Article

Natural convection in an annulus between two rotating vertical cylinders

Department of Mathematics, Bangalore University, Bengalūru, Karnataka, India
Acta Mechanica (Impact Factor: 1.27). 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.

1 Bookmark
 · 
268 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: A theoretical analysis of an unsteady magnetohydrodynamic free-convective flow of a viscous incompressible and electrically conducting fluid between two concentric vertical cylinders is carried out considering thermal boundary condition of the second kind at the outer surface of the inner cylinder. The governing equations of motion and energy are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. A parametric study depicting the effect of the various parameters on the temperature, velocity, and their related quantities is conducted. On the outer surface of the inner cylinder, the skin friction is seen to decrease with the Hartmann number and increase with time. An opposite behavior is seen on the inner surface of the outer cylinder. [DOI:10.1115/1.4005109]
    Journal of Heat Transfer 04/2012; 134(4):042502. DOI:10.1115/1.4005109 · 2.06 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating incompressible axisymmetric thermal flows in porous media at the representative elementary volume (REV) scale. In the model, a D2Q9 MRT-LB equation is proposed to solve the flow field in addition to the D2Q5 LB equation for the temperature field. The source terms of the model are simple and contain no velocity and temperature gradient terms. The generalized axisymmetric Navier-Stokes equations for axisymmetric flows in porous media are correctly recovered from the MRT-LB model through the Chapman-Enskog analysis in the moment space. The present model is validated by numerical simulations of several typical axisymmetric thermal problems in porous media. The numerical results agree well with the data reported in the literature, demonstrating the effectiveness and accuracy of the present MRT-LB model for simulating axisymmetric thermal flows in porous media.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: ___________________________________________________ ABSTRACT The present study aims to investigate experimentally fluid flow and performance characteristics of a double-pipe heat exchanger with rotating inner tube. Parameters that can be used to measure the performance of this type of heat exchanger are also presented, investigated and estimated. The experimental results are reported for the effect of cold and hot water mass flow rates, the heat exchanger arrangement (parallel or counter) and the rotation speed on NTU and effectiveness of the heat exchanger. This study was done for 0 ≤ N ≤ 1000 R.P.M, 0.022 ≤ m c ≤ 0.09 kg/s and 0.022 ≤ m h ≤ 0.09 kg/s. INTRODUCTION Heat exchanger is a piece of equipment built for efficient heat transfer from one medium to another. They are widely used in space heating, refrigeration, air conditioning, power plants, chemical plants, petrochemical plants, petroleum refineries, natural gas processing, and sewage treatment. The classic example of a heat exchanger is found in an internal combustion engine in which a circulating fluid known as engine coolant flows through radiator coils and air flows past the coils, which cools the coolant and heats the incoming air. Heat transfer in rotating systems has been the subject of many experimental and theoretical studies. Many engineering applications involve rotating machinery components with flow in an annulus formed between two concentric cylinders where one or both of the cylindrical surfaces is or are rotating one. Kim and Hwang [1] studied the experimental concerns the characteristics of vortex flow in a concentric annulus with a diameter ratio of 0.52, whose outer cylinder was stationary and inner one was rotating. Taylor [2, 3] performed analytical and experimental works to predict flow, and thermal fields, stability, heat and mass transfer characteristics, etc., inside the concentric annular space. Mathew and Hegab [4] developed an analytical solution for counter flow micro channel heat exchanger subjected to external heat flux while operating under balanced and unbalanced flow conditions. With the addition of heat from the external heat source, the effectiveness of hot and cold A heat transfer characteristic of laminar flow in a circular annulus with a rotating inner cylinder in the presence of a laminar axial flow was investigated using sublimation techniques by Molki et al. [5]. The work focused on the entrance region of the annulus with simultaneous development of velocity and temperature profiles. Lei et al. [6] studied the existence of hydrodynamic instabilities leads to the formation of Taylor vortices in flows in the annulus between two concentric cylinders with one or both cylinders rotating.

Full-text

Download
54 Downloads
Available from
Jun 5, 2014