Porous Region Research Articles

High power and energy density of a wavy PCM unit embedded in a solar air heater utilizing fractional porous media

This experimental and numerical investigation presents the optimization of a wavy PCM unit to obtain high power and energy density with and without porous media for solar air heater applications at low ambient temperature (12oC≤Ta≤24oC). Hence, paraffin wax as a thermal energy storage material and wire mesh as a porous media are selected in this investigation. The effect of the fractional porous region (25%≤ψ≤100%) and porosity (94%≤ϕ≤100%) of the PCM unit is investigated to obtain desired power and energy density. The obtained numerical results revealed that the porous fraction region (ψ) of 50% and porosity (ϕ) of 96% are the optimum value in wavy PCM unit to obtain high power and energy density. As an extension of this work, the optimized thermal energy storage unit is further utilized in an impinging jet solar air heater design to obtain instant and long thermal backups and, consequently, outlet air at high temperature. The wavy PCM unit embedded impinging jet solar air heater is experimentally investigated under outdoor conditions for two cases; viz, to obtain instant and long thermal backups. To obtain instant and long thermal backups, a full day and alternative operations are conducted. Whereas, in case of alternative operation, charging of the PCM unit is only done up to the maximum sunshine hour of the day and solar air heater is operated during the night to utilize stored thermal energy at high power and energy density to deliver outlet air at high temperature for the long duration. Moreover, the experimental results revealed a maximum outlet air temperature of 59°C at 0.01 kg/s and a significant thermal energy backup up to 5 h at an outlet air temperature gain of ≥ 5°C. The economic analysis is also conducted for the solar air heater design and the operating cost is obtained as 0.02 INR/kWh at the optimum condition.

Entropy generation analysis of non-miscible couple stress and Newtonian fluid in an inclined porous channel with variable flow properties: HAM Analysis

The aim of this study is to investigate the entropy production characteristics of two non-miscible fluids in an inclined porous channel with temperature-dependent thermal conductivity and viscosity. The porous region of the channel is divided in two regions. In region-1 and region-2, the Couple stress and Newtonian fluid take place due to constant pressure gradient, respectively, under the influence of a uniform magnetic field. Here, the Darcy–Brinkman model is used for the flow of immiscible fluid through the porous media. In this work, we used a semi-analytical method named as homotopy analysis method (HAM) to solve the coupled nonlinear ordinary differential equations. The goal of the considered problem is to examine the consequences of a variety of thermophysical parameters, including Hartmann number, varying viscosity parameter, varying thermal conductivity parameters, and Grashof number on the characteristics of entropy generation, Bejan number distribution, thermal behavior and flow characteristics of non-miscible couple stress and Newtonian fluid passing through a porous channel. The novel aspect of this study is the formation of entropy and Bejan number as a result of non-miscible Newtonian and couple stress fluids with varying thermal conductivity and viscosity in porous media. In terms of rheological investigation, a semi-analytical simulation for changeable thermal and flow properties in an immiscible Newtonian and couple stress fluid via an inclined porous channel is a brand-new concept, and the behaviors of such flows have not been examined yet. From this study, it is concluded that on raising the variable thermal conductivity, Hartmann number and the permeability of the porous medium, the flow velocity, thermal characteristics and entropy generation number decrease. The authors also come to the significant conclusion that non-miscible Newtonian and couple stress fluids have larger entropy production numbers, flow velocities, and temperature profiles for higher values of Grashof number, variable viscosity parameter, and couple stress parameter. The findings of this work have also been graphically validated through the previously established work. The results of the present analysis can be used in petroleum industry, lubrication theory, etc.

