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Unlike silicon carbide ceramic, the alumina ceramic and zirconia ceramic are by its very nature weakly absorbing in visible and near infrared wavebands. Therefore, open-cell foams made of such ceramics are rarely used in applications requiring strong absorption of radiation energy, such as solar absorbers. In order to improve the potential of such foams, open-cell foams with dual-scale pores were digitally designed in the limit of geometric optics. The first-order pores are obtained by Voronoi tessellation technique and then the second-order pores are realized by the design of 'porous strut'. A Monte Carlo Ray-tracing method is applied in the dual-scale foam structure for radiative transfer calculation. The parameterized study is conducted on the radiation absorption of alumina foam sheets and zirconia foam sheets. The results show that for the present cases, the designed dual-scale alumina foams with strut porosity ps = 0.3 can increase the normal absorptance within the wavebands from 0.4 µm to 7.0 µm by 62.7% than the foams with single-scale pores. For the zirconia foams, this increase is 115.9% within the wavebands from 1.2 µm to 7.6 µm. The findings can provide strong confidence on dual-scale foams to enhance the absorption of radiation energy in potential applications. [ABSTRACT FROM AUTHOR]

Porous solar receiver is the key component converting the solar energy to high-temperature thermal energy of working fluid. However, a large pressure drop brings additional energy consumption. In this work, an adjoint algorithm is employed to optimize the structure of tomographied porous solar receiver for reducing pressure drop. To this end, the flow and heat transfer characteristics of the porous receiver are analyzed and compared between the original and optimized receiver. The structural optimization is carried out with a pore-level method, which mainly consists of the incompressible Navier-Stokes equations and their adjoint counterpart. The results indicate that the pressure drop of the porous receiver decreased significantly after optimization with the porosity unchanged. In addition, although the solid skeleton temperature of the optimized foam is higher, the comprehensive efficiency η = h v /(Δ P)1/3 does not decrease. Finally, it is found that under different inlet velocities between 1 and 5 m/s, the pressure drops of three samples (φ = 0.87, 0.77 and 0.70) are reduced by 30%, 34% and 43% after optimization, respectively. The present work can provide useful guidance for improving the performance of porous volumetric solar receiver. • Pore-level approach to model flow in tomography-based solar receiver. • Adjoint method is used to optimize the structure for reducing the pressure drop at pore-level. • The pressure drop of the solar reciever is reduced by up to 43% after optimization. [ABSTRACT FROM AUTHOR]

High-temperature radiative properties of open-cell foam ligaments are rather sparse due to measurement limitation. This study aims to numerically predict the infrared radiative properties of nickel foam ligaments at high temperatures. In this work, rough surfaces of ligaments are modeled with SEM scanning pictures, and optical properties of nickel components are simulated using ab initio molecular dynamics method at 298 K, 673 K, 873 K, 1073 K and 1273 K. The reflectivity of smooth surface is determined with empirical formulas at high temperatures. Moreover, the spectral radiative properties of nickel foam ligaments are predicted with finite difference time domain method at the waveband of 0.8–8.5 μm based on the modeled surfaces and high-temperature optical properties of components. It is found high temperature can marginally strengthen radiation scattering of the ligament surfaces, while having little effect on the distribution of radiation scattering. For instance, the directional-hemispherical reflectivity increases approximately linearly with temperature. As the incident wavelength grows, the directional-hemispherical reflectivity and proportion of specular reflection both show a rapid increase in the studied waveband, while the value of reflection main peak of directional-hemispherical reflectivity declines. With the growth of incident angle, the center position of main reflection peak is moving to the direction of increasing angles. Polynomial fit is applied to anticipate the relationship between proportion of specular reflection and incident wavelength with a RSME less than 0.02. This work demonstrates a practical method for obtaining the infrared radiative properties of open-cell metal foam ligaments at high temperatures. [ABSTRACT FROM AUTHOR]

