Natural Convection From a Horizontal Cylinder—Turbulent Regime

1982 ◽  
Vol 104 (2) ◽  
pp. 228-235 ◽  
Author(s):  
B. Farouk ◽  
S. I. Gu¨c¸eri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Equation Model ◽  
Turbulence Structure ◽  
Turbulent Regime ◽  
Closed Set ◽  
Number Range ◽  
Turbulent Natural Convection ◽  
Nusselt Numbers

A two-equation model has been adopted in obtaining numerical solutions of turbulent natural convection from an isothermal horizontal circular cylinder. The k-ε model employed in this study characterizes turbulence through the kinetic energy and its volumetric rate of dissipation. The transport equations for these two variables, along with those for time-averaged stream function, vorticity, and temperature, form a closed set of five coupled partial differential equations. These equations are solved for the entire flow domain, without boundary layer approximations. Buoyancy effects on the turbulence structure are also accounted for. Results are presented for a Rayleigh number range of 5×107 to 1010 and the average Nusselt numbers are compared with existing correlations and limited available experimental data.

Laminar and Turbulent Natural Convection in the Annulus Between Horizontal Concentric Cylinders

1982 ◽  
Vol 104 (4) ◽  
pp. 631-636 ◽  
Author(s):  
B. Farouk ◽  
S. I. Gu¨c¸eri
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Solutions ◽  
Outer Cylinder ◽  
Turbulence Structure ◽  
Number Range ◽  
Turbulent Natural Convection ◽  
Cylinder Diameter ◽  
Concentric Cylinders ◽  
Good Agreement

Numerical solutions are presented for the steady-state, two-dimensional natural convection in the annulus between two horizontal concentric cylinders which are held at different constant temperatures. Solutions for the laminar case are obtained up to Rayleigh number (based on gap width, L) of 105. Turbulent flow results are presented for the Rayleigh number range of 106–107. the k-ε turbulence model has been applied to obtain the results. Buoyancy effects on the turbulence structure are also accounted for. The results for both the laminar and turbulent cases are in good agreement with available experimental data and other solutions in the literature. All results presented are for the outer cylinder diameter to inner cylinder diameter ratio of 2.6.

Observed Flow Reversals and Measured-Predicted Nusselt Numbers for Natural Convection in a One-Sided Heated Vertical Channel

1984 ◽  
Vol 106 (2) ◽  
pp. 325-332 ◽  
Author(s):  
E. M. Sparrow ◽  
G. M. Chrysler ◽  
L. F. Azevedo
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Threshold Value ◽  
Channel Length ◽  
Heated Wall ◽  
Number Range ◽  
Channel One ◽  
Recirculating Flow ◽  
Nusselt Numbers

A three-part study encompassing both experiment and analysis has been performed for natural convection in an open-ended vertical channel. One of the principal walls of the channel—the heated wall—was maintained at a uniform temperature, while the other principal wall was unheated. The experiments, which included flow visualization and Nusselt number measurements, were carried out with water in the channel and in the ambient which surrounds the channel. At Rayleigh numbers which exceeded a threshold value, the visualization revealed a pocket of recirculating flow situated adjacent to the unheated wall in the upper part of the channel. The recirculation was fed by fluid drawn into the top of the channel, adjacent to the unheated wall. Average Nusselt numbers for the heated wall were measured over a three orders of magnitude range of a single correlating parameter, which includes the Rayleigh number and the ratio of the channel length to the interwall spacing. The Nusselt numbers were found to be unaffected by the presence of the recirculation zone. Numerical solutions obtained via a parabolic finite difference scheme yielded Nusselt numbers in good agreement with those of experiment. The numerical results covered the Prandtl number range from 0.7 to 10.

