Improved Lattice Boltzmann Method Research Articles

3D printing food flow in different extruders based on crazy and adaptive salp swarm algorithm-deep extreme learning machine improved-lattice Boltzmann method

Extrusion is significant in achieving 3D printing emulsion. The piston and screw extruders are the common structures to achieve the extrusion. The chocolate emulsion is taken for example, two extruders are numerically investigated and compared based on the fluid dynamic analysis. To conduct the simulations, the crazy and adaptive salp swarm algorithm-deep extreme learning machine (CASSA-DELM) is proposed to predict the viscosity of the chocolate emulsion, which is used to replace the traditional fitted model. The built model can avoid non-consistency in the whole shearing rate range. Then, an improved lattice Boltzmann method (I-LBM) is introduced to process the non-Newtonian behavior of the emulsion. In the simulation, the CASSA-DELM model provides the viscosities for each iteration in I-LBM based on the obtained shearing rates. Because the attachment(s) may be generated on the walls, the no-attachment and with-attachment(s) cases are explored, and the necessary results are obtained, which indicate that the piston extruder is more suitable for extruding the single component of food fluid. The screw extruder is recommended for the multiple components of food fluid because the vortex in the X-Y cross-section contributes to further mixing action for the emulsion containing different materials, such as the investigated chocolate emulsion. The indirect experiments are conducted to validate the above conclusions. The current work can contribute to improving the extruding theory of material extrusion technologies.

A numerical simulation study on the spontaneous imbibition and hydro-thermal coupling in soil using the lattice Boltzmann method

This study presents a numerical simulation of underground water spontaneous upward imbibition at high density ratios using the improved lattice Boltzmann method coupled with the P-R equation of state. Porous media was created using the Quartet Structure Generation Set (QSGS) method. The research delved into the impact of factors such as porosity, soil particle size, capillary force, gravity and temperature on spontaneous imbibition. The results indicated that the permeability coefficient of water spontaneous imbibition rises with higher porosity or larger particles. The influence of gravity on spontaneous imbibition became more significant with increased porosity. Three levels of porosity, namely 0.80, 0.65, and 0.50, were simulated to determine the prevailing force between the thermal-driven force and the gravitational hindrance. The variation of groundwater spontaneous imbibition permeability coefficient under the influence of gravity at different temperature gradients was simulated, as was the change in the permeability coefficient without the influence of gravity. The results revealed that for temperature differences above 4 K, gravity had minimal impact with temperature being the main influential factor. For example, for simulation with temperature difference of 10 K, the permeability coefficient differences were 0.006, 0.015, and 0.014 for the three different porosity levels, respectively. When the temperature difference was below 4 K, the disparity in the permeability coefficient increased significantly compared to zero-gravity conditions. Under these conditions, the influence of gravity was greater. For example, for simulation with temperature difference of 2 K or greater, the permeability coefficient differences were 0.306, 0.300, and 0.108 for the corresponding porosity values respectively.

Direct simulations of external flow and noise radiation using the generalized interpolation-supplemented cascaded lattice Boltzmann method

Direct simulations of external flow and the associated noise radiation are studied by an improved lattice Boltzmann method, i.e., the generalized interpolation-supplemented cascaded lattice Boltzmann method (GICLBM). In this method, the cascaded collision scheme is used to improve the numerical stability of the conventional collision schemes, and the generalized interpolation approach is used in the particle streaming process so as to allow a non-uniform and body-fitted mesh partition. With that, both near- and far-field flow dynamics and noise radiation are resolved simultaneously. In order to capture sound waves, the perfectly matched layer is also implemented so as to avoid waves reflecting to and polluting the inner acoustic field. Moreover, a novel index technique is developed for the GICLBM to enable implicit streaming, which brings an efficient memory reduction. Three cases are then performed to showcase the feasibility, accuracy, extensibility, and efficiency of the present framework, including flow past a square cylinder, flow past an elliptic cylinder, and flow past a NACA 0012 airfoil, each implemented with a type of body-fitted mesh. Both the fluid dynamic and noise radiation are found to be in good agreement with results using the Navier–Stokes solvers. This study demonstrates the potential of the GICLBM for accurately and efficiently simulating external problems as well as sound generation and propagation.

