The Effect of Temperature Gradient on the Stability of Flow between Vertical, Concentric, Rotating Cylinders

1979 ◽  
Vol 21 (6) ◽  
pp. 403-409 ◽  
Author(s):  
M. M. Sorour ◽  
J. E. R. Coney
Keyword(s):  
Temperature Gradient ◽  
Velocity Ratio ◽  
Axial Flow ◽  
Wave Number ◽  
Taylor Vortex ◽  
Effect Of Temperature ◽  
Neutral Stability ◽  
Radial Temperature ◽  
Annular Gap ◽  
The Stability

The effect of a radial temperature gradient on the hydrodynamic stability in the annular gap formed by two, vertical, concentric cylinders, the inner being rotatable and the outer both stationary and isothermally heated, was studied for the cases of zero and imposed axial fluid flow in the annular gap. For zero axial flow, it was found that the temperature gradient destabilizes the flow while not affecting the form of the secondary flow, viz. the classic Taylor vortex. For imposed axial flow, the point of neutral stability was modified only when natural convection was strong enough to affect the parabolic velocity profile associated with that flow; the extent of this modification was shown to depend on the direction of the axial flow. Also, the longitudinal temperature gradients within the gap were found to influence the axial wave number and the drift-velocity ratio.

An Experimental Investigation of the Stability of Spiral Vortex Flow

1979 ◽  
Vol 21 (6) ◽  
pp. 397-402 ◽  
Author(s):  
M. M. Sorour ◽  
J. E. R. Coney
Keyword(s):  
Vortex Flow ◽  
Outer Cylinder ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Vortex Cell ◽  
Annular Gap ◽  
Spiral Vortex ◽  
Axial Pressure Gradient ◽  
The Stability

The hydrodynamic stability of the flow in an annular gap, formed by a stationary outer cylinder and a rotatable inner cylinder, through which an axial flow of air can be imposed, is studied experimentally. Two annulus radius ratios of 0.8 and 0.955 are considered, representing wide- and narrow-gap conditions, respectively. It is shown that, when a large, axial pressure gradient is superimposed on the tangential flow induced by the rotation of the inner cylinder, the characteristics of the flow at criticality change significantly from those at zero and low axial flows, the axial length and width of the resultant spiral vortex departing greatly from the known dimensions of a Taylor vortex cell at zero axial flow. Also, the drift velocity of the spiral vortex is found to vary with the axial flow. Axial Reynolds numbers, Rea, of up to 700 are considered.

scholarly journals STABILITY OF VISCOUS FLOW IN A CURVED CHANNEL WITH RADIAL TEMPERATURE GRADIENT

2016 ◽  
Vol 15 (8) ◽  
pp. 6957-6966
Author(s):  
Sadhana Pandey ◽  
Neelabh Rai
Keyword(s):  
Temperature Gradient ◽  
Outer Cylinder ◽  
Critical Values ◽  
Wave Number ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Eigen Value ◽  
Cell Patterns ◽  
The Difference ◽  
The Stability

In this paper, the stability of Dean’s problem in the presence of a radial temperature gradient is studied for narrow gap case. The analytical solution of the eigen value problem is obtained by using the Galerkin’s method. The critical values of parameters and Λ are computed, where  is wave number and Λ is a parameter determining the onset of stability from the obtained analytical expressions for the first, second and third approximations. It is found that the difference between the numerical values of critical Λ corresponding to the second and third approximations is very small as compared to the difference between first and second approximations. The critical values of Λ obtained by the third approximation agree very well with the earlier results computed numerically by using the finite difference method. This clearly indicates that for the better result one should obtain the numerical values by taking more terms in approximation. Also, the amplitude of the radial velocity and the cell-patterns are shown on the graphs for different values of the parameter M, which depends on difference of temperatures of outer cylinder to the inner one i.e. on (), where is the temperature of inner cylinder and  is the temperature of outer cylinder.

Flow Regimes in Two-Phase Hexane/Water Semibatch Vertical Taylor Vortex Flow

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Charlton Campbell ◽  
Michael G. Olsen ◽  
R. Dennis Vigil
Keyword(s):  
Vortex Flow ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Flow Patterns ◽  
Water Phase ◽  
Taylor Vortex ◽  
Two Phase ◽  
Annular Gap ◽  
Taylor Vortex Flow ◽  
Regime Map

Optical-based experiments were carried out using the immiscible pair of liquids hexane and water in a vertically oriented Taylor–Couette reactor operated in a semibatch mode. The dispersed droplet phase (hexane) was continually fed and removed from the reactor in a closed loop setup. The continuous water phase did not enter or exit the annular gap. Four distinct flow patterns were observed including (1) a pseudo-homogenous dispersion, (2) a weakly banded regime, (3) a horizontally banded dispersion, and (4) a helical flow regime. These flow patterns can be organized into a two-dimensional regime map using the azimuthal and axial Reynolds numbers as axes. In addition, the dispersed phase holdup was found to increase monotonically with both the azimuthal and axial Reynolds numbers. The experimental observations can be explained in the context of a competition between the buoyancy-driven axial flow of hexane droplets and the wall-driven vortex flow of the continuous water phase.

