scholarly journals A Steady Flow of The Viscous Compressible Liquid in Vertical Pipe

2021 ◽  
Vol 89 (2) ◽  
pp. 150-159
Author(s):  
Farman Mamedov ◽  
Nazire Memmedzade
Keyword(s):  
Velocity Distribution ◽  
Cross Section ◽  
Stokes Equations ◽  
Ground Surface ◽  
Ground Level ◽  
Compressible Liquid ◽  
Navier Stokes ◽  
Deep Zone ◽  
Vertical Pipe ◽  
Emden Equation

In the study of the flow of gas-liquid mixture over circular vertical pipe rising from the deep zone to ground level, it is observed that, the velocity on surface of tube is much more than in the center of flow. Such a picture is seen also in the water filtration process in sands ordering from high permeability zone to lower. Same phenomena occur in transportation of the water carbon nana-tubes. In order to predict behavior of those processes in this paper, we have studied the compressible liquid flow over the circular vertical pipe ordered from the deep zone to the ground surface for some concrete inlet and outlet regimes of the pipe. The Navier-Stokes equations system as a model of study. For certain inlet and outlet regimes of the flow splitting the equation into the cross section and axes variables, the pressure and velocity distribution are found. The Lane-Emden equation arises for determining the pipe cross section velocity distribution, which is also justified by our calculations on the used model.

Laminar Flow in a Porous Tube

1983 ◽  
Vol 105 (3) ◽  
pp. 303-307 ◽  
Author(s):  
R. M. Terrill
Keyword(s):  
Velocity Distribution ◽  
Cross Section ◽  
Axial Velocity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Axisymmetric Solution ◽  
Axial Velocity Distribution ◽  
Porous Pipe ◽  
Suction Or Injection

It is shown that an axisymmetric solution of the Navier-Stokes equations can be obtained for potential flow superimposed on Poiseuille flow. The result is used here to obtain a fully developed solution for flow in a porous pipe with variable suction or injection and to show how to obtain the suction distribution needed to change a specified axial velocity distribution at one cross-section to a specified axial velocity distribution at another cross-section.

scholarly journals Asymptotically based self-similarity solution of the Navier–Stokes equations for a porous tube with a non-circular cross-section

2017 ◽  
Vol 826 ◽  
pp. 396-420 ◽  
Author(s):  
M. Bouyges ◽  
F. Chedevergne ◽  
G. Casalis ◽  
J. Majdalani
Keyword(s):  
Cross Section ◽  
Similarity Solution ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Internal Flow ◽  
Navier Stokes ◽  
Solid Rocket Motor ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Radial Deviation

This work introduces a similarity solution to the problem of a viscous, incompressible and rotational fluid in a right-cylindrical chamber with uniformly porous walls and a non-circular cross-section. The attendant idealization may be used to model the non-reactive internal flow field of a solid rocket motor with a star-shaped grain configuration. By mapping the radial domain to a circular pipe flow, the Navier–Stokes equations are converted to a fourth-order differential equation that is reminiscent of Berman’s classic expression. Then assuming a small radial deviation from a fixed chamber radius, asymptotic expansions of the three-component velocity and pressure fields are systematically pursued to the second order in the radial deviation amplitude. This enables us to derive a set of ordinary differential relations that can be readily solved for the mean flow variables. In the process of characterizing the ensuing flow motion, the axial, radial and tangential velocities are compared and shown to agree favourably with the simulation results of a finite-volume Navier–Stokes solver at different cross-flow Reynolds numbers, deviation amplitudes and circular wavenumbers.

Numerical Analysis of Vapor Bubble Growth and Wall Heat Transfer During Flow Boiling of Water in a Microchannel

2005 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Vapor Bubble ◽  
Bubble Growth ◽  
Stokes Equations ◽  
Flow Boiling ◽  
Navier Stokes ◽  
Channel Cross Section ◽  
Wall Heat Transfer ◽  
Wall Superheat

The present study is performed to analyze the wall heat transfer mechanisms during growth of a vapor bubble inside a microchannel. The microchannel is of 200 μm square cross section and a vapor bubble begins to grow at one of the walls, with liquid coming in through the channel inlet. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. The bubble grows rapidly due to heat transfer from the walls and soon turns into a plug filling the entire channel cross section. The average wall heat transfer at the channel walls is studied for different values of wall superheat and incoming liquid mass flux. The results show that the wall heat transfer increases with wall superheat but is almost unaffected by the liquid flow rate. The bubble growth is found to be the primary mechanism of increasing wall heat transfer as it pushes the liquid against the walls thereby influencing the thermal boundary layer development.

