Multiple-relaxation-time Lattice Boltzmann Method Research Articles

A parallel computational study of power-law non-Newtonian nanofluid in a C-shaped enclosure by multiple-relaxation-time lattice Boltzmann simulation

ABSTRACT This study aims to numerically examine the heat transfer and entropy generation of non-Newtonian power-law nanofluids in a C-shaped cavity filled with porous media considering the Brinkman-Forchheimer extended Darcy model (BFEDM). The graphics processing unit (GPU) based multiple-relaxation-time lattice Boltzmann method (MRT-LBM) was used through computing unified device architecture (CUDA) C/C++ platform. It is a known fact that the fluid viscosity varies with the shear rate and nanoparticle sizes and the thermal conductivity also varies with the fluid temperature. However, the extension of such phenomena needs to be further investigated to understand any specific threshold in heat transfer application. To leverage such characteristics, it is permissible to add certain input parameters. As a result, the power-law indices ( n ), the Darcy number ( Da ), the volume fraction of nanoparticles ( ϕ ), the Rayleigh number ( Ra ), and the fixed porosity ( ε = 0.4 ) were the five key parameters considered to analyze the numerical results. The GPU-based numerical code was validated with the available benchmark results, and good agreements were obtained. The results showed that the average rate of heat transfer in terms of the average Nusselt number ( Nu ‾ ) increased due to an increase in Ra due to the enhanced buoyancy force and a reduction in the .

Simulation of High-Viscosity Generalized Newtonian Fluid Flows in the Mixing Section of a Screw Extruder Using the Lattice Boltzmann Model.

The mixing quality of polymer melts in the mixing section of a single-screw extruder and an injection molding machine has considerable effects on the properties of the molded products. Therefore, the study of the flow field of polymer melts in the mixing section is of great importance. The lattice Boltzmann method (LBM) exhibits unique advantages in simulating non-Newtonian fluids. Many researchers have used LBM to study the flow of medium- and low-viscosity fluids. In their studies, the Reynolds number of fluid flows is generally moderate. However, polymer melts are typical high-viscosity fluids, and their flow Reynolds number is generally very small. The single-relaxation-time lattice Boltzmann method (SRT-LBM) has been used previously to study the flow field of power law fluids in the mixing section. Herein, the flow field of high-viscosity generalized Newtonian fluids in the mixing section of a single-screw extruder is studied using SRT-LBM, the two-relaxation-time lattice Boltzmann method (TRT-LBM), and the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). Through comparison, TRT-LBM has been found to exhibit obvious advantages regarding stability, calculation accuracy, calculation efficiency, and selection of simulation parameters. The TRT-LBM is more suitable for studying high-viscosity generalized Newtonian fluids than SRT-LBM and MRT-LBM. SRT-LBM has low computational efficiency when simulating high-viscosity generalized Newtonian fluids, and instability is easily caused when the fluid has a yield stress. For MRT-LBM, only by studying the relaxation parameters can its advantages be fully utilized. However, optimizing the accuracy and stability of the MRT-LBM via parameter research and linear stability analysis is difficult. For non-Newtonian fluids, it is difficult to optimize the relaxation parameters to make the MRT-LBM more stable and accurate than the TRT-LBM. It is difficult for the MRT-LBM to realize its potential when simulating high-viscosity generalized Newtonian fluids. In addition, we studied the flow pattern in the cross section of the screw channel and compared it to the results reported in previous studies.

Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues.

