Search results for: Newtonian fluid model

Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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Authors: Alireza Gholipour, Mergen H. Ghayesh, Anthony Zander, Stephen J. Nicholls, Peter J. Psaltis

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A three-dimensional numerical model of an atherosclerotic coronary ‎artery is developed for the determination of high-risk situation and ‎hence heart attack prediction. Employing the finite element method ‎‎(FEM) using ANSYS, fluid-structure interaction (FSI) model of the ‎artery is constructed to determine the shear stress distribution as well ‎as the von Mises stress field. A flexible model for an atherosclerotic ‎coronary artery conveying pulsatile blood is developed incorporating ‎three-dimensionality, artery’s tapered shape via a linear function for ‎artery wall distribution, motion of the artery, blood viscosity via the ‎non-Newtonian flow theory, blood pulsation via use of one-period ‎heartbeat, hyperelasticity via the Mooney-Rivlin model, viscoelasticity ‎via the Prony series shear relaxation scheme, and micro-calcification ‎inside the plaque. The material properties used to relate the stress field ‎to the strain field have been extracted from clinical data from previous ‎in-vitro studies. The determined stress fields has potential to be used as ‎a predictive tool for plaque rupture and dissection.‎ The results show that stress concentration due to micro-calcification ‎increases the von Mises stress significantly; chance of developing a ‎crack inside the plaque increases. Moreover, the blood pulsation varies ‎the stress distribution substantially for some cases.‎

Keywords: atherosclerosis, fluid-structure interaction‎, coronary arteries‎, pulsatile flow

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Authors: G. St-Pierre-Lemieux, E. Askari Mahvelati, D. Groleau, P. Proulx

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Mathematical modeling has become an important tool for the study of foam behavior. Computational Fluid Dynamic (CFD) can be used to investigate the behavior of foam around foam breakers to better understand the mechanisms leading to the ‘destruction’ of foam. The focus of this investigation was the simple cone foam breaker, whose performance has been identified in numerous studies. While the optimal pumping angle is known from the literature, the contribution of pressure drop, shearing, and centrifugal forces to the foam syneresis are subject to speculation. This work provides a screening of those factors against changes in the cone angle and foam rheology. The CFD simulation was made with the open source OpenFOAM toolkits on a full three-dimensional model discretized using hexahedral cells. The geometry was generated using a python script then meshed with blockMesh. The OpenFOAM Volume Of Fluid (VOF) method was used (interFOAM) to obtain a detailed description of the interfacial forces, and the model k-omega SST was used to calculate the turbulence fields. The cone configuration allows the use of a rotating wall boundary condition. In each case, a pair of immiscible fluids, foam/air or water/air was used. The foam was modeled as a shear thinning (Herschel-Buckley) fluid. The results were compared to our measurements and to results found in the literature, first by computing the pumping rate of the cone, and second by the liquid break-up at the exit of the cone. A 3D printed version of the cones submerged in foam (shaving cream or soap solution) and water, at speeds varying between 400 RPM and 1500 RPM, was also used to validate the modeling results by calculating the torque exerted on the shaft. While most of the literature is focusing on cone behavior using Newtonian fluids, this works explore its behavior in shear thinning fluid which better reflects foam apparent rheology. Those simulations bring new light on the cone behavior within the foam and allow the computation of shearing, pressure, and velocity of the fluid, enabling to better evaluate the efficiency of the cones as foam breakers. This study contributes to clarify the mechanisms behind foam breaker performances, at least in part, using modern CFD techniques.

Keywords: bioreactor, CFD, foam breaker, foam mitigation, OpenFOAM

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Authors: Hyun-Kyu Cho, Jun-Su Kim, Choon-Geun Huh, Geon Lee Young-Chul Park

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In this study, the relationship between flow properties and fluid projection distance look into connection for shape variations of foam monitor. A numerical analysis technique for fluid analysis of a foam monitor was developed for the prediction. Shape of foam monitor the flow path of fluid flow according to the shape, The fluid losses were calculated from flow analysis result.. The modified model used the length increase model of the flow path, and straight line of the model. Inlet pressure was 7 [bar] and external was atmosphere codition. am. The results showed that the length increase model of the flow path and straight line of the model was improved in the nozzle projection distance.

