Mathematical and Experimental Investigation of Liquid-Gas Interfaces in Porous Wicks

2002 ◽  
Author(s):  
Yuelei Yang ◽  
Frank M. Gerner ◽  
H. Thurman Henderson
Keyword(s):  
Mathematical Model ◽  
Experimental Investigation ◽  
Stokes Equations ◽  
Small Diameter ◽  
Flow In Porous Media ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vapor Interface ◽  
Porous Plastic ◽  
Capillary Pore

This paper focuses on the investigation of the liquid-gas (or vapor) interface, which occurs in very small diameter pores. A mathematical model is built to formulate the movements of a liquid column trapped in a capillary pore. The Navier-Stokes equations are applied to the liquid side with assumed no-slip conditions, while the Young-Laplace equation is used to formulate the shape of the interface. This theoretical model calculates both velocity profiles in the liquid side and transient profiles of the interface itself; and of particular interest, it predicts the pressure difference, oscillation frequency and amplitude required to burst this interface. These predicted parameters are examined by the experiments with both oscillating Coherent Porous Silicon (CPS) wicks and porous plastic wicks. This research helps better understanding the phenomena such as multiphase flow in porous media or de-watering process that happens in vibro-separators.

Mathematical study of a single leukocyte in microchannel flow

2018 ◽  
Vol 13 (5) ◽  
pp. 43 ◽  
Author(s):  
S. Boujena ◽  
O. Kafi ◽  
A. Sequeira
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Microchannel Flow ◽  
Navier Stokes Equations ◽  
Coupled Problem ◽  
Inflammatory Drugs ◽  
The Mathematical Model ◽  
Rate Type

The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.

Mathematical and Physical Modeling of Three-Phase Gas-Stirred Ladles

2016 ◽  
Vol 1812 ◽  
pp. 29-34
Author(s):  
Juan A. López ◽  
Marco A. Ramírez-Argáez ◽  
Adrián M. Amaro-Villeda ◽  
Carlos González
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Stokes Equations ◽  
Steel Slag ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Steel Ladle ◽  
Phase System ◽  
Navier Stokes Equations ◽  
Three Phase

ABSTRACTA very realistic 1:17 scale physical model of a 140-ton gas-stirred industrial steel ladle was used to evaluate flow patterns measured by Particle Image Velocimetry (PIV), considering a three-phase system (air-water-oil) to simulate the argon-steel-slag system and to quantify the effect of the slag layer on the flow patterns. The flow patterns were evaluated for a single injector located at the center of the ladle bottom with a gas flow rate of 2.85 l/min, with the presence of a slag phase with a thickness of 0.0066 m. The experimental results obtained in this work are in excellent agreement with the trends reported in the literature for these gas-stirred ladles. Additionally, a mathematical model was developed in a 2D gas-stirred ladle considering the three-phase system built in the physical model. The model was based on the Eulerian approach in which the continuity and the Navier Stokes equations are solved for each phase. Therefore, there were three continuity and six Navier-Stokes equations in the system. Additionally, turbulence in the ladle was computed by using the standard k-epsilon turbulent model. The agreement between numerical simulations and experiments was excellent with respect to velocity fields and turbulent structure, which sets the basis for future works on process analysis with the developed mathematical model, since there are only a few three-phase models reported so far in the literature to predict fluid dynamics in gas-stirred steel ladles.

Numerical Investigation of the “Poor Man’s Navier–Stokes Equations” with Darcy and Forchheimer Terms

2016 ◽  
Vol 26 (05) ◽  
pp. 1650086
Author(s):  
Tingting Tang ◽  
Zhiyong Li ◽  
J. M. McDonough ◽  
P. D. Hislop
Keyword(s):  
Porous Media ◽  
Numerical Investigation ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Flow In Porous Media ◽  
Phase Portraits ◽  
Navier Stokes ◽  
Flow Through Porous Media ◽  
Navier Stokes Equations ◽  
Flow Through

In this paper, a discrete dynamical system (DDS) is derived from the generalized Navier–Stokes equations for incompressible flow in porous media via a Galerkin procedure. The main difference from the previously studied poor man’s Navier–Stokes equations is the addition of forcing terms accounting for linear and nonlinear drag forces of the medium — Darcy and Forchheimer terms. A detailed numerical investigation focusing on the bifurcation parameters due to these additional terms is provided in the form of regime maps, time series, power spectra, phase portraits and basins of attraction, which indicate system behaviors in agreement with expected physical fluid flow through porous media. As concluded from the previous studies, this DDS can be employed in subgrid-scale models of synthetic-velocity form for large-eddy simulation of turbulent flow through porous media.

