Stability Analysis on Single-Phase Natural Circulation in Argonne Lead Loop Facility

2002 ◽  
Author(s):  
Qiao Wu ◽  
James J. Sienicki
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Single Phase ◽  
Natural Circulation ◽  
Stability Boundary ◽  
One Dimensional ◽  
Cooling Conditions ◽  
Characteristic Wavelength ◽  
Nyquist Criterion ◽  
High Reynolds

One-dimensional linear stability analysis was performed for single-phase lead-bismuth eutectic natural circulation. The Nyquist criterion and a root search method were employed to find the linear stability boundary of both forward and backward circulations. It was found that the natural circulations could be linearly unstable in a high Reynolds number region. Increasing loop friction makes a forward circulation more stable, but destabilizes the corresponding backward circulation under the same heating/cooling conditions. The characteristic wavelength of an unstable disturbance is roughly equal to the entire loop length.

A semi-analytical model for linear stability analysis of rectangular natural circulation loops

2018 ◽  
Vol 192 ◽  
pp. 892-905 ◽  
Author(s):  
Saikrishna Nadella ◽  
Abhishek Kumar Srivastava ◽  
Naresh Kumar Maheshwari
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Analytical Model ◽  
Linear Stability Analysis ◽  
Natural Circulation

A Linear Stability Analysis for an Improved One-Dimensional Two-Fluid Model

2003 ◽  
Vol 125 (2) ◽  
pp. 387-389 ◽  
Author(s):  
Jin Ho Song
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Model ◽  
Two Phase ◽  
One Dimensional ◽  
Proposed Model ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

A linear stability analysis is performed for a two-phase flow in a channel to demonstrate the feasibility of using momentum flux parameters to improve the one-dimensional two-fluid model. It is shown that the proposed model is stable within a practical range of pressure and void fraction for a bubbly and a slug flow.

Stability of Single-Phase Natural Circulation With Inverted U-Tube Steam Generators

1988 ◽  
Vol 110 (3) ◽  
pp. 735-742 ◽  
Author(s):  
J. Sanders
Keyword(s):  
Mathematical Model ◽  
Single Phase ◽  
Flow Direction ◽  
Natural Circulation ◽  
Boussinesq Equations ◽  
Test Facility ◽  
Normal Flow ◽  
Steam Generators ◽  
One Dimensional ◽  
Water Flows

For natural circulation it is shown that parallel flow in the tubes of an inverted U-tube steam generator can be, at certain power levels, unstable. A mathematical model, based on one-dimensional Oberbeck-Boussinesq equations, shows that stability can be attained if in some tubes the water flows backward, opposite to the normal flow direction. The results are compared to measurements obtained from the natural circulation test A2-77A in the LOBI-MOD2 integral system test facility.

Linear stability analysis of channel inception: downstream-driven theory

2000 ◽  
Vol 419 ◽  
pp. 239-262 ◽  
Author(s):  
NORIHIRO IZUMI ◽  
GARY PARKER
Keyword(s):  
Shear Stress ◽  
Stability Analysis ◽  
Froude Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Shear Stress ◽  
Resistance Coefficient ◽  
Critical Depth ◽  
Sheet Flow ◽  
Characteristic Wavelength

A linear stability analysis of incipient channellization on hillslopes is performed using the shallow-water equations and a description of the erosion of a cohesive bed. The base state consists of a laterally uniform Froude-subcritical sheet flow down a smooth, downward-concave hillslope profile. The downstream boundary condition consists of the imposition of a Froude number of unity. The process of channellization is thus driven from the downstream end. The flow and bed profiles describe a base state that migrates at constant, slow speed in the upstream direction due to bed erosion. Transverse perturbations corresponding to a succession of parallel incipient channels are introduced. It is found that these perturbations grow in time, so describing incipient channellization, only when the characteristic spacing between incipient channels is on the order of 6–100 times the Froude-critical depth divided by the resistance coefficient. The characteristic wavelength associated with maximum perturbation growth rate is found to scale as 10 times the Froude-critical depth divided by the resistance coefficient. Evaluating the friction coefficient as on the order of 0.01, an estimate of incipient channel spacing on the order of 1000 times the Froude-critical depth is obtained. The analysis reveals that downstream-driven channellization becomes more difficult as (a) the critical shear stress required to erode the bed becomes so large that it approaches the Froude-critical shear stress reached at the downstream boundary and (b) the Froude number of the subcritical equilibrium flow attained far upstream approaches unity. Alternative mechanisms must be invoked to explain channellization on slopes high enough to maintain Froude-supercritical sheet flow.

Linear stability analysis and metastable solutions for a phase-field model

1999 ◽  
Vol 129 (3) ◽  
pp. 571-600 ◽  
Author(s):  
A. Jiménez-Casas ◽  
A. Rodríguez-Bernal
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Phase Field ◽  
Field Model ◽  
Equilibrium Points ◽  
Phase Field Model ◽  
One Dimensional ◽  
Stability And Instability ◽  
The One

We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable solutions that evolve very slowly in time.

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