Numerical Simulation Of Fluid Research Articles

Numerical Simulation of MHD Oldroyd-B Fluid with Thermal Radiation and Chemical Reactions Using Chebyshev Wavelets

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme.

Study on the Diffusion Characteristics of Polymer Grouting Materials Applied for Crack Filling in Underground Mines Based on Numerical Simulation and Experimental Methods.

Polymer grouting materials are increasingly used in the filling of mine fissures. Unlike conventional inorganic grouting materials, the self-expansion of polymers adds complexity to their diffusion process within the crack. The objective of this research was to examine how polymer grouting material spreads in cracks at ambient temperatures and pressure. The investigation involved conducting grouting tests and performing numerical fluid simulation calculations using the finite-volume method in the computational fluid dynamics software, ANSYS FLUENT 2022 R1. The fluid volume approach was employed to determine the boundary between fluid and air and to ascertain the variation patterns of density in the slurry and the fracture system. This study applied the principles of fluid mechanics to investigate the patterns of variation in the physical characteristics of polymer grouting materials, including their density, pressure, flow velocity, and movement distance, during the diffusion process. The results indicated that the density of the polymer grouting material decreased exponentially over time throughout the diffusion process. With the increase in the grouting's volume, the grout's pressure and the permeable distance of the grout increased. The slurry's pressure near the grouting hole exceeded the other points' pressure. The physical parameters of the slurry were numerically simulated by ANSYS FLUENT 2022 R1 software, and the results were compared with the experimental data. After comparing the numerical simulation results with the test data, it was clear that the numerical simulation method was superior in accurately predicting the distribution pattern of each parameter of the polymer slurry during diffusion. The grouting volume, pressure distribution, and real-time change in the position of the flow of slurry could be efficiently determined through numerical calculation and simulated grouting tests. This work can offer valuable information for designing polymer grouting materials used in underground mine fissures.

Flow and Aeroacoustic Characteristics of Underexpanded Supersonic Jets Exhausting from a Conical Converging Nozzle

Ensuring the safety of space flights and solving the problems of reducing acoustic loads during the launch of space vehicles requires not only the development of new technical systems for launch complexes, but also methods for the numerical simulation of fluid and aeroacoustic fields generated by supersonic jets. The growing regulations for space vehicle noise also explain the interest in developing models and techniques that anticipate flow and the aeroacoustic characteristics of supersonic jets. Together with integral techniques for computing far-field noise, development of relevant mathematical models and implementation of numerical tools, the concepts of computational fluid dynamics (CFD) and computational aeroacoustics (CAA) are covered. The noise generated by a supersonic underexpanded jet is used to illustrate the capabilities of current numerical modelling and simulation tools. The jet structure, flow properties, and aeroacoustic quantities are affected by the nozzle pressure ratio. The outcomes of numerical simulation are contrasted with existing experimental and computational data. The available numerical modelling and simulation tools facilitate the development of novel computational methods and methodologies for challenges in CFD and CAA, in addition to solving research and engineering problems.

Tellurium Transport and Enrichment in Volcanogenic Massive Sulfide Deposits: Numerical Simulations of Vent Fluids and Comparison to Modern Sea-Floor Sulfides

