AbstractIn order to develop improved filters for metal melt filtration, different physical phenomena that take place during depth filtration of liquid metals need to be well understood. Due to the difficult accessibility of the process, the harsh process conditions and the randomness of the typically employed ceramic foam filters, representative experimental investigations are extremely difficult to perform and often provide only integral quantities or selective information. This chapter presents a numerical model for simulating the depth filtration of liquid metal at the pore-scale, i.e., fully resolving the complex filter geometry, which can also accurately handle the curved filter walls. In the model, the velocity and pressure distribution of the melt flow is obtained by the lattice-Boltzmann method and the temperature field is calculated using the finite volume method, while the transport and filtration of the inclusions are predicted by solving the equation of motion for particles in a Lagrangian reference frame. In order to obtain a consistent representation of the curved filter walls for both particle transport and fluid flow, the Euclidean distance field of the filter structures is employed. By comprehensive parametric studies, the sensitivity of the filtration process with respect to various geometric parameters and process conditions is investigated. Therefore, geometries of conventionally manufactured filters, acquired from 3D μCT scanning, as well as computer-generated filter structures are considered. Their performance is assessed by evaluating various effective properties, such as the viscous and inertial permeability and the filtration coefficient. The numerical predictions allow to draw conclusions with respect to the dominant physical mechanisms and are compared with those from simplified physical models, which are shown to be sufficiently accurate for the pre-screening of filters. On the basis of the detailed results, suggestions for improved filter geometries are made, depending on the considered filtration process. Further, simplified models for the prediction of the effective thermal conductivity of open-cell foams in presence and absence of radiation are presented and validated using the detailed numerical predictions.

The present numerical investigation is conducted to improve the understanding of the physical processes, encountered during the filtration of steel melt. For this purpose, the process conditions in a pouring experiment are considered. The effects of increasing either the superficial melt velocity or the pore count of the filter are studied. The turbulent flow is modeled using the large eddy simulation in the context of the lattice Boltzmann method and the motion of nonmetallic inclusions is predicted using discrete Lagrangian particle tracking. The simulations show that turbulent flow develops as the melt advances through the filter, with the length scale of the smallest flow structures lying in the same order as the particle size. The pressure drop and the filtration coefficient are found to agree with the previous studies.

The combination of additive manufacturing and replication technique enables the development of new ceramic foam filters (CFFs) for the filtration of metal melts based on computer‐generated templates. This article presents a numerical study on the sensitivity of filtration performance with respect to different geometric modifications, applied to an artificial monodisperse base structure. Three different geometric modifications are implemented, namely, elliptical elongation and flattening of the strut cross section with respect to the flow direction, additional finger‐like struts protruding into the pore cavity, and addition of deliberately closed windows. All modifications are implemented for overall porosities of 70–90%. The performance of the new structures is evaluated for continuous casting of aluminum by comparing the hydraulic tortuosity, the permeability, the Forchheimer coefficient, and the filtration coefficient, which are obtained from detailed pore‐scale simulations of the melt flow and inclusions transport using an Euler–Langrange approach. For the fast determination of the permeability coefficients, a novel and extremely simple model for the prediction of the Forchheimer coefficient is described. The investigation shows that geometric modifications to open‐cell foams potentially improve the filtration performance without significant decrease in filter porosity and can be considered as templates for the design of efficient CFFs.

In this investigation, L-fd* and Delta p in the entrance region of circular and parallel plate microchannels have been determined for 10(-2) <= Re <= 10(4) and 10(-4) <= Kn <= 0.2, employing the second-order velocity slip condition at the wall with C-1 = 1 and 0 <= C-2 <= 0.5. Results indicate that although local velocity slip at the wall is always higher than that for the fully developed section, local wall shear stress for higher Kn and C-2 could be lower than its fully developed value, which is also more prominent for lower Re. Therefore, depending upon the operating condition, K(x) and K-fd could assume negative values, implying that pressure gradient in the developing region could even be less than that in the fully developed section. It has been further observed that both L-fd* and K-fd are characterized by the low and the high Re asymptotes, using which extremely accurate correlations have been proposed for both geometries.