Keywords: injection performance, finite element method, foam monitor, Projection distance

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Authors: Y. El Khchine, M. Sriti

Abstract:

In the present work, the forced convection heat transfer and fluid flow past an unconfined semi-circular cylinder is investigated. The two-dimensional simulation is employed for Reynolds numbers ranging from 10 ≤ Re ≤ 200, employing air (Pr = 0.71) as an operating fluid with Newtonian constant physics property. Continuity, momentum, and energy equations with appropriate boundary conditions are solved using the Computational Fluid Dynamics (CFD) solver Ansys Fluent. Various parameters flow such as lift, drag, pressure, skin friction coefficients, Nusselt number, Strouhal number, and vortex strength are calculated. The transition from steady to time-periodic flow occurs between Re=60 and 80. The effect of the Reynolds number on heat transfer is discussed. Finally, a developed correlation of Nusselt and Strouhal numbers is presented.

Keywords: forced convection, semi-circular cylinder, Nusselt number, Prandtl number

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Authors: Debadi Chakraborty, John E. Sader

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Nanomechanical devices have emerged as a versatile platform for a host of applications due to their extreme sensitivity to environmental conditions. For example, mass measurements with sensitivity at the atomic level have recently been demonstrated. Ultrafast laser spectroscopy coherently excite the vibrational modes of metal nanoparticles and permits precise measurement of the vibration characteristics as a function of nanoparticle shape, size and surrounding environment. This study reports that the vibration of metal nanoparticles in simple liquids, like water and glycerol are not described by conventional fluid mechanics, i.e., Navier Stokes equations. The intrinsic molecular relaxation processes in the surrounding liquid are found to have a profound effect on the fluid-structure interaction of mechanical devices at nanometre scales. Theoretical models have been developed based on the non-Newtonian viscoelastic fluid-structure interaction theory to investigate the vibration of nanoparticles immersed in simple fluids. The utility of this theoretical framework is demonstrated by comparison to measurements on single nanowires and ensembles of metal rods. This study provides a rigorous foundation for the use of metal nanoparticles as ultrasensitive mechanical sensors in fluid and opens a new paradigm for understanding extremely high frequency fluid mechanics, nanoscale sensing technologies, and biophysical processes.

Keywords: fluid-structure interaction, nanoparticle vibration, ultrafast laser spectroscopy, viscoelastic damping

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Authors: Pranitha Janapatla, Venkata Suman Gontla

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The present paper investigates the effects of MHD, double dispersion and variable properties on mixed convection flow from a vertical surface in a power-law fluid saturated non-Darcy porous medium. The governing non-linear partial differential equations are reduced to a system of ordinary differential equations by using a special form of Lie group transformations viz. scaling group of transformations. These ordinary differential equations are solved numerically by using Shooting technique. The influence of relevant parameters on the non-dimensional velocity, temperature, concentration for pseudo-plastic fluid, Newtonian and dilatant fluid are discussed and displayed graphically. The behavior of heat and mass transfer coefficients are shown in tabular form. Comparisons with the published works are performed and are found to be in very good agreement. From this analysis, it is observed that an increase in variable viscosity causes to decrease in velocity profile and increase the temperature and concentration distributions. It is also concluded that increase in the solutal dispersion decreases the velocity and concentration but raises the temperature profile.

Keywords: power-law fluid, thermal conductivity, thermal dispersion, solutal dispersion, variable viscosity

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Authors: M. Meenasaranya, S. Saravanan

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Nonlinear stability analysis is carried out to determine the effect of surface temperature modulation in an infinite horizontal porous layer heated from below. The layer is saturated by an electrically conducting, viscous, incompressible and Newtonian fluid. The Brinkman model is used for momentum equation, and the Boussinesq approximation is invoked. The system is assumed to be bounded by rigid boundaries. The energy theory is implemented to find the global exponential stability region of the considered system. The results are analysed for arbitrary values of modulation frequency and amplitude. The existence of subcritical instability region is confirmed by comparing the obtained result with the known linear result. The vertical magnetic field is found to stabilize the system.