THz dual-core liquid photonic crystal fiber with high negative dispersion

A novel photonic crystal fiber (PCF) design is proposed and analyzed with highly negative dispersion for THz applications. The reported PCF has TOPAS background material due to its low material loss in THz regime. Further, dual porous cores are constructed and selectively infiltrated with liquid crystal (LC) material to control the dispersion characteristics of the reported PCF. The basic operation of the suggested dual core LCPCF (DC-LCPCF) depends on the optical coupling between the supported modes of the two porous core regions in the THz regime to achieve high negative dispersion for the two fundamental polarizations: transverse electric (TE) and transverse magnetic (TM). The coupling can be switched between the TE and TM modes by applying an external electric field on the LC material via two metallic electrodes. The full vectorial finite element method (FVFEM) is utilized to study the dispersion characteristics of the DC-LCPCF structure. The obtained results reveal that the TE and TM modes have large negative chromatic dispersions of − 44.57 ps/THz/cm and − 30.59 ps/THz/cm at frequencies of 0.386 THz and 0.4027 THz, respectively. So, it will be a solution for further innovation of fiber devices in the THz regime.

Rapid Prediction of the In Situ Pyrolysis Performance of Tar-Rich Coal Using the POD Method

In this paper, a POD reduced-order interpolation model for solving the in situ pyrolysis process of tar-rich coal is employed to predict the flow and heat transfer performance in the porous media region so as to save computational resources and realize fast calculations. Numerical simulation using the finite volume method (FVM) is firstly used to obtain sample data, based on the samples through the primary function and spectral coefficients of the solutions. The physical field information and parameter distribution under different conditions of inlet temperature, inlet velocity and permeability are predicted. The results are compared with those of FVM to verify the accuracy of the calculated results. The relative mean deviation (RME) of the results of the POD prediction of each parameter for each working condition was synthesized to be no more than 5%. The performance of in situ pyrolysis of tar-rich coal is then investigated, and the oil and gas production are predicted. As the inlet velocity increases from 0.3 m/s to 0.9 m/s, the fraction of high-quality oil and gas production reaches 0.47 and then decreases to 0.38. Increasing the inlet temperature and permeability has a negative effect on the fraction of high-quality hydrocarbon production, after which the quality fraction of high-quality oil and gas dropped sharply to about 0.22. Porosity has a positive impact on the oil and gas production. When the porosity reaches 0.3, the quality fraction of high-quality oil and gas can reach 0.27.

Application of graded phase change materials for solar energy inter-seasonal storage heating and thermal storage characteristics

Abstract In this paper, firstly, the heat transfer characteristics of the stepped phase change accumulator are studied, and the location of the solid-liquid phase interface is determined by the phase fraction in a fixed grid scheme, while the phase change heat transfer process is simulated using Fluent. Secondly, for the phase change heat transfer problem, the enthalpy-porosity method in the Solidification/Melting model is used to treat the solid-liquid mixed paste region of the phase interface as a porous media region, and the evaluation system is constructed in terms of heat storage and discharge efficiency, heat storage, and heat recovery efficiency. Then the mathematical model, boundary conditions and solution parameters of the stepped phase change heat accumulator are set, and the data analysis of the effect of the pool height-to-diameter ratio on the heat storage in the solar inter-seasonal storage heating system is carried out by using ANSYSCFD software. The results show that the heat storage of the system also shows an overall increasing trend with the increase of the pool height-to-diameter ratio, and the heat storage of the system increases faster when the height-to-diameter ratio increases from 0.2 to 1.0 in sequence, and the heat storage of the system increases less when the height-to-diameter ratio changes between 0.9 and 1.8, and basically tends to be stable. This study realizes the graded heat storage and graded heat use of solar energy, which is useful for the research of solar heat supply and heat storage.

