Free Two-Dimensional Convective Bifurcation in a Horizontal Annulus

1992 ◽  
Vol 114 (1) ◽  
pp. 99-106 ◽  
Author(s):  
A. Cheddadi ◽  
J. P. Caltagirone ◽  
A. Mojtabi ◽  
K. Vafai
Keyword(s):  
Natural Convection ◽  
Initial Conditions ◽  
Laser Doppler Anemometry ◽  
Perturbation Solution ◽  
Two Dimensional ◽  
Governing Equations ◽  
Cylindrical Annulus ◽  
Numerical Predictions ◽  
Rayleigh Numbers ◽  
Good Agreement

Natural convection is investigated numerically and experimentally in a cylindrical annulus. The governing equations based on primitive variables are solved using Chorin’s method. In addition to the unicellular flows reported in the literature, depending on initial conditions, bicellular flows are observed for high Rayleigh numbers. The bifurcation point is determined numerically. The velocity field for unicellular flows is measured by laser-Doppler anemometry in an air-filled annulus. A perturbation solution is also presented. The experimental results are in good agreement with numerical predictions and the perturbation solution.

Comparative Numerical Simulation of Natural Convection in a Porous Horizontal Cylindrical Annulus

2014 ◽  
Vol 670-671 ◽  
pp. 613-616 ◽  
Author(s):  
Jabrane Belabid ◽  
Abdelkhalek Cheddadi
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Saturated Porous Medium ◽  
Published Data ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Concentric Cylinders ◽  
Good Agreement

This work presents a numerical study of the natural convection in a saturated porous medium bounded by two horizontal concentric cylinders. The governing equations (in the stream function and temperature formulation) were solved using the ADI (Alternating Direction Implicit) method and the Samarskii-Andreev scheme. A comparison between the two methods is conducted. In both cases, the results obtained for the heat transfer rate given by the Nusselt number are in a good agreement with the available published data.

scholarly journals A modification of the CABARET scheme for numerical simulation of multicomponent gaseous flows in two-dimensional domains

2015 ◽  
pp. 436-445
Author(s):  
А.В. Данилин ◽  
А.В. Соловьев ◽  
А.М. Зайцев
Keyword(s):  
Numerical Simulation ◽  
Initial Conditions ◽  
Experimental Studies ◽  
Two Dimensional ◽  
Governing Equations ◽  
Cabaret Scheme ◽  
Gaseous Flows ◽  
Multicomponent Gas ◽  
Good Agreement ◽  
Made In

Предложен явный численный алгоритм для расчета течений смесей идеальных газов в двумерных областях. Приведены физическая модель и уравнения движения смеси в консервативной и характеристической формах. Дискретизация уравнений движения произведена по методике Кабаре. Алгоритм испытан на задачах о прохождении ударной волны в воздухе через неоднородности из легкого и тяжелого газов, начальные условия для которых адаптированы из рассмотренных другими авторами натурных и численных экспериментов. Показано хорошее совпадение расчетов по предложенному алгоритму с результатами этих экспериментов. An explicit numerical algorithm for calculation of two-dimensional motion of multicomponent gas mixtures is proposed. A physical model as well as conservative and characteristic forms of governing equations are given. The discretization of the governing equations is made in accordance with the CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) approach. The proposed algorithm is tested on problems of air shock waves passing through dense and dilute volume inhomogeneities with initial conditions adopted from numerical and experimental studies of other authors. A good agreement between the results of these studies and those obtained by the CABARET approach is shown.

scholarly journals NUMERICAL ANALYSIS OF THE NATURAL CONVECTION IN HORIZONTAL ANNULI AT LOW AND MODERATE Ra

2006 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
E. L. M. Padilla ◽  
R. Campregher ◽  
A. Silveira-Neto
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Governing Equations ◽  
Concentric Cylinders ◽  
Wide Range ◽  
Horizontal Annuli ◽  
Rayleigh Numbers ◽  
The Heat Transfer Coefficient ◽  
Good Agreement

The natural convection at low and moderate Rayleigh numbers (Ra) incylindrical horizontal annuli with imposed temperatures in both surfaces isnumerically studied. This flow inside concentric cylinders classic configuration has a wide range of practical and technological applications, which justifies its growing studies efforts. In this work, the governing equations are discretized by the volume finite technique over a staggered grid, with second-order accuracy in space and time. The flow pattern is presented by several Rayleigh numbers, with an analysis of the heat transfer coefficient and flow properties. Furthermore, a three-dimensional field is shown at a moderate Ra number. The results showed a good agreement with the experimental data.