Abstract Volcanogenic massive sulfide deposits may represent a significant future source of Te, which is a critical element important for the green energy transition. Tellurium is enriched in these settings by up to 10,000 times over its crustal abundance, indicating that fluids in sea-floor hydrothermal systems may transport and precipitate Te. The major element composition of these hydrothermal fluids is controlled by fluid-rock interaction and is well documented based on experimental, modeling, and natural studies; however, controls on Te mobility are still unknown. To better understand Te enrichment in this deposit type, numerical simulations of the mafic-hosted Vienna Woods and the felsic-hosted Fenway sea-floor vents in the Manus basin were performed to predict Te mobility in modern sea-floor hydrothermal vent fluids and Te deposition during sulfide formation. These simulations demonstrate that the mobility of Te in sea-floor hydrothermal systems is primarily controlled by fluid redox and temperature. Tellurium mobility is low in reduced hydrothermal fluids, whereas mobility of this metal is high at oxidized conditions at temperatures above 250°C. Numerical simulations of the reduced vent fluids of the mafic-hosted Vienna Woods site at the back-arc spreading center in the Manus basin yielded Te concentrations as low as 0.2 ppt. In contrast, the more oxidized model fluids of the felsic-hosted Fenway site located on Pual Ridge in the eastern Manus basin contain 50 ppt Te. The models suggest that Te enrichment in these systems reflects rock-buffer control on oxygen fugacity, rather than an enriched source of Te. In fact, the mafic volcanic rocks probably contain more Te than felsic volcanic rocks. The association of elevated Te contents in the felsic-hosted Fenway system likely reflects magmatic volatile input resulting in lower pH and higher Eh of the fluids. More generally, analysis of sulfide samples collected from modern sea-floor vent sites confirms that redox buffering by the host rocks is a first-order control on Te mobility in hydrothermal fluids. The Te content of sulfides from sea-floor hydrothermal vents hosted by basalt-dominated host rocks is generally lower than those of sulfides from vents located in felsic volcanic successions. Literature review suggests that this relationship also holds true for volcanogenic massive sulfides hosted in ancient volcanic successions. Results from reactive transport simulations further suggest that Te deposition during sulfide formation is primarily temperature controlled. Modeling shows that tellurium minerals are coprecipitated with other sulfides at high temperatures (275°–350°C), whereas Te deposition is distinctly lower at intermediate (150°–275°C) and low temperatures (100°–150°C). These predictions agree with geochemical analyses of sea-floor sulfides as Te broadly correlates positively with Cu and Au enrichment in felsic-hosted systems. The findings of this study provide an important baseline for future studies on the behavior of Te in hydrothermal systems and the processes controlling enrichment of this critical mineral in polymetallic sulfide ores.

Analysis of Fluid Pressure Drop through a Globe Valve using Computational Fluid Dynamics and Statistical Techniques

Fluid mechanics plays a crucial role in everyday life, enabling the selection of accessories, materials, and various components essential for a system through which fluid flows. Pressure drop stands out as one of the most relevant factors in the design of fluid flow systems. However, analytical and experimental physical methods can increase these analyses' costs and time. Hence, in this study, statistical tools are employed to carry out specific experiments supported by numerical fluid simulation, aiming to comprehend the pressure drop behavior in a fluid as it passes through a globe valve. This valve, in turn, possesses distinct operating and manufacturing characteristics. The methods employed encompass a complete factorial system of response surface as support to construct the experimental design path through computational fluid dynamics. Among the key findings, it is demonstrated that, for systems with relatively low flow rates, the valve opening percentage does not exhibit a significant relationship with fluid pressure drop. Conversely, significant effects are observed for systems with relatively high flow rates regarding the valve opening percentage and pressure drop, reaching values of up to 73% pressure drop in this study. It can be inferred that the integration of statistical experimental design techniques and computational fluid dynamics constitutes a valuable resource for studying the pressure drop of a fluid passing through a system.

Numerical simulation and experimental study of fluid–structure interactions in elastic structures based on the SPH method

