Modeling aspects in linear stability analysis of a self-pressurized, natural circulation integral reactor

Natural convection in a saturated horizontal porous layer heated from below and cooled at the top with a constant flux is studied both analytically and numerically. Linear stability analysis indicates that unicellular recirculation remains a stable mode of flow as the aspect ratio (A) of the layer is increased, in contrast to the situation for an isothermally heated and cooled layer. An analytical solution is presented for fully developed counterflow in the infinite-aspect-ratio limit; this flow is found to be linearly stable to transverse disturbances for Rayleigh number (Ra) as high as 506, at which point a Hopf bifurcation sets in; however, further analysis indicates that an exchange of stability due to longitudinal disturbances will occur much sooner at Ra ≈ 311.53. The velocity and temperature profiles of the counterflow solution, whilst not strictly speaking valid in the extreme end regions of the layer, otherwise agree very well with full numerical computations conducted for the ranges 25 [les ] Ra [les ] 1050, 2 [les ] A [les ] 10. However, for sufficiently high Rayleigh number (Ra between 630 and 650 for A = 8 and Ra between 730 and 750 for A = 4, for example), the computations indicate transition from steady unicellular to oscillatory flow, in line with the Hopf bifurcation predicted by the linear stability analysis for infinite aspect ratio.

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Natural Circulation and Linear Stability Analysis for Liquid-Metal Reactors with the Effect of Fluid Axial Conduction

Nuclear Technology ◽

10.13182/nt12-a13595 ◽

2012 ◽

Vol 178 (3) ◽

pp. 298-317 ◽

Cited By ~ 8

Author(s):

Piyush Sabharwall ◽

Yeon Jong Yoo ◽

Qiao Wu ◽

James J. Sienicki

Keyword(s):

Stability Analysis ◽

Liquid Metal ◽

Linear Stability ◽

Linear Stability Analysis ◽

Natural Circulation ◽

Axial Conduction

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Optimal Disturbances in Three-Dimensional Natural Convection Flows

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2012-72386 ◽

2012 ◽

Cited By ~ 1

Author(s):

Elia Merzari ◽

Paul Fischer ◽

W. David Pointer

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Natural Circulation ◽

Three Dimensional ◽

Boussinesq Approximation ◽

Spectral Element ◽

Base Flow ◽

The Stability ◽

Optimal Disturbances

Buoyancy-driven systems are subject to several types of flow instabilities. To evaluate the performance of such systems it is becoming increasingly crucial to be able to predict the stability of a given base flow configuration. Traditional Modal Linear stability Analysis requires the solution of very large eigenvalue systems for three-dimensional flows, which make this problem difficult to tackle. An alternative to modal Linear stability Analysis is the use of adjoint solvers [1] in combination with a power iteration [2]. Such methodology allows for the identification of an optimal disturbance or forcing and has been recently used to evaluate the stability of several isothermal flow systems [2]. In this paper we examine the extension of the methodology to non-isothermal flows driven by buoyancy. The contribution of buoyancy in the momentum equation is modeled through the Boussinesq approximation. The method is implemented in the spectral element code Nek5000. The test case is the flow is a two-dimensional cavity with differential heating and conductive walls and the natural circulation flow in a toroidal thermosiphon.

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