Modeling Of Turbulent Heat Transfer Research Articles

Modeling of convective turbulent heat transfer of water-based [formula omitted] nanofluids in an uniformly heated pipe

Turbulent convective heat transfers of Al2O3-water nanofluid flowing in a circular tube subjected to an uniform wall heat flux are numerically investigated using different turbulence models. Four nanoparticle volume concentrations φ up to 2% are considered for bulk Reynolds numbers within the range 3000⩽Re⩽20,000. The effects of the nanoparticle concentration and the Reynolds number on the Nusselt number and friction factor are reported. Two different numerical approaches including the single-phase and the mixture two-phase models with variable thermophysical properties are favorably compared to experimental results obtained from the literature for low nanoparticle concentrations (φ⩽0.5%). The results at a higher volume fraction φ=2% show the necessity to use a mixture model. Eight turbulence models in their low-Reynolds number formulation are also compared to assess their ability to predict the effect of turbulence on the convective heat transfer. The SST k-ω model was found to perform the best with errors in terms of the average Nusselt number and friction coefficient of 0.44% and 1.82% respectively. On the contrary, the linear pressure-strain Reynolds Stress Model completely failed to provide the good values with discrepancies of 41.91% and 133.54%, respectively. Finally, the benefit of using this nanofluid is discussed regarding four merit criteria.

Numerical analysis of microholes film/effusion cooling effectiveness

Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three-dimensional discrete hole film cooling RSM-AKN turbulent heat transfer models based on variable turbulent Prandtl number approaches were considered. Obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology. All implemented models for turbulent heat transfer performed sufficiently well for the considered case. It was confirmed, however, that the two-equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models. The RSM-AKN turbulent model was used in micoholes case too. The main target of simulations was maintain the same level of cooling efficiency ratio in both cases and confirm that is possible significantly reduce mass flows of the coolant in microholes case.

CFD modeling of turbulent forced convective heat transfer and friction factor in a tube for Fe3O4 magnetic nanofluid in the presence of a magnetic field

Computational fluid dynamics (CFD) tool is used to study numerically a nanofluid mixture of water and Fe3O4 with MHD effect. The simulation is performed in order to determine the turbulence forced convection heat transfer in a circular tube. This is implemented by using the single and two phase mixture approaches with assumption that the particles are spherical and diameter equal to 36nm. The simulation output data compared with an experimental literature data from other study and found matching. The result shows that Nu and friction factor at fixed Reynolds number is proportional to the magnetic field.

Two-phase mixture model for nanofluid turbulent flow and heat transfer: Effect of heterogeneous distribution of nanoparticles

In this work, a two-phase mixture model for evaluation of flow and heat transfer performance of SiO2/water nanofluids under turbulent flow was proposed by considering the heterogeneity of concentration due to crossed effect and the influences of shear rate, viscosity gradient, thermophoresis and Brownian motion on the diffusion of the nanoparticles. The effects of Peclet number, Reynolds number, nanoparticle size and nanofluid mean concentration on the distribution of nanoparticles have been evaluated. The values of thermal conductivity and viscosity as the main thermophysical properties of nanofluids changed across different layers of the liquid due to the heterogeneous distribution of concentration. It was observed that an increase in the Peclet number caused heterogeneity in the distribution of the properties. The achieved nanoparticle distribution has been implemented for analysis of nanofluid using two-phase mixture model. It was found that the effect of nanofluid concentration on the Nusselt number was more noticeable in lower Reynolds numbers due to the insignificant effect of flow momentum on heat transfer. The maximum of 43.9% enhancement in convection heat transfer was achieved by dispersion of 4% SiO2 nanoparticles inside DI-water at Re=25,000.

Numerical modeling of turbulent flow structure and heat transfer in a droplet-laden swirling flow in a pipe with a sudden expansion

ABSTRACTThis contribution presents the mathematical model to simulate the swirling turbulent gas-droplet flow in a sudden pipe expansion. The set of axisymmetrical steady-state Reynolds averaged Navier–Stokes equations (RANS) for the two-phase flow is utilized. The dispersed phase is modeled by the Eulerian approach. The flow swirl causes an increase in the intensity of heat transfer (more than 1.5 times compared with the nonswirling mist flow at other identical inlet conditions). Evaporation of the droplets leads to a significant increase in the heat transfer intensity in the swirling two-phase flow (more than 2.5 times compared with the single-phase flow).

