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.

Thermodynamic Analysis of the Darcy Law

1961 ◽  
Vol 28 (2) ◽  
pp. 208-212 ◽  
Author(s):  
R. G. Mokadam
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Gravitational Force ◽  
Equation Of Motion ◽  
Darcy Law ◽  
Navier Stokes ◽  
Proportionality Factor ◽  
Navier Stokes Equation ◽  
Special Case

The Darcy law is used extensively to describe the flow of fluids through porous media. According to this law the fluid flow is linearly dependent upon the pressure gradient and the gravitational force. The proportionality factor is generally known as the permeability of the porous medium. The Darcy law cannot be derived from the Navier-Stokes equation since this equation includes terms which characterize the fluid only. With the help of nonreversible thermodynamics it is possible to develop a general equation of motion of a fluid through a porous body, and obtain the Darcy law as a special case of such an equation.

Numerical Simulation of Supersonic Flow and Particle Motion in Aerodynamic Lenses

2003 ◽  
Author(s):  
Omid Abouali ◽  
Goodarz Ahmadi
Keyword(s):  
Equation Of Motion ◽  
Aerodynamic Performance ◽  
Computational Grid ◽  
Stagnation Pressure ◽  
Sensitivity Analyses ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Stagnation ◽  
Airflow Field ◽  
Particles Trajectories

Airflow and particle motions in aerodynamic lenses are studied. The computational grid is generated with the use of GAMBIT code and FLUENT 5 is used in the analysis. The axisymmetric compressible form of the Navier-Stokes equation is solved and the airflow conditions are evaluated. One-way coupling is assumed in that the air transports the particles, but the effect of dilute particle concentrations on flow field is ignored. The particle equation of motion including drag, lift and Brownian forces is used and the particle trajectories in the aerodynamic a lens are analyzed. In addition, the airflow field and particles motions downstream of the nozzle are also studied. A series of sensitivity analyses on the effect of inlet flow stagnation pressure and backpressure of the nozzle on the aerodynamic performance of the lens is performed. Sample streamlines and particles trajectories in an axisymmetric plane of a combination of three aerodynamic lenses and a nozzle are shown in the figures.

Learning the Dynamics of Objects by Optimal Functional Interpolation

2012 ◽  
Vol 24 (9) ◽  
pp. 2457-2472
Author(s):  
Jong-Hoon Ahn ◽  
In Young Kim
Keyword(s):  
Functional Data ◽  
Continuity Equation ◽  
Particle Concentration ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Conserved Quantities ◽  
Time Varying ◽  
Science And Engineering ◽  
Navier Stokes Equation ◽  
Over Time

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.

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 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 CONTINUITY AND MOTION (NAVIER-STOKES) EQUATIONS

2018 ◽  
Author(s):  
Dmitriy Provorov
Keyword(s):  
Differential Equations ◽  
Continuity Equation ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Integral Forms ◽  
Correct Form

The paper is considering of the basic differential equations of hydrodynamics: the equation of continuity and motion. On the simplest example, it is shown that the equation of continuity in a system with the equation of motion leads to contradictions and erroneous results of modeling. A more correct form of the continuity equation is described. It is shown that the equations of motion can be written in the form of complete differentials. Three possible integral forms of the equations of motion are presented. As a conclusion, the existence and smoothness of the solution of the Navier-Stokes equations are considered.

scholarly journals Numerical Approximate Solution to Flow over a Flat Plate ( the Balusis Problem) By Perturbation Iteration- Algorithm

2021 ◽  
Author(s):  
Abeer Jasim
Keyword(s):  
Continuity Equation ◽  
Perturbation Technique ◽  
Navier Stokes ◽  
Iteration Algorithm ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Homotopy Perturbation ◽  
Blasius Problem ◽  
Layer Flow ◽  
Homotopy Perturbation Technique

This paper applied perturbation iteration- algorithm (PI-A) to solve the problem of the incompressible two-dimensional laminar boundary layer flow over a flat plat as wall as called the Blasius problem (BP). BP is governed by Navier- Stokes equation (NSE) and continuity equation which were transformed into ordinary differential equation using similarity transforms. The results presented are tabulated for similarity stream function and can be seen highly of accuracy through comparable with that obtained by Ganji et al.[3] who studied BP using Homotopy perturbation technique (HPT) , Research results for the same problem using the variationally This paper applied perturbation iteration- algorithm (PI-A) to solve the problem of the incompressible two-dimensional laminar boundary layer flow over a flat plat as wall as called the Blasius problem (BP). BP is governed by Navier- Stokes equation (NSE) and continuity equation which were transformed into ordinary differential equation using similarity transforms. The results presented are tabulated for similarity stream function and can be seen highly of accuracy through comparable with that obtained by Ganja et al.[3] who studied BP using Homotopy perturbation technique (HPT) , Research results for the same problem using the variational iteration technique (VIT) before Aiyesimi and Niyi[5] and results numerical by Blasius[1]. Finally, The method that is efficient and widely applicable for solving ODE.

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