Total Exchange Areas Research Articles

Improved Monte Carlo Method for Total Radiant Exchange Areas in Cylindrical Enclosure

An improved Monte Carlo method (IMCM) is developed to solve radiative heat transfer in participating media in this work. Monte Carlo method (MCM) as a high-precision method has good applicability for the calculation of radiative heat transfer in a complex-shape medium. However, it is highly time-consuming for a large number of energy beams tracing, which limits its application in practical engineering. To overcome this problem of the MCM, there are two improvements proposed: 1) the location of the zone emission points and the number of emission energy beams are subdivided; and 2) the energy of reflection and scattering part is solved by proportional iteration accumulation. In the IMCM, the reflection and scattering processing only needs to be calculated once, which significantly reduces the computing time of a large number of energy beams tracing. A series of radiative heat transfer problems in a two-dimensional cylindrical enclosure with different absorption coefficients, wall emissivity, and scattering albedo are studied, and results show that the IMCM is a high-precision and high-efficiency method for radiative heat transfer.

Modeling and determination of total heat exchange factor of regenerative reheating furnace based on instrumented slab trials

Regenerative heating furnace as a high-efficiency and energy-saving heating equipment is widely applied in iron and steel industry. Accurate knowledge of total heat exchange factor of regenerative heating furnace is of great significance to improve its on-line control performance. Therefore, determination of total heat exchange factor of regenerative reheating furnace is investigated in this work. A three-dimensional mathematical model of regenerative reheating furnace based on the analysis of heat transfer process is established. The zonal method is used to solve the temperatures of gas zone, slab surface zone and wall surface zone, in which the Monte Carlo method is used to compute the total radiant exchange areas of thermocouple to all other zones in the furnace. The total heat exchange factors of regenerative reheating furnace are determined and the effects of thermal and operational parameters, such as productivity, fuel consumption and slab hot charging temperature are analyzed. The results show that the total heat transfer factor increases with the decrease of fuel consumption or slab hot charging temperature, and increases with the increase of productivity. The present work is valuable for dynamical compensation of total heat exchange factor of the online control mathematical models in regenerative reheating furnace.

An improved Monte Carlo method for radiative heat transfer in participating media

An improved Monte Carlo method (IMCM) is developed in this paper to solve the total radiant exchange areas (TEAs), which can greatly improve calculation accuracy and save CPU time. This approach, features two main improvements on the basis of the Monte Carlo method (MCM). First, the location of the surface emission points and the number of emission energy beams are subdivided, thereby improving the calculation accuracy. Specifically, it is assumed that the energy beams emitted by one micro-element are emitted from M points on average. Second, the energy beams emitted by the surface and gas micro-elements are only arranged once, and the sampling of surface reflection is eliminated, thereby improving the calculation efficiency. Specifically, the ratio of the energy beams emitted by one micro-element directly to other micro-elements can be calculated. The reflection and scattering energy of one micro-element to other micro-elements are obtained by iterative accumulation. This approach can greatly save CPU time compared with sampling the reflected and scattered energy beams. The application of IMCM to a two-dimensional (2D) square cavity is considered in this study. The effects of surface emissivity and boundary temperature on radiative heat transfer are analyzed. IMCM was used to solve the TEAs, and the calculated results of IMCM, MCM and the pathlength method (PLMCM) were compared based on the results of the reduced integration scheme (RIS). The all results show that the IMCM is more accurate than the MCM and PLMCM and is more efficient than the MCM and PLMCM for calculating the TEAs.

New application method of the zonal model for simulations of pulverized coal-fired furnaces based on correction of total exchange areas

New application method of the zonal model in numerical simulations of pulverized coal-fired furnaces, continual corrections of the total exchange areas (CCTEA), is presented. The method is based on the corrections of the surface–surface, surface–volume, and volume–volume total exchange areas according to the changes of the surface zone emissivities during the iterative calculation of the numerical simulation and summation rules of the total exchange areas, so that it provides zero radiative exchange in an isothermal system. The method was developed for the homogeneous and uniform flame radiative properties. The results obtained by the CCTEA method were compared with the results obtained by the previously developed repeated run of numerical simulation (RRNS) method, based on multiple succesive run of the numerical simulation. The differences of the result obtained by the methods were found for various conditions of numerical investigations: initial wall emissivity, total extinction coefficient, and thickness of the ash deposit layer. The gas-phase phase radiative properties were determined by the simple gray gas model and weighted sum of gray gases model. Investigation showed small differences of the results obtained by the methods and their sensitivity to conditions of numerical investigation. The CCTEA method is an improvement of the RRNS method as it provides almost the same results after the single run of the numerical simulation and reduces the computation time.

