scholarly journals Application of Navier – Stokes Equation to Solve Fluid Flow Problems

2020 ◽  
pp. 101-114
Author(s):  
Ebiendele Ebosole Peter ◽  
Adamu Bala
Keyword(s):  
Fluid Flow ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Flow Through

The Navier – Stokes equations were used to obtain the velocity profile for two different fluid flow problems, firstly to a laminar flow through a pipe and secondly to flow of incompressible fluid between two boundaries, one boundary is the air and the other boundary moving with a velocity, inclined at an angle . The velocity profiles were obtained and presented in a diagram of showing how the fluid flow through the channels.

The developing tangential velocity profile for axial flow in an annulus with a rotating inner cylinder

1968 ◽  
Vol 307 (1488) ◽  
pp. 55-69 ◽  
Keyword(s):  
Velocity Profile ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Axial Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Taylor Vortices ◽  
Flow Through ◽  
Momentum Integral ◽  
Tangential Velocity Profile

A method is described of predicting the growth of a tangential velocity profile in fully developed laminar axial flow through a concentric annulus when the inner surface is rotated at speeds which are insufficient to generate Taylor vortices. The treatment, which is based on simplification and subsequent solution of the Navier-Stokes equations, as Fourier-Bessel series, appears preferable to momentum-integral techniques through greater simplicity of expression and in requiring fewer assumptions about the developing tangential profile. The validity of the predictions is best at high axial Reynolds number.

scholarly journals A pore scale study on fluid flow through two dimensional dual scale porous media with small number of intraparticle pores

2016 ◽  
Vol 18 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Safa Sabet ◽  
Moghtada Mobedi ◽  
Turkuler Ozgumus
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Permeability Tensor ◽  
Navier Stokes ◽  
Pore Scale ◽  
Navier Stokes Equations ◽  
Pressure Distributions ◽  
Flow Through ◽  
Dual Scale

Abstract In the present study, the fluid flow in a periodic, non-isotropic dual scale porous media consisting of permeable square rods in inline arrangement is analyzed to determine permeability, numerically. The continuity and Navier-Stokes equations are solved to obtain the velocity and pressure distributions in the unit structures of the dual scale porous media for flows within Darcy region. Based on the obtained results, the intrinsic inter and intraparticle permeabilities and the bulk permeability tensor of the dual scale porous media are obtained for different values of inter and intraparticle porosities. The study is performed for interparticle porosities between 0.4 and 0.75 and for intraparticle porosities from 0.2 to 0.8. A correlation based on Kozeny-Carman relationship in terms of inter and intraparticle porosities and permeabilities is proposed to determine the bulk permeability tensor of the dual scale porous media.

scholarly journals Linearization of the Navier-Stokes equations

2020 ◽  
Vol 216 ◽  
pp. 01060
Author(s):  
Serdar Nazarov ◽  
Muhammetberdi Rakhimov ◽  
Gurbanyaz Khekimov
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Heat Transfer Process ◽  
Navier Stokes ◽  
Functional Dependencies ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Optimal Modeling ◽  
Optimal Control Methods

This paper studies mathematical models of the heat transfer process of a viscous incompressible fluid. Optimal control methods are used to solve the problem of optimal modeling. Questions of linearization of the Navier-Stokes equation for a plane fluid flow are considered. The optimal modes (optimal functional dependencies) of the pump and heating device are found depending on the fluid flow rate.

scholarly journals Experimental evidence of velocity profile inversion in developing laminar flow using magnetic resonance velocimetry

2018 ◽  
Vol 851 ◽  
pp. 545-557 ◽  
Author(s):  
A. Reci ◽  
A. J. Sederman ◽  
L. F. Gladden
Keyword(s):  
Magnetic Resonance ◽  
Laminar Flow ◽  
Finite Difference ◽  
Velocity Profile ◽  
Experimental Evidence ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Magnetic Resonance Velocimetry

A discrepancy exists between the predictions of analytical solutions of approximate Navier–Stokes equations and numerical finite-difference solutions of the full Navier–Stokes equations regarding the development of laminar flow at the entrance to cylindrical pipes for Newtonian fluids. Starting from a uniform velocity profile at the entrance to the pipe, analytical solutions of approximate Navier–Stokes equations predict the velocity profile to have a maximum at the centre of the pipe at all times. In contrast, numerical finite-difference solutions of the full Navier–Stokes equations have suggested that the location of the velocity maximum moves from the wall towards the centre of the pipe at a short distance from the entrance, after which it remains at the centre of the pipe. This study presents the first experimental evidence of the moving velocity maximum from the wall towards the centre of the pipe. The initial uniform velocity profile was achieved by flowing the fluid through a monolith composed of narrow parallel channels and the flow development was investigated using magnetic resonance velocimetry. The experimentally observed variation of the position and size of the velocity maximum with the Reynolds number and the distance from the entrance to the pipe is shown to be in good agreement with the predictions of numerical finite-difference solutions of the full Navier–Stokes equations.

scholarly journals A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation

2019 ◽  
Vol 76 (2) ◽  
pp. 60-87 ◽  
Author(s):  
Renato M. Cotta ◽  
Kleber M. Lisboa ◽  
Marcos F. Curi ◽  
Stavroula Balabani ◽  
João N. N. Quaresma ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Integral Transform ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Hybrid Integral

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

Steady Laminar Flow through Twisted Pipes: Fluid Flow in Square Tubes

1981 ◽  
Vol 103 (4) ◽  
pp. 785-790 ◽  
Author(s):  
J. H. Masliyah ◽  
K. Nandakumar
Keyword(s):  
Laminar Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dissipation Term ◽  
Axial Velocity Profile ◽  
Secondary Motion ◽  
Qualitative Nature ◽  
Flow Through ◽  
Steady Laminar

The Navier-Stokes equation in a rotating frame of reference is solved numerically to obtain the flow field for a steady, fully developed laminar flow of a Newtonian fluid in a twisted tube having a square cross-section. The macroscopic force and energy balance equations and the viscous dissipation term are presented in terms of variables in a rotating reference frame. The computed values of friction factor are presented for dimensionless twist ratios, (i.e., length of tube over a rotation of π radians normalized with respect to half the width of tube) of 20, 10, 5 and 2.5 and for Reynolds numbers up to 2000. The qualitative nature of the axial velocity profile was observed to be unaffected by the swirling motion. The secondary motion was found to be most important near the wall.

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