• Microscopic morphology characteristics of ceramic ligament and pore-level structure are analyzed comprehensively and reconstructed. • Spectral radiative properties of ligament surface and internal medium are predicted. • A trans -scale prediction method for radiative transfer inside ceramic foams is presented. • Apparent radiative properties and equivalent volumetric radiative properties of alumina foams are numerically discussed. In this work, based on the complete structure model consisting of microscopic ligament morphology and pore-level structure, a trans -scale analysis method is presented for accurately predicting the spectral radiative properties of open-cell ceramic foams. The characteristic models of microscopic ligament morphologies are obtained by the SEM technique, while the network structure of ligaments is reconstructed by the μ-CT technique. According to the SEM data, the microscopic statistical models are developed for the rough surfaces and the internal porous media of ligaments. Additionally, based on the statistical models, the FDTD method is employed to analyze the spectral radiative transfer behaviors on the surfaces and inside the ligament media. The spectral directional-hemispherical reflectivity and specularity parameter for the ligament surface, as well as the extinction coefficient, the scattering albedo and the scattering phase function for the ligament medium are extracted from the FDTD simulations. The above parameters are used as the input data for the pore-level simulations of spectral radiative transfer inside the ligament network, where the Monte Carlo method is conducted. The apparent spectral absorptivity and reflectivity, as well as the equivalent volumetric spectral radiative properties of alumina foam sheets are predicted by the presented trans -scale analysis method. The trans -scale predicting method is verified and compared with the single pore-level simulations of radiative transfer inside alumina foams. The spectral radiative characteristics of alumina foams are analyzed for various wavelengths and incident angles. From the analysis, only when the specularity parameter is properly chosen, the pore-level simulation is also reliable for predicting the spectral radiative properties of ceramic foams. [ABSTRACT FROM AUTHOR]

To further understand the heat transfer behavior of open-cell alumina ceramics, the FVM combined with an improved mesh-agglomeration Monte Carlo ray-tracing method is developed to solve the coupled conductive-radiative heat transfer in open-cell alumina ceramics, where the spectral radiative properties are dealt with gray-band model. The radiative behavior of tomography-based foams and cinema4d-based foams are analyzed and compared, which indicates that the radiative characteristics of the two types of foams are very similar. On the basis of this, cinema4d-based foams with various porosities are used for the evaluation of effective/radiative thermal conductivity, where the porosity and temperature ranges from 0.5 to 0.8 and 1400 to 2000 K, respectively. The results show that for different temperature/porosities, the variation range of the effective thermal conductivity is limited (2.7–5.0 W/m·K), however, the variation range of the share of thermal radiation /conduction is very large. It can be also found that when the porosity is low, the thermal conduction dominates; when the porosity is high and the temperature is high, the effect of thermal radiation becomes important and accounts for >75% of the coupled conductive-radiative heat transfer. These findings can provide a deeper understanding of the conductive-radiative heat transfer in alumina ceramics. [ABSTRACT FROM AUTHOR]

In this work, with all the characteristic morphologies considered, a numerical method for achieving the prediction of radiative properties of open-cell metal foam integrating different scales is presented. For the modeled micro-scaled rough ligament surface, the FDTD method is adopted for predicting the radiative properties of ligament surface elements. Meanwhile, at macro scale, the metal foam sheet is reconstructed by the CT technique, and the radiative properties of reconstructed foam sheet are numerically calculated with the Monte Carlo method. In the procedure of applying the introduced method, the radiative parameters of ligament surface elements, including the directional-hemispherical reflectivity and specularity parameter, are extracted from radiative properties of ligament surfaces. Then, these radiative properties are used for achieving the further numerical prediction of radiative behaviors of metal foams. The integrated-scale prediction of radiative properties of open-cell metal foam is accomplished by the introduced method, which integrates microscopic morphology of ligament surface and macroscopic solid ligament network. Furthermore, the presented method is applied for calculating the spectral radiative properties of nickel foams. The presented method is proven to be valid by comparing with experimental results. Additionally, the effects on the radiative properties caused by incident wavelength and angle are discussed. [ABSTRACT FROM AUTHOR]