Outward Melting in a Cylindrical Annulus

1986 ◽  
Vol 108 (3) ◽  
pp. 240-245 ◽  
Author(s):  
C. J. Ho ◽  
K. C. Lin
Keyword(s):  
Numerical Simulation ◽  
Natural Convection ◽  
Melting Process ◽  
Two Dimensional ◽  
Melting Front ◽  
Cylindrical Annulus ◽  
Solid Region ◽  
Finite Difference Solution ◽  
Rayleigh Numbers ◽  
Change Material

A two-dimensional numerical simulation of outward melting process of a phase change material, n-octadecane, contained in a horizontal cylindrical annulus has been performed with a finite-difference solution of the governing partial differential equations of the system. Both conduction in the unmelted solid and natural convection induced in the melt have been taken into account. Results have been obtained for Rayleigh numbers up to Ra = 2.4 × 105 and the radius ratio of the annulus in a range of 1.6–3.0. The simulations are examined in the light of the effects of both the natural convection in the melt region and/or the subcooling in the solid region on the time-variation of the melting front during the process.

Natural Convection in a Porous, Horizontal Cylindrical Annulus

1994 ◽  
Vol 116 (3) ◽  
pp. 621-626 ◽  
Author(s):  
J. P. Barbosa Mota ◽  
E. Saatdjian
Keyword(s):  
Natural Convection ◽  
Initial Conditions ◽  
Hysteresis Loops ◽  
Boussinesq Equations ◽  
Radius Ratio ◽  
Fine Grid ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Fluid Layers ◽  
Horizontal Cylinders

Natural convection in a porous medium bounded by two horizontal cylinders is studied by solving the two-dimensional Boussinesq equations numerically. An accurate second-order finite difference scheme using an alternating direction method and successive underrelaxation is applied to a very fine grid. For a radius ratio above 1.7 and for Rayleigh numbers above a critical value, a closed hysteresis loop (indicating two possible solutions depending on initial conditions) is observed. For a radius ratio below 1.7 and as the Rayleigh number is increased, the number of cells in the annulus increases without bifurcation, and no hysteresis behavior is observed. Multicellular regimes and hysteresis loops have also been reported for fluid layers of same geometry but several differences between these two cases exist.

Natural Convection in a Micro Size Horizontal Cylindrical Annulus With Periodic Volumetric Heat Flux

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) Horizontal Cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

scholarly journals Analytical Solution of Two-Dimensional Sine-Gordon Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Alemayehu Tamirie Deresse ◽  
Yesuf Obsie Mussa ◽  
Ademe Kebede Gizaw
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Test Problems ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Science And Engineering ◽  
Transform Method ◽  
Differential Transform ◽  
Good Agreement

In this paper, the reduced differential transform method (RDTM) is successfully implemented for solving two-dimensional nonlinear sine-Gordon equations subject to appropriate initial conditions. Some lemmas which help us to solve the governing problem using the proposed method are proved. This scheme has the advantage of generating an analytical approximate solution or exact solution in a convergent power series form with conveniently determinable components. The method considers the use of the appropriate initial conditions and finds the solution without any discretization, transformation, or restrictive assumptions. The accuracy and efficiency of the proposed method are demonstrated by four of our test problems, and solution behavior of the test problems is presented using tables and graphs. Further, the numerical results are found to be in a good agreement with the exact solutions and the numerical solutions that are available in literature. We have showed the convergence of the proposed method. Also, the obtained results reveal that the introduced method is promising for solving other types of nonlinear partial differential equations (NLPDEs) in the fields of science and engineering.

Natural Convection With Porous Medium in a Narrow Horizontal Cylindrical Annulus With Constant Heat Generation

2010 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Natural Convection ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Constant Heat ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow horizontal cylindrical annulus filled with porous medium due to a constant temperature variation on the outer and adiabatic conditions at the inner boundaries with constant volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the gap ratio to the power of two, and Rayleigh number. The series is extended by means of symbolic calculation up to 28 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small, but Pade approximation leads our results to be good even for much higher value of the similarity parameter.

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