This study aims to develop a numerical model devoted to the simulation of the early stages of viscous flow sintering of glassy materials using the discrete element method (DEM). An amorphous and spherical silica powder is selected as model glassy material. The green compacts were shaped using cold uniaxial pressing. A key innovation is the creation of an accurate digital twin of the microstructure, uniquely reconstructed in 3D from real FIB/SEM images using a machine learning algorithm for particle recognition. New DEM contact laws, derived from finite element analysis, incorporate attractive forces, viscosity, and neck growth. The DEM simulation's macroscopic shrinkage trajectory deviates by less than 1% from experimental dilatometry data during the isothermal dwell, validating the model's ability to describe the initial and intermediate sintering stages.

Understanding the interactions between processing, microstructure, and properties during sintering is required for designing materials with tailored functionalities. This study validates a Discrete Element Method (DEM) model for viscous flow sintering of silica glass, focusing on microstructural evolution and effective elastic property prediction. Microstructures at various sintering stages were reconstructed in 3D using neural networks applied to FIB-SEM imaging. A quantitative comparison between the DEM-simulated microstructures and these 3D reconstructed microstructures confirm the model’s robustness to capture densification. The validated DEM microstructures were employed as Representative Volume Elements (RVEs) for Finite Element Method (FEM) simulations to compute the effective Young’s modulus. The numerical predictions align with experimental measurements for the intermediate sintering stage (relative density > 0.8). The stiffness overestimation observed during the initial consolidation phase (relative density < 0.7) is attributed to the continuous representation of the granular network and boundary condition effects. This coupled DEM-FEM methodology bridges discrete particle-level mechanics with macroscopic material performance, providing a predictive framework to assist the mechanical design of sintered materials.

A Monte Carlo Ray Tracing (MCRT) homogenization is proposed to compute the spectral effective radiative and optical characteristics ( α _eff , σ _eff , g_eff , n_eff , k_eff ) of real heterogeneous semi-transparent media. Performed on statistically representative numerical microstructures, with the knowledge of the intrinsic indices of the constituents identified from normal-hemispherical reflectance and transmittance measurements, the method delivers all five characteristics in a single forward pass, with no further inversion: in particular, the asymmetry factor is read directly from the ray statistics, and the effective refractive index is obtained by a numerical time-of-flight method free of any external assumption. Because it operates on the microstructure itself, the approach assumes no particular object shape. It is demonstrated on two real aluminosilicate fibrous insulators, MAFTEC 96 and FOX. The practical relevance of the identified characteristics is illustrated by coupled conductive–radiative simulations compared against transient temperature measurements for both materials. The comparison shows that the identified characteristics capture the radiative contribution to heat transfer, and that a gray diffusion (Rosseland) approximation remains insufficient even for thick semi-transparent media, so that full spectral coupling is needed to reproduce the experimental response.

The consolidation and densification mechanisms occurring in the early sintering stages within a pure silica-based glassy material have been thoroughly investigated. Dilatometry curves were studied through several analytical approaches. In isothermal conditions at 1200 degrees C, the identified m exponent value (correlating relative shrinkage to dwell time) is equal to 1.02 +/- 0.08, which agrees with the analytical model of Coble for viscous flow sintering. Apparent activation energy and viscosity for sintering process were determined by applying the constant heating rate method and cyclic loading dilatometry respectively. The measured evolutions of specific surface area and relative density at the macroscale were correlated to microstructural features (i.e. pore size and interparticle neck radius). As shown, the silica material undergoes first a consolidation stage without significant shrinkage, before the occurrence of densification through particles coalescence. The shrinkage-neck growth trajectory characteristic of viscous flow sintering was established for this real glassy material, and compared to predictions of numerical models at the meso-scale from the literature.

