Turbulence, Heat and Mass Transfer 6
K. Hanjalić, Y. Nagano and S. Jakirlić (Editors)
 2009 Begell House, Inc.
Heat and fluid flow simulations for deciding
tomorrow’s energies
J.P. Chabard1,2, D. Laurence1
1
EDF, Research & Development Division, 1, avenue du Général de Gaulle - 92100,
Clamart, France, jean-paul.chabard@edf.fr
2
École des Ponts ParisTech, 6 et 8 avenue Blaise Pascal, Cité Descartes,
Champs-sur-Marne, 77455, Marne-la-Vallée Cedex, France
Abstract - This paper presents a review of recent applications of Computational Fluid Dynamics on problems
dealing with power generation. Various turbulence models are used on different configurations involving heat
transfer, ranging from Reynolds Averaged Navier-Stokes Equations (RANSE) with first or second order
moment closure to Large Eddy Simulation (LES). These simulations are clearly demonstrating the interest of
using second order moment closure turbulence models even if they are requiring finer mesh to deliver
reasonable accurate solutions. For addressing real industrial problems, developments are mandatory for taking
every advantages of performance computing facilities available and especially large parallel computers. The
Code_Saturne software coupled with SYRTHES for conjugated heat transfer proved to be very well suited to
this kind of architecture. They are available as free software under GNU GPL.
1. Introduction
EDF background in numerical simulation, and especially in Computational Fluid
Dynamics, is directly linked with the nuclear program launched in the 1970s as EDF assumed
the responsibility to be both architect and owner-operator of its fleet. It means that EDF takes
responsibility for all the design and specifies and assembles components coming from
different vendors (as Areva NP for the nuclear island or Alstom for the turbines). Today, the
fleet of 58 standardized PWR nuclear units represents an installed capacity of 63 GWe and an
annual electricity generation of 428 TWh with very low CO2 emissions. As a consequence of
its status of architect-owner-operator of this fleet, EDF needs to permanently demonstrate to
the Safety Authorities that it operates it securely whilst optimizing operations and
maintenance from a cost-effective point of view. Special focuses are devoted to nuclear fuel
management and life time extension. These topics require an ability to explain complex
physical phenomena involving a coupling between fluid mechanics, heat transfer, structural
mechanics and damage analysis. This is why EDF has been developing a special skill in
numerical simulation of turbulent flows and heat transfer. Moreover, in-house code
development is a very good means of professionalizing young researchers. This skill has been
capitalized for over 20 years in in-house code families which facilitate the transfer of
knowledge from research to operation, provided a strict process of code validation and
qualification is followed.
Today, EDF is facing new challenges with the development of new nuclear plants both in
France with EPR but also in foreign countries like China, UK, USA, with different
technologies and different safety standards. Moreover, EDF needs to prepare for GenIV
nuclear plants. Numerical simulation and CFD are indispensable tools for dealing with these
new problems. In this paper, will be presented first some important issues of code validation
and qualification when dealing with turbulent flows and heat transfer. Validity domain and
Turbulence, Heat and Mass Transfer 6
limitations of various models based on the Reynolds Averaged Navier-Stokes Equations and
on Large Eddy Simulation will be addressed.
The necessity of using high performance computing will be demonstrated and the
performances of EDF codes on advanced architectures will be presented. Then, the ability of
the EDF in-house software to solve complex industrial problems related to tomorrow energies
will be assessed.
2. A short Software Description
2.1. Code_Saturne software [1 & 2]
The CFD software Code_Saturne is based on a co-located Finite Volume approach that can
handle three-dimensional meshes built with any type of cell (tetrahedral, hexahedral, prismatic,
pyramidal, polyhedral) and with any type of grid structure (unstructured, block structured,
hybrid). It is able to simulate either incompressible or variable density flows, with a variety of
models to account for turbulence [1]. From a numerical point of view, velocity and pressure
coupling is insured by a prediction/correction method with a SIMPLEC algorithm and the
Poisson equation is solved with a conjugate gradient method. A Rhie and Chow interpolation
is used in the correction step to stabilize the solution. In 2007, in order to establish a large
community of users and to extend, by this means, the confidence it can have in its software,
EDF made Code_Saturne open-source [2]. It is provided under the Gnu General Public
Licence. Associated libraries for “Base Functions and Types” and “Finite Volume Mesh” are
provided under the Gnu Library General Public Licence (LGPL).
2.2. SYRTHES software [4 & 5]
SYRTHES solves conjugated heat transfer and radiation problems. It is using a Finite Element
