Modeling Of Turbulent Heat Transfer Research Articles

Modelling turbulent heat flux accounting for Turbulence-Radiation Interactions

The present work investigates the modeling of turbulent heat transfer in flows where radiative and convective heat transfer are coupled. In high temperature radiatively participating flows, radiation is the most relevant heat transfer mechanism and, due to its non-locality, it causes counter intuitive interactions with the turbulent temperature field. These so-called Turbulence-Radiation Interactions (TRI) largely affect the temperature field, modifying substantially the turbulent heat transfer. Therefore, in the context of modeling (RANS/LES), these interactions require a closure model. This work provides the inclusion of TRI in the modeling of the turbulent heat transfer by adopting a unique approach which consists in approximating the fluctuations of the radiative field with temperature fluctuations only. Based on this approximation, coefficients of proportionality are employed in order to close the unknown terms in the relevant model equations. A closed form of all radiation-temperature-velocity correlation is explicitly derived depending on the chosen turbulent heat transfer model. This model is applied to a standard two-equation turbulent heat transfer closure and used to reproduce results obtained with high-fidelity DNS simulations. While a standard approach (i.e., neglecting TRI) is not able to correctly predict the DNS data, the new model’s results shows exceptional agreement with the high-fidelity data. This clearly proves the validity (and the necessity) of the proposed model in non-reactive, radiative turbulent flows.

RANS Model development on temperature variance in conjugate heat transfer

In this study, a RANS model of turbulent conjugate heat transfer has been developed, which is applicable across a range of different combination of fluid and solid thermal properties. This is achieved by focusing on the transport equations for the temperature variance and its dissipation rate across the solid walls which bound the flow region. In this investigation we make use of a wider range of DNS data reported by other researchers, to advance our understanding of the processes involved and to revise and extend the capabilities of the model of Craft et al [12] including a more physical fluid-solid interface condition on the dissipation of thermal fluctuations and a dependence of model coefficients on Prandtl number. The resulting model is shown to successfully reproduce the penetration of thermal fluctuations into solid regions, and their subsequent decay across the solid, for a wide range of fluid to solid thermal property ratios, and Prandtl numbers, thereby bringing a step change to RANS capabilities in turbulent conjugate heat transfer analysis.

Numerical simulation of heat transfer in a large room with a working gas infrared emitter

The article presents a new approach to determining the main characteristics of the thermal regime in the buildings and structures heated by the gas infrared emitters, based on the analysis of convective heat transfer in the air and thermal conductivity in the enclosing structures. The authors have considered a mathematical model of turbulent heat transfer in the framework of the standard k-e model under radiant heating conditions. The simulation was carried out for a large room with an approximation to the real operating conditions of an industrial facility. The options for heating an empty room and the room with an object were considered.

Mathematical model of turbulent heat transfer based on the dynamics of two fluids

A new approach to modeling turbulent heat transfer based on the thermodynamics of two fluids is presented in the paper. This study is a development of a two-fluid turbulence model. It was shown that the temperature fluctuation in a turbulent flow is due to the temperature difference of these fluids. A mathematical model of turbulent heat transfer was built on the basis of the two-fluid approach. The obtained mathematical model of turbulence was used to study turbulent heat propagation when flowing past a plane plate, in round and plane jets, and between two rotating cylinders. To verify the model, numerical results were compared with known experimental data. The results obtained showed that the two-fluid model of turbulent transfer describes the thermodynamic properties of the turbulent flow with great accuracy.

A Logarithmic Turbulent Heat Transfer Model in Applications with Liquid Metals for Pr = 0.01–0.025

The study of turbulent heat transfer in liquid metal flows has gained interest because of applications in several industrial fields. The common assumption of similarity between the dynamical and thermal turbulence, namely, the Reynolds analogy, has been proven to be invalid for these fluids. Many methods have been proposed in order to overcome the difficulties encountered in a proper definition of the turbulent heat flux, such as global or local correlations for the turbulent Prandtl number and four parameter turbulence models. In this work we assess a four parameter logarithmic turbulence model for liquid metals based on the Reynolds Averaged Navier-Stokes (RAN) approach. Several simulation results considering fluids with P r = 0.01 and P r = 0.025 are reported in order to show the validity of this approach. The Kays turbulence model is also assessed and compared with integral heat transfer correlations for a wide range of Peclet numbers.