An ultrasonic phantom for cortical and cancellous bone

There is interest in developing ultrasonic techniques for diagnosing osteoporosis. Many techniques perform measurements at skeletal sites such as the heel, hip, and spine where the bone tissue consists of a non-porous outer layer of cortical bone that surrounds a porous interior region of cancellous bone. The goal of the present study was to develop an ultrasonic phantom that simulates this tissue configuration. A block of polymer open cell rigid foam (OCRF) was partially embedded in a thin layer of clear epoxy casting resin to create the phantoms. The resulting phantoms were 40mm × 40 mm × 20 mm with one 40 mm × 40 mm face embedded in ∼3mm of resin. Ultrasonic measurements were performed to characterize the speed of sound and attenuation of the resin and the OCRF separately and together, as configured in the phantom. Backscatter measurements were also performed. The resulting specimens can be used to investigate how non-normal incidence of an ultrasonic wave on the bone cortex may produce errors in these measurements.

Corrosion behavior of Al2O3-modified Yb2SiO5 environmental barrier coating under water vapor conditions at 1500 °C

Al2O3-modified Yb2SiO5 was prepared as environmental barrier coating (EBC), and the water vapor corrosion behavior at 1500 °C was investigated. The residual phase, Yb2O3, was observed in the as-prepared coating besides Yb2SiO5 and Al2O3, which preferred to react with Al2O3 to form toughened Yb3Al5O12, meanwhile gave rise to the growth of diffusion layer (Yb2Si2O7) and prevented the generation of the porous region under EBC layer after exposure. The growth stress of the TGO layer and the thermal stress during cooling were the driving sources of delamination, which limited the service life of EBCs. Conclusions on phase transformation and interface evolution in this work are expected to guide the design of rare earth silicate EBCs.

Scattering Study of a Composite Breakwater Placed in Front of an Impermeable Back Wall under the Action of Water Waves

Based on the assumption of linear potential flow theory, the scattering problem of a composite breakwater placed in front of an impermeable back wall is theoretically investigated. The velocity potential in each subregion is found using the eigenfunction expansion method. The boundary conditions of the porous region are treated using Darcy’s law. The semi-analytical solution of a composite breakwater placed in front of an impermeable back wall is then obtained based on the matching conditions of the boundaries of the different regions. The effects of different parameters on the wave loads and wave amplitudes are investigated. In addition, to better understand the performance of the composite breakwater, the scattering problem of the composite breakwater without considering an impermeable back wall is also investigated. The correctness of this theoretical model is verified by comparing the results with previous work. Based on the results of hydrodynamic calculations and analysis of various aspects of a composite breakwater placed in front of an impermeable back wall, the study of the effect of a composite breakwater placed in front of an impermeable back wall allows us to propose a long-term and cost-effective solution for the protection of various marine facilities from wave attacks.

Mathematical Model of the Flow in a Nanofiber/Microfiber Mixed Aerosol Filter

A new mathematical model of an aerosol fibrous filter, composed of a variety of nano- and microfibers, is developed. The combination of nano- and microfibers in a mixed-type filter provides a higher overall quality factor compared with filters with monodisperse fibers. In this paper, we propose a mathematical model of the flow of an incompressible fluid in a porous region consisting of a set of cylinders of various diameters in the range of nano- and micrometers to describe a mixed-type aerosol filter. The flow domain is a rectangular periodic cell with one microfiber and many nanofibers. The motion of the carrier medium is described by the boundary value problem in Stokes flow approximation with the no-slip boundary condition for microfibers and the slip condition for nanofibers. The boundary element method taking into account the slip and non-slip conditions is developed. The calculated velocity field, streamlines, vorticity distribution, and drag of separate fibers and the entire periodic cell are presented. Numerical results for the drag force of the porous medium of a mixed-type filter for the various ratios of mass proportion of nano- and microfibers, porosity, and filtration velocity are presented. The obtained results are compared with the analytical formulas based on the approximate theory of filtration of bimodal filters and with known experimental data. It is shown that with an increase in the mass fraction of nanofibers, the total drag force of the cell increases, while the relative contribution of nanofibers to the total drag force tends toward the value that is less than unity. An approximate analytical formula for the drag coefficient of a mixed aerosol filter is derived. The developed flow model and analytical formulas allow for estimating the aerodynamic drag of a mixed filter composed by nano- and microfibers.