DETERMINATION OF THE WALL VARIABLES WITHIN THE ZONAL MODEL OF RADIATION INSIDE A PULVERIZED COAL-FIRED FURNACE

Determination of the wall variables (wall emissivities, wall temperatures, and heat fluxes) when the zonal model of radiation is used in numerical simulations of processes inside a pulverized coal-fired furnaces is described. Two methods for determination of the wall variables, i.e., a repeated run of numerical simulation (RRNS) and a temporary correction of the total exchange areas (TCTEA) are compared. Investigation was carried out for three values of the flame total extinction coefficient and four values of the initial wall emissivities. Differences of the wall variables were determined using the arithmetic means (AMs) of the relative differences. The AMs of the relative differences of the wall variables increased with an increase in the flame total extinction coefficient and changed a little with an increase in the initial values of the wall emissivities. For the selected furnace, the smallest differences of the wall variables were obtained for Kt=0.3 m-1 and ew,in=0.7. Although both methods can be used for determination of the wall variables, the RRNS method was recommended because the manipulation with files was easier for it. mmended because the manipulation with files was easier for it.

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.

Determination and evaluation of the operation characteristics for two configurations of combined heat and power systems depending on the heating plant parameters in low-temperature geothermal applications

This paper analyzes impact of the required heating plant parameters on the Organic Rankine Cycle (ORC) power plant and the total plant behavior for two connections of CHP systems; they are the parallel plant and CHP integration according to Glewe-plant, Germany. And also, degree of utilizing the geothermal heat source will be discussed, and all CHP systems presented in the literature will be compared under the same conditions. R134a as working fluid in power plant will be employed. Exergy efficiency, net output power of ORC, irreversibility especially with exhausted geothermal water and the total heat exchange areas will be evaluated. From the calculations, it could be concluded that when operating the power plant in the both aforementioned CHP connections, its performances will be destructed at high heating plant parameters. So the compromised values of the low return temperatures and the heat exchange areas will enhance the power production and the performance of the total CHP systems at unchanged heat demand and supply temperature. The supply temperature does not have any effects on the power generation in case of the parallel connection, while the high values of this temperature affect negatively the other integration. The analysis also proved that the increasing heat demand will reduce the ORC productivity, but it will enhance the heat source utilization. The comparison between the CHP plants showed that the parallel connection is more economical and the series connection is energetically more efficient, while the integration according to Glewe-plant does not provide significant optimization. Finally, it could be noticed that the maximal optimized mechanical power in all present CHP configurations is so restricted, where it does not surpass 50% of the maximal power produced by stand-alone ORC plant.

The Re-Plating Algorithm for Radiation Total Exchange Area Calculation

Great efforts have been made to date toward modeling nongray radiative heat transfer accurately. In this article, a new version of the plating algorithm, designated the re-plating algorithm, for total exchange areas (TEAs) calculation from direct exchange areas (DEAs) for nongray radiative problems is presented. The re-plating algorithm calculates TEAs for a given band number b from those of band number b − 1 by performing successive re-plating procedures. The effectiveness of the new algorithm is demonstrated for thermal modeling of an aluminum brazing furnace and a glass treatment furnace. CPU requirements for TEA calculation were reduced significantly.

Reducing CPU Time for Radiative Exchange and Transient Heat Transfer Analysis Using Zone Method

CPU time for radiative heat transfer analysis using the zone method is greatly reduced. Reduction in CPU time is attributed to the development of a simplified version of the plating algorithm for calculation of total exchange areas (TEAs) and of a model reduction algorithm for eliminating low-energy-level exchange areas from the matrix of radiative transfer. The accuracy and efficiency of the algorithms are examined for a windscreen bending furnace and a gas quenching chamber. Total CPU time is reduced by a factor of 17 for both applications.

