Radiation Heat Transfer Model Research Articles

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

Radiative heat transfer (RHT) is often the dominant mode of heat transfer in flames, fires, and combustion systems and affects significantly temperature distributions directly and kinetically controlled chemical processes indirectly. Modeling RHT accurately in multidimensional flames and combustion systems is challenging mainly due to the highly spectrally dependent radiative properties of combustion products, the high computational cost of solving the radiative transfer equation (RTE), and the strong turbulence and radiation interactions (TRI). Significant progress has been made in all three aspects in the last three decades and the state-of-the-art models and methods have been incorporated into CFD practice for modeling fires, turbulent jet flames, and turbulent combustion in combustion systems. In this article, we first discuss the coupling between RHT and combustion and the important role played by RHT in some fundamental flame phenomena. Then we discuss the state-of-the-art radiation models with a focus on RTE solvers, radiative property models and TRI. Next, we review the recent simulations of turbulent combustion systems involving these state-of-the-art radiation models. Finally, we provide concluding remarks and some potential research areas to advance RHT modeling in multiphase reacting flows.

Convective and Radiative Heat Transfer in Molten Salts

Molten salts have been proposed as heat transfer media due to their superior thermal performance at elevated temperatures. A number of heat transfer correlations have been proposed in the literature for molten salts without explicitly considering the radiative heat transfer effect in the salts, which may not be negligible. This study therefore attempts to (1) quantitatively analyze the convective and radiative heat transfer of molten salts using an overall heat transfer model that includes a radiative heat transfer model developed in this research and an existing conventional convective heat transfer model/correlation, such as the Sieder-Tate or Hausen correlation, and (2) provide rationale on under what conditions it is necessary to consider the radiative heat transfer effect in salts. A parametric study was performed using the radiative heat transfer model developed to investigate the effects of various input variables, including the tube size (inner diameter 5 to 50 mm), salt temperature (500°C to 1000°C), salt and wall temperature difference (5°C to 100°C), and salt absorption coefficient (1 to 100 m-1). Our study indicates that (1) the proposed overall heat transfer model reasonably predicts the salt convective and radiative heat transfer, (2) the radiative heat transfer is more important for laminar flows than transitional and turbulent flows, (3) the radiative heat transfer is more important in tubes of larger inner diameter, (4) the salt temperature affects the radiative heat transfer significantly while the temperature difference between the salt and wall has a slightly smaller effect for the range investigated (ΔT = 5°C to 100°C), and (5) the salt absorption coefficient significantly affects the salt radiative heat transfer.

Experimental study of radiative heat transfer from laminar non-premixed methane flames diluted with CO2 and N2

This paper presents an experimental study about the effect of fuel dilution with inert gases on the radiative heat transfer characteristics of laminar non-premixed coflow methane flames. The visible flame lengths were determined and flickering is characterized when necessary. Radiative heat flux distributions were measured and used to determine the radiative fraction of each flame. In total, 55 flames were studied with powers up to 0.554 kW and with CO2 and N2 dilutions up to 60%. The flames were grouped in series of constant power and constant flow rate. It is shown that the addition of CO2 may decrease or increase the radiative fraction depending on the dilution level and on the characteristic residence time of the flame. Dilution with N2 always leads to a decrease of the radiative fraction. The results are relevant for practical applications as in biogas combustion and also proved to be useful for validation of radiative heat transfer models.

Reduced-order models for radiative heat transfer of hypersonic vehicles

Aerothermoelastic analysis of hypersonic vehicles is a complex multidisciplinary coupling problem. Thus, accurate modeling of varying disciplines with low computational cost is necessary. This work developed a tractable approach-based reduced-order modeling technology to solve the radiative thermal transfer problem in a hypersonic simulation. A method that combines proper orthogonal decomposition and unassembled discrete empirical interpolation method is developed to construct the reduced-order modeling. First, high-dimensional original systems are projected on the optional basis generated by proper orthogonal decomposition, and the nonlinear term is further approximated by unassembled discrete empirical interpolation method. Then, a numerical integration method for the solution of the reduced system of nonlinear differential equations is provided. Case studies that use a classical hypersonic control surface model, in which the time history and spatial distribution of the thermal load are known a priori, are conducted to validate the accuracy and efficiency of the reduced-order modeling methodology and to assess the robustness of the reduced-order modeling for thermal solution. Results indicate the ability of reduced-order modeling to reduce the nonlinear system size with reasonable accuracy.