• Establishment of a pore scale model to investigate the radiative properties. • Microstructure of several carbon foams is gain. • Verification in spectral radiative properties with experimental data. • High-temperature radiative behaviors of carbon foams are obtained. A pore scale model was established to investigate the high-temperature radiative properties of carbon foams with high porosity. Voronoi Tessellation for the random structure of carbon foams and Monte Carlo ray-tracing method was employed to simulate the apparent radiative behaviors and volumetric radiative properties. By compared with the measured data at room temperature in Ref. (Celzard et al., 2012), the numerical model was verified to possess a high precision, which the maximum deviation are 1.8% for normal absorptance, 0.3% for normal-hemispherical transmittance and 1.5% for normal-hemispherical reflectance, respectively. It is also acceptable for the simulated results of volumetric radiative properties. Based on the spectral radiative properties of carbon basic material found in Ref. (Touloukian and DeWitt, 1972), the spectral radiative properties of carbon foam sheets at high temperature between 1183 K and 2073 K were predicted. It was found that absorptance is dominant in the apparent radiative behaviors of carbon foams at high temperatures with a wavelength of 0.665 μm. Then, the bidirectional reflectance distribution function was numerically investigated. The results showed a backward scattering of the reflected energy at the foam sheet surface and reflected energy peaks are always located at around respective incident angles. For volumetric radiative properties at high temperatures, extinction coefficient ranged between 200 m−1 and 450 m−1, which had been verified with relation formula in an error of less than 1%. In addition, scattering albedo and scattering phase function were not only simulated but also compared with the empirical formulas, to some extent, agreed well with them. [ABSTRACT FROM AUTHOR]

• Complex morphology of ligament surface is reconstructed approximately. • Analytical formulations are obtained for predicting the radiative parameters. • Effects of incident wavelength and incident angle are discussed. Accurately predicting the spectral radiative properties of ligament surface is vital for exploring the heat transfer inside open-cell foam materials. In this work, the complex morphology of ligament surface in open-cell nickel foam is reconstructed by analyzing the SEM scanning pictures of ligament surfaces. Then, the radiative parameters including the directional-hemispherical reflectivity, directional-directional reflectivity and proportion of specular reflection of rough ligament surface in the waveband from visible to near infrared light are numerically predicted by applying the FDTD method. Furthermore, the effects of incident angle and wavelength on the predicted radiative properties are compared and summarized. Besides, a fifth-degree polynomial is put forward for characterizing the directional-hemispherical reflectivities under different incident angles and wavelengths. The distributions of directional-directional reflectivities of ligament surface are compared and analyzed in order to predict the various value and dominated scope of reflection peak in the specular reflection direction. Additionally, the proportions of specular reflection under different incident conditions are achieved properly and characterized by proposed mathematical formulas. This work is helpful for the multi-scale numerical prediction of radiative transfer inside open-cell nickel foams, which is beneficial to further researches about engineering applications of open-cell foam materials. [ABSTRACT FROM AUTHOR]

Alumina foam has potential application value in aerospace, solar energy, and other fields. This study proposes a combined radiative-conductive heat transfer model, in which the thermal conductivity and extinction coefficient are temperature-dependent, and the radiation transfer equation is solved by the Monte Carlo method. A self-designed setup is used to measure the high temperature thermal response experiments of alumina foams in 10PPI, 20PPI, and 40PPI. Combined with the genetic algorithm, the thermal conductivity, extinction coefficient, albedo and asymmetry factor of scattering are solved. According to the inversion results, the extinction coefficient of materials with a high pore density is more sensitive to temperature than those with a lower pore density. The thermal conductivity of high pore density materials is greater than that of low pore density materials. The thermal conductivity and extinction coefficient slightly remain basically unchanged as atmospheric pressure increases. [ABSTRACT FROM AUTHOR]

