scholarly journals Classification of Flow Modes for Natural Convection in a Square Enclosure with an Eccentric Circular Cylinder

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2788
Author(s):  
Hyun-Sik Yoon ◽  
Yoo-Jeong Shim
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Circular Cylinder ◽  
Flow Structures ◽  
Two Dimensional ◽  
Square Enclosure ◽  
Wide Range ◽  
Secondary Vortices ◽  
Rayleigh Numbers

The present study investigated the natural convection for a hot circular cylinder embedded in a cold square enclosure. The numerical simulations are performed to solve a two-dimensional steady natural convection for three Rayleigh numbers of 103, 104 and 105 at a fixed Prandtl number of 0.7. This study considered the wide range of the inner cylinder positions to identify the eccentric effect of the cylinder on flow and thermal structures. The present study classifies the flow structures according to the cylinder position. Finally, the present study provides the map for the flow structures at each Rayleigh number (Ra). The Ra = 103 and 104 form the four modes of the flow structures. These modes are classified by mainly the large circulation and inner vortices. When Ra = 105, one mode that existed at Ra = 103 and 104, disappears in the map of the flow structures. The new three modes appear, resulting in total six modes of flow structures at Ra = 105. New modes at Ra = 105 are characterized by the top side secondary vortices. The corresponding isotherms are presented to explain the bifurcation of the flow structure.

Development of Multicellular Solutions in Natural Convection in an Air-Filled Vertical Cavity

1997 ◽  
Vol 119 (1) ◽  
pp. 97-101 ◽  
Author(s):  
S. Wakitani
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Multiple Solutions ◽  
Initial Condition ◽  
Two Dimensional ◽  
Reverse Transition ◽  
Wide Range ◽  
Flow Through ◽  
Rayleigh Numbers ◽  
Vertical Cavity

Consideration is given to the multiple solutions of two-dimensional natural convection in a vertical air-filled tall cavity with differentially heated sidewalls. Numerical simulations are carried out for a wide range of Rayleigh numbers from the onset of the steady multicellular flow, through the reverse transition to the unicellular pattern, to the unsteady multicellular flow. The dependence of the flow structure on the initial condition is clarified from the simulations by means of starting from a motionless and isothermal state, and gradually increasing or decreasing the Rayleigh number.

Natural Convection Liquid Cooling of a Substrate-Mounted Protrusion in a Square Enclosure: A Parametric Study

1992 ◽  
Vol 114 (2) ◽  
pp. 401-409 ◽  
Author(s):  
S. B. Sathe ◽  
Y. Joshi
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Flow Behavior ◽  
Air Cooling ◽  
Square Enclosure ◽  
Simple Boundary ◽  
Wide Range ◽  
Solid Region ◽  
Rayleigh Numbers ◽  
Thermal Conductivities

The coupled conduction and natural convection transport from a substrate-mounted heat generating protrusion in a liquid-filled square enclosure is numerically examined. The governing steady two-dimensional equations are solved using a finite-difference method for a wide range of Rayleigh numbers, protrusion thermal conductivities and widths, substrate heights, and enclosure boundary conditions. The results presented apply to liquids with 10≤Pr≤1000. It was established that in many situations it may be inappropriate to specify simple boundary conditions on the solid surface and decouple the conduction within the substrate or the protrusion. Higher Rayleigh numbers, protrusion thermal conductivities, and widths enhanced cooling. A variation in the substrate height did not affect the maximum protrusion temperature; however, the flow behavior was considerably altered. An empirical correlation for the maximum protrusion temperature was developed for a wide range of parametric values. The enclosure thermal boundary conditions changed the heat transfer in the solid region to only a small extent. Immersion cooling in common dielectric liquids was shown to be advantageous over air cooling only if the thermal conductivity of the protrusion was larger than that of the liquid.

scholarly journals A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus

1999 ◽  
Vol 381 ◽  
pp. 27-61 ◽  
Author(s):  
MARK P. DYKO ◽  
KAMBIZ VAFAI ◽  
A. KADER MOJTABI
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Three Dimensional ◽  
Flow Stability ◽  
Secondary Flows ◽  
Flow Structures ◽  
Wide Range ◽  
First Time ◽  
Rayleigh Numbers

A numerical and experimental study of buoyancy-driven flow in the annulus between two horizontal coaxial cylinders at Rayleigh numbers approaching and exceeding the critical values is presented. The stability of the flow is investigated using linear theory and the energy method. Theoretical predictions of the critical Rayleigh number for onset of secondary flows are obtained for a wide range of radius ratio R and are verified by comparison with results of previous experimental studies. A subcritical Rayleigh number which provides a necessary condition for global flow stability is also determined. The three-dimensional transient equations of fluid flow and heat transfer are solved to study the manifestation of instabilities within annuli having impermeable endwalls, which are encountered in various applications. For the first time, a thorough examination of the development of spiral vortex secondary flow within a moderate gap annulus and its interaction with the primary flow is performed for air. Simulations are conducted to investigate factors influencing the size and number of post-transitional vortex cells. The evolution of stable three-dimensional flow and temperature fields with increasing Rayleigh number in a large gap annulus is also studied. The distinct flow structures which coexist in the large gap annulus at high Rayleigh numbers preceding transition to oscillatory flow, including transverse vortices at the end walls which have not been previously identified, are established numerically and experimentally. The solutions for the large-gap annulus are compared to those for the moderate-gap case to clarify fundamental differences in behaviour. Heat transfer results in the form of local Nusselt number distributions are presented for both the moderate- and large-gap cases. Results from a series of experiments performed with air to obtain data for validation of the numerical scheme and further information on the flow stability are presented. Additionally, the change from a crescent-shaped flow pattern to a unicellular pattern with centre of rotation at the top of the annulus is investigated numerically and experimentally for a Prandtl number of 100. Excellent agreement between the numerical and experimental results is shown for both Prandtl numbers studied. The present work provides, for the first time, quantitative three-dimensional descriptions of spiral convection within a moderate-gap annulus containing air, flow structures preceding oscillation in a large-gap annulus for air, and unicellular flow development in a large-gap annulus for large Prandtl number fluids.

Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107

2009 ◽  
Vol 21 (4) ◽  
pp. 047101 ◽  
Author(s):  
Hyun Sik Yoon ◽  
Man Yeong Ha ◽  
Byung Soo Kim ◽  
Dong Hun Yu
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Circular Cylinder ◽  
Square Enclosure

Unsteady Darcian Natural Convection within Porous Media of Square Enclosure at Various Rayleigh Numbers

2013 ◽  
Vol 390 ◽  
pp. 18-22
Author(s):  
Ali Hooshyar Faghiri ◽  
Hikmet Şeli Aybar ◽  
Mehrdad Khamooshi
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Constant Temperature ◽  
Transient State ◽  
Left Wall ◽  
Square Enclosure ◽  
Transient Period ◽  
The Right ◽  
Rayleigh Numbers

Transient natural convection within a 2D square cavity filled with a porous medium is numerically investigated. The left wall is suddenly heated to a constant temperature Th, while the right wall is suddenly cooled to a constant temperature Tc. Both the horizontal walls are insulated. The Finite Volume numerical method is used to solve the dimensionless governing equations. The results are obtained for the initial transient state assuaging to the steady state, and for Rayleigh number values of 102–104. It is indicated that the average Nusselt number showing an undershoot during the transient period and that the time needed to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

scholarly journals Pressure-Velocity Coupling Schemes for Bouyancy Driven Flow in a Differentially Heated Cavity Using F.V.M and Matlab

2021 ◽  
pp. 19-39
Author(s):  
Purity Mberia ◽  
Stephen Karanja ◽  
Mark Kimathi
Keyword(s):  
Fluid Flow ◽  
Rayleigh Number ◽  
Bench Mark ◽  
Three Dimension ◽  
Two Dimensional ◽  
Central Difference ◽  
Square Enclosure ◽  
Simpler Algorithm ◽  
Simplec Algorithm ◽  
Rayleigh Numbers

Numerical analysis of fluid flow is anchored on the laws of conservation. A challenge in solving the momentum equation arises due to the unavailability of an explicit pressure equation. To avoid solving the pressure term most researchers have eliminated it by cross differentiating the x and the y two dimensional momentum equations and subtracting them. This method introduces more variables to be solved in comparison to the primitive variables and is  restricted to two-dimensional flows as streamlines do not exist in three-dimension. This method thus presents a serious limitation in analysis of fluid flow. In this study an equation for computing pressure has been developed using pressure - velocity coupling and used in solving the governing equations. The performance of three pressure velocity schemes namely; the Semi Implicit Method for Pressure linked Equation (SIMPLE), SIMPLE Revised (SIMPLER) and SIMPLE Consistent (SIMPLEC) for laminar buoyancy driven flow has been tested in order to establish the scheme that gives results consistent with bench mark data. The equations governing the flow are solved iteratively using finite volume method together with the central difference interpolating scheme. The solutions are presented for Rayleigh numbers of 103, 104, and 105. This resulted in the velocity profiles for the SIMPLE, SIMPLER, and SIMPLEC algorithm for a Rayleigh number of 104 and 105 converging to the same path. At a Rayleigh number of 103 however, SIMPLER algorithm undergoes a degradation in convergence with grid refinement at the baffle region. Results predicted by using the SIMPLEC algorithm are thus able to effectively compute the velocity of fluid flow in a differentially heated square enclosure with baffles for both low and higher Rayleigh numbers irrespective of the grid size.

Effects of magnetic field on the liquid gallium thermosyphon fluid flow; a numerical study

2019 ◽  
Vol 30 (2) ◽  
pp. 681-703
Author(s):  
Hamid Teimouri ◽  
Amin Behzadmehr
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Liquid Gallium ◽  
Two Dimensional ◽  
Left Wall ◽  
Content Type ◽  
Wide Range

Purpose This paper aims to numerically study the laminar natural convection in a thermosyphon filled with liquid gallium exposed to a constant magnetic field. The left wall of the thermosyphon is at an uniformed hot temperature, whereas the right wall is at a uniform cold temperature. The top and bottom walls are considered to be adiabatic. All walls are electrically insulated. The effects of Hartmann number, in a wide range of Rayleigh number and aspect ratio combinations, on the natural convection throughout the thermosyphon, are investigated and discussed. Furthermore, different forces that influence the natural flow structure are studied. Design/methodology/approach A Fortran code is developed based on the finite volume method to solve the two-dimensional unsteady governing equations. Findings Imposing a magnetic field improves the stability of the fluid flow and thus reduces the Nusselt number. For a given Hartmann and Rayleigh number, there is an optimum aspect ratio for which the average velocity becomes maximum. Research limitations/implications This paper is a two-dimensional investigation. Originality/value To the best of the authors’ knowledge, the effect of the magnetic field on natural convection of liquid gallium in the considered thermosyphon has not been studied numerically in detail. The results of this paper would be helpful in considering the application of the low Prandtl number’s liquid metals in thermosyphon MHD generators and certain cooling devices.

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