Incompressible Model Research Articles

Numerical simulation of hydro-cyclone separator used for separation of highly dense suspended particulate matter

Cyclone separators are the most cost-effective and economically gas separation devices. They are not very complex to design and offer high collection efficiency; still, their use for the waste management field, i.e., separating solid waste from the liquid, is not explored to its full extends. This paper presents a Computational Fluid Dynamics-based numerical simulation of a hydro-cyclone separator planned to separate suspended particles from the digestate of a biogas plant. The turbulent incompressible flow model is employed during the simulation. The discrete particle method is used to model and track the suspended solid particle trajectory. The fluid properties of the digestate are assigned to the fluid supplied with suspended particle sizes ranging from 10 to 100 µm during the simulation to obtain realistic flow results. The Stairmand high-efficiency hydro-cyclone geometry is redesigned by the numerical experiment method to obtain high collection efficiency for solid particles. Here the effect of inlet flow velocity and suspended solid particle diameter are simulated to understand their effects on the hydro-cyclone collection efficiency. The fluid flow dynamics are observed, and the detailed distribution of particles inside the hydro-cyclone is presented.

Numerical algorithm based on regularized equations for incompressible flow modeling and its implementation in OpenFOAM

Various aspects of incompressible viscous flow modeling using regularized equations are considered: from the formulation of quasi hydrodynamic (QHD) equations for fluid motion to the demonstration of the capabilities of the associated OpenFOAM solver QHDFoam.The numerical algorithm for fluid flow simulations is devised using the QHD approach. Unlike prominent operator splitting techniques (PISO, SIMPLE and their variants), the QHD approach provides an equation for pressure explicitly. Practical issues of QHD approximation and stability criteria for the numerical scheme are presented.Several problems are used to validate the developed solver and to demonstrate its capabilities: backward facing step, skewed cavity flow, natural convection and generation of internal gravity waves attractor. Results of simulations for the last case are obtained using 3 different methods to show peculiarities of the quasi hydrodynamic equations approach in comparison with the standard PISO algorithm and finite-volume method and with the solution based on the spectral element method.The source code of the developed OpenFOAM solver(s) can be downloaded from the GitHub repository: https://github.com/unicfdlab/QGDsolver.

Numerical simulation of the shear stress produced by the hot metal jet on the blast furnace runner

During steel casting process a jet of molten metal runs out of the blast furnace hearth and strikes the runner. The continuous impact of hot fluids causes significant damage to its surface, which is made of refractory concrete. In particular, the initial impact on the dry runner is expected to be critical. This work deals with the analysis of the mechanical impact on the runner through the numerical simulation of the process. We propose an incompressible turbulent isothermal Navier-Stokes model, where turbulence is modelled considering two k−ω models (standard and SST). The interface dynamics is described by applying the Volume of Fluid (VOF) method, while the surface tension vector is provided by the Continuum Surface model (CSF). Their numerical results are performed in 2D. A comparative analysis of the most suitable transient turbulent multiphase model is presented by simulating benchmark physical experiments. The shear stress arising from the impact of the jet on the runner is also analyzed. An improvement of the classical analytical expression given in [1] is proposed. Both, the chosen turbulence model, and the formulas to compute the shear stress are validated using two benchmark laboratory tests and three numerical experiments. Numerical results are given for the impact of the jet on the dry runner of the blast furnace.

Microfluidic chip of concentration gradient and fluid shear stress on a single cell level

Concentration gradient and fluid shear stress (FSS) for cell microenvironment were investigated through microfluidic technology. The Darcy–Weisbach equation combined with computational fluid dynamics modeling was exploited to design the microfluidic chip, and the FSS distribution on the cell model with varying micro-channels (triangular, conical, and elliptical). The diffusion with the incompressible laminar flow model by solving the time-dependent diffusion–convection equation was applied to simulate the gradient profiles of concentration in the micro-channels. For the study of single cell in-depth, the FSS was investigated by the usage of polystyrene particles and the concentration diffusion distribution was studied by the usage of different colors of dyes. A successful agreement between model simulations and experimental data was obtained. Finally, based on the established method, the communication between individual cells was envisaged and modeled. The developed method provides valuable insights and allows to continuously improve the design of microfluidic devices for the study of single cell, the occurrence and development of tumors, and therapeutic applications.