In this paper, we develop a general rectangular multiple-relaxation-time lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations(NSEs) and nonlinear convection-diffusion equation(NCDE) by extending our recent unified framework of the multiple-relaxation-time lattice Boltzmann (MRT-LB) method [Chai and Shi, Phys. Rev. E 102, 023306 (2020)10.1103/PhysRevE.102.023306], where an equilibrium distribution function (EDF) [Lu et al., Philos. Trans. R. Soc. A 369, 2311 (2011)10.1098/rsta.2011.0022] on a rectangular lattice is utilized. The anisotropy of the lattice tensor on a rectangular lattice leads to anisotropy of the third-order moment of the EDF, which is inconsistent with the isotropy of the viscous stress tensor of the NSEs. To eliminate this inconsistency, we extend the relaxation matrix related to the dynamic and bulk viscosities. As a result, the macroscopic NSEs can be recovered from the RMRT-LB method through the direct Taylor expansion method. Whereas the rectangular lattice does not lead to the change of the zero-, first- and second-order moments of the EDF, the unified framework of the MRT-LB method can be directly applied to the NCDE. It should be noted that the RMRT-LB model for NSEs can be derived on the rDdQq (q discrete velocities in d-dimensional space, d≥1) lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, while there are no rectangular D3Q13 and D3Q15 lattices within this framework of the RMRT-LB method. Thanks to the block-lower triangular relaxation matrix introduced in the unified framework, the RMRT-LB versions (if existing) of the previous MRT-LB models can be obtained, including those based on raw (natural) moment, central moment, Hermite moment, and central Hermite moment. It is also found that when the parameter c_{s} is an adjustable parameter in the standard or rectangular lattice, the present RMRT-LB method becomes a kind of MRT-LB method for the NSEs and NCDE, and the commonly used MRT-LB models on the DdQq lattice are only its special cases. We also perform some numerical simulations, and the results show that the present RMRT-LB method can give accurate results and also have a good numerical stability.

Multiple upscaling procedures for gas transfer in tight shale matrix-fracture systems

Multiple upscaling schemes for gas transfer in nanoporous media, microporous matrix, core-scale matrix, and centimeter-scale matrix-fracture systems are investigated. An Open Multi-Processing (OpenMP)-based parallelized multi-scale numerical solver for micro-gaseous flow in composite microporous media is developed by coupling the pore-scale multiple-relaxation-time lattice Boltzmann method (MRT-LBM) and representative elementary volume (REV)-scale LBM model. The permeability of the microporous matrix is calculated through hundreds of pore-scale simulations for gas transfer in nanoporous media, before being imported into the REV-scale LBM to predict the core-scale matrix permeability. It is followed by the investigations of the variations of core-scale permeability with the heterogeneous spatial distribution of organic matter aggregates, mineral aggregates, interparticle pores, and microfractures. The parallel and sequential gas transfer processes in a larger shale system containing the tight matrix and hydraulic fractures are studied and analyzed. The results reveal several new insights: 1) the microscale spatial distribution of multiple constituents has relatively little effect on the core-scale permeability; 2) an ultra-large local pressure gradient occurs in a thin boundary layer of tight shale matrix, which is shown to be proportional to the square root of the permeability ratio, resulting in considerable flow characteristic velocity in the matrix; 3) the in-situ matrix-fracture transfer satisfies a sequential transport process due to a long equilibration time delay between the tight matrix and fractures; 4) the observed high production rate for tight shale may be caused by the ultra-large local pressure gradient in the matrix (and not by a large apparent permeability as commonly assumed). The results also reveal some anomalous phenomena for multiscale gas transfer in tight shale formations.

A joint absorbing boundary for the multiple-relaxation-time lattice Boltzmann method in seismic acoustic wavefield modeling

Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation, and then obtains the corresponding seismic wavefield. Usually, when the subsurface structure is finely constructed and the continuity of media is poor, this strategy is difficult to meet the requirements of accurate wavefield calculation. This paper uses the multiple-relaxation-time lattice Boltzmann method (MRT-LBM) to conduct the seismic acoustic wavefield simulation and verify its computational accuracy. To cope with the problem of severe reflections at the truncated boundaries, we analogize the viscous absorbing boundary and perfectly matched layer (PML) absorbing boundary based on the single-relaxation-time lattice Boltzmann (SRT-LB) equation to the MRT-LB equation, and further, propose a joint absorbing boundary through comparative analysis. We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional (2D) and three-dimensional (3D) cases, respectively. Then, we verify the effects of this absorbing boundary scheme on a 2D homogeneous model, 2D modified British Petroleum (BP) gas-cloud model, and 3D homogeneous model, respectively. The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary, the joint absorbing boundary has the best absorption performance, although it is a little bit complicated. Therefore, this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields, which is pivotal to its wide application in the field of exploration seismology.

