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We propose a multiple-relaxation-time lattice Boltzmann method for anisotropic convection-diffusion equation with a divergence-free velocity field. In this approach, the convection term is handled as a source term in the lattice Boltzmann evolution equation; thus, the derivation term that may be induced by the convection term disappears. By using the Chapman-Enskog analysis, the anisotropic convection-diffusion equation is recovered up to second-order accurate in space. In particular, we also present a local scheme for computing the convection term, indicating that the present method retains the main advantages of the lattice Boltzmann method. We then test the proposed model by considering the Gaussian hill problem and an anisotropic convection diffusion equation with constant velocity and diffusion tensor. The results illustrate that our model has acceptable numerical accuracy and can be a good candidate for simulating anisotropic convection-diffusion equation. • A MRT LB model is constructed for anisotropic CDE with divergence-free velocity field. • The convection term is treated as a source term in the LB equation. • No deviation term exists in the corresponding recovered equation. [ABSTRACT FROM AUTHOR]

Several numerical simulations of fluid flow were performed using the Lattice Boltzmann method and image processing techniques to estimate the effective properties of 2-D porous rocks. The effective properties evaluated were the physical characteristics that allow fluid flow including the effective porosity, permeability, tortuosity, and average throat size to determine the storage and transport of fluids in porous rocks. The permeability was compared using the Darcy model simulation and the empirical Kozeny–Carman Equation. The results showed that the Lattice Boltzmann method and image processing techniques can estimate the effective parameters of porous rocks. Furthermore, there was a good correlation between permeability and parameters such as effective porosity, tortuosity, and average throat size. The Darcy model simulation revealed a gamma distribution in the permeability, while the empirical Kozeny–Carman Equation showed a log-normal distribution. [ABSTRACT FROM AUTHOR]

In the present paper, a generalized dithering approach using the Lattice Boltzmann Method (LBM) is proposed. This generalization enables to experiment different models, and to adapt them accordingly to targeted features and problems. As illustrations, 4 models are introduced and tested, including anisotropic gradient-based relaxation time and enhanced equilibrium distribution function, aiming for robust quality and artefacts reduction. These models are implemented on graphics processing units and generically interfaced with the OBLiX framework. The several test-cases performed demonstrate that such models yield better qualitative and quantitative results, proving the adaptability of the generalization. This paper, by providing a general framework for dithering using the LBM, allows an adaptation of the algorithms to complex situations deviating from classically encountered cases. [ABSTRACT FROM AUTHOR]

In this article, the lattice Boltzmann method with two relaxation time (TRT) for the D2Q9 model is used to investigate numerical results for 2D flow. The problem is performed to show the dissipation of the kinetic energy rate and its relationship with the enstrophy growth for 2D dipole wall collision. The investigation is carried out for normal collision and oblique incidents at an angle of 30° . We prove the accuracy of moment -based boundary conditions with slip and Navier-Maxwell slip conditions to simulate this flow. These conditions are under the effect of Burnettorder stress conditions that are consistent with the discrete Boltzmann equation. Stable results are found by using this kind of boundary condition where dissipation of the kinetic energy is found to be proportional to Re −1 in the first regime and it is ∝ Re −0.5 in the second part of the regime as expected. An excellent agreement with the benchmark data is observed. [ABSTRACT FROM AUTHOR]

The lattice‐Boltzmann method (LBM) is becoming increasingly popular for simulating multi‐phase flows on the microscale because of its advantages in terms of computational efficiency. Many applications of the method are restricted to relatively simple geometries. When a more complex geometry is considered—circular and inclined microchannels—some important physical phenomena may not be accurately captured, especially at low capillary numbers. A Y‐Y micro‐fluidic channel, widely used for a range of applications, is an example of a more complex geometry. This work aims to capture the various flow phenomena, with an emphasis on parallel flow and leakage, using the Rothman–Keller (RK) model of the LBM. To this purpose, we modify the forcing term to implement the surface tension for use at low capillary numbers. We compare the simulation results of the RK model with and without the force modification with experiments, Volume of Fluid and the phase field method and observe that the modified forcing term is an improvement over the current RK model at low capillary numbers, and it also captures parallel flow and leakage more accurately than the other simulation techniques. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Fuzhou University is the property of Journal of Fuzhou University, Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Partial storage strategy can save energy and reduce emissions. In this study, analysis of the partial melting process of ice inserted with nanoparticles inside a square enclosure is investigated for thermal energy storage. The lattice Boltzmann method is for melting and heat transfer in the storage unit. The validation demonstrates strong concurrence between the current findings and the experimental data documented in the literature. The analysis is performed for various Rayleigh numbers, nanoparticle volume fractions, and their effect on melting time and energy storage. Two types of nanoparticles are tested that is, copper and alumina. The outcomes indicate that the Rayleigh number and volume fraction of nanoparticles have a significant impact on the phase change process. The nanoparticles addition leads to homogenous and hence expedited melting process including the final stage of the ice melting process which is very slow without nanoparticles. Furthermore, copper nanoparticles are slightly more effective than alumina. Moreover, using 6% copper nanoparticles can reduce the melting time by up to 12.4%. [ABSTRACT FROM AUTHOR]