Numerical simulation of cascaded cyclone separator for nanosize aerosol

ABSTRACT Among the conventionally used sampling methods, the cyclone-based air samplers are considered to be the most effective and simplest method. However, the collection efficiency of these commercially available air samplers is found to be limited. It reaches a critically low value for nanosized aerosol particle separation. This paper presents a computational fluid dynamics-based numerical simulation of a cascaded cyclone separator planned to be used for the separation of nanosize airborne viruses. The turbulent incompressible flow model with a volume of a fluid formulation is employed during the simulation. The discrete particle method is used to model and track the nanosized aerosol particle trajectory. The fluid properties of the airborne viruses are assigned to the aerosol particles during the simulation to obtain realistic flow results. The Stairmand high-efficiency cyclone geometry is redesigned by the numerical experiment method to obtain high collection efficiency for nanosize aerosol particles, and a new set of geometrical ratios has been proposed. Then the effect of inlet flow rate on the collection efficiency is presented. The fluid flow dynamics are observed, and the detailed distribution of particles collected in various portions of the cascaded cyclone is presented. The present cascaded cyclone could separate nanosized aerosol particles with an average efficiency of more than 93%.

On the well-posedness of Banach spaces-based mixed formulations for the nearly incompressible Navier-Lamé and Stokes equations

In this paper we introduce and analyze, up to our knowledge for the first time, Banach spaces-based mixed variational formulations for nearly incompressible linear elasticity and Stokes models. Our interest in this subject is motivated by the respective need that arises from the solvability studies of nonlinear coupled problems in continuum mechanics that involve these equations. We consider pseudostress-based approaches in both cases and apply a suitable integration by parts formula for ad-hoc Sobolev spaces to derive the corresponding continuous schemes. We utilize known and new preliminary results, along with the Babuška-Brezzi theory in Banach spaces, to establish the well-posedness of the formulations for a particular range of the indexes of the Lebesgue spaces involved. Among the aforementioned new results from us, we highlight the construction of a particular operator mapping a tensor Lebesgue space into itself, and the generalization of a classical estimate in L2 for deviatoric tensors, which plays a key role in the Hilbertian analysis of linear elasticity, to arbitrary Lebesgue spaces. No discrete analysis is performed in this work.

A Stabilized Finite Element Formulation of Non-Newtonian Fluid Model of Blood Flow in A Bifurcated Channel with Overlapping Stenosis

A stabilized form of finite element formulation known as the Galerkin least-squares (GLS) method is implemented here for solving the two-dimensional incompressible non-Newtonian fluid model of blood flow in a diseased artery. The modelling for this type of flow is based on the conservation of mass and momentum equations, coupled with the generalised Newtonian liquid (GNL) constitutive equation characterized by the generalised power law (GPL) model. The flow of blood in this present study are assumed as steady, laminar and fully developed. The finite element algorithms considered herein are first solved for the Newtonian fluid in a straight artery with a bell shaped stenosis for validation purposes. As the efficiency and validity of the proposed algorithms are obtained through comparison with the findings from existing literature and COMSOL Multiphysics 5.2 software. Then, the algorithms are being implemented to the generalised power law fluid model of blood flow in a bifurcated artery with overlapping stenosis located at the parent's arterial lumen. The numerical results illustrate the arising of distinct sizes of vortex shedding downstream of the stenotic region for each generalised power law index.

The Lattice-Boltzmann Modeling of Microflows in a Cell Culture Microdevice for High-Throughput Drug Screening

The aim of our research was to develop a numerical model of microflows occurring in the culture chambers (CC) of a microfluidic device of our construction for high-throughput drug screening. The incompressible fluid flow model is based on the lattice-Boltzmann equation, with an external body force term approximated by the He-Shan-Doolen scheme and the Bhatnagar-Gross-Krook approximation of the collision operator. The model accuracy was validated by the algebraic solution of the Navier–Stokes equation (NSE) for a fully developed duct flow, as well as experimentally. The mean velocity prediction error for the middle-length cross-section of CC was 1.0%, comparing to the NSE algebraic solution. The mean error of volumetric flow rate prediction was 6.1%, comparing to the experimental results. The analysis of flow hydrodynamics showed that the discrepancies from the plug-flow-like velocity profile are observed close to the inlets only, and do not influence cell cultures in the working area of CC. Within its workspace area, the biochip provides stable and homogeneous fully developed laminar flow conditions, which make the procedures of gradient generation, cell seeding, and cell-staining repeatable and uniform across CC, and weakly dependent on perturbations.

Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator

This study presents a novel method for modelling of Eulerian incompressible fluid flow by using peridynamic differential operator. The peridynamic differential operator is used to calculate partial derivatives in the Navier-Stokes equations. The pressure Poisson equation is used to obtain the pressure field whereas the velocity field is obtained by solving momentum equations. The numerical procedure to solve Navier-Stokes equations in peridynamics for the incompressible fluid is also provided. The capability of the proposed peridynamic incompressible fluid model is demonstrated by considering problems of two-dimensional cavitation, a flow inside an open channel, and a flow over a cylinder. Moreover, to demonstrate the capabilities of the proposed model, the problems of two-dimensional cavitation and a flow over a cylinder are investigated for different Reynolds numbers. The vortex shedding is also captured for the problem of a flow over a cylinder at Reynolds number of Re=100. For verification purposes, the peridynamic results are compared with the results obtained by ANSYS Fluent, a commercial fluid dynamics software.

Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting.

Second order linear thermodynamically consistent approximations to nonlocal phase field porous media models

We present a weakly compressible, thermodynamically consistent, hydrodynamical model for the binary fluid flow in porous media using the one-fluid multiple component formulation, consisting of a force balance equation with a weak inertia, weakly perturbed continuity equation, and a volume-preserving, nonlocal Allen–Cahn equation for the phase field variable. This model is called the nonlocal Allen–Cahn-Extended-Darcy (NACED) model. In the incompressible and/or the inertialess limit, it reduces to two limiting models that we focus on in this study: the incompressible, nonlocal Allen–Cahn-Extended-Darcy (NACED) model and nonlocal Allen–Cahn–Darcy (NACD) model, respectively. The weakly compressible model provides a pathway for us to develop thermodynamically consistent numerical algorithms for the incompressible models. Guided by the energy variational formulation of the models, we use the energy quadratization method in time and finite difference method in space on staggered grids to derive second-order, linear, coupled and decoupled, energy dissipation rate preserving schemes for the incompressible models. The decoupled schemes for NACED model are obtained by exploiting the intrinsic relation between the incompressible and weakly compressible model. We then prove that the linear systems resulted from the linear schemes are uniquely solvable. Mesh refinement tests are conducted to confirm the convergence rates and benchmark examples of binary fluid flow motion in porous media with and without gravity are presented to showcase the schemes’ accuracy and usefulness.

Constitutive Model of Radiation Aging Effects in Filled Silicone Elastomers under Strain.

Filled silicone elastomers, an essential component in many technological applications, are often subjected to controlled or unintended radiation for a variety of reasons. Radiation exposure can lead to permanent mechanical and structural changes in the material, which is manifested as altered mechanical response, and in some cases, a permanent set. For unfilled elastomers, network theories developed and refined over decades can explain these effects in terms of chain-scission and cross-link formation and a hypothesis involving independent networks formed at different strain levels of the material. Here, we expose a filled silicone rubber to gamma radiation while being under finite elongational strain and show that the observed mechanical and structural changes can be quantitatively modeled within the same theoretical framework developed for unfilled elastomers as long as nuances associated with the Mullins effect are accounted for in a consistent manner. In this work, we employ Ogden's incompressible hyperelastic model within the framework of Tobolsky's two-network scheme to describe the observed permanent set and mechanical modulus changes as a function of radiation dosage. In the process, we conclude that gamma radiation induces both direct cross-linking at chain crossings (H-links) and main-chain-scission followed by cross-linking (Y-links). We provide an estimate of the ratio of chain-scission to cross-linking rates, which is in reasonable agreement with previous experimental estimate from Charlesby-Pinner analysis. We use density functional theory (DFT)-based quantum mechanical calculations to explore the stability of -Si and -SiO radicals that form upon a radiation-induced chain-scission event, which sheds light on the relative rates of Y-linking and H-linking processes.

Second order linear decoupled energy dissipation rate preserving schemes for the Cahn-Hilliard-extended-Darcy model

The thermodynamically consistent Cahn-Hilliard-Extended-Darcy (CHED) model has been used to describe transient motion of a binary incompressible fluid flow in porous media. In this paper, we develop a series of linear, second-order, energy-dissipation-rate preserving numerical algorithms for the CHED model based on the energy quadratization strategy. We first extend the incompressible CHED model into a weakly compressible, thermodynamically consistent one using the generalized Onsager principle. Guided by the weakly compressible model, we then devise a couple of linear, second-order, decoupled, semi-discrete, temporal algorithms in the form of projection and the energy quadratization (EQ) method. The fully discrete algorithms are obtained by the use of the second-order finite difference method on staggered grids in space. We show theoretically that the obtained numerical algorithms respect the energy-dissipation-rate and the volume conservation property at the discrete level for any time steps, making them unconditionally energy stable. Mesh refinement tests, coarsening dynamics of binary fluids, and the buoyancy-driven binary fluid motion in porous media are investigated numerically. In buoyancy-driven flow simulations, a new set of inflow and outflow boundary conditions are devised using the model. The numerical results compare well with the results in the literature.

