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A numerical model for evaporation along with internal radiation absorption of a non-spherical droplet is presented. In this model, the VOF method is utilized to trace the interface and the radiative transfer is taken into account by using the Monte Carlo method combined with a contour based interface reconstruction algorithm. Meanwhile, the dynamic mesh technique is applied to increase the computational efficiency. The validated model is used to investigate the radiation absorption inside prolate and oblate water droplets under infrared laser irradiation, and a parametric study for the effects of droplet’s shape and size is presented. The results reveal that the shape of droplet dominates the spectral absorptance when the droplet’s optical thickness is small, but for optically thick droplets, the radiation absorption turns to be dominated by the spectral reflectivity of the irradiated surface. For a deformable droplet under asymmetrically radiative heating, the incident radiation can significantly enhance the heat transfer and evaporation processes. In addition, the assumption of uniform radiation absorption is found to be valid to optical thin droplets, whereas this assumption will underestimate the average interface temperature and evaporation rate of droplets with large optical thickness.

Considering the existence of edge effect caused by the cut surface of struts or sintering points will affect the actual radiative transfer process in metallic foams, a three-layer structure model is constructed to obtain their spectral radiative properties. Using the double-thickness model for reference, the real spectral radiative properties of metallic foams are calculated based on transmittance spectra. To verify the feasibility of this method, transmittance spectra of nickel foams with different cell sizes and thicknesses are measured by FTIR spectrometer system in the near infrared band. Through comparing extinction coefficients obtained by traditional single-layer structure model and the three-layer structure model proposed in this paper, it is found that extinction coefficient will be underestimated by the latter method, while the deviation can reach 13% for 20ppi nickel foam and 8% for 40ppi nickel foam. Then absorption coefficient and scattering coefficient are calculated by a prediction model with parameters corrected. Based on this method, temperature influence on extinction coefficient of nickel foam is studied from 293 K to 773 K and it is found that extinction coefficient decreases with temperature in the researched band while the maximum changing rate is 2.1% in the researched band.

The radiative characterization of open-cell foams made from semitransparent solids is more complex than that made from opaque media. This study aims to understand how the component radiative properties and structural parameters of such open-cell foams affect their radiative characteristics. A radiative transfer model was established in the limit of geometric optics for the radiative characterization of a family of numerically generated Voronoi foams with open cells. It considers the reflection and refraction at the solid surface and the transmission, absorption and scattering process inside the solid phase. It is found that when the solid phase is in reality partially transparent, the opaque solid assumption will lead to inaccurate outcomes. Strongly scattering solid phase may cause much radiative energy to be rejected via reflection behavior, which will weaken the absorptive capability of the foam sheets as radiation absorbers. In addition, the radiative transfer model established was applied in three popular ceramic foams (alumina, silicon carbide and zirconia). The model shows advances in the field of analyzing and explaining the spectral radiative characteristics of ceramic foams. The present work can provide useful guidance when open-cell foams made from semitransparent media become potential candidates for thermal applications.

Ice-templated porous materials from freeze-casting have attracted widespread attentions in many research fields. Several apparatuses based on the freeze-casting have been proposed to fabricate aligned porous materials, where the unidirectional growth of ice is mainly controlled by changing temperatures at the sample ends. The thermal conduction cross the whole sample restricts the freezing process in traditional freeze-casting methods. In this paper, a new approach of freeze-casting is proposed, where the thermal gradient and the solidification rate can be controlled independently for continuous directional freezing. The lateral thermal conduction provides an effective way to produce axially homogeneous porous structural materials with unrestricted length and controllable microstructures. Moreover, the axial homogeneity can also be further improved by adding a small amount of sucrose.

