Particle–gas reacting flow under concentrated solar irradiation

A transient heat transfer model is developed for a reacting flow of CH₄ laden with carbon particles directly exposed to concentrated solar radiation and undergoing thermal decomposition into carbon and hydrogen. The unsteady mass and energy conservation equations, coupling convective heat and mass transfer, radiative heat transfer, and chemical kinetics for a two-phase solid–gas flow, are formulated and solved numerically for both phases by Monte Carlo and finite volume methods using the explicit Euler time integration scheme. Parametric study is performed with respect to the initial particle diameter, volume fraction, gas composition, and velocity. Validation is accomplished by comparing temperatures and reaction extent with those measured experimentally using a particle-flow solar reactor prototype subjected to concentrated solar radiation. Smaller particles and/or high volume fractions increase the optical thickness of the medium, its radiative absorption and extinction coefficients, and lead to higher steady-state temperatures, reaction rates, and consequently, higher extent of chemical conversion.     

COMBINED MACROSCOPIC AND MICROSCOPIC ANALYSIS OF THERMOELASTOPLASTIC STRESSES OF A FUNCTIONALLY GRADED MATERIAL PLATE

This article discusses the elastoplastic thermal stresses induced in a ceramic-metal functionally graded material plate (FGP) subjected to a thermal load taking the fabrication process into consideration. The FGP is divided into three regions. The first region near the cooling, metal, surface of the FGP is produced by ceramic particle-reinforced metal; while the second region near the heat-resistant, ceramic, surface is the opposite; and the third middle region is perfectly mixed by the metal and the ceramic. The first and second regions are governed by the particle-reinforced thermoelastoplastic constitutive equation, while the third region is expressed by the macroscopic analysis. Three cases of the temperature condition are studied: cooling from the fabricated temperature to room temperature, heating from the room temperature, and heating after cooling from the fabricated temperature. The temperature-dependent material properties are considered, and the particle volume fraction is assumed to vary according to a power function along the thickness direction of the FGP. The effect of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix, and the stress in the particle in the FGP are discussed and illustrated in figures. Also, the effect of the fabricated temperature on the maximum tensile matrix stress is discussed.     

Coupled radiation and flow modeling in ceramic foam volumetric solar air receivers

Ceramic foams are promising materials for the absorber of volumetric solar air receivers in concentrated solar thermal power (CSP) receivers. The macroscopic temperature distribution in the volumetric solar air receiver is crucial to guarantee that volumetric solar air receivers work steadily, safely and above all, efficiently. This study analyzes the temperature distribution of the fluid and solid phases in volumetric solar air receivers. The pressure drop in the ceramic foams and the interfacial heat transfer between the flowing fluid and solid are included in the model. The radiative heat transfers due to concentrated solar radiation absorption by the ceramic foam and the radiation transport in the media were modeled with the P₁ approximation. The energy fields of the fluid and solid phases were obtained using the local thermal non-equilibrium model (LTNE). Comparison of the macroscopic model with experimental results shows that the macroscopic model can be used to predict the performance of solar air receivers. Sensitivity studies were conducted to analyze the effects of velocity, porosity, mean cell size and the thermal conductivity of the solid phase on the temperature fields. The results illustrate that the thermal non-equilibrium phenomena are locally important, and the mean cell size has a dominant effect on the temperature field.     

Monte Carlo radiative transfer simulation of a cavity solar reactor for the reduction of cerium oxide

Radiative heat transfer in a solar thermochemical reactor for the thermal reduction of cerium oxide is simulated with the Monte Carlo method. The directional characteristics and the power distribution of the concentrated solar radiation that enters the cavity is obtained by carrying out a Monte Carlo ray tracing of a paraboloidal concentrator. It is considered that the reactor contains a gas/particle suspension directly exposed to concentrated solar radiation. The suspension is treated as a non-isothermal, non-gray, absorbing, emitting, and anisotropically scattering medium. The transport coefficients of the particles are obtained from Mie-scattering theory by using the optical properties of cerium oxide. From the simulations, the aperture radius and the particle concentration were optimized to match the characteristics of the considered concentrator.     