Linear stability of longitudinal convective rolls in a non-Darcy porous layer filled with nanofluid due to viscous dissipation effect: A realistic approach

The onset of longitudinal convective rolls of nanofluid flow inside a horizontal porous material using Brinkman theory due to the viscous dissipation effect has been addressed numerically. An infinitely long horizontal porous region has been considered which is confined between two rigid boundaries. The boundaries of the channel are considered adiabatic (lower) and isothermal (upper). Brownian motion and thermophoresis properties are taken into consideration for nanofluid. In the linear stability analysis, oblique roll disturbances with arbitrary orientation are taken into account, where the preferred mode of instability i.e., longitudinal rolls (when P=0 or ϑ=π/2) are shown. Finally, the resulting eigenvalue problem is solved in MATLAB using the bvp4c technique. The impact of improving the modified diffusivity ratio (NA<10), Lewis number (Le<,=,>1), concentration Rayleigh number (Rn) and modified particle density increment (NB≈10−2−10−5) is to accelerate the instability boundaries, while the switching parameter (ξ) has a dual character on it. Further, the pattern of the streamlines are slightly compressed in the channel’s center for large values of ξ, whereas no markable changes are noticed for higher values of NA. The isotherms lines are closer near the adiabatic boundary when ξ takes small values.

Optical, vibrational, electrical, and electrochemical studies of new plasticized methylcellulose‐based solid polymer electrolytes for supercapacitor application

AbstractIn this work, new plasticized solid polymer electrolytes (SPEs) are developed using MC (methylcellulose) as a polymer host, and sodium iodide (NaI) as a dopant via the solution casting method. Ethyl carbonate (EC) is used as a plasticizing agent to improve the properties of the SPEs. Polarized optical microscopy analysis reveals that the surface morphology of the MC‐NaI‐EC films contained porous amorphous regions owing to the presence of EC. The complex formation between MC, NaI, and EC is confirmed by Fourier‐transform infrared spectra. The addition of EC in the MC‐NaI polymer salt matrix enhances the electrochemical properties of the prepared films. The highest ionic conductivity of 5.06×10−3 S/cm is achieved for the composition: MC+50 wt. % NaI +10 wt. % EC. The linear sweep voltammetry test reveals that the optimal plasticized‐SPE can withstand up to 2.5 V. The ionic transference number analysis reveals that 99% of ions contribute to the total conductivity. The optimized SPE film and graphene oxide‐based electrodes are used to manufacture a solid‐state electrical double‐layer capacitor. The coulomb efficiency of the supercapacitor cell is 100%, and the specific capacitance of the supercapacitor is found to be 18.56 F/g utilizing impedance data at low frequency.

Heat and mass transfer analysis of nonmiscible couple stress fluid in a porous saturated channel

The present flow problem analyzes the impact of radiative heat and mass transfer with inclined magnetic field on thermal exchange and entropy production of two immiscible nature of electrically conducting couple stress fluid in a static porous saturated conduit. In this model, the lower and upper porous regions of the rectangular channel are occupied by two different types of couple stress fluids. The static horizontal parallel plates of the porous duct are completely isothermal and the flow of immiscible fluid through the porous duct develops because of a constant pressure gradient at the entry zone of the duct. The Brinkman model is utilized in the modeling of fluid flow through porous saturated domain and Rosseland’s approximation is utilized to compute the radiative thermal exchange effect on nonmiscible couple stress fluid. In this work, authors have analyzed the effect of various thermo-physical parameters such as the Hartmann number (Ha), permeability parameter (Da), Schmidt number (Sc), Soret number (Sr) and couple stress parameter ([Formula: see text]) on the entropy generation characteristics, Bejan number distribution, thermal behavior, concentration distribution and flow characteristics of immiscible couple stress fluid which passes through the porous channel. The parameters Ha, Da, [Formula: see text], Sc, Sr correspond to magnetic field effect, permeability of porous media, couple stress, mass diffusion and thermal diffusion, respectively. The most significant findings of this research work are as follows: • In a porous saturated channel, the immiscible couple stress fluid velocity, entropy production number and thermal profile get enhanced on increasing the couple stress parameter. • On increasing the Hartmann number and decreasing the permeability of porous region, the thermal properties and entropy production number both decrease. • The couple stress fluid’s concentration field and Bejan number distribution get decreased on enhancing Soret number Sr and Schmidt number Sc. • The entropy generation near the wall of the channel rapidly increases on increasing the Schmidt number and Soret number. The emerging finding of this research work exhibits excellent agreement with previously published work. This research work can be utilized in food processing, petroleum products and chemical process.

