shell-and-tube heat exchanger for syngas cooling in an IGCC

This work investigates the flow field and the heat transfer characteristics of a shell-and-tube heat exchanger for the cooling of syngas. Finite volume method based on FLUENT software was used and the RNG k–ε turbulence model was adopted for modeling turbulent flow. The porosity rate, the distribution of the resistance and the distribution of the heat source are introduced to FLUENT by coupling the user defined function. The pressure drop, the temperature distribution and the variation of local heat transfer are studied under the effects of the syngas components and the operating pressure, and the effect of the arrangement of the baffles on the heat transfer is studied. The results show that higher operation pressure can improve the heat transfer, however brings bigger pressure drop. The components of the syngas significantly affect the pressure drop and the heat transfer. The arrangement of the baffles influences the fluid flow.     

The Effect of Conjugate Heat Transfer on Film Cooling Effectiveness

The film cooling effectiveness of a two-dimensional gas turbine endwall is compared for the cases of conjugate heat transfer and an adiabatic wall condition using five common turbulence models. The turbulence models employed in this study are: the RNG k–ε model, the realizable k–ε model, the standard k–ω model, the SST k–ω model, and the RSM model. The computed flow field and surface temperature profiles along with the film effectiveness for one and two cooling slots at different injection angles are presented. The results show the strong effect of conjugate heat transfer on the film effectiveness compared to the adiabatic case and also compared to the effectiveness values obtained from analytically solvable models.     

Turbulence models application on CFD simulation of hydrodynamics,heat and mass transfer in a structured packing

In this study, turbulence model applications on two-phase flow simulation in a structured packing are investigated using CFD application. Dry pressure drop, irrigated pressure drop, mass transfer and heat transfer are studied by k–ε, RNG k–ε, k–ω and BSL turbulence models. The best results obtained by k–ω and BSL models, but k–ω is recommended because it is more robust than BSL. The mean absolute relative error (MARE) between CFD prediction of k–ω model and experimental data for dry pressure drop, irrigated pressure drop, mass transfer and heat transfer are 16.9%, 10.7%, 8.1%, 0.9%, respectively.     

A modified k–ε turbulence model for the simulation of two-phase flow and heat transfer in condensers

A modified k–ε turbulence model is developed in this study to simulate the gas–liquid two-phase flow and heat transfer in steam surface condensers. A quasi-three-dimensional algorithm is used to simulate the fluid flow and heat transfer in steam surface condensers. The numerical method is based on the conservation equations of mass and momentum for both gas-phase and liquid-phase, and mass fraction conservation equation for non-condensable gases. The numerical simulation of an experimental steam surface condenser has been conducted using the proposed modified k–ε turbulence model. The results obtained from the proposed model agree well with the experimental results and the results also show an obvious improvement in the prediction accuracy comparing with previous results where a constant value for the turbulent viscosity was used.     

Study of turbulent heat transfer of aviation kerosene flows in a curved pipe at supercritical pressure

The flow and heat transfer characteristics of China No. 3 aviation kerosene in a heated curved tube under supercritical pressure are numerically investigated by a finite volume method. A two-layer turbulence model, consisting of the RNG k–ε two-equation model and the Wolfstein one-equation model, is used for the simulation of turbulence. A 10-species kerosene surrogate model and the NIST Supertrapp software are applied to obtain the thermophysical and transport properties of the kerosene at various temperature under a supercritical pressure of 4 MPa. The large variation of thermophysical properties of the kerosene at the supercritical pressure make the flow and heat transfer more complicated, especially under the effects of buoyancy and centrifugal force. The centrifugal force enhances the heat transfer, but also increases the friction factors. The rise of the velocity caused by the variation of the density does not enhance the effects of the centrifugal force when the curvature ratios are less than 0.05. On the contrary, the variation of the density increases the effects of the buoyancy.     

