G1301 Calculation of the critical Rayleigh number for the natural convection flows in the 8:1 differentially-heated square cavity

2001 ◽  
Vol 2001 (0) ◽  
pp. 257
Author(s):  
Masaaki MATSUMOTO ◽  
Takafumi MAKIHARA ◽  
Takahiko TANAHASHI
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Critical Rayleigh Number ◽  
Square Cavity

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.

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.

Scaling of the Turbulent Natural Convection Flow in a Heated Square Cavity

1994 ◽  
Vol 116 (2) ◽  
pp. 400-408 ◽  
Author(s):  
R. A. W. M. Henkes ◽  
C. J. Hoogendoorn
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection ◽  
Convection Boundary ◽  
Vertical Walls ◽  
Rayleigh Numbers

By numerically solving the Reynolds equations for air and water in a square cavity, with differentially heated vertical walls, at Rayleigh numbers up to 1020 the scalings of the turbulent natural convection flow are derived. Turbulence is modeled by the standard k–ε model and by the low-Reynolds-number k–ε models of Chien and of Jones and Launder. Both the scalings with respect to the Rayleigh number (based on the cavity size H) and with respect to the local height (y/H) are considered. The scalings are derived for the inner layer, outer layer, and core region. The Rayleigh number scalings are almost the same as the scalings for the natural convection boundary layer along a hot vertical plate. The scalings found are almost independent of the k–ε model used.

A Numerical Study of Natural Convection in a Cavity With Two Fins Attached to Its Vertical Walls

2007 ◽  
Author(s):  
G. A. Sheikhzadeh ◽  
M. Pirmohammadi ◽  
M. Ghassemi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Vertical Walls ◽  
The Mean ◽  
Energy Equations ◽  
Rayleigh Numbers

Numerical study natural convection heat transfer inside a differentially heated square cavity with adiabatic horizontal walls and vertical isothermal walls is investigated. Two perfectly conductive thin fins are attached to the isothermal walls. To solve the governing differential mass, momentum and energy equations a finite volume code based on Pantenkar’s simpler method is developed and utilized. The results are presented in form of streamlines, isotherms as well as Nusselt number for Rayleigh number ranging from 104 up to 107. It is shown that the mean Nusselt number is affected by the position of the fins and length of the fins as well as the Rayleigh number. It is also observed that maximum Nusselt number occurs about the middle of the enclosure where Lf is grater the 0.5. In addition the Nusselt number stays constant and does not varies with width of the cavity (lf) when Lf is equal to 0.5 and Rayleigh number is equal to 104 and 107 as well as when Lf is equal to 0.6 and low Rayleigh numbers.

scholarly journals Pore-Scale Investigation on Natural Convection Melting in a Square Cavity with Gradient Porous Media

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4274
Author(s):  
Jiangxu Huang ◽  
Kun He ◽  
Lei Wang
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Thermal Performance ◽  
Liquid Fraction ◽  
Particle Diameter ◽  
Numerical Data ◽  
Melting Time ◽  
Pore Scale ◽  
Square Cavity

In this paper, natural convection melting in a square cavity with gradient porous media is numerically studied at pore-scale level by adopting the lattice Boltzmann method. To generate the gradient porous media, a Monte Carlo technique based on the random sampling principle is used. The effects of several factors, such as Rayleigh number, gradient porosity structure, gradient direction, and particle diameters on natural convection melting are investigated in detail. Based on the numerical data, it is observed that the thermal performance of the gradient porous media always depends on the Rayleigh number and, specifically, as the Rayleigh number is set to 106, the total melting time obtained for the case of the negative gradient porous media is always shorter than the cases of positive gradient and uniform porous media. However, if the Rayleigh number is equal to 104, at which the heat transfer is dominated by the heat conduction, it is noted that the performance of the positive gradient porous media is better than the other cases. To have a better understand on this point, various simulations are also performed and we found that there usually exists a critical value of Rayleigh number to determine the thermal performance of the gradient porous media. Moreover, our numerical results also show that the influence of the particle diameter on the liquid fraction is insignificant as Rayleigh number is set to 104, while it has a great impact on the liquid fraction when Rayleigh number equals 106.

scholarly journals Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium

2021 ◽  
Author(s):  
Florinda Capone ◽  
Jacopo A. Gianfrani
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Linear Instability ◽  
Brinkman Model ◽  
Linear Instability Analysis ◽  
Non Equilibrium

AbstractThe onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to $$L^2$$ L 2 -norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed.

scholarly journals Prediction of Unsteady Natural Convection within a Square Cavity Containing an Obstacle at High Rayleigh Number Value

2015 ◽  
Vol 55 ◽  
pp. 19-26
Author(s):  
Basma Souayeh ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya ◽  
Taieb Lili
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Stokes Equations ◽  
Computer Code ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Convection Flow ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Volume Method

The present work deals with the prediction of a natural convection flow in a square cavity, partially heated by an obstacle placed at the bottom wall. The two transverse walls and the top wall of the cavity are supposed to be cold, the remaining walls are kept insulated. The main parameter of numerical investigations is the Rayleigh number (engine convection) varying from 103 to 105. When Ra is fixed at 107, the flow and thermal fields bifurcate and undergoes an unsteady behavior at critical positions. Flow patterns corresponding to the unsteady state are presented and analyzed in the current study. The simulations were conducted using a numerical approach based on the finite volume method and the projection method, which are implemented in a computer code in order to solve the Navier-Stokes equations.

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