An analytical solution of the potential velocity field induced by a growing bubble from a plate orifice

1993 ◽  
Vol 2 (3) ◽  
pp. 157-164
Author(s):  
Tao Zhi ◽  
Kang Ning
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Potential Velocity

Application of the Tornado-Like Flow Theory to the Study of Blood Flow in the Heart and Main Vessels: Study of the Potential Swirling Jets Structure in an Arbitrary Viscous Medium

2019 ◽  
Author(s):  
E. Talygin ◽  
G. Kiknadze ◽  
A. Agafonov ◽  
A. Gorodkov
Keyword(s):  
Blood Flow ◽  
Velocity Field ◽  
Analytical Solution ◽  
Coordinate System ◽  
Biologically Active ◽  
Time Dependent ◽  
Characteristic Functions ◽  
Swirling Jet ◽  
Cylindrical Coordinate ◽  
Definition Of

Abstract In previous works it has been proved that the dynamic geometry of the streamlined surface of the flow channel of the heart chambers and main arteries corresponds with a good agreement to the shape of the swirling flow streamlines. The vectorial velocity field of such a flow in a cylindrical coordinate system was described by means of specific analytical solution basing on the potentiality of the longitudinal and radial velocity components. The viscosity of the medium was taken into account only in the expression for the azimuthal velocity component and the significant effect of viscosity was manifested only in a narrow axial region of a swirling jet. The flow described by the above relations is quasipotential, axisymmetric, and convergent. The structural organization of this flow implies the elimination of rupture and stagnation zones, and minimizes the viscous losses. The proximity of the real blood flow under the normal conditions to the specified class of swirling flows allows us to determine the basic properties of the blood flow possessing the high pressure-flow characteristics without stability loss. The blood flow has an external border, and the interaction with the channel wall and between moving fluid elements is weak. These properties of the jet explain the possibility of a balanced blood flow in biologically active boundaries. Violation of the jet properties can lead to the excitation of biologically active components and trigger the corresponding cascade protective and compensatory processes. The evolution of the flow is determined by the time-dependent characteristic functions, which are the frequency characteristics of the rotating jet, as well as functions depending on the dimension of the swirling jet. Previous experimental studies revealed close connection between changes in the characteristic functions and dynamics of the cardiac cycle. Therefore, it is natural to express these functions in analytical form. For these purposes it was necessary to establish the link between these functions and the spatial characteristics of the swirling jet. To solve this problem the analytical solution for the velocity field of a swirling jet was substituted into the Navier-Stokes system and continuity differential equations in a cylindrical coordinate system. As a result, a new system of differential equations was obtained where the characteristic functions could be derived. The solution of these equations allows the identification of time-dependent characteristic functions, and the establishment of a link between the characteristic functions and the spatial coordinates of the swirling jet. This link gives the opportunity to substantiate a theoretical possibility for the modeling of quasipotential viscous flows with a given structure. The definition of characteristic functions makes it possible to obtain the exact solution which allows formalization of the boundary conditions for physical modeling and experimental study of this flow type. Such transformations allow the definition of the conditions supporting renewable swirling blood flow in the transport arterial segment of the circulatory system and provide the basis for new principles of modeling, diagnosis and surgical treatment of circulatory disorders associated with the changes in geometry of the heart and great vessels.

MHD FLOWS DUE TO NON-COAXIAL ROTATIONS OF POROUS DISK AND A VISCOUS FLUID AT INFINITY: GRAPHICAL SOLUTIONS USING MATLAB

2020 ◽  
Vol 9 (11) ◽  
pp. 9287-9301
Author(s):  
R. Lakshmi ◽  
Santhakumari
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Daily Life ◽  
Vital Role ◽  
Navier Stokes ◽  
Porous Disk ◽  
Navier Stokes Equations ◽  
Complex Phenomena

Fluids play a vital role in many aspects of our daily life. We drink water, breath air, fluids run through our bodies and it controls the weather. The study of motion of fluids is a complex phenomena. The equations which govern the flows of Newtonian fluids are Navier-Stokes equations. In this paper, the flows which are due to non – coaxial rotations of porous disk and a fluid at infinity are considered. Analytical solution for the velocity field using Laplace transform is derived. MATLAB coding is written to get the graphical solutions. The results are compared with the existing results. MATLAB software provides accurate results depending on the solution we obtained.

scholarly journals On the Positive Bias of Peak Horizontal Velocity from an Idealized Doppler Profiler

2005 ◽  
Vol 22 (1) ◽  
pp. 98-104
Author(s):  
David A. Short ◽  
Francis J. Merceret
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Vertical Velocity ◽  
Gumbel Distribution ◽  
Extreme Value Distribution ◽  
Value Distribution ◽  
Horizontal Velocity ◽  
Simple Function ◽  
Type I ◽  
Positive Bias

Abstract In the presence of 3D turbulence, peak horizontal velocity estimates from an idealized Doppler profiler are found to be positively biased due to an incomplete specification of the vertical velocity field. The magnitude of the bias was estimated by assuming that the vertical and horizontal velocities can be separated into average and perturbation values and that the vertical and horizontal velocity perturbations are normally distributed. Under these assumptions, properties of the type-I extreme value distribution for maxima, known as the Gumbel distribution, can be used to obtain an analytical solution of the bias. The bias depends on geometric properties of the profiler configuration, the variance in the horizontal velocity, and the unresolved variance in the vertical velocity. When these variances are normalized by the average horizontal velocity, the bias can be mapped as a simple function of the normalized variances.

