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Marginal frequency of the azimuthal traveling wave for the modes kÄ1 and 2 "only non-zero m are shown…
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The three-dimensional axisymmetry-breaking instability of an axisymmetric convective flow in a vertical cylinder with a partially heated sidewall is studied numerically. The central part of the sidewall is maintained at constant temperature, while its upper and lower parts are thermally insulated. The dependence of the critical Grashof number on th...
Citations
... Hence, studies on partial heating have gained greater importance and have been investigated by many researchers. The three-dimensional stability analysis of convective phenomena in a partially heated cylindrical geometry has been numerically analyzed [8]. Natural convection with discrete heating in an annulus has been the main focus of the numerical studies of Sankar et al. [9][10][11]. ...
The present investigation is devoted to analyze the buoyancy-driven flow behavior and associated thermal dissipation rate in a nanofluid-filled annular region with five different single source-sink and three different dual source-sink arrangements along the vertical surfaces. The remaining region on the vertical boundaries and horizontal surfaces are kept adiabatic. Numerical simulations have been performed by solving the dimensionless model equations by employing finite difference method. To analyze the impacts of the type of nanofluid, nanoparticle volume fraction, Rayleigh number, size and arrangement of sources and sinks, the results are graphically represented through streamline and isotherm contours, thermal profiles, average Nusselt number and cup-mixing temperature. Comparison of the results of current investigation reveal fairly good agreement with the existing benchmark results. The results showed that identifying an optimum location and length of source-sink with a proper selection of other control parameters can lead to enhanced thermal transport and thermal mixing in the enclosure. Also, the calculated enhancement ratio of the heat dissipation rate enhances with an increment in nanoparticle concentration.
... He highlighted the influence of unheated exit and unheated entry on combined heat and mass transfer by free convection flow in the cylindrical enclosure. Rubinov et al. [19] carried out 3D instabilities of an axisymmetric free convection flow in a vertical cylindrical enclosure with partially heated sidewall. They examined the similarities and differences of instabilities through two numerical approaches, finding that the instability which is directly linked to the aspect ratio, involves the generation of a steady or oscillatory flow. ...
The current study reports a numerical analysis of free convection of air in an isothermal horizontal cylinder, cooled and heated at different wall locations. Three heater sizes are discussed in this study. The first heated zone is spread across one-quarter of the sidewall; the second is uniformly distributed over the half of the wall and the third active wall covers three-quarters of the cylinder. Five various locations are considered and examined for each active zone of the sidewall. The computation is carried out for Rayleigh number ranging from 102 to 106. Numerical results characterizing heat transfer and flow features are achieved using an iterative model developed in COMSOL Multiphysics. The effect of Rayleigh number on heat transfer and fluid flow characteristics within the cavity are investigated. Particular attention is paid to the influence of heater location and heater size on energy efficiency. It is found that the mean Nusselt number and dimensionless velocity increase when increasing the Rayleigh number. Moreover, the optimal level of energy efficiency is achieved if the heating zone is centered at the upper part of the cylinder, regardless of the heater size. It is also shown that the optimal configuration providing higher energy efficiency is obtained when three-quarters of the sidewall are locally heated, and more precisely, if the active zone is centered at the top of the cylinder.
... On the contrary, partial heating was introduced as a new heat transfer process in order to obtain higher energy efficiency with respect to exergy losses. [20][21][22][23][24][25] Mazgar et al. 26 highlighted the effects of natural convection coupled to non-gray gas radiation between two vertical plates partially heated and made of two equal parts, alternately isotherm and insulated. They proved that attenuation of the radiative contribution between heating from the bottom and from the top is not as expected. ...
