Three-dimensional analysis of critical Rayleigh number for natural convection in a rectangular enclosure

2003 ◽  
Vol 2003 (0) ◽  
pp. 389-390
Author(s):  
Kazunari MOMOSE ◽  
Yuuki FUTSUHARA ◽  
Hideo KIMOTO
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Dimensional Analysis ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Rectangular Enclosure

Numerical Simulations of an Unsteady Confined Natural Convection Flow

2009 ◽  
Author(s):  
Gillian Leplat ◽  
Emmanuel Laroche ◽  
Philippe Reulet ◽  
Pierre Millan
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Large Scale ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
High Amplitude ◽  
Joint Fluid ◽  
Convection Flow ◽  
Two Dimensional ◽  
Natural Convection Flow

A two-dimensional numerical analysis of a laminar natural convection flow within an air-filled enclosure is proposed in this paper from an unstable configuration previously studied experimentally. The flow is driven by a heated square-section cylinder located at the center of a square-section enclosure. Instabilities are observed for an aspect ratio (height of the cylinder over the height of the cavity) of 0.4 and cause the flow to turn into a three-dimensional and unsteady regime characterized by a symmetry breaking and large scale high amplitude flappings around the cylinder. The multi-physic computational software CEDRE, developed at the ONERA, is used to study this unstable behavior and a time-dependent compressible flow solver is used to perform the two-dimensional simulations under the low Mach number approximation, corresponding to the mid-depth cross-section of the enclosure from the experimental configuration. The first results on the investigation of the first unstable modes confirm the onset of the instabilities at the Rayleigh number of the experiment with asymmetrical motions of the fluid around the cylinder. Further analyses highlight the critical Rayleigh number that defines the instability threshold of the first bifurcation which origin and nature could have been identified. Finally, joint fluid-solid simulations are performed to determine more precisely the role of boundary conditions in the onset of instabilities.

Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results

1995 ◽  
Vol 117 (4) ◽  
pp. 910-917 ◽  
Author(s):  
T. J. Heindel ◽  
F. P. Incropera ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Number Flow ◽  
Experimental Geometry

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

Numerical Investigation of the Onset of Steady Natural Convection in a Square Cavity Partially Filled With a Single Porous Block

2014 ◽  
Author(s):  
Vinicius Daroz ◽  
Silvio L. M. Junqueira ◽  
Admilson T. Franco ◽  
José L. Lage
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Critical Rayleigh Number ◽  
Contour Plot ◽  
Viscous Effects ◽  
Square Cavity ◽  
Heterogeneous Model ◽  
Porous Block ◽  
Vertical Walls ◽  
Volume Method

The critical Rayleigh number at the onset of natural convection within a square cavity filled with a centralized porous block was investigated. The porous medium is modeled by using the heterogeneous model and the governing equations are solved for each phase separately. The thermal gradient is applied from the bottom to the top horizontal walls while the vertical walls are kept adiabatic. The amount of solid within the cavity was kept constant by fixing both external and internal porosity in 36% and 40%, respectively. The equations are solved using the Finite Volume Method and the interpolation scheme for the convective terms is the Hybrid Scheme. For the pressure-velocity coupling, the SIMPLEC method is used. The effects on the conductive-convective regime transition, reads critical Rayleigh Number, characterized by the average Nusselt number and the heatlines contour plot, was investigated by varying the Rayleigh number and the porous block permeability. The results show that the so called critical Rayleigh number is affected by the block permeability. As the permeability decreases, the flow tends to recirculate around the block being squeezed against the cavity walls and therefore, more susceptible to viscous effects. A correlation to the critical Rayleigh number is presented as a function of the agglomerate permeability showing that the higher the permeability the lower the amount of energy required to trigger the convection.

Three-dimensional analysis on natural convection inside a T-shaped cavity with water-based CNT–aluminum oxide hybrid nanofluid

2019 ◽  
Vol 139 (3) ◽  
pp. 2089-2098 ◽  
Author(s):  
Mohammed A. Almeshaal ◽  
K. Kalidasan ◽  
Faouzi Askri ◽  
R. Velkennedy ◽  
Ali Sulaiman Alsagri ◽  
...  
Keyword(s):  
Natural Convection ◽  
Aluminum Oxide ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Hybrid Nanofluid ◽  
Water Based

Three-dimensional analysis of natural convection in nanofluid-filled parallelogrammic enclosure opened from top and heated with square heater

2019 ◽  
Vol 26 (5) ◽  
pp. 1077-1088 ◽  
Author(s):  
Abdullah A. A. A Al-Rashed ◽  
Walid Hassen ◽  
Lioua Kolsi ◽  
Hakan F. Oztop ◽  
Ali J. Chamkha ◽  
...  
Keyword(s):  
Natural Convection ◽  
Dimensional Analysis ◽  
Three Dimensional

Convection in a box: linear theory

1967 ◽  
Vol 30 (3) ◽  
pp. 465-478 ◽  
Author(s):  
Stephen H. Davis
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Linear Theory ◽  
Cross Sections ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Wave Number ◽  
Spatial Variables ◽  
Zero Velocity ◽  
The Cross

The linear stability of a quiescent, three-dimensional rectangular box of fluid heated from below is considered. It is found that finite rolls (cells with two non-zero velocity components dependent on all three spatial variables) with axes parallel to the shorter side are predicted. When the depth is the shortest dimension, the cross-sections of these finite rolls are near-square, but otherwise (in wafer-shaped boxes) narrower cells appear. The value of the critical Rayleigh number and preferred wave-number (number of finite rolls) for a given size box is determined for boxes with horizontal dimensions h, ¼ ≤ h/d ≤ 6, where d is the depth.

Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

1996 ◽  
Vol 326 ◽  
pp. 399-415 ◽  
Author(s):  
M. Wanschura ◽  
H. C. Kuhlmann ◽  
H. J. Rath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Onset Of Convection ◽  
Buoyant Convection ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Prandtl Numbers

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

Sign in / Sign up

Export Citation Format

Share Document