A lattice Boltzmann model (LBM) with sharp interface tracking is developed to simulate the motion and growth of dendrites in non-equilibrium solidification of alloys. The model is validated through comparative analysis with the drafting-kissing-tumbling (DKT) phenomena of two and three particles and the continuous growth model (CGM), and demonstrates its computational efficiency advantage without compromising accuracy by comparison with the multi-phase field (MPF) model. Subsequently, the model is utilized to investigate the dendrite morphology transition and primary dendritic arm spacing (PDAS). It is found that the velocity dependent solute partition and the resulting changes in constitutional undercooling strongly influence the estimated morphology region and PDAS. Moreover, the segregation and microstructure evolution during the rapid solidification were studied. And the results revealed that free dendrites lead to significant changes in microstructure and segregation under the influence of non-equilibrium effects. This work illustrates the great potential of the proposed model in simulating dendrites and microstructure evolution under a wide range of solidification conditions. Its suitability for extreme conditions and non-equilibrium solidification can contribute to the understanding of microstructure formation patterns and solute segregation in rapid solidification.

Abstract Lattice Boltzmann (LB) methods with reactive boundary conditions are widely used in pore-scale simulations of dissolution and ablation processes. The staircase approximation of curved boundary is often employed because of its simplicity in handling solid structure changes. In this work, the mass transfer of two typical LB reactive boundary schemes are analyzed for the staircase boundary. The Type I boundary scheme is based on relations of local distribution functions and a wet-node boundary mesh. The Type II boundary scheme adopts the half-way bounce-back scheme. Boundary concentrations are determined by finite difference, and a link-wise boundary mesh is used. The analyses demonstrate that for straight boundaries, both the boundary schemes have accurate mass transfer rates, which means the mass transfer calculated by exchanges of distribution functions is the same as that calculated by reaction rates. For curved boundaries with staircase approximation, including interfacial normal directions in the Type I boundary scheme can provide accurate mass transfer for inclined straight boundaries. However, if the staircase boundary geometry is used directly without normal directions, the reaction rate will be overestimated. One-dimensional and two-dimensional reaction-diffusion processes with dissolution are simulated to validate the analyses. Both the boundary schemes work well for one-dimensional simulations. For two-dimensional simulations, the Type II boundary scheme significantly overestimates the reaction rate, and stronger artificial anisotropic effects are observed. The Type I boundary scheme with normal directions has better performance, but error still exists.

The use of high-conductivity porous medium is an effective method to enhance the heat transfer rate of phase change material (PCM) in thermal energy storage (TES), reducing the energy consumption of low-carbon buildings. This paper establishes a solid-liquid phase change lattice Boltzmann model of a TES unit and investigates the effects of Rayleigh number, inclination angle, porous array, and porosity. The findings indicate that inserting the porous medium enhances conductive heat transfer and weakens convective heat transfer. When the Rayleigh number is increased from 103 to 104, the liquid fraction increases by 3.0%, while an increase from 104 to 105 only results in a 1.6% increase, suggesting a diminishing effect of increasing the Rayleigh number. Results also show that the inclination angle can be disregarded in this study. Furthermore, increasing the specific surface area enhances conductive heat transfer. However, when the array n is changed to 7, the fastest variation of liquid fraction is obtained among the range from 5 to 9. Increasing the porosity will delay the moment that temperature standard deviation reaches to the maximum, getting the temperature distribution more nonuniform. The findings from this paper are valuable for the design of TES systems in low-carbon buildings. Practical application: The porous medium can enhance heat transfer in the phase change process. In the field of low-carbon buildings, porous medium is applied to strengthen the energy storage rate. By investigating the parameters of the Rayleigh numbers, inclination angles, porosities and arrangement of porous medium arrays of the composed energy storage unit, the regularity of the effects on the energy characteristics are obtained, which would provide some valuable practice references for designing these parameters of the energy storage units in the future energy-efficient building sector. [ABSTRACT FROM AUTHOR]