A New Multi-Level Grid Multiple-Relaxation-Time Lattice Boltzmann Method with Spatial Interpolation

The traditional multi-level grid multiple-relaxation-time lattice Boltzmann method (MRT-LBM) requires interpolation calculations in time and space. It is a complex and computationally intensive process. By using the buffer technique, this paper proposes a new multi-level grid MRT-LBM which requires only spatial interpolation calculations. The proposed method uses a center point format to store multi-level grid information. The grid type determination in the flow field calculation domain is done using the axis aligned bounding box (AABB) triangle overlap test. According to the calculation characteristics of MRT-LBM, the buffer grid is proposed for the first time at the interface of different levels of grids, which is used to remove the temporal interpolation calculation and simplify the spatial interpolation calculation. The corresponding multi-level grid MRT-LBM algorithm is also presented for two-dimensional and three-dimensional flow field calculation problems. For the two-dimensional problem of flow around a circular cylinder, the simulation results show that a four-level grid MRT-LBM proposed in this paper can accurately obtain the aerodynamic coefficients and Strouhal number at different Reynolds numbers, and it has about 1/9 of the total number of grids as a single-level grid MRT-LBM and is 6.76 times faster. For the three-dimensional flow calculation problem, the numerical experiments of flow past a sphere are simulated to verify the numerical precision of the presented method at Reynolds numbers = 100, 200, 250, 300, and 1000. With the streamlines and velocity contours, it is demonstrated that the multi-level grid MRT-LBM can be calculated accurately even at the interface of different size grids.

GPU-optimized LBM-MRT simulation of free convection and entropy generation of non-Newtonian power-law nanofluids in a porous enclosure at REV scale

The present research investigates the heat transfer and entropy generation of a non-Newtonian power-law Cu-water nanofluid in a square porous enclosure at a representative elementary volume (REV) scale using the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). The Graphics Processing Unit (GPU) accelerated the computations involved. The Brinkman-Forchheimer-extended Darcy model and the shear rate dependent power-law viscosity model were taken into account to characterise the non-Newtonian fluid flow in porous medium. Three types of model validations have been conducted, followed by the mandatory grid independence test, to demonstrate the precision and accuracy of the computational code. The numerical results were obtained by varying five key parameters namely, Darcy number (Da = 10−3, 10−2, 10−1); power-law index (n = 0.6–1.0); Rayleigh number (Ra = 104, 105, 106); porosity parameter (ϵ = 0.6); volume fraction of nanoparticles (ϕ = 0.0–0.05), and the Darcy Rayleigh number (Ram = 100, 1000). The numerically simulated outcomes were presented in terms of streamlines, isotherms, velocity, and temperature profiles as well as the Nusselt (Nu) numbers. Furthermore, a correlation among the parameters to determine the average Nu was developed using the Levenberg-Marquardt (LM) algorithm. The mathematical correlation was also subject to validations, and, in general, good correlation coefficients were obtained.

Accuracy improvement of immersed boundary-lattice Boltzmann and finite element method by iterative velocity correction

In an analysis of the fluid–structure interaction (FSI) problem, the non-slip boundary condition at solid walls cannot be accurately satisfied by the conventional immersed boundary-lattice Boltzmann coupling schemes due to insufficient interpolation accuracy. To solve this problem, an improved iterative velocity correction procedure for the immersed boundary-lattice Boltzmann coupling scheme is proposed by introducing a modified velocity operator. The particle distribution function was modified at each time step, and the evolution governing equation of the multiple relaxation time-lattice Boltzmann method was performed. A numerical framework for coupling lattice Boltzmann and finite element methods for transient problems involving FSI was established, and the iterative velocity correction immersed boundary method was used for the partitioned approach. The solid structure was discretized with the finite element method, while the single-component fluid flows were simulated with the lattice Boltzmann method. An FSI benchmark model was employed to verify the efficiency of the proposed coupling method. The results show that the developed method guarantees the non-slip boundary condition and maintains the convergence rate of the conventional immersed boundary method. In viscous flow and strong shearing flow, the accuracy of both stationary and moving solid boundaries is obviously improved.