Evaluation of Turbulence Models in the Prediction of Heat Transfer Due to Slot Jet Impingement on Plane and Concave Surfaces

The performance of several turbulence models in the prediction of convective heat transfer due to slot jet impingement onto flat and concave cylindrical surfaces is evaluated against available experimental data. The candidate models for evaluation are (1) the standard k – ε model, (2) the RNG k – ε model, (3) the realizable k – ε model, (4) the SST k – ω model, and (5) the LRR Reynolds stress transport model. Various near-wall treatments such as equilibrium wall function and two-layer enhanced wall treatment are used in combination with these turbulence models. The computations are performed using the commercial computational fluid dynamics (CFD) code Fluent. From the validation exercises, it is found that when the impingement surface is outside the potential core of the jet, most of the turbulence models predict reasonably accurate thermal data (local Nusselt number variation along the impingement surface). When the impingement surface is within the potential core of the jet, the turbulence models grossly overpredict the Nusselt number in the impingement region, but in the wall jet region the Nusselt number prediction is fairly accurate. Overall, the RNG k – ε model with the enhanced wall treatment and the SST k – ω model predict the Nusselt number distribution better than the other models for the flat plate as well as for the concave surface impingement cases. However, the hydrodynamic data such as the mean velocity profiles are not accurately predicted by the SST k – ω model for the concave surface impingement case, whereas the RNG k – ε model predictions of the velocity profiles agree very well with the experiment. The Reynolds stress model does not show any distinctive advantage over the other eddy viscosity models.     

Simulation of air curtains for vertical display cases with a two-fluid model

In a vertical open display case, air curtains are used to weaken the influence of ambient air on the store. The flow and heat transfer characteristics of air curtains in a vertical display case are simulated with a two-fluid turbulence model in this paper, which takes the fluid in the space to be simulated as a mixture of turbulent fluid and non-turbulent fluid. The air curtains are taken as a turbulent fluid and described by the conventional k–ε turbulence model. The ambient air outside the display case is considered as a non-turbulent fluid and calculated by a laminar model. The exchanges of mass, momentum and energy between the turbulent and the non-turbulent fluids are expressed by empirical relations. The simulation results based on the two-fluid model are compared not only with experimental data, but also with the simulation results when the k–ε model is used for the whole simulated space. The comparisons indicate that the two-fluid model enables to predict thermal stratification phenomenon more accurately and shows better agreement with the measured values than the k–ε model.     

Numerical solution of film condensation from turbulent flow of vapor–gas mixtures in vertical tubes

A complete two-phase model is presented for film condensation from turbulent downward flow of vapor–gas mixtures in a vertical tube. The model solves the complete parabolic governing equations in both phases including a model for turbulence in each phase, with no need for additional correlation equations for interfacial heat and mass transfer. A finite volume method is used to form the discretized mean flow equations for conservation of mass, momentum, and energy. A fully coupled solution approach is used with a mesh that automatically adapts to the changing film thickness. The results of using three turbulence models involving combinations of mixing length and k–ε models in the film and mixture regions are compared. This new model is extensively compared with previous numerical and experimental studies. In the experimental comparisons, it was found that a model consisting of a k–ε turbulence model for both the film and the mixture flows produced the best agreement. Results are also presented for a parametric study of condensation from steam-air mixtures. The effects of changes to the inlet Reynolds number, the inlet gas mass fraction, and the inlet-to-wall temperature difference on the film thickness and heat transfer are presented and discussed. Local profiles of axial velocity, temperature, and gas mass fraction are also presented.     

Transonic turbine blade loading calculations using different turbulence models – effects of reflecting and non-reflecting boundary conditions

The objective of this study is to simulate the transonic gas turbine blade-to-blade compressible fluid flow. We are interested mainly in the determination of the pressure distribution around the blade. The particular blade architecture makes these simulations more complex due to the variety of phenomena induced by this flow.Our study is based on the experiment performed by Giel and colleagues. Tests were conducted in a linear cascade at the NASA Glenn Research Center. The test article was a turbine rotor with design flow turning of 136° and an axial chord of 12.7 cm.Simulations were performed on an irregular quadratic structured grid with the FLUENT software package which solves the Navier–Stokes equations by using finite volume methods. Two-dimensional stationary numerical simulations were made under turbulent conditions allowing us to compare the characteristic flow effects of Reflecting Boundary Conditions (RBC) and Non-Reflecting Boundary Conditions (NRBC) newly implemented in FLUENT 6.0. Many simulations were made to compare different turbulence models: a one equation model (Spalart–Allmaras), several two-equation models (k–ε, RNG k–ε, Realizable k–ε, SST k–ω), and a Reynolds-stress model (RSM). Also examined were the effects of the inlet turbulence intensities (0.25% and 7%), the exit Mach numbers (1.0 and 1.3) and the inlet Reynolds numbers (0.5 × 10⁶ and 1 × 10⁶). The results obtained show a good correlation with the experiment.     