Abstract Three different numerical models for simulating the well-known experimental flash method are presented and compared. These models consider conduction-radiation coupling and are applied within a one-dimensional grey semi-transparent slab enclosed between two opaque surfaces. The first model (A) is deterministic, dating back to about a decade, and is based on three assumptions regarding radiation transfer: isotropic intensity within each of the two hemispheres, the scattering phenomenon is supposed to be isotropic, and linearization of terms involving differences of temperatures to the fourth power. The other two models are completely new and do not make these assumptions. While the first one (B) is purely deterministic and serves as a reference for validation, the other one (C) is fully stochastic, and is the focus of this paper. A comparison shows excellent agreement between (B) and (C), validating our new model of interest (C). On the other hand, (A) exhibits significant discrepancies with the other two, highlighting the importance of its limiting assumptions.

This article presents two very different models for the resolution of conduction-radiation coupling within grey Beerian and non-Beerian semi-transparent slabs enclosed between two black surfaces imposing their intensities and temperatures. The first model is deterministic, based on finite differences and discrete ordinates. The second one is fully stochastic, using Monte Carlo ray tracing for the modeling of the radiative transfer and a Brownian walkers method for the modeling of conduction. These two models allow the evaluation of the temperature, surface flux, and radiative volume power fields in Beerian and fictitious non-Beerian semi-transparent media. They provide the very first resolution of the coupled Generalized Radiative Transfer Equation and energy equation. The results of these two models are compared and show excellent agreement. The results obtained on fictitious non-Beerian media show significant differences with the classical Beerian cases.

Complex refractive indices of micrometric aluminosilicate fibers and of silica aerogel, components of a biphasic and semi-transparent material, were identified in the mid-infrared range from 295 to 1350 K. The identification was carried out by successive applications of a methodology combining infrared spectroscopy (FTIR), X-ray microtomography and Monte Carlo Ray Tracing. This identification technique proves to be an interesting tool for material design since it is now possible to forecast the radiative properties of heterogeneous and semi-transparent materials composed of identical microphases but involving different proportions and spatial distributions. With this approach, it is no longer necessary to identify effective indices or perform systematic FTIR spectroscopy measurements to get a first overview of the radiative properties of a new spatial layout of the microphases.

Complex refractive indices of micrometric aluminosilicate fibers and of silica aerogel, components of a biphasic and semi-transparent material, were identified in the mid-infrared range from 295 to 1350 K. The characterization was carried out by successively applying the same methodology combining infrared spectroscopy (FTIR), X-ray microtomography and Monte Carlo Ray Tracing, The use of these tools was mandatory for the extraction of radiative characteristics at the microscale from macroscale measurements, and enabled the current remaining difficulties of identifying radiative characteristics from direct microscale measurements up to high temperatures to be overcome.Spectral normal emittances at elevated temperatures of a bulk aerogel sample were then simulated using the spectral complex refractive index of this phase extracted from the previously studied biphasic material. Good agreement between predictions and spectral normal emittance measurements by FTIR spectroscopy confirmed the accuracy of the extracted indices from room to high temperatures of the aerogel phase within the impregnated biphasic material.Finally, the developed methodology proves to be an interesting tool for material design since it is now possible with this tool to forecast the radiative properties of heterogeneous and semi-transparent materials composed of identical microphases but involving different proportions and spatial distributions. With this approach, it is then no longer necessary to identify effective indices or perform systematic FTIR spectroscopy measurements to get a first estimation of the radiative properties of a new spatial layout of the microphases.

A new methodology was developed to identify the spectral complex refractive index of semi-transparent solid phases within heterogeneous media up to high temperatures. In this methodology, numerical sam-ples are first generated from statistical information about the microstructure of a given material obtained by X-ray micro-tomography. The radiative properties of these numerical samples (reflectance, transmit-tance, and emittance) are then simulated with a Geometric Monte Carlo Ray Tracing code while the radiative properties of the real material are measured by Fourier Transform Infrared spectroscopy. The spectral complex refractive index is then extracted thanks to an optimization algorithm, by minimizing the discrepancies between the experimental and numerical radiative properties. This methodology was applied to a fibrous sample made of pure silica. The complex index was extracted at 295 K and 1010 K. In both cases, it enabled a good prediction of the radiative properties of the material and proved the relevance of performing calculations with characteristics identified at the local scale instead of the bulk ones.(c) 2023 Elsevier Ltd. All rights reserved.