method on linear IsoP1 triangle or tetrahedral elements. It can deal with transient 2D, 2D-axi
and 3D geometries. All physical parameters and source terms can depend on time, position
and local values such as temperature. Radiation module is only considering wall to wall
radiation through transparent media. SYRTHES can be easily coupled with Code_Saturne.
From end 2008, SYRTHES is also made open-source and provided under Gnu GPL [4, 5].
3. CFD Verification and Validation Strategy with RANSE
3.1. Needs for Verification and Validation (V&V) in CFD
After several decades of active research and collaboration on Computational Fluid Dynamics
and Turbulence Modelling these topics are often considered as “mature”, or perhaps more
realistically, the potential for further improvement of the models now tends to be perceived,
by funding bodies, as marginal. While current academic research is increasingly, if not
exclusively, focussed on DNS and LES, cognizant industries are concerned by the lack of
reliability of CFD predictions, which are and will be mostly based on the RANSE in the vast
majority of cases and where turbulence models are still a major cause of uncertainty. Indeed
even a large scale validation exercise such as the recent FLOMANIA EU Project [6], with
20 expert partners, failed to recommend a “best overall” RANSE model, not even for a
limited range of flows.
But the industrial need is not so much for improvement of turbulence models, but the ability
to surround CFD predictions with “error bars”, particularly in the nuclear power industry, for
safety issues obviously, but also as a guide for hundred billion Euros investments in new
J.P. Chabard & D. Laurence
plants with lifetime exceeding half a century: “Simuler pour Décider”1 is one of EDF R&D’s
adage and challenge! Building confidence in CFD predictions entails very many complex
issues beyond turbulence modelling, numerical analysis, software development under QA
procedures, and very extensive user training to raise awareness of the very many pitfalls in
real engineering applications of CFD. Most reliable CFD users are probably code developers
themselves, hence, in addition to HPC hardware, EDF R&D has invested heavily in “People”,
as well as collaborative CFD development and V&V activities.
The “Forward Look on Computational Science” organised in 2006 by the EU’s Engineering
Science Foundation concluded that Computational Fluid Dynamics (CFD) software has
evolved to level of complexity where it is often not possible to sustain an in-house effort and
switch to commercial codes is natural. Nevertheless, after a number of mergers, the choice of
commercial CFD software is increasingly restricted and even “proprietary” turbulence models
are now being marketed. Meanwhile as even academics and students increasingly use these
“black box codes”, there is a severe shortage of young CFD experts on the market and lack of
understanding of CFD models in industry. In this context open source CFD codes such as
OpenFoam and Code_Saturne, as detailed above, are beginning to be adopted by Academics.
3.2. Best Practice Guidelines and Database Initiatives
EDF R&D has been involved since the beginning in IAHR and ERCOFTAC V&V activities.
The Special Interest Group on Refined Turbulence Modelling led by Prof. K. Hanjalic is now
organising its 14th benchmarking workshop. The related “classic collection” database
administered by Dr. Craft at Manchester with over 80 test-cases is perhaps the best source of
Data for V&V of CFD on turbulent flow and several of its test cases are used for Q&A of
Code_Saturne. The ERCOFTAC BPG (“Best Practice Guidelines”) [7] and the related
“QNET-CFD” Knowledge Base2 also feed on this source but were led mainly by industrial
partners while participation from academia has been modest. The result covers a perhaps too
wide range of applications to include detailed scientific backing. Links to theses resources are
provided below:
 Special Interest Group on Refined Turbulence Modeling (ERCOFTAC-IAHR);
 ERCOFTAC “Classic Collection” Database at Manchester;
 QNET-CFD Trust and Quality in CFD, Knowledge base at Surrey University;
 ERCOFTAC Best Practice Guidelines;
 OECD Nuclear Energy Agency's BPG for use of CFD in reactor safety applications.
The Nuclear Energy Agency’s BPG for CFD [8], a recent addition, independent of the
previous collaborative works, is focussed on power plants. But its test-cases appear far too
complex for the detailed recommendations one attempts to derive, and indeed, authors fail to
fully follow their own recommendations in all cases (e.g. mesh refinement studies are
replaced by upwinding and the only low-RANSE test case is in fact a fully laminar flow).
Moreover, it is regrettable that advice on turbulence models is more specifically oriented
toward models developed for aeronautical applications rather than power plants.
As one-off funded EU/Gov or industrial projects on validation activities have lead to great but
rapidly obsolescent websites, and further centralised funding is getting even harder to secure.
Perhaps “Wikinomics” and the Wikipedia model could be the answer. Mass collaboration,
1
2
Simulate for Decision Making.