Copyright of Chemical Engineering (China) / Huaxue Gongcheng is the property of Hualu Engineering Science & Technology Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Lattice Boltzmann (LB) methods with reactive boundary conditions are widely used in pore-scale simulations of dissolution and ablation processes. The staircase approximation of curved boundary is often employed because of its simplicity in handling solid structure changes. In this work, the mass transfer of two typical LB reactive boundary schemes are analyzed for the staircase boundary. The Type I boundary scheme is based on relations of local distribution functions and a wet-node boundary mesh. The Type II boundary scheme adopts the half-way bounce-back scheme. Boundary concentrations are determined by finite difference, and a link-wise boundary mesh is used. The analyses demonstrate that for straight boundaries, both the boundary schemes have accurate mass transfer rates, which means the mass transfer calculated by exchanges of distribution functions is the same as that calculated by reaction rates. For curved boundaries with staircase approximation, including interfacial normal directions in the Type I boundary scheme can provide accurate mass transfer for inclined straight boundaries. However, if the staircase boundary geometry is used directly without normal directions, the reaction rate will be overestimated. One-dimensional and two-dimensional reaction-diffusion processes with dissolution are simulated to validate the analyses. Both the boundary schemes work well for one-dimensional simulations. For two-dimensional simulations, the Type II boundary scheme significantly overestimates the reaction rate, and stronger artificial anisotropic effects are observed. The Type I boundary scheme with normal directions has better performance, but error still exists. [ABSTRACT FROM AUTHOR]

Inkjet printing technology for solar cell metallization is considered as an important alternative with inherent non-contact characteristics. The melting process of silver particles plays the key role which determines the final structure of finger electrodes. To explore the melting of silver particles inside the silicon wafers, an enthalpy-based LB-FD model is presented to simulate the solid-liquid phase transitions in the multiphase system. In vertical thermal fields, silver particles melt from bottom to upper layers. The adhesion and coalescence behaviors of multiple particles are well captured in multiphase melting. The melting fluids near the sidewall are simulated with the interfacial tension and gravitational force. The effects of solid phase ratio and textured features of silicon wafers are also studied. The presented 3D enthalpy-based LB-FD model exhibits powerful capacities to solve the solid-liquid phase transitions in multiphase system. The numerical analysis provides a better insight to understand and improve the inkjet-printed solar cell metallization process. • 3D enthalpy-based LB-FD coupled model is presented in multiphase system. • The adhesion and coalescence behaviors of multiple particles are well captured in multiphase melting. • The effects of solid phase ratio and textured features of silicon wafers on melting rate are presented. [ABSTRACT FROM AUTHOR]

We performed two‐dimensional simulations of the slicing of a rising droplet by a vertical knife and by two knives. We used a free‐energy lattice Boltzmann method. Most simulations are for an Eötvös number of 3.96 and a Morton number of 1.24 × 10−4. We carefully probed effects of the spatial resolution on the rising speed and slicing process. The effect of wettability of the knife(s) was studied by varying the equilibrium contact angle of the drop on the knife in the range of 45° to 135°. Slicing time as well as fine droplet fragments staying behind on the knife depend on the knife's wettability. [ABSTRACT FROM AUTHOR]

In recent years, quantum Boltzmann methods have gained more and more interest as they might provide a viable path toward solving fluid dynamics problems on quantum computers once this emerging compute technology has matured and fault-tolerant many-qubit systems become available. The major challenge in developing a start-to-end quantum algorithm for the Boltzmann equation consists in encoding relevant data efficiently in quantum bits (qubits) and formulating the streaming, collision and reflection steps as one comprehensive unitary operation. The current literature on quantum Boltzmann methods mostly proposes data encodings and quantum primitives for individual phases of the pipeline, assuming that they can be combined to a full algorithm. In this paper, we disprove this assumption by showing that for encodings commonly discussed in the literature, either the collision or the streaming step cannot be unitary. Building on this landmark result, we propose a novel encoding in which the number of qubits used to encode the velocity depends on the number of time steps one wishes to simulate, with the upper bound depending on the total number of grid points. In light of the non-unitarity result established for existing encodings, our encoding method is to the best of our knowledge the only one currently known that can be used for a start-to-end quantum Boltzmann solver where both the collision and the streaming step are implemented as a unitary operation. [ABSTRACT FROM AUTHOR]

