On Oscillatory Instability of Convective Flows at Low Prandtl Number

1997 ◽  
Vol 119 (4) ◽  
pp. 823-830 ◽  
Author(s):  
A. Yu. Gelfgat ◽  
P. Z. Bar-Yoseph ◽  
A. L. Yarin
Keyword(s):  
Aspect Ratio ◽  
Prandtl Number ◽  
Lower Boundary ◽  
Oscillatory Instability ◽  
Weakly Nonlinear ◽  
Convective Flows ◽  
Stability Diagrams ◽  
Aspect Ratios ◽  
The Stability ◽  
Upper Boundary

Numerical investigation of the oscillatory instability of convective flows in laterally heated rectangular cavities is presented. Cavities with no-slip isothermal vertical boundaries, no-slip adiabatic lower boundary, and stress-free adiabatic upper boundary are considered. Dependence of the critical Grashof number and the critical frequency of oscillations on the aspect ratio (A = length/height) of the cavity are investigated. The stability diagrams were obtained for the whole interval of the aspect ratio 1 ≤ A ≤ 10. The study was carried out for two values of the Prandtl number, Pr = 0 and 0.015. It was shown that the oscillatory instability sets in as a result of the Hopf bifurcation. It was found that at two different values of the Prandtl number considered the instability is caused by different infinitely small dominant perturbations, which means that the convective heat transfer strongly affects stability of the flow even for cases having small Prandtl number. No asymptotic behavior for large aspect ratios was found up to A = 10. Slightly supercritical oscillatory flows were approximated asymptotically by means of the weakly nonlinear analysis of the calculated bifurcation.

On the Oscillatory Instability of Closed-Loop Thermosyphons

1985 ◽  
Vol 107 (4) ◽  
pp. 826-832 ◽  
Author(s):  
K. Chen
Keyword(s):  
Turbulent Flows ◽  
Closed Loop ◽  
Numerical Solutions ◽  
Angular Frequency ◽  
Oscillatory Instability ◽  
Neutral Stability ◽  
Horizontal Segment ◽  
Aspect Ratios ◽  
The Stability ◽  
Laminar And Turbulent Flows

The stability of natural convection flows in single-phase closed-loop thermosyphons is investigated. The thermosyphons considered in the present analysis are fluid-filled tubes bent into rectangular shapes. The fluid is heated over the lower horizontal segment and cooled over the upper horizontal segment. Analytical and numerical solutions are presented for a range of loop aspect ratios and radii for both laminar and turbulent flows. It is found that the steady-state results for thermosyphons with different aspect ratios and radii can be expressed in terms of a single dimensionless parameter. When this parameter is less than a critical value, the flow is always stable. Above this critical point, oscillatory instability exists for a narrow range of a friction parameter. The calculated neutral stability conditions show that the flow is least stable when the aspect ratio of the loop approaches unity. The frequency of the convection-induced oscillation is slightly higher than the angular frequency of a fluid particle traveling along the loop.

scholarly journals Effect of Rotational Speed Modulation on the Weakly Nonlinear Heat Transfer in Walter-B Viscoelastic Fluid in the Highly Permeable Porous Medium

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1448
Author(s):  
Anand Kumar ◽  
Vinod K. Gupta ◽  
Neetu Meena ◽  
Ishak Hashim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Rotational Speed ◽  
Weakly Nonlinear ◽  
Speed Modulation ◽  
The Stability ◽  
The Impact

In this article, a study on the stability of Walter-B viscoelastic fluid in the highly permeable porous medium under the rotational speed modulation is presented. The impact of rotational modulation on heat transport is performed through a weakly nonlinear analysis. A perturbation procedure based on the small amplitude of the perturbing parameter is used to study the combined effect of rotation and permeability on the stability through a porous medium. Rayleigh–Bénard convection with the Coriolis expression has been examined to explain the impact of rotation on the convective flow. The graphical result of different parameters like modified Prandtl number, Darcy number, Rayleigh number, and Taylor number on heat transfer have discussed. Furthermore, it is found that the modified Prandtl number decelerates the heat transport which may be due to the combined effect of elastic parameter and Taylor number.

