The Nonrecursive Plating Algorithm (NRPA) for Computing the Total Radiative Exchange Factors in Enclosures

Many numerical methods for computing radiation exchange in enclosures are based on the computation of direct exchange areas (DEAs) and total exchange areas (TEAs). Excessively long computation times can be associated with TEAs computation. Among the best performing methods, the plating algorithm (PA) computes TEAs from DEAs based on a set of simple recursive equations. An efficient CPU and GPU parallelization of the PA are represented. Nevertheless, PA computation complexity is O(N ³). A novel formulation, the nonrecursive plating algorithm (NRPA), is introduced. It allows the computation of TEAs with a single nonrecursive step. Its equations are formulated by identification to the PA equations giving TEAs from DEAs, requiring one simple assumption. The NRPA is then written in matrix form as mainly a square matrix multiplication operation. Based on advancement in matrix multiplication computation, the NRPA complexity is proven to be O(N ^2.38) for the number of multiplications. CPU and GPU NRPA are implemented based on the optimized linear algebra library BLAS for CPU and cuBLAS for GPU CUDA programs. NRPA is found to highly outperform PA in both CPU and GPU computation times. Finally, a test enclosure is considered and serves to validate the accuracy of the NRPA by comparison to the PA.     

A High-Order-Accurate GPU-Based Radiative Transfer Equation Solver for Combustion and Propulsion Applications

In this article we present a high-order-accurate solver for the radiative transfer equation (RTE) which uses the discontinuous Galerkin (DG) method and is designed for graphics processing units (GPUs). The compact nature of the high-order DG method enhances scalability, particularly on GPUs. High-order spatial accuracy can be used to reduce discretization errors on a given computational mesh, and can also reduce the mesh size needed to achieve a desired error tolerance. Computational efficiency is a key concern in solutions to radiative heat transfer problems, due to potentially large problem sizes created by (a) the presence of participating nongray media in a full-spectrum analysis, (b) the need to resolve a large number of angular directions and spatial extent of the domain for an accurate solution, and (c) potentially large variations in material and flow properties in the domain. We present here a simulation strategy, as well as a set of physical models, accompanied by a number of case studies, demonstrating the accuracy and superior performance in terms of computational efficiency of this approach.     

Theoretical approach of a flat plate solar collector with clear and low-iron glass covers taking into account the spectral absorption and emission within glass covers layer

Accurate modeling of solar collector system using a rigorous radiative model is applied for the glass cover which represents the most important component of the system and greatly affects the thermal performance. The glass material is analyzed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in one dimensional case using the radiation element method by ray emission model (REM²). The optical constants of a clear and low-iron glass materials proposed by Rubin have been used. These optical constants, 160 values of real part n and imaginary part k of the complex refractive index of such materials, cover the range of interest for calculating the solar and thermal radiative transfer through the glass cover. The computational times for predicting the thermal behavior of solar collector were found to be prohibitively long for the non-gray calculation using 160 values of n and k for both glasses. Therefore, suitable semi-gray models have been proposed for rapid calculation. The temperature distribution within the glass cover shows a good agreement with that obtained with iterative method in case of clear glass. It has been shown that the effect of the non-linearity of the radiative heat exchange between the black plate absorber and the surroundings on the shape of the efficiency curve is important. Indeed, the thermal loss coefficient is not constant but is a function of temperature, due primarily to the radiative transfer effects. Therefore, when the heat exchange by radiation is dominant compared with the convective mode, the profile of the efficiency curve is not linear. It has been also shown that the instantaneous efficiency of the solar collector is higher in case of low-iron glass cover.     

A MONTE CARLO (MC) METHOD APPLIED TO THE MEDIUM WITH NONGRAY ABSORBING-EMITTING-ANISOTROPIC SCATTERING PARTICLES AND GRAY APPROXIMATION

A Monte Carlo (MC) method is applied to calculate radiative transfer in a nongray medium using spectral radiative exchange factor RD ij u . The creditability of the present MC model has been validated by comparing it with the results using other research methods. Meanwhile, the radiative transfer in an isothermal and nonisothermal medium with nongray absorbing-emitting-anisotropic ash particles is calculated by a nongray model and several gray approximation methods. A simplification from a nongray problem to a gray one by Rosseland's mean extinction coefficient, mean albedo y bar 2 , and Planck mean phase function is suggested.     