MHD natural convection heat and mass transfer flow over an inclined porous plate with thermophoresis and nonlinear thermal radiation effects

This study examined magnetohydrodynamic natural convection mass and heat transfer flow of an electrically conducting and viscous incompressible fluid over an inclined porous plate with thermophoresis, suction/injection, and uniform magnetic field. The mathematical model governing the fluid behavior surrounding an inclined plate is solved through the Runge–Kutta–Fehlberg fourth–fifth order after utilizing the shooting method. The implication of active dimensionless parameters in the governing equations is fully discussed in detail. The results obtained show that, in the existence of nonlinear thermal radiation and suction/injection, the heat transfer rises with the increase in the angle of inclination but it decreases with the mass transfer and plate shear stress. Furthermore, the heat transfer rate experiences a serious setback due to the increase in the buoyancy force but improves the plate shear stress. The mass transfer is directly proportional to the thermophoresis effect. In addition, Particle suction increases the velocity and temperature curves while it declines the concentration profile, but the opposite is valid for injection. Nonlinear thermal radiation positively affects the temperature, velocity, and concentration profiles. The Lorentz force suppresses the fluid transport and retard the rate of particle concentration, but promotes the fluid temperature distribution. It is also deduced that increasing the rate of particle suction from 0 to 1, accounts for over 76% increase in the particle deposition at the plate surface. However, increasing the rate of particle injection from 0.004 to 0.250 accounts for an over 83% decrease in the particle deposition at the plate surface.     

THERMAL STRESSES IN PARTIALLY ABSORBING FLAT PLATE DUE TO SUDDEN INTERRUPTION OF STEADY-STATE ASYMMETRIC RADIATION,I: CONVECTIVE COOLING AT REAR SURFACE

An analysis is presented of the thermal stresses in a partially absorbing flat plate due to sudden interruption of steady-state asymmetric thermal radiation on the front face with convection cooling at the rear face. Maximum transient tensile stresses occur in the rear surface and are almost independent of the heat transfer coefficient, h. For optical thicknesses of ≥ 0.5 μa, the maximum tensile stress initially rises to reach a peak and then decreases with time. In contrast, for thicknesses ≤ 0.5 μa, the stresses decrease monotonically. It is shown that a plot of nondimensional stress as a function of nondimensional time for a given value of pa and h does not result in a universal plot from which thermal stresses can be obtained for any value of plate thickness.     

The calculation and analysis of glass-to-metal sealing stress in solar absorber tube

The failure or degradation of solar absorber tubes is the single largest cost factor for current parabolic trough solar power plant. The main failure reason is that there are residual stresses in the glass-to-metal joint which are generated during the cooling process of sealing. According to the thin shell theory and thermal stress theory, this paper presents the analytic solution for the glass-to-metal sealing residual stress. It also analyses how the thickness of glass tube, thickness of metal ring, and thermal expansion coefficient affect the residual stress distribution. In order to verify the calculation results, the photoelastic technique is used to measure the residual stress and the tensile test is used to obtain the point of the most dangerous stress and the tensile strength for the sealed specimens. It can be concluded that the maximum tensile stress happens at some distance near the sealing interface on the outer surface of glass tube. The seal strength increases when the thickness of the glass tube is increased. The analytic solution is proved feasible to analyze the residual stress of glass-to-metal seals in solar absorber tubes.     

Absorption of thermal radiation in large semi-transparent particles at arbitrary illumination of the polydisperse system

An approximate theoretical model for nonuniform absorption of the external thermal radiation in a large semi-transparent spherical particle is suggested. As applied to heat transfer problems with diffuse radiation in the wide spectral range, the asymmetric illumination of single particle is considered at each spectral interval as a uniform illumination from backward and forward hemispheres (with respect to the direction of spectral radiation flux). The Mie theory is employed in calculations for particles illuminated from a hemisphere. The modified differential approximation suggested earlier by the author is used in the case of spherically symmetric illumination. Approximate analytical relations for distribution of absorbed radiation power inside a particle are obtained. Results of calculations for typical polydisperse sprays of water and diesel fuel droplets are presented.     