• 2D coupled heat transfer model with MCRT for thermal analysis of windowed VSR. • Effects of porosity and cell size of porous on thermal efficiency of windowed VSR. • Models based on P 1 approximation were compared with MCRT. • High thermal efficiency results from at a large cell size or a low porosity. • P 1 underestimates the thermal efficiency and overestimates the window temperature. A two-dimensional coupled heat transfer model with Monte-Carlo ray tracing (MCRT) method is developed to analyze the heat transfer in windowed volumetric solar receiver. The local thermal non-equilibrium (LTNE) effects in ceramic foam absorber and spectral selectivity of quartz window are considered. With the solar absorption term calculated by the MCRT, the P 1 -approximation for thermal radiative exchange in the foam absorber is examined by comparing with the MCRT. In the model based on P 1 -approximation, net radiation method (NRM) and MCRT are applied to calculate the thermal radiative exchange between the window and absorber. The effects of porosity and cell size of the absorber foam on temperature distribution and thermal efficiency are investigated. The results show that for heat transfer in foam absorber at a highest temperature below 1727 K, the P 1 -approximation underestimates the absorber temperature by about 27 K and overestimates the window temperature by 106–133 K. And the thermal efficiency is underestimated by about 2.1% using the P 1 -approximation. There is small difference between the temperature in the absorber predicted by different models, but the NRM cannot predict the axial temperature gradient in the window. Under a constant air mass flow rate, within the absorber foam with the cell size range of 2–4 mm and porosity range of 0.7–0.9, a higher thermal efficiency can be reached at a larger cell size or a lower porosity. [ABSTRACT FROM AUTHOR]

• Start-up duration of a tubular receiver filled with nickel foam is predicted. • Preheating performances are compared by operating synergy electric heater and solar simulator. • Transient temperature and thermal stress distribution of solar receiver is obtained. • The maximum difference of duration is 11 min between cold and hot start-up strategy. A cylindrical tubular receiver filled with nickel foam (CTRNF) appears to be a promising receiver concept due to its capability to provide temperatures over 900 °C at a high pressure. Nevertheless, CTRNF is challenged by the unsteadiness and high intensity of radiant flux may cause inaccurate start-up time predictions, providing unrealistic and unstable outlet temperatures. In this article, these matters are addressed by a numerical model coupling the Monte Carlo ray tracing (MCRT) method and discrete coordinate (DO) radiative transfer model. The model considers the cold, semi-cold, semi-hot, and hot start-up strategies on the CTRNF using N 2 and Ar as the working medium. Three preheating methods and their influence on the thermal characteristic of the CTRNF are proposed. Temperature and equivalent stress distribution of internal heat absorber is simulated and analyzed. The results indicate that the duration for four start-up strategies takes 1711 s, 2189 s, 1212 s and 1032 s as the outlet temperature reaches to 1200 K, respectively, when Ar is used as the working medium (10 g/s) and radiative power of 10.5 kW incidents on the solar receiver. Compared with the 68.44 kg Ar consumption of cold start-up strategy, the Ar working medium consumption decrease by 24.44 kg, 51.68 kg, and 63.16 kg for semi-cold start-up, semi-hot start-up, and hot start-up strategy. However, the maximum equivalent stress of the CTRNF under the hot start-up strategy is 100 MPa higher than under the cold start-up strategy, which requires accurate monitoring of the cavity temperature in solar receiver. [ABSTRACT FROM AUTHOR]