The study of fluid–structure interactions in elastic structures is highly important in hydraulic structural engineering. This paper adopts the smooth particle hydrodynamics (SPH) coupling method to simulate dam failure water impact elastic plate flow and solid coupling problems. In addition, a numerical simulation is performed on the study of the free surface flow impact of the elastic plate structure on the main dynamic characteristics, including the impact force distribution and the change process. Additionally, the elastic structure of the vibration amplitude and frequency change rule, as well as the drastic changes in free surface flow, are also carried out. In this paper, the synchronous finite element algorithm is used to analyze the problem to obtain FEM results Additionally, two-dimensional benchmark physical tests are designed for dam-break water flow impacting an elastic plate are conducted, focusing on a comparative analysis of the numerical results of the SPH method with the results of physical tests and verifying the validity, accuracy, and superiority of the SPH coupling method for solving the problem of fluid‒solid coupling in elastic structures. On this basis, to explore the relevant physical quantities that cannot be measured or described during the test process, the flow–solid coupling characteristics of the elastic plate impacted by water flow are further understood by analyzing the nature of the flow field, the change in the flow–solid force of the elastic plate and the change rule of the frequency spectrum. The results show the following: (i) The jumps in velocity between the streams and the strong curvature of the free liquid surface lead to the creation of vortices at the cavities. (ii) The flow solid force under the impact of water flow increases and then decreases, and the smaller the deformation of the elastic structure is, the greater the force is. (iii) The vibration frequency of the fixed end of the elastic structure gradually decreases along the free end frequency, and the larger the deformation of the free end of the elastic plate is, the weaker its vibration response is. In addition, the natural frequency of the elastic plate under water flow impact is slightly lower than that under free vibration of the elastic plate. The related research results provide reference and guidance for the fluid–structure interaction problem.

Inelastic Solution for Power Law Fluid with Taylor Galerkin-Pressure Correction Finite Element Method: Axisymmetric Contraction Flows

In this study we examine the flow of inelastic fluids with various shear properties in axisymmetric contractions with various contraction ratios are selected as 4:1, 6:1 and 8:1 with both rounded-corner and sharp. Particular attention is paid to the effect of shear thickening and shear thinning upon the solution behavior. Power-law inelastic model is employed coupling with the conservation of momentum equation and continuity equation. The numerical simulation of such fluid is performed by using the Taylor Galerkin pressure correction (T-G/P-C) finite element algorithm. The effects of geometry structure and many factors such as Reynolds number (Re) and the parameters of power law model are presented in this study. Particularly, in this study we are focused on the influence of these factors on the solution components and the level of convergence. This research was a comparative study between sharp and rounded-corner contraction geometries with a ratio of 4:1, and to another comparative study among sharp contraction geometries with ratios of 4:1, 6:1, and 8:1. The practical implications of this study focused on vortex length and the impact of varying the parameters of the power law model and the Reynolds number (Re) on it for 4:1 contraction flow. The study dealt with the effect of different geometries on the rates of convergence of velocity and pressure as well as the characteristics of axial velocity and pressure on the axis of symmetry.

Fluid–structure interaction with a Finite Element–Immersed Boundary approach for compressible flows

This paper presents the mathematical modeling and numerical simulations of fluid–structure interaction (FSI) problems. The fluid domain is discretized using a Cartesian block-structured mesh and solved using the Finite Volume Method (FVM), using the LES methodology with Smagorinsky turbulent closure model. The fluid flow in the system is considered compressible, with properties that vary. The Immersed Boundary Method (IBM) is used to model the solid–fluid interface, and the structure deformation was solved using the Finite Element Method (FEM). The Multi-direct Forcing Scheme is used to calculate the fluid-dynamics forces through the IBM. After calculating the fluid forces exerted on the solid, the forces are interpolated and transferred to the FEM model, providing the deformation of the structure at each time step. The structural domain was discretized with Hexahedral eight-noded element with extra shape functions. The simulations were carried out using MFSIm (in-house code), a multiphysics simulation framework developed by the Fluid Mechanics Laboratory of the Federal University of Uberlândia with financial support from Petrobras. This paper demonstrates the practical application of FSI analysis in an industrial context, specifically focusing on a pipeline system within a Fluid Catalytic Cracking Unit (FCCU) used in the oil and gas industry. The analysis involves the use of butterfly valves positioned at different angles of opening. The results are treated statistically, and a surface response is generated. Machine learning is employed to predict the surface response, showing the valve configurations that yield the maximum and minimum displacement magnitudes of the evaluated structural probes.

