Unsteady natural convection in a triangular enclosure induced by absorption of radiation – a revisit by improved scaling analysis

2009 ◽  
Vol 622 ◽  
pp. 75-102 ◽  
Author(s):  
YADAN MAO ◽  
CHENGWANG LEI ◽  
JOHN C. PATTERSON
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Scaling Analysis ◽  
Buoyancy Driven Flows ◽  
Flow Features ◽  
Radiation Induced ◽  
Maximum Water ◽  
Triangular Enclosure ◽  
Flow Domain ◽  
Unsteady Natural Convection

The present study is concerned with radiation-induced natural convection in a water-filled triangular enclosure with a sloping bottom, which is directly relevant to buoyancy-driven flows in littoral regions. An improved scaling analysis is carried out to reveal more detailed features of the flow than a previously reported analysis. Two critical functions of the Rayleigh number with respect to the horizontal position are derived from the scaling for identifying the distinctness and stability of the thermal boundary layer. Four flow scenarios are possible, depending on the bottom slope and the maximum water depth. For each flow scenario, the flow domain may be composed of multiple subregions with distinct thermal and flow features, depending on the Rayleigh number. The dividing points between neighbouring subregions are determined by comparisons of the critical functions of the Rayleigh number with the global Rayleigh number. Position-dependent scales have been established to quantify the flow properties in different subregions. The different flow regimes for the case with relatively large bottom slopes and shallow waters are examined in detail. The present scaling results are verified by numerical simulations.

scholarly journals Unsteady natural convection in a triangular enclosure induced by absorption of radiation

2002 ◽  
Vol 460 ◽  
pp. 181-209 ◽  
Author(s):  
CHENGWANG LEI ◽  
JOHN C. PATTERSON
Keyword(s):  
Numerical Simulation ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Regimes ◽  
Scaling Analysis ◽  
Triangular Domain ◽  
Typical Situation ◽  
Relative Value ◽  
Dimensional Parameters ◽  
Unsteady Natural Convection

The authors have previously reported a model experiment on the unsteady natural convection in a triangular domain induced by the absorption of solar radiation. This issue is reconsidered here both analytically and numerically. The present study consists of two parts: a scaling analysis and a numerical simulation. The scaling analysis for small bottom slopes reveals that a number of flow regimes are possible depending on the Rayleigh number and the relative value of certain non-dimensional parameters describing the flow. In a typical situation, the flow can be classified broadly into a conductive, a transitional or a convective regime determined merely by the Rayleigh number. Proper scales have been established to quantify the flow properties in each of these flow regimes. The numerical simulation has verified the scaling results.

Unsteady nearshore natural convection induced by constant isothermal surface heating

2012 ◽  
Vol 707 ◽  
pp. 342-368 ◽  
Author(s):  
Yadan Mao ◽  
Chengwang Lei ◽  
John C. Patterson
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Velocity ◽  
Thermal Boundary Layer ◽  
Scaling Analysis ◽  
Local Flow ◽  
Entire Flow ◽  
Flow Domain

AbstractThe present investigation is concerned with natural convection in a wedge-shaped domain induced by constant isothermal heating at the water surface. Complementary to the study of daytime heating by solar radiation relevant to nearshore regions of lakes and reservoirs previously reported by the same authors, this study focuses on sensible heating imposed by the atmosphere when it is warmer than the water body. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. Two flow regimes are identified depending on the comparison between the Rayleigh number and the inverse of the square of the bottom slope. For the lower Rayleigh number regime, the entire flow domain eventually becomes isothermal and stationary. For the higher Rayleigh number regime, the flow domain is composed of two distinct subregions, a conductive subregion near the shore and a convective subregion offshore. Within the conductive subregion, the maximum local flow velocity occurs when the thermal boundary layer reaches the local bottom, and the subregion eventually becomes isothermal and stationary. In the offshore convective subregion, a steady state is reached with a distinct thermal boundary layer below the surface and a steady flow velocity. The dividing position between the two subregions and the major time and velocity scales governing the flow development in both subregions are proposed by the scaling analysis and validated by corresponding numerical simulation.

