DNS_PhD_Proposal_July04.05 - Severe Accident Research

fingersfieldMechanics

Feb 22, 2014 (3 years and 8 months ago)

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Proposal to the PSI Research Committee


X



Proposal for additional funds (PSI
-
reserves)

-

Investment proposal





-

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(Main goals, work in progress, significant results to this date, future plans)

Recent experimental data have highlighted some interesting phenomena of particle
-
turbule
nt flow interactions which are
yet to be fully understood: for instance, it has been shown that particles in large volumes with turbulent natural
convective currents settled at a rate which is greater than that expected under quiescent conditions. This par
allels
previous findings in channel flows which found that droplet settling rates are very much enhanced when turbulence is
present in the carrier gas. Still more recently, the ARTIST data showed the tendency of particles to deposit more readily
on horizon
tal surfaces when the carrier gas velocity (i.e. turbulence level) is increased. In light of this, one may assume
that the coupling between the gas fluctuations and aerosol motion controls aerosol removal in the presence of turbulence
within a closed cavit
y.

To confirm this assumption, the following PhD project is proposed with a two
-
fold objective: First, it would allow one
to experiment numerically on interactions between turbulence and particles in closed volumes using state
-
of
-
the
-
art
numerical methods
. Secondly, it would allow, even if under idealized conditions, to help explain some of the unexpected
experimental results mentioned earlier, which are very important for reactor safety.

Recent flow simulations have shown that particles dispersed in turb
ulent flows tend to display stark preferential
concentration profiles in the boundary layer because of inhomogeneous turbulence effects (so
-
called turbophoresis).
Therefore, a good basic description of turbulence is required. The method of choice for the t
reatment of turbulence is the

Direct Numerical Simulation (DNS), which involves the solution of the transient, non
-
linear Navier
-
Stokes equations
without any modelling of turbulence. DNS provides thus a complete description of a turbulent flow, and the
ins
tantaneous flow variables (e.g. velocity and pressure) are known as a function of space and time. The DNS resolves
all dynamically important turbulence scales, from the largest turbulence generating eddies, down to the smallest
dissipative Kolmogorov scale
s.

To simplify the problem, this investigation proposes to use the so
-
called Differential Heated Cavity (DHC) as a model
of a closed volume where turbulent flow is predominant. The DHC is a 3D rectangular domain, where the two opposite
vertical walls are
kept isothermal at different temperatures whereas all other walls are insulated. Particle trajectories will
be computed using the Lagrangian particle tracking (LPT) methods, including the relevant forces on the particle (drag,
gravity, thermophoresis, lift
).

In addition to a more rigorous understanding of particle settling in a turbulent flow cavity,
the study would also help elucidate the exact role of thermophoresis in the transport of particles towards and away from
the walls. In terms of application of
DNS to practical problems such as aerosol deposition in nuclear reactor
containments, DNS results of this current investigation should be complemented by future work concentrating on use of
dimensional analysis and scaling at the relevant scales as determi
ned by the proposed work.

The PhD program will be supervised by Prof. Dr. M. Deville of the EPFL for the description of the turbulent flow and
Prof. Dr. A. Soldati of the University of Udine, Italy for the simulations of the particle behaviour in the turbu
lent flow.

The PhD program has a strong link with the mission of NES on severe accidents in nuclear power plants. The depletion
of particles suspended in a turbulent fluid is also of great interest to many industrial and environmental applications.
Some of

these include: chemical reactors, combustion chambers, cloud dynamics, dust storms, sediment deposition on
river banks, as well as occupational exposure to indoor air pollutants.

In the particular case of nuclear safety, most severe accident scenarios le
ad to the presence of fission products in aerosol
form in the closed containment atmosphere where turbulent convection currents are dominant. The particle deposition
inside the containment plays a significant role in limiting the release of radioactivity t
o the environment, and therefore a
thorough understanding of the aerosol deposition mechanisms inside an enclosure is of utmost importance.





Würenlingen/Villigen, 4
th

July 2005



-

2

-

Begin: 2005

End: 2008


Units

Own KST

LOG + Constr.

Other KST

Total

-

Total Investments
(incl. facilities extensio
ns):

-

Personnel
(for Construction):

kCHF

PY

8
1






8


-

O & M Costs:

-

Personnel
(for O&M and research)
:

kCHF/a

PY/a


0.58






0.58

-

Decommissioning and Disposal Costs:

kCHF





-

Expected / Available External Resources:

of which Materials:

Personn
el:

kCHF

kCHF

PY













Partners:

PY

1.2

-

Duration:



for contracts with third parties, if different to project duration

3





Budget of the requested additional funds

Personnel:
Ph.D
. students, post
-
docs, etc.

