Finite Volume Method Simulation Research Articles

Shear-induced permeability anisotropy in liquefiable sands

In principle, numerical simulations of boundary value problems that involve fluid-soil interaction should account for the evolution of permeability due to soil deformation. For many applications of interest in geotechnical engineering, an accurate assessment of the permeability is key to an accurate prediction of settlements and pore water pressure changes. Finite element models rely on laboratory or field testing to characterise permeability; however, these methods cannot easily evaluate anisotropy or moderate variations of permeability. Current testing tools have a limited accuracy and a rigid experimental set-up, and are usually restricted to consider one flow direction. In this study, the influence of shearing on the intrinsic permeability and the anisotropy of permeability in medium-loose liquefiable sands is investigated. The discrete element method (DEM) was used to simulate monotonic undrained and drained triaxial test simulations on model soils comprising spherical particles. The particle positions were recorded at discrete strain levels and the data were taken as input into finite volume method (FVM) simulations which were used to evaluate intrinsic permeability in selected subsamples. In the FVM simulations, permeability was evaluated in the three orthogonal directions. The results indicate that shear deformation induces an anisotropy in permeability, in both drained and undrained triaxial conditions and this anisotropy increases with axial strain. Specifically, the results show an increase in permeability in the direction of the major principal stress, whereas a reduction permeability is observed in the orthogonal plane. Undrained simulations exhibit a jump in vertical permeability around the liquefaction onset; this can be attributed to the sudden loss of particle contacts.

Improving the capturing ability of swirl-based microfluidic chip by introducing baffle wall.

Microfluidics technology is promising in developing microparticle manipulation technology due to its nondestructive control and notable adaptability. The manipulation of microparticle based on swirling stagnation point is one of the feasible microfluidics biotechnologies. Aiming to improve the regulation and control of microparticle, baffle wall is introduced into the 2-microchannel flow field. The theory of wall attachment jet is employed to elucidate the effect of baffle wall. Subsequently, finite volume method simulation is conducted by modeling the swirling flow region (SFR), and the swirling strength is calculated to characterize the SFR's particle-capturing ability. Experimental validation of the modeling and simulation methods is performed using a printed microfluidic chip, which has demonstrated exceptional reliability. Simulation results show that the baffle wall makes considerable influence on the SFR. Strikingly, a global range adjustment of stagnation point is realized when the baffle wall is configured with a convex shape, which has remarkably outperformed our previous work, where the stagnation point could only move within half range of the field. This work significantly contributes to advanced flow field structure and provides insight into better regulation of stagnation point as well as microparticles. These findings have potential applications in the analysis of the effect of bio/chemical substances on single cell.

Simulation and Experimental of Infiltration and Solidification Process for Al2O3(3D)/5083Al Interpenetrating Phase Composite for High Speed Train Prepared by Low-Pressure Infiltration.

Understanding the infiltration and solidification processes of liquid 5083Al alloy into Al2O3 three-dimensional reticulated porous ceramic (Al2O3(3D) RPC) is essential for optimizing the microstructure and properties of Al2O3(3D)/5083Al interpenetrating phase composites (IPCs) prepared by low-pressure infiltration process (LPIP). This study employs ProCAST software to simulate the infiltration and solidification processes of liquid 5083Al with pouring velocities (PV) of 0.4 m/s infiltrating into Al2O3(3D) RPC preforms with varying porosities at different pouring temperatures (PT) to prepare Al2O3(3D)/5083Al IPCs using LPIP. The results demonstrate that pore diameter of Al2O3(3D) RPC preforms and PT of liquid 5083Al significantly influence the of the infiltration. Solidification process analysis reveals that the Al2O3(3D) RPC preform with smaller pore diameters allows the lower pouring velocity of 5083Al to solidify faster compared to the preform with larger pore diameters. Al2O3(3D)/5083Al IPCs were prepared successfully from Al2O3(3D) RPC porosity of 15 PPI with liquid 5083Al at PV 0.4 m/s and PT 800 °C using LPIP, resulting in nearly fully dense composites, where both Al2O3(3D) RPCs and 5083Al interpenetrate throughout the microstructure. The infiltration and solidification defects were reduced under air pressure of 0.3 MPa (corresponding to PV of 0.4 m/s) during LPIP. Finite volume method simulations are in good agreement with experimental data, validating the suitability of the simplified model for Al2O3(3D) RPCs in the infiltration simulation.