Infrared radiative heat transfer in nongray nonisothermal gases

In the present paper, both nongray and nonisothermal behaviors of an infrared emittingabsorbing gas have been taken into account in radiative transfer analyses through the use of the nonisothermal band absorptance. Consideration is given specifically to a simple system consisting of a radiating medium bounded by two infinite parallel black surfaces of different temperatures. Solutions are presented for the cases of radiative equilibrium and combined conduction and radiation. Results based on different methods of evaluating the nonisothermal band absorptance are also compared among themselves. Differences in several fundamental features are exhibited in the nongray nonisothermal solutions as compared to those with nongray but isothermal properties.     

Nongray inverse boundary design problems in enclosures at radiative equilibrium

In this paper, an inverse analysis is used to find an appropriate heat flux distribution over the heater surface of radiant enclosures, filled with nongray media at radiative equilibrium from the knowledge of desired (prespecified) temperature and heat flux distributions over the given design surface. Regular and irregular 2D enclosures filled with nongray combustive gas products are considered. Radiation is considered the dominant mode of heat transfer and the medium temperature is obtained from the energy equation. To evaluate the nongray behavior of the participating gases properly, the spectral‐line weighted‐sum‐of‐gray‐gases (SLW) model with updated correlations is used. The dependence of absorption coefficients and the weights of the SLW model on the temperature of the medium makes the inverse problem nonlinear and difficult to handle. Here, the inverse problem is formulated as an optimization problem and the Levenberg‐Marquardt method has been used to solve it. The finite volume method is exploited for the discretization of the energy equation and the spatial discretization of the radiative transfer equation (RTE). The discrete ordinates method (TN quadrature) is used for the angular discretization of RTE. Five test cases, including homogeneous and inhomogeneous media, are investigated to prove the ability of the present methodology for achieving the desired conditions.     

Free Liquid Jet Impingement from a Slot Nozzle to a Curved Plate

This article explores the heat transfer characteristics of a free liquid jet discharging from a slot nozzle and impinging vertically on a curved cylindrical shaped plate of finite thickness. Computations were done for Re = 500–1800, β = 0.75–3, R _i /d _n  = 4.16–16.66, b/d _n  = 0.08–1.5, and d _n  = 0.3–2.4 mm. Results are presented for dimensionless solid–fluid interface temperature, dimensionless maximum temperature in the solid, and local and average Nusselt numbers. The local Nusselt number increases with Reynolds number. Decreasing the nozzle width increases the local heat transfer coefficient. Decreasing the nozzle to target spacing or plate thickness or plate inner radius of curvature all enhances the Nusselt number.     

Interaction of Surface Radiation With Laminar and Turbulent Natural Convection in Tall Vertical Cavities: Analysis and Heat Transfer Correlations

The interaction of surface radiation with laminar and turbulent natural convection in differentially heated vertical cavities, filled with air and of large aspect ratio (greater than 10), is analyzed in this study. The k ? ωSST turbulence model is used for the formulation of the convection fluid flow and heat transfer, while the governing equations are discretized by the finite-volume method. As an extension of the scarce previous studies, more realistic conditions with a wide range of parameters are considered in the performed simulations. The presented results show the effect of surface radiation on streamlines, isotherms, turbulent kinetic energy, and temperature and vertical velocity profiles, as well as on local and on average convective and radiative heat transfer. Globally, it is found that surface radiation has a weak effect on the dynamic and thermal fields in the major part of the cavity; however, some influence in the upper and lower zones of the cavity is observed. For design purposes, accurate correlations are developed for average convective and radiative Nusselt numbers that cover emissivity of surfaces between 0 and 1, cold wall temperature ranging from 263 K to 303 K, temperature difference between vertical walls ranging from 5 K to 40 K, width of the cavity between 2.5 cm and 7.5 cm, and height of the cavity between 0.25 m and 6 m (this leads to a Rayleigh number ranging from 10³ to 2 × 10⁶ and an aspect ratio between 10 and 80).     