• Different microscopic and pore-level structure models are compared comprehensively. • Effects on the radiative transfer caused by multi-scale structures inside alumina foams are analyzed. • Spectral transfer mechanism associated with various structural parameters are discussed. The radiative behaviors occurring inside ceramic alumina foams are influenced by the multi-scale structures ranging from micro-scale to pore-level, which determine the equivalent radiative properties. In this work, the microscopic morphologies of ligament and pore-level porous structure of alumina foam are introduced, while the spectral apparent and volumetric radiative parameters are predicted by performing a trans -scale simulation coupling the FDTD method with the Monte Carlo ray tracing method. By applying different simplified models at different scales and reconstructed realistic structure models respectively, the corresponding spectral radiative parameters of alumina foam sheets are compared and discussed, with different microscopic morphology characteristics and pore-level structure parameters considered. By comprehensive analysis, it can be observed that the spectral radiative properties of alumina foam are affected by complex multi-scale structural characteristics. The pore-level parameters have great influences on the apparent spectral radiative properties and equivalent extinction coefficient, while the micro-scale ligament structures change the spectral selectivity and scattering asymmetry factor obviously. For the scattering albedo, the effects produced by various micro-scale and pore-level structural parameters are close. [ABSTRACT FROM AUTHOR]

In this work, the structure of porous foams is optimized for enhancing heat transfer and reducing pressure drop simultaneously at pore level. The optimization model consists of the pyoptsparse package integrates with an adjoint method. The flow and heat transfer characteristics are compared between the original and optimized foams. The influence of the inlet velocity (u in = 0.2, 1.0 and 5.0 m/s) on optimization is first analyzed. The results show that the pressure drop is significantly reduced, and the maximum decrease of the pressure drop is over 27% after optimization. For the heat transfer enhancement, when the inlet velocity of the fluid is low, the effect of optimization is slight due to the saturation of heat transfer; when the inlet velocity is high, the heat transfer enhancement is obvious, and the maximum increase of the outlet dimensionless temperature is over 12%. Finally, the effect of the porosity on optimization is analyzed, and the results indicate, it is easy to achieve significant pressure drop reduction for all porosities, and heat transfer enhancement can be only achieved for higher inlet velocity. The present work can provide useful guidance for improving the performance of porous materials in thermal applications. [ABSTRACT FROM AUTHOR]

The optimization of metal foam structure parameters is crucial for enhancing the heat transfer and pressure drop performance of cylindrical tube heat exchangers. In this study, thermal output performance of 16 different nickel foam-filled solar receivers with varying thicknesses and positions is numerically simulate. An optical-thermal conversion model is established using the Monte Carlo ray tracing (MCRT) method and user-defined functions. The influences of foam filling thickness and position on heat absorber, wall hot spot distribution, heat loss type, thermal efficiency, pressure drop, thermohydraulic performance, exergy loss, and outlet temperature were analyzed. Furthermore, a multi-objective optimization algorithm called non-dominated sorting genetic algorithm II (NSGA II) is used to generate the best trade-off solutions between improvement of thermal efficiency and pressure drop. The results show that enhancing the thickness of the filled foam within the CTR tube enhances thermal efficiency and elevates pressure drop. However, optimizing the length and filling position of the foam can effectively mitigate excessive pressure drop caused by longer foam, without compromising thermal efficiency. This approach results in a reduced pressure drop while maintaining optimal performance. The optimal solution of multi-objective optimization is that the 123 mm thickness foam is filled at 0 mm from the inlet of the tube, and the pressure drop and thermal efficiency of the solar receiver are 830.2Pa and 83.1 %, respectively, when the mass flow rate is 0.01 kg/s. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: The behavior of a family of polymeric structural foams with various initial bulk densities (porosity levels) was experimentally investigated under quasistatic and high strain rate loading conditions. The high strain rate loading for the low-density foams was implemented using a polymer split Hopkinson pressure bar (SHPB) and for the high-density foams using a magnesium SHPB. It was found that the Young''s modulus, the yield strength, the maximum stress and the strain to failure increased with increasing initial foam density under quasistatic loading. The fracture modes were also found to be considerably different for these foams. The low-density foams fractured in a brittle manner, especially under dynamic loads, where as, the high-density foams exhibited shear-dominated failure at all strain rates. Under dynamic loading, the failure strength increased with strain rate but the strain to failure decreased. Based on the quasistatic and dynamic test results, the strain rate sensitivity of failure strength was determined and it was found that this rate sensitivity parameter increases with increasing foam density. [Copyright &y& Elsevier]