A consistently compressibleMooney‐Rivlinmodel for the vulcanized rubber based on the Penn's experimental data

AbstractBased on the Penn's experimental data, a consistently compressible Mooney‐Rivlin model is developed for the vulcanized rubber. First, the Penn's experimental data are re‐analyzed, which show the near incompressibility. Next, the incompressible Mooney‐Rivlin model and three conventional types of compressible model are studied for the vulcanized rubber, which exhibit an apparent inconsistence with the incompressible model due to the dissimilar initial shear modulus. Finally, a consistently compressible model with extra constants is proposed, which obeys the normalization conditions and the consistent conditions, and a procedure to identify model constants is suggested, and then applied to the Penn's experimental data. The consistently compressible Mooney model is eventually established for the vulcanized rubber, and then compared with other four hyper‐elastic models.

Improving stability of moving particle semi-implicit method by source terms based on time-scale correction of particle-level impulses

The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum conservation regarding particle-level collisions, hereinafter refered to as time-scale correction of particle-level impulses (TCPI), is proposed to derive new source terms of pressure Poisson equation (PPE). This results in more stable computations with drastic reduction of unphysical pressure oscillations and more robust simulation with pressure magnitudes almost independent to time step. Moreover, compared to other strategies, no additional computational effort is required, its implementation is extremely simple, and the only numerical parameter is the propagation speed of the perturbations, of which the calibration is much more straightforward due to its physical meaning. Simulations were carried out using moving particle semi-implicit (MPS) method improved by the proposed approach. The comparisons of computed results with theoretical and experimental ones confirmed the effectiveness of the proposed approach.

Numerical simulation of the thermal regime of an underground spent fuel storage facility (built-in structure variant)

The results of a numerical simulation of the thermal regime of an underground facility for long-term storage of spent nuclear fuel in a built-in reinforced concrete structure are presented. Two computer models were constructed in a three-dimensional formulation in the COMSOL programme. The first model is based on the incompressible fluid approximation, while the second model is based on the "incompressible ideal gas" approximation. The mathematical basis of models: the continuity equation, Navier - Stokes equations averaged by Reynolds, the standard (k - ε) turbulence model, and the general heat transfer equation. Consideration of mixed convection conditions is implemented in the "incompressible ideal gas" approximation, where the air density is a function of temperature only. The most thermally stressful arrangement of spent fuel placement is investigated: U-Zr - defective - U-Be. The air rate is varied in the range from 21 to 0.656 m3/s. Numerical experiments were performed for up to 5 years of fuel storage. The principal difference between the non-stationary structure of the velocity fields predicted in the "incompressible ideal gas" model and the "frozen" picture of the aerodynamic parameters in the incompressible fluid model is emphasized. It is shown that the requirements for exceeding the temperature limit values are met when the object operates under conservative ventilation conditions (rate 0.656 m3/s) with a minimum of costs for organizing ventilation. The dynamics of heat flows directed into the rock mass through the base and from the surface of the built-in structure of the U-Zr fuel compartment to the air environment are analyzed. The predominance of the heat flow from the surface of the structure and the different times when the curves of the heat flow dynamics reach their maximum values are noted. The heat flow to the array reaches its maximum significantly faster than to the air.

The impact of myocardial compressibility on organ-level simulations of the normal and infarcted heart

Myocardial infarction (MI) rapidly impairs cardiac contractile function and instigates maladaptive remodeling leading to heart failure. Patient-specific models are a maturing technology for developing and determining therapeutic modalities for MI that require accurate descriptions of myocardial mechanics. While substantial tissue volume reductions of 15–20% during systole have been reported, myocardium is commonly modeled as incompressible. We developed a myocardial model to simulate experimentally-observed systolic volume reductions in an ovine model of MI. Sheep-specific simulations of the cardiac cycle were performed using both incompressible and compressible tissue material models, and with synchronous or measurement-guided contraction. The compressible tissue model with measurement-guided contraction gave best agreement with experimentally measured reductions in tissue volume at peak systole, ventricular kinematics, and wall thickness changes. The incompressible model predicted myofiber peak contractile stresses approximately double the compressible model (182.8 kPa, 107.4 kPa respectively). Compensatory changes in remaining normal myocardium with MI present required less increase of contractile stress in the compressible model than the incompressible model (32.1%, 53.5%, respectively). The compressible model therefore provided more accurate representation of ventricular kinematics and potentially more realistic computed active contraction levels in the simulated infarcted heart. Our findings suggest that myocardial compressibility should be incorporated into future cardiac models for improved accuracy.