Group theoretical analysis for magnetohydrodynamic generalized Stokes’ flow and radiative heat transfer model of a non-Newtonian nanofluid with heat generation/absorption

The fully developed boundary layer flow and heat transfer model of an unsteady, incompressible, electrically conducting, optically thick and thermodynamically compatible third-grade nanofluid are investigated from the viewpoint of Lie symmetry approach. We have studied the Stokes’ model in which flow is generated due to motion of the bounding surface with an impulsive time-dependent velocity. The mathematical model also includes the effect of thermal radiation and internal heat source or sink in the flow regime. Lie symmetry approach is employed to obtain the symmetry algebra of the governing nonlinear partial differential equations for both flow and heat transfer models. The governing nonlinear partial differential equations describing the flow and heat transfer model are reduced to different classes of nonlinear ordinary differential equations under the implication of symmetry generators. The reduced ordinary differential equations are investigated using the compatibility and generalized group theoretical method. The exact closed-form solutions for nanofluid motion and temperature distribution within the boundary layer are obtained. The effect of various thermophysical parameters on the characteristics of flow and heat transfer for Cu-water nanofluid model is explored from a physical point of view.

Experimental and numerical studies for applying hybrid solar chimney and photovoltaic system to the solar-assisted air cleaning system

Under the background of global energy shortage and environment deterioration, researchers of the world pay high attention to develop renewable energy. This paper proposes a hybrid solar chimney and photovoltaic system for the novel solar-assisted air cleaning system. Small-scale laboratory setups are designed and fabricated. Experimental results reveal that replacing 50.60% acrylic glass of the collector top with photovoltaic panels will reduce the thermal air flow rate only by 14%, but generate significant electric power output. A three-dimensional numerical simulation model is established and validated by experimental results (air flow rate, temperature distribution). The model includes solar ray tracing model, surface to surface radiation model, buoyancy-driven flow and heat transfer model and power generation model. Then, this model is used to predict a large-scale system based on the Manzanares pilot power plant in Spain. For the large-scale system, the electrical energy generated by the photovoltaic panels can be used to drive suction fans to increase air input. Covering the entire top surface of the collector by photovoltaic panels (113-meter-wide), the total air flow rate would increase to 2.21 times compared with the system without photovoltaic panels. And setting photovoltaic panels on the collector bottom with 113-meter-wide, the total air flow rate would increase to 2.42 times. Thus, adding photovoltaic panels for the collector can greatly improve the utilization of solar energy. It can increase the amount of air purification, or reduce land requirement for the same flow rate.

Assessment of improved banded model for spectral thermal radiation in presence of non-gray particles in fluidized bed combustors

In this study, Bordbar’s banded model is coupled with a 3-D radiation model based on method of lines (MOL) solution of discrete ordinates method (DOM) for modeling of radiative heat transfer in freeboard of METU 0.3 MWt ABFBC test rig where a typical Turkish lignite is fired with and without fly ash recycling. The accuracy and the computational efficiency of the model were assessed by benchmarking its predictions against banded SLW model. Furthermore, in order to show the effect of gas composition on predictive accuracy of Bordbar’s 10 band model, assessment of the accuracy of Bordbar’s 10 band model is also tested by using gas compositions corresponding to oxy-fired combustion. Bordbar’s 10 band model requires around 50 times less CPU than that of banded SLW under all conditions. Incident wall heat flux predictions of Bordbar’s 10 band model are found to be in reasonable agreement with those of banded SLW and measurements in all test cases. However, Bordbar’s 10 band model considerably overestimates source terms in the air-fired test case without recycle. The change in gas composition to oxy-fired combustion conditions and higher particle loads lead to significant improvement in the accuracy of source term predictions. In conclusion, Bordbar’s 10 band model can be utilized to reduce CPU requirement of the spectral RTE solution for bubbling fluidized bed combustors with recycle or circulating fluidized bed combustors where radiative heat transfer is dominated by particles.