Study of Maneuverability of Container Ship With Nonlinear and Roll-Coupled Effects by Numerical Simulations Using RANSE-Based Solver

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
R. Rajita Shenoi ◽  
P. Krishnankutty ◽  
R. Panneer Selvam
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Container Ship ◽  
Navier Stokes Equations ◽  
Hydrodynamic Derivatives ◽  
Computational Fluid Dynamics Cfd ◽  
Experimental Values ◽  
The Mathematical Model

The examination of maneuvering qualities of a ship is necessary to ensure its navigational safety and prediction of trajectory. The study of maneuverability of a ship is a three-step process, which involves selection of a suitable mathematical model, estimation of the hydrodynamic derivatives occurring in the equation of motion, and simulation of the standard maneuvering tests to determine its maneuvering qualities. This paper reports the maneuvering studies made on a container ship model (S175). The mathematical model proposed by Son and Nomoto (1981, “On Coupled Motion of Steering and Rolling of a High Speed Container Ship,” J. Soc. Nav. Arch. Jpn., 150, pp. 73–83) suitable for the nonlinear roll-coupled steering model for high-speed container ships is considered here. The hydrodynamic derivatives are determined by numerically simulating the planar motion mechanism (PMM) tests in pure yaw and combined sway–yaw mode using an Reynolds-Averaged Navier–Stokes Equations (RANSE)-based computational fluid dynamics (CFD) solver. The tests are repeated with the model inclined at different heel angles to obtain the roll-coupled derivatives. Standard definitive maneuvers like turning tests at rudder angle, 35 deg and 20 deg/20 deg zig-zag maneuvers are simulated using the numerically obtained derivatives and are compared with those obtained using experimental values.

scholarly journals On the time dependent mathematical model of ateroma plaque formation

1970 ◽  
Vol 1 ◽  
pp. 10-11
Author(s):  
Myriam Cilla ◽  
Estefanía Peña ◽  
Miguel Ángel Martínez
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Plaque Formation ◽  
Diffusion Reaction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Atheroma Plaque ◽  
Plaque Growth ◽  
Reaction Equations

A mathematical model to reproduce the atheroma plaque growth is presented. This model employs the Navier-Stokes equations and Darcy's law for fluid dynamics, convection-diffusion-reaction equations for modeling the mass balance in the lumen and intima, and the Kedem-Katchalsky equations for the interfacial coupling at membranes, i.e., endothelium.

scholarly journals RESEARCH OF RESEARCH OF νt-92 TURBULENCE MODEL FOR CALCULATING AN AXISYMMETRIC SOUND JET

2020 ◽  
Vol 4 (2) ◽  
pp. 82-90
Author(s):  
Murodil Erkinjon oglu Madaliev ◽  
◽  
Dilshod Primkulovich Navruzov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Comparative Analysis ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculation Results ◽  
The One ◽  
Subsonic Jet

A comparative analysis of the use of the turbulence model is carried out: the one-parameter Secundov νt-92 model on the problem of an axisymmetric subsonic jet. The calculation results are compared with experimental results on the propagation of speed, voltage, and temperature. The flow is turbulent, therefore, as a mathematical model, the system of Navier-Stokes equations averaged by Reynolds (RANS) is used. For the posed problem, a generalized stream function ψ is introduced. A comparison was made of the results of the νt-92 model with experimental data from [5] the dimensionless axial velocity from the distance to the nozzle

scholarly journals Peculiarities of Simulation of Biomechanical and Biological Systems

2017 ◽  
Vol 17 (2) ◽  
pp. 79-85 ◽  
Author(s):  
A. O. Lopatiev ◽  
A. P. Vlasov ◽  
A. P. Demichkovskyi
Keyword(s):  
Mathematical Model ◽  
Heart Rate ◽  
Continuum Mechanics ◽  
Stokes Equations ◽  
Continuous System ◽  
Time Of Day ◽  
Navier Stokes ◽  
Numerical Series ◽  
Navier Stokes Equations ◽  
Large Vessels

The objective is to combine the methods and principles of biomechanics and continuum mechanics in order to pose and solve problems that have practical application in extreme conditions. Materials & methods: the movement of blood through large vessels was studied on the basis of the Euler and Navier-Stokes equations. Analysis of the cardiovascular system was used for the examination of the functional state of the athlete. The initial experimentally measured heart rate (HR) was determined by the Polar RC800 cardiac monitor. The resulting time series is analyzed using the software package Kubios HRV. Results: the article proposes to consider a model describing human body as a discrete-continuous system. Using the Euler equation, a mathematical model of the movement of blood through large vessels is considered. A mathematical model of the process of pulse wave propagation in blood vessels is given. We found and interpreted  hidden periodicities relative to the numerical series occurring during analysis of biological and heart rhythms of athletes during training and competitive activities. Conclusions: the use of methods and principles of continuum mechanics makes it possible to pose and solve the problems of mathematical physics for practical purposes. These include the movement of blood through large vessels, the issue of heat protection, and so on. The heart rate changes during the day and has a fluctuating character with certain periods. Periods of heart rate depend on the activity of a person and the time of day. Moreover, the heart rate tends to increase the amplitude and depend significantly on person’s workload.  

STUDY OF A GENERALIZED FRAGMENTATION MODEL FOR SPRAYS

2009 ◽  
Vol 06 (01) ◽  
pp. 185-206 ◽  
Author(s):  
NICHOLAS LEGER ◽  
ALEXIS F. VASSEUR
Keyword(s):  
Mathematical Model ◽  
Kinetic Equation ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Fragmentation Model ◽  
Global Weak Solutions ◽  
Navier Stokes Equations ◽  
Drag Forces ◽  
Break Up

We study a mathematical model for sprays which takes into account particle break-up due to drag forces. In particular, we establish the existence of global weak solutions to a system of incompressible Navier–Stokes equations coupled with a Boltzmann-like kinetic equation. We assume the particles initially have bounded radii and bounded velocities relative to the gas, and we show that those bounds remain as the system evolves. One interesting feature of the model is the apparent accumulation of particles with arbitrarily small radii. As a result, there can be no nontrivial hydrodynamical equilibrium for this system.

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