A Fully Coupled Simulation of Planar Deposition Flow and Fiber Orientation in Polymer Composites Additive Manufacturing.

Numerical studies for polymer composites deposition additive manufacturing have provided significant insight promoting the rapid development of the technology. However, little of existing literature addresses the complex yet important polymer composite melt flow–fiber orientation coupling during deposition. This paper explores the effect of flow–fiber interaction for polymer deposition of 13 wt.% Carbon Fiber filled Acrylonitrile Butadiene Styrene (CF/ABS) composites through a finite-element-based numerical approach. The molten composite flow in the extrusion die plus a strand of the deposited bead contacting the deposition substrate is modelled using a 2D isothermal and incompressible Newtonian planar flow model, where the material deposition rate is ~110 mm/s simulating a large scale additive manufacturing process. The Folgar–Tucker model associated with the Advani–Tucker orientation tensor approach is adopted for the evaluation of the fiber orientation state, where the orthotropic fitted closure is applied. By comparing the computed results between the uncoupled and fully coupled solutions, it is found that the flow-orientation effects are mostly seen in the nozzle convergence zone and the extrusion-deposition transition zone of the flow domain. Further, the fully coupled fiber orientation solution is highly sensitive to the choice of the fiber–fiber interaction coefficient , e.g., assigning as 0.01 and 0.001 results in a 23% partial relative difference in the predicted elastic modulus along deposition direction. In addition, Structural properties of deposited CF/ABS beads based on our predicted fiber orientation results show favorable agreements with related experimental studies.

Well-posedness analysis of multicomponent incompressible flow models

In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities stays constant. In this type of models, the velocity field in the Navier–Stokes equations is not solenoidal and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the local-in-time well-posedness in classes of strong solutions, and the global-in-time existence of solutions for initial data sufficiently close to a smooth equilibrium solution.

Influence of Varying the Stage Aspect Ratio on the Performance of Multi-Stage Savonius Wind Rotors

Abstract Although using a multi-stage rotor of Savonius vertical-axis wind turbine enhances the self-starting ability, it reduces the power coefficient. To improve power coefficient, the influence of varying the stage aspect ratio is investigated. Therefore, two-, three-, and four-stage Savonius rotors at stage aspect ratios ranging from 0.5 to 1.5 with increments of 0.25 are considered. To determine performance parameters such as coefficients of torque, power, and thrust, a comprehensive three-dimensional unsteady incompressible turbulent flow model using Reynolds-averaged Navier–Stokes (RANS) equations along with a k–ω shear stress transport turbulence model is developed. The developed numerical model is validated utilizing the available experimental results. Moreover, a novel assessment technique relying on flow field characteristics such as pressure distribution in conjunction with streamlines around the proposed multi-stage Savonius rotor with various stage aspect ratios is carried out. The contribution of each stage on the performance of the whole rotor is computed and presented. The findings of the current study illustrate that utilizing a multi-stage rotor with stage aspect ratio equal to or greater than 1.0 significantly enhances the output power. By rising the stage aspect ratio within the range of 0.5–1.5, the peak coefficient of power boosts from 0.163 to 0.213 for a two-stage rotor and from 0.183 to 0.23 for a four-stage rotor. In addition, three-stage rotors with stage aspect ratio ranging from 0.5 to 1.5 show increased average static coefficient of torque from 0.196 to 0.272 with positive values at whole rotation angles. This improves the self-starting abilities of the multi-stage rotor and makes it suitable in areas where the wind is intermittent and very low. Furthermore, raising the stage aspect ratio from 0.5 to 1.5 significantly mitigates the oscillations of both torque and thrust coefficients throughout the entire cycle for all multi-stages. This lowers the mechanical vibrations and noise emission during operation conditions. Accordingly, multi-stage Savonius rotors with stage aspect ratio equal to or greater than 1.0 are highly recommended for practical applications.