Self-absorption of radiation in turbulent molecular gases

Departures of radiant heating rates from predictions based upon the well-storred chamber model are obtained with a nongray, nonlinear analysis of radiant heat transfer in a turblent molecular gas Reynolds number is used to characterize the turbulence, and a radiation-molecular conductopm ratio and maximum optical depth characterize the gas properties. Results are obtained for wall to gas temperature ratios from 0.235 deoth characterize the gas properties. results are obtained average temperature ratios are presented. A sample calculation illustrates the effect of self-absorption on radiative transfer and reactor temperature.     

Coupled Natural Convection and Radiation in a Horizontal Rectangular Enclosure Discretely Heated from Below

A numerical study is carried out to investigate the interaction between natural convection and thermal radiation in a horizontal enclosure filled with air and heated discretely from below. The results are presented for a cavity having an aspect ratio A _r  = L′/H′ = 10, while the Rayleigh number and the emissivity of the walls are varied in the ranges 10³ ≤ Ra ≤ 10⁶ and 0 ≤ ε ≤ 1, respectively. The results of the study, presented in terms of flow and temperature patterns, average convective, radiative and total Nusselt numbers, evaluated on the cold wall, show that the problem has multiple solutions. Each of these solutions is characterized by a specific flow structure, and its appearance and range of existence depend strongly on the parameters Ra and ε. The amount of heat evacuated through the cold surface is dependent on the type of solution.     

Heating Process Simulation of Steel Coil in Bell‐Type Annealing Furnace

This study examines two important parameters: the convective heat‐transfer coefficient and radiative heat‐transfer coefficient, which have a significant impact on coil temperature in a furnace. A new three‐dimensional model is proposed for convective heat transfer, and the factors affecting the Nusselt number (Nu) are studied using the orthogonal test method. Finally, the relationship between the Nu number and flow rate is determined. Considering the complex geometric structure of a furnace, this study uses the Monte Carlo method to calculate the angle factor and obtains the radiant heat flux using a radiation network diagram. The calculated values are applied to steel coil temperatures for accurate boundary conditions. The results show that the temperature simulated by using the mathematical model is in good agreement with the experimental data obtained with the thermocouple insert experiment.     

Numerical Investigation on the Steady State Natural Convection in a Horizontal Open-Ended Cavity with a Heated Upper Wall

In this article, the investigation is focused on a configuration made of two horizontal parallel plates with the upper plate heated at uniform heat flux and the lower one adiabatic. Results are presented in terms of velocity and temperature fields, and both the temperature and the velocity profiles at different sections are shown. They are reported at two Rayleigh numbers, 10³ and 10⁵, and for two aspect ratio values, 1 and 10. Results are also shown in terms of the upper and lower wall temperature profiles. Correlations for average Nusselt numbers and maximum dimensionless wall temperature, in terms of Rayleigh number and aspect ratio, are given for 10³ ≤ Ra ≤ 10⁵ and 1 ≤ L/b ≤ 10.     

Momentum and Heat Transfer Characteristics for the Flow of Power-Law Fluids over a Semicircular Cylinder

In this study, the two-dimensional steady flow of power-law fluids past a semicircular cylinder (flat face oriented upstream) has been investigated numerically. The governing equations (continuity, momentum, and energy) have been solved in the steady symmetric flow regime over the range of the Reynolds number (0.01 ≤ Re ≤ 25), power-law index (0.2 ≤ n ≤ 1.8), and Prandtl number (0.72 ≤ Pr ≤ 100). Extensive new results reported here endeavor to elucidate the role of power-law index (0.2 ≤ n ≤ 1.8) on the critical Reynolds number denoting the onset of flow separation (Re ^c ) and of vortex shedding (Re _c ). In shear-thinning fluids, both of these transitions are seen to be delayed than that in Newtonian and shear-thickening fluids. Furthermore, the influence of the Reynolds and Prandtl numbers, power-law index on drag phenomenon, and heat characteristics of semicircular cylinder have been studied in the steady flow regime. Finally, the present numerical values of the critical Reynolds numbers and the average Nusselt number have been correlated by simple forms which are convenient for interpolating these results for the intermediate values of the governing parameters in a new application.     

