Numerical Calculation of Three-Dimensional Turbulent Natural Convection in a Cubical Enclosure Using a Two-Equation Model for Turbulence

1986 ◽  
Vol 108 (4) ◽  
pp. 806-813 ◽  
Author(s):  
H. Ozoe ◽  
A. Mouri ◽  
M. Hiramitsu ◽  
S. W. Churchill ◽  
N. Lior
Keyword(s):  
Natural Convection ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Spiral Flow ◽  
Vertical Side ◽  
Turbulent Natural Convection ◽  
Cubical Enclosure ◽  
Side Walls

This paper presents a model and numerical results for turbulent natural convection in a cubical enclosure heated from below, cooled on a portion of one vertical side wall and insulated on all other surfaces. Three-dimensional balances were derived for material, energy, and the three components of momentum, as well as for the turbulent kinetic energy k and the rate of dissipation of turbulent kinetic energy ε. The constants used in the model were the same as those used by Fraikin et al. for two-dimensional convection in a channel. Illustrative transient calculations were carried out for Ra = 106 and 107 and Pr = 0.7. Both the dominant component of the vector potential and the Nusselt number were found to converge to a steady state. Isothermal lines and velocity vectors for vertical cross sections normal to the cooled wall indicated three-dimensional effects near the side walls. A top view of the velocity vectors revealed a downward spiral flow near the side walls along the cooled vertical wall. A weak spiral flow was also found along the side walls near the wall opposing the partially cooled one. The highest values of the eddy diffusivity were 2.6 and 5.8 times the molecular kinematic viscosity for Ra = 106 and 107, respectively. A coaxial double spiral movement, similar to that previously reported for laminar natural convection, was found for the time-averaged flow field. This computing scheme is expected to be applicable to other thermal boundary conditions.

scholarly journals Numerical Study of Three- Dimensional Natural Convection in a Differentially Heated Cubical Enclosure

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Numerical Study ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Cubical Enclosure ◽  
Side Walls ◽  
The Right ◽  
Rayleigh Numbers

—A high-resolution, finite difference numerical studyis reported on three-dimensional steady-state natural convectionof air, for two Rayleigh numbers, in a cubical enclosure, which isheated differentially at one side walls. The temperature of thewall is TC except for the right vertical wall, in which is TH.Thedetails of the three-dimensional flow and thermal characteristicsare described.

Effect of Periodic Imposed Heat Flux on Three-Dimensional Natural Convection in a Partially Heated Cubical Enclosure

2016 ◽  
Vol 831 ◽  
pp. 83-91
Author(s):  
Lahoucine Belarche ◽  
Btissam Abourida
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Maximum Temperature ◽  
Cubical Enclosure ◽  
Simplec Algorithm ◽  
Volume Method

The three-dimensional numerical study of natural convection in a cubical enclosure, discretely heated, was carried out in this study. Two heating square sections, similar to the integrated electronic components, are placed on the vertical wall of the enclosure. The imposed heating fluxes vary sinusoidally with time, in phase and in opposition of phase. The temperature of the opposite vertical wall is maintained at a cold uniform temperature and the other walls are adiabatic. The governing equations are solved using Control volume method by SIMPLEC algorithm. The sections dimension ε = D / H and the Rayleigh number Ra were fixed respectively at 0,35 and 106. The average heat transfer and the maximum temperature on the active portions will be examined for a given set of the governing parameters, namely the amplitude of the variable temperatures a and their period τp. The obtained results show significant changes in terms of heat transfer, by proper choice of the heating mode and the governing parameters.

Enhancement of Heat Transfer Rate by Application of a Static Magnetic Field During Natural Convection of Liquid Metal in a Cube

1997 ◽  
Vol 119 (2) ◽  
pp. 265-271 ◽  
Author(s):  
T. Tagawa ◽  
H. Ozoe
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Natural Convection ◽  
Liquid Metal ◽  
Average Nusselt Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Heated Wall ◽  
Horizontal Magnetic Field ◽  
Cubical Enclosure

Natural convection of liquid metal in a cubical enclosure under an external magnetic field was investigated by three-dimensional numerical analyses. The system parameters were Ra = 105 and 106, Pr = 0.025, and Ha = 0–1000. One vertical wall of the cubical enclosure was heated, and the opposing vertical wall was cooled, both isothermally; the other four walls were thermally insulated. A uniform horizontal magnetic field was applied parallel to the heated and cooled walls. At Ra = 105 and Ha = 50, the average Nusselt number on the heated wall attained almost the maximum value and was greater than that at Ha = 0. The velocity vectors along the vertical walls, and those along the horizontal planes, were rectified in a two-dimensional way at Ha = 50 or over, and the average Nusselt number decreased gradually for higher values of the Hartmann number. Similar characteristics were obtained at Ra = 106. The agreement with our earlier experiments was moderately good.

scholarly journals Sensitivity analysis of a coupled hydrodynamic-vegetation model using the effectively subsampled quadratures method (ESQM v5.2)

2017 ◽  
Vol 10 (12) ◽  
pp. 4511-4523 ◽  
Author(s):  
Tarandeep S. Kalra ◽  
Alfredo Aretxabaleta ◽  
Pranay Seshadri ◽  
Neil K. Ganju ◽  
Alexis Beudin
Keyword(s):  
Sensitivity Analysis ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Aquatic Vegetation ◽  
Three Dimensional ◽  
Sensitivity Analyses ◽  
Stem Density ◽  
Sobol Indices ◽  
Plant Stem ◽  
Wave Induced

Abstract. Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as the Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant stem density, height, and, to a lesser degree, diameter. Wave dissipation is mostly dependent on the variation in plant stem density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance to optimize efforts and reduce exploration of parameter space for future observational and modeling work.

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.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

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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