Keywords: Brinkman model, energy method, magnetic field, surface temperature modulation

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Authors: K. Khanafer

Abstract:

The aim of this investigation was to validate the fluid-structure interaction (FSI) model of type B aortic dissection with our experimental results from a bench-top-model. Another objective was to study the relationship between the size of a septectomy that increases the outflow of the false lumen and its effect on the values of the differential of pressure between true lumen and false lumen. FSI analysis based on Galerkin’s formulation was used in this investigation to study flow pattern and hemodynamics within a flexible type B aortic dissection model using boundary conditions from our experimental data. The numerical results of our model were verified against the experimental data for various tear size and location. Thus, CFD tools have a potential role in evaluating different scenarios and aortic dissection configurations.

Keywords: aortic dissection, fluid-structure interaction, in vitro model, numerical

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Authors: Nosheen Zareen Khan, Abdul Majeed Siddiqui, Muhammad Afzal Rana

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The steady flow of a second order fluid through constricted tube with slip velocity at wall is modeled and analyzed theoretically. The governing equations are simplified by implying no slip in radial direction. Based on Karman Pohlhausen procedure polynomial solution for axial velocity profile is presented. An expressions for pressure gradient, shear stress, separation and reattachment points and radial velocity are also calculated. The effect of slip and no slip velocity on velocity, shear stress, pressure gradient are discussed and depicted graphically. It is noted that when Reynolds number increases velocity of the fluid decreases in both slip and no slip conditions. It is also found that the wall shear stress, separation and reattachment points are strongly effected by Reynolds number.

Keywords: approximate solution, constricted tube, non-Newtonian fluids, Reynolds number

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

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Authors: Aymen Laadhari

Abstract:

We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: finite element method, level set, Newton, membrane

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Authors: Li Ji, Kaiwei Chu, Shibo Kuang, Aibing Yu

Abstract:

Hydrocyclones are widely used to classify particles by size in industries such as mineral processing and chemical processing. The particles to be handled usually have a broad range of size distributions and sometimes density distributions, which has to be properly considered, causing challenges in the modelling of hydrocyclone. The combined approach of Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) offers convenience to model particle size/density distribution. However, its direct application to hydrocyclones is computationally prohibitive because there are billions of particles involved. In this work, a CFD-DEM model with the concept of the coarse-grained (CG) model is developed to model the solid-fluid flow in a hydrocyclone. The DEM is used to model the motion of discrete particles by applying Newton’s laws of motion. Here, a particle assembly containing a certain number of particles with same properties is treated as one CG particle. The CFD is used to model the liquid flow by numerically solving the local-averaged Navier-Stokes equations facilitated with the Volume of Fluid (VOF) model to capture air-core. The results are analyzed in terms of fluid and solid flow structures, and particle-fluid, particle-particle and particle-wall interaction forces. Furthermore, the calculated separation performance is compared with the measurements. The results obtained from the present study indicate that this approach can offer an alternative way to examine the flow and performance of hydrocyclones

Keywords: computational fluid dynamics, discrete element method, hydrocyclone, multiphase flow

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Authors: Sungho Kim, Dae Shik Kim, Jong Min Lee

Abstract:

Fluid catalytic cracking (FCC) process is one of the most important process in modern refinery indusrty. This paper focuses on the fluid catalytic cracking (FCC) process. As the FCC process is difficult to model well, due to its nonlinearities and various interactions between its process variables, rigorous process modeling of whole FCC plant is demanded for control and plant-wide optimization of the plant. In this study, a process design for the FCC plant includes riser reactor, main fractionator, and gas processing unit was developed. A reactor model was described based on four-lumped kinetic scheme. Main fractionator, gas processing unit and other process units are designed to simulate real plant data, using a process flowsheet simulator, Aspen PLUS. The custom reactor model was integrated with the process flowsheet simulator to develop an integrated process model.

Keywords: fluid catalytic cracking, simulation, plant data, process design

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Authors: Karla E. Sanchez-Cazares, Kim H. Parker, Jennifer H. Tweedy

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The purpose of this work is to develop a simple compartmental model of cerebral fluid balance including blood and cerebrospinal-fluid (CSF). At the first level the cerebral arteries and veins are modelled as bifurcating trees with constant scaling factors between generations which are connected through a homogeneous microcirculation. The arteries and veins are assumed to be non-rigid and the cross-sectional area, resistance and mean pressure in each generation are determined as a function of blood volume flow rate. From the mean pressure and further assumptions about the variation of wall permeability, the transmural fluid flux can be calculated. The results suggest the next level of modelling where the cerebral vasculature is divided into three compartments; the large arteries, the small arteries, the capillaries and the veins with effective compliances and permeabilities derived from the detailed vascular model. These vascular compartments are then linked to other compartments describing the different CSF spaces, the cerebral ventricles and the subarachnoid space. This compartmental model is used to calculate the distribution of fluid in the cranium. Known volumes and flows for normal conditions are used to determine reasonable parameters for the model, which can then be used to help understand pathological behaviour and suggest clinical interventions.