One-dimensional model of solar thermal reactors for the co-production of hydrogen and carbon black from methane decomposition

The solar thermal decomposition of methane is a promising route for the large scale production of hydrogen and carbon black with zero CO₂ emissions, however careful control of the reactor is required to ensure product particles of specific sizes. A one-dimensional model employing a sectional method is developed to simulate the evolution of polydisperse fresh and seed particle populations in an indirectly heated solar reactor. The model accounts for the homogeneous nucleation of fresh particles, the heterogeneous growth of the fresh and seed particles, particle coagulation, and the growth of carbon on the walls of the reactor from heterogeneous reaction and particle deposition. The heat transport mechanisms modelled include wall-gas convection, wall-particle radiation exchange, particle-gas convection and heat release from chemical reaction. The model is validated in terms of methane conversion against a 10 kW experimental solar reactor and used to extract kinetic parameters for the homogeneous and heterogeneous reaction paths. The model shows promise as a quick and simple tool for the design and control of industrial scale solar reactors.     

THERMAL STRESSES IN A PARTIALLY ABSORBING FLAT PLATE ASYMMETRICALLY HEATED BY CYCLIC THERMAL RADIATION AND COOLED BY CONVECTION

Abstract

An analysis is presented for the temperatures and thermal stresses in a partially absorbing flat plate subjected to normally incident cyclic thermal radiation on the front face, and cooled by convection on the rear face.

The resulting temperature and stress responses are cyclic in nature, with the temperatures and stresses in the center and the back face lagging behind those in the front face. The amplitude of the temperature fluctuation is found to be a maximum in the front face. During the initial thermal cycles the maximum stress in the plate is compressive. In contrast, when the plate approaches thermal equilibrium after many cycles, the maximum stress is tensile. The values of the maximum tensile and compressive stresses were found to depend on the frequency of the incident cyclic radiation.     

OXIDATION RATES OF CARBON BLACK PARTICLES EXPOSED TO CONCENTRATED SUNLIGHT

Small carbon particles have excellent absorption properties for concentrated solar radiation. Oxidation rates of micron and submicron sized carbon black particles have been investigated under high flux solar conditions. These oxidation rates are required for a thermal model of direct absorbing particle receivers as well as for the development of solar chemical technologies to treat toxic wastes. An experimental set-up has been developed for kinetic measurements in the solar furnace of the DLR. In the temperature range 600–900°C no significant acceleration of the oxidation could be observed due to insolation up to irradiances I≤700 kW m⁻² as compared to thermal oxidation of carbon particles (Derussol C©).     

Steady state and transient thermal stress analysis in planar solid oxide fuel cells

Resulting from elevated temperatures the major structural problem foreseen with planar SOFCs is their thermal stress. Due to the brittle nature of ceramic material, operation in or near the material plastic limit can be very critical. Therefore stress levels must always be kept below the tensile and shear limits. The analysis is focused on determination of the stress caused by the difference in thermal expansion coefficients when high temperature gradients occur in the SOFC layers during steady state and transient operation (heat-up, start-up and shut-down). Utilizing an in-house developed tool for assessment of the electrochemical and thermal performance of a bipolar planar cell the input temperature profiles are generated for a finite element analysis code to predict thermal component of the stress. The failure criterion adopted is based on the strength of the cell materials and the principal stresses developed by the thermal loading. To visualize the stress concentration in the fuel cell layers, maximum principal stress is calculated and compared with the yield strength of the SOFC materials found in the literature. The in-house code is capable to predict both steady state and dynamic temperature profiles. Of particular importance is the knowledge gained of the transient stress in the cell, which can be used to establish control parameters during transient operations.     