0.5 PY/a

75 kCHF

Materials



kCHF

Total requested additional funds


75 kCHF

1. needed for a high performance PC

Note: travel costs between PSI
-
EPFL
-
Udine (will not exceed a few kCHF) will be financed through the
general project budget of the severe accident project.
1.

Research Activitie
s

1.1

International Status of Research Field

(Goals of the international research; Open questions; Approaches used to this date; Priorities. Indicate at
maximum 5 relevant references of external authors)

The depletion of particles suspended in a turbulent

fluid is of great interest to many industrial and
environmental applications. Some of these include: chemical and nuclear reactors, combustion chambers,
cloud dynamics, dust storms, sediment deposition on river banks, as well as occupational exposure to i
ndoor
air pollutants. In the particular case of nuclear safety, most severe accident scenarios lead to the presence of
aerosol fission products in the closed containment atmosphere where turbulent convection currents are
induced by natural circulation betw
een the cold structures and hot, aerosol
-
laden gas.
The particle
deposition inside the containment plays a significant role in limiting the release of radioactivity to the
environment, and therefore a thorough understanding of the aerosol deposition mechan
isms inside an
enclosure is of utmost importance.

Generally, the natural circulation gas speeds are several orders of magnitude greater than the settling
velocities of typical aerosols, and therefore, the aerosol particles will tend to be entrained by the
flow rather
then settle under the sole influence of gravity. Recent related experimental data have highlighted some
interesting phenomena of particle
-
turbulent flow interactions which are yet to be fully understood: for
instance, it has been shown in the P
hebus [1] project that particles in the containment settled at a rate which
is greater than that expected under quiescent conditions. This parallels previous experimental findings [2] in
channel flow, which found that droplets settling rates are very much
enhanced when turbulence is present in
the carrier gas. Figure 1 taken from [2] presents the experimental enhancement in the settling rate
(normalized with the normal fluctuating component rate u’) versus particle inertia as measured by its Stokes
number
1

(V
z

is the actual settling velocity and V
St

is the settling velocity in quiescent conditions). The
Phebus data [1] also showed that the settling rate of particles displays a much weaker dependence on
particle inertia than would be anticipated in the absenc
e of turbulence. Still more recently, the ARTIST data
[3] showed the tendency of particles to deposit more readily on horizontal surfaces when the carrier gas
velocity (i.e. turbulence level) is increased. In light of this, the coupling between the gas tur
bulent
fluctuations and aerosol motion needs to be carefully investigated to determine the controlling mechanisms
responsible for aerosol removal in the presence of turbulence within a closed cavity.


Figure 1: Enhancement of droplet settling velocity as

a function of its Stokes number




1

Stokes number St=particle relaxation time/typical fluid time scale

-

4

-

The effect of turbulence on the settling rates of particles has also been demonstrated in numerical
simulations [4] for isotropic homogeneous turbulence; however, these results cannot be easily extrapolated
if the flow is n
aturally driven inside a closed volume, with the added complication of thermal effects.

The released nuclear aerosols can deposit on containment surfaces by a variety of mechanisms which
depend on the size of the aerosols as well as on the prevailing turbu
lent flow conditions. The most important
forces acting on the particles in the containment are: the drag, gravity, diffusiophoresis (force due to vapour
condensation), thermophoresis (force due to thermal gradients), and lift. The removal of aerosols by th
ese
forces depends, among others, on the aerosol concentration close to the walls. The latter, in turn, has been
shown [5,6,7] to display stark preferential profiles in the boundary layer of channel/pipe flows because of
inhomogeneous turbulence effects (s
o
-
called turbophoresis [8]). Therefore,

a
description
of turbulence at a
very fundamental level is required if one is to achieve an accurate prediction of aerosol motion and
ultimately depletion rates.

The method of choice for the understanding of turbulen
ce is the Direct Numerical Simulation (DNS) which
involves the solution of the transient, non
-
linear Navier
-
Stokes equations without any modelling. DNS
provides thus a complete description of a turbulent flow, and the instantaneous flow variables (e.g. vel
ocity
and pressure) are known as a function of space and time. The DNS resolves all dynamically important
turbulence scales, from the largest turbulence generating eddies, down to the smallest dissipative
Kolmogorov scales
2
. Since accurately capturing the
effect of turbulence is important to the study of aerosol
dispersion/deposition, DNS is a very useful tool for the problem at hand.

Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot
be easily attai
ned in the laboratory. Direct numerical simulation was initially used to analyze various basic
incompressible turbulent flows such as: forced and decaying homogeneous turbulence, homogeneous
turbulent shear flow, fully developed turbulent channel flows, fl
at plate boundary layers, and temporally
evolving mixing layers [9]. The recent increase in computer power with the advent of powerful personal
computers and clusters has expanded the application of DNS of low
-
Reynolds number flows to a wide
variety of flo
w patterns with higher Reynolds number. The plane channel flow was simulated up to bulk
Reynolds number of 12500 [10]. However, practical Reynolds numbers will remain out of reach for many
years to come. Overall, the DNS methodology has been applied to a w
ide variety of flows in the last 5−6
years. Although significant breakthroughs in turbulence modelling have yet to occur, the accurate simulation
of turbulence has helped analyze the influence of turbulence on various other processes.

The major limitation
of DNS is that the range of scales in turbulent flows increases rapidly with the
Reynolds number (for forced flows) and Rayleigh number (for buoyancy driven flows), so that DNS
simulations are very time
-
consuming and require powerful computational resource
s even at moderate
Reynolds/Rayleigh numbers. As a result, most practical engineering problems have too wide a range of
scales to be directly computed using DNS. Therefore, idealizations have to be made in both the geometry of
the problem and the level of
turbulence (Reynolds/ Rayleigh

numbers) in order for DNS computations to be
tractable. Judicious use of dimensional analysis and scaling will be needed to complement basic DNS
studies and arrive at practical estimates. Hence, this investigation proposes to

use the so
-
called Differential
Heated Cavity (DHC) as a model of a closed volume where turbulence flow is predominant. The DHC is a
3D rectangular domain, where the two opposite vertical walls are kept isothermal at different temperatures
whereas all the
other walls are insulated. In DNS computations will be performed under as high as possible
turbulent conditions. It is assumed that the particle concentration is small enough that the particles have no
influence on the gas flow (one
-
way coupling). Particle

behaviour will be treated with Lagrangian particle
tracking (LPT) methods, by solving the particle equation of motion subject to relevant forces.

The DHC problem is governed by

the following parameters: A
d
, the depth aspect ratio, A
h
, the height aspect
ra
tio,


the wall

temperatures differential,
Pr

the Prandtl number (order of 1), and
Ra

the Rayleigh number
defined as:




2

T
he
Kolmogorov scale is the smallest length/time scale which must be resolved to capture all turbulent effects

-

5

-










v
L
T
g
Ra
3

(1)


where g is the gravity acceleration,


the fluid thermal expansion coefficient, L the vertical height of th
e
cavity, and


and


are the fluid kinematic viscosity and thermal diffusivity, respectively. Even

though the
problem statement appears simple, the physical nature of the resulting flow regimes can be a very complex
function of the independent parameters.


The two

dimensional version of the DHC problem has been extensively studied and several benchmarks are
in existence for CFD code validation including the effect of Ra, aspect ratios, and the wall temperature
differential [11]. Three

dimensional investiga
tions have been relatively few and recent. Recently, Soria et
al. [12] have carried out three

dimensional direct numerical simulations of a DHC to compare two
-

and
three

dimensional flows with A
d

= 1, and A
h

= 4 for

Ra such that the flow is three

dimension
al and
unsteady (in the DNS sense). They report that the majority of the previous numerical simulations of
turbulent flows have been carried out assuming two

dimensional flows. They emphasize the importance of
carrying out systematic three

dimensional simu
lations. They found that the second
-
order statistics such as
the Reynolds stresses were significantly different. A similar DNS investigation by Bastiaans et al. [13] dealt
with free convection induced by a line heat source inside a confined cavity at a Ra
number of 10
10
. It was
again found that the flow is essentially 3D, especially near the walls. This indicates further that three
-
dimensional DNS is the tool of choice to get an accurate understanding of particle motion and depletion
inside an enclosure wit
h turbulence natural convection flow.

To the best of our knowledge, no one has thus far addressed particle depletion inside an enclosure using a
fundamental tool such as DNS. There was a recent effort to use the Lagrangian tracking technique to
compute par
ticle dispersion in a two
-
dimensional ventilated cavity [14]. In this study, the instantaneous air
velocity field was computed by so
-
called proper orthogonal decomposition (POD), which transforms the
Navier
-
Stokes equations into a set of low
-
dimensional or
dinary differential equations. Although allowing a
substantial decrease in computing time compared to DNS, the POD method is a poor predictor of the
controlling dynamics, and there
is no straightforward way that defines how optimal model truncations are to

be done.

