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.  

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.

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.

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.

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

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.

Modelling of the Influence of Vegetative Barrier on Concentration of PM10 and PM2,5 from Highway

2016 ◽  
Vol 821 ◽  
pp. 97-104
Author(s):  
Hynek Řezníček ◽  
Luděk Beneš
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Fluid Flow ◽  
Vegetative Barrier ◽  
Orthogonal Grid ◽  
Different Types

The influence of different types of the vegetative barrier near a highway on dustiness was studied. Transport, dispersion and sedimentation of pollutants PM10 and PM2.5 emitted from the highway was numerically simulated. Mathematical model was based on the Navier-Stokes equations for turbulent fluid flow in Boussinesq approximation. The AUSM-MUSCL scheme in finite volume formulation on structured orthogonal grid was used.The influence of the shape of the barrier and of its obstructing properties on the concentration of pollutants was studied.

scholarly journals Influence of the Angular Momentum in Problems Continuum Mechanics

2021 ◽  
Vol 16 ◽  
pp. 1-8
Author(s):  
Evelina Prozorova
Keyword(s):  
Conservation Laws ◽  
Continuum Mechanics ◽  
Stokes Equations ◽  
Theory Of Elasticity ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Potential Flows ◽  
Balance Of Forces ◽  
And Mathematics

- For continuum mechanics a model is proposed, that is built with consideration outside the integral term when deriving conservation laws using the Ostrogradsky-Gauss theorem. Performed analysis shows discrepancy between accepted classical conservation laws and classical theoretical mechanics and mathematics. As a result, the theory developed for potential flows was extended to flows with significant gradients of physical parameters. We have proposed a model that takes into account the joint implementation of the laws for balance of forces and angular momentums. It does not follow from the Boltzmann equation that the pressure in the Euler and Navier-Stokes equations is equal to one third of the sum the pressures on the corresponding coordinate axes. The vector definition of pressure is substantiated. It is shown that the symmetry condition for the stress tensor is one of the possible conditions for closing the problem. An example of solving the problem of the theory of elasticity is given

scholarly journals DEVELOPMENT OF A MATHEMATICAL MODEL FOR RESEARCHING THE PROCESS OF REDUCTION OF TUNGSTEN HEXAFLUORIDE BY GASEOUS HYDROGEN

2021 ◽  
pp. 225-230
Author(s):  
А.К. Шубин
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tungsten Hexafluoride ◽  
Numerical Studies ◽  
Cylindrical Coordinate ◽  
Transfer Equations ◽  
Flow Motion

В работе рассмотрена математическая модель, описывающая движение течения стационарной, ламинарной, вязкой, несжимаемой смеси газа в трехмерном осесимметричном канале. Математическая модель, описывающая этот процесс, состоит из уравнений Навье – Стокса, уравнения неразрывности и массообмена, которые записаны в безразмерной форме с учетом осесимметричности в цилиндрической системе координат. Решение уравнений осуществляется в физических переменных «скорость – давление» на разнесенной разностной сетке. Показано влияние характерных параметров на распределение концентрации смеси газа гексафторида вольфрама и водорода в канале. Полученная математическая модель позволяет проводить численные исследования по выбору оптимальных условий осуществления процесса восстановления гексафторида вольфрама водородом. The paper considers a mathematical model describing the flow motion of a stationary, laminar, viscous, incompressible gas mixture in a three-dimensional axisymmetric channel. The mathematical model describing this process consists of the Navier-Stokes equations, the continuity and mass transfer equations, which are written in dimensionless form taking into account axisymmetry in a cylindrical coordinate system. The equations are solved in the physical variables "velocity - pressure" on a spaced difference grid. The influence of characteristic parameters on the concentration distribution of a mixture of tungsten hexafluoride gas and hydrogen in the channel is shown. The obtained mathematical model makes it possible to conduct numerical studies on the choice of optimal conditions for the process of reduction of tungsten hexafluoride with hydrogen.

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