phd thesis - Turbulence Mechanics/CFD Group

PhD Thesis: Modelling Natural and Mixed Convection for
Turbulent Flows for industrial applications
Introduction
Heat transfer phenomena are of crucial importance in many industrial applications and in
particular in the nuclear power generation field. Either in the nuclear vessels, in the steam
generators or for nuclear storage, optimizing and mastering heat transfer is mandatory for
safety reasons (thermal chocks or fatigue) and for the economical performance (gaining 1°C
could save millions of euros).
The fluid motions, thanks to gravity effects, could be partially or totally entailed by
temperature gradients. The comprehension of such phenomena is still undergoing either in the
experimental and numerical fields. On the one hand, the lack of experimental data in the field
of natural and mixed convection makes the research more challenging. On the other hand,
many ways of modelling turbulence and heat transfer exist. Whereas RANS (Reynolds
Averaged Navier Stokes) and LES (Large Eddy Simulation) techniques have reached certain
maturity for the dynamic field although some progress has still to be done, modelling the
thermal field either concerning mixing effects due to turbulence or heat exchanges at the wall
has a to be more deeply investigated in RANS and LES.
The program
An idea of the program is given bellow. Some parts can of course overlap.
Bibliographical investigations (4-6 months): The first aim of the present thesis is to
summarize the state of art in the field of Natural and Mixed convection in the academic area
and in the industrial one. A non-exhaustive list of experimental and numerical references is
given at the end of the present proposal and cover a large part of the different items one wants
to investigate. At the end of this part a bibliographical report will be written.
Modelling the thermal fluxes in RANS (24 months): one will focus on two major
categories of RANS models: low Reynolds one and two moment closures. The objective is
not to enhance modelling the velocity and the Reynolds stresses (although they could be
strongly coupled with the thermal field) but to reach the state of art [13] [15], [16]of
modelling the turbulent thermal fluxes and to test these modifications on industrial test-cases
such as Promethée [3] and Valida [11],[18] experiments. This will be done after appropriate
developments and a period of validation on academic test-cases based on DNS data (one can
use the rich DNS Japanese database [7] or experiments and DNS found in [1] [2], [4], [5], and
[14]). Two major physical issues will be particularly investigated, the inlet conditions one has
to employ for open channels and the laminarization effects due to buoyancy (one knows for
example that v2f and Launder Sharma models give a good prediction of the Nusselt number
while the k-ω-SST and other low-Reynolds models fail, the reason for that is unknown [14]).
Although the theses focuses on mixed and natural convection, some cases of forced
convection will be investigated as the prediction of the heat exchanges are not that
satisfactory with the RANS models).
Modelling the thermal fluxes with LES (24 months overlapping with RANS modelling):
The subgrid-scale for the scalar fields employs for the moment a classical notion of turbulent
Prandtl number. This is insufficient and has to be investigated more deeply. After the
bibliographical part, some models will be implemented (contrary to RANS approaches, some
development of subgrid-scale models or other types of model could be necessary). The

computing power available at EDF will allow fast and big computations. The test-cases will
be similar to those used in the RANS part. The computing power available at EDF R&D will
allow fast and large scale computations.
Optional Investigations (6 months): The two previous major items focus on low Reynolds
approaches at the wall (the velocity vanishes naturally). In Industrial, the Reynolds and
Rayleigh numbers are usually high and refining the mesh at the wall is impossible and will
remain impossible for decades even with the current growth of computing power. Some
complementary investigations based on the use of extended wall functions approaches (or
Thin Boundary Layer approach) could be considered in RANS [8], [9], [19] and LES [10],
[12], [17].
Writing-up (6 months): Except some complementary calculations, the writing up should
start eight months before the official end of the theses. This period will include several
iterations between the researchers and the PhD student.
Other important Information:
• The thesis will be co-financed by EDF (Electricité De France) and ANRT
(Association Nationale de la Recherche Technique).
• Location (10 kms from Paris city centre): EDF R&D, Fluid Mechanic, Power
Generation and Heat Transfer Department, 06, Quai Watier, 78401, Chatou.
• PhD director : Eric Lamballais and Rémi Manceau (LEA/ Université de Poitiers)
• EDF responsible: Sofiane Benhamadouche
Bibliography
Experimental references
[1] Fedorov A.G. and Viskanta R. 1997. 'Turbulent natural convection heat transfer in an
asymmetrically heated, vertical parallel-plate channel'. International Journal of Heat and Mass
Transfer. 40. pp.3849-3860.
[2] P.L. Betts , I.H. Bokhari. Experiments on turbulent natural convection in an enclosed tall
cavity. International Journal of Heat and Fluid Flow 21 (2000) 675-683.
[3] Gaillard, Jean-Philippe. Promethee experiment and analysis. The 11th international
meeting on nuclear reactor thermal-hydraulics , Avignon,France, 2 au 6 Octobre 2005, 352.
[4] T. Ayinde, S. Said, and M. Habib. 'Experimental investigation of turbulent natural
convection flow in a channel'. Heat and Mass Transfer. 42. pp.169-177 (2005).
[5] T. F. Ayinde, S. A. M. Said, M. A. Habib. Turbulent natural convection flow in a vertical
channel with anti-symmetric heating. Heat and Mass Transfer (2007).
Numerical references