Qnet Knowledge Base (URL: http://eddie.mech.surrey.ac.uk/).
Turbulence, Heat and Mass Transfer 6
relying on individuals cooperating freely to solve a problem or improve know-how, seems
particularly suited to deal with V&V of software (it is a huge task, but if several contribute a
little then very many will benefit a lot). A “Wikipedia” type of website is under development
at U. Manchester to support a growing community of CFD users, starting with a special focus
on test cases with heat transfer and relevant to reactor thermal hydraulics, see table 1.
Table 1: Test cases wiki at www.saturne.cfdtm.org.
Icon
Status (progress and quality of test-case)
documentation good enough for users to run simulations and contribute results
recommended test-case, some reference solutions available
recommended test-case, reference solutions confirmed and consensus reached
Case now thoroughly checked and locked as it is used as reference in QA
procedures
suggestion for new test case, help welcome
under construction, help wanted
Case
Authors
Type
Flow past a heated circular cylinder
Exp.
Vertical Heated Pipe
Scholten and
Murray
Krauss and
Meyer
J. You et al.
Num.
Flow through a Tube bundle
Moulinec et al.
Num.
Fuel Rod Bundle
SFR Fuel Rods with spiral wire
Asymmetric plane diffuser
Flow over 2D periodic hills
Turbulent Natural Convection in an Enclosed Tall
Cavity
Thermal mixing in a T-junction
Exp.
Num.
Buice, and Eaton,
J.K.
Temmerman and
Leschziner
Betts and Bokhari
Num.
Westin et al.
Exp.
Swirling Flow in a Pipe
T-junction mixing zone followed by elbow
Status
Exp.
Exp.
Exp.
EDF & partners
Exp.
A special feature of this database is that, in addition to experimental or DNS data, it will
contain reference solutions, for well-known RANSE models, generated with different codes.
Over time all meshing, parameters and results files of Code_Saturne will be available on this
website. This will be done as part of the usual V&V activity for each new version release of
Code_Saturne. Presently, mostly PhD students in partner universities are contributing new test
cases or reference solutions, and further verification and editing by permanent staff will be
needed to conform to QA procedures (none of the cases yet have the “3 stars + lock” symbol
of table 1.). But, with regular “on the fly” contributions, no specific funded project is then
needed to extend the database, which makes it sustainable as is the “Classic Database”
administrated by T. Craft [3]. For EDF, contributing its code validation cases is also a logical
extension of its open-source code policy. Since one objective behind it is to show confidence
in the software, posting V&V information is an even more powerful statement.
J.P. Chabard & D. Laurence
4. Example of Test Cases
4.1. Heated vertical pipe
In the cores of many nuclear reactors heat is extracted by ascending flows in a large number of
parallel passages between fuel rods. At lower flow-rate conditions such heated turbulent flows
may be significantly modified from the forced convection condition by the action of buoyancy,
particularly in gas-cooled reactors. The heat transfer rate may drop to less than half of the
forced convection value, as shown in figure 1. Building on previous turbulence model
comparison works (see [3]), Keshmiri et al. [9] further benchmarked different CFD codes
‘CONVERT’, ‘STAR-CD’, and ‘Code_Saturne’, (respectively academic, commercial, and
industrial packages) and popular RANS models. Similar models providing similar results in
the different codes enable verification of their proper implementation. The test-case wiki [3]
contains not only experimental results but also numerical simulation results, as well as mesh
and parameter files for each code so that they can be re-launched by anyone, as a tutorial, or
rerun by developers for new versions of the codes.
Buoyancy-aided pipe
flow (heated+upward or
cooled+downward)
Gr
Bo  8  10 4 3.425 0.8
Re
Pr
Figure 1: Impairment of heat transfer coefficient as function of Bo. Number. (Keshmiri [9])
As sketched in figure 1, when the near wall layer is accelerated by buoyancy, the high velocity
gradient region is pushed closer to the wall and as a result turbulence production is restrained
by wall proximity, and eventually (for a certain range of Buoyancy parameter values) the flow
relaminarises (fig. 2). This highlights a models ability to account for interaction between the
actual turbulence length-scale (size of large eddies), and the non-local influence of a solid
wall. The DNS data (3 red dots in fig. 1) was confirmed by 6 refined LES (by Y. Addad) also
showing that the collapse of Nusselt number is very sudden (6 dark green squares).
The Launder & Sharma or Lien & Leschziner k- models and V2F models all perform fairly
well, whereas the k-, and even its SST variant miss the relaminarisation, possibly because
2
they rely mostly on the artificially high (non-physical) boundary condition   6 (  y ) to
sensitize the model to wall proximity, with little feedback information from the actual near
wall level of k. In the SST version, further explicit reference to the wall distance “ y “ is
Turbulence, Heat and Mass Transfer 6
2



