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The solution of radiative heat transfer problems in participating media is often obtained using the standard discrete ordinates method (SDOM). This method produces anomalies caused by ray effects if radiative boundary conditions have discontinuities or abrupt changes. Ray effects may be mitigated using the modified discrete ordinates method (MDOM), which is based on superposition of the solutions obtained by considering separately radiation from the walls and radiation from the medium. The purpose of this paper is to study the role of ray effects in combined conduction‐radiation problems and investigate the superiority of the MDOM over SDOM.

The MDOM has been used to calculate radiative heat transfer in irregular geometries using body‐fitted coordinates. Here, the blocked‐off region concept, originally developed in computational fluid dynamics, is used along with the finite volume method and SDOM or MDOM to solve combined conduction‐radiation heat transport problems in irregular geometries. Enclosures with an absorbing, emitting and isotropically or anisotropically scattering medium are analyzed.

The results confirm the capability of the MDOM to minimize the anomalies due to ray effects in combined heat transfer problems, and demonstrate that MDOM is more computationally efficient than SDOM.

The paper demonstrates the application of MDOM to combined conduction‐radiation heat transfer problems in irregular geometries using blocked‐off method.

This paper aims to present an evolutionary algorithm (EA) to accelerate the convergence for the radiative transfer equation (RTE) numerical solution using high-order and high-resolution schemes by the relaxation coefficients optimization.

The objective function minimizes the residual value difference between iterations in each control volume until its difference is lower than the convergence criterion. The EA approach is evaluated in two configurations, a two-dimensional cavity with scattering media and absorbing media.

Experimental results show the capacity to obtain the numerical solution for both cases on all interpolation schemes tested by the EA approach. The EA approach reduces CPU time for the RTE numerical solution using SUPERBEE, SWEBY and MUSCL schemes until 97% and 135% in scattering and absorbing media cases, respectively. The relaxation coefficients optimized every two numerical solution iterations achieve a significant reduction of the CPU time compared to the deferred correction procedure with fixed relaxation coefficients.

The proposed EA approach for the RTE numerical solution effectively reduces the CPU time compared to the DC procedure with fixed relaxation coefficients.

This paper seeks to review the literature on methods for solving the radiative transfer equation (RTE) and integrating the radiant energy quantities over the spectrum required to predict the flow, the flame and the thermal structures in chemically reacting and radiating combustion systems.

The focus is on methods that are fast and compatible with the numerical algorithms for solving the transport equations using the computational fluid dynamics techniques. In the methods discussed, the interaction of turbulence and radiation is ignored.

The overview is limited to four methods (differential approximation, discrete ordinates, discrete transfer, and finite volume) for predicting radiative transfer in multidimensional geometries that meet the desired requirements. Greater detail in the radiative transfer model is required to predict the local flame structure and transport quantities than the global (total) radiation heat transfer rate at the walls of the combustion chamber.

The RTE solution methods and integration of radiant energy quantities over the spectrum are assessed for combustion systems containing only the infra‐red radiating gases and gas particle mixtures. For strongly radiating (i.e. highly sooting) and turbulent flows the neglect of turbulence/radiation interaction may not be justified.

Methods of choice for solving the RTE and obtaining total radiant energy quantities for practical combustion devices are discussed.

The paper has identified relevant references that describe methods capable of accounting for radiative transfer to simulate processes arising in combustion systems.

This paper sets out to give an overview about state‐of‐the‐art optical tomographic image reconstruction algorithms that are based on the equation of radiative transfer (ERT).

An objective function, which describes the discrepancy between measured and numerically predicted light intensity data on the tissue surface, is iteratively minimized to find the unknown spatial distribution of the optical parameters or sources. At each iteration step, the predicted partial current is calculated by a forward model for light propagation based on the ERT. The equation of radiative is solved with either finite difference or finite volume methods.

Tomographic reconstruction algorithms based on the ERT accurately recover the spatial distribution of optical tissue properties and light sources in biological tissue. These tissues either can have small geometries/large absorption coefficients, or can contain void‐like inclusions.

These image reconstruction methods can be employed in small animal imaging for monitoring blood oxygenation, in imaging of tumor growth, in molecular imaging of fluorescent and bioluminescent probes, in imaging of human finger joints for early diagnosis of rheumatoid arthritis, and in functional brain imaging.

The aim of this paper is to present advanced experimental–numerical methods for identification of spectral absorption and scattering properties of highly porous ceria ceramics in the range of semi-transparency at room and elevated temperatures.

At room temperature, a period of quasi-steady oscillations of the sample surface temperature generated in response to recurrent laser heating at fixed values of the maximum and minimum temperature of the irradiated surface is measured along with the normal-hemispherical reflectance. Radiative properties are then identified using a combined heat transfer model. At elevated temperatures, an analytical solution proposed in an earlier study for zirconia ceramics is used to retrieve spectral absorption coefficient of ceria ceramics from the measured normal emittance.

This method can be used to obtain small absorption coefficient of ceria ceramics at room temperature. The required measurements of both the normal-hemispherical reflectance and the period of quasi-steady oscillations of the irradiated surface temperature of the ceramics sample between fixed values of the maximum and minimum temperatures can be readily conducted using thermal laboratory equipment. Another method has been suggested for identification of the spectral absorption coefficient of ceria ceramics at elevated temperatures. This method is based on a relation between the measured normal emittance of an isothermal sample and the absorption coefficient.

This paper sets out to implement bounded high‐order (HO) resolution schemes in a hybrid finite volume/finite element method for the solution of the radiative transfer equation.