Correlations for Natural Convection Between Heated Vertical Plates

1991 ◽  
Vol 113 (1) ◽  
pp. 97-107 ◽  
Author(s):  
S. Ramanathan ◽  
R. Kumar
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
Vertical Direction ◽  
Numerical Results ◽  
Maximum Temperature ◽  
Parallel Plates ◽  
Plate Temperature ◽  
Aspect Ratios ◽  
Prandtl Numbers

This paper presents the numerical results of natural convective flows between two vertical, parallel plates within a large enclosure. A parametric study has been conducted for various Prandtl numbers and channel aspect ratios. The results are in good agreement with the reported results in the literature for air for large aspect ratios. However, for small aspect ratios, the present numerical results do not agree with the correlations given in the literature. The discrepancy is due to the fact that the published results were obtained for channels where the diffusion of thermal energy in the vertical direction is negligible. The results obtained in this paper indicate that vertical conduction should be considered for channel aspect ratios less than 10 for Pr = 0.7. Correlations are presented to predict the maximum temperature and the average Nusselt number on the plate as explicit functions of the channel Rayleigh number and the channel aspect ratio for air. The plate temperature is a weak function of Prandtl number for Prandtl numbers greater than 0.7, if the channel Rayleigh number is chosen as the correlating parameter. For Prandtl numbers less than 0.1, the plate temperature is a function of the channel Rayleigh number and the Prandtl number. A correlation for maximum temperature on the plate is presented to include the Prandtl number effect for large aspect ratio channels.

FIV Characteristics of U-Tubes Due to Relocation of the Tube Support Plate

2005 ◽  
Author(s):  
Ki-Wahn Ryu ◽  
Hyung-Jin Kim ◽  
Chi-Yong Park
Keyword(s):  
Aspect Ratio ◽  
Steam Generator ◽  
Mode Shapes ◽  
Design Stage ◽  
Parameter Study ◽  
Stability Ratio ◽  
Integrity Assessment ◽  
Support Plate ◽  
Aspect Ratios ◽  
The Stability

Fluid-elastic instability and turbulence excitation for an under developing steam generator are investigated numerically. The stability ratio and the amplitude of turbulence excitation are obtained by using the PIAT (Program for Integrity Assessment of Steam Generator Tube) code from the information on the thermal-hydraulic data of the steam generator. The aspect ratio, the ratio between the height of U-tube from the upper most tube support plate (h) and the width of two vertical portion of U-tube (w), is defined for geometric parameter study. Several aspect ratios with relocation of tube support plates are adopted to study the effects on the mode shapes and characteristics of flow-induced vibration. When the aspect ratio exceeds value of 1, most of the mode shapes at low frequency are generated at the top of U-tube. It makes very high value of the stability ratio and the amplitude of turbulent excitation as well. We can consider that the local mode shape at the upper side of U-tube will develop the wear phenomena between the tube and the anti-vibration bars such as vertical, horizontal, and diagonal strips. It turns out that the aspect ratio reveals very important parameter for the design stage of the steam generator. The appropriate value of the aspect ratio should be specified and applied.

Nonlinear convection in high vertical channels

1984 ◽  
Vol 143 ◽  
pp. 223-242 ◽  
Author(s):  
C. Normand
Keyword(s):  
Specific Treatment ◽  
Finite Size ◽  
Stationary Solutions ◽  
Amplitude Equation ◽  
Weakly Nonlinear ◽  
Convective Systems ◽  
Horizontal Extent ◽  
Aspect Ratios ◽  
Infinite Height ◽  
The Stability

Application of Landau's ideas to the theory of weakly nonlinear instabilities shows that the amplitude of the unstable modes behaves as the square root of the reduced control parameter ε, its critical value being ε = 0. When applied to cellular structures the theory has been improved by taking into account the slow spatial variations of the amplitude and phase of the unstable modes. Until now the case of thermo-convective instabilities in high vertical channels has not been studied using this approach. In high vertical structures the nonlinear terms disappear in the limit of an infinite height, and the supercritical behaviour requires a specific treatment. It differs from the standard analysis valid for the case of fluid layers of infinite horizontal extent, where the nonlinearities and the finite-size effects are disconnected. In the limit of high aspect ratios (height [Gt ] horizontal extent) we have derived an amplitude equation for convective systems where the nonlinear terms contain derivatives at the lowest order. As a consequence the amplitude equation cannot be put into a variational form and the stability of the stationary solutions cannot be deduced from an ordering in decreasing values of a Lyapunov functional.

scholarly journals Effect of Nonreciprocal Forces on the Stability of Dust Clusters