Conductive sublayer of turbulent heat transfer for heating of water in a circular tube

The steady-state and transient turbulent heat transfer coefficients in circular platinum (Pt) test tubes (inner diameters: 3 and 6 mm; heated lengths: 66.5 and 100 mm and 69.6 mm, respectively) were systematically measured using an experimental water loop for a wide range of flow velocities, inlet liquid temperatures, Prandtl numbers, inlet pressures, and exponentially increasing heat inputs (Q 0 exp(t/τ), τ: exponential period). The Reynolds-averaged Navier–Stokes equations and the k–e turbulence model for unsteady turbulent heat transfer in circular test sections were numerically solved for heating of water with heated sections of diameter 3 and 6 mm and length 67 and 100 mm and 70 mm, respectively, by using computational fluid dynamics code under the same conditions as those in the experiment and with temperature-dependent thermophysical fluid properties. The thickness of the conductive sublayer, δ CSL,st and δ CSL [=(Δr) out /2], and the nondimensional thickness of the conductive sublayer, (y , + ) TEM [=(f F /2)0.5 ρ l u δ CSL,st /μ l ] and (y + ) TEM [=(f F /2)0.5 ρ l u δ CSL /μ l ], for steady-state and transient turbulent heat transfer at various heated length-to-inner diameter ratios, inlet liquid temperatures, and exponential periods were measured on the basis of the numerical solutions. The correlations of the thickness of the conductive sublayer, δ CSL,st , and nondimensional thickness of the conductive sublayer, (y , + ) TEM , for steady-state turbulent heat transfer and those of the thickness of the conductive sublayer, δ CSL , and nondimensional thickness of the conductive sublayer, (y + ) TEM , for transient turbulent heat transfer in a circular tube were derived.

Numerical modeling of turbulent heat transfer of a nanofluid at supercritical pressure

A numerical study has been conducted to examine the turbulent heat transfer of a nanofluid, methane-CuO, in a circular cooling tube at a supercritical pressure of 8MPa, a phenomenon relevant to the rocket engine cooling application. Results reveal that at a surface heat flux of 3MW/m2 and an inlet flow velocity of 25m/s, the addition of nanoparticles decreases the heat transfer rate, dictated by significant increase of the nanofluid viscosity, which leads to the decreased turbulent viscosity in the near-wall buffer zone. As the surface heat flux is increased to 7MW/m2 or the inlet velocity is decreased to 10m/s, however, two physical phenomena of heat transfer improvement are observed in the nanofluid. The first phenomenon, which starts almost immediately from the beginning of the heated section, is controlled by strong increase of the nanofluid density, which results in the increased turbulent viscosity in the near-wall buffer zone. The second phenomenon is dictated by thermophysical property variations in the near-wall turbulent flow region as fluid temperature transits from the subcritical to supercritical state (the transcritical process). Results indicate potential applications of nanofluids in enhancing heat transfer at supercritical pressures.

Closure of a macroscopic turbulence and non-equilibrium turbulent heat and mass transfer model for a porous media comprised of randomly packed spheres

Turbulent heat and mass transfer in packed beds of spheres is widely encountered in industrial and food storage applications and, as such, modeling of such cases is of interest in design and development. Herein, we propose a closure of the volume- and time-averaged (macroscopic) turbulence, and non-equilibrium turbulent heat and mass transfer equations for randomly packed spheres, based on computational results of flow and heat transfer for a unique geometric model. In this respect, the closure results are derived from pore-level (microscopic) information obtained from numerical simulations of turbulent heat and fluid flow. Turbulence is incorporated at both levels using the k–ɛ model, and the dispersive effects of turbulence are also considered. For the momentum equation, the closure is sought for the Darcy and Forchheimer terms. For the non-equilibrium heat and mass transport equations, we obtain closures for the dispersion, turbulent flux, turbulent dispersion, and interfacial heat and mass transfer terms. The closure results are found to be dependent upon the porosity and Reynolds number. However, the mean sphere diameter and its local variation inside the representative elemental volumes only weakly affect the results. The closure results are presented as power law-based correlations, such that they can be easily implemented in a volume-time-averaged framework.