Practical procedure for predicting non-uniform temperature on the exposed face of arch dams

Temperature distribution on the exposed face (especially the downstream face) of arch dams is non-uniform, to a certain extent, due to the variation in solar radiation striking the surface. However, the temperature at the same elevation across the dam axis is generally assumed to be uniform in the design specifications for arch dams because there is no accepted procedure for defining the non-uniform temperature field. In this paper, a practical model for predicting the non-uniform temperature of the exposed face is presented by considering both solar radiation and shading effects. The ASHRAE clear sky model was adopted to calculate the solar radiation, and a ray-tracing algorithm was used to analyze the shade of surrounding terrain and the structure per se. The real-life case study presented in this study shows that the proposed model was effective in simulating and accessing reasonable thermal distribution. Subsequently, the case study also reveals that the non-uniform temperature had a significant effect on surface thermal stress and crack propagation.     

Performance Characteristics of a Volumetric Solar Receiver: Presence of an Absorber Plate with a Selective Surface

Performance characteristics of a concentrated solar volumetric absorber are examined numerically. The thermal system considered consists of parabolic trough, glass tube, absorbing plate, and slurry containing 7% lauric acid as a phase change material and water as a carrier fluid. To assess the effect of the absorbing plate on performance characteristics, two locations of the absorbing plate on the glass tube surface are incorporated in the analysis. A selective surface is considered at the absorber plate surface for improved absorption of solar radiation and reduced thermal emission due to temperature increase at the surface. Temperature ratio, gain parameter, and pump power loss parameters are introduced to quantify the performance characteristics of the volumetric receiver. The study is extended to include the effect of Reynolds number on the receiver performance characteristics. A heating model incorporating radiation, convection, and conduction is adopted to simulate the thermal process. It is found that the gain parameter of the concentrated solar volumetric receiver improves by 15% when the absorber plate is located at the left face of the glass tube opposing the trough surface. The effect of Reynolds number on gain parameter is found to be inconsiderable.     

A preliminary experimental investigation on characteristics of natural convection based on solar thermal collection using supercritical carbon dioxide

In this paper, an experimental work is carried out to investigate the characteristics of solar thermal collection using supercritical CO₂. This solar thermal conversion is based on supercritical CO₂ natural convection, which is much easily induced because a small change in temperature can result in large change in density close to the critical point. In addition, its critical temperature is 31.1°C and low enough to be easily reached in the low‐temperature solar thermal conversion system. The obtained results show that the supercritical CO₂ flow rate is smooth curve and not affected by the sudden variation of the solar radiation. The solar thermal conversion operation process can be divided into three periods: starting‐up, transition, and stable period. When the system reaches the stable period, the CO₂ flow rate will keep at a high value even if the solar radiation stays at a low level. It is also found that the smaller local solar radiation variation is, the better ability of keeping the flow rate near the peak level the supercritical CO₂ fluid owns. It is also found that a small pressure difference can drive a supercritical CO₂ flow with high flow rate. Furthermore, high solar thermal conversion efficiency is found at a high mass flow rate and under operation pressure near the critical point. Copyright © 2012 John Wiley & Sons, Ltd.     

Infrared temperature measurements on solar trough absorber tubes

The temperature distribution on solar trough absorber tubes determines thermal losses and hotspots can lead to material stress and limit absorber tube lifetime. The concentrated solar radiation, however, makes it difficult to determine the temperature on solar absorbers. Temperature sensors that require contact to the measurement object are not appropriate and even pyrometry fails, when external light sources interfere. Only solar-blind pyrometry offers reliable temperature readings without perturbation through reflected solar radiation. This paper presents two concepts for a pyrometric solar-blind measurement on solar trough absorber tubes. One solar-blind approach is a spectral measurement range in regions, where the solar spectrum shows gaps due to the discrete absorption of the atmosphere. Another possibility for a solar-blind pyrometric temperature measurement results from the optical behavior, i.e. the distinct angle dependence of the directional reflectance and emittance of a typical selective trough absorber coating. First experimental results are shown and the accuracy and performance advantages and disadvantages of the setups are reported and discussed.     