 2 k 500   


 
introduced in the eddy viscosity t  0.31k max a1;  tanh  max 
;
2 


0.09

y

y


  



 is the mean vorticity vector, or, in the more recent versions (2003) mean strain.
1
Figure 2: Heated vertical pipe flow. Temperature (left) and kinetic energy (right) profiles.
There is some similarity here with the failure of the same SST model in accelerating boundary
layers or flat plate transition, since in the present case, with buoyancy effects in the k-equation
negligible in all models, the relaminarisation is only due to a change in mean velocity profile.
It is quite remarkable that, with damping functions tuned only on data available in 1974,
the Launder & Sharma k-model is still able to best predict new experiments and DNS data
40 years later. By contrast, the form and constants of more recent models seem to be
continuously evolving, which shows how difficult it has become to further progress in
RANSE modelling. EDF R&D itself invested early on the elliptic relaxation idea of P. Durbin
[10] (supporting PhD works of Wizmann, Parneix, Manceau, Uribe and collaborating with P.
Durbin and K. Hanjalic). The absence of damping functions and references to wall distances
was indeed appealing for FE (N3S) or FV (Code_Saturne) unstructured CFD codes and held
promises for complex geometries. While performance on many academic test cases was
excellent, heat transfer and natural convection in particular, stability remained quite an issue
in industrial applications until the recent development of “code friendly” versions [11-13].
The V2F model is based on the
constitutive
relation  t  C v 2 T
which does not require damping
functions when the wall normal
velocity fluctuation (v) is properly
predicted with the elliptic relaxation
strategy. The fact that it is now
available in commercial codes is a sign
of its maturity and growing popularity.
Perhaps one of its key features is that it
incorporates a non-zero parameter at
the wall in the form of a length-scale.
Figure 3 - top shows 2 point pressure
-velocity correlations (from DNS data)
Figure 3: Elliptic relaxation lengthscale (Manceau [14])
J.P. Chabard & D. Laurence
are skewed as the wall is approached. Integrating these correlations produces DNS lengthscale
values (squares in fig. 3 bottom) which are then found remarkably close to Durbin’s elliptic
relaxation length-scale L (lines), as it is used to make pressure-strain related terms “f” , tuned
for homogeneous cases, more sensitive to non local effects: (1  L2 2 ) f actual  f homogeneous
4.2. Tube bundles in cross-flow
Figure 4: Streamlines in tube array. Left to right P/D = 1.2; 1.5; 1.6; and 1.75. All cases with “inline”
(horizontal) mean pressure gradient & normally symmetric. From I. Afgan thesis, see [3]& [16]
Heat exchange and fluid forces on tube bundles have been studied since development of CFD
at EDF R&D in 1980s. For cross-flow in staggered arrangements (Benhamadouche [15])
confirmed that LES or Reynolds Stress Transport is the required level of modeling. Figure 4
shows the asymmetric streamlines in case of a densely packed inline tube array. A
non-symmetric pressure distribution trend is confirmed by experiments but more clearly by
two LES on different grids and codes ([16] and fig. 5). The classical symmetrical recirculation
pair is recovered when pitch/D ratio reaches 1.75. For P/D = 1.4 to 1.5 (actual PWR steam
generator values) the depth of the gap compared to its width is simply too shallow for a
symmetrical mean flow vortex pair to develop.
Figure 5: Comparison of pressure coefficient around tube, P/D = 1.5 inline flow (from I. Afgan).
Right: Actual steam generator entry case (from Jusserand et al. ASME PPVP 2009).
In terms of fluid-structure interaction modeling, finding an asymmetric mean flow solution
even for a nil displacement of the central tube is highly important. Figure 5 shows the
asymmetry is also captured by RANS models, but less obviously, and in decreasing accuracy
order: the SSG Re Stress Transport model, the k- SST, the standard k-, and the RNG k-.
4.3. Swirling flow in pipes
The BPG mentioned in section 3 all tend to recommend Re Stress Transport Models for
stratified, rotating, swirling or secondary flows, yet these are not frequently used in industrial
Turbulence, Heat and Mass Transfer 6
applications, besides cyclone separators and pipe bends perhaps. In the BPG [7] EDF had
reported, for swirling flows in dead leg T junctions, the need to use finer grids with RSTM to
see its true advantage over eddy-viscosity models.
Figure 6: RSTM simulation of heterogeneities at the exit of a PWR upper plenum; scalar tracers
through plenum to 4 hot leg exits (left); geometrical details as seen from actual mesh surface (right);
secondary motion in hot leg cross section. (from JP Juhel and Martinez & Alvarez [17])
Figure 6 now shows a truly industrial RSTM HPC simulation with Code_Saturne to predict
secondary motions in the hot fluid exit of the upper plenum of a PWR. In this hot leg flow and
scalar inhomogeneities need to be studied. The pipe is straight and orthogonal to the vessel
wall so this secondary motion originates only from conditions in the upper vessel and hence
the 4 main legs, 89 column guides, 52 instrumentation guides and many fine details are
represented on this 61 Million cells mesh. At this level of detail, the improvement from a k-,
to a RSTM is clearer than on the previous 1 M cell mesh.
Figure 7: Turbulent shear stress across a rotating channel ( from [18]).
The wider availability of HPC resource will possibly make obsolete many ad hoc “curvature
& rotation corrections” to eddy viscosity models since such effects are accounted for exactly
in RSTM, as used to be well known but is today maybe worth summarizing. Decomposing a
generic source-term/body-force into mean + fluctuating components, ( Fi  fi ) as for velocity
(Ui  ui ) and applying the Reynolds averaging process, a generic tonsorial source term for the
Re stress equation is obtained: Gij  u j fi  ui f j , i.e.
 t (Ui  ui )  Fi  fi  u j  t ui  ui  t u j  ...  u j fi  ui f j ...  Gij ...
For a rotating channel flow (1-flow direction, 2-wall to wall, 3-rotation axis), the Coriolis
force simply leads to the Re Stress tensorial generation/sink term:
J.P. Chabard & D. Laurence
 F1 
F 
 2
 F3 
f1   0  U1  u1 
f 2    0    0  u2 
   