A hybrid Finite Volume-Smoothed Particle Hydrodynamics approach for shock capturing applications

A hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach for shock capturing in compressible fluids is presented. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. New FVM-SPH coupling approaches are explored, including online SPH particle injection and deletion around time persistent SPH regions around shocks. The SPH simulation is coupled to the FVM simulation through boundary particles surrounding the active SPH regions, with FVM values interpolated to SPH boundary particles at each timestep. Values in active SPH regions are similarly interpolated to the overlying FVM mesh at each timestep. The performance of the hybrid FVM-SPH scheme in comparison to the individual FVM and SPH methods on two-dimensional test problems is assessed. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy, although it remains slower than the FVM. This hybrid SPH algorithm may enable future compressible fluid simulations with more extensive capabilities than grid-based methods alone, offering potential applications in modeling fluid–structure interaction and solid deformation and fracturing in blast simulations. Further research will focus on applying the hybrid method to three-dimensional blast problems, where the relative computational cost reduction is expected to be more significant.

Finite Volume Method for Transient Pipe Flow with an Air Cushion Surge Chamber Considering Unsteady Friction and Experimental Validation

In various water transmission systems such as long-distance water transfer projects and hydropower stations, accurate simulation of water hammer is extremely important for safe and stable operation and the realization of intelligent operations. Previous water hammer calculations usually consider only steady-state friction, underestimating the decay of transient pressure. A second-order Finite Volume Method (FVM) considering the effect of unsteady friction factor is developed to simulate the water hammer and the dynamic behavior of air cushion surge chamber in a water pipeline system, while an experimental pipe system is conducted to validate the proposed numerical model. Two unsteady friction models, Brunone and TVB models, were incorporated into the water hammer equations, which are solved by the MUSCL–Hancock method. One virtual boundary method was proposed to realize the FVM simulation of Air Cushion Surge Chamber. Comparisons with water hammer experimental results show that, while the steady friction model only accurately predicts the first pressure peak, it seriously underestimates pressure attenuation in later stages. Incorporating an unsteady friction factor can better predict the entire pressure attenuation process; in particular, the TVB unsteady friction model more accurately reproduces the pressure peaks and the whole pressure oscillation periods. For water pipeline systems with an air cushion surge chamber, energy attenuation of the elastic pipe water hammer is primarily due to pipe friction and the air cushion. The experimental results with the air cushion surge chamber demonstrate that the proposed FVM model with the TVB unsteady friction model and the air chamber polytropic exponent near 1.0 can well reproduce the experimental pressure oscillations.

Single and Multiple Gate Design Optimization Algorithm for Improving the Effectiveness of Fiber Reinforcement in the Thermoplastic Injection Molding Process.

Fiber reinforcement orientation in thermoplastic injection-molded components is both a strength as well as a weak point of this largely employed manufacturing process. Optimizing the fiber orientation distribution (FOD) considering the shape of the part and the applied loading conditions allows for enhancing the mechanical performances of the produced parts. Henceforth, this research proposes an algorithm to identify the best injection gate (IG) location/s starting from a 3D model and a user-defined load case. The procedure is composed of a first Visual Basic Architecture (VBA) code that automatically sets and runs Finite Volume Method (FVM) simulations to find the correlation between the fiber orientation tensor (FOT) and the IG locations considering single and multiple gates combinations up to three points. A second VBA code elaborates the results and builds a dataset considering the user-defined loading and constraint conditions, allowing the assignment of a score to each IG solution. Three geometrical components of increasing complexity were considered for a total of 1080 FVM simulations and a total computational time of ~390 h. The search for the best IG location has been further expanded by training a Machine Learning (ML) model based on the Gradient Boosting (GB) algorithm. The training database (DB) is based on FVM simulations and was expanded until a satisfactory prediction accuracy higher than 90% was achieved. The enhancement of the local FOD on the critical regions of three components was verified and showed an average improvement of 26.9% in the stiffness granted by a high directionality of the fibers along the load path. Finite element method (FEM) simulations and laboratory experiments on an industrial pump housing, injection-molded with a polyamide-66 reinforced with 30% of short glass fibers (PA66-30GF) material were also carried out to validate the FVM-FEM simulation frame and showed a 16.4% local stiffness improvement in comparison to the currently employed IG solution.

