Turbulent Natural Convection in Enclosures With Clear Fluid and Completely Filled With Porous Material

2002 ◽  
Author(s):  
Edimilson J. Braga ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Turbulent Flows ◽  
Energy Transport ◽  
Numerical Solutions ◽  
Clear Fluid ◽  
Turbulent Natural Convection ◽  
Onset Of Turbulence ◽  
Volume Method

Steady laminar and turbulent natural convection in a two-dimensional square cavity, isothermally heated from the left side and cooled from the opposing side, is numerically analyzed using the finite volume method. Benchmark results for laminar and turbulent flows are compared with similar numerical solutions in the literature. The cases of clear and porous media are considered. Governing equations are written in terms of primitive variables and are recast into a general form. The effects of Rayleigh number on flow pattern and energy transport are investigated for Ra ranging from 103 to 1010 for clear media and 101 to 106 for porous media. The turbulence model used was the standard k–ε along with the wall function approach. All results presented herein showed reasonable agreement with calculations presented in the literature. Critical values for the Rayleigh number for the onset of turbulence are suggested. The main objective of this work is to validate a numerical tool for simulating turbulent natural convection in both clear and porous media.

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.

DIMENSIONLESS PHYSICAL-MATHEMATICAL MODELING OF TURBULENT NATURAL CONVECTION

2021 ◽  
Vol 20 (3) ◽  
pp. 37
Author(s):  
S. A. Verdério Júnior ◽  
V. L. Scalon ◽  
S. R. Oliveira ◽  
P. C. Mioralli ◽  
E. Avellone
Keyword(s):  
Mathematical Modeling ◽  
Natural Convection ◽  
Turbulent Flows ◽  
Convection Heat Transfer ◽  
Thermal Engineering ◽  
Physical Parameters ◽  
Problem Situation ◽  
Dimensionless Numbers ◽  
Turbulent Natural Convection ◽  
Cooling Coils

Natural convection heat transfer is present in the most diverse applications of Thermal Engineering, such as in electronic equipment, transmission lines, cooling coils, biological systems, etc. The correct physical-mathematical modeling of this phenomenon is crucial in the applied understanding of its fundamentals and the design of thermal systems and related technologies. Dimensionless analyses can be applied in the study of flows to reduce geometric and experimental dependence and facilitate the modeling process and understanding of the main influence physical parameters; besides being used in creating models and prototypes. This work presents a methodology for dimensionless physical-mathematical modeling of natural convection turbulent flows over isothermal plates, located in an “infinite” open environment. A consolidated dimensionless physical-mathematical model was defined for the studied problem situation. The physical influence of the dimensionless numbers of Grashof, Prandtl, and Turbulent Prandtl was demonstrated. The use of the Theory of Dimensional Analysis and Similarity and its application as a tool and numerical device in the process of building and simplifying CFD simulations were discussed.

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.

Computational fluid dynamics for modeling the turbulent natural convection in a double air-channel solar chimney system

2016 ◽  
Vol 27 (08) ◽  
pp. 1650095 ◽  
Author(s):  
I. Zavala-Guillén ◽  
J. Xamán ◽  
G. Álvarez ◽  
J. Arce ◽  
I. Hernández-Pérez ◽  
...  
Keyword(s):  
Natural Convection ◽  
Mexico City ◽  
Mass Flow ◽  
Solar Chimney ◽  
Turbulent Natural Convection ◽  
Air Turbulence ◽  
Warm Summer ◽  
Air Channel ◽  
Arid Desert ◽  
Volume Method

This study reports the modeling of the turbulent natural convection in a double air-channel solar chimney (SC-DC) and its comparison with a single air-channel solar chimney (SC-C). Prediction of the mass flow and the thermal behavior of the SC-DC were obtained under three different climates of Mexico during one summer day. The climates correspond to: tropical savannah (Mérida), arid desert (Hermosillo) and temperate with warm summer (Mexico City). A code based on the Finite Volume Method was developed and a [Formula: see text] turbulence model has been used to model air turbulence in the solar chimney (SC). The code was validated against experimental data. The results indicate that during the day the SC-DC extracts about 50% more mass flow than the SC-C. When the SC-DC is located in Mérida, Hermosillo and Mexico City, the air-changes extracted along the day were 60, 63 and 52, respectively. The air temperature at the outlet of the chimney increased up to 33%, 38% and 61% with respect to the temperature it has at the inlet for Mérida, Hermosillo and Mexico City, respectively.

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.