Open-cell foams consisting of interconnected struts are widely used in thermal applications such as volumetric solar receivers. The thermal performance of foams strongly relies on their radiative behaviors which intrinsically depends on the radiative properties of struts. This study proposed a feasible approach to determine the radiative properties of solid struts by a pore scale identification from a macro scale measurement. First, the normal-hemispherical transmittance and reflectance spectra of two nickel foams were measured by an experimental system. Second, a pore scale forward calculation was conducted by a combination of Monte Carlo Ray-tracing method and real foam structures obtained from micro-computed tomography technique. Last, an Adaptive Particle Swarm Optimization algorithm was adopted to retrieve the spectral reflectivity and specularity of nickel struts from the measured spectra. The results show that it is unreasonable to assume the reflection behavior of strut surface simply as either specular or diffused, and also, it is unreliable to assign the reflectivity of strut surface directly by Fresnel's law. Within the investigated wavebands 0.4–2.2 μm, the average reflectivity of nickel struts is 12% lower than that of a nickel mirror. The proportion of specular reflection at nickel strut surface is between 37%–52%, almost increasing with wavelengths. [Display omitted] [ABSTRACT FROM AUTHOR]

l Pore-level approach to modeling combined conductive-radiative heat transfer in metal foams. l A high efficient monte carlo ray-tracing method based on mesh-agglomeration approach to solve radiative transfer in a CT-scan structure porous media. l Absorbed radiative flux distribution and radiative heat flux distribution are simulated within the porous media. l Effective thermal conductivity and radiative conductivity are evaluated considering conduction and radiation. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Highlights • A three-layer structure model is adopted to consider the effect of edge in foams. • Extinction coefficients are compared between traditional and the three-layer model. • Radiative properties of nickel foam are obtained in the near infrared band. • Temperature influence on the radiative properties is analyzed in 1.3–2.2 μm. Abstract 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. [ABSTRACT FROM AUTHOR]

This study aims to analyze the effect of edge layers on the volumetric radiative properties of open-cell nickel foam based on a three-layer structure model composed of two edge layers and one complete layer. Pore-scale simulation was performed for five nickel foams with typical structural parameters, using their component optical properties and reconstructed digitalized foams. First, the ligament morphology of foam samples was rebuilt and the optical properties of rough ligament surfaces were predicted with the finite difference time domain method. Then, pore-scale radiative transfer models were established which absorption and scattering were computed using Monte Carlo Ray-Tracing (MCRT) method. Afterwards, the size of representative elementary volumes was determined, and it illustrates that at least three foam cells in the thickness of a foam structure are required to characterize volumetric radiative transfer. Moreover, the MCRT results show that accounting for the existence of edge layers, the extinction coefficients were underestimated by 7% for 20PPI nickel foam and 13% for 40PPI nickel foam by Beer's law in the studied wave band. When compared with the results by present simulation, the values of extinction coefficients by the double-thickness model in the reference are quite close within the wave band of 0.83–2.2 μm. While the scattering coefficients was overweighed for about 107 m−1 of sample 2 and 84 m−1 of sample 3 at the wavelength of 0.83 μm. Additionally, the extinction coefficients of five samples changed slightly in the wavelength from 0.75 μm to 12.5 μm. Scattering albedos approach to the reflectivity of the nickel component and scattering phase functions of all nickel foams show an obviously backward predominance. • Establishment of the pore-scale radiative transfer models. • Analysis of the edge-layers effect on the radiative properties. • Determination on representative elementary volumes of open-cell metal foams. • Verification in spectral radiative properties with experimental data. [ABSTRACT FROM AUTHOR]

