scholarly journals Testing the Magnetohydrodynamic Analysis Software with Natural Convection and Geodynamo Problems

2021 ◽  
pp. 6-13
Author(s):  
И. В. Бычин
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Control Volume ◽  
Benchmark Problems ◽  
Quick Method ◽  
Simpler Algorithm ◽  
Induction Equation ◽  
Hydromagnetic Dynamo ◽  
Volume Method

В рамках метода контрольного объема разработан программный код для численного решения задач неидеальной магнитной гидродинамики вязкой несжимаемой жидкости на структурированных разнесенных сетках в сферических координатах. При дискретизации уравнения индукции магнитного поля использован алгоритм ограниченного переноса (Сonstrained Transport Algorithm) и схема QUICK с методом отложенной коррекции для аппроксимации конвективных членов. Для решения уравнений гидродинамики использован алгоритм SIMPLER. Программный код разработан для моделирования естественной конвекции и гидромагнитного динамо во вращающемся шаре или сферическом слое. Представлены результаты решения тестовых задач естественной конвекции и геодинамо с вакуумными граничными условиями, демонстрирующие достаточно точное соответствие результатам эталонных расчетов. Программное обеспечение разработано для ускорителей вычислений, поддерживающих технологию CUDA, с использованием набора расширений к языку программирования Фортран.   Using the control volume method we developed the software for the numerical solution of viscous incompressible fluid resistive magnetohydrodynamics problems on structured staggered meshes in spherical coordinates. The constrained transport algorithm and the QUICK method with delayed correction for the approximation of the convective terms were used for the discretization of the magnetic field induction equation. The SIMPLER algorithm was applied to solving the hydrodynamic equations. We developed software for modeling natural convection and the hydromagnetic dynamo in a rotating sphere or spherical shell. We proposed an algorithm for the numerical solution of the geodynamo problem with vacuum boundary conditions. The results of solving natural convection and geodynamo benchmark problems with vacuum boundary conditions are presented; they demonstrate a fairly accurate agreement with the reference calculations. The software supports CUDA-enabled accelerators and uses a set of extensions to the Fortran programming language.

scholarly journals Numerical study of the coupled natural convection with surface radiation in a cylindrical annular enclosure

2020 ◽  
Vol 330 ◽  
pp. 01029
Author(s):  
Mohamed Amine MEDEBBER ◽  
Abderrahmane AISSA ◽  
Belkacem OULD SAID ◽  
Noureddine RETIEL ◽  
Mohammed EL GANAOUI
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Surface Radiation ◽  
Navier Stokes ◽  
Simpler Algorithm ◽  
Energy Equations ◽  
Volume Method ◽  
Rayleigh Numbers ◽  
Total Average

The interaction of natural convection with thermal radiation of black surfaces in a cylindrical enclosure filled with air has been numerically investigated. The steady-state continuity, Navier-Stokes and energy equations were discretized using the control volume method and solved numerically via the SIMPLER algorithm. Effects of Rayleigh number (Ra), wall emissivity (εp) and height ratio parameter (X) are studied. The result shows that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers. The total average Nusselt number has also been discussed for valuating heat transfer through the enclosure.

Numerical Simulation of Natural Convection in a Mold

2010 ◽  
Vol 297-301 ◽  
pp. 456-461
Author(s):  
Mohsen Pirmohammadi ◽  
Ghanbar Ali Sheikhzadeh ◽  
Majid Ghassemi ◽  
Mohsen Hamedi
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Linear Equations ◽  
Convection Heat Transfer ◽  
Square Enclosure ◽  
Simpler Algorithm ◽  
Volume Method ◽  
Hot Surface

Numerical study of natural convection heat transfer inside a differentially heated square enclosure with adiabatic horizontal walls and vertical isothermal walls is investigated. Two insulated ribs are symmetrically located on horizontal walls. The governing non-linear equations are solved in a two-dimensional domain using a control volume method and the SIMPLER algorithm for the velocity–pressure coupling is employed. The results will be presented in forms of streamlines, isotherms and Nusselt number for Rayleigh number 106. It is shown that for small rib height the isotherms indicate the laminar boundary regime with high temperature gradient near the bottom of the hot surface and the top of cold one. However, as rib height increases this boundary layer is vanished. Also it is found that as the length and height of the ribs increase the mean Nusselt number decreases.