Development of Particle Resolved - Subgrid Corrected Simulations: Hydrodynamic force calculation and flow sub-resolution corrections

Particle Resolved - Direct Numerical Simulation (PR-DNS) of fluid–solid particles is conducted to study hydrodynamic interactions at the interface between phases. An original distinction is proposed between Particle Resolved Simulation (PRS) and Particle Resolved - Direct Numerical Simulation (PR-DNS). In PR-DNS, velocity gradients and pressure are fully resolved, which required several dozens of meshes in the diameter of the particles (40 in Stokes configuration), whereas for PRS, with grid resolution of 10 meshes per diameter, the gradients are only partly resolved, resulting in a sub-resolution of hydrodynamic forces exerted by the fluid to the interface of solid particles. The very high computational cost, associated to PR-DNS, limits its application to academic cases, even though, it was originally developed to study the collective physical effects of a fluid–particle assembly. It explains why numerous simulations with a grid resolution of only a dozen meshes in the particle’s diameter – typically between 10 and 16 – referred to here as PRS, can be found in the literature. In these cases, the velocity gradients and pressure are not accurately computed, inducing an error in the hydrodynamic forces exerted by the fluid to the interface of particles. This paper aims to clarify the hydrodynamic interactions at this scale for a single particle settling in an infinite medium under Stokes configuration. For this purpose, an original method, designed for solid particles, is proposed to compute hydrodynamic forces. A mesh-dependent correlation is then built to numerically correct the partially resolved hydrodynamic forces obtained with PRS, in what we call Particle Resolved - Subgrid Corrected Simulations (PR-SCS). Finally, the correction is assessed for various Reynolds numbers and density ratios under the Stokes assumption.

Numerical simulation of miscible multiphase flow and fluid–fluid interaction in deformable porous media

AbstractThe focus of the underlying research work is on the macroscopic modeling of unstable multiphase fluid flow in deformable porous media, where a lower‐viscous fluid is displaced by a more viscous fluid. This process leads to the formation of channel‐like networks, called viscous fingering. The instability effect is involved in a wide range of different fields in engineering. Some of the most common applications include carbon sequestration to store carbon dioxide (CO2) in underground reservoirs, contaminant transport in geostructures, in industrial processes, such as filtration, catalytic reactions, and in the operation of polymer electrolyte membrane fuel cells with multiphase flow in the gas diffusion layers. In this work, ideal miscible water–glycerin fluids are considered. It is assumed that the interacting fluids in the deformable porous media are incompressible. In addition, a dispersion–diffusion law is applied to capture the fluid–fluid interactions. The presence of a deformable porous material adds additional effects to the problem of the multiphase flow in porous media. The stresses in the porous solid matrix lead to changes in the porosity and influence the flow velocity of the fluids. To couple the deformable porous media with the multiphase flow, a macroscopic approach is used that relies on the theory of porous media. For the porous solid matrix, a linear elastic material model within small strains assumption is applied. The influence of the deformation‐dependent porosity on the instability is studied for 2D simulations, such as a multilayered geometry with different elastic parameters. The presented coupled nonlinear system of differential equations is simulated with the finite element method. Furthermore, a stabilization technique based on the quasi‐compressibility method is used.

Analysis of droplet behavior and breakup mechanisms on wet solid surfaces

The behavior and dynamics of droplet spreading are pivotal phenomena that exert a profound influence on numerous scientific disciplines, technological advancements, and natural processes. This study was conducted with the aim to investigate factors influencing the shape and geometry of a liquid droplet on a solid surface using the lattice Boltzmann method (LBM). LBM as a mesoscale numerical fluid simulation has gained increasing popularity among the most favorable numerical methods for simulating multi-phase/multi-component fluid flow in complex geometries. Accordingly, parameters dependency, surface tension, two-phase diagram, and wettability were evaluated in the LBM, and stable and calibrated forms were used for the droplet simulations. Also, an equation was obtained to determine the contact angle in the LBM system with a determination coefficient of 0.988. Then, droplet behavior was examined for its dependency on wettability, interfacial tension, and line tension. The results showed droplets breakup in a certain interfacial tension at high adhesive force. These breakups were due to the force balance in the triple line. They were not monotonic and first decreased and then increased the volume of the droplets.