Numerical study on heat transfer of turbulent channel flow over periodic grooves

A numerical investigation of turbulent forced convection in a two-dimensional channel with periodic transverse grooves on the lower channel wall is conducted. The lower wall is subjected to a uniform heat flux condition while the upper wall is insulated. To investigate turbulence model effects, computations based on a finite volume method, are carried out by utilizing four turbulence models: the standard k − ε, the Renormalized Group (RNG) k − ε, the standard k − ω, and the shear stress transport (SST) k − ω turbulence models. Parametric runs are made for Reynolds numbers ranging from 6000 to 18,000 with the groove-width to channel-height ratio (B/H) of 0.5 to 1.75 while the groove pitch ratio of 2 and the depth ratio of 0.5 are fixed throughout. The predicted results from using several turbulence models reveal that the RNG and the k − ε turbulence models generally provide better agreement with available measurements than others. Therefore, the k − ε model is selected to use in prediction of this complex flow. In addition, the results of the heat transfer coefficient, friction factor, skin friction coefficient and thermal enhancement factor are also examined. It is found that the grooved channel provides a considerable increase in heat transfer at about 158% over the smooth channel and a maximum gain of 1.33 on thermal performance factor is obtained for the case of B/H = 0.75. This indicates that the reverse/re-circulation flow in a channel with transverse grooves can improve the heat transfer rate.     

Turbulence forced convection heat transfer over double forward facing step flow

Turbulent forced heat transfer for double forward facing step flow was studied numerically. The bottom wall of the channel is heated at uniform temperature and the flow temperature at the upstream is colder than the wall. Two adiabatic steps are located together with different lengths and heights. The solutions are done using commercial code FLUENT which uses finite volume method. The standard k − ε turbulence model is employed to obtain turbulence flow modeling for double forward step. Effects of step heights, step lengths and Reynolds numbers on heat transfer and fluid flow are investigated as main parameters. Results showed that the second step can be use as a control device for both heat transfer and fluid flow.     

Features of convective heat transfer in heated helium channel flow

The aim of the present work is to choose an optimal method for thermohydraulic calculation of the gas flow in channels with intense heating at the flow Reynolds number below 10,000. These conditions are typical of the cooling channels of the High-Flux-Test Module of the International-Fusion-Materials-Irradiation-Facility (IFMIF/HFTM). A low Reynolds number and a high heating rate can result in partial relaminarization of the initially turbulent flow, and hence in a decrease in the heat transfer. A number of turbulence models offered by the commercial STAR-CD code were tested on the basis of the comparison of the numerical predictions with experimental data. This comparison showed that the low-Reynolds-number k-ε turbulence models predict the heat transfer characteristics close to the experimental data. The k-ε linear low Reynolds number turbulence model of Lien was applied as more appropriate for the thermohydraulic analysis of the IFMIF high flux test module.     

Three-dimensional CFD analysis for simulating the greenhouse effect in solar chimney power plants using a two-band radiation model

The greenhouse effect in the solar collector has a fundamental role to produce the upward buoyancy force in solar chimney power plant systems. This study underlines the importance of the greenhouse effect on the buoyancy-driven flow and heat transfer characteristics through the system. For this purpose, a three-dimensional unsteady model with the RNG k–ε turbulence closure was developed, using computational fluid dynamics techniques. In this model, to solve the radiative transfer equation the discrete ordinates (DO) radiation model was implemented, using a two-band radiation model. To simulate radiation effects from the sun's rays, the solar ray tracing algorithm was coupled to the calculation via a source term in the energy equation. Simulations were carried out for a system with the geometry parameters of the Manzanares power plant. The effects of the solar insolation and pressure drop across the turbine on the flow and heat transfer of the system were considered. Based on the numerical results, temperature profile of the ground surface, thermal collector efficiency and power output were calculated and the results were validated by comparing with experimental data of this prototype power plant. Furthermore, enthalpy rise through the collector and energy loss from the chimney outlet between 1-band and two-band radiation model were compared. The analysis showed that simulating the greenhouse effect has an important role to accurately predict the characteristics of the flow and heat transfer in solar chimney power plant systems.     