THE METHOD OF HYDRODYNAMIC MODELING USING A CONVOLUTIONAL NEURAL NETWORK

Context. Solving hydrodynamic problems is associated with high computational complexity and therefore requires considerable computing resources and time. The proposed approach makes it possible to significantly reduce the time for solving such problems by applying a combination of two improved modeling methods.
 Objective. The goal is to create a comprehensive hydrodynamic modeling method that requires significantly less time to determine the dynamics of the velocity field by using the modified lattice Boltzmann method and the pressure distribution by using a convolutional neural network.
 Method. A method of hydrodynamic modeling is proposed, which realizes the synergistic effect arising from the combination of the improved lattice Boltzmann method and a convolutional neural network with a specially adapted structure. The essence of the method consists of implementing a sequence of iterations, each of which simulates the process of changing parameters when moving to the next time layer. Each iteration includes a predictor step and a corrector step. At the predictor step, the lattice Boltzmann method works, which allows us to obtain the field of fluid velocities in the working area at the next time layer using the field of velocities at the previous layer. At the corrector step, we apply an improved convolutional neural network trained on a previously created data set. Using a neural network allows us to determine the pressure distribution on a new time layer with a predetermined accuracy. After adding the fluid compressibility correction on the new time layer, we get a refined value of the velocity field, which can be used as initial data for applying the lattice Boltzmann method at the next iteration. Calculations stop when the specified number of iterations is reached.
 Results. The operation of the proposed method was studied on the example of modeling fluid movement in a fragment of the human gastrointestinal tract. The simulation results showed that the time spent implementing the simulation process was reduced by 6–7 times while maintaining acceptable accuracy for practical tasks.
 Conclusions. The proposed hydrodynamic modeling method with a convolutional neural network and the lattice Boltzmann method significantly reduces the time and computing resources required to implement the modeling process in areas with complex geometry. Further development of this method will make it possible to implement real-time hydrodynamic modeling in threedimensional domains.

Simulation study on the coupled heat and mass transfer of CO2 in a heavy oil-water liquid system based on an improved lattice Boltzmann (LB) method

This study investigates the heat and mass transfer when low-temperature CO2 diffuses in a heavy oil–water liquid system based on an improved Lattice Boltzmann (LB) method. First, we determine the CO2 diffusion coefficients in heavy oil and water and the heat transfer coefficients of heavy oil and water using the pressure drop (DP) method and the laser flash (LF) method, respectively. Then, a numerical model that couples the heat and mass transfer in the system is established based on the improved LB method. The effect of low-temperature CO2 on the temperature field of the system and the effect of changes in the temperature field on CO2 diffusion are investigated. Finally, we develop a micro-model reproducing the heat and mass transfer of CO2 in water and heavy oil-saturated porous media to validate the accuracy of the numerical model. The results demonstrate that the CO2 diffusion coefficients in heavy oil and water linearly increase with the temperature increases. The heat transfer coefficients of heavy oil and water are insensitive to the changes in temperature. The heat transfer process has a great impact on the mass transfer of CO2 in the liquid system. The CO2 diffusion velocity slows down as the system temperature decreases because of the heat transfer (from 400 K to 300 K), leading to a reduction percentage of 300 % in the CO2 front movement velocity. Compared to the scenarios neglecting heat transfer, CO2 diffusion distance and amount decrease by 38 % and 50 %, respectively because of the changes in the temperature field of the system.

Flow and mixing dynamics in face-to-face and rear-end collisions of pairs of equal-sized droplets

In this work, the behaviors of pairs of equal-sized droplets in rear-end and face-to-face collisions were simulated using the improved lattice Boltzmann method for incompressible two-phase flows. First, the time evolution of the droplet shape was investigated by tracing colored particles, and this was compared between the rear-end and face-to-face collisions. For collinear collisions, the droplet shapes in the rear-end collisions were found to be similar to those in the face-to-face collisions. However, the behaviors of the tracer particles were different: the droplets in the rear-end collisions mixed more easily than those in the face-to-face collisions. For offset collisions, it was found that the rolling motion of the coalesced droplet accelerates the mixing inside it in both face-to-face and rear-end collisions. A new index—the total mixing intensity—was introduced, and the droplet mixing can be quantitatively evaluated by calculating its value. The results indicate that the droplet mixing process of a collinear collision can be characterized by the velocity ratio, which is defined as the ratio of the center-of-mass velocity to the relative impact velocity.