Keywords: cerebrovascular, compartmental model, CSF model, vascular network

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Authors: P. Naderi, M. N. Ouarzazi, S. C. Hirata, H. Ben Hamed, H. Beji

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The stability of mixed convection in a Newtonian fluid medium heated from below and cooled from above, also known as the Poiseuille-Rayleigh-Bénard problem, has been extensively investigated in the past decades. To our knowledge, mixed convection in porous media has received much less attention in the published literature. The present paper extends the mixed convection problem in porous media for the case of a viscoelastic fluid flow owing to its numerous environmental and industrial applications such as the extrusion of polymer fluids, solidification of liquid crystals, suspension solutions and petroleum activities. Without a superimposed through-flow, the natural convection problem of a viscoelastic fluid in a saturated porous medium has already been treated. The effects of the viscoelastic properties of the fluid on the linear and nonlinear dynamics of the thermoconvective instabilities have also been treated in this work. Consequently, the elasticity of the fluid can lead either to a Hopf bifurcation, giving rise to oscillatory structures in the strongly elastic regime, or to a stationary bifurcation in the weakly elastic regime. The objective of this work is to examine the influence of the main horizontal flow on the linear and characteristics of these two types of instabilities. Under the Boussinesq approximation and Darcy's law extended to a viscoelastic fluid, a temporal stability approach shows that the conditions for the appearance of longitudinal rolls are identical to those found in the absence of through-flow. For the general three-dimensional (3D) perturbations, a Squire transformation allows the deduction of the complex frequencies associated with the 3D problem using those obtained by solving the two-dimensional one. The numerical resolution of the eigenvalue problem concludes that the through-flow has a destabilizing effect and selects a convective configuration organized in purely transversal rolls which oscillate in time and propagate in the direction of the main flow. In addition, by using the mathematical formalism of absolute and convective instabilities, we study the nature of unstable three-dimensional disturbances. It is shown that for a non-vanishing through-flow, general three-dimensional instabilities are convectively unstable which means that in the absence of a continuous noise source these instabilities are drifted outside the porous medium, and no long-term pattern is observed. In contrast, purely transversal rolls may exhibit a transition to absolute instability regime and therefore affect the porous medium everywhere including in the absence of a noise source. The absolute instability threshold, the frequency and the wave number associated with purely transversal rolls are determined as a function of the Péclet number and the viscoelastic parameters. Results are discussed and compared to those obtained from laboratory experiments in the case of Newtonian fluids.

Keywords: instability, mixed convection, porous media, and viscoelastic fluid

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Authors: Rei-Tang Tsai, Chih-Yang Wu, Chia-Yuan Chang, Ming-Ying Kuo

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This study aims to investigate the mixing behaviors of deionized (DI) water and carboxymethyl cellulose (CMC) solutions in C-shaped serpentine micromixers over a wide range of flow conditions. The flow of CMC solutions exhibits shear-thinning behaviors. Numerical simulations are performed to investigate the effects of the mean flow speed, fluid properties and geometry parameters on flow and mixing in the micromixers with serpentine channel of the same overall channel length. From the results, we can find the following trends. When fluid mixing is dominated by convection, the curvature-induced vortices enhance fluid mixing effectively. The mixing efficiency of a micromixer consisting of semicircular C-shaped repeating units with a smaller center-line radius is better than that of a micromixer consisting of major-segment repeating units with a larger center-line radius. The viscosity of DI water is less than the overall average apparent viscosity of CMC solutions, and so the effect of curvature-induced vortices on fluid mixing in DI water is larger than that in CMC solutions for the cases with the same mean flow speed.