The removal of nonmetallic inclusions from metal melts is a crucial step in producing high-quality castings that have to meet strict requirements regarding strength, toughness, and machinability. To separate the unwanted impurities, the liquid metal is usually passed through ceramic foam filters (CFF), in which the inclusions adhere to the surface of a complex strut network. The development of improved CFF structures requires a good understanding of the physical phenomena involved in the filtration process. In this respect, an experimental investigation of the real system is challenging, due to the opacity of the melt, high temperature, and the presence of a protective atmosphere. Therefore, the present study relies on water model experiments, which are conducted for different pore counts and flow velocities. To achieve a high degree of similarity to the real system, the wetting properties of the filters and particles are adjusted accordingly. Experimentally evaluated filtration efficiencies are compared with predictions obtained from a detailed numerical model that considers the CFF geometry, which is digitized using 3D X-Ray micro-computed tomography, and previously measured particle adhesion forces. The results suggest that a considerable fraction of particles does not remain attached after collision with the CFF struts.

This work deals with modelling and numerical simulation of complete evaporation process inside anisotropic porous media. Based on the modified enthalpy formulation of Two-Phase Mixture Model (TPMM) along with the assumption of Local Thermal Non-Equilibrium (LTNE), a modified formulation has been proposed that can easily accommodate the anisotropy in the porous media properties. The governing equations have been solved using the Finite Volume Method (FVM) on staggered grid layout. The simulations have been carried out by applying the proposed smoothing algorithm for the effective diffusion coefficient in order to avoid the non-physical jump in the predicted temperature distribution during the numerical simulations. The effects of the permeability ratio, solid thermal conductivity ratio, thermal conductivity of the solid phase and the Darcy number have been investigated. The computed results show that the anisotropy of permeability and thermal conductivity of the solid phase have significant effect on the initiation and termination of phase change process. It is also observed that the anisotropic properties of the porous medium have significant influence on the flow behaviour and heat transfer rate from that expected under isotropic conditions. The results indicated that the effect of thermal conductivity of the solid phase plays an important role and hence adequate care must be taken while designing such evaporators. The results also show that the smoothing algorithm is successful in dealing with the rapid change in the effective diffusion coefficient during the simulations of complete evaporation process.

The variations in the total effective thermal conductivity (k(eff,t)) of a tetrakaidecahedra unit cell structure as functions of porosity (phi), thermal conductivity of the solid phase (k(s)) and the average temperature of the medium (T-avg), in the presence of combined conduction and radiation heat transfer, are presented in this article. For this purpose, the governing energy conservation equation is numerically solved using the blocked-off region approach based on the finite volume method. In addition, the variations in the radiative properties of the structure as functions of surface reflectivity (rho(s)), pore density (PPC) and phi are investigated, for which, a pure radiation heat transfer based numerical model is developed and used. From the detailed numerical simulations, three different correlations for k(eff,t) are proposed. Correlation 1 is developed by fitting the raw simulated data, although its form does not respect some of the limiting conditions. Particularly for k(s) < 5 W/mK and in the absence of thermal radiation, it under-predicts the effective thermal conductivity due to pure heat conduction (k(eff,PC)). Correlation 2, on the other hand, satisfies all possible limiting conditions, although it requires one additional simulation or correlation for k(eff,PC). Finally, correlation 3 is obtained by superposing the effective thermal conductivities due to pure radiation (k(eff.R)) and k(eff,PC), while introducing an adjustable coefficient in order to account for the coupling between them. From the investigation on radiative properties, it is observed that the extinction coefficient increases with the decrease in phi and with the increase in PPC as well as rho(s) and hence k(eff,t) as well as k(eff,R) is expected to decrease for these conditions. (C) 2018 Elsevier Ltd. All rights reserved.