Bingham-type fluids are crucial in many industries and in geology. This study examines their behavior in reinforcing fractured rocks. Rheological properties were derived from experimental data of a water-cement mixture. Computational simulations were conducted using Lattice Boltzmann Method, with a modification to the relaxation parameter. Behavior of these mixtures in narrow ducts that widen and narrow suddenly, common in fractured rocks, was analyzed. Comparing Bingham and Newtonian fluids in various duct shapes provided insight into pressure distribution. Findings demonstrate that both cement-water mixtures, with or without addition of cement, adhere to Forchheimer flow patterns. Furthermore, it is observed that Newtonian fluids generate more intense vortices in expansive and contractive areas, resulting in higher pressure drops compared to Bingham plastics. The ultimate goal is to propose a predictive model based on mortar reinforcement for fractured rocks, taking into account rheological properties and water-cement ratio, thus reducing the need for costly experiments.

Several numerical simulations of fluid flow were performed using the Lattice Boltzmann method and image processing techniques to estimate the effective properties of 2-D porous rocks. The effective properties evaluated were the physical characteristics that allow fluid flow including the effective porosity, permeability, tortuosity, and average throat size to determine the storage and transport of fluids in porous rocks. The permeability was compared using the Darcy model simulation and the empirical Kozeny–Carman Equation. The results showed that the Lattice Boltzmann method and image processing techniques can estimate the effective parameters of porous rocks. Furthermore, there was a good correlation between permeability and parameters such as effective porosity, tortuosity, and average throat size. The Darcy model simulation revealed a gamma distribution in the permeability, while the empirical Kozeny–Carman Equation showed a log-normal distribution.

In the present paper, a novel approach for image denoising based on the numerical solution to the nonlinear diffusion equation is proposed. The Perona–Malik-type equation is solved by employing a hybrid lattice Boltzmann model with five discrete velocities. In this method, the regions with large values of the diffusion coefficient are modeled with the lattice Boltzmann scheme for which hyper-viscous defects are reduced, while other regions are modeled with the conventional lattice Boltzmann model. The new method allows us to solve Perona–Malik-type equations with relatively large time steps and good accuracy. In numerical experiments, the removal of salt and pepper, speckle and Gaussian noise is considered. For salt and pepper noise, the novel scheme yields better peak signal-to-noise ratios in image denoising problems compared to the standard lattice Boltzmann approach. For certain non-small values of time steps, the novel model shows better results for speckle and Gaussian noise on average. [ABSTRACT FROM AUTHOR]

Using thin-section images to estimate core permeability is an economical and less time-consuming method for reservoir evaluation, which is a goal that many petroleum developers aspire to achieve. Although three-dimensional (3D) pore volumes have been successfully applied to train permeability models, it is very expensive to carry out. In this regard, deriving permeability from two-dimensional (2D) images presents a novel approach in which data are fitted directly on the basis of pore-throat characteristics extracted from more cost-effective thin sections. This work proposes a Fluid–MLP workflow for estimating 3D permeability models. We employed DIA technology combined with artificial lithology and pore classification to calculate up to 110 characteristic parameters of the pore-throat structure on the basis of 2D rock cast thin sections. The MLP network was adopted to train the permeability prediction model, utilizing these 110 parameters as input. However, the accuracy of the conventional MLP network only reached 90%. We propose data preprocessing using fluid flow simulations to improve the training accuracy of the MLP network. The fluid flow simulations involve generating a pore network model based on the 2D pore size distribution, followed by employing the lattice Boltzmann method to estimate permeability. Subsequently, six key structural parameters, including permeability calculated by LBM, pore type, lithology, two-dimensional porosity, average pore–throat ratio, and average throat diameter, were fed into the MLP network for training to form a new Fluid–MLP workflow. Comparing the results predicted using this new Fluid–MLP workflow with those of the original MLP network, we found that the Fluid–MLP network exhibited superior predictive performance. [ABSTRACT FROM AUTHOR]