Numerical Investigation of Conjugate Heat Transfer and Natural Convection Using the Lattice-Boltzmann Method for Realistic Thermophysical Properties

To enable the lattice-Boltzmann method (LBM) to account for temporally constant but spatially varying thermophysical properties, modifications must be made. Recently, many methods have emerged that can account for conjugate heat transfer (CHT). However, there still is a lack of information on the possible physical property range regarding realistic properties. Therefore, two test cases were investigated to gain further insight. First, a differentially heated cavity filled with blocks was used to investigate the influence of CHT on the error and stability of the LBM simulations. Reference finite volume method (FVM) simulations were carried out to estimate the error. It was found that a range between 0.5 to 1.5 is recommended for the fluid relaxation time to balance computational effort, stability, and accuracy. In addition, realistic thermophysical properties of fluids and solids were selected to test whether the lattice-Boltzmann method is suitable for simulating relevant industry-related applications. For a stable simulation, a mesh with 64 times more lattices was needed for the most extreme test case. The second test case was an insulated cavity with a heating pad as the local heat source, which was investigated in terms of the accuracy of a transient simulation and compared to a FVM simulation. It was found that the fluid-phase relaxation time mainly determines the error and that large thermal relaxation times for the solid improve accuracy. Observed deviations from the FVM reference simulations ranged from approximately 20% to below 1%, depending on collision operator and combination of relaxation times. For processes with a large temperature spread, the temporally constant thermophysical properties of the LBM are the primary constraint.

Finite Volume Method for Modeling the Load-Rejection Process of a Hydropower Plant with an Air Cushion Surge Chamber

The pipe systems of hydropower plants are complex and feature special pipe types and various devices. When the Method of Characteristics (MOC) is used, interpolation or wave velocity adjustment is required, which may introduce calculation errors. The second-order Finite Volume Method (FVM) was presented to simulate water hammer and the load-rejection process of a hydropower plant with an air cushion surge chamber, which has rarely been considered before. First, the governing equations were discretized by FVM and the flux was calculated by a Riemann solver. A MINMOD slope limiter was introduced to avoid false oscillation caused by data reconstruction. The virtual boundary strategy was proposed to simply and effectively handle the complicated boundary problems between the pipe and the various devices, and to unify the internal pipeline and boundary calculations. FVM results were compared with MOC results, exact solutions, and measured values, and the sensitivity analysis was conducted. When the Courant number was equal to 1, the results of FVM and MOC were consistent with the exact solution. When the Courant number was less than 1, compared with MOC, the second-order FVM results were more accurate with less numerical dissipation. As the Courant number gradually decreased, the second-order FVM simulations were more stable. For the given numerical accuracy, second-order FVM had higher computational efficiency. The simulations of load rejection showed that compared with the MOC results, the second-order FVM calculations were closer to the measured values. For hydropower plants with complex pipe systems, wave velocity or the Courant number should be adjusted during MOC calculation, resulting in calculation error, and the error value is related to the parameters of the air cushion surge chamber (initial water depth, air cushion height, etc.). The second-order FVM can more accurately, stably, and efficiently simulate the load-rejection process of hydropower plants compared with MOC.

Efficient Simulation of 3D Reaction-Diffusion in Models of Neurons and Networks.