This article reports a numerical analysis of combined natural convection and non-gray gas radiation within a cylindrical enclosure, isothermally heated and cooled on various arc lengths of the sidewall. Three active zone locations are studied in this article. The first heating section extends quarter the perimeter of the cavity, the second spreads across one-half of the cylinder, and the third one is made of three-quarters of the sidewall. The participating media are considered as emissive, absorbent, and non-scattering. The radiative transfer equation is resolved using the Ray-Tracing method associated to the Statistical Narrow Band–correlated K model. The effect of heater size and its location on heat transfer, fluid flow, and entropy generation are presented and discussed in this work. The results show that the optimum heater size is obtained for three-quarters heated enclosure. It was also found that choosing a heat source centered at the top of the enclosure provides the best heat transfer performance.
... In recent years, an instability analysis of partially heated natural convection flows have been considered by many researchers; for instance, Rubinov et al. (2004) numerically studied the 3D axisymmetry-breaking instability of an axisymmetric convective flow in a vertical cylinder with a partially heated sidewall; the central part of the sidewall is maintained at a constant temperature, while its upper and lower parts are thermally insulated. The dependence of the critical Grashof number (Gr = Ra/Pr) on the cylinder aspect ratio, A, is obtained for a fixed value of the Pr number. ...
Recent experimental configurations like the liquid metal electrode for the development of a liquid metal battery and the inverted Bridgman configuration for growing crystals involve natural convection of fluids confined in vertical cylinders heated from below and partially cooled from above. A cylindrical cavity subjected to such conditions is studied from a numerical point of view, assuming the Rayleigh number, the noncooled size, and the aspect ratio (height/diameter) parameters over ranges 10³ ≤ Ra ≤ 10⁵, 0 ≤ γ ≤ 0.875, and 0.5 ≤ a ≤ 1.25, respectively, for all cases with Pr = 6.67 being assumed. The governing equations for natural convection are discretized employing a mixed Fourier-Finite volume method using the SIMPLEC algorithm as velocity decoupling strategy. Steady flow transitions from axisymmetric to nonaxisymmetric were obtained; interestingly, the average Nusselt number shows a monotonic decreasing behavior as a function of γ while an increasing behavior as function of Ra is observed. In particular, symmetry breaking instability as a function of critical parameters of the convective flow is determined by a numerical stability analysis. Finally, a stability map for Ra vs. γ is constructed for a = 1.0.
... The eects of multiplicity and transition of natural convection has been neglected to estimate the shape and movement of the solid/liquid interface of two-phase ow [14]. The eects of BC and specially temperature gradient are investigated by Erenburg et al. [17]. Partially heated walls are set up as boundary condition to analyze the multiplicity and bifurcations of natural convection. ...
... It should be mentioned that the benchmark problems for axisymmetric flows, especially including their three-dimensional instability, are not established as well as the benchmark problems in rectangular cavities considered in [1]. We can mention recently formulated benchmark [2] and results of [3-6], which were used for the benchmarking purposes in [7][8][9][10][11][12][13][14] and other studies. Also, the spectral and pseudospectral methods that yield a high-accuracy benchmark data for the flows in rectangular enclosures are not so usual for the cylindrical domains. ...
... Such discontinuities are rather common for both model flows and more complicated technological applications. A special care should be taken to treat a discontinuity by a spectral method [5,6,9], and even then the discontinuity can cause undesirable numerical problems when three-dimensional perturbations are calculated [9]. For loworder methods, such discontinuities do not pose any technical difficulties, however can slow down the convergence. ...
... Such discontinuities are rather common for both model flows and more complicated technological applications. A special care should be taken to treat a discontinuity by a spectral method [5,6,9], and even then the discontinuity can cause undesirable numerical problems when three-dimensional perturbations are calculated [9]. For loworder methods, such discontinuities do not pose any technical difficulties, however can slow down the convergence. ...
