scholarly journals Mathematical modelling of fluid flow in electromagnetically stirred weld pool

2021 ◽  
Vol 1201 (1) ◽  
pp. 012025
Author(s):  
K Enger ◽  
M G Mousavi ◽  
A Safari
Keyword(s):  
Fluid Flow ◽  
Grain Refinement ◽  
Weld Pool ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Turbulent Fluid Flow ◽  
Flow Modelling ◽  
Weld Parameters ◽  
The Relationship

Abstract In this paper, a mathematical model has been proposed to study the relationship between electromagnetic stirring (EMS) weld parameters and the mode of fluid flow on grain refinement of AA 6060 weldments. For this purpose, fluid flow modelling using Navier-Stokes equation is described first, and then, the proposed mathematical approach has been discussed in detail. For demonstration, calculations to determine the fluid velocity in the weld pool of thin plate AA6060 were performed. The application of the model on the experimental results indicates that the best grain refinement is achieved at a transition mode from laminar to turbulent fluid flow.

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

<p>Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.</p><p>[1] U. Frisch, Z.S. She and P. L. Sulem, “Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,” Physica D, Vol. 28, No. 3, 1987, pp. 382-392.</p>

scholarly journals Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 175 ◽  
Author(s):  
Dmitry Bratsun ◽  
Vladimir Vyatkin
Keyword(s):  
Viscous Flow ◽  
Closed Form ◽  
General Procedure ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Chemical Transformations ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

Toward a Global Model for FSI in Tube Bundles

2008 ◽  
Author(s):  
Daniel Broc ◽  
Marion Duclercq
Keyword(s):  
Fluid Flow ◽  
Euler Equations ◽  
Dynamic Behaviour ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Navier Stokes Equation ◽  
Dissipative Effects ◽  
Tube Bundles ◽  
Homogenization Methods ◽  
Physical Phenomena

It is well known that a fluid may strongly influence the dynamic behaviour of a structure. Many different physical phenomena may take place, depending on the conditions: fluid at rest, fluid flow, little or high displacements of the structure. Inertial effects can take place, with lower vibration frequencies, dissipative effects also, with damping, instabilities due to the fluid flow (Fluid Induced Vibration). In this last case the structure is excited by the fluid. The paper deals with the vibration of tube bundles in a fluid, under a seismic excitation or an impact. In this case the structure moves under an external excitation, and the movement is influenced by the fluid. The main point in such system is that the geometry is complex, and could lead to very huge sizes for a numerical analysis. Many works has been made in the last years to develop homogenization methods for the dynamic behaviour of tube bundles (/2/ and /3/). The size of the problem is reduced, and it is possible to make numerical simulations on wide tubes bundles with reasonable computer times. These homogenization methods are valid for “little displacements” of the structure (the tubes), in a fluid at rest. The fluid movement is governed by the Euler equations. In this case, only “inertial effects” will take place, with globally lower frequencies. It is well known that dissipative effects due to the fluid may take place, even if the displacements of the tube are no so high, or if the fluid is not still (/4/, /5/, /6/ and /8/). Such effects may be described in the homogenized models by using a Rayleigh damping, but the basic assumption of the model remains the “perfect fluid” hypothesis. It seem necessary, in order to get a best description of the physical phenomena, to build a more general model, based on the general Navier Stokes equation for the fluid. The homogenization of such system will be much more complex than for the Euler equations. The paper doesn’t pretend to give a general solution of the problem, but only points out the most important key points to build such homogenized model for the dynamic behaviour of tubes bundles in a fluid.

scholarly journals SIMULATION OF HYDRO-MECHANICAL PROCESSES IN CENTRIFUGAL PUMPS

2016 ◽  
Vol 2016 (1) ◽  
pp. 100-105
Author(s):  
Ризван Шахбанов ◽  
Rizvan Shakhbanov ◽  
Леонид Савин ◽  
Leonid Savin
Keyword(s):  
Fluid Flow ◽  
Continuity Equation ◽  
Equation Of Motion ◽  
Theoretical Description ◽  
Navier Stokes ◽  
Centrifugal Pumps ◽  
Navier Stokes Equation ◽  
Rotary Pumps ◽  
Rotating Coordinates ◽  
Graphical Presentation

The peculiarities in current and kinematics of hydromechanical processes in centrifugal (rotary) pumps are considered. The theoretical description and graphical presentation of velocity profiles in an impeller are shown. A complex current in an impeller is described with the aid of a continuity equation and Navier-Stokes equation for rotating coordinates. A nonviscous character of fluid flow in the setting of an im-peller is taken into account by means of averaging of the equation of motion for that purpose the equation of a turbulence model is introduced in addition. The scheme of the digitization of a modeling area with the aid of a volumetric endelement grid is presented. As an example a computer model as a part of an impeller is shown.