Tin Solidification in the Presence of Turbulent Natural Convection

2002 ◽  
Author(s):  
Luis Joaquim Cardoso Rocha ◽  
Angela O. Nieckele
Keyword(s):  
Natural Convection ◽  
Domain Size ◽  
Solidification Process ◽  
Special Treatment ◽  
Liquid Region ◽  
Turbulent Regime ◽  
Closed Cavity ◽  
Turbulent Natural Convection ◽  
Solid Region ◽  
Volume Method

The solidification process of tin, inside a closed cavity, is numerically investigated by the finite volume method. A non-orthogonal system of coordinates is employed to adapt to the irregular geometry, with a moving mesh to account for the changing domain size. The momentum equations are solved for the contravariant velocity components. The SIMPLEC algorithm handles the coupling between velocity and pressure. A special treatment is given at the liquid-solid interface to obtain the momentum and energy balance. The phase change process is strongly influenced by natural convection in the melt. At the beginning of the process, the cavity is full of liquid, and the natural convection slightly influences the interface shape. But as the liquid region diminishes during the process, the influence of natural convection increases. Further, at the same time as the liquid size region is reduced, the intensity of the flow increases, and the flow can became turbulent, affecting the heat flux at the interface and consequently the size of the solid region. Therefore, the purpose of the paper is to analyze the influence of the turbulent regime on the kinetics of the solidification process. The turbulent flow is taken into account by a low Reynolds number model. The influence of the Rayleigh number on the velocity and temperature field is investigated.

Turbulent Natural Convection Flow on a Heated Vertical Wall Immersed in a Stratified Atmosphere

1989 ◽  
Vol 111 (2) ◽  
pp. 378-384 ◽  
Author(s):  
A. K. Kulkarni ◽  
S. L. Chou
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Leading Edge ◽  
Transitional Flow ◽  
Convection Flow ◽  
Ambient Atmosphere ◽  
Ambient Conditions ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection

This paper presents a comprehensive mathematical model and numerical solutions for a natural convection flow over an isothermal, heated, vertical wall immersed in an ambient atmosphere that is thermally stratified. The model assumes a laminar flow near the leading edge, which then becomes a transitional flow, and finally becomes fully turbulent away from the leading edge. Effects of several typical cases of ambient stratification on heat transfer to the wall, peak velocity, and temperature are examined. It is found that the velocity field is affected more significantly by the “memory” of upstream ambient conditions than the temperature field.

Entropy Generation in Laminar and Turbulent Natural Convection Heat Transfer From Vertical Cylinder With Annular Fins

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Jnana Ranjan Senapati ◽  
Sukanta Kumar Dash ◽  
Subhransu Roy
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Entropy Generation ◽  
Vertical Cylinder ◽  
Turbulent Regime ◽  
Maximum Heat ◽  
Turbulent Natural Convection ◽  
Maximum Heat Transfer ◽  
Wide Range ◽  
Annular Fins

Entropy generation due to natural convection has been calculated for a wide range of Rayleigh number (Ra) in both laminar (104 ≤ Ra ≤ 108) and turbulent (1010 ≤ Ra ≤ 1012) flow regimes, for diameter ratio of 2 ≤ D/d ≤ 5, for an isothermal vertical cylinder fitted with annular fins. In the laminar regime, the entropy generation was predominantly caused by heat transfer (conduction and convection) and the viscous contribution was negligible with respect to heat transfer. But in the turbulent regime, entropy generation due to fluid friction is significant enough although heat transfer entropy generation is still dominant. The results demonstrate that the degree of irreversibility is higher in case of finned configuration when compared with unfinned one. With the deployment of a merit function combining the first and second laws of thermodynamics, we have tried to delineate the thermodynamic performance of finned cylinder with natural convection. So, we have defined the ratio (I/Q)finned/(I/Q)unfinned. The ratio (I/Q)finned/(I/Q)unfinned gets its minimum value at optimum fin spacing where maximum heat transfer occurs in turbulent flow, whereas in laminar flow the ratio (I/Q)finned/(I/Q)unfinned decreases continuously with the increase in number of fins.