For high transparent materials, the difference among the transmittances of various slabs in different thicknesses is very slight since the index of absorption is rather small. However, the divergence of transmittances is very necessary to provide multiple independent constraints for retrieving spectral intrinsic properties from transmitted data with an acceptable accuracy. A Multi-Layer-Combination (MLC) method in which multiple sheets compose a transmitted combination is proposed to provide obviously different transmittances. In this study, the measurements on MLC slabs of C-plane sapphire were performed between 0.8 and 7.0 µm from room temperature to 1800 K. For a given total thickness, the measured results show that the stacking structure of multiple layers can obviously diminish the transmittance, but has no influence on the infrared cutoff and infrared border of high transparency. The spectral refractive indexes and absorption indices within 0.8–5 µm were extracted from transmittance data by minimizing the standard deviation between measurements and predictions. The results indicate that all the properties are wavelength dependent and temperature dependent. Spectral refractive indexes rise regularly with growing temperature and decrease slowly with increasing wavelength. For a researched temperature, the index of absorption levels off in the high transparent interval and climbs steadily in the next spectrum as the wavelength increases. In the tested temperature range of 300–1800 K, the spectral absorption indices rise gradually with increasing temperature. The absorption edge moves forward to the short wavelength infrared from about 3.5 µm at 300 K to about 2.75 µm at 1800 K.

The apparent radiative behaviors of open cell nickel foams and their dependency on textural features and intrinsic optical properties are numerically investigated in the limit of geometrical optics. Five realistic nickel foams with high porosity from 0.87 to 0.97 and pore density from 10 to 40 PPI were used as samples. First, the representations of foams and their microstructures were obtained by using computed tomography and scanning electron microscope techniques. Second, a Backward Monte Carlo method that employed the realistic representations and their intrinsic optical properties facilitated the computation of the apparent directional spectral emissivity. The apparent emissivity and its dependency on textural features and intrinsic optical properties were subsequently investigated based on a specially defined Representative Elementary Volume. It was noted that at pore scale, the non-homogenized apparent emissivity fields can vary according to the local compositions near to the foam surface (solid strut and void space) and the void pore behaves somewhat like a “black cavity” for thermal radiation. For open cell foams composed of low emittance nickel struts, high-porosity cell network may increase the intrinsic emissivity by a maximum of nearly 4 times. A predictive relationship was established that links the homogenized apparent emissivity to the open porosity and the intrinsic emissivity of solid struts. These findings will provide a deeper understanding of both the non-homogenized and homogenized radiative behaviors of open cell foams.

The transient thermal performance of coupled radiative and convective heat transfer in a circular tube exchanger filled with porous material subjected to constant wall temperature is investigated numerically. The porous material is considered as a homogeneous, absorbing, emitting and isotropic scattering medium. Monte Carlo method is used to solve the radiative heat transfer. The local thermal non-equilibrium model is employed to represent the energy transport within the porous material. The temporal temperature difference between the fluid and solid phases is analyzed to assess the availability of local thermal equilibrium model. The effects of different parameters are discussed, such as porosity, average particle diameter, inlet fluid velocity and the solid-phase thermal conductivity. The results indicate that the local thermal non-equilibrium mainly exists in the entrance region during the transient coupled heat transfer within porous material. Increasing the porosity, average particle diameter and inlet fluid velocity causes obvious temperature difference during the transient process. Besides, the solid-phase thermal conductivity has a considerable effect on the temporal temperature difference.

In order to understand the heat transfer behavior of forced airflow in open-cell porous foam, a tubular device filled with porous foam is built to conduct the experimental measurement. Three kinds of porous foams of Cu, Ni and SiC with various pore diameters and high porosity from 0.87 to 0.97 are used in the experiment, respectively. The tested sample is heated transiently by the hot airflow with an inlet velocity varying from 2.0 m/s to 9.0 m/s. And the transient temperature data of airflow are measured to determine the volumetric heat transfer coefficients by an inverse analysis. The experimental results are compared with those predicted by seven groups of experimental correlations available at present. Furthermore, an improved correlation of volumetric heat transfer coefficient is presented, which has two independent structure parameters of porosity and pore diameter and is valid for a wide range of Reynolds number 20 ⩽ Red ⩽ 103. By comparing with all of the available experiment data, the proposed correlation shows an error of ±40%.