Computation fluid dynamics (CFD)
-
type studies were performed with the widely used CFX and FLUENT
commercial codes to determine the steady
-
state flow field and particle decay rates in a large volume
simulating a containment [15]. The results provi
ded reasonably accurate estimates of the particle depletion
rates in the Phebus containment [1] when only the mean flow velocities were used (fluctuating turbulent
components ignored). However, the non
-
inclusion of turbulent components of the velocity led
to the
artificial trapping of up to one third of the particles in infinite circulation loops, clearly an unphysical result.

DNS stands then as the only tool to allow a rigorous treatment of particle
-
turbulence interactions inside a
closed cavity.

Referenc
es

[1]

Clément B., Hanniet
-
Girault H., Repetto G., Jacquemain D., Jones A., Kissane M., von der Hardt P.,

LWR severe accident simulation: synthesis of the results and interpretation of the first Phebus FP
experiment FPT0, Nuclear Engineering and Design (2
003), 226, Issue 1, 5
-
82.

[2]

Aliseda A, Cartellier A., Hainaux F., Lasheras J.C., “ Effect of preferential concentration on the
settling velocity of heavy particles in homogenous isotropic turbulence”, J. Fluid Mechanics, (2002),
468, 77
-
105.

[3]

Güntay

S., Suckow D., Dehbi A., Kapulla R., ARTIST: Introduction and first results,
Nuclear
Engineering and Design

(2004), 231, 109
-
120.

[4]

Wang L.P., Maxey M.R., “Settling velocity and concentration distribution of heavy particles in
homogenous isotropic turbu
lence”, J. Fluid Mechanics, (1993), 256, 27
-
68.

-

6

-

[5]

Pedinotti, S., Mariotti, G., Banerjee, S.,
Direct numerical simulation
of particle behaviour in the wall
region of turbulent flow in horizontal channels, Int. J. Multiphase Flow (1992), 18, 927
-
941.

[6]

Marchioli
, C.,
Giusti
, A.,
Salvetti
, M.,
Soldati A., Direct numerical simulation of particle wall transfer
and deposition in upward turbulent pipe flow,
Int. J. Multiphase Flow (2003), 29, 1017
-
1038.

[7]

Narayanan C., Lakehal D., Botto L., Soldati A., Me
chanisms of particle deposition in a fully

developed turbulent open channel flow, Phys. Fluids 15, 763

(2003).

[8]

Reeks, M. W., The transport of discrete particles in inhomogeneous turbulence. J. Aerosol Sci. 14
(1983), 729
-
739.

[9]

Moin P., Mahesh K., D
irect numerical simulation: A tool in turbulence research, Ann. Rev. Fluid
Mech. 30, 539

578 (1998).

[10]

Moser R. D., Kim J., Mansour, N. N.,

Direct numerical simulation of turbulent channel flow up to
Re

= 590. Phys. Fluids, 11, 943

945
(
1999
).

[11]

Paolucci S., Chenoweth D. R
., Transition to chaos in a differentially heated vertical cavity,


J. Fluid Mech. (1989), 201, 379

410.

[12]

Soria, M., Trias, F. X., Perez
-
Segarra, C. D., Oliva, A.
,
Direct numer
ical simulation of a three
dimensional natural

convection flow in a differentially heated cavity of aspect ratio 4
,
Numerical
Heat Transfer

(2004),
Part A 45, 649

673.

[13]

Bastiaans J.M., Rindt C.C.M., Nieuwstadt F.T.M., van Steenhoven A.A., Direct and l
arge
-
eddy
simulation of the transition of two
-

and three
-
dimensional plane plumes in a confined enclosure, Int. J.
of Heat and Mass Transfer (2000), 43, 2375
-
2393.

[14]

Allery C., Beghein C., Hamdouni A.,
Applying proper orthogonal decomposition to the co
mputation
of particle dispersion in a two
-
dimensional ventilated cavity,

Communications in Nonlinear Science
and Numerical Simulation (2005), 10, Issue 8, 907
-
920

[15]

Dehbi A., Tracking of aerosol particles in large volumes with the help of CFD, Proceedin
gs of 12
th

International Conference on Nuclear Engineering, paper ICONE12
-
49552, CD ROM (2004).