Numerical simulation of bubbly flows by the improved lattice Boltzmann method for incompressible two-phase flows

Bubbly flow problems are simulated to verify the effectiveness of the improved lattice Boltzmann method for incompressible two-phase flows. In this method, it is possible to compute two-phase fluid flows with high density ratios accurately and efficiently compared with the previous method. Firstly, we simulate a stationary bubble to investigate the accuracy of the interfacial tension. As a result, the calculated pressure differences are in good agreement with the theoretical predictions, and the relative errors of the pressure difference are less than 5%. Secondly, we simulate a single bubble rising in a liquid under gravity. It is found that the terminal bubble shapes and Reynolds numbers are in good agreement with available numerical and experimental data. Thirdly, we simulate two bubbles rising in a liquid under gravity for different initial arrangements. It is found that the bubble shapes and transient Reynolds numbers during the coalescence process are generally in agreement with the available numerical results. Finally, we simulate typical slug and churn flows in a square duct. It is found that transition from slug flow to churn flow occurs when the pressure difference between inlet and outlet of the duct is increased. In addition, it is found that square ducts with larger width tend to generate churn flows. These results demonstrate that the present method is applicable to complicated bubbly flow problems.

Meso-scale simulation of Li–O2 battery discharge process by an improved lattice Boltzmann method

The discharge process of lithium–oxygen battery (LOB) is a highly complicated multi-physics coupling phenomenon. Moreover, the cathode morphology presents a complex multi-scale structure with pore size ranging from nanometers to micronmeters, and plays a crucial role in determining the discharge performance. In this work, the cathodes consisting of carbon paper, electrode material, and electrolyte are first numerically reconstructed using a two-step reconstruction method considering the multi-scale morphology. A lattice Boltzmann model with an improved partial bounce-back scheme is proposed for modeling the discharge process given that the electrode porosity changes with the progress of discharge. The effects of micron-scale electrode spatial distribution on the O2 diffusion and LOB discharge performance are investigated. Results show that the increment of the electrode dispersion degree increases the O2 diffusion resistance due to the increase of electrolyte-electrode specific interface area. A large local electrode load near O2 inlet leads to a high O2 diffusion resistance and low O2 concentration owing to the large specific interface area and electrode volume. Cathodes with the minimum electrode load and maximum electrode dispersion degree present the optimal specific capacity of LOB. However, the specific capacity first increases significantly and then slightly decreases with the increase of local electrode load.

Investigation of effect of the profile of screw flight on chocolate flow in 3D printing using an improved lattice Boltzmann method.

3D printing provides a new way of molding chocolate with complex geometrical structures. The screw extruder can efficiently transport the liquid chocolate, which has been adopted to investigate the effect of the profile of the screw flight on the flow. First, the rheological behavior of the liquid chocolate is measured and the Cross equation is demonstrated as the proper rheological model. Then, based on the rheological behavior, an improved lattice Boltzmann method is creatively proposed, for which the effectiveness is validated by the classical Poiseuille flow. Third, the geometrical structure of the screw extruder is analyzed and transformed. The possible changes in the profiles of the screw flights are listed. Finally, the fluid analysis is conducted and the necessary streamlines figures, cloud charts and velocity distributions are obtained. The large dip angle in straight cases has an obvious effect on the velocity distribution and the common flow area. The position of the convex point is the additional important factor, whereas the concave profiles are the most moderate in the proposed cases. The changes in the profiles will affect the chocolate flow. The work is significant for extrusion theory in 3D printing. © 2022 Society of Chemical Industry.

Melting processes of phase change materials in a horizontally placed rectangular cavity

This paper revisits the melting process of phase change materials (PCMs) enclosed in a horizontally placed rectangular cavity, with isothermal and adiabatic conditions subjected to the vertical and horizontal walls, respectively. First, numerical simulations based on an improved lattice Boltzmann method are conducted to illustrate and to inform the theoretical modelling. It is shown that, compared with the traditional two-stage conduction–convection melting description, it is more reasonable to include a third stage in terms of the heat transfer behaviour. During the third stage, the remnant solid PCM is located in the corner formed by the cold and bottom walls of the cavity, and an increasing part of the input energy will be transferred directly out of the cavity without compensating for the melting latent heat, thus inducing a continuously decreasing melting rate until the end of the melting process. Then theoretical predictions are derived piecewise for the melted liquid fraction during the entire melting process, and the corresponding transitions between two successive stages are also discussed. The results are validated successfully via the available experimental and numerical data in the literature, and could guide the design and operation of latent heat storage systems.

Effect research of cement block on paste flow for 3D cement printing based on an improved lattice Boltzmann method

3D cement printing can realize the rapid prototyping of the building materials effectively. Similar to other additive manufacturing (AM) methods, the extruding velocity is an important factor on the printing performance. Cement paste is easy to set when it flows through the extruding device (extruder screw), which will result in the formation of cement block(s) on the wall. It is essential to investigate the effect of the block on the flow. In order to facilitate the analysis, three simplified common geometries (rectangle, circle, trapezium) in a section of the expanded channel are taken as blocks for fluid analysis. Firstly, an improved lattice Boltzmann method (LBM) is put forward for the non-Newtonian cement paste and validated by Poisuille flow, which is beneficial for the stability and accuracy of numerical simulation. Then, a series of numerical cases on the factors of geometry, size, position and number are conducted. The results show that all of the mentioned factors have important influences on the flow trace, the high/low velocity-region distribution and the outlet velocity.