The immersed boundary–lattice Boltzmann (IB-LB) coupling scheme is known as an efficient scheme for fluid–structure interactions (FSIs). However, the conventional IB-LB schemes suffer from instability because they involve a high-Reynolds-number flow or a larger stiffness structure. An averagely weighted iteration approach is presented to improve the stability restriction in this paper. This new approach, which improves the stability by mitigating the high-frequency fluctuations, is implemented by iteratively calculating the external force, and averagely weighting the force obtained at every iterative step. Five cases are simulated to verify the accuracy and effectiveness of the present approach. Under the premise of maintaining the accuracy of the conventional IB-LB method, the implementation of the present approach can significantly enhance the numerical stability. Compared with the conventional IB-LB method, the present approach can significantly expand the material parameter range for simulation; in particular, this approach qualitatively improves the upper limit of the bending rigidity coefficient by approximately 8000 times. To use the outstanding stability of the present approach, the IB inertia force can be directly incorporated into the simulation. In addition, under the low-viscosity condition, the present approach can effectively simulate the large-deformation FSI problem. [ABSTRACT FROM AUTHOR]

Objetivo: El modelado de flujos y contaminantes enfrenta grandes desafíos que van desde la definición de geometrías complejas hasta la convergencia del algoritmo y la determinación de los parámetros del modelo. El método presentado aquí aborda este problema a través de una aplicación conjunta de los métodos de Lattice-Boltzmann y diferencias finitas. La solución numérica de las ecuaciones de Navier-Stokes y advección-difusión permite simular los niveles de dispersión de la contaminación espaciotemporal en una fuente hídrica. Metodología: El método resolvió las ecuaciones de Navier-Stokes a través de la propuesta de Lattice Boltzmann, que proporciona el campo vectorial de velocidades del fluido. La solución de la ecuación de difusión-advección por diferencia finita requiere este campo de velocidad conocido. La solución codificada en C++, primero digitaliza el mapa, etiqueta cada píxel del mapa como fluido o sólido. El código usa la imagen digital para configurar la geometría de la zona de flujo, luego simula la dinámica del fluido y la concentración del contaminante. La comparación entre las soluciones analíticas de modelos ideales advectivo-difusivo, y las obtenidas a través de este método, facilita la medición de la confiabilidad del método; aplicado a una sección del río Sogamoso (Colombia), el algoritmo arrojó la velocidad, la presión y la concentración del agente. Resultados: Se encontró que el término advectivo predomina en gran parte de cada uno de los tramos del río Sogamoso. Sin embargo, hay una sección en el tramo superior, en donde predomina la componente difusiva. Esto ocurre porque allí la velocidad es muy baja. Conclusión: Los resultados señalan la confiabilidad, estabilidad y robustez del método para simular fenómenos de advección-difusión en cuerpos con geometrías irregulares.

We discuss the role and impact of lattice fluid dynamics, namely Lattice Gas Cellular Automata and lattice Boltzmann, on the general framework of Computational Fluid Dynamics.

A new scalar advection algorithm is presented for the lattice Boltzmann (LB) method in which numerical diffusion is reduced by a one-dimensional linear approximation paired with a flux limiter and numerical dispersion is minimized by using fluid flux calculations based on the LB distribution function. The algorithm is designed to be conservative and have low memory requirements. A finite volume method (FVM) based on the LB velocity field is also presented for comparison. We validate with uniform velocity and turbulent flow simulations showing that numerical diffusion error matches FVM results while numerical dispersion is reduced. A performance analysis indicates it is less efficient, but we demonstrate that adjusting the scalar advection time step relative to the fluid time step can improve efficiency with minor effects on accuracy. [ABSTRACT FROM AUTHOR]

This study aims to validate the lattice Boltzmann method and assess its ability to accurately describe the behavior of gaseous flows in packed beds. To that end, simulations of a model packed bed reactor, corresponding to an experimental bench, are conducted, and the results are directly compared with experimental data obtained by particle image velocimetry measurements. It is found that the lattice Boltzmann solver exhibits very good agreement with experimental measurements. Then, the numerical solver is further used to analyze the effect of the number of packing layers on the flow structure and to determine the minimum bed height above which the changes in flow structure become insignificant. Finally, flow fluctuations in time are discussed. The findings of this study provide valuable insights into the behavior of the gas flow in packed bed reactors, opening the door for further investigations involving additionally chemical reactions, as found in many practical applications. [ABSTRACT FROM AUTHOR]