1.2

Status of Research at PSI

(Describe briefly the research activities in the framework of the project. What are the most significant scientific
achievements
and findings within the last 3 years? What are the highlights? List of main publications / reports?)

Steam generator tube ruptures (SGTR) of a pressurised water reactor with a concurrent stuck open safety
relief valve are counted among the risk dominant ac
cident sequences because of the potential for radioactive
products to bypass the containment. Owing to the absence of relevant empirical data and the complexity of
the geometry and controlling processes, the aerosol removal in the steam generator (SG) tube
s and in the
secondary side is not well understood. Therefore, little or no credit is usually taken for aerosol retention due
to natural processes in the various components of a SG. To help reduce the uncertainties associated with
fission product release f
ollowing an SGTR sequence, the Paul Scherrer Institut has initiated an international
experimental project to be performed in the ARTIST (AeRosol Trapping In a Steam generaTor) facility
[3,16,17,18], which is
a scaled model of a real steam generator. ARTIST

is aimed at providing data on solid
and droplet aerosol removal mechanisms in the various steam generator components (tube bundle, separator
and dryer) and help reduce the uncertainty in the source term during the containment by
-
pass sequence
involving SG
TR.

The first ARTIST data was produced within the 5
th

European Framework Project SGTR. The data will be
used by the 6
th

EU Framework Network of Excellence Project SARNET [19] partners for their analysis and
model development. These first tests addressed a
erosol deposition phenomena on two different scales: near
the tube break, where the gas velocities are sonic, and far away from the break (
"
far
-
field
"
), where the flow
velocities are three orders of magnitude lower. With a dry tube bundle and the full flow

representing the
near break conditions, there is strong evidence that the TiO
2

aerosols used (AMMD 2

4

m) disintegrate
into much smaller particles because of the sonic conditions at the break, hence promoting particle escape
-

7

-

from the secondary side and lowering the overall decontamination factor (DF), which is found to be between
2.5 and 3. With a dry bund
le and a small flow reproducing the far
-
field velocities, the overall bundle DF for
the 3 stage ARTIST bundle is of the order of 5, implying a DF of about 1.7 per stage, where a stage is
defined as the segment of the tube bundle which is between two consec
utive support plates. Extrapolating
the results of the dry tests, it turns out that for real steam generators with nine or more stages, it is expected
that substantial DF’s could be achieved when the break is located near the bottom of the steam generator.

When the bundle is flooded, the DF is found to be between 45 and 5740, depending on the mass flow rate,
the steam content, and the water submergence.

The data will be used to develop models describing aerosol deposition as a result of various natural aero
sol
removal processes active under conditions very much different than the conditions at which the currently
available models have been developed. Computational fluid dynamics (CFD) models accompanied with
particle tracking will be employed to provide a be
tter insight needed for the development of simplified one
-

dimensional model predicting the retention as a function of important boundary conditions, such as gas flow
rate, aerosol concentration, aerosol size, etc. The system level codes, e.g. MELCOR, comm
only used for
safety analysis of pressurised water reactors require such simplified treatment.

However, due to the poorly understood physics of aerosol removal/transport under turbulent conditions,
investigations of a fundamental nature are foreseen as a
part of the ARTIST project, especially for those
topics that are also important for non
-
nuclear applications. Such investigations fit very well for PhD or post
-
doctoral studies. The foreseen investigations are schematically shown in the table below.


Six
-
pronged investigation of

aerosol
-
turbulence interactions in closed volumes


I.

Aerosol
deagglomeration
due to turbulence







PhD
-
ongoing

II.

Improved
model for
particle tracking
in turbulent
fields
(development
and
implementation
in FLUENT
code)


Colla
boration
PSI
-
FLUENT
-
ongoing

III.

Fundamental
investigation
of particle
-
turbulence
interactions in
closed
volumes using
DNS
techniques


This PhD
proposal

IV.

Large
Eddy
Simulation
(LES) of
particle
-
turbulence
interactions in
closed
volumes



Foreseen PhD

V.

Experimental
investigation of
particle
-
turbulence
interactions in
closed volumes






Foreseen PhD

VI.
Synthesis
and simplified
model of
particle
-
turbulence
interactions in
closed
volumes



Foreseen
Post
-
doc


The ongoing particle deagglomeration PhD (
entry I of the table above, cooperation between PSI and the
University of Newcastle) aims at understanding how and why particles disintegrate when pushed through a
sonic front, such as a breached SG tube. The end result of this research is to provide a rea
listic estimate of
the size distribution of the aerosols, which will be injected in the secondary side of a SG following a tube
rupture.