Semiempirical Model of Convective Heat Transfer of Turbulent Gases

On the basis of the Prandtl semiempirical wall-turbulence hypothesis, the author has substantiated theoretically the possibility of setting boundary conditions to the equations of a mathematical model of turbulent motion and convective heat transfer of a gaseous medium on a coarse grid. It has been shown that the results of numerical simulation are in agreement with experimental data on the heat transfer of air and high-temperature gases in tubes.

Numerical and experimental analysis of a planar jet with heated co-flow at medium and low Prandtl-number values

In the present work, we combine experiments and numerical simulations of a planar jet with heated co-flow with medium (air) and low-Prandtl (He-Xe gas mixture) fluids. Jets are recognized as representative test cases to be investigated in large components of pool-type liquid metal-cooled nuclear systems, like the Multi-purpose hYbrid Research Reactor for High-tech Applications (MYRRHA), currently under design at SCK•CEN. The present planar jet configuration mimics a closed wind tunnel that is designed and operated at VKI to generate an experimental database for velocity and temperature fields of a turbulent forced-convection flow regime. The performed experiments combine the Particle Imaging Velocimetry (PIV) (in characteristic planes) and thermocouple (single point) measurements. In parallel with experiments, comprehensive numerical simulations have been performed within the RANS modeling framework. Next to the standard eddy-viscosity based two-equation k-ε model, an extended variant based on the low-Reynolds elliptic relaxation concept (so-called ζ-f model) has been applied too. To investigate the low-Prandtl effects on the heat transfer, series of the turbulent heat transfer models have been applied, ranging from a conventional constant turbulent Prandtl number to a more elaborate kθ-εθ model. The combination of the low-Reynolds ζ-f and kθ-εθ models was explored for the first time in the content of nuclear engineering applications. The focus of the numerical studies is to address in details the effects of low-Prandtl fluid in the strongly forced convection flow (central planar cold jet) in presence of a strong shear (hot co-flow). We demonstrate the importance of the proper specification of the inlet boundary conditions in numerical simulations to mimic correctly experimentally observed asymmetrical distributions of the cross-wise profiles of stream-wise velocity, turbulent kinetic energy and temperature. Finally, the minor differences in results between the assumed constant turbulent Prandtl number and more advanced kθ-εθ model of the turbulent heat flux confirmed the overly dominant mechanisms of the strong convection and molecular diffusion in the present configuration.

Mathematical modelling of conjugate laminar and turbulent heat transfer in a cavity: Effect of a vertical glazed wall

A numerical analysis of the laminar and turbulent natural convection combined with surface thermal radiation in a square cavity with a glazed wall is presented. The enclosure is composed of one left vertical isothermal wall, two horizontal adiabatic walls, and one right vertical partially semitransparent wall (clear glass sheet). Different values of the aspect ratio of the right vertical glazed wall (A=0.15,0.25,0.5,0.75,1.0) are analyzed, and the incoming solar irradiation (G) over the glass is varied from 0 to 750 W/m2 at intervals of 150 W/m2. Three different case studies were considered based on the position of the clear glass sheet on the right wall: (a) located at bottom side/Case 1 (C1), (b) located at the middle side/Case 2 (C2), and (c) located at the upper side/Case 3 (C3). The numerical solution was carried out using an in-house code based on the finite volume method. The numerical code was validated against experimental data for the turbulent natural convection problem. A comparison between the predicted and measured dimensionless vertical velocity, temperature profiles and local and average Nusselt numbers are presented, obtaining good agreement. Results show that convective heat transfer increases from about 70 to 250 as the aspect ratio increases from 0.15 to 1.0, for all solar radiation intensities, and all cases of turbulent flow. Also, radiative heat transfer decreases as the aspect ratio and solar radiation increase, which implies that it could become lower than convective heat transfer for some aspect ratio values set. When a laminar flow regime is considered, lower average convective and radiative heat transfer rates are obtained regarding the case of turbulent flow. In general, they are between 2.0<Nuconv<7.5 and 2.0<Nurad<13.5 for all cases under analysis. Finally, a set of correlations for the total Nusselt number were obtained for turbulent conjugate heat transfer.

Development of a data-driven model for turbulent heat transfer in turbomachinery

Machine Learning (ML) algorithms have become popular in many fields, including applications related to turbomachinery and heat transfer. The key properties of ML are the capability to partially tackle the problem of slowing down of Moore’s law and to dig-out correlations within large datasets like those available on turbomachinery. Data come from experiments and simulations with different degree of accuracy, according to the test-rig or the CFD approach. When dealing with modelling of turbulent flows in turbomachinery there is a constant trade-off between accuracy and computational costs, but starting from the large amount of data on turbomachinery performance, with ML it is possible to train a learner to correct and improve CFD. The aim of this work is to investigate an innovative data-driven approach that could lead to a significant improvement in the analysis of heat transfer in turbulent flows. The effects of Reynolds number and wall temperature on heat transfer for a double forward-facing step with two squared obstacles were investigated by numerical simulations carried out in OpenFOAM. Then a machine-learnt model was derived using a regression algorithm. The results of regressor showed that a data-driven approach can effectively predict results of the RANS model.