A Lattice Boltzmann simulation on fin enhanced water cooling of a solar CPV-T receiver

A fin enhanced cooling of a Solar Concentrated Photovoltaic Thermal (CPV-T) receiver is studied with the new computational method, i.e., an improved Lattice Boltzmann Method (LBM). Transient flow patterns and temperature fields have been obtained by the mesoscopic scale simulations with Non-dimensional Lattice Boltzmann Methods (NDLBM). The results show that the application of metal fins such as material copper will enhance the cooling slightly, while glass fins are not friendly to enhance heat transfer although they can keep high light transportation ratio. Geometry factors such as fin heights, gap distance, and thicknesses are also compared. It is found out that shorter smaller gap thicker fins are better designs because they reduce the impeding effects on fluid flow and increase the heat transfer areas between solid and fluid phases.

A modified LBM for non-Newtonian effect of cement paste flow in 3D printing

Purpose The screw extruder is applied in cement-three-dimensional (3D) printing. The cement paste flow in 3D printing is the typical Herschel–Bulkley fluid. To understand the flow in the channel, the improved lattice Boltzmann method (LBM) is proposed. Design/methodology/approach For Herschel–Bulkley flow, an improved LBM is presented to avoid the poor stability and accuracy. The non-Newtonian effect is regard as a special forcing term. The Poiseuille flow is taken to discuss the detailed process of the method. With the method, the analytical solution and numerical solution are obtained and compared. Then, the effect of the initial yield stress on the numerical solution is both explored by the shear-thickening fluid and the shear-thinning fluid. Moreover, the variations of the relative errors under different lattice nodes and different power-law indexes are analyzed. Finally, the method is applied into the simulation of the flow in the extruder of cement-3D printing. Findings The results show that the improved method is effective for Herschel–Bulkley fluids, which can simulate the flow in the extruder stably and accurately. Practical implications The simulation can contribute to understand the cement paste flow in the screw extruder, which helps to optimize the structure of the extruder in the following periods. Originality/value The improve method provide a new way to analyze the flow in the extruder of cement-3D printing. Also, in the past research, LBM for Herschel–Bulkley fluid is ignored, whereas the study can provide the reference for the numerical simulation.

Study of Cavitation Bubble Collapse near a Wall by the Modified Lattice Boltzmann Method

In this paper, an improved lattice Boltzmann Shan‒Chen model coupled with Carnahan-Starling equation of state (C-S EOS) and the exact differential method (EDM) force scheme is used to simulate the cavitation bubble collapse in the near-wall region. First, the collapse of a single cavitation bubble in the near-wall region was simulated; the results were in good agreement with the physical experiment and the stability of the model was verified. Then the simulated model was used to simulate the collapse of two cavitation bubbles in the near-wall region. The main connection between the two cavitation bubble centre lines and the wall surface had a 45° angle and parallel and the evolution law of cavitation bubbles in the near-wall region is obtained. Finally, the effects of a single cavitation bubble and double cavitation bubble on the wall surface in the near-wall region are compared, which can be used to study the method to reduce the influence of cavitation on solid materials in practical engineering. The cavitation bubble collapse process under a two-dimensional pressure field is visualized, and the flow field is used to describe the morphological changes of cavitation bubble collapse in the near-wall region. The improved lattice Boltzmann Method (LBM) Shan‒Chen model has many advantages in simulating cavitation problems, and will provide a reference for further simulations.

Validation of an improved lattice Boltzmann method for incompressible two-phase flows

In this communication, in order to validate a two-phase lattice Boltzmann method proposed by Inamuro et al. [14] furthermore, we simulate two-phase Poiseuille flows with density ratios of 50 and 1000 and a milk crown with density ratio of 800. In the simulations of two-phase Poiseuille flows, the computed results are compared with the analytical solution in good agreement. In the simulations of a milk crown, the droplet splashing from a crown sheet is clearly computed. Also, the crown radius evolution agrees well with theoretical predictions.