Keywords: curved channel, microfluidics, mixing, non-newtonian fluids, vortex

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Authors: Muhammad Yousaf, Shoaib Usman

Abstract:

Numerical studies were conducted using Lattice Boltzmann Method (LBM) to study the natural convection in a square cavity in the presence of roughness. An algorithm basedon a single relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice Boltzmann Method (LBM) was developed. Roughness was introduced on both the hot and cold walls in the form of sinusoidal roughness elements. The study was conducted for a Newtonian fluid of Prandtl number (Pr) 1.0. The range of Ra number was explored from 103 to 106 in a laminar region. Thermal and hydrodynamic behavior of fluid was analyzed using a differentially heated square cavity with roughness elements present on both the hot and cold wall. Neumann boundary conditions were introduced on horizontal walls with vertical walls as isothermal. The roughness elements were at the same boundary condition as corresponding walls. Computational algorithm was validated against previous benchmark studies performed with different numerical methods, and a good agreement was found to exist. Results indicate that the maximum reduction in the average heat transfer was16.66 percent at Ra number 105.

Keywords: Lattice Boltzmann method, natural convection, nusselt number, rayleigh number, roughness

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Authors: N. H. Z. Abidin, N. F. M. Mokhtar, S. S. A. Gani

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The influence of diffusion of the thermal or known as Soret effect in a heated Binary fluid model with Coriolis force is investigated theoretically. The linear stability analysis is used, and the eigenvalue is obtained using the Galerkin method. The impact of the Soret and Coriolis force on the onset of stationary convection in a system is analysed with respect to various Binary fluid parameters and presented graphically. It is found that an increase of the Soret values, destabilize the Binary fluid layer system. However, elevating the values of the Coriolis force helps to lag the onset of convection in a system.

Keywords: Benard convection, binary fluid, Coriolis, Soret

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Authors: Sungho Kim, Dae Shik Kim, Jong Min Lee

Abstract:

Fluid catalytic cracking (FCC) process is one of the most important process in modern refinery industry. This paper focuses on the fluid catalytic cracking (FCC) process. As the FCC process is difficult to model well, due to its non linearities and various interactions between its process variables, rigorous process modeling of whole FCC plant is demanded for control and plant-wide optimization of the plant. In this study, a process design for the FCC plant includes riser reactor, main fractionator, and gas processing unit was developed. A reactor model was described based on four-lumped kinetic scheme. Main fractionator, gas processing unit and other process units are designed to simulate real plant data, using a process flow sheet simulator, Aspen PLUS. The custom reactor model was integrated with the process flow sheet simulator to develop an integrated process model.

Keywords: fluid catalytic cracking, simulation, plant data, process design

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Authors: Bhavya Tripathi, Bhupendra Kumar Sharma

Abstract:

In blood, the concentration of red blood cell varies with the arterial diameter. In the case of narrow arteries, red blood cells concentrate around the center of the artery and there exists a cell-free plasma layer near the arterial wall due to Fahraeus-Lindqvist effect. Due to non- uniformity of the fluid in the narrow arteries, it is preferable to consider the two-phase model of the blood flow. In the present article, coupled nonlinear differential equations have been developed for momentum, energy and concentration of two phase model of the blood flow assuming the Newtonian fluid in both central core and cell free plasma layer and the exact solutions have been found for the problem. For having an adequate insight into the stenosed arterial two-phase blood flow, major components of the flow as flow resistance, total flow rate, and wall shear stress have been estimated for different values of magnetic and radiation parameter. Results show that the increase in the effects of magnetic field decreases the velocity of both cores as well as plasma regions. This result can be helpful to control the blood flow in narrow arteries during surgical process. Temperature of core as well plasma regions decrease as value of radiation parameter increases. The present result is implemented in the form of radiation therapy which is very helpful for cancer patients.

Keywords: two phase blood flow, radiation, magnetohydrodynamics (MHD), stenosis

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Authors: Ahmed El-Banbi

Abstract:

Several PVT models exist to represent how PVT properties are handled in sub-surface and surface engineering calculations for oil and gas production. The most commonly used models include black oil, modified black oil (MBO), and compositional models. These models are used in calculations that allow engineers to optimize and forecast well and reservoir performance (e.g., reservoir simulation calculations, material balance, nodal analysis, surface facilities, etc.). The choice of which model is dependent on fluid type and the production process (e.g., depletion, water injection, gas injection, etc.). Based on close to 2,000 reservoir fluid samples collected from different basins and locations, this paper presents some conclusions on the occurrence of reservoir fluids. It also reviews the common methods used to classify reservoir fluid types. Based on new criteria related to the production behavior of different fluids and economic considerations, an updated classification of reservoir fluid types is presented in the paper. Recommendations on the use of different PVT models to simulate the behavior of different reservoir fluid types are discussed. Each PVT model requirement is highlighted. Available methods for the calculation of PVT properties from each model are also discussed. Practical recommendations and tips on how to control the calculations to achieve the most accurate results are given.