Impact of variation of nanoparticle shape on free convective MHD water-based flow of Hamilton–Crosser model radiative nanofluids over a permeable surface

The present analysis explores the impact of shape of the nanoparticles on the conducting nanofluids past a porous surface. The electrically conducting fluid possesses enhanced physical properties due to the thermal buoyancy, and the radiative heat energy enhances the thermal properties of the water-based nanofluid. The suitable choice of a nanoparticle, that is, considering the metal particle like copper (Cu) and oxide particle such as TiO₂ in conjunction with the Hamilton–Crosser model thermal conductivity, augments the heat transfer properties. The appropriate transformation of similarity variable and the stream function helps to convert the leading partial differential equations to nonlinear ordinary differential equations (ODEs). Furthermore, these distorted ODEs are handled by using numerical technique such as Runge–Kutta–Fehlberg along with the shooting technique. The graphical presentation of the profiles of flow phenomena due to the interaction of relevant parameters is deployed for the physical significance, and the comparison of the present investigation shows a good agreement with the earlier results. However, the major outcomes are as follows; backflow occurs near the surface region due to the impermeable surface also increasing shape of the nanoparticle decelerates the fluid temperature and it is useful by considering the spherical shaped nanoparticles for the enhanced heat transfer.     

Thermal model for the optimization of a solar rotary kiln to be used as high temperature thermochemical reactor

The present study focuses on a thermal model describing a rotary kiln reactor. Several applications can be foreseen for this reactor, for example high temperature heat storage for thermal solar power plants. The energy is provided by concentrated solar radiation that heats up the cavity walls. A thermal model, describing the reactor behavior, is developed and validated. Particular attention is given to the radiation model, which constitutes the most important heat transfer. An innovative way of modeling the reactor aperture through a fictive surface at an imposed equivalent temperature leads to a significant decrease of the simulation time, without decreasing the precision of the solution. The model is validated by comparison first with other models, which make different assumptions and second with experimental results. After the validation, the model can be used for simulating the behavior under different operating condition or to define the possible improvements by a change of the reactor geometry such as the insulation’s thermal conductivity or thickness.     

THERMAL STRESSES IN ISOTROPIC CELL-DIVIDED PARTICLE-MATRIX SYSTEM: SPHERICAL ANDCUBIC CELLS

Thermal stresses are studied in an isotropic particle-matrix system of homogeneously distributed spherical particles in an infinite matrix. The isotropic particle-matrix system is divided into cells containing the central spherical particle embedded in the matrix and is of dimensions equal to an interparticle distance. The cell surface is assumed to be acted on by nonzero stresses derived by a criterion of a minimum of the cell elastic energy of the thermal stresses. The thermal stresses originate during a cooling process as a consequence of the difference in thermal expansion coefficients between the matrix and the particle. The formulae for the thermal stresses acting in the isotropic cell-divided particle-matrix system for the ratio of a spherical particle volume to a cell volume v_p = 0 reduce to those for the isotropic particle-matrix system of one spherical particle embedded in an infinite matrix. The thermal stresses are derived for spherical and cubic cells, depending on the spherical particle distribution.     

An estimate of stability of large solidifying droplets in fuel–coolant interaction

An initial period of surface solidification of large opaque particles of molten metal oxides is considered. It is shown that low overheating and very high melting temperature of corium lead to very fast formation of solid crust on the particle surface. The transient problem solution showed that maximal tensile stress in this crust due to pressure drop in expanding steam bubble around the particle is much less than the stress in relatively thin crust layer on the surface of alumina particle. The solidifying corium particle seems to be more stable as compared with the alumina particle of the same size. The latter is treated as one of the reason of the experimental results on relatively low explosivity of corium.