Mitigating the rise and spread of contaminants is a major challenge faced during any contagious disease outbreak. In densely occupied areas, such as a breakroom, the risk of cross-contamination between healthy and infected individuals is significantly higher, thereby increasing the risk of further spread of infectious diseases. In this study, a high fidelity transient fluid solver and Lagrangian particle-based method were used to predict the airflow distribution and contaminant transmission inside a detailed 3D virtual twin of an emergency hospital breakroom. The solver efficiently captured the contaminants emitted simultaneously from multiple talking occupants as well as their propagation inside the breakroom. The influence of airflow distribution on the aerosol spread inside the breakroom for two different air conditioning vent positions was demonstrated with all occupants and with reduced occupants. The baseline simulation with all occupants in the breakroom showed a higher risk of contamination overall as well as between adjacent occupants. It was observed that there was a 26% reduction in the contaminants received by the occupants with the proposed modified vent arrangement and a 70% reduction with the scenarios considering a reduced number of occupants. Furthermore, the fomite deposition and cross-contamination between adjacent humans significantly changed with different ventilation layouts. Based on the simulation results, areas with higher contaminant concentrations were identified, providing information for the positioning of UV lights in the breakroom to efficiently eliminate/reduce the contaminants. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering for Thermal Energy & Power / Reneng Dongli Gongcheng is the property of Journal of Engineering for Thermal Energy & Power and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Torsional nano-scanners have a variety of applications in nano/micro-electro-mechanical systems. In this paper, two- and three-dimensional numerical solutions based on the lattice Boltzmann are proposed for simulating the dynamic behavior of an electromechanical torsional nano-scanner. The complete governing equations are modified based on the couple stress theory and developed by considering the effect of the Casimir force. Furthermore, the physics of the system is extended by considering the effects of dissolved electric agents on the dynamic performance of the nano-scanner. The passive/active electrolyte flow behavior with the moving solid boundary is described and simulated using Nernst-Plank-Poisson compensation of the electrolyte flow. The proposed numerical results are validated by comparing them with those available in the literature. Finally, the influence of scale dependency and Casimir force on the nano-scanner's dynamic performance and pull-in instability are investigated. Also, as torsional nano-scanners might be immersed in ionic media, the impact of ionic concentration on the pull-in voltage of a nano-scanner is investigated. The obtained results demonstrate that increasing the ionic concentration reduces the instability voltage of the nano-scanner considerably. [ABSTRACT FROM AUTHOR]

In this study, the water convection flow within a right‐angled, inclined, and isosceles triangle enclosure for various inclination angles was numerically analyzed using the lattice Boltzmann method with the multirelaxation time model. On the hypotenuse side, the enclosure is thermally insulated, while the left and horizontal walls are kept, respectively, at cold and hot temperatures. This study was conducted to show the effects of two key parameters, the tilt angle ϕ $\phi $ and the Rayleigh number Ra $Ra$, whose changes span from 0∘ ${0}^{\circ }$ to 315∘ $31{5}^{\circ }$ and 5×103 $5\times 1{0}^{3}$ to 106 $1{0}^{6}$, respectively. The effect of these variables is presented in terms of streamlines, isotherms, velocity profiles, temperature plots, and the average Nusselt number. Furthermore, the impact of the size of a hot square obstruction inside the cavity on the isotherms and streamlines has been investigated. The findings demonstrate that the rate of heat transport is enhanced as the Rayleigh number increases. This result is in good agreement with earlier research without tilting the cavity. Depending on the Rayleigh number, the tilt angle has a significant effect on the rate of heat transmission. [ABSTRACT FROM AUTHOR]

