Flow Of Viscous Incompressible Fluid Research Articles

Fluid Flow and Solute Transfer in a Permeable Tube with Influence of Slip Velocity

In this paper, the influence of slip velocity on the fluid flow and solute transfer in a tube with permeable boundary is studied as a mathematical model for blood flow in glomerular capillaries. The viscous incompressible fluid flow across the permeable tube wall, as a result of differences in both hydrostatic and osmotic pressure, is considered. The solutions of differential equations governing the fluid flow and solute transfer are obtained using analytical and Crank-Nicolson type numerical methods. It is observed that the effect of slip on the hydrostatic and osmotic pressures, velocity profiles, concentration profile, solute mass flux and total solute clearance is significant and the results are presented graphically.

Parabolic evolution equations in interpolation spaces: boundedness, stability, and applications

We develop a general approach for the study of the boundedness and stability of solution to general parabolic semi-linear evolution equations in real-interpolation spaces. Our approach yields a unified method to handle problems in Newtonian viscous incompressible fluid flows. Moreover, our method will be applied to derive new results for the existence and polynomial stability of bounded solutions to the Ornstein–Uhlenbeck semi-linear equations and various diffusion equations with rough coefficients. The method is based on a combination of interpolation functors, duality estimates, smoothing properties of the linearized equation, and fixed point arguments.

Two-dimensional turbulent flow in a channel of constant width

The paper deals with the classical problem about a flow of viscous incompressible fluid in an infinite channel of constant width. The problem is solved in the two-dimensional case, both in the laminar and turbulent flow regimes, using as a mathematical model the Navier-Stokes equations in terms of vorticity-stream functions. The presented algorithm is a semi-analytical iterative method, based on the construction of special Green’s functions in the form of expansion in a Fourier series over the transverse coordinate for the channel.

Расщепление уравнений Навье-Стокса для одного класса осесимметричных течений

В рамках уравнений Навье-Стокса рассмотрены нестационарные осесимметричные течения однородной вязкой несжимаемой жидкости, в которых осевая и окружная скорости зависят только от радиуса и от времени, а радиальная скорость равна нулю. Показано, что скорость таких течений представляет собой сумму скоростей двух течений вязкой несжимаемой жидкости: осевого течения (радиальная и окружная скорости равны нулю) и окружного течения (радиальная и осевая скорости равны нулю). Осевое и окружное движения происходят независимо, не оказывая никакого взаимного влияния. Это позволяет расщеплять краевые задачи для рассматриваемого типа течений, содержащие три неизвестные функции (давление, окружная и осевая скорости), на две задачи, каждая из которых содержит две неизвестные функции (давление и одна из компонент скорости). При этом сумма давлений осевого и окружного течений будет давлением исходного течения. Обнаруженная возможность расщепления позволяет с использованием известных решений пополнить «запасы» осевых и окружных точных решений. Эти решения, в свою очередь, можно суммировать в различных комбинациях и в результате получать скорости и давления новых точных решений уравнений Навье-Стокса.

Steady Plane Poiseuille Flow of Viscous Incompressible Fluid between Two Porous Parallel Plates in Magnetic Field

In this paper we have investigated the steady plane Couette flow of viscous incompressible fluid between two porous parallel plates in magnetic field. We have studied the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines. Keywords: Steady Couette flow, viscous parallel plates, incompressible fluid and magnetic field. NOMENCLATURE u = velocity component along x - axis v = velocity component along y - axis t = the time = the density of fluid P = the fluid pressure K= the thermal conductivity of the fluid

Stability analysis and optimal control of a stationary Stokes hemivariational inequality

In this paper, we provide stability analysis for a stationary Stokes hemivariational inequality where along the tangential direction of the slip boundary, an inclusion relation involving the generalized subdifferential of a superpotential is specified. With viscous incompressible fluid flows as application background, stability is analyzed for solutions with respect to perturbations in the superpotential and the density of external forces. We also present a result on the existence of a solution to an optimal control problem for the stationary Stokes hemivariational inequality.

Mixed boundary value problems of the system for steady flow of heat-conducting incompressible viscous fluids with dissipative heating

Mixed boundary value problems of the system for steady flow of heat-conducting incompressible viscous fluids with dissipative heating

Computation of 3D Water Flows by the Double Potential Method for the Simulation of Electromagnetic Water Purification

In this paper, we discuss the modeling of the electromagnetic water purification. This model requires a velocity distribution in a study domain. For that purpose, the double potential method for simulating incompressible viscous fluid flows was used. The system of equations was discretized with the help of the finite volume method using an exponential transformation for the vortex calculation. As a result, a software implementation of the developed numerical scheme was obtained. The simulation of the three-dimensional flow was carried out in a study domain. The results were compared with Ansys CFD. The comparison showed a good degree of consistency between the two distributions. Using the obtained velocity field, we simulated the process of water purification using the induction of the electromagnetic field.