Lattice Boltzmann Modelling of Fluid Flow through Porous Media: A Comparison between Pore-Structure and Representative Elementary Volume Methods

In this study, we present a novel comparison between pore-structure (PS) and representative elementary volume (REV) methods for modelling fluid flow through porous media using a second-order lattice Boltzmann method (LBM). We employ the LBM to demonstrate the importance of the configuration of square obstacles in the PS method and compare the PS and the REV methods. This research provides new insights into fluid flow through porous media as a novel study. The behaviour of fluid flow through porous media has important applications in various engineering structures. The aim of this study is to compare two methods for simulating porous media: the PS method, which resolves the details of the solid matrix, and the REV method, which treats the porous medium as a continuum. Our research methodology involves using different arrangements of square obstacles in a channel including in-line, staggered and random for the PS method and a porosity factor and permeability value for the REV method. We found that the porosity and obstacle arrangement have significant effects on the pressure drop, permeability and flow patterns in the porous region. While the REV method cannot simulate the details of fluid flow through pore structures compared to the PS method, it is able to provide a better understanding of the flow field details around obstacles (Tortuosity). This study has important applications in improving our understanding of transport phenomena in porous media. Our results can be useful for designing and optimizing various engineering systems involving porous media.

Thermal performance of nanofluids in a sinusoidal channel with embedded porous region

Inclusion of porous structures in micro-channels enhances heat transfer rates in energy harvesting devices, which signifies as the working fluid becomes a nanofluid. The present study compares the thermal performance of CuO-water, TiO2-water and graphene-water nanofluids in a sinusoidal channel with a porous insert. The flow and heat transfer characteristics are simulated and the effects of volumetric fraction of nanofluids, Reynolds number ( Re), porous insert width, and its permeability on the flow and temperature fields are examined. The findings reveal that CuO-water nanofluid results in higher heat transfer rates than those of other nanofluids considered. Graphene-water nanofluid gives rise to lower performance than that of CuO-water nanofluid in terms of convection heat transfer despite the fact that graphene has higher thermal conductivity than CuO. In this case, a decrease in Nusselt number of as much as 6.34% is observed for CuO-water nanofluid among all the cases considered for the Reynolds number of 100. Increasing the permeability of the porous insert slightly enhances (∼0.24%) the average Nusselt number. The porous insert with a small width in the channel improves the heat transfer rates (2.25% increase in Nusselt number), i.e. the average Nusselt number reduces as the porous insert width increases.

Chemical and thermal performance analysis of a solar thermochemical reactor for hydrogen production via two-step WS cycle

Ceria-based H2O/CO2-splitting solar-driven thermochemical cycle produces hydrogen or syngas. Thermal optimization of solar thermochemical reactor (STCR) improves the solar-to-fuel conversion efficiency. This research presents two conceptual designs and thermal modelling of RPC-ceria-based STCR cavities to attain the optimal operating conditions for CeO2 reduction step. Presented hybrid geometries consisting of cylindrical–hemispherical and conical frustum–hemispherical structures. The focal point was positioned at x = 0, -10 mm, and -20 mm from the aperture to examine the flux distribution in both solar reactor configurations. Case-1 with 2 milliradian S.E (slope error) yields a 27% greater solar flux than case-1 with 4 milliradians S.E, despite the 4 milliradian S.E produces an elevated temperature in the reactor cavity. The mean temperature in the reactive porous region was most significant for case-2 (x = -10 mm) with 4 mrad S.E for model-2, reaching 1966 K and 2008 K radially and axially, respectively. In case-2 (x = -10 mm) for 4 mrad S.E, model-1 attained 1720 K. The efficiency analysis shows that the highest conversion efficiency value was obtained to be 7.95% for case-1 with 4 milliradian S.E.