The influence of permeability anisotropy in the upper ocean crust on advective heat transport by a ridge-flank hydrothermal system

In this study, we highlight the importance of permeability anisotropy on the hydrogeological regime of a ridge-flank hydrothermal system. Our study site, North Pond, is a marine sediment pond on ∼8 Ma seafloor in the North Atlantic, and represents a low-temperature, end-member ridge-flank hydrothermal system. Previous simulations of North Pond elucidated long-standing hypotheses concerning hydrothermal fluid and heat transport in the upper volcanic crust but failed to fully explain observed patterns of seafloor heat flux in this area. Here we use variography, a geostatistical method, to quantify relations between seafloor heat-flux measurements, and coupled numerical simulations of fluid and heat flow to simulate the hydrogeologic regime. Directional variography shows that heat-flux observations are correlated along-strike of the regional crustal fabric. Three-dimensional simulations that include permeability anisotropy are able to replicate seafloor heat-flux patterns across North Pond. The simulations that result in the best match to thermal data incorporate permeability anisotropy in the horizontal plane. We find that the feedback between permeability anisotropy and the asymmetric geometry of North Pond combine to promote advective removal of heat and mass within the crustal aquifer. These findings suggest that permeability anisotropy in the oceanic crust may influence ridge-flank hydrothermal circulation more broadly.

Numerical heat and solutal transfer simulation of fluid flowing via absorptive shrinkable sheet with Ohmic heat resistance

This work mainly deals with the effect of heat, mass transmission, and heat generating (sinking) on the time-independent two-dimensional boundary-layer flowing of radiative MHD over a sheet, which is dwindling including Joule heating. The governing formulas have been converted into nonlinear ordinary differential equations (NLODE). The final step aims to obtain the graphical numerical illustrations from the set of NLODE; this method is namely as shooting using MATLAB. The accuracy of the outcomes from this study are examines and the comparison have been made by using bvp4c routine of MATLAB. The effect of different material factors on the flow speed, energy, and concentricity have been depicted in diagrams and tables and also discussed in detail. It is found that velocity is enhanced by increasing suction, whereas temperature is increased due to radiation, heat source/sink, and Eckert number. Meanwhile, concentration profile is always being suppressed by magnetic fields, suction, Schmidt number, and chemical reaction parameter. The streamline of the velocity is intensified at the region close to the dwindling surface, whereas the density is the highest for the thicker boundary layer thickness for the temperature and concentration streamlines.

Numerical simulation of Fluid–Structure Interaction problems with viscoelastic fluids using a log-conformation reformulation

In this paper the numerical simulation of the interaction between Oldroyd-B viscoelastic fluid flows and hyperelastic solids is approached. The algorithm employed is a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially. A Galerkin finite element approach has been employed for the numerical approximation of the solid, while the flow equations are approximated using a stabilized finite element method based on the Variational Multi-Scale approach to overcome the instabilities of the Galerkin method. To be able to deal with flows with dominant elasticity, a log-conformation reformulation of the constitutive equation can be employed; here this approach is extended to Fluid–Structure Interaction problems. Several numerical examples are presented and discussed to assess the robustness of the proposed scheme and its applicability to problems with viscoelastic fluids in which elasticity is dominant interacting with hyperelastic solids.