f3   2   0  u3 


4u1u2

G   2 u1u1  u2u2


0



2 u1u1  u2u2

4u1u2
0

0

0

0

and the shear stress production is then:
 d U1

d u1u2
  u2u2 
 2   2 u1u1  ...
dt
 dx2

While the mean velocity gradient changes sign across the channel, the Coriolis term doesn’t,
thus obviously creating an a-symmetry and possibly relaminarisation on one side, as in figure
7 and as shown frequently in 80’s and 90’s papers, (e.g. [18).
4.4. Thermal mixing in a T-junction
Figure 8: “HYPI, FATHER” and “WATLON” T junction mixing test cases (top). Comparison of
standard and advanced/”unsteady” wall functions for LES on the “WATLON” case [19]. Mean (left),
rms (right) temperatures profiles and iso (centre); LES results by T. Pasutto [20].
The main pipelines in certain PWR plants could age prematurely as result of fluctuating
thermal stresses in the vicinity of T junctions where cold water flowing in one pipe meets hot
water flowing in another. Incidents due to thermal fatigue have already been observed in PWR
throughout the world; USA, Germany, Japan, Belgium, France, leading to partial or complete
stoppage of the plant. There are a number of projects currently underway to numerically study
this sort of thermal fatigue. There remain a number of difficulties, some of which are related
to turbulence modeling and the coupling between the turbulence and the wall heat flux.
Several experiments have recently produced detailed data in the core of the flow and solid
wall temperatures in one case [19, 20]. Large Eddy Simulation is currently the preferred
modeling approach, but the high Reynolds numbers do not allow wall resolved LES for the
actual reactor conditions. The “Thin Boundary Layer Equations” (TBLE), a 1D unsteady
solver meant to replace the use of wall functions with LES, were coded, and they reproduced
the improvements reported in the literature, e.g. for separating flows over periodic hills, but
Turbulence, Heat and Mass Transfer 6
made very little change to the occasional over-prediction of the wall-temperature fluctuations
in T junction test case. Perhaps this is one case where simulations are resolving even finer
scales than measurable ones, and further investigations should attempt, in the conjugate
heat-transfer LES or post-processing, to account for possible extra attenuations from
temperature probes themselves (i.e. meshing down to “nut and bolt” level as in section 6.3).
5. Towards Predictive LES Computations
LES provides a much richer collection of results (time series, spectra, extremes), than the
RANS approach, and this level of detail is now required in several industrial problems, e.g.
thermal fatigue, aero-acoustics, and turbulence induced fluid-structure coupling. On the other
hand resorting systematically to LES with the expectation that “it is more accurate than
RANS” can be dangerous. LES is “eventually” accurate provided that appropriate meshes and
numerical schemes are used. But this is often only established after significant trial and error
that is seldom reported. As the LES application area is evolving from academic test-case
“post-dictions” to actual “pre-dictions” of flow features, the community is starting to focus on
LES quality criteria and best practice guidelines (e.g. [21]), but for other than channel flows,
this task is daunting.
Figure 9: Wall resolved channel flow LES with FV mesh locally adapted to the Taylor microscale.
A practical criteria is that meshes should be locally adapted to a fraction of the turbulent
integral length-scale, which is highly variable in complex flows or even in a simple boundary
layer, but this has been practiced by e.g. Y. Addad at U. Manchester on a range of practical
LES and a commercial code with surprisingly good results. Because LES is not a deterministic
approach it does not need to reproduce the actual space-time evolution of every single eddy,
but only their statistical behaviour. With this in mind, and using only second order FV
methods, phase errors may be allowed to cancel out through averaging, but not amplitude
errors leading to biased statistics (numerical dissipation from even minor upwinding). Simple
FV methods for unstructured grids as featured by commercial software might be the current
optimum for complex flow LES if we accept that mesh adaptation to the multi-scale and
inhomogeneous nature of turbulence is more important than formal accuracy.
The channel flow LES results in figure 9, using an unstructured grid matching growth of
Taylor micro-scales, show that commercial (STAR-CD) or in-house (Code-Saturne) FV
J.P. Chabard & D. Laurence
software can produce “statistical” results of “DNS quality” including for the second moments
(and even their budget - not shown here - possibly because Taylor scales in addition to
integral scales are being captured with this finely tuned mesh). However the non-orthogonality
and non-homogeneity of cells, which are inevitable when locally adapting to highly variable
turbulent scales, are known to degrade the accuracy of the numerical methods. Generating an
unstructured mesh, with cell sizes growing with the integral scale, while at the same time
keeping quasi equilateral tetrahedra or orthogonal hexa cells as required for second order
accuracy is a conundrum that automatic mesh generators are unable to solve, and yet
“hand-made” grids are very tedious and cannot constitute an industrial solution.
A 2nd paradox is that before generating the grid for a real LES “pre-diction”, turbulent