An improved full-spectrum correlated-k-distribution model for non-gray radiative heat transfer in combustion gas mixtures

Abstract To improve the efficiency of full-spectrum correlated-k-distribution (FSCK), a new method FSCK-RSM has been proposed based on response surface methodology (RSM) in this paper. The k-distributions of FSCK was used to fit the response surface model based on radial basis function and the radiative calculation efficiency was improved by avoiding multiple computations and interpolation in the FSCK-RSM. The thermal radiation heat transfer of five combustion gases (H2O, CO2, CO, C2H2 and C2H4) in a one-dimensional layer was investigated and the radiative sources calculated by the LBL, SNB, FSCK and FSCK-RSM methods were given at different distributions of temperature and gas concentration. The results showed that the needed amount of input data was reduced by 677 times using FSCK-RSM comparing to the FSCK and the maximum of the average normalized deviation for FSCK-RSM was 2.46% in the non-isothermal homogeneous medium. The model was finally used for radiation reabsorption calculations in planar C2H4/O2/N2/CO2 flames with full coupling to heat transfer and multi-species chemistry. The computational time using the FSCK-RSM was found to be at most half of that using the FSCK method. This FSCK-RSM model was an effective method for addressing the radiation problems that occur in combustion systems.

A Deep Neural Network Model of Particle Thermal Radiation in Packed Bed

Prediction of particle radiative heat transfer flux is an important task in the large discrete granular systems, such as pebble bed in power plants and industrial fluidized beds. For particle motion and packing, discrete element method (DEM) now is widely accepted as the excellent Lagrangian approach. For thermal radiation, traditional methods focus on calculating the obstructed view factor directly by numerical algorithms. The major challenge for the simulation is that the method is proven to be time-consuming and not feasible to be applied in the practical cases. In this work, we propose an analytical model to calculate macroscopic effective conductivity from particle packing structures Then, we develop a deep neural network (DNN) model used as a predictor of the complex view factor function. The DNN model is trained by a large dataset and the computational speed is greatly improved with good accuracy. It is feasible to perform real-time simulation with DNN model for radiative heat transfer in large pebble bed. The trained model also can be coupled with DEM and used to analyze efficiently the directional radiative conductivity, anisotropic factor and wall effect of the particle thermal radiation.

Advancing Radiative Heat Transfer Modeling in High-Temperature Liquid Salts

Liquid salts have become more attractive as coolants for low-carbon power generation due to needs for high-temperature heat and affordable energy storage. Of particular interest are halide salts utilized in fluoride-salt-cooled high-temperature reactors, molten salt reactors, and high-magnetic-field fusion machines, as well as in concentrated solar power systems. Because of their high-temperature operation and semitransparent nature, the liquid salts in these designs may experience the effects of participating media radiative heat transfer (RHT). While some work has been conducted on measuring the thermophysical properties of these fluids, there is currently very little known about their radiative properties. Here, we present the initial results of a two-part methodology to enhance RHT understanding and improve modeling in high-temperature liquid salts. First, an experimental apparatus designed to measure liquid chloride and fluoride salt absorption coefficients by Fourier transform infrared spectroscopy was completed and validated with water measurements. Second, computational fluid dynamics (CFD) simulations were run to determine the contribution of thermal radiation to the overall heat transfer for flow between parallel plates. This geometry was used to verify code accuracy and investigate requirements for absorption coefficient spectral banding. Future work will be to complete halide salt absorption measurements and couple them to the established CFD methods to identify geometries and temperatures where RHT is significant and enable prediction of heat transfer in such systems.

A matrix model of particle-scale radiative heat transfer in structured and randomly packed pebble bed

Thermal radiation in pebble bed is very hard to compute accurately and efficiently since it occurs between the surfaces no matter how far they are. Herein, radiative heat flux and effective thermal conductivity were derived mathematically by a matrix model to present the thermal radiation between particles in pebble beds. For structured packing, the transient radiative heat transfer is proven to be similar to thermal diffusion. This study proposed a correlation to predict the radiation exchange factor under different porosity. Radiative effective thermal conductivity was found to grow slightly with void fractions. For random pebble beds, a regression model of the multi-layer neural network was trained by large datasets to compute the view factor matrix efficiently. With the trained model and GPU acceleration, it is feasible to perform real-time-simulation of full-range radiations inside large-scale pebble beds, even for real reactors (e.g. HTR-PM). A thermal radiation simulation of the decay heat removal of a real reactor adopted this model as a demonstrative application and showed that the highest temperature is still within the design limitation of the packed bed.