TSI-SD: A time-sequence-involved space discretization neural network for passive scalar advection in a two-dimensional unsteady flow

Numerical simulation of fluid is a great challenge as it contains extremely complicated variations with a high Reynolds number. Usually, very high-resolution grids are required to capture the very fine changes during the physical process of the fluid to achieve accurate simulation, which will result in a vast number of computations. This issue will continue to be a bottleneck problem until a deep-learning solution is proposed to utilize large-scale grids with adaptively adjusted coefficients during the spatial discretization procedure—instead of traditional methods that adopt small grids with fixed coefficients—so that the computation cost is dramatically reduced and accuracy is preserved. This breakthrough will represent a significant improvement in the numerical simulation of fluid. However, previously proposed deep-learning-based methods always predict the coefficients considering only the spatial correlation among grids, which provides relatively limited context and thus cannot sufficiently describe patterns along the temporal dimension, implying that the spatiotemporal correlation of coefficients is not well learned. We propose the time-sequence-involved space discretization neural network (TSI-SD) to extract grid correlations from spatial and temporal views together to address this problem. This novel deep neural network is transformed from a classic CONV-LSTM backbone with careful modification by adding temporal information into two-dimensional spatial grids along the x-axis and y-axis separately at the first step and then fusing them through a post-fusion neural network. After that, we combine the TSI-SD with the finite volume format as an advection solver for passive scalar advection in a two-dimensional unsteady flow. Compared with previous methods that only consider spatial context, our method can achieve higher simulation accuracy, while computation is also decreased as we find that after adding temporal data, one of the input features, the concentration field, is redundant and should no longer be adopted during the spatial discretization procedure, which results in a sharp decrease of parameter scale and achieves high efficiency. Comprehensive experiments, including a comparison with SOTA methods and sufficient ablation studies, were carried out to verify the accurate and efficient performance and highlight the advantages of the proposed method.

Accretion Flow Morphology in Numerical Simulations of Black Holes from the ngEHT Model Library: The Impact of Radiation Physics

In the past few years, the Event Horizon Telescope (EHT) has provided the first-ever event horizon-scale images of the supermassive black holes (BHs) M87* and Sagittarius A* (Sgr A*). The next-generation EHT project is an extension of the EHT array that promises larger angular resolution and higher sensitivity to the dim, extended flux around the central ring-like structure, possibly connecting the accretion flow and the jet. The ngEHT Analysis Challenges aim to understand the science extractability from synthetic images and movies to inform the ngEHT array design and analysis algorithm development. In this work, we compare the accretion flow structure and dynamics in numerical fluid simulations that specifically target M87* and Sgr A*, and were used to construct the source models in the challenge set. We consider (1) a steady-state axisymmetric radiatively inefficient accretion flow model with a time-dependent shearing hotspot, (2) two time-dependent single fluid general relativistic magnetohydrodynamic (GRMHD) simulations from the H-AMR code, (3) a two-temperature GRMHD simulation from the BHAC code, and (4) a two-temperature radiative GRMHD simulation from the KORAL code. We find that the different models exhibit remarkably similar temporal and spatial properties, except for the electron temperature, since radiative losses substantially cool down electrons near the BH and the jet sheath, signaling the importance of radiative cooling even for slowly accreting BHs such as M87*. We restrict ourselves to standard torus accretion flows, and leave larger explorations of alternate accretion models to future work.

Influence of Aortic Valve Leaflet Material Model on Hemodynamic Features in Healthy and Pathological States