scholarly journals A MAGNETOHYDRODYNAMIC STUDY OF BEHAVIOR IN AN ELECTROLYTE FLUID USING NUMERICAL AND EXPERIMENTAL SOLUTIONS

2012 ◽  
Vol 11 (1-2) ◽  
pp. 53
Author(s):  
L. P. Aoki ◽  
M. G. Maunsell ◽  
H. E. Schulz
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Fluid Velocity ◽  
Flow Analysis ◽  
Test Chamber ◽  
Cross Product ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Vector Density ◽  
The Magnetic Field

This article examines a rectangular closed circuit filled with an electrolyte fluid, known as macro pumps, where a permanent magnet generates a magnetic field and electrodes generate the electric field in the flow. The fluid conductor moves inside the circuit under magnetohydrodynamic effect (MHD). The MHD model has been derived from the Navier Stokes equation and coupled with the Maxwell equations for Newtonian incompressible fluid. Electric and magnetic components engaged in the test chamber assist in creating the propulsion of the electrolyte fluid. The electromagnetic forces that arise are due to the cross product between the vector density of induced current and the vector density of magnetic field applied. This is the Lorentz force. Results are present of 3D numerical MHD simulation for newtonian fluid as well as experimental data. The goal is to relate the magnetic field with the electric field and the amounts of movement produced, and calculate de current density and fluid velocity. An u-shaped and m-shaped velocity profile is expected in the flows. The flow analysis is performed with the magnetic field fixed, while the electric field is changed. Observing the interaction between the fields strengths, and density of the electrolyte fluid, an optimal configuration for the flow velocity isdetermined and compared with others publications.

Heat Transfer Mode and Effect of Fluid Flow on the Morphology of the Weld Pool

2021 ◽  
Vol 406 ◽  
pp. 66-77
Author(s):  
Abdel Halim Zitouni ◽  
Pierre Spiteri ◽  
Mouloud Aissani ◽  
Younes Benkheda
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Weld Pool ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Transfer Mode ◽  
Thermal Fields ◽  
Welding Properties

In this work, the heat transfer by conduction and convection mode and effect of fluid flow on the morphology of the weld pool and the welding properties is investigated during Tungsten Inert Gas (TIG) process. In the first part, a computation code under Fortran was elaborated to solve the equations resulting from the finite difference discretization of the heat equation, taking into account the liquid-solid phase change with the associated boundary conditions. In order to calculate the velocity field during welding, the Navier-Stokes equations in the melt zone were simplified and solved considering their stream-vorticity formulation. A mathematical model was developed to study the effect of the melted liquid movement on the weld pool. The evolution of the fraction volume of the liquid and the thermal fields promoted the determination of the molten zone (MZ) and the Heat Affected Zone (HAT) dimensions, which seems to be in good agreement with literature.

The virtual power principle in fluid mechanics

2014 ◽  
Vol 744 ◽  
pp. 310-328 ◽  
Author(s):  
Yongliang Yu
Keyword(s):  
Incompressible Flows ◽  
Boundary Energy ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Analytical Mechanics ◽  
Virtual Power ◽  
Navier Stokes Equation ◽  
Fluid Medium ◽  
External Forces ◽  
The Relationship

AbstractA conceptual framework on analytical mechanics for continuous fluid medium, which connects the fluid motion and all of the (internal and external) forces with mechanical power, is proposed by using the virtual power and the virtual velocity. Based on this framework, it is found that the internal virtual power is equal to the external virtual power in fluid dynamics, which is called the virtual power principle. This framework is also proved to be equivalent to the vector dynamics (Cauchy’s equation or Navier–Stokes equation). Furthermore, based on the virtual power principle, a theorem is introduced for continuous fluid medium, which indicates the relationship between the force (or torque) acting on a body immersed in a fluid and the specified virtual power. Subsequently, according to Galilean invariance, the detailed relationship for Newtonian fluids in incompressible flows is derived and used to illustrate the mechanisms on instantaneous forces: the added inertial effects, the boundary energy flux and dissipation effects, the vortex contribution, and the explicit body force contribution. As an application of the principle, the advantage of the V formation flight of geese is preliminarily discussed in the view of aerodynamics. Specifically, the total drag of the flock is reduced by contrast with the simple sum of the drag in solo fight and the optimal angle of V ranges from $60^{\circ }$ to $120^{\circ }$. The principle could be a useful approach to reveal the contributions of the flow structures and the moving or deforming boundaries to the force and torque acting on a body, especially in a multibody system.

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