Numerical prediction of film cooling effectiveness over flat plate using variable turbulent prandtl number closures

Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensional discrete-hole film cooling arrangement. The effects of basic geometrical characteristics of the holes, i.e. diameter D, length L and pitch S/D were studied. Different turbulent heat transfer models based on constant and variable turbulent Prandtl number approaches were considered. The variability of the turbulent Prandtl number Prt in the energy equation was assumed using an algebraic relation proposed by Kays and Crawford, or employing the Abe, Kondoh and Nagano eddy heat diffusivity closure with two differential transport equations for the temperature variance kθ and its destruction rate eθ. The obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology. All implemented models for turbulent heat transfer performed sufficiently well for the considered case. It was confirmed, however, that the two- equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models.

Turbulence Model Evaluation for Numerical Modelling of Turbulent Flow and Heat Transfer of Nanofluids

In this work, Nusselt number and friction factor are calculated numerically for turbulent pipe flow (Reynolds number between 6000 and 12000) with constant heat flux boundary condition using nanofluids. The nanofluid is modelled with the single-phase approach and the simulation results are compared with experimental data. Ethylene glycol and water, 60:40 EG/W mass ratio, as base fluid and SiO2 nanoparticles are used as nanofluid with particle volume concentrations ranging from 0% to 10%. A prior turbulence model evaluation of k-ε-, k-ω- and k-ω-SST-model revealed substantial deviations between the tested models and resulted in applying the k-ω-SST-model for the simulation. Nusselt number predictions for the nanofluid are in agreement with experimental results and a conventional single-phase correlation. The mean deviation is in the range of 5%. Friction factor values show a mean deviation of 1.5% to a conventional single-phase correlation, however, they differ considerably from the nanofluid experimental data.

Modeling of MHD turbulent heat transfer in channel flows imposed wall-normal magnetic fields under the various Prandtl number fluids

Zero-equation heat transfer models based on the constant turbulent Prandtl number are evaluated using direct numerical simulation (DNS) data for fully developed channel flows imposed on a uniform wall-normal magnetic field. Quasi-theoretical turbulent Prandtl numbers are estimated by DNS data of various molecular Prandtl number fluids. From the viewpoint of highly-accurate magneto-hydrodynamic (MHD) heat transfer prediction, the parameters of the turbulent eddy viscosity of the k–ɛ model are optimized under the magnetic fields. Consequently, we use the zero-equation model based on a constant turbulent Prandtl number to demonstrate MHD heat transfer, and show the applicability of using this model to predict the heat transfer.

RANS modeling of flow structure and turbulent heat transfer in pulsed gas-droplet mist jet impingement

The turbulent flow structure and heat transfer of a pulsed gas-droplet impinging mist jet with low mass fraction of droplets (not more than 2%) are numerically carried out. A set of non-steady-state RANS equations for the two-phase flow is utilized. The dispersed phase is modeled by the Eulerian approach. Gas turbulence is computed with the Reynolds stress model for two-phase flow. The interaction between phases (two-way coupling) is considered by the addition of extra terms in equations for the mean and fluctuating motion. The effects of pulse frequencies, ratio of on time to total cycle time, distances between pipe outlet and impinging flat plate and Reynolds number on heat transfer are numerically studied. It is shown that both the increase (up to 45%) and the suppression (up to 25%) of heat transfer are characteristic of pulsed gas-droplet jet impingement, differently from the steady-state one. Reduced heat transfer in comparison with the steady-state impinging jet is typically in the low frequency range. The impingement heat transfer initially increases with distance from the pipe edge and target surface and the heat transfer decreases at distance from the pipe edge and flat plate.

