Natural Convection in a Narrow Horizontal Annulus: The Effects of Thermal and Hydrodynamic Instabilities

1998 ◽  
Vol 120 (4) ◽  
pp. 1019-1026 ◽  
Author(s):  
P. Cadiou ◽  
G. Desrayaud ◽  
G. Lauriat
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Base Flow ◽  
Hydrodynamic Instabilities ◽  
Convective Flows ◽  
A Value ◽  
Multicellular Structure ◽  
Reverse Transition ◽  
Imperfect Bifurcation ◽  
Number Of Cells

Multicellular natural convective flows in narrow horizontal air-filled concentric annuli are considered numerically in this paper. The results show that the multiplicity of the multicellular upper flows reported in the literature can be credited to the existence of an imperfect bifurcation with two stable branches. The emergence and extinction of the buoyancy-driven cells have been proved to be identical on both branches. The appearance of another secondary flow, the origin of which is purely hydrodynamic and located within the crescent base flow at the vertical portions of the annulus, has also been evidenced at moderate values of the Rayleigh number. As Ra is increased a reverse transition from a multicellular structure to a unicellular pattern occurs through a gradual decrease in the number of cells. In addition, it is shown that shear-driven instabilities cannot develop for radius ratios larger than a value close to R = 1.15.

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.

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.

Natural Convection from a Horizontal Cylinder—Laminar Regime

1981 ◽  
Vol 103 (3) ◽  
pp. 522-527 ◽  
Author(s):  
B. Farouk ◽  
S. I˙. Gu¨c¸eri
Keyword(s):  
Natural Convection ◽  
Horizontal Cylinder ◽  
Heat Transfer Characteristics ◽  
Convective Flows ◽  
Finite Difference Numerical Method ◽  
Temperature Boundary ◽  
Recirculation Zones ◽  
Boussinesq Fluid ◽  
Temperature Boundary Condition ◽  
Good Agreement

A finite-difference numerical method has been adopted to generate flow patterns and heat transfer characteristics for laminar, steady-state, two-dimensional natural convection around a circular cylinder submerged in an unbounded Boussinesq fluid. The approach allows the use of nonuniform as well as uniform specified temperature and heat flux distributions over the cylindrical surface. Part of the results are generated for reverse convective flows with recirculation zones which occur when part of the cylinder is below the ambient temperature while the remaining part is above. The results for uniform temperature boundary condition are in good agreement with the experimental data and other solutions available in literature.

scholarly journals Lattice Boltzmann Simulation of Natural Convection in an Annulus between a Hexagonal Cylinder and a Square Enclosure

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
L. El Moutaouakil ◽  
Z. Zrikem ◽  
A. Abdelbaki
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Square Enclosure ◽  
Lattice Boltzmann Simulation ◽  
Laminar Natural Convection ◽  
Heat Transfers ◽  
Boltzmann Method ◽  
Vertical Case

Laminar natural convection in a water filled square enclosure containing at its center a horizontal hexagonal cylinder is studied by the lattice Boltzmann method. The hexagonal cylinder is heated while the walls of the cavity are maintained at the same cold temperature. Two orientations are treated, corresponding to two opposite sides of the hexagonal cross-section which are horizontal (case I) or vertical (case II). For each case, the results are presented in terms of streamlines, isotherms, local and average convective heat transfers as a function of the dimensionless size of the hexagonal cylinder cross-section (0.1≤B≤0.4), and the Rayleigh number (103≤Ra≤106).

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

scholarly journals A RANS K-? SIMULATION OF 2D TURBULENT NATURAL CONVECTION IN AN ENCLOSURE WITH HEATING SOURCES

2019 ◽  
Vol 20 (1) ◽  
pp. 229-244
Author(s):  
Mehdi Ahmadi ◽  
Seyed Ali Agha Mirjalily ◽  
Seyed Amir Abbas Oloomi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Turbulent Natural Convection ◽  
Cold Source ◽  
Thermal Sources

ABSTRACT: This study is conducted to investigate turbulent natural convection flow in an enclosure with thermal sources using the low-Reynolds number (LRN) k-? model. This enclosure has a cold source with temperature Tc and a hot source with temperature Th as thermal sources, other walls of the enclosure are adiabatic. The aim of this study is to predict the effect of change in Rayleigh number, repositioning of cold and hot sources, and thermal sources aspect ratio on the flow field, temperature, and rate of heat transfer. To achieve this aim, the equations of continuity, momentum, energy, turbulent kinetic energy, and kinetic energy dissipation are employed in the case of 2D turbulence with constant thermo-physical properties except the density in the buoyancy term (Boussinesq approximation). To numerically solve these equations, the finite volume method and SIMPLE algorithm are used. According to the modeling results, the most optimal temperature distribution in the enclosure is seen when the hot source is below the cold source. With decreasing distance between hot and cold sources, heat transfer rate increases. The maximal heat transfer rate is derived via study of the heating sources aspect ratio. In constant positions of cold and hot sources on a wall, the heat transfer rate increases with increasing Rayleigh number (Ra=109-1011). ABSTAK: Kajian ini dijalankan bagi mengkaji perubahan semula jadi aliran perolakan dalam tempat tertutup dengan sumber haba menggunakan model k-? nombor Reynolds-rendah (LRN). Bekas tertutup ini mempunyai dua sumber haba iaitu sumber sejuk dengan suhu Tc dan sumber panas dengan suhu Th, manakala dinding lain bekas ini adalah adiabatik. Tujuan kajian ini adalah bagi mengesan perubahan nombor Rayleigh, mengubah sumber sejuk dan panas dan nisbah sumber haba kepada kawasan aliran, suhu dan halaju perubahan haba. Bagi mencapai tujuan tersebut, persamaan sambungan, momentum, tenaga, tenaga kinetik perolakan, dan pengurangan tenaga kinetik telah dilaksanakan dalam kes perolakan 2D dengan sifat fizikal-haba berterusan (malar) kecuali isipadu terma keapungan (anggaran Boussinesq). Bagi menyelesaikan persamaan ini secara berangka, kaedah isipadu terhad dan algorithma MUDAH telah digunakan. Berdasarkan keputusan model, suhu distribusi optimal dalam bekas tertutup dilihat apabila sumber panas adalah kurang daripada sumber sejuk. Dengan pengurangan jarak antara sumber panas dan sejuk, kadar pertukaran haba meningkat. Kadar pertukaran haba maksima telah diperoleh melalui kajian nisbah  aspek sumber pemanasan. Kadar pertukaran haba bertambah dengan bertambahnya nombor Rayleigh  (Ra=109-1011), pada posisi tetap sumber sejuk dan panas pada dinding bekas.

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