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.

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>

Numerical Analysis of a Floating Body With Two-Dimensional Moonpool Including Piston Mode

2010 ◽  
Author(s):  
Jaekyung Heo ◽  
Jong-Chun Park ◽  
Moo-Hyun Kim ◽  
Weon-Cheol Koo
Keyword(s):  
Free Surface ◽  
Viscous Flow ◽  
Experimental Results ◽  
Floating Body ◽  
Navier Stokes ◽  
Linear Potential ◽  
Navier Stokes Equation ◽  
Nonlinear Potential ◽  
Heave Motion ◽  
Piston Mode

In this paper, the potential and viscous flows are simulated numerically around a 2-D floating body with a moonpool (or a small gap) with particular emphasis on the piston mode. The floating body with moonpool is forced to heave in time domain. Linear potential code is known to give overestimated free-surface heights inside the moonpool. Therefore, a free-surface lid in the gap or similar treatments are widely employed to suppress the exaggerated phenomenon by potential theory. On the other hand, Navier-Stokes equation solvers based on a FVM can be used to take account of viscosity. Wave height and phase shift inside and outside the moon-pool are computed and compared with experimental results by Faltinsen et al. (2007) over various heaving frequencies. Pressure and vorticity fields are investigated to better understand the mechanism of the sway force induced by the heave motion. Furthermore, a nonlinear potential code is utilized to compare with the viscous flow. The viscosity effects are investigated in more detail by solving Euler equations. It is found that the viscous flow simulations agree very well with the experimental results without any numerical treatment.

Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate

2014 ◽  
Vol 24 (09) ◽  
pp. 1450110 ◽  
Author(s):  
Rodica Borcia ◽  
Michael Bestehorn
Keyword(s):  
Liquid Film ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solid Substrate ◽  
Navier Stokes ◽  
Bottom Plate ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations ◽  
Spatial Dimensions

We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.

Columnar eddy formation in freely decaying homogeneous rotating turbulence

2011 ◽  
Vol 677 ◽  
pp. 154-178 ◽  
Author(s):  
K. YOSHIMATSU ◽  
M. MIDORIKAWA ◽  
Y. KANEDA
Keyword(s):  
Coriolis Force ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Length Scale ◽  
Rotational Axis ◽  
Navier Stokes Equation ◽  
Direction Parallel ◽  
Substantial Growth ◽  
Rotating Turbulence

The roles of the Coriolis force and the convection associated with the fluid motion in the formation of columnar eddies in freely decaying homogeneous rotating turbulence at a moderate Rossby number are studied by direct numerical simulation of the Navier–Stokes equations in a periodic box. The simulated field is compared with a series of artificial fields generated by switching off the nonlinear and viscous terms in the Navier–Stokes equation at given instants. The comparison shows that, without the nonlinear convection effect, the Coriolis force cannot sustain the substantial growth in the direction parallel to the rotational axis of the length scale defined on the basis of the two-point correlation of the square of the vorticity, i.e. cannot sustain the formation of the columnar eddies. The length scale characterizes well the intuitive impression from visualization of flow obeying the dynamics with or without the nonlinear effect. It is shown that the lack of substantial growth is insensitive to the scale of the eddies, the box size and viscosity, at least in the case studied here.

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.

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.

INFLUENCE OF ELECTROLYTE COMPOSITION AND OVERHEATING ON THE SIDELEDGE IN THE ALUMINUM CELL

2018 ◽  
pp. 24-30 ◽  
Author(s):  
V. V. Stakhanov ◽  
A. A. Redkin ◽  
Yu. P. Zaikov ◽  
A. E. Galashev
Keyword(s):  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Navier Stokes Equation ◽  
Cryolite Ratio ◽  
Heat Transfer Coefficients ◽  
Aluminum Smelting ◽  
Block Wall ◽  
The Difference ◽  
Aluminum Cell

The paper presents a theoretical study conducted to investigate the effect that the chemical composition of electrolyte and its overheating have on the size of sideledge formed in an aluminum smelting bath. Three electrolyte compositions were chosen: (1) sodium cryolite with the cryolite ratio CR = 2,7; (2) cryolite CR = 2,7 + 5 wt.% CaF2; (3) cryolite CR = 2,7 + 5 wt.% CaF2 + 5 wt.% Al2О3. The electrolyte liquidus overheating temperatures were 5, 10, 15 and 20 °C. Calculations were performed using the finite element method. A simplified design of an aluminum cell was used with a prebaked anode. The temperature field was calculated using a mathematical model based on the Boussinesq approximation, which contains the Navier–Stokes equation as well as thermal conductivity and incompressibility equations. The key role of electrolyte overheating in sideledge formation was established. The resulting sideledge profile depends on the heat transfer coefficients and thermophysical properties of materials. The smallest sideledge thickness with the same electrolyte overheating was observed in cryolite composition 3, and the profiles of the formed sideledge for samples 1 and 2 were nearly the same. The thickness of the sideledge formed with a 5 degree overheating exceeded 7 cm and the difference in temperature between the sideledge in contact with electrolyte and the side block wall was 20–25 degrees. It was found that the virtually total disappearance of the sideledge occurs at electrolyte liquidus overheating by 20 degrees.

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.

Sign in / Sign up

Export Citation Format

Share Document