Mixed convection from a spheroid in Bingham plastic fluids: Effect of buoyancy-assisted flow

ABSTRACT

In this work, laminar mixed convection from an isothermal spheroidal particle immersed in a Bingham plastic fluid is studied numerically in the buoyancy-assisted regime. The results reported herein encompass the following ranges of conditions: Reynolds number, 0.1 ≤ Re ≤ 100; Prandtl number, 10 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 100; Richardson number, 0 ≤ Ri ≤ 8; and aspect ratio of the spheroid, 0.2 ≤ e ≤ 5. In particular, consideration is given to the effect of shape and orientation of the particle on the detailed flow and temperature fields (in terms of streamlines, iso-vorticity, and isotherm contours), morphology of the yielded–unyielded regions, and the local and surface-averaged Nusselt number. All else being equal, the propensity for flow separation is seen to be greater for oblates (e < 1) than that for prolates (e > 1). In both cases, this reduces with the increasing Bingham number and/or the Richardson number. Both drag coefficient and the Nusselt number show a positive dependence on the Bingham number as well as on the Richardson number. Overall, the drag coefficient increases as the particle shape changes from an oblate to prolate, whereas the reverse trend is obtained for the average Nusselt number, which is in line with the general inference that more drag corresponds to more heat transfer. Finally, the average Nusselt number is correlated with the pertinent dimensionless parameters (Re, Pr, Bn, Ri, e) via a simple correlation, thereby enabling its prediction for intermediate values of the parameters and/or in a new application.     

TRANSIENT RADIATION HEAT TRANSFER WITHIN A NONGRAY NONISOTHERMAL ABSORBING-EMITTING-SCATTERING SUSPENSION OF REACTING PARTICLES UNDERGOING SHRINKAGE

ABSTRACT

A nonisothermal, nongray, absorbing, emitting, and anisotropically scattering suspension of reacting particles exposed to concentrated thermal radiation is considered. The steam gasification of coal is selected as the model thermochemical reaction. The unsteady energy equation that couples the radiative heat flux with the chemical kinetics is solved by means of a numerical model that incorporates Monte Carlo ray tracing, the finite-volume method, and an explicit Euler time integration scheme. Two modeling approaches are applied: (1) a quasi-continuous model that assumes a homogeneous medium and utilizes its macroscopic radiative properties (absorption and scattering efficiencies and scattering phase function), and (2) a particle-discrete model that assumes an ensemble of randomly positioned particles and traces the interaction of radiation with each particle by geometric optics. Temperature profiles and reaction extent are computed using both approaches. The quasi-continuous approach is superior in accuracy at the expense of lower spatial resolution, while the particle-discrete approach gives detailed information for every single particle in the suspension at the expense of larger stochastic errors.     

Numerical Simulation of Low NO x Combustion Technology in a 100 MWe Bituminous Coal-Fired Wall Boiler

Computational fluid dynamics (CFD) has been applied to evaluate two NO _x reducing schemes in a 100 MW_e per hour (p/h) boiler that uses double volute burners without over-fire-air (OFA). The new schemes involve: a) changing the double volute burners for centrally fuel rich (CFR) burners, and b) using the OFA system in conjunction with a). In analyzing the results of these two schemes, various conclusions were drawn: 1) gas temperatures and related rise rates in the central zone of burners were higher, O₂ and NO _x concentrations were lower; and 2) cross-sectional gas temperature distributions through the burner centers in scheme employing b) is higher than that of original furnace set-up, and lower than that of scheme employing a). Comparing the b) scheme with those of the a) scheme and the original set-up, which is 277 mg/m³ (at 6% O₂) at the furnace outlet, the peak value of NO _x concentration has decreased 571 mg/m³ (67.4%) and 436 mg/m³ (61.2%), respectively.     