Long-term fiber tissue remodeling and the progressive thickening of the aortic valve leaflets called calcific aortic stenosis lead to cardiac blood outflow obstruction. This disease is the most prevalent heart valve pathology in developed countries. Surgeons can perform aortic valve replacement through traditional open-heart surgery involving a cut (incision) in the chest or use minimally invasive methods such as transcatheter aortic valve implantation (TAVI). These types of surgery have numerous advantages and limitations. Recently, the Ozaki operation for aortic valve replacement using tissue from the autologous pericardium has been proposed. Despite being a promising technique for aortic valve pathology treatment, there is a lack of long-term results and optimal selection of leaflet sizing. Numerical fluid simulations can help surgeons predict operation outcomes for each patient. Nevertheless, the description of the material model for leaflet mechanics leaves an open question. Furthermore, selecting the most suitable model to describe the different conditions of the aortic valve is difficult. We performed a numerical analysis of aortic valve leaflet material models to describe the hemodynamics in normal, pathological, and Ozaki cases. We also reveal wall shear stress, von Mises stress, and displacement distributions. Based on the parameters mentioned above, we found that the Ozaki case model behaved similarly to the mathematical model describing the normal case. Numerical simulations also provide information on the mechanisms of aortic valve work in different states of the heart cycle.

Numerical Simulation of Mixing Fluid with Ferrofluid in a Magnetic Field Using the Meshless SPH Method

In this study, a numerical investigation of the effect of different magnetic fields on ferrofluid-fluid mixing processes in a two-dimensional microchannel is performed An improved version of smoothed particle hydrodynamics, SPH, by shifting particle algorithm and dummy particle boundary condition, is implemented to solve numerical continuity, ferrohydrodynamics-based momentum and mass transfer equations. SPH is formulated through the irregular arrangement of the nodes where the fields are approximated using the fifth-order Wendland kernel function. After validating the computational approach, the influence of the number (from one to three) of parallel electrical wires positioned perpendicular to the microchannel on the mixing efficiency is studied for the first time. It has originally been found that the mixing efficiency highly non-linearly depends on the Reynolds number and the number of electrical wires. For Re ≤ 20 the mixing efficiency is almost the same for two and three electrical wires and about two times higher than one electrical wire. For Re ≥ 80, the mixing efficiency of three wires is much higher than one and two electrical wires. Optimum performance of the micromixer is achieved with three electrical wires, since the mixer performs well on a broader range of Re than the other two studied cases. The outcomes of this study, obtained by a meshless method, are important for the industrial design of micromixers.

Numerical simulation of viscoelastic fluid–structure interaction benchmarks and their application to the human eye

We present a numerical solution method for time-dependent viscoelastic fluid–structure interaction employing the arbitrary Lagrangian Eulerian framework. The derived monolithic variational formulation is discretized in time using the shifted Crank–Nicolson scheme and in space using the finite element method. For the linearisation we employ Newton’s method with exact Jacobians. The viscoelastic fluid is modelled either using the Oldroyd-B or a Burgers-type model. The elastic structures are non-linear hyperelastic materials. We validate the implementation on benchmark problems and numerically analyse the convergence for global mesh refinement and adaptive mesh refinement using the dual-weighted residual method. Furthermore we numerically analyse the influence of the viscoelasticity of the fluid on typical goal functionals like the drag, the lift and the displacement. The derived numerical solution method is applied to ophthalmology where we analyse the interaction of the viscoelastic vitreous with its surrounding elastic structures.

Investigation of the numerical simulation of debris flow fluid with concern of phase transition

From a variety of yield stress fluid models, an elastoviscoplastic Herschel-Bulkley (EVPHB) model written in 3D is selected and coupled with a Finite Element Method with Lagrangian Integration Points (FEMLIP) to solve boundary value problems with large deformation process. By tracing the historical variables of a material point, it is verified that in a time-independent flow the elastic strain and viscous strain rate could be accurately reproduced by EVPHB model. For a time-dependent flow, because of the addition of elasticity, the EVPHB model makes the material experience a deformation process which is significantly distinctive from that produced by a pure regularized Herschel-Bulkley model. Benchmarks also show that in FEMLIP the yielded and unyielded zones could be easily defined by EVPHB model according to the stress of a material point. Lastly, it is shown that EVPHB model also induces a stress relaxation process for materials under constant strain. The suitability of FEMLIP to model elastoviscoplastic fluid is verified.