Neuronal activity is the result of both the electrophysiology and chemophysiology. A neuron can be well-represented for the purposes of electrophysiological simulation as a tree composed of connected cylinders. This representation is also apt for 1D simulations of their chemophysiology, provided the spatial scale is larger than the diameter of the cylinders and there is radial symmetry. Higher dimensional simulation is necessary to accurately capture the dynamics when these criteria are not met, such as with wave curvature, spines, or diffusion near the soma. We have developed a solution to enable efficient finite volume method simulation of reaction-diffusion kinetics in intracellular 3D regions in neuron and network models and provide an implementation within the NEURON simulator. An accelerated version of the CTNG 3D reconstruction algorithm transforms morphologies suitable for ion-channel based simulations into consistent 3D voxelized regions. Kinetics are then solved using a parallel algorithm based on Douglas-Gunn that handles the irregular 3D geometry of a neuron; these kinetics are coupled to NEURON's 1D mechanisms for ion channels, synapses, pumps, and so forth. The 3D domain may cover the entire cell or selected regions of interest. Simulations with dendritic spines and of the soma reveal details of dynamics that would be missed in a pure 1D simulation. We describe and validate the methods and discuss their performance.

Coupling Lattice-Boltzmann and Finite Volume CFD Methods for Efficient Co-Simulation of Two-Phase Flow in the Porous Transport Layers of PEM Water Electrolyzers

Polymer electrolyte membrane water electrolysis (PEMWE) can be modeled using computational fluid dynamics (CFD) for research and development purposes. Continua that contain multiple phases or represent porous media are typically treated as homogeneous regions with bulk-average properties. Per this assumption, the finite volume method (FVM) can be employed to solve such problems with simple geometries. This is computationally inexpensive, and it can be utilized to assist the design of macroscopic cell components such as flow fields. However, this method is limited in its ability to link porous transport layer (PTL) morphology to local phase composition and cell performance.The Lattice-Boltzmann method (LBM) has demonstrated the ability to accurately simulate two-phase flow in detailed porous media for fuel cells1,2. Being a particle-based CFD method enables it to resolve the liquid/gas interphase within the pores of replica PTL samples at higher computing speed than other methods. Figure 1 shows an example of oxygen evolution inside the Ti powder PTL sample for a PEMWE device at an average current density of 2 A/cm2. This outcome can aid in the development of porous media for both fuel cell and electrolysis applications3.We always strive to build the simplest possible models that fully describe a system at the length scale of interest. Macroscale FVM simulations can be used to aid the investigation of porous media properties and morphology by providing a realistic current distribution. Meanwhile, experimentally validated LBM simulations produce output data that are useful for modeling two-phase flow in a homogeneous region using the FVM. Satjaritanun, S. Hirano, I. V. Zenyuk, J. W. Weidner, N. Tippayawong, and S. Shimpalee, J. Electrochem. Soc., 167, 013516 (2019).Satjaritanun, S. Hirano, A. D. Shum, I. V. Zenyuk, A. Z. Weber, J. W. Weidner, and S. Shimpalee, J. Electrochem. Soc., 165, F1115 (2018).Satjaritanun, M. O'Brien, D. Kulkarni, S. Shimpalee, C. Capuano, K. E. Ayers, N. Danilovic, D. Y. Parkinson, and I. V. Zenyuk, iScience, 12, 101783 (2020). Figure 1

Finite volume method for simulation of flowing fluid via OpenFOAM

Finite volume method for simulation of flowing fluid via OpenFOAM

Fractal analysis of CT images of tight sandstone with anisotropy and permeability prediction

For developing unconventional oil and gas resources, it is necessary to quantify the heterogeneity embodied in both pore-size distribution (PSD) and pore spatial distribution, on the basis of which the relationship between the seepage characteristics and the microstructure of heterogeneous porous media could then be clarified. In this work, micro computed tomography (μCT) and image processing technology were applied to characterise matrix pore structure in tight sandstone. Fractal theory was used to investigate the image-based heterogeneity of tight porous media. On the basis of the verification that the PSD of the tight rock is statistically self-similar at a certain scale, we investigated the relationships between porosity and fractal dimension, and between 2D and 3D fractal dimensions, respectively. The results showed that the pore structure characteristic parameters with anisotropy, i.e., the ratio of the minimum pore size to the maximum pore size λ max /λ min and a proportionality constant C KT , could be obtained by liner fitting fractal dimension and porosity. Moreover, the 2D PSD characteristics of the ‘standard cross section’ were consistent with the 3D PSD characteristics of pore network. A fractal permeability model was established by treating the connected pores in the matrix as a bundle of conical micropipes. The permeability values predicted by the proposed model agreed well with those predicted by finite volume method simulation under the condition where irreducible pores were removed. A sensitivity analysis indicated that increasing the heterogeneity of the PSD and pore spatial distribution reduced the flow capacity of the matrix, particularly for low-porosity porous media. • A method to verify the fractal self-similarity of pore size distribution in CT images. • D f-2 vs D f-3 of microstructure in heterogeneous porous media was explored. • Fractal anisotropic model for permeability prediction in heterogeneous porous media.