On torsional wave in void type porous layers between viscoelastic and piezoelectric media with parabolic irregularity

The viscoelastic earth model is increasingly utilized by seismologists for studying surface seismic wave propagation through Earth’s porous crustal regions such as granular materials, including rock, soils, and synthetic porous bodies. The present study characterizes torsional wave propagation in an irregular void-type porous layer sandwiched between an initially stressed inhomogeneous viscoelastic layer and a piezoelectric substratum. Displacement fields for the layer and half spaces are obtained separately using a variable separable technique, whereas volume fraction and electric potential field are derived for layer and substratum, respectively using the matrix calculus approach. Dispersion relations have been derived for both electrically open and short circuit conditions and agree with standard results. Particular cases have been deduced to validate the finding of the study with literature results. Effects of change in relevant parameters such as initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity and dissipation factor have been analyzed on the phase velocity of the torsional wave through various plots and summarized in a tabular form for ready reference to researchers. Analysis of the present geophysical problem may be useful in characterizing torsional velocity in porous silicate rocks which are abundantly found in the transition zone between oceanic and continental crust called Conrad discontinuity. Highlights Torsional propagation in a void-type porous layer crammed between an initially stressed inhomogeneous viscoelastic layer and piezoelectric half-space has been investigated. Variable separable technique, the matrix calculus approach is used for computing the displacement fields of respective media. A comparative study has been carried out for both electrically open and short conditions. The impact of pertinent parameters including initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity, and dissipation factor on the phase velocity of the torsional wave has been examined.

STRUCTURAL DEFECTS AND VARIABLE POROSITY IN 3D-PRINTED CUPS FROM SIX MANUFACTURERS

3D printing is rapidly being adopted by manufacturers to produce orthopaedic implants. There is a risk however of structural defects which may impact mechanical integrity. There are also no established standards to guide the design of bone-facing porous structures, meaning that manufacturers may employ different approaches to this. Characterisation of these variables in final-production implants will help understanding of the impact of these on their clinical performance.We analysed 12 unused, final-production custom-made 3D printed acetabular cups that had been produced by 6 orthopaedic manufacturers. We performed high resolution micro-CT imaging of each cup to characterise the morphometric features of the porous layers: (1) the level of porosity, (2) pore size, (3) thickness of porous struts and (4) the depth of the porous layers. We then examined the internal cup structures to identify the presence of any defects and to characterise: (1) their total number, (2) volume, (3) sphericity, (4) size and (5) location.There was a variability between designs in the level of porosity (34% to 85%), pore size (0.74 to 1.87mm), strut thickness (0.28 to 0.65mm), and porous layer depth (0.57 to 11.51mm). One manufacturer printed different porous structures between the cup body and flanges; another manufacturer printed two differing porous regions within the cup body.5 cups contained a median (range) of 90 (58–101) defects. The median defect volume was 5.17 (1.05–17.33) mm3. The median defect sphericity and size were 0.47 (0.19–0.65) and 0.64 (0.27–8.82) mm respectively. The defects were predominantly located adjacent to screw holes, within flanges and at the transition between the flange and main cup body; these were between 0.17 and 4.66mm from the cup surfaces.There is a wide variability between manufacturers in the porous titanium structures they 3D print. The size, shape and location of the structural defects identified are such that there may be an increased risk of crack initiation from them, potentially leading to a fracture. Regulators, surgeons, and manufacturers should be aware of this variability in final print quality.