Numerical analysis of heat transfer in pulsating turbulent flow in a pipe

Convection heat transfer in pulsating turbulent flow with large velocity oscillating amplitudes in a pipe at constant wall temperature is numerically studied. A low-Reynolds-number (LRN) k–ε turbulent model is used in the turbulence modeling. The model analysis indicates that Womersley number is a very important parameter in the study of pulsating flow and heat transfer. Flow and heat transfer in a wide range of process parameters are investigated to reveal the velocity and temperature characteristics of the flow. The numerical calculation results show that in a pulsating turbulent flow there is an optimum Womersley number at which heat transfer is maximally enhanced. Both larger amplitude of velocity oscillation and flow reversal in the pulsating turbulent flow also greatly promote the heat transfer enhancement.     

Numerical simulation of 3D turbulent isothermal flow in a vortex combustor

Numerical simulations of strongly swirling turbulent flows in a vortex combustor (VC) are conducted. A comprehensive investigation of a three-dimensional isothermal VC flow using three first-order turbulence models: the standard k–ε turbulence model, Renormalized Group (RNG) k–ε model and shear stress transport (SST) k–ω model; and a second-order turbulence model, Reynolds stress model (RSM) together with a second-order numerical differencing scheme is conducted in the present work. The computation indicates that the RSM is superior to the other turbulence models in capturing the swirl flow effect in comparison with measurements. The numerical results for the VC flow provide the characteristics of the flow in terms of relevant parameters for the VC design and operation, composed of axial and tangential velocities, pressure fields, and turbulence kinetic energy.     

Numerical study of stratified oil-water two-phase turbulent flow in a horizontal tube

Stratified oil-water two-phase turbulent flow in a horizontal tube is numerically simulated using a volume of fluid model. A single momentum equation is solved throughout the domain. The RNG k-ε model combined with a near-wall low-Re turbulence model is applied to each phase, and a continuum surface force approximation is adopted for the calculation of surface tension. The simulation is performed in a time-dependent way and the final solution which corresponds to steady-state flow is analyzed. Results of pressure loss, slip ratio, local phase fraction profile and the axial velocity profile are verified by experimental data in literature. Based on the numerical results of extensive calculations, the flow field characteristics are explored and correlations for pressure loss and hold-up are presented.     

Heat transfer predictions with a cubic k-ε model for axisymmetric turbulent jets impinging onto a flat plate

Local heat transfer in turbulent axisymmetric jets, impinging onto a flat plate, is predicted with a cubic k-ε model. Both the constitutive law for the Reynolds stresses and the transport equation for the dissipation rate ε contribute to improved heat transfer predictions. The stagnation point value and the shape of the profiles of the Nusselt number are well predicted for different distances between the nozzle and the flat plate. Accurate flow field predictions, obtained with the presented turbulence model, are the basis for the quality of the heat transfer results. The influence of the nozzle-plate distance on the stagnation point Nusselt number, is also correctly captured. For a fixed nozzle-plate distance, the influence of the Reynolds number on the stagnation point heat transfer is correctly reproduced. Comparisons are made to experimental data and to results from a low-Reynolds standard k-ε model [1] and the v²-f model [2].     

Numerical study of liquid film cooling in a rocket combustion chamber

A numerical study is reported to investigate the liquid film cooling in a rocket combustion chamber. Mass, momentum and heat transfer characteristics through the interface are considered in detail. A marching procedure is employed for solution of the respective governing equations for the liquid film and gas stream together. The standard turbulence k–ε model is used to simulate the turbulence gas flow and a modified van Driest model is adopted to simulate the turbulent liquid film flow. Radiation of gas stream is also considered and simulated with the flux model. Downstream of the liquid film the gaseous film cooling is numerically studied simultaneously. Results are presented for a mixed gases–water system under different condition. Various effects on the liquid film length are examined in detail. There is a good agreement between the numerical prediction and experimental result on the liquid film length.