Keywords: PVT models, fluid types, PVT properties, fluids classification

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Authors: Sebastian Kohlstädt, Michael Vynnycky, Stephan Goeke, Jan Jäckel, Andreas Gebauer-Teichmann

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This paper summarizes the progress in the latest computational fluid dynamics research towards the modeling in of lost core viability in high-pressure die casting. High-pressure die casting is a process that is widely employed in the automotive and neighboring industries due to its advantages in casting quality and cost efficiency. The degrees of freedom are however somewhat limited as it has been so far difficult to use lost cores in the process. This is right now changing and the deployment of lost cores is considered a future growth potential for high-pressure die casting companies. The use of this technology itself is difficult though. The strength of the core material, as chiefly salt is used, is limited and experiments have shown that the cores will not hold under all circumstances and process designs. For this purpose, the publicly available CFD library foam-extend (OpenFOAM) is used, and two additional fluid models for incompressible and compressible two-phase flow are implemented as fluid solver models into the FSI library. For this purpose, the volume-of-fluid (VOF) methodology is used. The necessity for the fluid-structure interaction (FSI) approach is shown by a simple CFD model geometry. The model is benchmarked against analytical models and experimental data. Sufficient agreement is found with the analytical models and good agreement with the experimental data. An outlook on future developments concludes the paper.

Keywords: CFD, fluid-structure interaction, high-pressure die casting, multiphase flow

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Authors: Muhammad Zubair Akbar Qureshi, Abdul Bari Farooq

Abstract:

The intention of the current study to analyze the significance of nano-layer in incompressible magneto-hydrodynamics (MHD) flow of a Newtonian nano-fluid consisting of carbon nano-materials has been considered through an absorbent channel with moving porous walls. Using applicable similarity transforms, the governing equations are converted into a system of nonlinear ordinary differential equations which are solved by using the 4th-order Runge-Kutta technique together with shooting methodology. The phenomena of nano-layer have also been modeled mathematically. The inspiration behind this segment is to reveal the behavior of involved parameters on velocity and temperature profiles. A detailed table is presented in which the effects of involved parameters on shear stress and heat transfer rate are discussed. Specially presented the impact of the thickness of the nano-layer and radius of the particle on the temperature profile. We observed that due to an increase in the thickness of the nano-layer, the heat transfer rate increases rapidly. The consequences of this research may be advantageous to the applications of biotechnology and industrial motive.

Keywords: carbon nano-tubes, magneto-hydrodynamics, nano-layer, thermal conductivity

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Authors: Mostafa Sefidgar, Sohrab Zendehboudi, Hossein Bazmara, Madjid Soltani

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Based on findings from clinical applications, most drug treatments fail to eliminate malignant tumors completely even though drug delivery through systemic administration may inhibit their growth. Therefore, better understanding of tumor formation is crucial in developing more effective therapeutics. For this purpose, nowadays, solid tumor modeling and simulation results are used to predict how therapeutic drugs are transported to tumor cells by blood flow through capillaries and tissues. A solid tumor is investigated as a porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multi scale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. In this work, the mathematical model in our previous studies is developed by considering two model of momentum equation for porous media: Darcy and Brinkman. The mathematical method involves processes such as fluid flow through solid tumor as porous media, extravasation of blood flow from vessels, blood flow through vessels and solute diffusion, convective transport in extracellular matrix. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model does.