Modeling and Simulation of Supercritical-Pressure Turbulent Heat Transfer of Aviation Kerosene with Detailed Pyrolytic Chemical Reactions

Regenerative cooling of the high-temperature components in propulsion and power-generation systems plays a paramount role in maintaining the reliability and durability of the systems. In this paper, a mathematical model is developed for studying fluid dynamics and heat-transfer characteristics of the aviation kerosene RP-3 at supercritical pressures. The model accommodates a detailed pyrolytic chemical reaction mechanism, which consists of 18 species and 24 elementary reactions (Jiang, R.; Liu, G.; Zhang, X. Thermal cracking of hydrocarbon aviation fuels in regenerative cooling microchannels. Energy Fuels 2013, 27, 2563−2577). Accurate calculations of thermophysical properties at supercritical pressures are properly incorporated. After rigorous model validations, numerical studies of turbulent heat transfer of RP-3 in a micro cooling tube at a supercritical pressure of 5 MPa are conducted under operating conditions of both constant wall heat flux and constant surface temperature to obtain a fundamental understanding of the complex physicochemical processes. Results indicate that the endothermic fuel pyrolysis, which prevails once the bulk fluid temperature rises above 750 K, dictates the fluid flow and heat-transfer process in the high fluid temperature region. Significant variations of the fluid thermophysical properties also make strong impacts; two scenarios of heat-transfer enhancement resulting from property variations under the tested conditions are analyzed. This work has fundamental and practical implications for effective thermal management in propulsion and power-generation systems.

CFD based approach for modeling direct contact condensation heat transfer in two-phase turbulent stratified flows

This paper describes a CFD based strategy for the modeling of stratified two-phase flows with heat and mass transfer across a moving steam-water interface due to direct contact condensation. Such flows have been of major importance for example in connection with the analysis of nuclear reactor safety systems, in particular during two-phase Pressurized Thermal Shock (PTS) scenarios. The approach is based on the two-fluid phase-average model. The interfacial friction was modeled by using an Algebraic Interfacial Area Density (AIAD) framework where the drag coefficient is a function of the local flow characteristics. To show the impact of the modeling of interfacial friction the simulation with the AIAD model was compared with a simulation where a constant drag coefficient of 0.44 was used in the whole domain. For the modeling of interfacial heat and mass transfer two correlations for the water heat transfer coefficient based on the penetration theory were utilized. The CFD simulations were validated against a steady-state TOPFLOW-PTS steam/water experiment. In the experiment, very detailed temperature measurements were conducted using special thermocouple lances and infrared thermography. Total condensation rate was determined indirectly by using three different methods. The simulations have shown that the results obtained with the AIAD model are considerably closer to the experimental observations than the results obtained with the constant drag coefficient. The condensation models used in the current study predict quite different total condensation rates. That caused significant differences in the temperature field. The simulations of the TOPFLOW-PTS steam/water experiment with condensation have shown that the proposed CFD modeling approach can be successfully applied for the prediction of temperature field and condensation rate during two-phase Pressurized Thermal Shock scenarios. However, the modeling of turbulent interfacial heat transfer should be improved.

Direct numerical simulation of low-Prandtl number turbulent convection above a wavy wall

Turbulent forced convection is investigated by Direct Numerical Simulation in a channel with one sinusoidal wavy wall and one flat wall. Fluid flow and heat transfer are periodically fully developed, the simulated Reynolds number of the bulk velocity and the hydraulic diameter is Re=18, 880 while three Prandtl numbers are considered, i.e. Pr=0.025, Pr=0.2, and Pr=0.71. The fluid flow is characterized by separation, reattachment and a shear layer downstream the wave peak, these are conditions relevant for turbulent heat transfer and passive scalar transport applications.In the range of Péclet numbers investigated, the most important heat transfer mechanism is by mean flow advection. Accordingly, the peak heat transfer region is in the upslope part of the domain. The separation bubble instead acts as a barrier to convection and the heat transfer rate is minimum close to separation. An a priori analysis is performed in order to assess the accuracy of turbulent heat transfer models based on the Generalized Gradient Diffusion Hypothesis.

Mathematical Modelling of Methane-Air Combustion in a Channel with a Porous Axial Insert

In the paper we construct a mathematical model of turbulent flow, combustion and heat transfer in an axisymmetric chamber with an axial zone of a compacted particulate material. The averaged equations written using the model of interacting and interpenetrating continua contain diffusion equations of individual components, the energy equation for the gas and the porous structure, the motion equation for a mixture of gaseous components, as well as the equation of the turbulence model. This system is closed by the equations of continuity and condition of the mixture. In the flow, an irreversible chemical reaction of stoichiometric mixture of methane and oxygen proceeds. Numerical study of porosity influencing the nature of turbulent combustion is conducted.