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.

Numerical Study of Natural Convection in Vertical Cylindrical Annular Enclosure Filled with Cu-Water Nanofluid under Magnetic Fields

2019 ◽  
Vol 392 ◽  
pp. 123-137 ◽  
Author(s):  
Mohamed A. Medebber ◽  
Abderrahmane Aissa ◽  
Mohamed El Amine Slimani ◽  
Noureddine Retiel
Keyword(s):  
Natural Convection ◽  
Magnetic Fields ◽  
Volume Fraction ◽  
Numerical Study ◽  
Physical Parameters ◽  
Cold Temperatures ◽  
Simpler Algorithm ◽  
Wide Range ◽  
Nanoparticles Volume Fraction ◽  
Volume Method

The two dimensional study of natural convection in vertical cylindrical annular enclosure filled with Cu-water nanofluid under magnetic fields is numerically analyzed. The vertical walls are maintained at different uniform hot and cold temperatures, THand TC, respectively. The top and bottom walls of the enclosure are thermally insulated. The governing equations are solved numerically by using a finite volume method. The coupling between the continuity and momentum equations is effected using the SIMPLER algorithm. Numerical analysis has been carried out for a wide range of Rayleigh number (103≤Ra≤106), Hartmann number (1 ≤Ha≤100) and nanoparticles volume fraction (0 ≤φ≤0.08). The influence of theses physical parameters on the streamlines, isotherms and average Nusselt has been numerically investigated.

Basic Boundary Conditions for Incompressible and Compressible Flows Using Unstructured Meshes

2003 ◽  
Author(s):  
Branislav Basara
Keyword(s):  
Convergence Rate ◽  
Boundary Conditions ◽  
Compressible Flows ◽  
Unstructured Grids ◽  
Control Volume ◽  
Unstructured Meshes ◽  
Control Volume Method ◽  
Polyhedral Cells ◽  
Volume Method ◽  
Basic Boundary

The paper compiles the basic and frequently used boundary conditions in CFD calculations. Regardless of the type of boundary conditions, Dirichlet or Neumman, there are very important differences in the implementation procedure depending on the solved equations as well as on variables which are updated on the boundaries. Boundary conditions in the frame of the control volume method presented here, are adopted for the unstructured grids consisting of arbitrary polyhedral cells. There are no limitations on the employment of boundary conditions regarding mesh type. Some special treatments to improve results and the convergence rate are proposed. The emphasis is on the wall and the pressure boundaries.

Determining the Optimum Arrangement of Micromixers in a Microchannel Filled with CuO-Water Nanofluid via Minimizing Entropy Generation

2017 ◽  
Vol 378 ◽  
pp. 39-58 ◽  
Author(s):  
Ahmad Ababaei ◽  
Mahmoud Abbaszadeh ◽  
Ali Akbar Abbasian Arani
Keyword(s):  
Boundary Conditions ◽  
Parallel Plate ◽  
Slip Velocity ◽  
Temperature Jump ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Governing Equations ◽  
Simpler Algorithm ◽  
Optimum Arrangement ◽  
Volume Method

In this study, the flow of CuO-water nanofluid in a parallel-plate microchannel in the presence of several micromixers is examined to find optimum arrangements of the micromixers. The governing equations, which are accompanied with the slip velocity and temperature jump boundary conditions, are solved by the Finite Volume Method and SIMPLER algorithm. The study is conducted for the Reynolds numbers in the range of 10 ≤ Re ≤ 100, Knudsen numbers ranging of 0 ≤ Kn ≤ 0.1 and volume fraction of nanoparticles ranging of 0 ≤ ϕ ≤ 4%. The results show that the optimum arrangements of the micromixers belong to cases in which the heights of micromixers are smaller, the distance between them is lower, and their numbers are more.