• Ligament microstructure and porous parameter affect radiative properties of foams. • Three simplified reflection models show obvious deviation in ligament reflectivity. • Apparent and volumetric radiative properties of nickel foams are investigated. • Extinction coefficient increases with increasing pore density and deceasing porosity. The radiative properties of metal foam are determined by the complex multi-scale characteristics. The effects of microscopic morphology of ligament and porous parameter on the apparent and volumetric radiative properties are investigated by performing a trans -scale simulation, which are respectively presented by the absorptance and transmittance, the extinction coefficient and scattering albedo here. The spectral reflective property of ligament surface ranging from 0.5 ∼ 7 μm is firstly modeled with Finite Difference Time Domain (FDTD) method considering the micro-scale roughness, and then compared with other three simplified reflection models (specular, diffuse and harmonic reflection). With the reconstructed foam structure and Monte Carlo method simulation, the spectral radiative properties of different nickel foam slabs are repetitively calculated to analyze the effects of above two factors. The results show that three reflection models for the ligament surface all have a non-negligible deviation, and the maximum greater than 20% is found. Besides, micro-scale morphology of ligament significantly affects the absorptance, transmittance and scattering albedo of the nickel foam slab. By contrast, porous structural parameters have noticeable influence on the apparent properties and extinction coefficient, while negligible effect on the scattering albedo. [ABSTRACT FROM AUTHOR]

A key challenge to model the heat transfer in refractory ceramic foams at high temperature is to characterize properly the transport of thermal radiation, especially when the foams are directly exposed to a high irradiation beam such as concentrated solar radiation. Characterization of the radiation transport in a single strut is representative and fundamental for the radiation transfer modelling of foams. This study numerically investigates the radiation transport and temperature response in a real foam strut under high irradiation beam. The digitalized strut was obtained by the X-ray micro-computed tomography imaging measurements, and then meshed within the strut volume and on the surface. The Discrete Ordinate Method is used to solve the Radiative Transfer Equation, since the strut material (alumina ceramic) is by nature semitransparent for incident radiation, resulting absorbing, scattering and emitting inside the solid phase. The volumetric propagation of radiation intensity is tracked and the absorbed radiation energy is recorded. Besides, the temperature response of the strut irradiated by a beam with periodic heat flux is investigated. The knowledge of radiation transport and temperature response in foam struts can provide fundamental information for understanding the pore-level heat transfer and for developing high-quality simulation and experiments. [Display omitted] • Visualized characterization of volumetric radiation transport in a foam strut. • Wavelength-dependent radiative properties from 0.4 μm to 7 μm. • A real strut obtained by X-ray micro-computed tomography measurements. • Semitransparent struts with semitransparent boundaries. • Temperature response under high irradiation beam with periodic heat flux. [ABSTRACT FROM AUTHOR]

• A new approach to determine radiative properties of semitransparent struts. • Measurements of radiative properties of foams at macro scale. • Forward numerical prediction by pore-scale simulation. • Identification of local scale radiative properties from measured quantities. • Extinction coefficient of alumina struts is 33.5% lower than that of dense bulks. The radiative properties of a ceramic strut cannot be strictly the same as that of a dense sintered ceramic bulk composed of the same material. This contribution develops an approach to determine the radiative properties of semitransparent ceramic struts of open-cell foams. First, a macro-scale measurement was conducted to obtain the normal-hemispherical transmittance and reflectance spectra of alumina foam slices. Second, a pore-scale forward model was established to predict the radiative behaviors of 3D digital porous structures obtained from micro-computed tomography technique. Last, an identification method was proposed to retrieve the radiative properties of semitransparent ceramic struts from the measured data. The results indicate that it is unreasonable to simply assume the radiative properties of alumina struts as that of corresponding dense bulks. Within the investigated wavebands 0.4–2.2 μm, the average extinction coefficient of alumina struts is 33.5% lower than that of dense bulks. The scattering albedo shows a slight difference between alumina struts and dense bulks. Besides, the retrieved extinction coefficients and scattering albedos of alumina struts are proposed as a function of wavelengths, which can be used in potential applications. [ABSTRACT FROM AUTHOR]