Pore-scale study on the effects of randomly distributed void cavities on the thermal performance of composite phase change materials

Composite phase change materials (PCMs) can increase the overall effective thermal conductivity of latent heat thermal energy storage (LHTES) systems and improve their heat transfer performance. However, owing to density differences caused by solid–liquid phase change, void cavities with low thermal conductivity are generated in small spaces where the volume shrinks, thereby increasing the heat transfer resistance. To analyze the pore-scale effects of void cavities on the thermal performance of composite PCMs, a model without void cavities and six models with randomly distributed void cavities were established in this study. A graphics processing unit (GPU) accelerated multiple-relaxation time lattice Boltzmann method was adopted to implement the phase change process and obtain the evolutions of temperature distribution, average liquid fraction, and energy storage performance. The results indicated that, as the volume fraction of the void cavities increased, the average liquid fraction of the composite PCMs slightly increased, whereas the heat storage significantly decreased. At a Fourier number of 0.1, the heat storage per unit width of the composite PCMs was reduced by 3.81 %, 8.02 %, and 11.22 % when the volume fractions were 5 %, 10 %, and 15 %, respectively, compared to the case without void cavities. Additionally, the composite PCMs with large pore-size void cavities had slightly better heat storage efficiency than those with small pore sizes at the same volume fraction of void cavities. It was also found that the LHTES cavity with right-half void cavities had the minimal influence on the heat storage performance.

Research on the gas migration trend and mechanism of the transition flow regime in coal based on MRT-LBM simulation

In order to reveal the process and mechanism of gas flow in a low-permeability coal seam, a new multiple-relaxation-time lattice Boltzmann method (MRT-LBM) model of gas migration in coal micro/nanopores based on Langmuir monolayer adsorption theory, the slip boundary scheme and Bosanquet effective viscosity was established. The software MATLAB was used to carry out the simulation study of uniform pore gas flow based on the MRT-LBM model, and the results were compared and verified with the porous anodic alumina membrane gas flow experimental results. On this basis, the gas flow in coal pores with different micro/nanopore sizes considering adsorption was simulated. The results show that the dimensionless permeability coefficient increases with decreasing pore size under the same pressure, which reflects the subsequent enhancement of the microboundary constraint effect and reveals that the pore system becomes the main controlling factor of coal seam permeability within the coal matrix in the middle and late stages of coal seam gas extraction, while the role of the microboundary constraint effect needs to be considered. The gas adsorption layer weakens the pore gas flow capacity, but for pores with a radius greater than 16 nm, the apparent change in permeability caused by the adsorption layer is less than 5%, and the adsorption effect can be ignored. N2, CH4, and CO2 enter the transition flow regime under different pressure conditions; with gas extraction, the gas pressure decreases, and the difference in the gas flow characteristics of the three gases increases.

Numerical Investigation of Convective Heat Transfer and Fluid Flow Past a Three Square Cylinders Controlled by a Partition in Channel

This document presents a research article on the control of fluid flow around three heated square cylinders placed side by side in a 2D horizontal channel using a flat plate. The objective of this research is to examine the effect of the position, length and height of a flat plate on fluid flow and heat transfer. For this purpose, numerical simulations are performed by using the Boltzmann double relaxation time multiple network method (DMRT-LBM). The MRT-D2Q9 and MRT-D2Q5 models are used to treat the flow and temperature fields respectively. In contrast to several existing investigations in the literature in this domain which study the passive control of the flow using a horizontal or vertical plate around a single cylinder, this work presents a numerical study on the effect of the position, length and height of a flat plate (horizontal and vertical) on three heated square cylinders on the flow and temperature fields. First, the effect of the position and length of the horizontal flat plate is examined. This study shows that the implementation of a flat plate of length Lp = 4D at a position g=3 behind the central cylinder reduces the amplitude of the Von Karman Street and allows large and regular heat exchange. Thus, in the second part, the effect of the position and height of the vertical flat plate is studied. The results obtained show that the implementation of a flat plate of height h=2D at a position g=3 behind the central cylinder improves the thermal exchange between the incoming fluid and the heated cylinders. This numerical work could lead to the prediction of the cooling of the electronic components: The cooling of the obstacles is all the better when the control plate is arranged at g = 3 and its height h = 2D in the case of the vertical plate or its length Lp equal to 4D in the case where the plate is implemented horizontally