length-scales are needed, which means (for other than the eternal channel flow LES) a RANS
run as precursor study, and brings us back to the previous section on need for refined and
reliable RANS models. Clearly in an industrial context LES cannot be considered as an
alternative to RANS, but rather a companion approach, when a deeper investigation is needed.
Figure 10: near wall layer RANS-LES coupling in channel flows with the 2 velocities method [23].
Another combination is the upstream-RANS downstream-LES coupling or rather chained
simulations for non-homogenous cases. The Synthetic Eddy Method of Jarrin [22] developed
in Code_Saturne since a couple of years was proven very effective and very suitable for
unstructured grids and complex geometries. It also requires a refined RANS model to provide
the full Re stress tensor and length-scales from which it then generates very realistic and
sustainable synthetic turbulent structures as inlet conditions for the LES. It is used in the T
junction mixing case mentioned previously. For this flow the Re number is 2 million with
near-wall cells of the order of 100 wall-units requiring wall functions. This is one application
to motivate the development of hybrid RANS-LES coupling in the wall layer.
A major difficulty in most hybrid RANS-LES methods occurs when both models are
blended into a single eddy viscosity. In the blending region, on the one hand the RANS
eddy-viscosity tends to be too strong and damps the emerging LES fluctuations, while from
the RANS point of view viscosity is too low to reproduce the correct mean shear stress. This
classically leads to a kink (sharp velocity increase) in the velocity profile around the
RANS-LES matching plane. The hybrid method developed by Uribe [23] avoids this by
revisiting Schumann’s idea (1975) of decomposing the LES velocity field into a running time
average and a fluctuating component. The modeled Re stress is then defined as
 ij  1  3 kk ij  f 2 LES  S ij   S ij    (1  f ) 2 RANS  S ij  , where f is a blending function
(0 = RANS, 1 = LES) and <.> denotes the running time-average. The RANS model only sees
Turbulence, Heat and Mass Transfer 6
the time average velocity, while the LES resolved turbulent kinetic energy only sees
subgrid-scale viscosity and dissipation it induces. With this decoupling of mean and
fluctuating fields the RANS viscosity has no effect on the resolved scale fluctuations. Mean
velocity profile predictions are now excellent (figure 10) and near wall rms values are realistic
even on the same very coarse mesh used for all the considered Re numbers. The next step is to
test whether the large scale temperature fluctuations at the wall are representative of the
loading in conjugate heat transfer simulations.
6. Industrial Applications of Advanced Simulation in CFD to Tomorrow’s
Energies
6.1. High performance computing
Figure 11: Evolution in computing power at EDF R&D, in Tflops (left). Code_Saturne performance on
HPCx computer (Daresbury Lab. UK) for a channel flow LES (right).
As explained in the introduction, EDF has to deal with optimization problems in which design
margins are directly questioned as they are a key factor to control maintenance costs, allow for
increasing performances and extend plants lifetime. In this context, the advent of high
performance computing (HPC) in the petaflop range brings new opportunities as will be
shown below. As shown in figure 11, EDF is increasing dramatically the computing power
made available for its research teams in order to boost HPC-based simulation to solve
operational problems. This increase is based on the installation of two IBM BlueGene
machines (a 23 Tflops IBM BG/L and a 100 Tflops BG/P). CFD of course benefits from this
computing power enabling more sophisticated models and a better geometry description even
for tiny details. A special effort has been devoted by EDF to optimizing Code_Saturne on
massively parallel computers. Code_Saturne proves to be very efficient on different HPC
platforms as it was also awarded “gold” status in CFD by running on the UK HPCx
Supercomputer for a 78 Mcell LES channel flow calculation (Science and Technology Faculty
Council Daresbury Lab., a HPC service provider to the UK academic community).
Code_Saturne was 1.84x faster on 1024 processors than on 512 processors (a factor of 1.7
earns “gold” status). As a consequence, Code_Saturne has been chosen as one of the principal
applications benchmarks for the Partnership for Advanced Computing in Europe project
(www.prace-project.eu).
6.2. Application of high performance computing to uncertainty control
Through many years of collaborative benchmarking, workshops, and assembling databases for
J.P. Chabard & D. Laurence
the validation of CFD, the “popular” test cases that have emerged are the ones where most of
the sources of uncertainties have been removed or controlled, while those based on
experiments where discrepancies with models remained inexplicable have been discarded.
This deals for example with cases where the inlet conditions are not well known, where
unexpected 3D effects are present, where bifurcations or hysteresis effects are suspected,
where asymmetric flow patterns in nominally symmetric geometries appear. These
problematic/complex issues tend to be overlooked (the PhD student needs to submit his thesis,
the academic wants to publish, and so only the more successful or at least “explainable”