A new class of non-helical exact solutions of the Navier-Stokes equations

Приведен новый класс точных решений уравнений Навье-Стокса. Эти решения описывают нестационарные трехмерные по скоростям и двумерные по координатам течения вязкой несжимаемой жидкости. Процедура построения точного решения обобщает метод Тркала, предложенный для изучения винтовых течений. Новый класс точных решений позволяет описывать невинтовые течения (вектор скорости образует ненулевой угол с вектором завихренности) и течения жидкости, существующие конечное время.

An Artificial Compression Reduced Order Model

We propose a novel artificial compression, reduced order model (AC-ROM) for the numerical simulation of viscous incompressible fluid flows. The new AC-ROM provides approximations not only for veloc...

NUMERICAL MODELING OF THE WORKING PROCESS IN THE FLOW PART OF THE FRANCIS TURBINE AT A HEAD OF 45 M

The results of the viscous incompressible fluid flow calculation in the flow part of the full-scale Francis hydraulic turbine RO45, developed by Kharkovturboengineering OJSC and implemented by Go Goal (India) for the Dhalipur HPP modernization project (India), are presented. The model of the flow part offered by Kharkovturboengineering was tested on a hydrodynamic test bench. Its geometrical parameters slightly differ from the turbines of the Dhalipur hydroelectric power plant. The task was stated and solved by completely replacing the experimental studies with the numerical ones to determine the hydrodynamic parameters of the turbine in a wide range of operating modes, to confirm the high performance of the turbine and their compliance with tender requirements. The viscous incompressible fluid flow in the flowing part of a RO45 Francis hydraulic turbine was simulated using the IPMFlow software package based on the numerical integration of the Reynolds equations with an additional term containing artificial compressibility. To consider turbulent effects, the Menter’s SST two-parameter differential turbulence model is used. The numerical integration of the equations is carried out using the implicit quasimonotonic Godunov scheme of the second order of accuracy in space and time. Discretization of the computational domain in question was performed using a structured (channel of the guiding apparatus and impeller) and unstructured (spiral chamber with stator columns and suction pipe) mesh with hex cells. As a result of numerical studies, the following results were obtained: the flow structure was determined in all elements of the flow part and the value of the turbine efficiency for operating modes corresponding to 60; 70; 80; 90; 100% of rated power at rated and maximum heads of the plant; the parameters of the optimal efficiency modes for these heads are determined. An analysis of the results of numerical studies confirmed the high energy characteristics of the turbine and their compliance with customer requirements. It was confirmed that some difference in the geometrical parameters of the admission did not significantly affect the parameters of the flow part.

Helical Vortex Lines in Axisymmetric Viscous Incompressible Fluid Flows

This paper considers the steady and unsteady swirling axisymmetric flows of a homogeneous viscous incompressible fluid. The possibility of the existence of helical vortex lines on the surface of revolution homeomorphic to a torus is investigated. An example of unsteady flow in which there are helical vortex lines is given. It is proved that the existence of helical vortex lines lying on the surface of revolution homeomorphic to a torus is impossible in a steady axisymmetric flow of a viscous incompressible fluid.

Up-down asymmetric exact solutions to the Navier-Stokes equations

Exact up-down asymmetric solutions to the Navier-Stokes equations for a viscous and incompressible fluid with time-dependent viscosity ν(t) are derived. Transformations of the exact solutions are defined that produce an infinite sequence of new solutions from each known one. The solutions are presented in terms of elementary functions and have no singularities. Three infinite-dimensional families of new exact axisymmetric unsteady solutions to the viscous magnetohydrodynamics equations are derived. Dynamics of vortex rings and vortex blobs is studied for some exact up-down asymmetric incompressible viscous fluid flows and viscous plasma flows.

A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids

In this paper we are concerned with a non-steady system for motion of incompressible viscous Newtonian heat-conducting fluids under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions based on total stress, velocity, total pressure, rotation, total stress together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity and shape of boundary surface, we get variational formulation. The formulation consists of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. We first study existence, estimation and relative compactness of solutions to an approximate equation. By passing to limits as the parameter for approximation goes to zero, we get existence of a solution with “defect measure” for temperature.