The complete evaporation process inside an asymmetrically heated porous channel, under steady-state condition, has been numerically investigated in this article, based on the modified enthalpy formulation along with the assumption of Local Thermal Non-Equilibrium (LTNE). The governing equations have been discretised using finite volume method on both staggered and non-staggered grid arrangements and solved iteratively in a SIMPLE-like manner. All simulations have been carried out by applying the proposed smoothing algorithm for the effective diffusion coefficient in order to avoid the non-physical jump in the predicted temperature distributions. The performance of staggered and non-staggered grid layouts have been compared only on orthogonal coordinates for various parameters and the results show that the accuracy and effectiveness of the non-staggered and staggered grid layouts are identical. Different models for the partitioning of the wall heat flux have no influence on the total evaporated volume fraction. Effects of various parameters on the temperature and liquid saturation distributions have been carefully investigated, which clearly indicate that imposed heat flux, Reynolds number, Darcy number and thermal conductivity of the solid phase strongly influence the initiation and termination of phase change process, whereas the porosity has only a minor impact. Therefore, operating conditions and properties of porous media are required to be properly designed in order to achieve the desired objective. In addition, the results obtained using the modified h- and H-formulations have been compared and excellent agreement have been observed. It has been found that the modified h-formulation requires considerably less computation time as compared to that for the H-formulation and hence the method is strongly recommended for the future use. Nevertheless, it should now be extended in order to accommodate the multi-dimensional complex geometries that require the employment of curvilinear coordinates using non-staggered grid layout.

Numerical simulations carried out in powerful High-Perfomance-Computing (HPC) environments are becoming increasingly important for the design of improved filters for metal melts. However, the massive amount of data generated by such simulations impose challenges on data management and analysis. A particularly limiting factor is file system access, i.e. the so-called I/O bottleneck, that affects both data storage in the HPC environment and, more frequently and arguably more critically, the loading of data for analysis and visualization purposes in less powerful local workstations or visualization clusters. This article introduces LITE-QA, a method for reducing the amount of data in large-scale scientific simulations. During a simulation in the HPC environment, it supports both in-situ data compression and additional data indexing in an integrated fashion. During the analysis phase, it supports efficient query-based data retrieval where only data of interest to the user is loaded from the file system. The proposed approach is evaluated in a simulation of metal melt filtration using the lattice-Boltzmann method. As compared to conventional data storage methods, the amounts of data generated by the simulation are significantly reduced even including the additional indices. For exemplary visualization tasks, the amounts of data to be read from the file system are reduced to ~1.8-23.9% of the original data size, while yielding an overall speed-up of loading times by ~4.9-16.5×.

This study investigates the particle size distribution's effect on the microstructure and effective thermal conductivity (ETC) of alumina castables. The ETC was measured by the transient plane source method and predicted numerically based on a two-scale model describing the structure on a fine and coarse scale. The prediction considered particle and pore size distributions, porosity (around 20%) and grain morphology. The microstructure was investigated by scanning electron microscopy. For a constant fines content, increasing the coarse grain fraction while decreasing the medium fraction enhanced sintering of the matrix. Small pores (≤250nm) increased the sintering activity. The densest castable contained the most small pores. The particles’ and pores’ contributions to the sintering activity led to intensified microcracking and a decreased ETC. The numerical model did not consider constituents ≤500nm like the small pores and microcracks and the calculated ETC values consequently deviated from the measured values.

This study deals with the topic of synthesis gas (syngas) production from preheated, rich methane/air mixtures. The examined process is based on non-catalytic partial oxidation within a small-scale porous media based reformer, intended for application in Solid Oxide Fuel Cell (SOFC) based systems. For this purpose, process characteristics like temperature profiles within the porous material and exhaust syngas compositions were experimentally and numerically investigated under conditions that can be encountered in such systems. The soot content of the generated syngas was also measured using the technique of Scanning Mobility Particle Sizing. An important feature of the reformer, which was demonstrated during the experiments for a wide range of thermal loads (380-1895 kW/m(2)) and equivalence ratios (1.9-2.6), is the ability to operate based on stationary flames. This is achieved using a two-section design. The sections show a conical and a cylindrical geometry, whereas the same porous medium is installed in both of them. For this study, the solid matrix was created as packed bed of Al2O3-Raschig rings (62% open porosity). The process was simulated with a quasi-1D numerical model, which uses a volume-averaged approach. The model solves both the gas- and solid-phase energy balances explicitly and accounts for the radiative heat transport in the solid-phase. Peak temperatures measured within the porous zone provide evidence of superadiabatic combustion, which is also confirmed by the numerically predicted temperature profiles with the model. Syngas compositions reveal a maximum reforming efficiency of 65% based on H-2 and CO, while the soot limit of the process was found to lie at phi = 2.2, regardless of thermal load and preheat temperature of the fresh mixture. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