A hybrid multiphase lattice Boltzmann model is adopted to investigate the flow boiling heat transfer process in a horizontal microchannel with consideration of bubble dynamics. The flow pattern transition in a microchannel, involving single-phase flow, bubbly flow, slug flow, and contact-slug flow, is reproduced by varying the heat flux. The influencing parameters, including the liquid mass flux, the heating wall wettability, and the confinement height of channels, on dynamic bubble behaviors and heat transfer performance are discussed. The results indicate that a sequence of single-phase flow, bubbly flow, slug flow, and contact-slug flow occurs in a microchannel with increasing heat flux. Correspondingly, the dominant heat transfer mechanism experiences the liquid convection (single-phase flow), nucleate boiling (bubbly flow), the microlayer evaporation (slug flow), and the hybrid gas convection and microlayer evaporation (contact-slug flow). The increase of mass flux or confinement height extends the range of heat flux for high-efficiency bubbly and slug flow. The hydrophilic heating wall is preferred for better heat transfer performance in a microchannel due to the strengthened microlayer evaporation and less vapor occupation of the effective nucleation area. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann schemes are efficient numerical methods to solve a broad range of problems under the form of conservation laws. However, they suffer from a chronic lack of clear theoretical foundations. In particular, the consistency analysis and the derivation of the modified equations are still open issues. This has prevented, until today, to have an analogous of the Lax equivalence theorem for lattice Boltzmann schemes. We propose a rigorous consistency study and the derivation of the modified equations for any lattice Boltzmann scheme under acoustic and diffusive scalings. This is done by passing from a kinetic (lattice Boltzmann) to a macroscopic (Finite Difference) point of view at a fully discrete level in order to eliminate the non-conserved moments relaxing away from the equilibrium. We rewrite the lattice Boltzmann scheme as a multi-step Finite Difference scheme on the conserved variables, as introduced in our previous contribution. We then perform the usual analyses for Finite Difference by exploiting its precise characterization using matrices of Finite Difference operators. Though we present the derivation of the modified equations until second-order under acoustic scaling, we provide all the elements to extend it to higher orders, since the kinetic-macroscopic connection is conducted at the fully discrete level. Finally, we show that our strategy yields, in a more rigorous setting, the same results as previous works in the literature. [ABSTRACT FROM AUTHOR]

High-porosity metal foams have been extensively studied as an attractive candidate for efficient and compact heat exchanger design. With the advancements in additive manufacturing, such foams can be manufactured with controlled topology to yield highly tailorable mechanical and transport properties. In this study, a lattice Boltzmann method (LBM)-based pore-scale model is implemented to simulate the fluid flow in additively manufactured (AM) metal foams with unit cell topologies of Cube, Face Diagonal (FD)-Cube, Tetrakaidecahedron (TKD), and Octet lattices. The pressure gradient versus average velocity profiles predicted by the LBM model were validated against in-house measurements on the AM lattice samples with the same unit cell topologies. Based on the simulation results, a novel hybrid model is proposed to accurately predict the volume averaged flow properties (permeability and inertial coefficients) of the four structures. Specifically, the linear LBM (neglecting inertial forces) is first implemented to obtain the intrinsic permeability, and then the standard LBM is applied to obtain the inertial coefficient. Convenient correlations for those flow properties as a function of porosity and fiber diameter are constructed. The effects of the AM print qualities on the flow properties are also discussed. The advantages of the hybrid model compared to the polynomial fitting approach for determining flow properties are discussed and compared quantitatively. The hybrid model and presented results are valuable for flow and thermal transport evaluation when designing new metal foams for specific applications and with different materials and topologies. The presented correlations based on pore-scale simulations can also be conveniently used in volume-averaged models to predict the macroscale flow behavior in such complex structures. [ABSTRACT FROM AUTHOR]

Copyright of Tecnura is the property of Tecnura and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies. [ABSTRACT FROM AUTHOR]

The design of flow processes to build a macroscopic bulk material from rod-shaped colloidal particles has drawn considerable attention from researchers and engineers. Here, we systematically explore and show that the characteristic strain rate of the flow universally determines the orientational ordering of colloidal rods. We employed the fluctuating lattice Boltzmann method by simulating hydrodynamically interacting Brownian rods in a Newtonian liquid moving under various flow types. By modeling a rigid rod as a chain of nonoverlapping solid spheres with constraint forces and torque, we elucidate rigid rod dynamics with an aspect ratio (L / d) either 4.1 or 8.1 under various rotational Péclet number (P e r) conditions. The dynamics of colloidal rods in dilute (n L 3 = 0.05) and semidilute suspensions (n L 3 = 1.1) were simulated for a wide range of P e r (0.01 < P e r < 1000) under shear flows including Couette and Poiseuille flows in a planar channel geometry, and an extensional and mixed-kinematics flow in a periodic four-roll mill geometry, where n is the number density, and d and L are the diameter and length of the rod, respectively. By evaluating the degree of orientational alignment of rods along the flows, we observed that there is no significant difference between flow types, and the flow-induced ordering of rods depends on the variation of P e r up to moderate P e r (P e r < 100). At a high P e r (P e r > --> 100), the degree of orientational ordering is prone to diversify depending on the flow type. The spatial inhomogeneity of the strain-rate distribution leads to a substantial decrease in the orientational alignment at high P e r. [ABSTRACT FROM AUTHOR]