Numerical Investigation of the Onset of Steady Natural Convection in a Square Cavity Partially Filled With a Single Porous Block

2014 ◽  
Author(s):  
Vinicius Daroz ◽  
Silvio L. M. Junqueira ◽  
Admilson T. Franco ◽  
José L. Lage
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Critical Rayleigh Number ◽  
Contour Plot ◽  
Viscous Effects ◽  
Square Cavity ◽  
Heterogeneous Model ◽  
Porous Block ◽  
Vertical Walls ◽  
Volume Method

The critical Rayleigh number at the onset of natural convection within a square cavity filled with a centralized porous block was investigated. The porous medium is modeled by using the heterogeneous model and the governing equations are solved for each phase separately. The thermal gradient is applied from the bottom to the top horizontal walls while the vertical walls are kept adiabatic. The amount of solid within the cavity was kept constant by fixing both external and internal porosity in 36% and 40%, respectively. The equations are solved using the Finite Volume Method and the interpolation scheme for the convective terms is the Hybrid Scheme. For the pressure-velocity coupling, the SIMPLEC method is used. The effects on the conductive-convective regime transition, reads critical Rayleigh Number, characterized by the average Nusselt number and the heatlines contour plot, was investigated by varying the Rayleigh number and the porous block permeability. The results show that the so called critical Rayleigh number is affected by the block permeability. As the permeability decreases, the flow tends to recirculate around the block being squeezed against the cavity walls and therefore, more susceptible to viscous effects. A correlation to the critical Rayleigh number is presented as a function of the agglomerate permeability showing that the higher the permeability the lower the amount of energy required to trigger the convection.

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.

Pressure Drop Characteristics of Parallel-Plate Channel Flow With Porous Obstructions at Both Walls

2003 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Luzia A. Tofaneli
Keyword(s):  
Numerical Solutions ◽  
Control Volume ◽  
Computational Domain ◽  
Algebraic Equations ◽  
Clear Fluid ◽  
Simple Method ◽  
Periodic Cell ◽  
Porosity And Permeability ◽  
Volume Method ◽  
Turbulence Transport

In this work, numerical solutions are presented for turbulent flow in a channel containing fins made with porous material. The condition of spatially periodic cell is applied longitudinally along the channel. A macroscopic tow-equation turbulence model is employed in both the porous region and the clear fluid. The equations of momentum, mass continuity and turbulence transport equations are written for an elementary representative volume yielding a set of equations valid for the entire computational domain. These equations are discretized using the control volume method and the resulting systems of algebraic equations is relaxed with the SIMPLE method. Results are presented for the velocity field as a function of Reynolds number, porosity and permeability of the fins.

Scaling of the Turbulent Natural Convection Flow in a Heated Square Cavity

1994 ◽  
Vol 116 (2) ◽  
pp. 400-408 ◽  
Author(s):  
R. A. W. M. Henkes ◽  
C. J. Hoogendoorn
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection ◽  
Convection Boundary ◽  
Vertical Walls ◽  
Rayleigh Numbers

By numerically solving the Reynolds equations for air and water in a square cavity, with differentially heated vertical walls, at Rayleigh numbers up to 1020 the scalings of the turbulent natural convection flow are derived. Turbulence is modeled by the standard k–ε model and by the low-Reynolds-number k–ε models of Chien and of Jones and Launder. Both the scalings with respect to the Rayleigh number (based on the cavity size H) and with respect to the local height (y/H) are considered. The scalings are derived for the inner layer, outer layer, and core region. The Rayleigh number scalings are almost the same as the scalings for the natural convection boundary layer along a hot vertical plate. The scalings found are almost independent of the k–ε model used.

Three-Dimensional Numerical Analysis of Transient Natural Convection in Rectangular Enclosures

1979 ◽  
Vol 101 (1) ◽  
pp. 114-119 ◽  
Author(s):  
A. M. C. Chan ◽  
S. Banerjee
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Numerical Analysis ◽  
Turbulent Flows ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Experimental Results ◽  
Primitive Form ◽  
Conservation Equations ◽  
Practical Utility

A simple numerical technique of considerable practical utility for the solution of transient multidimensional natural convection problems is described. It is based on the solution of the conservation equations in primitive form. The technique can be extended to calculation of natural convection problems in porous media and in turbulent flows where the eddy viscosities and conductivities can be predicted. It has been applied to the solution of several two and three-dimensional natural convection problems. The solutions compare well with the numerical and experimental results published by other investigators.

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