Several problems on three-dimensional instability of axisymmetric steady flows driven by convection or rotation or both are studied by a second-order finite volume method combined with the Fourier decomposition in the periodic azimuthal direction. The study is focused on the convergence of the critical parameters with mesh refinement. The calculations are done on the uniform and stretched grids with variation of the stretching. Converged results are reported for all the problems considered and are compared with the previously published data. Some of the calculated critical parameters are reported for the first time. The convergence studies show that the three-dimensional instability of axisymmetric flows can be computed with a good accuracy only on fine enough grids having about 100 nodes in the shortest spatial direction. It is argued that a combination of fine uniform grids with the Richardson extrapolation can be a good replacement for a grid stretching. It is shown once more that the sparseness of the Jacobian matrices produced by the finite volume method allows one to enhance performance of the Newton and Arnoldi iteration procedures by combining them with a direct sparse linear solver instead of using the Krylov-subspace-based iteration methods. Copyright © 2006 John Wiley & Sons, Ltd.
... The study is performed numerically using the finite volume discretization. The steady state and stability analysis are performed in the same way as in Rubinov et al. (2004) and Gelfgat et al. (2005). ...
The three-dimensional instability of the thermocapillary convection in cylindrical undeformable floating zones heated laterally is studied numerically. Different types of the boundary conditions, including ra- diation heating, linearized radiation and prescribed heat flux are used in the calculation. Stability diagrams showing the Prandtl number dependence of the critical Marangoni numbers that represent the thermocapillary forcing for different heating conditions are reported. It is shown that the primary instability of initially axisym- metric thermocapillary flows is defined mainly by the to- tal amount of heat supplied through the heated side sur- face. The way in which the heat is supplied has a less significant effect on the onset of instability.
The current study reports a numerical analysis of natural convection heat transfer phenomenon of air in a horizontal 11 cylinder, isothermally heated and cooled on various arc lengths of the sidewall. Three relative positions of the active zones are 12 discussed. The first heating section is spread across one-quarter of the circular wall; the second extends half the perimeter of the 13 cavity and the third is made of three-quarters of the sidewall. Five various angular configurations are considered and examined 14 for each active zone of the sidewall. Numerical results characterizing fluid flow proprieties and heat transfer are achieved using 15 an iterative model developed in COMSOL Multiphysics. The influences of Rayleigh number on heat transfer and the structure of 16 fluid flow within the cavity are investigated. Particular attention is paid to the effect of heating location on the energy efficiency 17 of the system. It is found that the system energy efficiency is significantly affected by the Rayleigh number. The results also show 18 that the optimum heater size and location are generally, but not necessarily obtained when three-quarters of the sidewall are 19 laterally heated. 20 21
In this paper the author reviews methodology of a version of the global Galerkin that was developed and applied in a series of his earlier publications. The method is based on divergence-free basis functions satisfying all the linear and homogeneous boundary conditions. The functions are defined as linear superpositions of the Chebyshev polynomials of the first and second types that are combined in divergence free vectors. The description and explanations of treatment of boundary conditions inhomogeneities and singularities are given. Possible implementation for steady state solvers, path-continuation, stability solvers and straight-forward integration in time are discussed. The most important results obtained using the approach are briefly reviewed and possible future applications are deliberated.
In this paper
the author reviews a version of the global Galerkin that was developed
and applied in a series of earlier publications. The method is based on divergence
-free basis
functions satisfying all the linear and homogeneous boundary conditions. The functions are
defined as linear superpositions of the Chebyshev polynomials of the first and second klinds
that
are combined in
to divergence free vectors. The description and explanations of treatment of
boundary conditions inhomogeneities and singularities are given.
Possible implementation for
steady state solvers, path
-continuation, stability solvers and straight
-forward integration in time
are discussed.
The most important results obtained using the approach are briefly reviewed and
possible future applications are discussed
.
Global Galerkin method for stability studies in incompressible CFD and other possible applications. Available from: https://www.researchgate.net/publication/324474843_Global_Galerkin_method_for_stability_studies_in_incompressible_CFD_and_other_possible_applications [accessed Apr 12 2018].