The influence of furnace design on the NO formation in high temperature processes

High temperature processes produce high NO_x emissions due to their elevated working temperatures. Strong regulations for emissions of pollutants [1] from industrial plants lead the operators to optimize their furnaces. In this paper a three-dimensional mathematical model for turbulent flow and combustion on the basis of turbulence-chemistry interactions and radiative heat transfer taking into account spectral effects of surrounding walls and combustion gases is described. The transport equation for radiative intensity was split into different wavelength ranges. A block-structured finite volume grid with local refinements was used to solve the governing equations. The calculation domain is subdivided into a number of subdomains which are linked within the solver based on the message passing interface (MPI) library. Computed distributions of velocity, temperature, species distribution and heat fluxes are given. Results of a parametric study in a producing horseshoe furnace by increasing the height of the furnace with regard to NO_x concentration distributions are presented.     

MHD Mixed Convection in a Lid-Driven Cavity Including Heat Conducting Solid Object and Corner Heaters with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a top sided lid-driven square enclosure is numerically simulated in this paper following a finite volume approach based on the SIMPLEC algorithm. The enclosure is heated by corner heaters which are under isothermal boundary conditions with different lengths in bottom and right vertical walls. The lid is having lower temperature than heaters. The other boundaries of the enclosure are insulated. A uniform magnetic field is applied along the horizontal direction. A heat conducting horizontal solid object (a square cylinder) is placed centrally within the outer enclosure. Shear forces through lid motion, buoyancy forces due to differential heating and magnetic forces within the electrically conducting fluid inside the enclosure act simultaneously. Heat transfer due to forced flow, thermal buoyancy, Joule dissipation and conduction within the solid object are taken into account. Simulations are conducted for various controlling parameters such as the Richardson number (0.1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50) and Joule heating parameter (0 ≤ J ≤ 5) keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number and bulk fluid temperature are also plotted to show the effects of Ha, J and Ri on them.     

Numerical investigation on heat transfer of supercritical water in a roughened tube

ABSTRACT

The turbulent mixed convection heat transfer of supercritical water flowing in a vertical tube roughened by V-shaped grooves has been numerically investigated in this paper. The turbulent supercritical water flow characteristics within different grooves are obtained using a validated low-Reynolds number κ-ε turbulence model. The effects of groove angle, groove depth, groove pitch-to-depth ratio, and thermophysical properties on turbulent flow and heat transfer of supercritical water are discussed. The results show that a groove angle γ = 120° presents the best heat transfer performance among the three groove angles. The lower groove depth and higher groove pitch-to-depth ratio suppress the enhancement of heat transfer. Heat transfer performance is significantly decreased due to the strong buoyancy force at T_b = 650.6 K, and heat transfer deterioration occurs in the roughened tube with γ = 120°, e = 0.5 mm, and p/e = 8 in the present simulation. The results also show that the rapid variation in the supercritical water property in the region near the pseudo-critical temperature results in a significant enhancement of heat transfer performance.     

Evolutionary Placement of Discrete Heaters in Forced Convection

This article aims to maximize the global conductance (C) of a symmetrical, discretely heated channel in forced convection, where the fluid flow is sustained by a fixed pressure difference given by the Bejan number. The maximization of C is obtained by determining the optimal arrangement of the discrete heaters along the channel and the optimal channel breadth with the help of a genetic algorithm (GA) that is fully coupled with the finite-element methods used for solving the conservation equations. The number of independent variables considered in the optimization process varies between N + 1 and 2N + 1, where N is the number of heat sources (1 ≤ N ≤ 20) and the extra unit represents the channel height. The numerical results agree with the available literature, showing that increased values of C are obtained with designs that do not use equally spaced heaters. The results show that a larger number of discrete heaters can provide higher values of global conductance when compared with fully optimized simpler designs (i.e., a small number of discrete heaters), which is also in agreement with previous studies. Designs with heaters of variable heat strength are also considered, to study the optimal allocation of the total heat input through the N heaters. This family of designs leads to even higher performance.