scholarly journals Obtaining Expressions for Time-Dependent Functions That Describe the Unsteady Properties of Swirling Jets of Viscous Fluid

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1860
Author(s):  
Eugene Talygin ◽  
Alexander Gorodkov
Keyword(s):  
Blood Flow ◽  
Viscous Fluid ◽  
Swirling Flow ◽  
Fluid Flows ◽  
Theoretical Method ◽  
Flow Channel ◽  
Navier Stokes ◽  
Swirling Jets ◽  
Continuity Equations ◽  
Dynamic Velocity

Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity equations for the class of centripetal swirling viscous fluid flows. In this paper, analytical expressions were obtained. They describe the functions C0t and Г0t, included in the solutions, for the velocity components of such a flow. These expressions make it possible to relate the values of these functions to dynamic changes in the geometry of the flow channel in which the swirling flow evolves. The obtained expressions allow the reconstruction of the dynamic velocity field of an unsteady potential swirling flow in a flow channel of arbitrary geometry. The proposed approach can be used as a theoretical method for correct numerical modeling of the blood flow in the heart chambers and large arteries, as well as for developing a mathematical model of blood circulation, considering the swirling structure of the blood flow.

scholarly journals Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yufang Gao ◽  
Zongguo Zhang
Keyword(s):  
Cardiovascular Disease ◽  
Blood Flow ◽  
Viscous Fluid ◽  
Boussinesq Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Term ◽  
Thin Tube ◽  
Elastic Tubes

Cardiovascular disease is a major threat to human health. The study on the pathogenesis and prevention of cardiovascular disease has received special attention. In this paper, we have contributed to the derivation of a mathematical model for the nonlinear waves in an artery. From the Navier–Stokes equations and continuity equation, the vorticity equation satisfied by the blood flow is established. And based on the multiscale analysis and perturbation method, a new model of the Boussinesq equation with viscous term is derived to describe the propagation of a viscous fluid through a thin tube. In order to be more consistent with the flow of the fluid, the time-fractional Boussinesq equation with viscous term is deduced by employing the semi-inverse method and the fractional variational principle. Moreover, the approximate analytical solution of the fractional equation is obtained, and the effect of viscosity on the amplitude and width of the wave is studied. Finally, the effects of the fractional order parameters and vessel radius on blood flow volume are discussed and analyzed.

Attractors for the modifications of the three-dimensional Navier-Stokes equations

1994 ◽  
Vol 346 (1679) ◽  
pp. 173-190 ◽  
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Initial Boundary Value ◽  
Dimensional Domain

The modifications of the three-dimensional Navier-Stokes equations, which I suggested earlier for the description of viscous fluid flows with large gradients of velocities, are considered. It is proved that the first initial-boundary value problem for these equations in any bounded three-dimensional domain has a compact minimal global B-attractor. Some properties of the attractor are established.

Self-Organization of Tornado-Like Jets in Flows of Gases and Liquids and the Technologies Utilizing This Phenomenon

2009 ◽  
Author(s):  
G. I. Kiknadze ◽  
I. A. Gachechiladze ◽  
A. Yu. Gorodkov
Keyword(s):  
Exact Solutions ◽  
Swirling Flow ◽  
Navier Stokes ◽  
Circulation System ◽  
Hydraulic Loss ◽  
Adequate Model ◽  
Continuity Equations ◽  
Flow Past ◽  
New Type ◽  
The Impact

Basic results are considered of aerohydrodynamic and thermophysical experiments, in which secondary tornado-like jets (TLJ) are revealed and investigated. These jets are self-organized under conditions of flow past surfaces with three-dimensional recesses (dimples) with a second-order curvilinear surface (TLJS – tornado-like jet surface). Exact solutions are given of unsteady-state Navier–Stokes and continuity equations, which describe the TLJ. The impact is considered, which is made on the flow in dimple by forces forming a flow of new type with built-in secondary tornado-like jets. These forces are absent in the case of flow past initially smooth surfaces. The problems are discussed of reducing the aerohydrodynamic drag on the TLJS, of enhancing the heat and mass transfer with the level of hydraulic loss lagging behind the degree of enhancement, of increasing the critical heat loads under conditions of boiling and supercritical flows of continuous medium past the TLJS, of preventing cavitation damage to the TLJS in hydraulic apparatuses, of reducing the adsorption of foreign matter on these surfaces, of reducing the friction between TLJS rubbing against one another, and of raising the efficiency of facilities for tornadolike conversion of energy of renewable low-potential sources. It is demonstrated that the obtained exact solutions of Navier–Stokes and continuity equations provide an adequate model of generation and evolution of swirling flow of blood in human blood circulation system, which enables one to proceed to development of safe and effective devices for substitution of organs in cardiac surgery. An inference is made about the universality of the flow of new type for raising the efficiency of technologies involving flows of various media.