This work directly follows the one presented in a previous article of V. Gonneau, D. Rochais and F. Enguehard (2022) [1]. This contribution describes new results and improvements to existing methods for the modeling of transient thermal conduction within a heterogeneous medium by the movement of Brownian walkers. The material structure is voxelized, and each walker transports an elementary enthalpy during its displacement within the structure. This enthalpy transport associated with the displacement of the walkers represents the conductive flow and makes it possible to simulate transient conduction with a quantitative stochastic approach. This article presents a new method for accounting for Dirichlet type boundary conditions that is quite efficient and that allows to relax quite substantially a constraint of maximum value of the time step of the Brownian walker simulations that had previously been pointed out in [1]. Other boundary condition treatments are also upgraded, in terms of speed (for Neumann type conditions) or generalization (for Robin type conditions). Then, a first non-linear conduction-radiation coupling model in an optically thick and gray semi-transparent medium is solved by Brownian walkers through two approaches: the first one based on a global conductivity function of temperature and allowing to confirm the validity of a stochastic transmission criterion at the interface of two constituents within a heterogeneous medium, and the second one based on the radiative volume power field. This second approach is preceded by the description and the validation of a procedure for the management of a volume power field using Brownian walkers. This procedure introduces the notion of negative Brownian walkers, which prove necessary for representing negative local values of the volume power field as is frequently the case with the radiative volume power. (c) 2023 Elsevier Ltd. All rights reserved.

For several decades now, numerous studies have been dedicated to porous refractory materials and their effectiveness in high temperature processes does not need to be proved anymore.Yet, an accurate identification of the thermal properties and the prediction of the thermal transfers in these media remains a challenge in some cases.A concrete example is the difficulty to predict the heat exchanges within semi-transparent materials.Indeed, in such media, the behavior towards thermal radiation varies with both the frequency of the radiation and the temperature.In other terms, the material can behave as opaque in a specific spectral range (conduction will then prevail) and can be totally transparent in another part of the spectrum where thermal radiation will be predominant.Therefore, a classic conducto-radiative simulation on a semitransparent medium, where the radiative properties of the material are assumed constant with frequency and temperature, will fail to reproduce the real thermal behavior of the medium.To illustrate this point, the behavior under a heat flux of a fibrous material impregnated with silica aerogel was analysed.The experiment carried out made it possible to bring the front face of a 10 mm thick plate of this material to 3 temperature levels (300, 500, and 800°C) in 200 s, maintain these levels until 600 s and measure the evolution of the temperature of its rear face over time.On the three thermograms, a sudden increase in temperature was observed.This was due to the silica aerogel becoming transparent to thermal radiation at a given spectral range and specific temperature [1].The French Alternative Energies and Atomic Energy Commission (CEA) develops a code to evaluate the conductoradiative exchanges within 3D voxelized microstructures [2][3].In this program, each voxel represents a unique phase (fluid or solid) and is considered homogeneous and non-scattering.The heat equation is computed in each voxel with a finite difference scheme where the radiative contribution is input as a power source.This latter is calculated by solving the Radiative Transfer Equation (RTE) within each voxel.During this work, this code was upgraded to take into account the spectral dependency in the calculation to correctly predict the evolution of temperature with time of a semi-transparent medium such as the one presented previously.To do so, the spectral domain is split into a number of N relevant bands and the RTE is solved with the corresponding radiative properties for each band.The resulting radiances of each of these bands are eventually summed up in order to get a total radiative heat flux as in a classic grey (non-spectral) computation, which is then input in the heat equation.Thanks to a methodology developed in a previous work (in process of publication), the spectral radiative properties of the material presented above were identified to compute both grey and spectral conducto-radiative exchanges in transient regime with the CEA code.The spectral simulation was in good agreement with the experiment while the grey one failed to reproduce the sudden increase in temperature observed experimentally.These results confirmed the relevance of performing spectral calculations instead of grey ones to characterize semi-transparent materials.