Open-cell metallic foams are increasingly used in various thermal systems. The temperature distributions are significant for the comprehensive understanding of the foam-based engineering applications. This study aims to numerically analyze combined conductive-radiative transfer in a tomography-based open-cell metallic foam. The method used to carry out the simulations consists of a Monte Carlo ray-tracing method based on mesh-agglomeration approach, which avoids the error caused by block-off treatment of porous media surfaces, while greatly minimizing the computation cost for solving the Radiative Transfer Equation. A validation test case has been considered for the distribution of wall heat flux against other benchmark available in the literature. The detailed absorbed radiative flux at local strut surface is analyzed for the real nickel foam, and great difference up to 100% between the front and the back of the strut is found. In addition, the effects of average temperature (i.e. the arithmetic mean temperature of the cold and hot boundary) on the distribution of temperature, the absorbed radiative flux and radiative heat flux are investigated. The results show great fluctuation of absorbed radiative flux and radiative heat flux distribution due to the irregular porous structure. On this basis, the effective thermal conductivity and radiative conductivity of nickel foam at different temperatures are also evaluated. Results show when the temperature increases from 800 K to 1100 K, the radiative conductivity increases from 0.18 W/m•K to 0.46 W/m•K, and the effective thermal conductivity decreases from 4.81 W/m•K to 4.76 W/m•K first and then increases to 4.92 W/m•K, which indicates though the value of radiative conductivity is relatively small, it still influences the variation trend of the effective thermal conductivity with the temperature. The results also show that radiative thermal conductivity and the effective thermal conductivity are strongly dependent upon porosity.

Heat transfer in porous materials is significantly important in various engineering fields. The temperature distributions are essential for comprehensive understanding of the process. The current study aims to investigate the uncertainties associated with the gas temperature measurement in porous material using thermocouples at high temperatures by means of two hierarchical models. The transient coupled radiative and convective heat transfer within porous material is firstly simulated using the local thermal non-equilibrium model with Monte Carlo method. The flow is transient, incompressible and laminar. The porous material is considered as a homogeneous, absorbing, emitting and isotropic scattering medium. Based on the velocity and temperature fields, a numerical heat transfer model for thermocouple junction is developed with the lumped energy balance. Monte Carlo method is also adopted for the radiation simulation between the junction and porous material. The transient temperature response of thermocouple is computed and compared with the local gas temperature. The effects of wall temperature and the emissivity and diameter of thermocouple junction are analyzed. The results show that thermal inertia of thermocouple and thermal radiation have a significant effect on the gas temperature measurement inside porous material. The measurement error varies obviously during the transient measurement process. The junction diameter has a higher influence on the measurement error than junction emissivity. In addition, compared with low emissivity, the error is larger for high junction emissivity when the steady state is reached.

Coupled radiation-convection heat transfer inside a unit metal foam layer with high-flux irradiation is studied using improved scale-integrated simulation. It integrates the discrete-scale CFD simulation with that of continuum-scale via the multi-domain concept with thermal radiation effect considered. Conservations of mass flux and energy are satisfied on these specified subdomain interfaces, and a special defined transition zone with geometry-dependent functional quantities is introduced within the continuum-scale subdomain. This zone is adjacent to the discrete-scale subdomain which ensures a reasonable transition. Absorbed radiative fluxes and radiative heat transfer within the whole domain are calculated with Monte Carlo method and treated as heat sources. The problem under consideration has been investigated via the discrete-scale simulation, the continuum-scale simulation, and the scale-integrated simulation. The accurateness of scale-integrated simulation has been fully validated for predicting both flow field and heat transfer characteristics in comparison with the outcomes of discrete-scale simulation and other investigations. Deviations between the outcomes of continuum-scale simulation and discrete-scale simulation are found to be mainly caused by inconsistent local absorbed radiative heat fluxes distribution and impinging effect around the entry region. Up to 70% and 60% reduction of computation time and memory footprints are achieved when scale-integrated strategy is employed for the CFD simulation compared with the discrete-scale simulation. Meanwhile, the detailed fluctuated characteristics of the local concerned region and overall heat transfer performance can be precisely reflected. It may break up the computation limitations of the discrete-scale simulation in studying the energy transport process in foam based solar receiver applications.

