Turbulence, Heat and Mass Transfer 5
K. Hanjalić, Y. Nagano and S. Jakirlic (Editors)
Turbulent Natural Convection in Horizontal Coaxial
Cylindrical Enclosures: LES and RANS Models
Y. Addad1, D. Laurence1,2, and M. Rabbitt3
1
The University of Manchester, School of Mechanical, Aerospace and Civil Eng.,
Manchester, M60 1QD, UK, yacine.addad@manchester.ac.uk
2
Electricite de France R&D, MFTT, 6 Quai Watier, F-78400 Chatou, France,
dominique.laurence@edf.fr
3
British Energy plc, Barnwood, Gloucester, GL4 3RS, UK, mike.rabitt@british-energy.com
Abstract
Buoyancy-driven flows in annular cavities bounded by coaxial, horizontal cylinders are very
common in many industrial applications. Such flows arise, for example, in nuclear reactors,
thermal storage systems, around electrical transmission cables, and electronic-component
cooling devices.
In the present study attention is given to a flow similar to those in boiler feed penetration
cavities of nuclear plants. These circular cavities contain pipes that are used for delivering hot
fluid from the boiler of a nuclear reactor to the power plant and, similarly, to transport cold
fluid from the power plant back to the boiler. Two different cross-sections of such penetration
cavities are shown in Figure-1. As seen, the penetration is filled with the gas which is
surrounded by the hot and the cold surfaces. Hot gas penetrates the cavity from the reactor,
while the inner tubes at the centre of the cavity are considerably cooler as they contain a fluid
transported into the reactor core. The feature examined here is the flow of pressurized CO2
gas between the hot and cold surfaces. The more industrial case would incorporate conjugate
heat transfer, as beyond the outer casing is the concrete wall of the nuclear reactor shield and
its temperature must be kept low, but this could only be feasible with RANS models. Hence
the main issue herein is the validation of RANS models via LES in this configuration.
In the simplified configurations shown in Figure-1, buoyancy is the only driving force for the
fluid motion and it also imposes significant effects on the turbulence evolution in the
near-wall layer. Adding to that, the curvature of the pipe surfaces and the impingement of the
accelerated flow on the bottom wall, as shown on the streamlines plot (Figure-2), introduce
further complexities that need to be captured correctly by the RANS models.
The proposed paper will be subdivided into two parts. The first one, describes the LES
computations carried out for these configurations extending the reference data (see Figure-3)
for one coaxial cylinder to Rayleigh number up to 2.38 1010 (based on the length of the gap
between the inner and outer cylinders) and providing for the first time a reference data base
for the second geometry with three coaxial cylinders. Although, the code Star-CD has already
been used in with success in previous studies [1], [2], [3], the paper will also include a
calibration and validation study of the constant Smagorinsky SGS model for the one coaxial
Turbulence, Heat and Mass Transfer 5
cylinder type of geometry using the experimental data of McLeod et al [4] at a lower
Rayleigh number of 1.18·109.
In the second part, a comparison will be made between different RANS models ranging from
k-e linear and non-linear models, k- and SST k- models, to second-moment closures to
illustrate their ability to predict the correct flow features in such flows. For example, the grid
independency tests carried out with a low Reynolds k- model of the low Rayleigh number
test case (see Figure-4) show the classical trend of the model to over-predict the turbulent
energy at the impingement location (angle 0o) but in general the model predictions are in fairly
good agreement with the reference data. On the other hand, for the second geometry with
three coaxial cylinders, this model along with the other two-equations based models are
observed to fail dramatically in predicting the correct trend of the flow (see Figure-5).
Therefore, the extension to the more elaborate RSM type of models seems inevitable.
References
[1]
[2]
[3]
[4]
Addad Y., Benhamadouche S., Laurence D., 2004, “The Negatively Buoyant Turbulent
Wall Jet: LES Results”, Int. J. Heat and Fluid Flow, Vol. 25, 5, 595-808.
Addad Y., Laurence D., Talotte C. and Jacob M. C., 2003, “Large Eddy Simulation of a
Forward-Backward Facing Step for Acoustic Source Identification”, Int. J. of Heat and
Fluid Flow, Vol. 24, 4, 562-571.
Y. Addad 2005 “Large Eddy Simulations of Bluff Body, Mixed and Natural Convection
Turbulent Flows with Unstructured FV Codes” PhD thesis, Department of Mechanical,
Aerospace and Manufacturing Engineering, UMIST.
McLeod E. A., Bishop E. H., 1989, “Turbulent Natural Convection of Gases in Horizontal
Cylindrical Annuli at Cryogenic Temperatures”, Int. J. Heat and Mass Transfer, Vol. 32, 10,
1967-1978.
Cold wall
65 C
0
o
90o
Hot wall
300 C
Figure 1. A schematic sketch of the annular cavities considered in the present study.
K. Hanjalic et al.
T
299
279.5
260
240.5
221
201.5
182
162.5
143
123.5
104
84.5
65
0.15
0.15
0.1
0.1
0.05
0
Y
Y
0.05
0
-0.05
-0.05
-0.1
-0.1
-0.15
-0.15
-0.15
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
-0.1
-0.05
0
0.05
0.1
0.15
X
X
Figure 2. Plots of streamlines superimposed on temperature variation.
Figure-3 The mean Nusselt numbers versus Rayleigh number
Figure-4. Comparison of LES results with Exp. Data [5] at Ra=1.18 109, as well as Low-Re. RANS
model predictions.
Turbulence, Heat and Mass Transfer 5
Figure-5 Predictions of the RANS models for the annular cavity case with three coaxial
cylinders. Left: flow predictions with k-e model, right: flow predictions with RSM model.