Experimental and numerical modeling of a viscous incompressible fluid flow with dispersed particles in a rectangular channel

In this paper, a laminar flow of a viscous incompressible fluid with suspended spherical particles in a channel of rectangular cross-section is considered. Physical and mathematical modeling of the investigated process is conducted. The physical model is a vertical channel of rectangular cross-section into which fluid with solid particles is injected. The mathematical model is written in the diffusion approximation and includes the Navier-Stokes system of equations, the continuity equation and the diffusion equation which written, taking into account the effect of gravitational forces on particles.

A free boundary problem associated with the isoperimetric inequality

This paper proves a 30 year old conjecture that disks and annuli are the only domains where analytic content - the uniform distance from $\bar{z}$ to analytic functions - achieves its lower bound. This problem is closely related to several well-known free boundary problems, in particular, Serrin's problem about laminar flow of incompressible viscous fluid for multiply-connected domains, and Garabedian's problem on the shape of electrified droplets. Some further ramifications and open questions, including extensions to higher dimensions, are also discussed.

Steady on MHD Heat and Mass Transfer Flow of an Inclined Porous Plate in the Presence of Radiation and Chemical Reaction

In the present paper steady on MHD heat and mass transfer flow of a viscous incompressible fluid flow through a porous medium in the presence of radiation, heat source and chemical reaction effects are considered. The set of non linear differential equations can be solved analytically. Effects of various parameters like magnetic parameter, permeability parameter, Grashof number, modified Grashof number, radiation parameter, heat source parameter, Prandtl number, Schmidt number, chemical reaction and an angle of inclination on the velocity, temperature and concentration profiles as well as the skin friction, Nusselt number and Sherwood number are discussed qualitatively and shown graphically.

Stokes Flow Through a Membrane Built up by Nonhomogeneous Porous Cylindrical Particles

This work deals with the creeping flow of an incompressible viscous fluid through a membrane. It is assumed that the membrane is composed of nonhomogeneous porous cylindrical particles with radially varying permeability enclosing a cavity. The flow within the nonhomogeneous porous medium is governed by the Darcy equation. The flow inside the cavity and outside the nonhomogeneous porous region is governed by the Stokes equations. An analytical solution of the problem is obtained by using the cell model technique. Exact expressions for the drag force acting on the membrane and hydrodynamic permeability of the membrane are derived. The influence of radially varying permeability on flow parameters is considered. The effects of various parameters of the problem on hydrodynamic permeability of the membrane are discussed for four models. Some previous results for hydrodynamic permeability are verified as special limiting cases.

Effect of Heat Source/Sink on Free Connective MHD Flow past an Exponentially Accelerated Infinite Plate with Mass Diffusion and Chemical Reaction

The effects of heat source/sink and chemical reaction with mass diffusion on free convective incompressible viscous fluid flow past an accelerated vertical plate with magnetic field has been investigated. Laplace transformation method has been applied to solve the system of linear partial differential equations. The result is presented in form of complementary error function and exponential function. The effect of non dimensional parameters such as Schmidt number (Sc), Accelerated parameter (a), Chemical reaction parameter (K), Prandtl number (Pr), Magnetic field parameter (M), Mass Grashof number (Gm), Heat source/sink parameter (H), Thermal Grashof number (Gr) on temperature, concentration, velocity has been discussed with graphs.

Effect of Prandtl number on leading edge accretion and ablation: A numerical study of unsteady boundary layer flow over a flat plate

AbstractAn efficient numerical method, namely, the Runge‐Kutta fourth order integration scheme with shooting technique is employed to give a suitable solution for the unsteady magnetohydrodynamic boundary layer flow of viscous incompressible fluid with accretion or ablation effects over a flat plate under the influence of homogenous first order chemical reaction. When compared to the other numerical techniques such as perturbation methods, this approach provides the accurate numerical results valid uniformly for all nondimensional time. The unsteady behavior of chemically reacting magnetohydrodynamic boundary layer flow is investigated by analyzing the nature of buoyancy and magnetic parameters in the momentum equation. Also, results are extended to the energy and concentration equations by considering the viscous dissipation, Joule heating and chemical reaction effects. With the help of suitable similarity transformations, the highly nonlinear, coupled, time‐dependent partial differential equations are reduced to ordinary differential equations. Furthermore, the numerical solutions in terms of velocity, temperature and concentration profiles within the boundary layer are presented for the various values of control parameters. Also, the impact of physical parameters on the flow, heat and mass transfer characteristics are examined thoroughly. The present investigation reports that, the increasing magnetic parameter increases the temperature field and decreases the velocity field. Also, Eckert number enhance the thermal field whereas, the chemical reaction parameter decays the concentration field. Before concluding the considered problem, present results are validated with the previous results and are found to be in good agreement.