High-temperature radiative properties of open-cell foams are relatively scarce due to measurement limitation. This study aims to numerically predict the volumetric radiative properties of irregular open-cell foams at high temperatures. The prediction is based on established relations which link the volumetric radiative properties to the structural parameters and/or component optical/radiative properties. Four typical foams are considered, including copper foams, nickel foams, zirconia foams and alumina foams. Former two are made of opaque metals, while latter two are made of semitransparent oxidized ceramics. For the four foams, the highest temperatures investigated are up to 1084 K, 1605 K, 1633 K and 2300 K, respectively. The variations of radiative properties with wavelength and temperature are analyzed. It was found that high temperature can strengthen radiation absorption inside metal and ceramic foams at most of wavebands. The temperature has almost no influence on the scattering phase function of metal and ceramic foams. Compared to copper foams, the nickel foams behave more absorbing at most of wavebands and temperatures. Alumina foams show an obviously forward predominance (asymmetry factor g > 0.4), and the fraction of forward scattering increases with increasing wavelength. Zirconia foams show a slight backward predominance (asymmetry factor g = -0.1) at short wavelengths, and a closely isotropic scattering was found at around wavelength λ = 7 μm. This study provides a feasible way to obtain the radiative properties of open-cell foams at high temperatures. Normal-normal transmittance and normal-hemispherical transmittance/reflectance of foams were measured at room temperature. The experimental results validate the numerical approach to obtaining radiative properties from analytical relations and bulk properties.

Capillary evaporation has been widely applied in petroleum industries, chemical process industries and soil science, while surfactants are usually existed in the working liquid for these applications. In this paper, we investigated effects of surfactant on capillary evaporation with thick films from aspects of evaporation rates, morphologies of meniscus and contact angles between the capillary and the working liquid. The results show that, different from that in an unconfined space, in capillary evaporation the evaporation rate decreased with the increase of surfactant concentrations. This discrepancy is attributed to the decisive role of surfactant concentration in the kinetics of capillary evaporation and the deterministic role of evaporating area in the unconfined space. Although the surfactant can alter the surface tension of vapor/liquid, but cannot affect the meniscus shape in the capillary evaporation process with thick films. Moreover, the contact angle between the capillary and the working liquid were not influenced by the addition of surfactant.

Optical constants effect on conjugate laminar natural convection and radiative heat transfer in an air filled rectangular enclosure with one vertical isothermal wall and one vertical semitransparent wall was numerically investigated. The steady-state continuity, Navier–Stokes and energy equations were carried out by the finite volume method, and the Discrete Ordinates Method (DOM) was used to solve the radiative heat transfer equation. Semitransparent radiation effect of vertical wall on laminar natural convection in rectangular enclosure was compared with non-semitransparent for Ra = 10 7 and Pr = 0.71. Detailed results including flow profiles, temperature fields, and Nusselt numbers were presented. The influence of optical constants of semitransparent wall on natural convection and radiation heat transfer in enclosure were also solved, considering different refractive indexes and absorption coefficients of semitransparent wall. It is found that optical constants effect of semitransparent wall on laminar natural convection in rectangular enclosure is marked.

