Linear Analysis of the Currents in a Pipe

1986 ◽  
Vol 41 (9) ◽  
pp. 1141-1153
Author(s):  
U. Brosa
Keyword(s):  
Exact Solutions ◽  
Cross Section ◽  
Bulk Viscosity ◽  
Stokes Equations ◽  
Simple Procedure ◽  
Circular Cross Section ◽  
Linear Analysis ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Infinite Set

A simple procedure to find solutions of the hydrodynamic Stokes equations is given. The procedure is used to determine the linear modes of a newtonian fluid in a pipe of circular cross section. Compressibility, shear and bulk viscosity are included, and no restrictions on the symmetry of the modes are made. Furthermore an infinite set of exact solutions of the Navier-Stokes equations is presented.

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.

Influence of Surface Roughness on Shear Flow

2004 ◽  
Vol 71 (4) ◽  
pp. 459-464 ◽  
Author(s):  
S. Bhattacharyya ◽  
S. Mahapatra ◽  
F. T. Smith
Keyword(s):  
Cross Section ◽  
Numerical Solutions ◽  
Flat Surface ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Uniform Shear

The local planar flow of incompressible fluid past an obstacle of semi-circular cross section is considered, the obstacle being mounted on a long flat surface. The far-field motion is one of uniform shear. Direct numerical solutions of the Navier-Stokes equations are described over a range of Reynolds numbers. The downstream eddy length and upstream position of maximum pressure gradient are found to agree with increased Reynolds number theory; in particular the agreement for the former quantity is close for Reynolds numbers above about 50.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

On the Generalized Navier-Stokes Equations

2003 ◽  
Author(s):  
Moustafa El-Shahed ◽  
Ahmed Salem
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hankel Transforms ◽  
Fourier Sine ◽  
Special Cases

In this paper, we present a general Inodel of the classical Navier-Stokes equations. With the help of Laplace, Fourier Sine transforms, finite Fourier Sine transforms, and finite Hankel transforms, an exact solutions for three different special cases have been obtained.

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