This work concerns the modelling of transient thermal conduction within a heterogeneous medium by the movement of Brownian walkers. The material structure is voxelised, and each walker transports an elementary enthalpy during its displacement within the structure. This enthalpy transport represents the conductive flow and makes it possible to simulate the conduction in a transient state with a quantitative stochastic approach. A study of the impact of the value of the time step is carried out to fix the choice conditions of this parameter, in particular in the presence of strong contrasts in thermophysical properties, and as such to define a validity framework of the diffusion model. Then several academic problems related to the behaviour of walkers are resolved in order to be able to account for different thermal solicitations and conditions at the boundaries (Dirichlet, Neumann, Newton) with Brownian walkers. These results have in particular made it possible to reproduce the so-called "rear face flash" experimental technique using a model by Brownian walkers over a homogeneous medium. Then, a stochastic transmission criterion based on the thermal effusivities is demonstrated to treat the meeting of a walker with an interface between two constituents within a heterogeneous medium. This work, focused on the mastery of the dynamics of Brownian walkers within heterogeneous media for the correct simulation of transient conduction, is a first step towards the modelling of the transient conduction-radiation coupling by means of Brownian walkers coupled to ray tracing techniques at the local scale of a voxelised structure.

Triply Periodic Minimal Surfaces are attractive porous media for the design of volumetric solar energy receivers; their design involves the evaluation of their heat transfer capabilities in the mixed conductive/radiative mode. We present image-based computations of effective thermal conductivities (ETC) for different radiation/conduction ratios in twenty distinct TPMS structures, using a Hybrid Random Walk numerical method, considering Opaque/Transparent media. Results are cast in simple analytical correlations : the ETC is the sum of a purely conductive contribution proportional to the relative density and of a radiative contribution proportional to the radiation/conduction ratio; the coefficient of proportionality contains an emissivity-independent contribution and another contribution proportional to the emissivity which fades out above a critical ratio. This critical ratio is linearly proportional to the solid/void volume ratio of the media. These results are compared to similar ones obtained on open-cell foams. Application of these dimensionless laws to two realistic cases are presented as illustrative examples.

In order to demonstrate that digital material engineering methodology is able to address the design and optimisation of architectured ceramic materials, solar volumetric receivers employed in Solar Thermal Power Plants (STPP) have been studied. A digital design approach for obtaining new receivers, at the macroscopic structural scale, is proposed. This approach couples virtual structure generation, ray tracing and thermal simulations at the scale of the base structural components (microscopic scale). Then, a recently developed process for manufacturing silicon carbide (SiC) parts by binder jetting is used to elaborate three optimised structures which are tested on-sun at high temperature in a solar concentrator reproducing the STPP operation conditions. The results obtained with these structures, having original shapes, are promising: the average experimental outlet air temperature reaches a maximum of 1133 K, energy yields can reach 0.49 despite high experimental heat losses, and all the SiC structures, made with a new material based on 3D printing, withstood the high temperatures reached, up to 1500 K. Comparison between digital and experimental results shows that the approach presented in this paper paves the way to a new digital material engineering approach.

Open porosity cellular SiC-based ceramics have a great potential for energy conversion, e.g. as solar receivers. In spite of their tolerance to damage, structural applications at high temperature remain limited due to high production costs or inappropriate properties. The objective of this work was to investigate an original route for the manufacturing of porous SiC ceramics based on 3D printing and chemical vapor infiltration/deposition (CVI/CVD). After binder jetting 3D-printing, the green α-SiC porous structures were reinforced by CVI/CVD of SiC using CH3SiCl3/H2. The multiscale structure of the SiC porous specimens was carefully examined as well as the elemental and phase content at the microscale. The oxidation and thermal shock resistance of the porous SiC structures and model specimens were also studied, as well as the thermal and mechanical properties. The pure and dense CVI/CVD-SiC coating considerably improves the mechanical strength, oxidation resistance and thermal diffusivity of the material.