The hybrid finite volume/finite element method had formerly been developed using the step scheme, which is only first‐order accurate, for the spatial discretization. Here, several bounded HO resolution schemes, namely the MINMOD, CLAM, MUSCL and SMART schemes, formulated using the normalized variable diagram, were implemented using the deferred correction procedure.

The results obtained reveal an interaction between spatial and angular discretization errors, and show that the HO resolution schemes yield improved accuracy over the step scheme if the angular discretization error is small.

Although the HO resolution schemes reduce the spatial discretization error, they do not influence the angular discretization error. Therefore, the global error is only reduced if the angular discretization error is also small.

The use of HO resolution schemes is only effective if the angular refinement yields low‐angular discretization errors. Moreover, spatial and angular refinement should be carried out simultaneously.

The paper extends a methodology formerly developed in computational fluid dynamics, and aimed at the improvement of the solution accuracy, to the hybrid finite volume/finite element method for the solution of the radiative transfer equation.

A new way of solving the steady‐state coupled radiative‐conductive problem in semi‐transparent media is proposed. An angular discretization technique is applied in order to express the radiative transfer equation (RTE) in an inhomogeneous system of linear differential equations associated with Dirichlet boundary conditions. The system is solved by a direct method, after diagonalizing the characteristic matrix of the medium. The RTE is coupled with the nonlinear heat conduction equation. A simulation of a real semi‐transparent medium composed of silica fibers is illustrated. Comparison with results of other methods validates the new model. Moreover, the general scheme is easy to code and fast. The algorithm proved to be robust and stable.

Carbonate-based heterogeneous reacting systems are investigated for the applications of thermochemical carbon dioxide capture and energy storage. This paper aims to review recent progress in numerical modeling of thermal transport phenomena in such systems.

Calcium oxide looping is selected as the model carbonate-based reacting system. Numerical models coupling heat and mass transfer to chemical kinetics are reviewed for solar-driven calcium oxide looping on the sorbent particle, particle bed, and reactor levels.

At the sorbent particle level, a transient numerical model of heat and mass transfer coupled to chemical kinetics has been developed for a single particle undergoing cyclic calcination and carbonation driven by time-periodic boundary conditions. Modeling results show cycle times impact the maximum sorbent utilization and solar-to-chemical energy efficiency. At the reactor level, a model of heat and mass transfer coupled to chemical kinetics of calcination of a packed-bed reactor concept has been developed to estimate the reactor’s performance. The model was used to finalize reactor geometry by evaluating pressure drops, temperature distributions, and heat transfer in the reactor.

Successful solar thermochemical reactor designs maximize solar-to-chemical energy conversion by matching chemical kinetics to reactor heat and mass transfer processes. Modeling furthers the understanding of thermal transport phenomena and chemical kinetics interactions and guides the design of solar chemical reactors.

This study aims to methodologically investigate heat transfer effects on reacting flow inside a liquid-fueled, swirl-stabilized burner. Furthermore, particular attention is paid to turbulence modeling and the results of Reynolds-averaged Navier–Stokes and large eddy simulation approaches are compared in terms of velocity field and flame temperature.

Simulations consist liquid fuel distribution using Eulerian–Lagrangian approach. Flamelet-Generated Manifold combustion model, which is a mixture fraction-progress variable formulation, is used to obtain reacting flow field. Discrete ordinates method is also added for modeling radiation heat transfer effect inside the burner. As a parametric study, different thermal boundary conditions namely: adiabatic wall, constant temperature and heat transfer coefficient are applied. Because of the fact that the burner is designed for operating with different materials, the effects of burner material on heat transfer and combustion processes are investigated. Additionally, material temperatures have been calculated using 1 D method. Finally, soot particles, which are source of luminous radiation in gas turbine combustors, are calculated using Moss-Brookes model.

The results show that the flow behavior is obviously different in recirculation region for both turbulence modeling approach, and this difference causes change on flame temperature distribution, particularly in the outer recirculation zone and region close to swirler. In thermal assessment of the burner, it is predicted that material of the burner walls and the applied thermal boundary conditions have significant influence on flame temperature, wall temperature and flow field. The radiation heat transfer also makes a strong impact on combustion inside the burner; however, luminous radiation arising from soot particles is negligible for the current case.

These types of burners are widely used in research of gas turbine combustion, and it can be seen that the heat transfer effects are generally neglected or oversimplified in the literature. This parametric study provides a basic understanding and methodology of the heat transfer effects on combustion to the researchers.

Notes that, in a full‐scale application of the Monte Carlo method for combined heat transfer analysis, problems usually arise from the large computing requirements. Here the method to overcome this difficulty is the parallel execution of the Monte Carlo method in a distributed computing environment. Addresses the problem of determination of the temperature field formed under the assumption of radiative equilibrium in an enclosure idealizing an industrial furnace. The medium contained in this enclosure absorbs, emits and scatters anisotropically thermal radiation. Discusses two topics in detail: first, the efficiency of the parallelization of the developed code, and second, the influence of the scattering behavior of the medium. The adopted parallelization method for the first topic is the decomposition of the statistical sample and its subsequent distribution among the available processors. The measured high efficiencies showed that this method is particularly suited to the target architecture of this study, which is a dedicated network of workstations supporting the message passing paradigm. For the second topic, the results showed that taking into account the isotropic scattering, as opposed to neglecting the scattering, has a pronounced impact on the temperature distribution inside the enclosure. In contrast, the consideration of the sharply forward scattering, that is characteristic of all the real combustion particles, leaves the predicted temperature field almost undistinguishable from the absorbing/emitting case.