Application of Tornado-Flow Fundamental Hydrodynamic Theory to the Study of Blood Flow in the Heart: Further Development of Tornado-Like Jet Technology

2011 ◽  
Author(s):  
L. A. Bockeria ◽  
G. I. Kiknadze ◽  
I. A. Gachechiladze ◽  
A. Y. Gorodkov
Keyword(s):  
Exact Solution ◽  
Blood Flow ◽  
Structural Parameters ◽  
Close Correlation ◽  
Hydrodynamic Theory ◽  
Navier Stokes ◽  
Diagnostic Purpose ◽  
Continuity Equations ◽  
Intraventricular Flow ◽  
And Function

It has been proved previously that the Tornado-like swirling flows have strictly ordered hydrodynamic structure which can be exhaustively described by using the exact solution of non-stationary Navier-Stokes and continuity equations for this class of flows [1]. Analysis of the geometry of the flowing channel of the left ventricle (LV) and aorta has shown close correlation between the shape of the cavities and intraventricular trabeculae orientation with the streamlines of Tornado-like flows. LV casts morphometry, MRI tomography and 4D velocimetry of the flow velocity field in the aorta, allowed to prove that the blood flow in the LV and aorta corresponds to this class of flows and may be described using the exact solution [7,8,10]. The current study proposes a method of measurement and calculation of the flow structural parameters derived from the exact solution, using LV cavity casts morphometry in humans and dogs and Multislice computed tomography (MSCT) of LV in two patients without severe cardiac pathology. It has been shown that the dynamic expression of intracardiac trabeculae and instant shape of LV cavity within a complete cardiac cycle correspond closely to the stages of single Tornado-like jet evolution. Since the intraventricular trabeculae profile is streamlined continuously by the blood flow, it should determine the hydrodynamic flow structure as an ensemble of guiding vanes. Therefore it has been concluded that the intraventricular flow dynamics can be analyzed and quantified using the exact solution. Application of this analysis to the MSCT visualization of LV cavity dynamics has shown the validity of this approach, which may be used for clinical diagnostic purpose. A realistic mathematical model of intraventricular blood flow has been proposed and evaluated. The results showed a good agreement between the model and known cardiac anatomy and function.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

Experimental investigation of the influence of the hydraulic performance of an axial blood pump on intraventricular blood flow

2021 ◽  
pp. 039139882110130
Author(s):  
Guang-Mao Liu ◽  
Fu-Qing Jiang ◽  
Xiao-Han Yang ◽  
Run-Jie Wei ◽  
Sheng-Shou Hu
Keyword(s):  
Blood Flow ◽  
Particle Image ◽  
Swirling Flow ◽  
Blood Stasis ◽  
Systemic Circulation ◽  
Operating Conditions ◽  
Blood Pump ◽  
Image Velocimetry ◽  
Ct Data

Blood flow inside the left ventricle (LV) is a concern for blood pump use and contributes to ventricle suction and thromboembolic events. However, few studies have examined blood flow inside the LV after a blood pump was implanted. In this study, in vitro experiments were conducted to emulate the intraventricular blood flow, such as blood flow velocity, the distribution of streamlines, vorticity and the standard deviation of velocity inside the LV during axial blood pump support. A silicone LV reconstructed from computerized tomography (CT) data of a heart failure patient was incorporated into a mock circulatory loop (MCL) to simulate human systemic circulation. Then, the blood flow inside the ventricle was examined by particle image velocimetry (PIV) equipment. The results showed that the operating conditions of the axial blood pump influenced flow patterns within the LV and areas of potential blood stasis, and the intraventricular swirling flow was altered with blood pump support. The presence of vorticity in the LV from the thoracic aorta to the heart apex can provide thorough washing of the LV cavity. The gradually extending stasis region in the central LV with increasing blood pump support is necessary to reduce the thrombosis potential in the LV.

scholarly journals Computational Analysis to Factor Wind into the Design of an Architectural Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Hassam Nasarullah Chaudhry ◽  
John Kaiser Calautit ◽  
Ben Richard Hughes
Keyword(s):  
Fluid Dynamics ◽  
Power Generation ◽  
Computational Fluid Dynamics ◽  
Three Dimensional ◽  
Numerical Data ◽  
Navier Stokes ◽  
Windward Side ◽  
Average Value ◽  
Continuity Equations ◽  
Prevailing Wind Direction

The effect of wind distribution on the architectural domain of the Bahrain Trade Centre was numerically analysed using computational fluid dynamics (CFD). Using the numerical data, the power generation potential of the building-integrated wind turbines was determined in response to the prevailing wind direction. The three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations along with the momentum and continuity equations were solved for obtaining the velocity and pressure field. Simulating a reference wind speed of 6 m/s, the findings from the study quantified an estimate power generation of 6.4 kW indicating a capacity factor of 2.9% for the benchmark model. At the windward side of the building, it was observed that the layers of turbulence intensified in inverse proportion to the height of the building with an average value of 0.45 J/kg. The air velocity was found to gradually increase in direct proportion to the elevation with the turbine located at higher altitude receiving maximum exposure to incoming wind. This work highlighted the potential of using advanced computational fluid dynamics in order to factor wind into the design of any architectural environment.

Lattice-Boltzmann Simulation of Two-Phase Fluid Flows

1998 ◽  
Vol 09 (08) ◽  
pp. 1383-1391 ◽  
Author(s):  
Yu Chen ◽  
Shulong Teng ◽  
Takauki Shukuwa ◽  
Hirotada Ohashi
Keyword(s):  
Lattice Boltzmann ◽  
Fluid Flows ◽  
Navier Stokes ◽  
Interface Model ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Lattice Boltzmann Simulation ◽  
Dam Breaking ◽  
Volumetric Stress ◽  
Phase Fluid

A model with a volumetric stress tensor added to the Navier–Stokes Equation is used to study two-phase fluid flows. The implementation of such an interface model into the lattice-Boltzmann equation is derived from the continuous Boltzmann BGK equation with an external force term, by using the discrete coordinate method. Numerical simulations are carried out for phase separation and "dam breaking" phenomena.

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