CO2-oil diffusion, adsorption and miscible flow in nanoporous media from pore-scale perspectives

Enhancing shale/tight oil and sequestering CO2 by CO2 huff-n-puff have gained extensive attentions in recent years. However, the fundamental understanding of CO2-oil diffusion, competitive adsorption and miscible flow behaviors are mainly limited to the single pore scale based on molecular dynamics (MD) simulations, and that in nanoporous media are still ambiguous. In this work, we propose a novel multiple relaxation time lattice Boltzmann method (MRT-LBM) to simulate CO2-oil diffusion, adsorption and miscible flow in pore-scale nanoporous media, which is successfully verified by the Fick’s second law and MD simulations. The proposed model can obtain various fluid-surface molecular interaction forces (adsorption capacities) of CO2/oil single phase and CO2-oil miscible phase, and quantify the attraction and repulsion from the pore surface to CO2 and oil. Then, the effects of CO2 and oil phase heterogeneous adsorption capacity on CO2 diffusion, storage and oil extraction are quantitatively analyzed. Additionally, based on the MD simulations, we also study the adsorption and flow behaviors of CO2-nC8 miscible adsorption and flow behaviors in calcite nanoporous media. The results show that CO2 can diffuse into the oil phase in porous media more readily from the regions that are relatively attractive to CO2 and repulsive to oil. In porous media with heterogeneous adsorption capacity, CO2 first contacts with the CO2-friendly surface which is attractive to CO2 during diffusion, beneficial to CO2 storage. With an increasing nC8 mass percentage (OMP), the proportion of adsorbed CO2 increases, and that of free CO2 decreases. That indicates that the CO2 diffusing into the oil phase is firstly adsorbed on the surface. When CO2 adsorption reaches saturation, the density of CO2 in the bulk phase begins to increase. We also observed a critical OMP equaling 81% below which CO2 can enhance nC8 flow while having a negligible enhanced impact on nC8 flow beyond 81%. Additionally, with an increasing porous media size, the proportion of adsorbed CO2 decreases, and the critical OMP increases.

Convective heat transfer in I-shape heat sink under the action of Lorentz force via LBM

Via the non-orthogonal multiple-relaxation time Lattice Boltzmann Method, the natural convection phenomenon inside I-shape heat sink under the effect of Lorentz force is investigated. The cavity is filled with MWCNT-Fe3O4/water hybrid nanofluid, and three cold and three hot tubes exist inside the cavity at the same time. The influences of Rayleigh number (103–106), Hartmann number (0–100), magnetic field tilt angle θ (0 – π/2), and different cold and heat pipe arrangements (Case 1–Case 5) on the heat transfer and fluid flow are numerically simulated. The calculated results are shown by the variation of flow lines, isotherms and the average Nusselt number. The results show that the amplitude of the flow function is always the largest for Case 5, which is the best arrangement from the fluid motion point of view, while Case 2 has the largest Nusselt number for different Rayleigh numbers, magnetic field inclination angle θ and different Hartmann numbers, which is the best arrangement from the heat transfer efficiency point of view. However, with different cold and hot pipe arrangements, the average Nusselt number increases when the Rayleigh number and the magnetic field inclination angle θ increase. In contrast, as Hartmann number increases, the average Nusselt number decreases. The local Nusselt number of the cold and hot tubes is further investigated, comparing the discrepancy of the heat transfer performance near each wall surface.

