Article

Natural convection in an annulus between two rotating vertical cylinders

Department of Mathematics, Bangalore University, Bengalūru, Karnataka, India
Acta Mechanica (Impact Factor: 1.47). 02/2001; 147(1):173-196. DOI: 10.1007/BF01182360

ABSTRACT

A numerical study is conducted to understand the effect of rotation on the axisymmetric flow driven by buoyancy in an annular cavity formed by two concentric vertical cylinders which rotate about their axis with different angular velocities. The inner and outer side walls are maintained isothermally at temperature
c
and
h
, respectively, while the horizontal top and bottom walls are adiabatic. The vorticity-stream function form of the Navier-Stokes equations and the energy equation have been solved by modified Alternating Direction Implicit method and Successive Line Over Relaxation method. Numerical results are obtained for a wide range of the Grashof number, Gr, nondimensional rotational speeds
i
,
o
of inner and outer cylinders and for different values of the Prandtl number Pr. The effects of the aspect ratio,A, on the heat transfer and flow patterns are obtained forA=1 and 2. The numerical results show that when the outer cylinder alone is rotating and the Grashof number is moderate, the outward bound flow is confined to a thin region along the bottom surface while the return flow covers a major portion of the cavity. For a given inner or outer cylinder rotation the temperature field is almost independent of the flow in the annulus for fluids with low Prandtl number, while it depends strongly for high Prandtl number fluids. At a high Grashof number, with moderate rotational speeds, the dominant flow in the annulus is driven by thermal convection, and hence an increase in the heat transfer rate occurs. In the case of unit aspect ratio, the flow pattern is unicellular for the rotation of the cylinders in the same direction, and when they rotate in the opposite direction two or more counter rotating cells separated by a stagnation surface are formed. The rate of heat transfer at the hot cylinder is suppressed when its speed of rotation is higher than that of the cooler cylinder. The computed heat transfer and flow patterns are compared with the available results of a nonrotating cylindrical annulus, and good agreement is found.

Download full-text

Full-text

Available from: Sankar Mani
  • Source
    • "A numerical solution based on the false transient method and alternating direction implicit (ADI) scheme has been used to solve the vorticity transport and energy equations. Another numerical study was performed by Venkatachalappa et al. [13] to understand the effect of rotation on the axisymmetric flow driven by buoyancy in an annular cavity formed by two concentric vertical cylinders which rotate about their axes with different angular velocities. A numerical technique based on the two-step ADI method has been used to solve the vorticity transport, swirl velocity and energy equations. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The study of axisymmetric flows is carried out using finite volume method on hybrid unstructured grids. In this context, a numerical solver has been developed to take into account the flow characteristics of axisymmetric, swirl and heat transfer phenomena. For discretizing the governing equations, a cell-centered finite volume methodology has been adopted with a collocated arrangement of flow variables as well as the scalars. The developed solver is at first validated for simple axisymmetric flow problems (without swirl) like flow over a sphere at different Reynolds numbers (Re). Subsequently, swirl is incorporated and validated for flow inside a cylindrical lid-driven cavity with rotating lid. The code is further validated for axisymmetric thermal flows. Different numerical validations presented in this paper demonstrate that the solver can predict the flow characteristics of axisymmetric flows with swirl phenomenon and heat transfer with good accuracy.
    Full-text · Conference Paper · Oct 2015
  • Source
    • "Wang et al. [2012] developed a finite volume model and analyzed transient natural convection in closed ended vertical annuli, with isothermally heated (or cooled) inner surface and insulated horizontal and outer surfaces. Venkatachalappa et al. [2001] conducted a numerical analysis to know the effect of rotation on the axisymmetric flow driven by buoyancy in an annular cavity formed by two concentric vertical cylinders which rotate about their axis with different angular velocities with inner and outer side walls at constant temperatures keeping the horizontal top and bottom walls as adiabatic. The governing equations were solved by Alternating Direction Implicit method and Successive Line over Relaxation method. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In this work, transient numerical analysis of two dimensional heat transfer and fluid flow has been carried out for natural convection in an internally heated vertical annulus. The finite volume SIMPLER technique is used for the solution of governing equations on a staggered mesh. The MPI parallel programming technique is used for domain decomposition and parallelization of the code. The results are obtained for an aspect ratio of 10, radius ratio of 2 and Rayleigh number equal to 1000. Prandtl number is varied from 1 to 10. Effects of varying prandtl number on temperature, pressure, axial & radial velocity profiles are evaluated and discussed in detail.
    Full-text · Conference Paper · Aug 2014
  • Source
    • "Wang et al. [2012] developed a finite volume model and analyzed transient natural convection in closed ended vertical annuli, with isothermally heated (or cooled) inner surface and insulated horizontal and outer surfaces. Venkatachalappa et al. [2001] conducted a numerical analysis to know the effect of rotation on the axisymmetric flow driven by buoyancy in an annular cavity formed by two concentric vertical cylinders which rotate about their axis with different angular velocities with inner and outer side walls at constant temperatures keeping the horizontal top and bottom walls as adiabatic. The governing equations were solved by Alternating Direction Implicit method and Successive Line over Relaxation method. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In this work, transient numerical analysis of two dimensional heat transfer and fluid flow has been carried out for natural convection in an internally heated vertical annulus. The finite volume SIMPLER technique is used for the solution of governing equations on a staggered mesh. The MPI parallel programming technique is used for domain decomposition and parallelization of the code. The results are obtained for an aspect ratio of 10, radius ratio of 2 and Rayleigh number equal to 1000. Prandtl number is varied from 1 to 10. Effects of varying prandtl number on temperature, pressure, axial & radial velocity profiles are evaluated and discussed in detail.
    Full-text · Conference Paper · Aug 2014
Show more