Flow Due to Eccentric Rotating a Porous Disk and a Fluid at Infinity

1976 ◽  
Vol 43 (2) ◽  
pp. 203-204 ◽  
Author(s):  
M. Emin Erdogan
Keyword(s):  
Exact Solution ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Porous Disk ◽  
Navier Stokes Equations ◽  
Uniform Suction ◽  
Asymptotic Profile

An exact solution of the steady three-dimensional Navier-Stokes equations is obtained for the case of flow due to noncoaxially rotations of a porous disk and a fluid at infinity. It is shown that for uniform suction or uniform blowing at the disk an asymptotic profile exists for the velocity distribution.

The effects of secondary flow on the laminar dispersion of an injected substance in a curved tube

1970 ◽  
Vol 315 (1520) ◽  
pp. 99-113 ◽  
Keyword(s):  
Secondary Flow ◽  
Cross Section ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Flux Ratio ◽  
Original Method ◽  
Asymptotic Solutions ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Mean Velocity

The numerical solution by McConalogue & Srivastava (1968) of Dean’s simplified Navier–Stokes equations for the laminar flow of an inviscid fluid through a tube of circular cross-section of radius a , coiled in a circular arc of radius L , and valid for k in the range (16.6, 77.1), where k = Re √( a / L ), Re the Reynolds number, is compared with experiment, correlated to the asymptotic solutions for k > 100, and extended to study the convective axial dis­persion of a substance injected into the tube. The variation of the calculated flux ratio agrees closely with White’s (1929) measurements of the inverse quantity over the same range, and the field patterns for the upper end of the range establish the validity of the two basic assumptions of the asymptotic solutions. The original method is extended to calculate the mean axial velocity of a typical particle of the fluid and to present the statis­tical distribution of mean velocity over the particles of a substance injected as a thin disk uniformly over the cross section of the tube. These distributions are used to display the varia­tion with k of the shape of indicator concentration-time curves. The expected effect of secondary flow, in producing a more uniform distribution of velocity over the fluid than in Poiseuille flow, is evident.

Inward Flow Between Stationary and Rotating Disks

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Rotating Disks ◽  
Navier Stokes Equations

The present study predicts the flow field and the pressure distribution for a laminar flow in the gap between a stationary and a rotating disk. The fluid enters through the peripheral gap between two concentric disks and converges to the center where it discharges axially through a hole in one of the disks. Closed form expressions have been derived by simplifying the Navier– Stokes equations. The expressions predict the backflow near the rotating disk due to the effect of centrifugal force. A convection effect has been observed in the tangential velocity distribution at high throughflow Reynolds numbers.

EQUILIBRIUM VELOCITY DISTRIBUTION FUNCTIONS FOR A KINETIC MODEL OF TWO-PHASE FLOWS

1995 ◽  
Vol 05 (02) ◽  
pp. 191-211 ◽  
Author(s):  
LIONEL SAINSAULIEU
Keyword(s):  
Velocity Distribution ◽  
Gas Flow ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Solid Particles ◽  
Navier Stokes ◽  
Two Phase ◽  
Entropy Balance

We consider a cloud of solid particles in a gas flow. The cloud is described by a probability density function which satisfies a kinetic equation. The gas flow is modeled by Navier-Stokes equations. The two phases exchange momentum and energy. We obtain the entropy balance of the gas flow and deduce some bounds for the volume fraction of the gas phase. Writing the entropy balance for the dispersed phase enables one to determine the particles equilibrium velocity distribution function when the gas flow is known.

scholarly journals Numerical simulation of cavitating two-phase gas-liquid three-dimensional flow in a duct of varying cross-section based on homogenous mixture model

2006 ◽  
Vol 28 (3) ◽  
pp. 134-144
Author(s):  
Nguyen The Duc
Keyword(s):  
Numerical Simulation ◽  
Numerical Method ◽  
Cross Section ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Grid Systems ◽  
Curvilinear Grid

The paper presents a numerical method to simulate two-phase turbulent cavitating flows in ducts of varying cross-section usually faced in engineering. The method is based on solution of two-phase Reynolds-averaged Navier-Stokes equations of two-phase mixture. The numerical method uses artificial compressibility algorithm extended to unsteady flows with dual-time technique. The discreted method employs an implicit, characteristic-based upwind differencing scheme in the curvilinear grid systems. Numerical simulation of an unsteady three-dimensional two-phase cavitating flow in a duct of varying cross-section with available experiment was performed. The unsteady important characteristics of the unsteady flow can be observed in results of numerical simulation. Comparison of predicted results with experimental data for time-averaged velocity and phase fraction are provided.

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