Heat and fluid flow simulations for deciding tomorrow’s ...cfd.mace.manchester.ac.uk/twiki/pub/Main/Thmt2009... · • ERCOFTAC Best Practice Guidelines; • OECD Nuclear Energy

Keynote Lecture for the 6th Int. Sym. on Turbulence, Heat and Mass Transfer

THMT6, 14-18 September 2009, Rome, Italy. http://www.thmt-09.org/

(THMT6 Preprint 2009-06-16) 1/16

Heat and fluid flow simulations for deciding

tomorrow’s energies

J.P. Chabard1,2

, D. Laurence1

1EDF, Research & Development Division, 1, avenue du Général de Gaulle - 92100, Clamart, France, [email protected] 2École 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

THMT6 Preprint 2009-06-16

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 Simulate for Decision Making.

2 Qnet Knowledge Base (URL: http://eddie.mech.surrey.ac.uk/).


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 Status

Flow past a heated circular cylinder Scholten and

Murray

Exp.

Fuel Rod Bundle Krauss and

Meyer

Exp.

Vertical Heated Pipe J. You et al. Num.

Flow through a Tube bundle Moulinec et al. Num.

SFR Fuel Rods with spiral wire Num.

Asymmetric plane diffuser Buice, and Eaton,

J.K.

Exp.

Flow over 2D periodic hills Temmerman and

Leschziner

Num.

Turbulent Natural Convection in an Enclosed Tall

Cavity

Betts and Bokhari Exp.

Thermal mixing in a T-junction Westin et al. Exp.

Swirling Flow in a Pipe Exp.

T-junction mixing zone followed by elbow 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.


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)

8.0425.34

PrRe

Gr108Bo ×=

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-ε models and V2F models all perform fairly

well, whereas the k-ω, and even its SST variant miss the relaminarisation, possibly because

they rely mostly on the artificially high (non-physical) boundary condition26 ( )yω ν β= 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


introduced in the eddy viscosity

12

1 2

2 5000.31 max ; tanh max ;

0.09t

kk a

y y

νν ω

ω ω

− = Ω

Ω is the mean vorticity vector, or, in the more recent versions (2003) mean strain.

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-ε 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 2

t C v Tµν =

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])


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: 2 2

actual homogeneous( )1 L f f+ ∇ =

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-ω SST, the standard k-ε, and the RNG k-ε.

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


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-ε,

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, ( )+i iF f as for velocity

( )+i iU u and applying the Reynolds averaging process, a generic tonsorial source term for the

Re stress equation is obtained: = +ij j i i jG u f u f , i.e.

( ) ... ... ...∂ + = + ⇒ ∂ + ∂ + = + =t i i i i j t i i t j j i i j ijU u F f u u u u u f u f G

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:


( )( )

1 2 1 1 2 21 1 1 1

2 2 2 1 1 2 2 1 2

3 3 3

4 2 00

0 0 2 4 0

2 0 0 0 0

− Ω Ω −+ +

+ = ∧ + = Ω − + Ω + Ω +

⇒

u u u u u uF f U u

F f u u u u u u u

F f u

G

and the shear stress production is then:

1 2 12 2 1 1

2

2 2 ...d u u d U

u u u udt dx

= − + Ω + Ω +

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


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


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 1 3 2 (1 )2τ τ δ ν ν − + / = − < > + − < > ij kk ij LES RANSij ij ijf fS S S , where f is a blending function

(0 = RANS, 1 = LES) and <.> denotes the running time-average. The RANS model only sees


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


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


(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

temperature-induced mechanical

constraints under the screw head.

Figure 13: Computation of the temperature field of bolts

holding the peripheral shielding in a nuclear core.

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

can.The meshing require solid mesh generation using

tetrahedral and fluid mesh generation based on a 2D mesh

which is twisted along the pin axis.

Figure 14: Solid & fluid meshes

for the 7-pin computation, and

(insert on left) zoom on the wire.

Two different turbulence models have been compared: the two equations k-ε model of Jones

& Launder and the Reynolds stress model of Speziale, Sarkar & Gatski (SSG model).


Figure 15: Fluid temperatures (a & b) near exit and

solid temperatures along the fuel assembly (c & d).

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

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.


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 eddy-

viscosity 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.

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Heat and fluid flow simulations for deciding tomorrow’s ...cfd.mace.manchester.ac.uk/twiki/pub/Main/Thmt2009... · • ERCOFTAC Best Practice Guidelines; • OECD Nuclear Energy