This paper mainly investigates the transient conjugate heat transfer characteristic that the high speed airflow invades into the gap–cavity–gap structure. For this purpose, a simplified and effective quasi-steady approach in order to improve the numerical computational efficiency in multi-domain transient conjugate problems is presented. In this quasi-steady approach the pretty difference of the characteristic time step between the fluid and solid domains is utilized, so the computational expense can be reduced by alternating the solution sequence between coupled convection/conduction analysis and conduction analysis. The control factors to impact on the accuracy of this quasi-steady state method are analyzed further, by analyzing the process that high speed airflow aerodynamically heats the solid cylinder. Based on this quasi-steady approach, the computational fluid dynamics model combined convection, conduction and surface thermal radiation is established. Then, the transient conjugate heat transfer for the gap–cavity–gap structure is discussed. The computational results and the experimental data are compared with each other and the relative errors between them are summarized. After that, during the transient process, the features of the temperature contour inside the structure are discussed. Finally, from viewpoint of initial pressure difference between high speed airflow outside the structure and the cavity, the transient conjugate heat transfer characteristics of this structure are analyzed.

On the basis of medium discretization and local linear approximation of refractive index distribution, the curved ray tracing technique is used in combination with the pseudo source adding method to numerically solve the radiative heat transfer in a semitransparent slab with an arbitrary refractive index distribution and two diffuse gray walls. The radiative equilibrium temperature field of a linear refractive index distribution is evaluated by this method and the results show excellent agreement with that of the previous research. For two types of sinusoidal refractive index distributions, the radiative equilibrium temperature field as well as the temperature and heat flux fields of coupled radiation–conduction are investigated in detail. The results show considerable significance of the gradient refractive index effect, and some important conclusions are to be obtained.

By the ray tracing⧹node method, the transient coupled radiative and conductive heat transfer in absorbing, scattering multilayer composite is investigated with one surface of the composite being opaque and specular, and the others being semitransparent and specular. The effect of Fresnel’s reflective law and Snell’s refractive law on coupled heat transfer are analyzed. By using ray tracing method in combination with Hottel and Sarofim’s zonal method and spectral band model, the radiative intensity transfer model have been put forward. The difficulty for integration to solve radiative transfer coefficients (RTCs) is overcame by arranging critical angles according to their magnitudes. The RTCs are used to calculated radiative heat source term, and the transient energy equation is discretized by control volume method. The study shows that, for intensive scattering medium, if the refractive indexes are arranged decreasingly from the inner part of the composite to both side directions respectively, then, the total reflection phenomenon in the composite is advantageous for the scattered energy to be absorbed by the layer with the biggest refractive index, so at transient beginning a maximum temperature peak may appear in the layer with the biggest refractive index.

The simultaneous radiation and conduction heat transfer in a semitransparent slab of absorbing–emitting gray medium is solved in this paper. The refractive index of the medium spatially varies in a linear relationship, and the two boundary walls are diffuse and gray. A curved ray tracing technique in combination with a pseudo-source adding method is employed to deduce the radiative intensities on gray walls. Resorting to some of the results presented by Ben Abdallah and Le Dez, an exact expression of the radiative flux in medium is deduced. The influences on the temperature and radiative flux fields are examined, which are caused by the refractive index distribution, absorbing coefficient, thermal conductivity and the boundary wall emissivities. The results display the significant influences of the refractive index distribution and boundary wall emissivities on the radiative flux and temperature in medium.

On the basis of our previous papers, the redistribution of radiative energy in the case of isotropic scattering is investigated and the radiative transfer coefficient (RTC) under specular reflection in an absorbing, emitting and isotropic scattering parallel slab is derived. Considering both multi-reflection and multi-scattering in the derivation, the RTC can accommodate various boundary conditions under specular reflection. By accumulating the RTC for specular reflection boundary and that for diffuse reflection boundary linearly, the RTC are calculated. The validity and high precision of the formula for the RTC are confirmed by comparing with references. The effects of single-scattering albedo ω, Planck number Np and refractive index of STM nm on the transient coupled heat transfer in a one-dimensional isotropic scattering medium are reviewed for: (a) two semi-transparent boundaries; and (b) one semi-transparent boundary and one opaque boundary. The presented calculation and formula for the redistribution of the scattering energy can also be applied to other radiative calculations, such as total radiative exchange area or total radiative transfer coefficient in multi-dimensional isotropic scattering media.