Direct numerical simulation of MHD heat transfer in high Reynolds number turbulent channel flows for Prandtl number of 25

The high-Prandtl number passive scalar transport of the turbulent channel flow imposed a wall-normal magnetic field is investigated through the large-scale direct numerical simulation (DNS). All essential turbulence scales of velocities and temperature are resolved by using 2048×870×1024 computational grid points in stream, vertical, and spanwise directions. The heat transfer phenomena for a Prandtl number of 25 were observed under the following flow conditions: the bulk Reynolds number of 14,000 and Hartman number of up to 28. These values were equivalent to the typical nondimensional parameters of the fusion blanket design proposed by Wong et al.As a result, a high-accuracy DNS database for the verification of magnetohydrodynamic turbulent heat transfer models was established for the first time, and it was confirmed that the heat transfer correlation for a Prandtl number of 5.25 proposed by Yamamoto and Kunugi was applicable to the Prandtl number of 25 used in this study.

Coherent structures in trailing-edge cooling and the challenge for turbulent heat transfer modelling

The present paper tests the capability of a standard Reynolds-Averaged Navier–Stokes (RANS) turbulence model for predicting the turbulent heat transfer in a generic trailing-edge situation with a cutback on the pressure side of the blade. The model investigated uses a gradient-diffusion assumption with a scalar turbulent-diffusivity and constant turbulent Prandtl number. High-fidelity Large-Eddy Simulations (LES) were performed for three blowing ratios to provide reliable target data and the mean velocity and eddy viscosity as input for the heat transfer model testing. Reasonably good agreement between the LES and recent experiments was achieved for mean flow and turbulence statistics. The LES yielded coherent structures which were analysed, in particular with respect to their effect on the turbulent heat transfer. For increasing blowing ratio, the LES replicated an also experimentally observed counter-intuitive decrease of the cooling effectiveness caused by the coherent structures becoming stronger. In contrast, the RANS turbulent heat transfer model failed in predicting this behaviour and yielded significantly too high cooling effectiveness. It is shown that the model cannot predict the strong upstream and wall-directed turbulent heat fluxes caused by large coherent structures, which were found to be responsible for the counter-intuitive decrease of the cooling effectiveness.

Direct numerical simulation of turbulent heat transfer in a fluid-porous domain

Turbulent heat transfer in a channel partially filled by a porous medium is investigated using a direct numerical simulation of an incompressible flow. The porous medium consists of a three-dimensional Cartesian grid of cubes, which has a relatively high permeability. The energy equation is not solved in the cubes. Three different heating configurations are studied. The simulation is performed for a bulk Reynolds number Reb = 5500 and a Prandtl number Pr = 0.1. The turbulent flow quantities are compared with the results of Breugem and Boersma [“Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach,” Phys. Fluids 17, 025103 (2005)] to validate the numerical approach and macroscopic turbulent quantities are analyzed. Regarding the temperature fields, original results are obtained. The temperature fields show an enhanced turbulent heat transfer just above the porous region compared to the solid top wall, which can be related to the large vortical structures that develop in this region. Furthermore, these large structures induce pressure waves inside the porous domain which are responsible of large temperature fluctuations deep inside the porous region where the flow is laminar. Finally, macroscopic turbulent quantities are computed to get reference results for the development of macroscopic turbulent heat transfer models in fluid-porous domain.

A Comparative Analysis of Single and Two-Phase Models of Turbulent Convective Heat Transfer in a Tube for TiO2 Nanofluid with CFD

In this article, turbulent forced convection flow of dilute water/TiO2 nanofluid with a particle diameter equal to 30 nm in a horizontal circular tube exposed to convection with saturated steam at the wall, is numerically analyzed. Two different approaches are taken into consideration: single and two-phase mixture models. It is comprehended that the convective heat transfer coefficient increases with the particle volume concentration and Reynolds number. On the other hand, the mixture model was in better agreement with experimental data than the single phase approach.