Unsteady natural convection in a cavity with internal heating and cooling

1984 ◽  
Vol 140 ◽  
pp. 135-151 ◽  
Author(s):  
John C. Patterson
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Transient Flow ◽  
Scaling Analysis ◽  
Steady State Flow ◽  
Internal Heating ◽  
Sources And Sinks ◽  
Heating And Cooling ◽  
Unsteady Natural Convection

The problem of transient natural convection in a cavity of aspect ratio A < 1 driven by internal buoyancy sources and sinks distributed linearly in the horizontal and uniformly in the vertical is considered. Scaling analysis is used to show that a number of possible transient flow regions are possible, collapsing ultimately onto one of conductive, transitional, or convective steady-state flow regimes. A number of numerical solutions are obtained, and their relationships to the scaling analysis are discussed.

scholarly journals Unsteady near-shore natural convection induced by surface cooling

2009 ◽  
Vol 642 ◽  
pp. 213-233 ◽  
Author(s):  
YADAN MAO ◽  
CHENGWANG LEI ◽  
JOHN C. PATTERSON
Keyword(s):  
Natural Convection ◽  
Scaling Analysis ◽  
Mean Flow ◽  
Flow Properties ◽  
Surface Cooling ◽  
Environmental Implications ◽  
Near Shore ◽  
Radiation Induced ◽  
The Stability ◽  
Convection Dominated

Natural convection in calm near-shore waters induced by daytime heating or nighttime cooling plays a significant role in cross-shore exchanges with significant biological and environmental implications. Having previously reported an improved scaling analysis on the daytime radiation-induced natural convection, the authors present in this paper a detailed scaling analysis quantifying the flow properties at varying offshore distances induced by nighttime surface cooling. Two critical functions of offshore distance have been derived to identify the distinctness and the stability of the thermal boundary layer. Two flow scenarios are possible depending on the bottom slope. For the relatively large slope scenario, three flow regimes are possible, which are discussed in detail. For each flow regime, all the possible distinctive subregions are identified. Two different sets of scaling incorporating the offshore-distance dependency have been derived for the conduction-dominated region and stable-convection-dominated region respectively. It is found that the scaling for flow in the stable-convection-dominated region also applies to the time-averaged mean flow in the unstable region. The present scaling results are verified by numerical simulations.

Numerical Simulation of Natural Convection of Water Near Its Density Maximum Around a Cylinder Inside a Concentric Triangular Enclosure

2012 ◽  
Author(s):  
Yu-Peng Hu ◽  
You-Rong Li ◽  
Chun-Mei Wu
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Inclination Angle ◽  
Temperature Fields ◽  
Density Inversion ◽  
Density Maximum ◽  
Triangular Enclosure ◽  
Density Inversion Parameter ◽  
Boussinesq Fluid

In this paper, a series of numerical simulations for natural convection of water near its maximum-density around a cylinder inside a concentric triangular enclosure were conducted using finite volume method. The effects of the density inversion parameter, the aspect ratio, the Rayleigh number and the inclination angle on natural convection were discussed. Furthermore, the flow and temperature fields, the local and average Nusselt numbers at different parameters were obtained and analyzed. The results show that the flow pattern and temperature distribution are unique for various density inversion parameters and inclination angles. The density inversion parameter, the aspect ratio, the Rayleigh number all have significant effects on the overall heat transfer rates, except for the inclination angle. The present results can also contribute further information on the natural convection of non-Boussinesq fluid in enclosures.

Unsteady natural convection in a triangular enclosure

1986 ◽  
Vol 20 (5) ◽  
pp. 811-815 ◽  
Author(s):  
Yu. E. Karyakin ◽  
Yu. A. Sokovishin
Keyword(s):  
Natural Convection ◽  
Triangular Enclosure ◽  
Unsteady Natural Convection

Unsteady natural convection in a cavity with non-uniform absorption of radiation

1993 ◽  
Vol 256 ◽  
pp. 133-161 ◽  
Author(s):  
Michael J. Coates ◽  
John C. Patterson
Keyword(s):  
Natural Convection ◽  
Attenuation Coefficient ◽  
Numerical Experiments ◽  
Laboratory Experiments ◽  
Surface Flux ◽  
Parameter Range ◽  
Scaling Analysis ◽  
Naturally Occurring ◽  
Unsteady Natural Convection

A study of the unsteady natural convection in a cavity which was heated by the absorption of radiation entering through part of the surface is reported. While a general scaling analysis is quite complex, involving five separate timescales, most naturally occurring problems fall into just one regime, and it is only this regime which is discussed. To test the scaling, a series of laboratory experiments were performed in which the radiation parameters (surface flux and attenuation coefficient) were varied. The method by which these parameters were determined is also discussed. Numerical experiments were used to extend the parameter range, and the results of all these experiments confirmed the validity of the scaling over a range of parameters.

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