Tangential flow development for laminar axial flow in an annulus with a rotating inner cylinder

1972 ◽  
Vol 328 (1572) ◽  
pp. 123-141 ◽  
Keyword(s):  
Velocity Profile ◽  
Tangential Velocity ◽  
Axial Flow ◽  
Axial Distance ◽  
Taylor Vortices ◽  
Developing Flow ◽  
Axial Velocity Profile ◽  
Displacement Thickness ◽  
Core Rotation ◽  
Tangential Velocity Profile

The numerical finite-difference procedure of Gosman et al. (1969) is used to predict the growth of the tangential velocity profile and boundary-layer displacement thickness across an isothermal laminar axial flow through a concentric annulus when the inner cylinder is rotated at speeds which are insufficient to generate Taylor vortices. Solutions are obtained for fully developed and for developing axial flow over the ranges 0.05 < R 1 /R 2 < 0.98, 0.0002 < l < 1.0 and 100 < Re < 1700. The axial velocity profile is predicted to be insensitive to core rotation and, if varied, to influence only marginally the development of the tangential velocity profile; this is such that its dimensionless displacement thickness is related to dimensionless axial distance by a power law except near full development and at very low Reynolds number. Predictions at high Re accord extremely well with measurements. Astill’s (1964) stability criterion for the onset of vortices in tangential developing flow is accordingly presented afresh in terms of system parameters readily available to the designer.

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 Determining the Tangential Velocity profile of a Rotating Fluid in a Static Container using Navier–Stokes equations

2020 ◽  
Author(s):  
RAJDEEP TAH ◽  
SARBAJIT MAZUMDAR ◽  
Krishna Kant Parida
Keyword(s):  
Angular Velocity ◽  
Velocity Profile ◽  
Velocity Gradient ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Rotating Fluid ◽  
Navier Stokes Equations ◽  
Similar Principle ◽  
Tangential Velocity Profile

The shape of the liquid surface for a fluid present in a uniformly rotating cylinder is generally determined by making a Tangential velocity gradient along the radius of the rotating cylindrical container. A very similar principle can be applied if the direction of the produced velocity gradient is reversed, for which the source of rotation will be present at the central axis of the cylindrical vessel in which the liquid is present. Now if the described system is completely closed, the angular velocity will decrease as a function of time. But when the surface of the rotating fluid is kept free, then the Tangential velocity profile would be similar to that of the Taylor-Couette Flow, with a modification that; due to formation of a curvature at the surface, the Navier-Stokes law is to be modified. Now the final equation may not seem to have a proper general solution, but can be approximated to certain solvable expressions for specific cases of angular velocity.

The Elimination of Wall Effects in Axial-Flow Compressor Stages

1953 ◽  
Vol 57 (508) ◽  
pp. 241-243
Author(s):  
J. M. Stephenson
Keyword(s):  
Velocity Profile ◽  
Axial Velocity ◽  
Radial Profile ◽  
Axial Flow ◽  
Gas Velocity ◽  
Wall Effects ◽  
Axial Velocity Component ◽  
Axial Velocity Profile ◽  
Flow Compressor ◽  
Work Done

Compressor stages are usually designed on the assumption that the gas velocity is nowhere affected by the friction at the walls. The only way in which viscosity is taken into account is in the assumed efficiency, and in a guessed “work-done factor,” which ensures that by aiming high the required work is actually attained.It is known that the radial profile of the axial velocity component becomes more and more peaked through successive stages of a compressor, so that the assumptions just quoted become very inaccurate. It is possible that the efficiency of a stage could be raised considerably if the axial velocity profile were controlled; moreover up to 20 per cent. more work could be done if a “ work-done factor ” did not have to be applied.