Keywords: solid tumor, porous media, Darcy model, Brinkman model, drug delivery

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Authors: Ihsane Modhaffar

Abstract:

Fiber orientation is essential for the physical properties of composite materials. The theoretical parameters of a given reinforcement are usually known and widely used to predict the behavior of the material. In this work, we propose an image processing approach to estimate true principal directions and fiber orientation during injection molding processes of short fiber reinforced thermoplastics. Generally, a group of fibers are described in terms of probability distribution function or orientation tensor. Numerical techniques for the prediction of fiber orientation are also considered for concentrated situations. The flow was considered to be incompressible, and behave as Newtonian fluid containing suspensions of short-fibers. The governing equations, of this problem are: the continuity, the momentum and the energy. The obtained results were compared to available experimental findings. A good agreement between the numerical results and the experimental data was achieved.

Keywords: injection, composites, short-fiber reinforced thermoplastics, fiber orientation, incompressible fluid, numerical simulation

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Authors: N. M. Arifin, S. P. M. Isa, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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In this paper, the steady forced convection boundary layer flow of a Casson fluid past a moving permeable semi-infinite flat plate beneath a uniform free stream is investigated. The mathematical problem reduces to a pair of noncoupled ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Both the cases when the plate moves into or out of the origin are considered. Effects of the non-Newtonian (Casson) parameter, moving parameter, suction or injection parameter and Eckert number on the flow and heat transfer characteristics are thoroughly examined. Dual solutions are found to exist for each value of the governing parameters.

Keywords: forced convection, Casson fluids, moving flat plate, boundary layer

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Authors: Giovanna Grosso, Martien A. Hulsen, Arash Sarhangi Fard, Andrew Overend, Patrick. D. Anderson

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In many industrial applications and, in particular in polymer industry, the quality of mixing between different materials is fundamental to guarantee the desired properties of finished products. However, properly modelling and understanding polymer mixing often presents noticeable difficulties, because of the variety and complexity of the physical phenomena involved. This is the case of the Cavity Transfer Mixer (CTM), for which a clear understanding of mixing mechanisms is still missing, as well as clear guidelines for the system optimization. This device, invented and patented by Gale at Rapra Technology Limited, is an add-on to be mounted downstream of existing extruders, in order to improve distributive mixing. It consists of two concentric cylinders, the rotor and stator, both provided with staggered rows of hemispherical cavities. The inner cylinder (rotor) rotates, while the outer (stator) remains still. At the same time, the pressure load imposed upstream, pushes the fluid through the CTM. Mixing processes are driven by the flow field generated by the complex interaction between the moving geometry, the imposed pressure load and the rheology of the fluid. In such a context, the present work proposes a complete and accurate three dimensional modelling of the CTM and results of a broad range of simulations assessing the impact on mixing of several geometrical and functioning parameters. Among them, we find: the number of cavities per row, the number of rows, the size of the mixer, the rheology of the fluid and the ratio between the rotation speed and the fluid throughput. The model is composed of a flow part and a mixing part: a finite element solver computes the transient velocity field, which is used in the mapping method implementation in order to simulate the concentration field evolution. Results of simulations are summarized in guidelines for the device optimization.

Keywords: Mixing, non-Newtonian fluids, polymers, rheology.

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Authors: Golden J. Zhang, Dongbao Zhou

Abstract:

Darcy’s law is the fundamental theory in fluid dynamics and engineering applications. Although Darcy linearity was found to be valid for slow, viscous flow, non-linear and non-Darcian flow has been well documented under both small and large velocity fluid flow. Various classical models were proposed and used widely to quantify non-Darcian flow, including the well-known Forchheimer, Izbash, and Swartzendruber models. Applications, however, revealed limitations of these models. Here we propose a general model built upon the Caputo fractional derivative to quantify non-Darcian flow for various flows (laminar to turbulence).Real-world applications and model comparisons showed that the new fractional-derivative model, which extends the fractional model proposed recently by Zhou and Yang (2018), can capture the non-Darcian flow in the relatively small velocity in low-permeability deposits and the relatively high velocity in high-permeability sand. A scale effect was also identified for non-Darcian flow in fractured rocks. Therefore, fractional calculus may provide an efficient tool to improve classical models to quantify fluid dynamics in aquatic environments.

Keywords: fractional derivative, darcy’s law, non-darcian flow, fluid dynamics

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Authors: M. Ghanbari, S. Hossainpour, G. Rezazadeh

Abstract:

In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model, the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.

Keywords: micro-polar theory, Galerkin method, MEMS, micro-fluid

Procedia PDF Downloads 185