Wetting Boundary Condition in an Improved Lattice Boltzmann Method for Nonideal Gases

Wetting Boundary Condition in an Improved Lattice Boltzmann Method for Nonideal Gases

An improved lattice Boltzmann method for simulating advective–diffusive processes in fluids

Lattice Boltzmann methods are widely used to simulate advective–diffusive processes in fluids. Lattice Bhatnagar–Gross–Krook methods presented in the literature mostly just exhibit first order spatial accuracy and introduce errors proportional to the velocity squared. Formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations. We present and demonstrate here a formulation that produces no such second order errors. This formulation suggests that a subtle, but important, adjustment is all it takes to improve the accuracy of the method. The key to the improved accuracy of this new model is the non-standard definition of the concentration that relates to the distribution function describing the advection–diffusion in lattice Boltzmann. The main advantage of the algorithm comes to view when simulating situations where fluid density variations appear. The present formulation of the advection–diffusion algorithm will, by taking into account these fluid density variations, drastically reduce the errors produced compared to the standard formulations. We also show how a source term is included in this new formulation without it losing its second order spatial accuracy.

An improved lattice Boltzmann method for incompressible two-phase flows with large density differences

We propose a new lattice Boltzmann method (LBM) for two-phase fluid flows with high density ratios by improving Inamuro et al.’s method [13] without solving the pressure Poisson equation. In the proposed method, we use the lattice kinetic scheme (LKS, an extended scheme of LBM) in the same way as Inamuro et al.’s method. The velocity and pressure fields are computed by using a single equilibrium distribution function and by adjusting the speed of sound in a high density region to satisfy the incompressible continuity equation even for high density ratios. In addition, an improved LKS is used for eliminating dissipation errors, and the continuous surface force (CSF) model is used for modeling interfacial tension of thin interfaces accurately. In order to show the validity of the method, we apply the method to the simulations of a stationary drop, binary droplet collision, rising bubbles, and the impact of a drop on a thin liquid film (a milk crown). In a stationary drop, pressure and density profiles are computed, and the effect of sound speed on time evolution of the pressure field in the drop is illustrated. The stable computations can be performed for high density ratios up to 855. In the simulations of a binary droplet collision and rising bubbles, the computed results by the proposed method are compared with those by Inamuro et al.’s method in good agreement. Also, the computation time of the proposed method is about 50 times faster than that of Inamuro et al.’s method . In the simulation of a milk crown, the time evolution of the crown radius is in good agreement with theoretical predictions.

Lattice Boltzmann method for overland flow studies and its experimental validation

ABSTRACTThe negative distribution functions exist when the kinematic wave equation of overland flow is solved using the traditional lattice Boltzmann method. To resolve this shortcoming, an improved lattice Boltzmann method is introduced involving the multi-scale expansion of time coordinate (but not spatial coordinate). Based on the improved multi-scale expansion, a multi-scale analysis method and an undetermined coefficient method are used to gain the equilibrium distribution functions. To validate the proposed approach, special experiments with water flows on the impervious and pervious (with soil macropores) slopes have been conducted. The experimental results show that the improved lattice Boltzmann method is effective in describing overland flows; there are no numerical oscillations, and the distribution functions are positive when the relaxation time is from 0.8 to 2.0.

Elucidating the Role of Interfacial Tension for Hydrological Properties of Two-Phase Flow in Natural Sandstone by an Improved Lattice Boltzmann Method

We investigated the interfacial tension (IFT) effect on fluid flow characteristics inside micro-scale, porous media by a highly efficient multi-phase lattice Boltzmann method using a graphics processing unit. IFT is one of the most important parameters for carbon capture and storage and enhanced oil recovery. Rock pores of Berea sandstone were reconstructed from micro-CT scanned images, and multi-phase flows were simulated for the digital rock model at extremely high resolution (3.2 $$\upmu $$ m). Under different IFT conditions, numerical analyses were carried out first to investigate the variation in relative permeability, and then to clarify evolution of the saturation distribution of injected fluid. We confirmed that the relative permeability decreases with increasing IFT due to growing capillary trapping intensity. It was also observed that with certain pressure gradient $$\Delta P$$ two crucial IFT values, $$\sigma _{1}$$ and $$\sigma _{2}$$ , exist, creating three zones in which the displacement process has totally different characteristics. When $$\sigma _{1}< \sigma < \sigma _{2}$$ , the capillary fingering patterns are observed, while for $$\sigma < \sigma _{1}$$ viscous fingering is dominant and most of the passable pore spaces were invaded. When $$\sigma > \sigma _{2}$$ the invading fluid failed to break through. The pore-throat-size distribution estimated from these crucial IFT values ( $$\sigma _{1 }$$ and $$\sigma _{2})$$ agrees with that derived from mercury porosimetry measurements of Berea sandstone. This study demonstrates that the proposed numerical method is an efficient tool for investigating hydrological properties from pore structures.