In the present investigation, the development of axial velocity profile, the requirement for development length ($L^*_{fd}=L/D_{h}$) and the pressure drop in the entrance region of circular and parallel plate micro-channels have been critically analysed for a large range of operating conditions ($10^{-2}\le Re\le 10^{4}$, $10^{-4}\le Kn\le 0.2$ and $0\le C_2\le 0.5$). For this purpose, the conventional Navier-Stokes equations have been numerically solved using the finite volume method on non-staggered grid, while employing the second-order velocity slip condition at the wall with $C_1=1$. The results indicate that although the magnitude of local velocity slip at the wall is always greater than that for the fully-developed section, the local wall shear stress, particularly for higher $Kn$ and $C_2$, could be considerably lower than its fully-developed value. This effect, which is more prominent for lower $Re$, significantly affects the local and the fully-developed incremental pressure drop number $K(x)$ and $K_{fd}$, respectively. As a result, depending upon the operating condition, $K_{fd}$, as well as $K(x)$, could assume negative values. This never reported observation implies that in the presence of enhanced velocity slip at the wall, the pressure gradient in the developing region could even be less than that in the fully-developed section. From simulated data, it has been observed that both $L^*_{fd}$ and $K_{fd}$ are characterised by the low and the high $Re$ asymptotes, using which, extremely accurate correlations for them have been proposed for both geometries. Although owing to the complex nature, no correlation could be derived for $K(x)$ and an exact knowledge of $K(x)$ is necessary for evaluating the actual pressure drop for a duct length $L^*0$ and $K_{fd}\le0$.

In this article, a numerical study on the sensitivity, related to the performance of open‐cell foams used for the depth filtration of liquid metals, on two characteristic morphological properties is presented. Therefore, simulations of fluid flow and particle transport inside an artificial foam structure are carried out, whose porosity and strut shape is varied within a certain expected range. For comparison purposes, however, the simulations are also performed for three typical ceramic foam filters (CFF) with pore densities of 20 and 30 PPI, whose geometries are obtained from CT scans. In order to allow for a comparison between the different structures, a reference length is introduced that relies upon the actual ratio of pores per volume. The evaluation is mainly based on the comparison of the hydraulic tortuosity, the viscous and the inertial permeability coefficients as well as the initial filtration coefficient for alumina inclusions, with their size ranging from of 10 to 40 μm at process conditions typically encountered during the aluminum filtration. It is shown that the ratio of filtration coefficient and pressure drop increases with the porosity, while the material distribution between the struts and the joints is less influential. Finally, the article also provides information on the anisotropy of CFFs and on the transition behavior from steady to unsteady flow in open‐cell foams.

In the present article, the performance and the efficiency of ceramic filters for continuous steel filtration in an induction crucible furnace, which is part of the steel casting simulator facility located at Technische Universität Bergakademie Freiberg, is investigated numerically. In order to achieve this objective, a macro‐scale simulation for the melt flow in the crucible is coupled with a pore‐scale simulation for the flow inside the ceramic filter that is adequately resolved by its detailed filter geometry, obtained from computed tomography scan images. The considerable influence of the filter on the flow field is indicated from the present results. Moreover, the efficiency of the employed filter is also determined and compared for two pore densities.