Fully developed turbulent convection of Lead Bismuth Eutectic in the elementary cell of the NACIE-UP Fuel Pin Bundle

One of the requirements for achieving high levels of safety in fourth generation nuclear power plants, is that core thermal-hydraulics can be simulated numerically at a good level of accuracy. To this aim, detailed validation of turbulent heat transfer models needs to be carried out and discussed, in relevant flow and heat transfer configurations, and for low Prandtl-number fluids.The focus of this research is the turbulent, fully developed convection in a heated rod bundle with a triangular arrangement, and a pitch-to-diameter ratio P/D=1.4. Statistics derived from a set of Direct Numerical Simulations (DNS) at the moderate Reynolds number of Re=8290 are compared to Reynolds Averaged Navier-Stokes (RANS) solutions where the closure is provided by the two-equation model SST k-ω and by the Reynolds-Stress Model. Comparisons are drawn for forced flow and in mixed convection conditions (Ri≈0.25). Global quantities extracted from experiments performed in very similar conditions are also compared against the numerical results. Profiles of the turbulent Prandtl number about the unit flow cell are also displayed and discussed.This work clarifies through detailed comparison that if, on the one hand, only the Reynolds-Stress model is able to reasonably capture important flow features like secondary flow components, on the other hand also the SST k-ω two-equation model considered is acceptably accurate in predicting the integral quantities of interest.

Direct Numerical Simulation of the Flow in a Bare Rod Bundle at Different Prandtl Numbers

Abstract A direct numerical simulation (DNS) of bare rod bundles with a low pitch-to-diameter ratio is performed with heat transfer at different Prandtl numbers. Turbulence statistics for temperature and velocity as well as the turbulent budgets have been collected. High-fidelity simulations are performed with the spectral element method (SEM) using Nek5000, a highly scalable code. To pertain to industrial-related flows, a rod bundle model is based on Hooper and Wood's (Hooper, J. D., and Wood, D., 1984, “Fully Developed Rod Bundle Flow Over a Large Range of Reynolds Number,” Nucl. Eng. Des., 83(1), pp. 31–46) experimental setup. Both wall normalized velocity profile and turbulent kinetic energy are validated with a Reynolds number of 22,600. Kolmogorov length scales and time scales are calculated to be within the simulation's spatial–temporal resolution. Moreover, gap vortices and coherent structures are quantified by using Lambda2 vortex criterion, frequency analysis, and two-point correlation. Heat transfer statistics are discussed with a constant heat flux for six different Prandtl numbers ranging from 2 to 0.002. This range shows significantly different characteristics in temperature for both mean and variance. Mean temperature profiles in the subchannel center are very sensitive to the Prandtl number when it becomes small. It is also found that the location of the local maxima for the variance of temperature fluctuations becomes very sensitive at larger Prandtl numbers. The temperature frequency analysis reveals a shift to lower frequencies for low Prandtl numbers. The DNS results provided in this work will contribute as benchmark for the improvement and development of existing and new turbulent heat transfer models at different Prandtl number regimes.

Reference numerical database for turbulent flow and heat transfer in liquid metals

Turbulent heat transfer is a complex phenomenon that has challenged turbulence modellers over various decades. In this regard, in the recent past, several attempts have been made for the assessment and further development/calibration of the available turbulent heat flux modelling approaches. One of the main hampering factors with respect to the further assessment of these modelling approaches is the lack of reference data. In the framework of the EU SESAME and MYRTE projects, an extensive effort has been put forward to generate a wide range of reference data, both experimental and numerical, to fill this gap. In that context, this article reports the numerical database that has been generated within these projects for various liquid metal flow configurations in different flow regimes. These high fidelity numerical data include seven different flow configurations: a wall-bounded mixed convection flow at low Prandtl number with varying Richardson number (Ri) values; a wall-bounded mixed and forced convection flow in a bare rod bundle configuration; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jets; a mixed-convection cold-hot-cold triple jet configuration corresponding to Ri=0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wire-wrapped fuel assembly. These high-fidelity numerical databases will serve the further development of turbulent heat transfer models by providing unique, new and detailed data for the thermal-hydraulic behaviour of liquid metals in various flow configurations.