Numerical Investigation of the Viscous Dissipation Term on 2D Heat Transfer

2014 ◽  
Vol 348 ◽  
pp. 279-284
Author(s):  
M.D. de Campos ◽  
E.C. Romão ◽  
L.F. Mendes de Moura
Keyword(s):  
Heat Transfer ◽  
Temperature Field ◽  
Velocity Field ◽  
Finite Difference ◽  
Analytical Solution ◽  
Finite Difference Method ◽  
Viscous Dissipation ◽  
Heat Transfer Equation ◽  
Dissipation Term ◽  
High Order Finite Difference

In this paper are analyzed, using high-order finite difference method, applications in which the viscous dissipation term can be neglected or not in the heat transfer equation. Some examples using various numerical values for the velocity field show that the viscous dissipation does not affect significantly the temperature field. Using the L2 norm, the numerical solution is compared with some examples that have an analytical solution.

Development of a Periodic Flow in a Rigid Tube

1968 ◽  
Vol 90 (3) ◽  
pp. 395-399 ◽  
Author(s):  
P. J. Florio ◽  
W. K. Mueller
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Axial Velocity ◽  
Circular Tube ◽  
Approximate Analytical Solution ◽  
Experimental Results ◽  
Oscillating Flow ◽  
Periodic Flow ◽  
Mean Flow ◽  
Rigid Tube

The development of a pulsating velocity field in a rigid, circular tube was experimentally investigated. The wall pressure and the radial variation of the axial velocity were measured at several axial locations. The measured inlet velocities were compared with the fully developed velocities. The experimental results show that, for the range of parameters investigated, the developing pulsating flow can be considered to be simply a superposition of a developing mean flow and a fully developed oscillating flow. These results are in agreement with a previous approximate analytical solution by Atabek and Chang.

Electro-osmotic and Pressure-Driven Flow in an Eccentric Microannulus

2019 ◽  
Vol 74 (6) ◽  
pp. 513-521
Author(s):  
F. Talay Akyildiz ◽  
Abeer F.A. AlSohaim ◽  
Nurhan Kaplan
Keyword(s):  
Boltzmann Equation ◽  
Velocity Field ◽  
Analytical Solution ◽  
Pressure Gradient ◽  
Bipolar Coordinates ◽  
Closed Form Analytical Solution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Pressure Driven

AbstractConsideration is given to steady, fully developed mixed electro-osmotic/pressure-driven flow of Newtonian fluid in an eccentric microannulus. The governing Poisson–Boltzmann and momentum equations are solved numerically in bipolar coordinates. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average viscosity (i.e. flow rate) under the same dimensionless pressure gradient and electro kinetic radius. For the Debye–Hückel approximation (linearised Poisson–Boltzmann equation), we show that closed-form analytical solution can be derived for velocity field. Finally, the effect of the electrokinetic radius, pressure gradient, and eccentricity on the flow field was investigated in detail.

scholarly journals Tank Drainage for an Electrically Conducting Newtonian Fluid with the use of the Bessel Function

2020 ◽  
Vol 10 (2) ◽  
pp. 5377-5381
Author(s):  
M. A. Khaskheli ◽  
K. N. Memon ◽  
A. H. Sheikh ◽  
A. M. Siddiqui ◽  
S. F. Shah
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Unsteady Flow ◽  
Flow Rate ◽  
Average Velocity ◽  
Series Solution ◽  
Solution Method ◽  
Electrically Conducting ◽  
Velocity Flow ◽  
Time Required

In this study, an unsteady flow for drainage through a circular tank of an isothermal and incompressible Newtonian magnetohydrodynamic (MHD) fluid has been investigated. The series solution method is employed, and an analytical solution is obtained. Expressions for the velocity field, average velocity, flow rate, fluid depth at different times in the tank and time required for the wide-ranging drainage of the fluid (time of efflux) have been obtained. The Newtonian solution is attained by assuming σΒ02=0. The effects of various developing parameters on velocity field υz and depth of fluid H(t) are presented graphically. The time needed to drain the entire fluid and its depth are related and such relations are obtained in closed form. The effect of electromagnetic forces is analyzed. The fluid in the tank will drain gradually and it will take supplementary time for complete drainage.

scholarly journals Two-Phase Flow in Wire Coating with Heat Transfer Analysis of an Elastic-Viscous Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Zeeshan Khan ◽  
Rehan Ali Shah ◽  
Saeed Islam ◽  
Bilal Jan
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Viscous Fluid ◽  
Two Phase Flow ◽  
Adomian Decomposition Method ◽  
Heat Transfer Analysis ◽  
Phase Flow ◽  
Two Phase ◽  
Adomian Decomposition ◽  
Grade Fluid

This work considers two-phase flow of an elastic-viscous fluid for double-layer coating of wire. The wet-on-wet (WOW) coating process is used in this study. The analytical solution of the theoretical model is obtained by Optimal Homotopy Asymptotic Method (OHAM). The expression for the velocity field and temperature distribution for both layers is obtained. The convergence of the obtained series solution is established. The analytical results are verified by Adomian Decomposition Method (ADM). The obtained velocity field is compared with the existing exact solution of the same flow problem of second-grade fluid and with analytical solution of a third-grade fluid. Also, emerging parameters on the solutions are discussed and appropriate conclusions are drawn.

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