(238e) CFD Simulation of Rayleigh Benard Convection in Annular Cylinder System: Heat Transfer Mechanism and Vortex Pattern

Title: CFD
simulation of Rayleigh Benard convection in annular cylinder system: Heat
transfer mechanism and vortex pattern

Authors:
Vedantam, S¹*., Dhotre, M.T.²

Affiliation: ¹Industrial
Flow Modeling Group (iFMg), CEPD Division, National Chemical Laboratory (NCL),
Pune, INDIA

²Institute of
Chemical Technology, Matunga, Mumbai, INDIA

*corresponding
author: spriya.vedantam@gmail.com

ABSTRACT

Introduction:

Thermal
convection is an important phenomenon in nature and coming in extreme use in technology.
Rayleigh- Benard convection refers to the instability which occurs in a viscous
fluid layer subjected to a vertical negative temperature gradient, in the same
direction as gravity. A key question is the dependence of the heat transfer
rate as measured by the Nusselt number (Nu) for a given temperature difference
between the hot bottom and the cold top plates (measure termed as
dimensionless Rayleigh number (Ra)),
a given fluid (properties termed as dimensionless Prandtl number
(Pr)),
and a given aspect ratio of the container. Since over the last two decades
there has been tremendous progress on this and related questions by experiment,
theory, and numerical simulation (Ahlers et al., 2009). However, most of
the work reported focused on the RB convection for single-phase flow. Various
situations in the process and the energy industries, involve liquid convection
in the presence of boiling: vapor generators in nuclear and conventional
electric power plants, reboilers, distillers, water purification systems,
cooling applications and many others ranging from material processing to
nuclear systems to atmospheric sciences.

Boiling
as a heat transfer mechanism has been a subject of interest for centuries and
the process has formed the object of a very large number of studies (Dhir,
1998). Most of the focus has been on the process by which the high thermal resistance
opposed by the visco-thermal layer adjacent to the hot surface is decreased by
the vapor bubbles; the two main mechanisms are believed to be micro-convection
and latent heat transport. Another significant effect of the bubbles, however,
is to promote strong convective currents in the liquid, thus helping to remove
the heated layer near the hot wall (Oresta, 2009). With this backdrop, it is of
interest to gain deeper understanding of the possible outcomes of such thermal
instability. It is realized important to venture on the hydrodynamic modeling
of thermal instability in combination with centrifugal instability
(Taylor-Couette flow, measure given by a dimensionless Taylor number (Ta)) and
with certain variations in the geometry of the domains of interest.

As
an initial step, single phase simulations have been carried out in concentric cylinder
system, including the heat transfer, in the presence of centrifugal
instability. The standard single-phase RBC under the Boussinesq approximation
is controlled by Rayleigh number and Centrifugal instability has been
introduced into the system, using Taylor number. Commercial software Ansys Fluent
has been used for all simulations. 2D axi-symmetric model with a swirl
component has been used to solve the flow equations. Turbulence has been
incorporated using the RSM model. It was assumed that density is the only
property that gets affected by the change in the temperature between both the
boundaries, and hence Boussinesq approximation has been used. Mercury has been
used as working fluid for the single phase simulations. Model has been
validated with the experimental data of Rossby (1969) as shown in the figure 1:

CFD
simulations in the annulus of coaxial cylinders (with no eccentricity) revealed
the formation of contra-rotative cells along the length for an established
temperature difference and rotational speed. The cell formation is in agreement
with experimental as well as theoretical observation.

It
is of interest to arrange the system with an eccentricity to see the impact on
the heat transfer mechanism in the annulus and the vortex patterns formed
therein. Hence two such co-axial systems have been simulated, in the initial
case without a rotation, which have been validated with the established data;
and with rotation such that these studies form a proof of concept for two-phase
studies. An annular gap width of 28.5 mm is used, for three different annulus
lengths of 10, 20 and 40 cm respectively. The two cases simulated are i)
concentric co-axial cylinders placed horizontally ii) non-concentric annular
cylinders with an eccentricity of -0.623. The effect on heat transfer mechanism
and vortex patterns along the length of the annulus are studied. Air as well as
low-Pr fluids are considered as the fluid systems in the domain of interest.
For all these simulations, commercial software Ansys FLUENT has been used. Heat
flux from the surface of the cylinders has been estimated and compared for the
two cases.

References

Ahlers, G., Grossmann,
S., and  Lohse, D., 2009,  Rev. Mod. Phys. 81, 503.

Dhir, V., 1998, Annu.
Rev. Fluid Mech., 30, 365.

Oresta, P.,
Verzicco, R, Lohse, D, Prosperretti, A, Physical Review E., 80, 026304 (1-11)
(2009).

 Rossby, T., J.
geophys. Res., 74, 5542-5545 (1969).