The purpose of this work is to deepen our understanding of natural convection with large Prandtl number fluids and to resolve some controversies in the previous publications. To achieve this purpose, a new thermal multiple-relaxation-time lattice Boltzmann model is proposed. Natural convection in a square cavity, a benchmark test case, is investigated numerically using the new model. The Prandtl number is up to 100. For the first time, it is numerically observed that there are two critical Prandtl numbers in the natural convection, which will affect the correlation between the Nusselt number and Prandtl number critically. Three heat transfer characteristic ranges of natural convection are defined in this work, according to the two critical Prandtl numbers. In each range, the dominant heat transfer mechanism is different, which can solve a long-standing issue in the discipline of heat and mass transfer: completely opposing statements on the correlation between the Nusselt number and Prandtl number for natural convection, were published in the open literature. For the first time, this work reveals cause behind the controversial reports and provides the guidance for the future research.

Deep saline permeable sandstones have the potential to serve as sites for CO2 storage. However, unstable CO2 storage in pores can be costly and harmful to the environment. In this study, we used lattice Boltzmann (LB) simulations to investigate the factors that affect steady-state CO2–brine imbibition flow in sandstone pores, with a focus on improving CO2 storage efficiency in deep saline permeable sandstone aquifers. We extracted three representative element volumes (REVs) from a digital rock image of a sandstone core and selected a tighter REV in the upper subdomain so that its permeability would apparently be lower than that of the other two based on single-phase LB simulation for further analysis. The results of our steady-state LB simulations of CO2–brine imbibition processes in the tighter REV under four differential pressures showed that a threshold pressure gradient of around 0.5 MPa/m exists at a differential pressure of 200 Pa, and that higher differential pressures result in a greater and more linear pressure drop and stronger channelization after the flow are initiated. Furthermore, we conducted simulations over a range of target brine saturations in the tighter REV at the optimal differential pressure of 400 Pa. Our findings showed that the relative permeability of CO2 is greatly reduced as the capillary number falls below a certain threshold, while the viscosity ratio has a smaller but still significant effect on relative permeability and storage efficiency through the lubrication effect. Wettability has a limited effect on the storage efficiency, but it does impact the relative permeability within the initial saturation range when the capillary number is low and the curves have not yet converged. Overall, these results provide micro-scale insights into the factors that affect CO2 storage efficiency in sandstones. [ABSTRACT FROM AUTHOR]

This study aims to consider lattice Boltzmann method (LBM)–magnetohydrodynamics (MHD) data to develop equations to predict the average rate of heat transfer quantitatively. The present approach considers a 2D rectangular cavity with adiabatic side walls, and the bottom wall is heated while the top wall is kept cold. Rayleigh–Bénard (RB) convection was considered a heat-transfer phenomenon within the cavity. The Hartmann ( H a ) number, by varying the inclination angle (θ), was considered in developing the equations by considering the input parameters, namely, the Rayleigh ( R a ) numbers, Darcy ( D a ) numbers, and porosity (ϵ) of the cavity in different segments. Each segment considers a data-driven approach to calibrate the Levenberg–Marquardt (LM) algorithm, which is highly linked with the artificial neural network (ANN) machine learning method. Separate validations have been conducted in corresponding sections to showcase the accuracy of the equations. Overall, coefficients of determination ( R 2 ) were found to be within 0.85 to 0.99. The significant findings of this study present mathematical equations to predict the average Nusselt number ( N u ¯ ). The equations can be used to quantitatively predict the heat transfer without directly simulating LBM. In other words, the equations can be considered validations methods for any LBM-MHD model, which considers RB convection within the range of the parameters in each equation. [ABSTRACT FROM AUTHOR]