Wettability-defined frosting dynamics between plane fins in quiescent air

Finned heat exchangers used in energy applications regularly undergo condensation frosting. Understanding the effects of fin spacing on frost growth with surfaces having differing wettability is important for the design of next-generation heat exchangers. This study presents an experimental investigation using high-resolution optical imaging of frost growth between two parallel vertical plain aluminum fins as a function of surface wettability (hydrophilic, superhydrophilic, superhydrophobic), fin surface temperature (-5 to -15 °C), fin spacing (2 to 8 mm), and relative humidity (≈ 50 and 70%). We observe two distinct regimes of frost growth for all test conditions. The effect of surface wettability on frost growth rate becomes significant for fin spacing ≤ 6 mm at fin surface temperatures below -10 °C. The fin surface temperature plays a significant role for fin spacing > 4 mm. Furthermore, for hydrophilic surfaces, the effect of relative humidity was found to be significant for fin spacing > 4 mm. To explain the frosting physics and mass transfer effects, we developed a three-dimensional finite volume method simulation to characterize the moist air flow field between fins at varying fin spacings. For similar humidity, fin surface temperature, and wettability, larger fin spacing resulted in higher frost growth rate due to higher access to moist air. We use the experimental data to develop an empirical correlation for predicting frost thickness. Furthermore, we develop an artificial neural network independent of predetermined functional form that can be trained with the experimental data to predict frost thickness with high accuracy.

Higher order fully implicit cell-centered finite volume method for simulation of oil-water displacement in porous medium

In this paper a fully implicit cell-centered finite volume method with Higher-Order Upwind scheme (HOU) for convective flow approximation is presented for numerical solution of oil-water displacement problem. Main advantages of this scheme are the robustness, accuracy and rapid convergence of Newton technique, used for linearization obtained discrete equations. Using of HOU scheme allows receive second order approximation of flux in the regions of slow saturation changing and stable solution near to the shocks. Efficiency of proposed scheme is verified by numerical tests.

The two-phase flow simulation and experimental research on the formation of solder voids in power module

This paper focuses on the formation of solder voids in the large-area die-attach (DA) in power modules. The finite volume simulation method was used to study the motion behaviors of bubbles in molten liquid solder. The experiments were carried out by changing the reflow atmosphere. The voids distribution in DA was characterized by X-Ray detection. Results suggest that vacuuming the molten solder can significantly reduce the void rate of the DA. The bubbles only need a short stroke to escape from the molten solder under the influence of negative pressure. From a mechanical point of view, the collapse of the solder during the phase change is one of the main forces for driving the bubble to coalesce and move horizontally, but it may also lead to an increase in void ratio due to the reduction of BLT (Bond Layer Thickness). Solders with larger wall contact angles tend to have a larger void rate due to the increase in viscous resistance. The nitrogen atmosphere has a positive effect on reducing the void rate by reducing the wall contact angle of liquid solder. Besides, the wall adhesion plays a leading role in the movement of the bubble, and the influence of the buoyancy is small.

Novel applications of re-tooled open-source acoustic simulation algorithms

Pachyderm Acoustic Simulation is an open-source acoustics simulation tool that is freely available to the public through the General Public License 3.0. In the 11 years, that Pachyderm Acoustic Simulation has been available, its open and conventional acoustics simulation algorithms (including geometrical, finite volume, transfer matrix, etc.) have been applied in ways that are less conventional by certain creative individuals. Users leverage access to the algorithms through its native interface, grasshopper (for visual generation of algorithms), IronPython, and the software’s native source language C#. Examples of these creative applications include augmented geometrical visualizations, customized finite volume method simulations for proof of concept, visualization of material data, and form-finding using genetic algorithms. This talk will explore several exemplary cases in which a user successfully applied the simulation and calculation algorithms in a way that was not originally intended.