Impact of controlled prewetting on part formation in binder jet additive manufacturing

Binder jetting is an additive manufacturing process that bonds powder through selectively depositing binder by inkjet printing. The part is then extracted and densified by sintering and/or infiltration. The process offers low costs and fast build rates, but properties can be poor due to residual porosity after sintering. The inkjet printing process may contribute to this residual porosity by creating large pores. The droplet kinetic energy ejects some powder particles from the bed and rearranges others. Particle ejection and rearrangement are theorized to create porous regions in binder-jetted parts. In this work, small amounts of moisture are added to the spread powder before printing and the impact on part formation, part properties, and printing parameters measured with varied droplet spacing, droplet velocity, and print frequency. Moisture is added by applying an atomized fluid mixture to the powder between layer spreading and binder printing. The fluid mixture partially evaporates but leaves a stable residue to increase cohesion and enhance imbibition. Moisture addition to the powder increases the range of droplet spacings for line formation while reducing particle ejection, powder rearrangement, and balling in layer and multilayer parts. Excessive moisture addition decreases the effective saturation of printed lines, but saturation in 3D parts is less impacted. Increased surface roughness in the first few layers of a print was also mitigated with prewetting. High-speed X-ray imaging verified prewetting reduction in particle ejection and rearrangement.

A fully decoupled numerical method for Cahn–Hilliard–Navier–Stokes–Darcy equations based on auxiliary variable approaches

A fully decoupled, linearized, and unconditionally stable finite element method is developed to solve the Cahn–Hilliard–Navier–Stokes–Darcy model in the coupled free fluid region and porous medium region. By introducing two auxiliary energy variables, we derive the equivalent system that is consistent with the original system. The energy dissipation law of the proposed equivalent model is proven. To lay a solid foundation, we first present a coupled linearized time-stepping method for the reformulated system, and prove its unconditionally energy stability. In order to further improve the computational efficiency, special treatment for the interface conditions and the artificial compression approach are utilized to decouple the two subdomains and the Navier–Stokes equation. Therefore, with the discretization techniques of two existing auxiliary variable approaches, a fully decoupled and linearized numerical scheme can be developed, under the framework of a semi-implicit semi-explicit scheme for temporal discretization and Galerkin finite element method for spatial discretization. The grad-div stabilization is also employed to further improve the stability of auxiliary variable algorithm. The full discretization obeys the desired energy dissipation law without any temporal restriction. Moreover, the implementation process is discussed, including the adaptive mesh strategy to accurately capture the diffuse interface. Ample numerical experiments are performed to validate the typical features of developed numerical schemes, such as the accuracy, energy stability without restriction for time step size, and adaptive mesh refinement in space. Furthermore, we apply the proposed numerical method to simulate the shape relaxation and the Buoyancy-driven flows, which demonstrate the applicability of the proposed method.

Cracking during freeze‐drying in dense freeze cast ceramics: Role of drying rate

AbstractCracks can form during the freeze‐drying of freeze cast ceramic suspensions while attempting to produce dense ceramics. The suspensions contain alumina particles dispersed in cyclohexane. The rate of drying is controlled by the pressure and temperature during drying (slow drying at atmospheric pressure and −15°C and fast drying under vacuum while the temperature slowly increases from −80°C to room temperature). X‐Ray micro‐computed tomography was used to characterize internal crack formation. Cracks were found to occur during freeze‐drying rather than during freezing. Both slow and fast drying produced cracks, although two different morphologies were observed. Mechanistic models are proposed for the formation of both types of cracks. The rate of freezing was found to influence the formation of cracks. Slow freezing tended to reduce the formation of drying cracks because the slower freezing produced a more heterogeneous distribution of particles and porous regions, which tends to allow stress to be relieved by opening up existing pores rather than forming cracks in the more homogeneous fast frozen bodies.