results get reported and problematic cases are forgotten). This bias introduced by natural
selection of “clean” test cases can lead to over-confidence in numerical predictions and it is
time to introduce uncertainty concepts in CFD, preferably together with V&V documents to
raise awareness of code users.
Uncertainty in inlet conditions or other “input parameters” can now be studied via a very large
number of CFD simulations, using Monte Carlo or better, Design of Experiments (DOE) and
Morris’s method, together with the availability of HPC hardware. This new dimension should
be documented in the thermal-hydraulics database even for apparently simple cases. Examples
are the in-line tube-bundle cross-flow for instance which is prone to asymmetric solutions, the
compressible flow through a diaphragm or sudden expansion with Coanda effect, the stratified
flow in a horizontal pipe sensitive to initial conditions and/or transient time-stepping, etc.
6.3. Application n°1: Impact of mixing grids effects on the water flow in nuclear fuel rod
assemblies
Figure 12: (12.a) Geometry of the fuel assembly. (12.b) Mesh on the wall of the mixing grids. (12.c)
3D flow around fuel rods. (12.d) velocity intensity vortices around fuel rods in a horizontal plane.
Nuclear fuel management is one of the key issues for increasing nuclear plant performance.
For this kind of applications, the evaluation of the fuel behavior under incidental or accidental
conditions will be required by Safety Authorities for new fuel management strategies. It is
clearly a domain where design margin has to be questioned by CFD. In this context, a
prototype study was conducted in order to evaluate the effects of tiny features of mixing grids
Turbulence, Heat and Mass Transfer 6
(see millimetric details on figure 12-b) on the mechanical loading in fuel rods. This study is
based on a stationary CFD flow calculation on part of the fuel assembly and required a 100 M
cell meshing and 1 month of computing with Code_Saturne on 8000 BG/L processors. The
validation of the numerical results is still underway.
6.4. Application n°2: Mechanical behavior of screws of core shielding
One of the first thermal hydraulics
application of HPC was the precise
evaluation of mechanical properties
of hundred of screws used to hold
the peripheral thermal shielding part
of the nuclear core. The purpose was
to certify that the screws are safe
thanks to a structural mechanics
analysis and fine calculations of
Figure 13: Computation of the temperature field of bolts
temperature-induced
mechanical
holding the peripheral shielding in a nuclear core.
constraints under the screw head.
For such an analysis, precise evaluation of the thermal loading of the screw was necessary
and required a detailed 3D thermal hydraulics simulation coupling Code_Saturne for flow
calculations, and SYRTHES for conjugated heat transfer. This simulation has to deal with
multi-scale complex geometric details as it has to combine the multimetric height of the core
with the millimetric scales at the screw level. The coupled CFD/heat transfer simulation was
satisfactorily run and the temperature field transferred to the structural analysis code for
constraints computation. The details of the geometry are given on figure 13. This calculation
required 11 days on 200 BG/L proc. for a 230 M cell mesh [24].
6.5. Application n°3: Conjugated heat transfer analysis in sodium fast reactor
Fast reactors with liquid metal coolant received a renewal
of interest recently due to their more efficient usage of the
primary uranium resources. They are one of the selected
technologies in the frame of the GenIV initiative. In order
to evaluate nuclear power plant design and safety, 3D
analysis of the flow and heat transfer in a wire spacer fuel
assembly are on-going [24]. The introduction of the wire
wrapped spacers, helically wound along the pin axis,
enhances the mixing of the coolant between sub-channels
and prevent the collision between fuel pins.
The purpose of the computation is to study possible
heterogeneities of flow and temperature in the core. The
simulation (figure 14) is scaled down to a 7-pin only fast
reactor fuel rod bundle enclosed within a hexagonal
Figure 14: Solid & fluid meshes
can.The meshing require solid mesh generation using
for the 7-pin computation, and
tetrahedral and fluid mesh generation based on a 2D mesh
(insert on left) zoom on the wire.
which is twisted along the pin axis.
Two different turbulence models have been compared: the two equations k- model of Jones
& Launder and the Reynolds stress model of Speziale, Sarkar & Gatski (SSG model).
J.P. Chabard & D. Laurence
The wall modeling is based on the
so-called scalable wall functions. In this
model, the minimum value of y+ is
limited to 11.06, so the value of the
velocity gradient at the first call is the
same as if it was at the edge of the
viscous sub-layer.
The goal of the computation is to be able
to compute the temperature distribution
and have access to the pin temperature in
order to check that cladding stay below
safe temperature criteria. Figure 15
presents a 3 helices computation with
inlet temperature of 395°C and a mean
velocity of 6.44m/s. The average
temperature naturally increases as the
fluid flows upwards along the pins but
Figure 15: Fluid temperatures (a & b) near exit and
solid temperatures along the fuel assembly (c & d).