Numerical simulation study of acoustic waves propagation and streaming using MRT-lattice Boltzmann method

This paper presents a numerical investigation of the propagation of acoustic waves generated by a linear acoustic source using the lattice Boltzmann method (LBM). The main objective of this study is to compute the sound pressure and acoustic force produced by a rectangular sound source located at the center of the west wall of a rectangular cavity, filled with water. The sound source is discretized into a set of point sources emitting waves according to the acoustic point source method. The interference between the generated cylindrical waves creates an acoustic beam in the cavity. An analytical study is carried out to validate these numerical results. The error between the numerical and analytical calculations of the wave propagation is also discussed to confirm the validity of the numerical approach. In a second step, the acoustic streaming is calculated by introducing the acoustic force into the LBM code. A characteristic flow structure with two recirculating cells is thus obtained.

Numerical investigation of natural convection in concentric cylinder partially heated based on MRT-lattice Boltzmann method

In the present paper, a numerical simulation of natural convection flow in annulus space with a partially heated inner cylinder is proposed. The numerical investigation is based on lattice Boltzmann method (LBM) with multiple relaxation time approximation. Each heating partial side length's is about 25% of the inner perimeter and is maintained at hot temperature. The heated regions are placed on the inner wall in four different configurations while the outer cylinder is maintained at cold temperature. A study of effect of Rayleigh number varying over the range of 104 - 5 × 105 and various cylinder ratio on Nusselt number and both velocity and thermal fields is carried out. It is found that the Nusselt number increases with the increase of Rayleigh number and the radius ratio. Otherwise, the fourth configuration where the heated zones are placed on the left and right sides of the inner cylinder, offers the better rate heat exchange for a fixed value of Rayleigh number and radius ratio.

Siamese-SR: A Siamese Super-Resolution Model for Boosting Resolution of Digital Rock Images for Improved Petrophysical Property Estimation

Digital Rock Physics leverages advances in digital image acquisition and analysis techniques to create 3D digital images of rock samples, which are used for computational modeling and simulations to predict petrophysical properties of interest. However, the accuracy of the predictions is crucially dependent on the quality of the digital images, which is currently limited by the resolution of the micro-CT scanning technology. We have proposed a novel Deep Learning based Super-Resolution model called Siamese-SR to digitally boost the resolution of Digital Rock images whilst retaining the texture and providing optimal de-noising. The Siamese-SR model consists of a generator which is adversarially trained with a relativistic and a siamese discriminator utilizing Materials In Context (MINC) loss estimator. This model has been demonstrated to improve the resolution of sandstone rock images acquired using micro-CT scanning by a factor of 2. Another key highlight of our work is that for the evaluation of the super-resolution performance, we propose to move away from image-based metrics such as Structural Similarity (SSIM) and Peak Signal to Noise Ratio (PSNR) because they do not correlate well with expert geological and petrophysical evaluations. Instead, we propose to subject the super-resolved images to the next step in the Digital Rock workflow to calculate a crucial petrophysical property of interest, viz. porosity and use it as a metric for evaluation of our proposed Siamese-SR model against several other existing super-resolution methods like SRGAN, ESRGAN, EDSR and SPSR. Furthermore, we also use Local Attribution Maps to show how our proposed Siamese-SR model focuses optimally on edge-semantics, which is what leads to improvement in the image-based porosity prediction, the permeability prediction from Multiple Relaxation Time Lattice Boltzmann Method (MRTLBM) flow simulations as well as the prediction of other petrophysical properties of interest derived from Mercury Injection Capillary Pressure (MICP) simulations.