Status and perspectives of turbulent heat transfer modelling in low-Prandtl number fluids

Thermal-hydraulics is recognized as a key safety challenge in the development of liquid metal cooled reactors. At nominal operating conditions, the Prandtl number of liquid metals which are used as primary coolants, such as lead and sodium, is very low: typically of the order of 0.025–0.001. Obtaining an accurate prediction of the turbulent heat transfer at such a low Prandtl number is not an easy task for the standard turbulence models and has challenged the modellers over several decades. In the framework of the EU SESAME project, an effort has been put forward to assess and/or further develop/calibrate different turbulent heat flux closures. In this regard, the present article reports an assessment of four different turbulent heat flux closures for applications involving low-Prandtl fluids. These closures include: (i) the Reynolds analogy based on a constant turbulent Prandtl number (ii) a four-equation explicit algebraic heat flux model (AHFM) (ii) a three-equation implicit AHFM called AHFM-NRG and (iv) a non-linear second-order heat flux model called Turbulence Model for Buoyant Flows (TMBF). The performance of these turbulence models has been assessed in three different test cases against high-fidelity numerical reference data been generated within the SESAME project. The three test cases are: a natural Rayleigh-Bénard convection flow, a mixed convection planar channel flow and a forced convection impinging jet flow. The shortcomings of the classical Reynolds analogy approach for low-Prandtl fluids in all flow regimes are highlighted; hence, more advanced and well-calibrated closures are recommended.

Modeling and computational simulation of fluid flow, heat transfer and inclusions trajectories in a tundish of a steel continuous casting machine

Currently, the continuous casting process is the main route used in the integrated steelmaking process. The tundish is an essential component of the caster machine and plays an important role in the control of inclusion in the production of the clean steels. Thus, viable methodologies and predictive models to evaluate this metallurgical reactor efficiency are important technological allies to improve the clean steel production. The main goal of the present study is to develop a computational tool to analyze the turbulent fluid flow, temperature distribution and inclusions removal during the continuous operation of the tundish of an industrial facility to improve its internal configuration. New configurations using weirs and dams are proposed which improve the steel quality. We used the Ansys CFX® software based on the element-based finite-volume method (EbFVM) to solve the coupled turbulent flow and heat transfer model equations in an Eulerian flame. A random nucleation mechanism for the inclusions generation and a modified Lagrangian model with a random walking model (RWM) to account for the effect of turbulence on the inclusions trajectories were proposed. The flow pattern was successfully validated with experimental data. The results were presented in terms of velocity and temperature fields and residence time distribution (RTD) curves. Then, the model was used to investigate new scenarios and enhanced geometry configurations.

Heat Transfer in a Square Ribbed Channel: Evaluation of Turbulent Heat Transfer Models

This paper presents the results of integral heat transfer measurements taken in a square ribbed cooling channel configuration for evaluating heat transfer and turbulent flow characteristics in convective cooled gas turbine blades and draws a comparison with numerical results. The heated section of the channel is either smooth or equipped with 45 ∘ crossed ribs on two opposite walls. The first part of the paper describes the instrumentation and experimental setup in detail. The second part compares the numerical calculations with the experimentally determined results. The turbulent heat transfer is calculated using two common algebraic models and three implemented explicit algebraic models, each time in combination with an explicit algebraic Reynolds stress model. The numerical calculations show that the use of higher-order models for the turbulent heat flux provides a higher accuracy of the heat transfer prediction for both configurations. The best model is able to predict almost all results within the experimental uncertainties.

Numerical simulation of forced and mixed convection turbulent liquid sodium flow over a vertical backward facing step with a four parameter turbulence model

Liquid metals are promising fluids for engineering applications since they have interesting physical properties such as high thermal conductivity and low kinematic viscosity with respect to the values of common operating fluids, i.e. air and water. This implies low Prandtl number values and therefore the similarity assumption between velocity and temperature fields does not hold. In the present work we solve a four parameter turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward facing step. On the wall behind the step a uniform heat flux is applied in order to study both forced and mixed convection flow regimes. This model for turbulent heat transfer, taking into account different boundary conditions, is analyzed and compared with the Kays correlation and Direct Numerical Simulation data. Profiles of velocity, turbulent kinetic energy, turbulent heat flux, temperature and its squared fluctuations are provided for two simulated Richardson number values, namely 0 and 0.338. Obtained results show a reasonable agreement with reference Direct Numerical Simulation values.