This article demonstrates an approach for the numerical modeling of open cell ceramic foams, in order to investigate the thermo‐mechanical behavior during metal melt filtration processes. The described methods include the creation of the geometric models, the fluid‐dynamic simulations of the melt flow using the lattice boltzmann method, and finite element simulations of the ceramic foam under general loads. The paper mainly focuses on the representative geometry generation process, such that the modeled geometry replicates the real foam as far as possible, since high quality models are essential for the quantitative analyses to be reliable. The present parametric studies demonstrate the manner, in which the foam properties may be influenced by changing the geometric and the topological properties, in order to improve the behavior during filtration processes.

The present article addresses the modeling issues, related to the numerical simulation of aluminum depth filtration inside a real filter section in presence of non-negligible temperature variation. The filter structure is obtained by digitizing the computed tomography (CT) scanned data of a characteristic ceramic foam filter. The modeling takes the process conditions of a filtration trial in a pilot casting line into account. The incompressible flow of liquid aluminum is solved by the lattice Boltzmann method (LBM) and the heat transfer is solved by the finite volume method (FVM). The temperature dependences of the viscosity and the density of liquid metal are specifically considered. Although the consideration of buoyancy force significantly affects the fluid flow, the temperature-dependent viscosity plays only a minor role. A Lagrangian tracking of particles is performed for modeling the filtration of inclusions. In accordance with the depth filtration theory, the computational results confirm an exponential decrease in the particle concentration with the filter depth. The overall filtration efficiency is found to remain almost unaffected by both buoyancy and temperature-dependent viscosity. Using the numerically determined filtration coefficient, the filtration efficiency is extrapolated for a real filter of larger length, although the experimental data are underpredicted.

In the present article, the numerical prediction of the effective thermal conductivity (k(eff)) of low-carbon refractory materials at high temperatures is investigated. The employed numerical methodology consists of computational geometry generation by a modified random sequential adsorption (RSA) algorithm and solution of a heat conduction problem in the generated material sample by the finite volume method (FVM). The probability distributions, employed for modelling the grain sizes, are reexamined. Several aspects are recognised as crucial for reasonable predictions of k(eff) in the considered range from the room to the coking temperature. First, an appropriate estimate of the equivalent thermal conductivity k(rest) of the unresolved fine-scaled material is required, which is obtained from the effective medium theory (EMT). Furthermore, modelling the thermal expansion of the coarse and medium grains, leading to the formation of air gaps between the grains and the continuous phase at lower temperature, is extremely important. The presence of these air gaps could be implemented in FVM. The numerical predictions of keff show reasonably good agreement with experimental data in the complete temperature range, only if this gap width is considered as a function of the operating temperature, along with k(rest) and the temperature-dependent thermal conductivities of the constituents.

In the present article, the effective thermal conductivity (ETC) of 10 ppi open-cell ceramic foams is measured at temperatures ranging from 22 degrees C to 750 degrees C using the transient plane source (TPS) technique. The detailed morphology of the foam structures is reconstructed from 3D Cr-scan images and their structural analysis is carried out using a volume image processing tool. The experimental results are compared with the predictions of directional ETC, obtained using a simplified 1D homogeneous model that considers coupled conduction-radiation heat transfer. The parameters, required by the model, are evaluated based only upon the information that could be extracted from 3D Cr-scan images under certain simplifying assumptions. It can be concluded that the predictions of ETC for the present ceramic foam samples clearly correlate with the geometric parameters obtained from their structural analysis. It is also observed that the estimated microscopic porosity of the foam, which is not captured by 3D Cr-scan images, has considerable influence on the reconstructed foam structure and hence on the predicted ETC. The predictions of ETC in the measured direction, obtained after the proposed directional averaging, compare extremely well with TPS measurements for the complete range of investigated temperatures. This suggests that the measurements of ETC, obtained employing TPS technique, are the directionally averaged representations of ETC in three perpendicular directions. The present investigation also clearly demonstrates the potential of the simplified modeling approach for characterizing even the directional ETC of open-cell ceramic foams, based primarily on their structural information. (C) 2016 Elsevier Ltd. All rights reserved.