2021 ◽  
Vol 47 (5) ◽  
pp. 410-418
Author(s):  
A. M. Ignatov
Keyword(s):  
Regular Polygon ◽  
Oscillatory Instability ◽  
Particle Cluster ◽  
Plasma Parameters ◽  
Directed Flow ◽  
Weakly Nonlinear ◽  
Nonlinear Stage ◽  
The Stability ◽  
Oscillatory Instabilities ◽  
Number Of Particles

Abstract Results are presented from studies of the stability of the plane dust clusters in the form of a regular polygon with the number of particles from two to five. It is assumed that the particles are placed in the plasma consisting of Maxwellian electrons and a directed flow of cold ions. It is shown that, in such clusters, the oscillatory instabilities can develop along with the aperiodic instabilities. The ranges of plasma parameters are determined, within which the oscillatory instability of the five-particle cluster becomes saturated at the weakly nonlinear stage. As a result, the cluster forms a time crystal, which can be a chiral crystal.

Three-dimensional Rayleigh-Taylor instability Part 1. Weakly nonlinear theory

1988 ◽  
Vol 187 ◽  
pp. 329-352 ◽  
Author(s):  
J. W. Jacobs ◽  
I. Catton
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Initial Surface ◽  
Surface Slope ◽  
Cross Sectional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Rayleigh Taylor Instability ◽  
The Stability

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analysed. The stability of a confined inviscid liquid and an overlying gas with density much less than that of the liquid is considered. An asymptotic solution for containers of arbitrary cross-sectional geometry, valid up to order ε3 (where ε is the root-mean-squared initial surface slope) is obtained. The solution is evaluated for the rectangular and circular geometries and for various initial modes (square, hexagonal, axisymmetric, etc.). It is found that the hexagonal and axisymmetric instabilities grow faster than any other shapes in their respective geometries. In addition it is found that, sufficiently below the cutoff wavenumber, instabilities that are equally proportioned in the lateral directions grow faster than those with longer, thinner shape. However, near the cutoff wavenumber this trend reverses with instabilities having zero aspect ratio growing faster than those with aspect ratio near 1.

The Plate Buckling Coefficient

1967 ◽  
Vol 71 (673) ◽  
pp. 37-40 ◽  
Author(s):  
P. S. Bulson
Keyword(s):  
Aspect Ratio ◽  
Close Approximation ◽  
Families Of Curves ◽  
Aspect Ratios ◽  
Plate Buckling ◽  
Plate Aspect Ratio ◽  
Exact Shape ◽  
Buckling Coefficient ◽  
Thin Walled ◽  
The Stability

SummaryThe stability of a compressed plate is examined, using the energy method, with transverse deflections defined by a function giving the exact shape, but never specified. By this means it is possible to make observations about the form of the plate buckling coefficient. This form is examined tor two cases of loading, and it is demonstrated that a close approximation to the complete curve linking the buckling coefficient with plate aspect ratio can be deduced. The method is applicable to single plates or thin walled members consisting of an assembly of plates, and enables families of curves connecting buckling coefficients with aspect ratios to be summarised in a single relationship.

Experimental Investigation on the Motion of Particle Cloud in Viscous Fluids

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Amir H. Azimi
Keyword(s):  
Aspect Ratio ◽  
Drag Coefficient ◽  
Viscous Fluids ◽  
Air Bubbles ◽  
Aspect Ratios ◽  
Particle Clouds ◽  
Flow Through ◽  
Using Data ◽  
The Stability ◽  
Individual Particles

Laboratory experiments were conducted to study the dynamics of particle clouds in viscous fluids. Different shapes of frontal head and trailing stems were observed, and particle clouds were classified using data mining methodology. The stability of the frontal head of particle clouds was found to be correlated with the nozzle diameter and mass of sand particles in the form of an initial aspect ratio. The formation of particle clusters into a torus and the split of the frontal head into two or three clusters were investigated in detail. The cluster of particles flow through viscous fluid experienced partial separation due to the release of air bubbles from the rear of frontal head. It was observed that the time and location of major particle separation increase linearly with the aspect ratio. The oscillatory motion of the frontal head, caused by an uneven release of air bubbles from the rear of the frontal head, was found to be correlated with the initial aspect ratio. Both amplitude and wavelength exhibited a linear relationship with nondimensional time. The average drag coefficient of particle clouds Cd in viscous fluids was calculated for different aspect ratios, and the results were compared with the drag coefficient of individual particles. It was found that the averaged drag coefficients of particle clouds were smaller than the drag coefficient of individual particles, and Cd slightly increases with the increasing initial aspect ratio.

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