Influence of magnetic field and thermal radiation on peristaltic motion with double‐diffusive convection in Jeffery nanofluids

AbstractA theoretical study is conducted to examine the peristaltic pumping with double‐diffusive convection in Jeffery nanofluids through a two‐dimensional infinite asymmetric channel. The flow is examined in a wave casing of orientation that moves pace with the velocity of the wave. The peristaltic wave train on the walls that have different amplitude and phase is chosen to form channel irregularity. Rosseland approximation is noticed in the modeling of the transmission radiation heat transfer and temperatures of the walls are recognized constants. The replica has a great impact in discovering nanofluid dynamic influences on peristaltic motion, in biological vessels as symbolized by transportation of heat in blood flow, food molecules, hormones, novel pharmacodynamics pumps, and engineered gastrointestinal motility enhancement. Peristaltic motion has applications in physiology, such as transport of urine, transport of food bolus through gastrointestinal tract, and transport of blood through small blood vessels. Analytical results have been established for stream function, axial velocity, temperature, and absorption and nanoparticle volume fraction. The effect of the principal hydrodynamic parameters (thermophoresis, Brownian motion, Dufour, and Soret) and Grashof numbers (concentration, thermal, nanoparticle) on peristaltic transport patterns with double‐diffusive convection are deliberated with the support of computational outcomes found. The pictorial investigation is done to investigate the possessions of miscellaneous limitations on flow quantities of curiosity.

CFD study of non-premixed swirling burners: Effect of turbulence models

Abstract This research investigates a numerical simulation of swirling turbulent non-premixed combustion. The effects on the combustion characteristics are examined with three turbulence models: namely as the Reynolds stress model, spectral turbulence analysis and Re-Normalization Group. In addition, the P-1 and discrete ordinate (DO) models are used to simulate the radiative heat transfer in this model. The governing equations associated with the required boundary conditions are solved using the numerical model. The accuracy of this model is validated with the published experimental data and the comparison elucidates that there is a reasonable agreement between the obtained values from this model and the corresponding experimental quantities. Among different models proposed in this research, the Reynolds stress model with the Probability Density Function (PDF) approach is more accurate (nearly up to 50%) than other turbulent models for a swirling flow field. Regarding the effect of radiative heat transfer model, it is observed that the discrete ordinate model is more precise than the P-1 model in anticipating the experimental behavior. This model is able to simulate the subcritical nature of the isothermal flow as well as the size and shape of the internal recirculation induced by the swirl due to combustion.

Cabaret-Sc1 Code Validation in Experiments on Hydrogen Explosion Safety at NPP

The mathematical models implemented in the CABARET-SC1 code are described and the code validation results characterizing its potential in the description of key processes influencing hydrogen propagation in the reactor containment in the course of a severe accident are presented. Agreement with experimental data was achieved by refining the computational grids and adding a radiative heat-transfer model with no adjustable parameters or semi-empirical models.

Thermo-mathematical model for parabolic trough collector using a complete radiation heat transfer model – A new approach

Solar Parabolic Trough Collectors (PTC) are alternative clean solution for the thermal power plants to generate electricity and thermal energy. It can be configured to support small, medium and high temperature applications. In PTC, solar radiation is concentrated to a pipe coated selectively and enclosed in a glass tube with vacuum maintained in the annulus, through which a heat transfer fluid is circulated. Heat transfer analysis of PTC is important to determine the operating characteristics as well as for optimization of the parameters under different operating conditions. In this paper a heat transfer model is developed for receiver tube with the focus on a complete radiation heat transfer model for the annulus. For the analysis the receiver tube is divided into severe elements where the governing energy equations are discretized using Finite Volume Method. Gerhart factor is used for modelling the radiation heat transfer. View factors are computed using contour integration technique and analytical solutions. Heat transfer results are then validated with the test results obtained from Sandia National Laboratory. The results obtained show close agreement with the test results. Also the result is compared with other four published models. Based on the RMSE analysis, it is proven that our model is the best among all the four models compared.