Mechanical behavior of TPMS-based scaffolds: a comparison between minimal surfaces and their lattice structures

Triply periodic minimal surfaces (TPMS) have drawn widespread attention out of their biomimetic features. This work compares skeletal-TPMS lattices with of strut-TPMS lattices in terms of their geometric and mechanical properties. Skeletal-TPMS lattices consist of continually smooth surfaces, while their counterparts, strut-TPMS lattices, are composed of cylindrical beams. These lattices derived from four kinds of TPMS, namely Gyroid (G), Schwarz Diamond (D), Schwarz Primitive (P), and iWp (W), having incremental nodal connectivity of 3, 4, 6, and 8, respectively. The scaling laws of Young’s modulus and yield strength are determined as power functions of volume fraction according to finite volume method (FVM) simulations. Their uniaxial compression behaviors are characterized by FVM simulations and are experimentally validated using additive manufacturing and uniaxial compression tests, showing that skeletal-TPMS lattices exhibit more homogeneous stress distribution. This work would not only broaden the material space for scaffolds, but shed light on the design criteria for tissue engineering.

Combined grand canonical Monte Carlo and finite volume method simulation method for investigation of direct air capture of low concentration CO2 by 5A zeolite adsorbent bed

A method that combines finite volume method (FVM) and grand canonical Monte Carlo (GCMC) method is proposed to investigate the direct air capture of low concentration CO2 by 5A zeolites in an adsorption bed of a space shuttle. In the FVM, the multicomponent Langmuir model and linear fitting formula are used to calculate saturation adsorption capacities and adsorption heat at macro-scale level, respectively. The GCMC method is used to obtain the parameters of the multicomponent Langmuir model and linear fitting formula at micro-scale level. The combined method overcomes the shortcomings of the saturation adsorption capacities and adsorption heat restricted by experiments or empirical formulas. The effects of inlet velocity, particle size, and porosity on heat and mass transfer in the adsorption bed are predicted. The saturation adsorption time for N2 is faster than that for CO2. The competitive adsorption process between CO2 and N2 is divided into three stages, namely, primary, intermediate, and saturation stage. The location of temperature difference peak between solid and gas phase moves toward the outlet of the adsorption bed with increasing velocity, porosity, adsorption time or decreasing particle size. An adsorption bed with high inlet velocity and porosity and small particle size is recommended to achieve improved performance.

Simulation and Analysis of Mechanical Properties of Silica Aerogels: From Rationalization to Prediction.

Silica aerogels are highly porous 3D nanostructures and have exhibited excellent physio-chemical properties. Although silica aerogels have broad potential in many fields, the poor mechanical properties greatly limit further applications. In this study, we have applied the finite volume method (FVM) method to calculate the mechanical properties of silica aerogels with different geometric properties such as particle size, pore size, ligament diameter, etc. The FVM simulation results show that a power law correlation existing between relative density and mechanical properties (elastic modulus and yield stress) of silica aerogels, which are consistent with experimental and literature studies. In addition, depending on the relative densities, different strategies are proposed in order to synthesize silica aerogels with better mechanical performance by adjusting the distribution of pore size and ligament diameter of aerogels. Finally, the results suggest that it is possible to synthesize silica aerogels with ultra-low density as well as high strength and stiffness as long as the textural features are well controlled. It is believed that the FVM simulation methodology could be a valuable tool to study mechanical performance of silica aerogel based materials in the future.

Coupled MLPG–FVM simulation of steady state heat conduction in irregular geometry

The two-dimensional steady-state heat conduction in irregular geometry is solved by a MLPG–FVM coupled method. The meshless local Petrove–Galerkin (MLPG) method is applied to the sub-region with skewed wall surface while the finite volume method (FVM) is used in the rest of the domain. The Dirichlet–Dirichlet method is adopted to couple the temperature between MLPG and FVM methods. In MLPG method, the Dirac's Delta function is taken as the test function to avoid the local domain integration which does not need the numerical integration and the solution is independent of the size of the test function. The proposed MLPG–FVM method is validated and proved to be an efficient numerical method for 2-D heat conduction in irregular geometry, which can exert their own advantages of MLPG and FVM.