the solid temperature field is quite different
from one section to the next due to a strong
influence of the wire angular position (all materials are given homogeneous steel properties).
Refined investigations are planed regarding the turbulence modeling (using LES or using finer
meshes on a reduced number of pins). These simulations will require an intensive use of HPC.
Conclusions
Need of CFD modeling and simulation in power plant design and operations, code validation
and qualification for turbulent flows and heat transfer, as well as user training and
“open-source” issues were discussed. High performance computing is perhaps the major
source of recent progress in realistic simulations of complex industrial problems for tomorrow.
Progress in turbulence modeling is slower, but steady, and bounded validity range of various
models, mean that several RANS models still need to be developed in CFD codes, in addition
to LES which should not be considered as a universal replacement for RANS.
Acknowledgements: The authors are grateful for contributions from many colleagues in the
Code_Saturne and SYRTHES teams, at EDF-R&D and U. Manchester, School of Mech. Aero
and Civil Eng.
References
1. Archambeau, F., Mechitoua, N. and Sakiz, M. A Finite Volume Method for the
Computation of Turbulent Incompressible Flows – Industrial Applications, Int. J. Finite
Volumes, Vol. 1. 2004.
2. Code_Saturne download URL: http://rd.edf.com/code_saturne (accessed 2009-05-11).
3. Testcases DB: www.saturne.cfdtm.org and http://cfd.mace.manchester.ac.uk/ercoftac/
4. Rupp I., Peniguel C., Tommy-Martin M. Large Scale Finite Element Thermal Analysis of
Bolts of a French PWR Core Internal Baffle Structure. 7th I. Topical Meeting on Nuclear
Reactor Thermal Hydraulics, Operation and Safety NUTHOS-7, Seoul, Korea, Oct. 2008.
Turbulence, Heat and Mass Transfer 6
5. SYRTHES code download URL: http://rd.edf.com/syrthes (accessed 2009-05-11).
6. FLOMANIA – A European Initiative on Flow Physics Modelling. Haase, Aupoix, Bunge,
Swamborn Eds. Notes on Numerical Fluid Mechanics Vol 94, Springer, 2006.
7. ERCOFTAC Best Practice Guidelines for Industrial Computational Fluid Dynamics of
Single Phase Flows. V1.0, Jan 2000. URL: http://www.ercoftac.org/index.php?id=77).
8. Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications.
Report NEA/CSNI/R(2007)5, 15 May 2007. Site: www.nea.fr/html/nsd/csni/cfd.htm
URL: http://www.nea.fr/html/nsd/docs/2007/csni-r2007-5.pdf. (accessed 2009-05-11).
9. Keshmiri A., Addad Y., Cotton M.A., Laurence D. and Billard F. "Refined Eddy Viscosity
Schemes and LES for Ascending Mixed Convection Flows" in Computational Heat
Transfer (CHT08) Symp., Marakkech,11-16 May 2008, 1, pp. 274-279, 2008.
10. Durbin, P.A., Separated flow computations with the k-esp-v2 model. AIAA Journal,
Vol.33(4), pp. 659-664, 1995.
11. Laurence D. R., Uribe J.C., Utyuzhnikov S.V., A Robust Formulation of the v2-f Model,
J. Flow, Turbulence and Combustion, 73, 3-4, pp169-185, 2005.
12. Hanjalic, K., Popovac, M. Hadziabdic, M., A robust near- wall elliptic- relaxation eddyviscosity model for CFD .I. J. Heat and Fluid Flow, 24, pp. 1047- 1051, 2004.
13. Manceau, R. An Improved Version of the Elliptic Blending Model. Application to
Non-Rotating and Rotating Channel Flows, in 4th Symp. Turb. Shear Flow Phenomena,
J.A.C. Humphrey et al., eds., Williamsburg, Virginia, USA, pp. 259-264, 2005.
14. Manceau, R.,Wang, M., Laurence, D. Inhomogeneity and anisotropy effects on the
redistribution term in RANS modeling. J. Fluid Mech., 438, pp. 307-338, 2001.
15. Benhamadouche S., Laurence D. LES, Coarse LES, and Transient RANS comparison on
the flow across a tube bundle. I .J. of Heat and Fluid Flow, 24, 470-479, 2003.
16. Benhamadouche S, Laurence D, Jarrin N, Afgan I, Moulinec C. Large Eddy Simulation of
flow across in-line tube bundles. NURETH-11 paper 405, Avignon, France, Oct. 2005.
17. Martinez P., D. Alvarez D, Société Française d'Energie Nucléaire - SFEN ST6 meeting
"CFD pour la conception et la sûreté des réacteurs", Chatou 29/04/ 2009.
18. Wizman, V., Laurence, D., Kanniche, M., Durbin, P., Demuren, A. Modeling near wall
effects in SMC by elliptic relaxation. I. J. Heat & Fluid Flow, 17, pp. 255-266, 1996.
19. H. Ogawa, M. Igarashi, N. Kimura, H. Kamide Experimental study on fluid mixing
phenomena in T-pipe junction with upstream elbow. NURETH 11– paper 448, 2005.
20. Pasutto T., Peniguel C., Stefan, Effects of the upstream elbows for thermal fatigues in
PWR T Junctions using LES. ICONE-15, Nagoya, Japan, Paper 10410, 2007.
21. Meyers J., B. Geurts B., P. Sagaut P., Edts. Quality and Reliability of LES, ERCOFTAC
Series vol. 12, Springer, 2008.
22. Jarrin N., Prosser R., Uribe J.C., S. Benhamadouche S., Laurence D. Reconstruction of
turbulent fluctuations for hybrid RANS/LES simulations using a Synthetic-Eddy Method.
I. J. Heat and Fluid Flow http://dx.doi.org/10.1016/j.ijheatfluidflow.2009.02.016 , 2009.
23. Uribe J.C., Jarrin N., Prosser R. and Laurence D., Two Velocities hybrid RANS-LES of a
trailing edge flow, IUTAM Symposium "Unsteady Separated Flows and their Control" Corfu Greece June 2007, To appear in J. Flow Turbulence and Combustion 2009.
24. Péniguel C., Rupp I., Juhel JP., Rolfo M., Guillaud M., Gervais N. 3D Conjugated Heat
Transfer Analysis in Sodium Fast-Reactor Wire-Wrapped Fuel-Assembly, I.C. on
Advances in nuclear Power Plants, ICAPP ‘09 Tokyo, Japan, Paper 9311, 2009.