Destabilization of the Taylor Vortex Flow by a Radial Temperature Gradient

2006 ◽  
Author(s):  
Vale´rie Lepiller ◽  
Jong-Yeon Hwang ◽  
Arnaud Prigent ◽  
Kyung-Soo Yang ◽  
Innocent Mutabazi
Keyword(s):  
Temperature Gradient ◽  
Vortex Flow ◽  
Taylor Vortex ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Taylor Vortices ◽  
Numerical Studies ◽  
Taylor Vortex Flow ◽  
Spatio Temporal ◽  
Small Inclination

Both experimental and numerical studies have shown that the Taylor vortices are destabilized by a weak radial temperature gradient and transit to spiral vortices with a small inclination. For a large radial temperature gradient, from Taylor vortices emerges a disordered pattern with some windows of spiral vortices. Spatio-temporal characteristics of resulting pattern are presented.

Experimental investigations of the stability of channel flows. Part 2. Two-layered co-current flow in a rectangular channel

1972 ◽  
Vol 52 (3) ◽  
pp. 401-423 ◽  
Author(s):  
Timothy W. Kao ◽  
Cheol Park
Keyword(s):  
Reynolds Number ◽  
Current Flow ◽  
Rectangular Channel ◽  
Shear Waves ◽  
Transition To Turbulence ◽  
Wave Number ◽  
Neutral Stability ◽  
Mean Flow ◽  
Transition Range ◽  
The Stability

The stability of the laminar co-current flow of two fluids, oil and water, in a rectangular channel was investigated experimentally, with and without artificial excitation. For the ratio of viscosity explored, only the disturbances in water grew in the beginning stages of transition to turbulence. The critical water Reynolds number, based upon the hydraulic diameter of the channel and the superficial velocity defined by the ratio of flow rate of water to total cross-sectional area of the channel, was found to be 2300. The behaviour of damped and growing shear waves in water was examined in detail using artificial excitation and briefly compared with that observed in Part 1. Mean flow profiles, the amplitude distribution of disturbances in water, the amplification rate, wave speed and wavenumbers were obtained. A neutral stability boundary in the wave-number, water Reynolds number plane was also obtained experimentally.It was found that in natural transition the interfacial mode was not excited. The first appearance of interfacial waves was actually a manifestation of the shear waves in water. The role of the interface in the transition range from laminar to turbulent flow in water was to introduce and enhance spanwise oscillation in the water phase and to hasten the process of breakdown for growing disturbances.

The stability of viscous axial flow in an annulus with a rotating inner cylinder

1977 ◽  
Vol 352 (1670) ◽  
pp. 351-380 ◽  
Keyword(s):  
Velocity Distribution ◽  
Tangential Velocity ◽  
Axial Flow ◽  
Radius Ratio ◽  
Neutral Stability ◽  
Axial Distribution ◽  
Critical Wavelength ◽  
Explicit Finite Difference ◽  
The Stability ◽  
The Galerkin Method

Predictions by two methods are presented of the onset of instability in developed tangential flow in a concentric annulus due to inner cylinder rotation. The first formulation is as an initial-value problem in which the time evolution of initially-distributed small random vorticity perturbations of given axial wavelength is monitored by numerically integrating the unsteady perturbation equations by explicit finite-difference procedure. The second method is the Galerkin approach where an eigenvalue problem is formulated in which the linearized disturbance equations are solved to predict the neutral stability condition. Comparisons for a radius ratio N of 0.9 and Re up to 350 show that an averaged axial velocity distribution and the exact axial distribution yield similar predictions of Ta c and the corresponding critical wavelength; these however, differ markedly from previous narrow-gap predictions based on a parabolic approximation to the axial distribution. The current use of the exact developed tangential velocity distribution permits investigation by the Galerkin method for 0.9≽ N ≽ 0.1 and Re up to 2000. Computations of Ta c are in satisfactory agreement with earlier measurements for N of 0.95, 0.82 and 0.81 and accord well with current measurements over the range 50 ≼ Re ≼ 400 in an annulus of radius ratio 0.9.

Dynamic Stability Analysis of Cans in Reactor Coolant Pump Subjected to Axial Flow

2014 ◽  
Author(s):  
Wenbo Ning ◽  
Dezhong Wang
Keyword(s):  
Dynamic Stability ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Geometrical Parameters ◽  
Coolant Pump ◽  
Critical Flow Velocity ◽  
Reactor Coolant ◽  
Annular Gap ◽  
The Stability ◽  
Canned Motor

The stator and rotor cans in canned motor reactor coolant pump are assumed to be elastic coaxial cylindrical shells due to their particular geometric structures in present study. Thin shell structures such as cans are prone to buckling instabilities. Furthermore, a lot of accidents were caused by losing stability. The dynamic behavior of coaxial circular cylindrical shells subjected to axial fluid flow in the annular gap between two shells is investigated in this paper. The outer shell is stiffened by ring-ribs because of its instability easily. The shell is modeled based on Donnell’s shallow theory. The “smeared stiffeners” approach is used for ring-stiffeners. The fluid is assumed to be an incompressible ideal fluid and the potential flow theory is employed to describe shell-fluid interaction. Numerical analyses are conducted by means of energy variation to obtain the critical flow velocity of losing stability with aid of Hamilton principle. This study shows effects of geometrical parameters on stability of shells. The size and number of ring-stiffeners on dynamic stability are examined. It is found that stiffeners can vary modes instability and enhance the stability of shells. The flow velocities of losing stability with different boundary conductions can be calculated and compared. The results show clamped shells are more stable than simply supported shells. The results presented are in reasonable agreement with those available in the literature.

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