Compressor Design

1953 ◽  
Vol 57 (511) ◽  
pp. 463-463
Author(s):  
R. G. Taylor
Keyword(s):  
Velocity Profile ◽  
Axial Velocity ◽  
Axial Flow ◽  
Technical Note ◽  
Basic Design ◽  
Wall Effects ◽  
Axial Flow Compressor ◽  
Axial Velocity Profile ◽  
Compressor Design ◽  
Flow Compressor

In Mr. J. M. Stephenson's Technical Note, “ The Elimination of Wall Effects in Axial-Flow Compressor Stages,” in the April 1953 issue of the Journal, the author suggests that the blade rows of an axial flow compressor are so closely spaced as to ensure that the axial velocity profile is unchanged across the rows. Whether this statement is correct or not such an assumption regarding the axial velocity profile is a basic design condition and when made it will not leave any flexibility in the choice of the function f(r).

The Stability of Viscous Axial Flow in the Entry Region of an Annulus with a Rotating Inner Cylinder

1976 ◽  
Vol 18 (5) ◽  
pp. 221-228 ◽  
Author(s):  
B. W. Martin ◽  
M. A. Hasoon
Keyword(s):  
Reynolds Number ◽  
Axial Length ◽  
Axial Velocity ◽  
Tangential Velocity ◽  
Axial Flow ◽  
Radius Ratio ◽  
Neutral Stability ◽  
Hot Wire ◽  
Core Rotation ◽  
The Stability

The stability of developing tangential flow induced by the imposition of an axial velocity on the tangential velocity distribution created by core rotation is theoretically and experimentally investigated. A linear stability analysis is used to examine the influence of axial length, axial Reynolds number and annulus radius ratio on the critical Taylor number for neutral stability when the axial velocity is assumed uniform. Predictions compare favourably with measurements obtained by hot-wire anemometer for air flowing in an annulus of radius ratio 0·9, particularly at small Reynolds number and large values of the axial length parameter.

Unstable Regions in Impulsively Started Pipe Entrance Flows Subjected to Infinitesimal Axisymmetric Disturbances

2003 ◽  
Author(s):  
E. A. Moss ◽  
A. H. Abbot
Keyword(s):  
Reynolds Number ◽  
Base Flow ◽  
Axial Distance ◽  
Flow Variable ◽  
Unconditionally Stable ◽  
Developing Flow ◽  
Displacement Thickness ◽  
Stability Data ◽  
Axisymmetric Disturbances ◽  
Spatially Developing Flow

This investigation presents computed base flow and stability data (axisymmetric disturbances) for impulsively started pipe entrance flows, and shows that at any given time, the displacement thickness (or any other flow variable) variation with axial distance is given by a varying portion which is accurately described by a steady, spatially developing flow, followed by a constant portion, described by the impulsively started parallel system. At the transition between these two systems is a small portion which is described by neither model. Arising from the inference that the latter region is sufficiently small to be neglected, variations in time and space of unstable regions in impulsively started pipe entrance flows were established, showing that (i) such flows are are unconditionally stable to infinitesimal axisymmetric disturbances for a Reynolds number of less than 23 350; (ii) for 38 770 > Re > 23 350, possible instability is confined to a maximum of 3.7% of the entire steady pipe entrance region; and (iii) for Re > 38 770, unstable regions may occur for finite time durations, over the entire length of the pipe.

Thermally developing forced convection flow through porous concentric pipes annular duct

2021 ◽  
pp. 095440622110022
Author(s):  
Farhan Ahmed
Keyword(s):  
Flow Region ◽  
Axial Direction ◽  
Darcy Number ◽  
Convection Flow ◽  
Axial Distance ◽  
Cross Sectional ◽  
Developing Flow ◽  
Annular Sector ◽  
Flow Through ◽  
The Cross

This article shows the thermally developing flow through concentric pipes annular sector duct by describing the Darcy Brinkman flow field. The cross sectional convection-diffusion terms are transformed in power law discretized form by integrating over the differential volume, whereas backward difference scheme is used in the axial direction of heat flow. With the help of semi implicit method for pressure linked equations-revised ( SIMPLE-R), we get the solution of the governing problem. The graphs of velocity profiles against R and average Nusselt number against axial distance are plotted for different values of Darcy number and geometrical configuration parameters. It has been pointed out that velocity and thermal entrance length decrease, when we decrease the value of Darcy number. By decreasing the cross section of the concentric pipes annular sector duct in the transverse direction, thermally fully developed flow region develops earlier.

Sign in / Sign up

Export Citation Format

Share Document