Development of a model for unsteady conjugate heat transfer simulations

Recent developments in CFD simulations go towards higher accuracy by using time-resolved simulations instead of steady RANS simulations and adding solid structures to the simulation instead of assuming constant wall temperatures or heat fluxes at wall boundaries. This means a very large number of time steps are necessary to both accurately resolve the turbulent fluctuations in the fluid parts and have a converged temperature field in the solid parts of the computational domain. Another problem in near-wall heat transfer is the often used assumption of a constant turbulent Prandtl number, which is not correct for many flow configurations. The present work therefore focuses on the development of a methodology for accelerated unsteady conjugated heat transfer simulations. Furthermore, the implementation of a near-wall heat transfer model that does not rely on a constant turbulent Prandtl number was evaluated. The models are implemented in the CFD solver ANSYS CFX. The validation of the turbulent heat transfer model shows improved agreement with the experimental results compared to a constant turbulent Prandtl number approach. The improved unsteady conjugate heat transfer methodology gives the same accuracy of the results as the implicit unsteady conjugate heat transfer model but with considerable reduction of the computational time.

Multi-time-scale turbulent heat transfer model for predictions of various turbulent heat transfer phenomena

The turbulent heat transfer model has been a useful and powerful tool in the calculation of turbulence heat transfer for designs of equipment with engineering and industrial problems. Among turbulent heat transfer models, two-equation turbulence models for both velocity and thermal fields are one of the best models because they have more accurate prediction performance and can carry out turbulence calculations at the proper calculation costs. In this study, in order to improve the prediction performance of two-equation heat transfer turbulence model in more complex problems of turbulent heat transfer, a turbulence model based on the multi-time-scale model proposed by Nagano and Hattori (Int J Heat Fluid Flow 51:221, 2015) for predictions of a velocity field is modified, and a turbulent heat transfer model with the multi-time-scale is newly proposed. The proposed turbulent heat transfer models are evaluated in complex fields of turbulent heat transfer problem such as a T-junction turbulent thermal mixing channel flow, a turbulent plane impinging jet with heat transfer and a turbulent plane wall jet with heat transfer, where databases of these complex turbulent heat transfer phenomena are obtained by our DNS. Based on the results, adequate improvement of the prediction performance of a proposed turbulent heat transfer model is validated.

Modeling and computation of turbulent slot jet impingement heat transfer using RANS method with special emphasis on the developed SST turbulence model

Based on the Reynolds-Averaged Navier-Stokes (RANS) method, this work has developed a combinational turbulence model for the numerical simulation of turbulent slot jet impingement heat transfer. The combinational model is constructed by taking the original Shear Stress Transport (SST) turbulence model as the parent model and coupling with the Kato-Launder model, the intermittency transition model and the crossflow transition model, which has been abbreviated as SST-KIC model. Detailed study has been conducted for the effect of different component models in terms of the turbulent kinetic energy, the local Nusselt number as well as the flow structures including the mean velocity, skin friction and the law of wall. By comparing with both experimental data and available numerical results of other researchers, it has been found that the proposed model possesses good performance in terms of different parameters for both two nozzle-plate spacing of 4 and 9.2. Finally, the effect of Reynolds number on the flow field characteristics was studied and it is noted that the positive gradient of turbulent intensity has similar variation tendency as the positive gradient of the Nusselt number.

CFD modeling of turbulent convection heat transfer of nanofluids containing green functionalized graphene nanoplatelets flowing in a horizontal tube: Comparison with experimental data

In this research, a series of numerical simulations were conducted utilizing computational fluid dynamics (CFD) software in order to predict the heat transfer performance of queues nanofluids containing clove-treated graphene nanoplatelets (CGNPs) flowing in a horizontal stainless steel heated pipe. The GNPs were covalently functionalized with clove buds using free radical grafting reaction using an eco-friendly process. The advantage of this synthesis method was that it did not use hazardous acids, which are typically used in traditional treatment methods of carbon nanostructures. The thermo-physical properties of the aqueous nanofluids obtained experimentally were used as inputs for the CFD simulations for solving the governing equations of heat transfer and fluid motion. The shear stress transport (SST) k-ω turbulence model was also used in these simulations. The corresponding convective heat transfer coefficient and friction factor of aqueous nanofluids for nanoparticle weight concentrations of 0.025, 0.075, and 0.1% were evaluated. The simulation results for both heat transfer coefficient and friction factor were shown to be in agreement with the experimental data with an average relative deviation of about ±10%. The presented results confirmed the applicability of the numerical model for simulating the heat transfer performance of CGNPs aqueous nanofluids in turbulent flow regimes.