scholarly journals Numerical investigation of natural convection heat transfer in a symmetrically cooled square cavity with a thin fin on its bottom wall

2014 ◽  
Vol 18 (4) ◽  
pp. 1119-1132 ◽  
Author(s):  
Saeid Jani ◽  
Mostafa Mahmoodi ◽  
Meysam Amini ◽  
Jafar Jam
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Constant Temperature ◽  
Convection Heat Transfer ◽  
Bottom Wall ◽  
Square Cavity ◽  
Remarkable Effect ◽  
Simpler Algorithm ◽  
The Right ◽  
Volume Method

In the present paper, natural convection fluid flow and heat transfer in a square cavity heated from below and cooled from sides and the ceiling with a thin fin attached to its hot bottom wall is investigated numerically. The right and the left walls of the cavity, as well as its horizontal top wall are maintained at a constant temperature Tc, while the bottom wall is kept at a constant temperature Th ,with Th > Tc. The governing equations are solved numerically using the finite volume method and the couple between the velocity and pressure fields is done using the SIMPLER algorithm. A parametric study is performed and the effects of the Rayleigh number and the length of the fin on the flow pattern and heat transfer inside the cavity are investigated. Two competing mechanisms that are responsible for the flow and thermal modifications are observed. One is the resistance effect of the fin due to the friction losses which directly depends on the length of the fin, whereas the other is due to the extra heating of the fluid that is offered by the fin. It is shown that for high Rayleigh numbers, placing a hot fin at the middle of the bottom wall has more remarkable effect on the flow field and heat transfer inside the cavity.

Characteristics of high Rayleigh number two-dimensional convection in an open-top porous layer heated from below

1999 ◽  
Vol 394 ◽  
pp. 241-260 ◽  
Author(s):  
ABDELLAH S. M. CHERKAOUI ◽  
WILLIAM S. D. WILCOCK
Keyword(s):  
Rayleigh Number ◽  
Control Volume ◽  
Flow Patterns ◽  
Convective System ◽  
Two Dimensional ◽  
Simpler Algorithm ◽  
Convective Pattern ◽  
Volume Method ◽  
Rayleigh Numbers ◽  
Type Of Transition

Using a control-volume method and the simpler algorithm, we computed steady-state and time-dependent solutions for two-dimensional convection in an open-top porous box, up to a Rayleigh number of 1100. The evolution of the convective system from onset to high Rayleigh numbers is characterized by two types of transitions in the flow patterns. The first type is a decrease in the horizontal aspect ratio of the cells. We observe two such bifurcations. The first occurs at Ra = 107.8 when the convective pattern switches from a steady one-cell roll to a steady two-cell roll. The second occurs at Ra ≈ 510 when an unsteady two-cell roll evolves to a steady four-cell roll. The second type of transition is from a steady to an unsteady pattern and we also observe two of these bifurcations. The first occurs at Ra ≈ 425 in the two-cell convective pattern; the second at Ra ≈ 970 in the four-cell pattern. Both types of bifurcations are associated with an increase in the average vertical convective heat transport. In the bi-cellular solutions, the appearance of non-periodic unsteady convection corresponds to the onset of the expected theoretical scaling Nu ∝ Ra and also to the onset of plume formation. Although our highest quadri-cellular solutions show signs of non-periodic convection, they do not reach the onset of plume formation. An important hysterisis loop exists for Rayleigh numbers in the range 425–505. Unsteady convection appears only in the direction of increasing Rayleigh numbers. In the decreasing direction, steady quadri-cellular flow patterns prevail.

Numerical Solution of Richards' Equation With Control Volume Method

2004 ◽  
Vol 15 (4-5) ◽  
pp. 291-308
Author(s):  
George K. Arampatzis, ◽  
Christos D. Tzimopoulos, ◽  
Christos Η. Evangelides,
Keyword(s):  
Numerical Solution ◽  
Control Volume ◽  
Richards Equation ◽  
Control Volume Method ◽  
Volume Method
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