A simple hydromechanical approach for simulating squirt-type flow

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D335-D344 ◽  
Author(s):  
Beatriz Quintal ◽  
J. Germán Rubino ◽  
Eva Caspari ◽  
Klaus Holliger
Keyword(s):  
Fluid Flow ◽  
Spatial Patterns ◽  
Elastic Solid ◽  
Viscous Friction ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Perfect Agreement ◽  
Type Flow ◽  
The Difference ◽  
Biot’S Equations

The deformations caused by an acoustic wavefield in subsurface rock can induce fluid flow within hydraulically interconnected mesoscopic fractures, from one fracture into the other. The viscous friction associated with this squirt-type fluid flow parallel to the fracture walls results in energy dissipation and velocity dispersion. We have developed a quasi-static hydromechanical approach that is suitable for simulating squirt-type flow in the mesoscopic scale range and microscopic squirt flow. Our approach couples Navier-Stokes equation with Hooke’s law to describe the laminar flow of a viscous compressible fluid in conduits embedded in an elastic solid background. Results from the proposed method were compared with those obtained with Biot’s equations for a model containing interconnected mesoscopic fractures embedded in a background of very low porosity and permeability. Despite significant differences in the flow and dissipation spatial patterns, we have observed an essentially perfect agreement of the attenuation and modulus dispersion characteristics predicted by the two approaches. The difference in the flow and dissipation spatial patterns are associated with the “upscaling” inherent to Biot’s equations and, correspondingly, with differing boundary conditions at the fracture walls. Our results demonstrate that the proposed hydromechanical approach can provide additional insights on the physics of squirt-type flow in the mesoscopic and microscopic scale ranges.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

scholarly journals Comparison and analysis of calculation of Bridge backwater based on Mike21 hydrodynamic model

2021 ◽  
Vol 233 ◽  
pp. 03043
Author(s):  
Jiang Chuan Liu ◽  
Zhu Qiu Hu ◽  
Mao Yuan Zhu
Keyword(s):  
Theoretical Basis ◽  
Impact Analysis ◽  
Navier Stokes ◽  
Efficiency Coefficient ◽  
Navier Stokes Equation ◽  
The Real ◽  
Comparison And Analysis ◽  
Simulation Results ◽  
The Difference ◽  
Local Water

The construction of bridges and other structures across the river will affect the flood discharge capacity and local water potential of the river.Based on navier-Stokes equation of MIKE21FM hydrodynamic module, this paper carries out two-dimensional numerical simulation of part of Shixi River. By optimizing the grid near the piers to reduce the difference brought by the terrain generalized grid of the real river, it simulates and analyzes the length of the curve of yong-high and Yong-water under different flood frequencies,the Nash-Sutcliffe efficiency coefficient and relative error analysis are used to verify the rationality of the results. The simulation results can accurately reflect the real changes of river water level, It provides a theoretical basis for flood impact analysis.

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 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.

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.

Experimental velocity profiles in laminar flow around spheres at intermediate Reynolds numbers

1975 ◽  
Vol 68 (3) ◽  
pp. 591-608 ◽  
Author(s):  
L. E. Seeley ◽  
R. L. Hummel ◽  
J. W. Smith
Keyword(s):  
Laminar Flow ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Separation Point ◽  
Navier Stokes ◽  
Similar Data ◽  
Navier Stokes Equation ◽  
Stream Functions ◽  
The Difference ◽  
Grid Points

Normal and tangential velocities in the boundary layer and out into the free stream have been obtained using a non-disturbing flow visualization technique for uniform laminar flow around a sphere. The non-similar data are available in tables at 2.5° intervals from 20° from the front to about 15° past the separation point a t Reynolds numbers of 290, 750, 1300 and 3000. Stream functions calculated by LeClair using a numerical solution of the Navier-Stokes equation at Re 21 300 are not in good agreement with measured values from 30° to 60°, but are in much better agreement around the separation point. Too few grid points near the sphere where the tangential velocities rise to a maximum above free-stream values may account for the difference.

Analytic Solution for Microscale Poiseuille Flow Based on Super-Burnett Equations

2013 ◽  
Vol 705 ◽  
pp. 609-615
Author(s):  
Cheng Qian Song ◽  
Xie Yuan Yin ◽  
Feng Hua Qin
Keyword(s):  
Poiseuille Flow ◽  
Constitutive Relations ◽  
Slip Boundary Condition ◽  
Continuous Model ◽  
Analytic Solutions ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
The Difference

The previous studies show that the transverse distribution of pressure and temperature in microscale Poiseuille flow cannot be predicted by Navier-Stokes equation with the slip boundary condition. In this paper, we analyzed the planar microchannel force-driven Poiseuille flow by high order continuum model. The super-Burnett constitutive relations were used and the nonlinear ordinary differential Equations of higher-orders were obtained by the hypothesis of parallel flow. With a perturbations theory, we linearized the equations and obtained the analytic solutions. The results show that the solutions can capture the temperature dip which is the same as the DSMC result. However, we also find that the temperature profile near the wall does always not match with the DSMC result. Especially, the difference in the qualitative exists when the Knudsen number is large enough. The non-equilibrium effect near the wall such as Knudsen layer can not be described entirely by continuous model even with high order constitutive relations and this confines the extension of the continuous model such as super-Burnett one.

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