1000 Islands Fluid Mechanics Meeting, 2005
CONVECTIVE HEAT TRANSFER IN TURBULENT FLOW NEAR A GAP
D. Chang and S. Tavoularis
Department of Mechanical Engineering
University of Ottawa, Ottawa, ON.
Introduction
Forced convective heat transfer in complex
channels with narrow gap regions between solid walls
flanked by wider subchannels occurs commonly in
rod bundles in the cores of nuclear reactors and other
heat exchangers. The fluid in narrow gap regions is
more likely to overheat than elsewhere. It is well
known, however, that flow near narrow gaps, and the
associated heat and mass transfer across the gap,
are dominated by strong, large-scale, quasi-periodic,
flow pulsations, characterized as coherent structures,
which greatly enhance inter-subchannel mixing and
heat transfer. In a recent numerical study (Chang and
Tavoularis, 2005, hereafter referred to as CT) we
have reproduced most experimental observations by
using the unsteady Reynolds averaged Navier-Stokes
equations (URANS) approach and a Reynolds stress
model. The present work is an extension of this study,
by the addition of heating. Our main objective is to
provide a thorough understanding of the influence of
coherent structures on heat transfer characteristics in
a simplified rod-bundle-like configuration.
x
z
y
containing a rod with a diameter D, as shown in
Figure 1. The gap between the rod wall and the
adjacent plane wall was set at  = 0.1D and the
equidistant plane was defined by y = ½. The
Reynolds number, based on the bulk velocity Ub and
the hydraulic diameter Dh  1.59D , was 108,000.
Two heated cases were considered, one with the rod
kept at a constant temperature and another with the
heat flux from the rod kept constant. The heat flux on
all plane walls was set to zero, corresponding to a
thermally insulated duct. The buoyancy force was
negligible and the physical and thermodynamic
properties of the fluid, taken to be air, were assumed
to be constant. To allow full development of the flow
properties in a relatively short domain, the periodic
boundary condition was applied to the velocity and the
temperature fields. Following a mesh independence
study by CT, the mesh for the heated flow simulations
was set to 8080202 elements along the spanwise
(x), transverse (y) and streamwise (z) directions,
respectively. The time step was set to 1.8810-2T,
where T  L / U b .
Results and Discussion
Consistent with the use of periodic boundary
conditions, the resolved flow temperature T(x,y,z) is
presented in dimensionless form as
  x, y, z, t  
Fig.1. Sketch of the test geometry
where
Computational procedure and conditions
The commercial software package FLUENT
(version 6.1.22) has been used for these simulations.
The domain consisted of a rectangular channel
Trod ,m  x, t   T  x, y, z, t 
Trod ,m  x, t   Tb  x, t 
(1)
Trod ,m  x, t  is the circumferentially-averaged
rod surface temperature at a given streamwise
position and Tb (x ) is the cross-section-averaged
(bulk) temperature at that position, defined as
1000 Islands Fluid Mechanics Meeting, 2005
Tb  x  
 U T
dA
 Ub A
(2)
Similar to the turbulent stresses discussed by CT,
the local variance of the temperature fluctuations may
be considered to be the sum of coherent and noncoherent components, as
t2   nc2  co2
The coherent component
(3)
co2
(a
)
is the variance of
the resolved temperature, given by

co2  T  T

2
(4)
The non-coherent temperature fluctuations are not
provided by the solution but are roughly estimated
assuming that the dominant heat flux correlation
coefficient has a magnitude of 0.5, as
 
2
nc
where
and
4 nc
(b
)
2
 nc2
(5)
 nc2  vnc2  wnc2
 nc  v 2nc  w 2nc
The Reynolds-averaged turbulent heat fluxes were
computed from the resolved temperature using a
gradient transport model.
Contours of the dimensionless, time averaged
temperature difference and the ratio of the coherent
and total temperature variances have been plotted in
Figure 2. It can be seen that the high temperature
regions are restricted around the rod and across the
gap. The coherent contributions to the temperature
fluctuations are dominant in the gap region.
Isocontours of the instantaneous dimensionless
temperature, shown in Figure 3, demonstrate the
presence of large instantaneous local temperature
differences, whose locations are well correlated with
the locations of the coherent structures.
Conclusion
The present simulations have clearly documented
the significance of coherent vortical structures in heat
transfer in a rod-wall gap region. These structures
create the flow transport across a narrow gap that
has the beneficial effect of moderating the timeaveraged temperature rise in the gap region, which
otherwise would have been significantly higher. The
ratio of the coherent and total temperature fluctuation
demonstrates that the coherent contributions to the
total temperature fluctuation are dominant in the gap
region.
Fig. 2. Isocontours of: a)

and b)
co2 t2 100
for
the constant temperature case (left) and the constant
heat flux case (right)
(a
)
(b
)
Fig.
3.
Isocontours
of
the
dimensionless
instantaneous temperature difference on the
equidistant plane: (a) constant rod temperature case;
(b) constant heat flux case; coherent structures
identified by the Q criterion are also shown in all plots;
the actual plot size is 7.2D long and 3D high
Reference
Chang, D. and S. Tavoularis, 2005, “Unsteady
numerical simulations of turbulence and coherent
structures in axial flow near a narrow gap,” J.
Fluids Eng., in press.