Turbulent natural convection along a vertical plate immersed in a stably stratified fluid

2009 ◽  
Vol 636 ◽  
pp. 41-57 ◽  
Author(s):  
EVGENI FEDOROVICH ◽  
ALAN SHAPIRO
Keyword(s):  
Natural Convection ◽  
Vertical Plate ◽  
Stationary Flow ◽  
Stratified Fluid ◽  
Buoyancy Frequency ◽  
Convection Flow ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Turbulent Natural Convection ◽  
Oscillatory Phase

The paper considers the moderately turbulent natural convection flow of a stably stratified fluid along an infinite vertical plate (wall). Attention is restricted to statistically stationary flow driven by constant surface forcing (heating), with Prandtl number of unity. The flow is controlled by the surface energy production rateFs, molecular viscosity/diffusivity ν and ambient stratification in terms of the Brunt–Väisälä (buoyancy) frequencyN. Following the transition from a laminar to a turbulent regime, the simulated flow enters a quasi-stationary oscillatory phase. In this phase, turbulent fluctuations gradually fade out with distance from the wall, while periodic laminar oscillations persist over much larger distances before they fade out. The scaled mean velocity, scaled mean buoyancy and scaled second-order turbulence statistics display a universal behaviour as functions of distance from the wall for given value of dimensionless combinationFs/(νN2) that may be interpreted as an integral Reynolds number. In the conducted numerical experiments, this number varied in the range from 2000 to 5000.

Natural Convection in a Stably Heated Corner Filled With Porous Medium

1985 ◽  
Vol 107 (2) ◽  
pp. 293-298 ◽  
Author(s):  
S. Kimura ◽  
A. Bejan
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Single Cell ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Number Range ◽  
Corner Flow ◽  
Horizontal Wall

This is a study of the single-cell natural convection pattern that occurs in a “stably heated” corner in a fluid-saturated porous medium, i.e., in the corner formed between a cold horizontal wall and a hot vertical wall situated above the horizontal wall, or in the corner between a hot horizontal wall and a cold vertical wall situated below the horizontal wall. Numerical simulations show that this type of corner flow is present in porous media heated from the side when a stabilizing vertical temperature gradient is imposed in order to suppress the side-driven convection. Based on numerical solutions and on scale analysis, it is shown that the single cell corner flow becomes increasingly more localized as the Rayleigh number increases. At the same time, the mass flow rate engaged in natural circulation and the conduction-referenced Nusselt number increase. Numerical results for the flow and temperature fields and for the net heat transfer rate are reported in the Darcy-Rayleigh number range 10–6000.

Flow Visualization Studies on Vortex Instability of Natural Convection Flow Over Horizontal and Slightly Inclined Constant-Temperature Plates

1988 ◽  
Vol 110 (3) ◽  
pp. 608-615 ◽  
Author(s):  
K. C. Cheng ◽  
Y. W. Kim
Keyword(s):  
Natural Convection ◽  
Flow Visualization ◽  
Ambient Air ◽  
Convection Flow ◽  
Turbulent Regime ◽  
Natural Convection Flow ◽  
Number Range ◽  
Grashof Number ◽  
Vortex Instability ◽  
Longitudinal Vortices

Flow visualization experiments were performed in a low-speed wind tunnel to study vortex instability of laminar natural convection flow along inclined isothermally heated plates having inclination angles from the horizontal of θ = 0, 5, 10, 15 and 20 deg. The temperature difference between plate surface and ambient air ranged from ΔT = 15.5 to 37.5°C and the local Grashof number range was Grx = 1.02×106 to 2.13×108. Three characteristic flow regimes were identified as follows: a two-dimensional laminar flow, a transition regime for developing longitudinal vortices, and a turbulent regime after the breakdown of the longitudinal vortices. Photographs are presented of side and top views of the flow and of cross-sectional views of the developing views of the developing secondary flow in the postcritical regime. Instability data of critical Grashof number and wavelength are presented and are compared with the theoretical predictions from the literature.

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