APPLICATION OF THE MONTE CARLO METHOD IN THE SOLUTION OF RADIATION HEAT TRANSFER IN PARTICIPATING MEDIA

The temperatures of the gases produced in combustion processes are very high so thermal radiation constitutes an important heat transfer mechanism in industrial furnaces. Most furnaces can be modeled as gray enclosures containing non-gray gases. The radiation heat transfer can be obtained with the aid of the weighted-sum-of-gray-gases model, determining the zonal exchange areas for each of the gray gases considered in the sum. For some enclosures with simple geometries, there are correlations to obtain the direct exchange-areas which can be used to determine the total exchange areas. However, for enclosures with complex geometries, determining the direct exchange areas can become a difficult task. In this case, the use of the Monte Carlo method is advantageous, for it allows one to approach geometric complexities without additional complications. Therefore, the method was applied to compute total exchange areas in enclosures containing participating media. Two cases were considered: cylindrical enclosures and enclosures that have generic geometries formed from cube combinations. The results presented a good agreement with solutions available in the literature.

The Zone Method: A New Explicit Matrix Relation to Calculate the Total Exchange Areas in Anisotropically Scattering Medium Bounded by Anisotropically Reflecting Walls

A new explicit matrix relation for the calculation of the total exchange areas (TEA) in emitting, absorbing and anisotropically scattering semi-transparent medium bounded by emitting, absorbing and anisotropically reflecting walls has been established. It has been used to directly determine the TEA as a function of radiative properties and geometry of the medium and its boundaries. Computation calls for direct exchange areas (DEA) and indirect exchange areas (IEA). A new definition of these exchange areas reduces their integration order and provides practical energy balance relations for their computation in the case of complex geometry elements. The new formulation is applied in the case of an emitting, absorbing and linearly anisotropic scattering semi-transparent slab bounded by black surfaces. This method is also applicable to nongray medium using the weighted sum of gray gases model.

Startup analysis of oil-fired furnace – the smoothing Monte Carlo model approach

A multi-dimensional mathematical thermal model of the oil-fired furnace has been developed. Radiation calculation of this model is based on the Hottel's zone method incorporating with the statistical Monte Carlo method to determine the total exchange areas. The whole furnace is divided into 4 gaseous zones and 18 surface zones. The Monte Carlo method integrated with the least square smoothing technique considering both conservation and reciprocity is used to evaluate the total exchange areas, i.e. surface–surface, surface–gas, gas–gas and gas–surface, directly for both the absorbing and emitting media. A better accuracy is achieved in the determination of the total exchange areas by using the proposed smoothing Monte Carlo method.

Multidimensional numerical simulation of heat radiation in direct injection diesel engines

A multidimensional theoretical model of radiation heat transfer in the cylinder of a direct injection (DI) diesel engine has been developed, which includes submodels of heat release, geometrical description, radiation temperature, soot formation and oxidation, the absorption coefficient and the Monte Carlo method for total exchange areas. In this code, the cylinder is divided into 10 surface zones and four gas zones. The Monte Carlo method integrated with a smoothing technique considering reciprocity and conservation is used to calculate the radiation total exchange areas directly for both the absorbing—emitting media and the complex structure of the cylinder. Using the multi—dimensional approach, the variation in radiant heat transfer with crank angle can be obtained across the whole combustion chamber. The computed results are analysed and discussed in the present study, and they are found to be in agreement with the experimental results.

Development of Fast Algorithm for Radiative Heat Transfer in Non-Gray-Gas Systems Surrounded by Gray Walls.

A fast algorithm is developed to solve radiative heat transfer problems is non-gray gas system surrounded by gray walls. In the problem, the distribution of the gas temperature and the wall heat flux in non-gray gas are estimated. In the present study, the time consuming Monte Carlo method is used only outside the iterational loop of the temperature convergence. For the purpose, the Rd values, the ratio of the radiative energy absorbed by an element to the energy emitted from a source element, are separated into two parts, the absorption-coefficient-dependent part and independent part. The calculated values of Rd are used as the input data for direct exchange areas for the zone method to obtain total exchange areas. The new method reduces the computation time by one sixth compared to the conventional Rd method. Therefore, the fast Rd method combined with zone method is advantageous for the analysis is non gray gas systems. Comparison between the results of the present method and exact solution shows the validity of the present method.

Modelling of radiative heat transfer in enclosures with obstacles

Radiation models suitable for incorporation in reactive fluid flow codes are extended to calculate radiation in enclosures containing obstacles of very small thickness. The discrete transfer, the discrete ordinates and the finite volume method are employed to predict the heat transfer in two-dimensional enclosures and the results are compared with zone method calculations, with the total exchange areas determined by the Monte-Carlo method. All the methods predict similar heat fluxes, but the computational requirements are different. The discrete ordinates and the finite volume method are the most economical ones. An application to a utility boiler is also presented.