Extended Abstract In many high temperature applications, porous refractory materials (for example alumina Al2O3 or zirconia ZrO2 felts) have become serious candidates as insulating materials. However, the modeling of heat transfer in these porous materials requires to solve several difficulties. First of all, the complex morphology of the medium makes it very difficult to realize a mesh for finite element or finite volume methods. Moreover, these methods require high amounts of computer storage and/or are time consuming. Thus, a 3D numerical voxel structure, issued from X-ray tomography for example, has been chosen to represent the material, allowing to avoid the meshing process. A second difficulty is the resolution of transient conduction transfer in these porous materials and the treatment of the boundary conditions in a numerical structure. The aim of this study is to develop a new modeling procedure of transient conduction in a numerical felt. The transient thermal conduction transfer is described as a stochastic process based on the motion of brownian walkers, a modeling approach that was initiated in [1]. Every walker carries an elementary enthalpy and the temperature of a volume V is proportional to the number of walkers within it. A computer code based on brownian walker motion was developed. Different boundary conditions were studied and implemented such as adiabatic wall, imposed thermal flux or imposed temperature. The code ensures the physical continuity of heat flux at interfaces and is able to model internal sources within the porous material. This study presents methods to set up boundary conditions and interface processing. Our stochastic treatment of transient thermal conduction was validated, in 1D transfer configurations, by comparison with Comsol results. Moreover, CEA has already developed a transient heat transfer numerical model operating on 3D voxel structures based on the deterministic finite difference method [2]. The stochastic (based on Brownian motion) and deterministic (based on finite differences) numerical tools are applied to a 3D numerical structure issued from X-ray tomography. This study compares the simulated temperature fields in this structure obtained by these two different modeling approaches, and highlights the strengths and weaknesses of each approach. In the future, our brownian motion based transient conduction model will be coupled to radiation heat transfer by the injection of a radiative heat source term. This radiative source will be determined by the resolution of the radiative transfer equation.

A process combining the pyrolysis of a lignocellulosic structure and reactive gas treatments has been developed to prepare porous TiC-SiC ceramics for solar receivers. The natural micro-porosity of balsa was complemented by a high open macro-porosity by laser cutting a periodical arrangement of parallel channels. The lignocellulosic structure was first pyrolysed into carbon. This reactive carbon material was then converted into TiC by Reactive Chemical Vapor Deposition (RCVD) using TiCl4/H2. After controlling the absence of cracks due to volume changes, the TiC structure was finally infiltrated by the Chemical Vapor Infiltration (CVI) of SiC using CH3SiCl3/H2. The density, porous structure, elemental and phase compositions, oxidation behavior and crushing strength were assessed after pyrolysis, RCVD and CVI. The SiC CVI coating significantly improves the compressive strength, the oxidation resistance and the thermal properties. The SiC layer is no longer fully protective at high temperature but the mechanical properties remain reasonably high.

CEA laboratory has developed an additive manufacturing technique with SiC powders and the material obtained need to be characterized. Therefore, we studied the change of optical properties and oxidation kinetics of SiC samples for the last step of the elaboration process. In this investigation, the optical properties and the oxidation kinetics of two SiC materials of two different densities and post-treated at LCTS laboratory have been compared. Their room-temperature optical properties were measured and both materials were oxidized using solar facilities at PROMES laboratory. It was observed that a higher porosity would increase both the solar absorptivity alpha and total emissivity epsilon of the SiC. Nevertheless, the alpha/epsilon ratio is improved with the density, increasing from 1.04 to 1.22. The less dense SiC presents also a faster oxidation kinetics, the determined activation energy increasing from 110 to 270 kJ ma(-1).

Polymer foams have many industrial applications because of their good mechanical properties combined with low material density. However, their study and the prediction of their behavior is challenging due to the massive influence of their complex microstructure. This paper focused on a polyurethane foam containing 70 vol% of porosity and aims at determining its behavior when submitted to large deformations under dynamic compressive loads. A model based on the material point method was set to study the whole stress-strain relationship of representative realistic foam sample, obtained from CT-scans. The dynamic model was validated to compression results from Split Hopkinson Pressure Bar experiments allowing the study of a shock due to a container fall. Direct influence of the microstructure was then evaluated. We first added virtual realistic manufacturing defects on the geometry and then studied the foam behavior of fully computer-designed microstructures. Recent developments in additive fabrication make the manufacturing of such structures possible and would widen the possibilities of virtually optimizing material designs.