[6] Boudjemadi, R., Maupu, V., and Laurence, D. 1997. 'Budgets of turbulent stresses and
fluxes in a vertical slot natural convection flow at Rayleigh Ra=105 and 5.4 105'.
International Journal of Heat and Fluid Flow. 18. pp.70-79.
[7] Hiroshi Kawamura, Hiroyuki Abe, Yuichi Matsuo. DNS of turbulent heat transfer in
channel flow with respect to Reynolds and Prandtl number effects. International Journal of
Heat and Fluid Flow 20 (1999) 196-207.
[8] Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002. Progress in the
generalization of wall-function treatments. International Journal of Heat and Fluid Flow 23
(2), 148–160.
[9] T.J. Craft, A.V. Gerasimov, H. Iacovides, J.W. Kidger, B.E. Launder. The negatively
buoyant turbulent wall jet: performance of alternative options in RANS modelling.
International Journal of Heat and Fluid Flow 25 (2004) 809–823.
[10] F. Tessicini, L. Temmerman, M.A. Leschziner . Approximate near-wall treatments based
on zonal and hybrid RANS–LES methods for LES at high Reynolds numbers .International
Journal of Heat and Fluid Flow, Volume 27, Issue 5, October 2006, Pages 789-799
[11] Benhamadouche, S., Bournaud, S., Duret, B., Clement, Ph., Lecocq, Y., 'Large Eddy
Simulation of mixed convection around a vertical heated cylinder cooled by a cross-flow air
circulation', Conference on Modelling Fluid Flow (CMFF’06), Budapest, Hungary,
September 6-9, 2006.
[12] Y. Benarafa, O. Cioni, F. Ducros, and P. Sagaut. RANS/LES coupling for unsteady
turbulent ow simulation at high Reynolds number on coarse meshes. Computer Methods in
Applied Mechanics and Engineering, 195(23-24):2939{2960, 2006.
[13] S. Kenjeres, K. Hanjalic, LES, T-RANS and hybrid simulations of thermal convection at
high Ra numbers, Int. J. Heat Fluid Flow 27 (2006) 800–810.
[14] W.S. Kim, S. He and J.D. Jackson. 'Assessment by comparison with DNS data of
turbulence models used in simulations of mixed convection'. International Journal of Heat
and Mass Transfer, Volume 51, Issues 5-6, Pages 1293-1312 (2008).
[15] Lecocq,Y., Manceau, R., Bournaud, S. and Brizzi, L.E. (2008). “Modelling of the
turbulent heat fluxes in natural, forced and mixed convection regimes”, 7th ERCOFTAC Int.
Symp. on Eng. Turb. Modelling and Measurements, Limassol, Cyprus.
[16] Shin J.K., An J.S., Choi Y.D., Kim Y.C.& Kim M.S. (2008), Elliptic relaxation second
moment closure for the turbulent heat fluxes, J. Turbulence, Vol. 9, pp. 1–29.
[17] Monfort, D., Benhamadouche, S. and Sagaut, P. (2008). “Meshless approach for wall
treatment in Large Eddy Simulation”, Computer Methods in Applied Mechanics and
Engineering, accepted.
[18] Y. Lecocq. Contribution à l’analyse et à la modélisation des écoulements turbulents en
régime de convection mixte – Application à l’entreposage de déchets radioactifs. Thèse de
doctorat, Université de Poitiers, 2008.
[19] Gant S.E. "Development and Application of a New Wall Function for Complex Turbulent
Flows" PhD Thesis, Dept. of Mechanical, Aerospace and Manufacturing Engineering,
UMIST, November 2002.