Monte Carlo simulation of indoor radiant environment

AbstractThis paper describes a numerical method of radiant environment analysis in a complicated enclosure containing human bodies and furniture. An arbitrary configuration expressed in a three‐dimensional co‐ordinate system can be treated by this method. A unique space index and another surface index are proposed to specify the geometry of solid body and surface in the enclosure. The Monte Carlo method is used to determine direct interchange areas, which are then transformed into total exchange areas using the zone method. Energy balance equations accounting for thermal radiation, convection, wall conduction and air ventilation are then formulated for each solid surface segment in the enclosure. A human body model with skin temperatures and clothing is also proposed to simulate its heat release and to predict local thermal sensation around the body. As a practical application, this method is applied to the analysis of the radiant environment in a floor‐heated meeting room with eight people seated around a table.

Development of the zone method for linearly-anisotropic scattering media

The purpose of this study is to extend the zone method to gray, absorping, emitting and linearly-anisotropic scattering media enclosed in an infinite plane layer. The medium is assumed to be homogeneous and has a refractive index of unity. The boundary surfaces are gray, diffusely emitting and reflecting, and opaque with constant temperature. The governing radiative transport equation is solved. The resulting integral expressions are discretized under the assumption of uniform temperature within each zone. The divergence of the radiative flux and net wall radiation terms are expressed in terms of total exchange areas (TEA). Expressions for special cases are presented and the results are compared with those of a previous study. The properties of TEA are also studied, and the results are summarized. The zone method is applied to radiative equilibrium and to heat transfer by combined conduction and radiation. Good agreement with results from other methods indicates the accuracy of the zone method as well as its compatibility with other modes of heat transfer. Based on the formulation, the same approach may be applied to develop zone method expressions for multi-dimensional problems.

Radiative and conductive transfer for a real gas in a cylindrical enclosure with gray walls

The purpose of this study is to examine the interaction of radiative and conductive transfer for a radiatively participating real gas stagnant in a cylindrical enclosure with gray diffuse walls. Consideration of reflecting boundaries represents an extension of previous black wall studies. Examination of radiative transfer was made by the zone method with gas radiative properties furnished by the weighted sum of gray gases model. Directed flux areas are expressed as the weighted sum of gray gas total exchange areas which are evaluated using the matrix formulation method from direct exchange areas. Axial and radial gas temperatures are examined along with wall heat flux or temperature for respective cases of either specified wall temperatures or heat fluxes. Emphasis is placed on examining results to show the effects of wall emittance and duct diameter. Results for heat generation within the gas are also presented.

The Exchange Factor Method: An Alternative Basis for Zonal Analysis of Radiating Enclosures

In zonal analysis of an enclosure containing a radiatively participating medium, the volume and bounding surface are divided into volume and area elements which are assumed to be isothermal. For a system of M elements consisting of N surfaces and Γ volume elements (M = N + Γ), M2 relationships (direct- or total-exchange areas of conventional zonal analysis) define all possible radiant interchange between element pairs. Due to reciprocity there are at most M(M + 1)/2 unique direct-exchange areas. The use of symmetry may greatly reduce the number of unique exchange areas. In the alternative form presented, exchange factors are defined such that a gray medium’s gas-to-gas exchange factors describe only the redistribution of radiative source terms. Only surface-to-surface and surface-to-gas (gas-to-surface) relationships are required to wholly define the system in radiative equilibrium. That is, a system in radiative equilibrium may be characterized by as many as Γ(Γ + 1)/2 fewer factors. These same exchange factors may be augmented by gas-to-gas exchange factors to analyze media not in radiative equilibrium. In an isotropically scattering, gray medium, exchange factors are functions of system geometry and total extinction only. The degree of extinction due to scattering does not affect exchange factors. Transformations between direct-exchange areas and exchange factors are developed.

A unified matrix formulation for the zone method: a stochastic approach

A new approach based on the Markov chain theory is utilized to derive three explicit matrix relations for the total exchange areas of the zone method. These relations are identical to those published earlier. The same method is used to derive a single explicit matrix relation for the total exchange areas. This expression is so general that it covers the same function as the aforementioned relations.