Analysis of solar radiation heat transfer of architectural fabric membrane material

In recent years, the application of membrane structures in industrial storage buildings has been widely praised due to its light weight, high transparency, self-cleaning, and other advantages. The textile membranes consist of polyester fiber substrate and polyvinyl chloride or polyvinylidene fluoride flame-retardant coatings. It occupies the main market of architectural membrane materials in China. However, the fabric membrane material has high heat transfer coefficient, poor thermal insulation, and high light transmittance performance, being affected significantly by solar radiation intensity. These thermal optical properties are lead to a poor indoor thermal environment of industrial storage buildings. This article aims to overcome the difficulties in analyzing the fabric membrane materials solar radiation heat transfer. The complexity of heat transfer is mainly caused by the hourly solar radiation and the curved roofing of fabric membrane structure industrial storage building. Therefore, a solar radiation heat transfer model was established using MATLAB program. In this article, the different directions hourly heat gained of an actual membrane structures storage building located at Wuhan in China was calculated. The calculation results of solar radiation heat gained between the grid generation method with MATLAB and the projection method were compared. This study may provide a reference for analyze the solar radiation heat transfer and design of the practical fabric membrane structures building application.

Study on melt stratification and migration in debris bed using the moving particle semi-implicit method

In the severe accident of nuclear reactors, the melt stratification and migration in debris bed directly affect the melt heat transfer characteristics and the heat flux distribution on the lower head wall, which in turn affect the follow-up accident progressions including the pressure vessel failure mode, melt leakage, and molten corium concrete interaction. They are the key issues in nuclear reactor severe accident research. In the present study, the MPS method was applied to analyze melt stratification and migration in debris bed by including the models of radiation heat transfer among debris, melt phase change and surface tension. To validate the numerical method, the experiment was performed using the metal tin and ternary nitrate as the core melt simulant. Then, the stratification behavior of oxide and metallic core melt was investigated under varied parameters and conditions. The results indicated that the crust formed at the oxide and metal melt interface could block the stratification, which had important influence to the layered configuration. The melt contact area increased in the conditions of crust formation prior to the stratification completion. The high melt and debris temperatures and surface tension could contribute to the stratification, but the high viscous melt when undergoing phase transition needed a long time. Moreover, the comparison of melt stratification under adiabatic and isothermal boundary conditions showed that the oxide melt solidification trapped some metal melt in the voids. The penetration distance of metal melt in the oxide debris bed increased rapidly in the initial moment and gradually in the following moment, and finally the migration was terminated by melt crust. The melt penetration distance increased as the increase of debris bed porosity and melt and debris temperatures.

Full-scale 3D-modelling of the radiative heat transfer in rotary kilns with a present bed material

This work discusses the development and use of a detailed 3D radiative heat transfer model of a rotary kiln with a present bed material, used for iron ore pelletizing. A discrete ordinates method is used to solve the radiative heat transfer equation with radiative properties calculated using a weighted-sum-of-grey-gases (WSGG) model for gases and Mie and Rayleigh theory for particles including fuel, ash and soot. Measurement data gathered from a pilot-scale test furnace, comprising temperature, gas composition and particle concentration, is used in combination with temperature data and operation parameters gathered from a conventional rotary kiln to model a full-scale rotary kiln with a present bed material. The modelled cases have a thermal input of about 37 MWth and in addition to radiative heat transfer, conductive heat transfer within, as well as between, the bed and wall material are included in the model along with convective heat transfer from the gas and heat release from exothermic reactions in the bed. The model also considers the rotational wall and includes a simplified mixing model of the bed material as well as heat losses from the outside wall of the rotary kiln due to radiation and convection. For two different flames, one coal and one oil flame, surface temperatures are calculated on the inside and outside of the rotary kiln and compared to measurements. The model appears to predict the inner wall and bed surface temperatures well with errors less than 11%. The total heat transfer to the present bed material was also studied revealing that more than 80% originated from the radiative heat transfer within the furnace.

CABARET scheme for modelling the stratification erosion in gas mixtures in hydrogen mitigation experiments for reactor safety

Experiments on atmosphere mixing and stratification in the large scale experimental facility (PANDA), where the initial helium stratification in a vessel is eroded by a vertical jet of steam, were simulated with the CABARET scheme. Good agreement between calculated and measured gas temperature and concentrations has been achieved by refining the mesh and adding the model of radiative heat transfer. The simulation results are presented and discussed.

Mathematical modelling of hydrogen safety problems with CABARET scheme

Experiments on overall fluid transfer and mixing in the large scale experimental facility (PANDA), where the initial helium-rich layer is eroded by a flow resulting from the interaction of a jet/plume with horizontal flow obstruction, were simulated with the CABARET scheme. Computational simulation results are provided for two mesh resolutions and are compared with the experimental data. Good agreement between calculated and measured gas temperature and the breakup of the helium layer dynamics was achieved by refining the mesh in the jet area and by adding the model of radiation heat transfer.