Effect mechanism of multiple obstacles on non-Newtonian flow in ceramic 3D printing (arcuate elements)

Direct ink writing (DIW), as an additive manufacturing method, can effectively mould ceramic parts. The single screw extruder is used here to extrude viscous SiC slurry. The deposits caused by the low viscosity and the agglomerations resulting from the nonuniform mixing, form the obstacles in the channel, which affect the normal theoretical flow of the slurry, and interaction with other printing parameters. Therefore, it is necessary to explore the effect mechanism of the obstacles on the flow. The obstacles are always irregular, which makes it difficult to directly analyse them. The irregular geometries are always composed of linear and/or arcuate elements; therefore, the obstacles can be simplified into regular geometries. In the previous work, linear elements have been analysed first. As the continuous work, arcuate elements are investigated in the current research. To conduct the required simulations, an improved MRT LBM (multiple relaxation time lattice Boltzmann method) with a pseudo external force is proposed. The above numerical method is combined with the rheological model to analyse cases with two obstacles, and the obtained results are used to reveal the general mechanism in cases with multiple obstacles. The results show that the central angles, radii, and positions of the obstacles are important factors affecting the flow. To obtain a stable and controllable slurry flow, it is recommended that the central angle and the radius should be small enough. The number of obstacles should be minimized, and the position of the last obstacle is expected to be far away from the outlet to avoid the negative velocity. In addition, the adjacent obstacles should maintain a certain distance to ensure the full development of the vortex and avoid affecting the following obstacles or back vortices.

Effect mechanism of multiple obstacles on non-Newtonian flow in ceramics 3D printing (linear elements)

Direct ink writing (DIW) provides a new way to mould ceramic parts. When a single screw extruder is used to extrude SiC slurry, the deposits caused by low viscosity and the agglomerations resulting from the nonuniform mixing, form the obstacles in the channel, which affect the normal flow of the slurry, theoretical outlet velocity, and interaction with other printing parameters. Therefore, it is necessary to study the mechanism responsible for the effects of the obstacles on the flow. The obstacles are always irregular, which makes it difficult to directly analyse them. Irregular geometries are always composed of linear and/or arcuate elements; therefore, the obstacles can be simplified into regular geometries. In the present work, linear elements are analysed first. Then, an improved MRT LBM (multiple relaxation time lattice Boltzmann method) with a pseudo external force is proposed for the flow analysis. The improved MRT LBM is combined with rheological test data to investigate cases with two obstacles, and the results are applied to reveal the general mechanism in cases with multiple obstacles. The results show that the angles, sizes, and positions of the obstacles are three important factors influencing the flow. To obtain a stable and controllable slurry flow, it is recommended that the first angle θ1 be an acute angle. In addition, the number of obstacles should be minimized, and the position of the last obstacle should be far away from the outlet.

Pore-scale modeling on supercritical CO2 invasion in 3D micromodel with randomly arranged spherical cross-sections

In this study the delicate invasion nature of pure supercritical carbon dioxide sCO2, alongside the determination of the main boundaries for sCO2 flow-pattern transitions inside the nanopores of treated 3D-porous matrix are investigated numerically. Sensitivity parameters under various sCO2 injection rates and flow regimes are discussed. The numerical outcomes are relied on MRT-Lattice Boltzmann method utilized in this study, while unyielded zones and inactive pores are identified by 3D voxels. The structural complexity of near-spherical porous matrices is addressed to study the flow behaviors of sCO2. This micrometer media followed a spherical approach with a studied random arrangement. The lengths of the computational domain in transverse directions were set to be five times as long as the highest diameter dp of the solid matrix, (highest dp= 50 nm), while the longitudinal direction was set to be 40 times dp. The simulations are carried out for a wide range of initial sCO2 velocities, which adimensionally denoted by Reynolds values. As well, unsteady-state flow regimes are adopted for precise interpretations of complex flow patterns and interactions in the nanopores. This numerical methodology allowed the study of the injection boundaries toward each flow regime of sCO2 inside the complex porous structure. Based on the above analysis, a primary flow-pattern chart is established for the invasion of sCO2.

Natural Convection Heat Transfer in a Porous Cavity with Sinusoidal Temperature Distribution Using Cu/Water Nanofluid: Double MRT Lattice Boltzmann Method

Natural Convection Heat Transfer in a Porous Cavity with Sinusoidal Temperature Distribution Using Cu/Water Nanofluid: Double MRT Lattice Boltzmann Method