The second project (entry II) which is ongoing is the collaboration between PSI and the CFD vendor
FLUENT to develop a
nd implement an improved model for the treatment of the effects of turbulence on
particle motion and deposition in highly turbulent shear flows, such as inside a broken SG tube. The model
introduces a special treatment of the important boundary layer effec
ts, which are ignored in the current
version of the code.

-

8

-

The third project (entry III) as described in this report aims at obtaining a very detailed understanding of the
interplay between turbulent structures and particles inside a closed volume where na
tural circulation is
dominant. This knowledge is of interest to aerosol removal rates in containments, as well as in certain
components of the SG secondary side where the aerosol
-
laden flow can be approximated as a closed cavity
flow. The project will invo
lve internationally acknowledged researchers from the EPFL (DNS) as well as
the University of Udine (DNS and aerosol physics in turbulent flows).

Future plans (entry IV) involve the use of Large Eddy Simulation (LES) to study the same phenomena as in
the D
NS research. The LES analysis, which requires some turbulence modelling of the small scales, will
take advantage of the insights gained from the DNS results to firstly choose the important turbulence scales
to be modelled, and secondly to run many more par
ametric studies than would be possible with the very
CPU
-
intensive DNS simulations, as well as go to higher turbulence (Rayleigh numbers) to extend the DNS
database. In addition to PSI, this project would involve the EPFL, the University of Newcastle as we
ll as the
University of Udine.

Lastly (entry V), it is envisioned to undertake an experimental investigation, which would assess the
DNS/LES results and confirm their main predictions (aerosol removal rates, preferential concentrations,
etc.).

The ultima
te goal of this six
-
step investigation is to develop realistic CFD
-
type models for particle
-
turbulence interactions in closed volumes, which will lead to simplified yet accurate lumped
-
parameter
models that can easily be incorporated in safety system codes

such as MELCOR. This will define further
work (entry VI) where the synthesis of the information and referred modelling would be developed.

The record of LTH teams concerning the behaviour of aerosols is well established. DNS studies have
already in the pa
st been conducted within LTH. Cortesi et al. [21] have investigated a temporally
-
growing
mixing layer with a pseudo
-
spectral technique. The birth and time evolution of the longitudinal structures
have been addressed. In a later contribution [22],
the inves
tigators looked at how the entrainment and mixing

processes in mixing
-
layer turbulence are altered under the combined influence of stable stratification and
thermal conductivity. Currently, the LTH has an active CFD group that conducts investigations of si
ngle
phase and two
-
phase flow phenomena that are of interest to LWR safety (PANDA, SETH, etc) and other
applications (MEGAPIE, UCN). The CFD group constitutes the right framework to provide guidance and
support to the PhD student.

Aerosol research as appli
ed to nuclear safety has strong roots at PSI, dating back to the beginning of the
1980’s. In various international projects, DEMONA [1983
-
1988], LOFT
-
FP2 [1983
-
1985], LACE [1985
-
1988], ACE [1989
-
1992], Phebus FP [1992
-

ongoing], PSI participated by providi
ng aerosol instrumentation
(photometer), support in planning as well as analysis.

In addition, PSI launched its own experimental programmes on various fundamental aspects of aerosol
physics: PARESS, resuspension of deposited aerosol particles from horizont
al surface, [1985
-
1989],
POSEIDON, pool scrubbing of aerosol particles in hot pools, [1991
-
1996], and aerosol and thermal
-
hydraulic coupling: AIDA [1993
-
1996], CESANE [1996
-
1999], verification and qualification of industrial
filtration devices: SULZER Filt
er [1993
-
1995, 1999
-
2003], Phebus Filter [1997
-
1999].

Fundamental research on bubble hydrodynamics [23] complemented the data bases generated in the
POSEIDON project [24]. The data base produced in own programmes or obtained from the participation in
the i
nternational programmes have been used to develop models and codes: BUSCA: removal of aerosol
particles by pool scrubbing, ARES: prediction of aerosol behaviour in multiple compartments and release
into environment, and the technology of predicting aerosol

behaviour in reactor safety: Source Term
Analysis for Nuclear Power plants Mühleberg [1993], Gösgen [1999], and Beznau [2004]. Detailed
information for all the current and past projects conducted in the severe accident group can be obtained from
the inter
net site http://sacre.web.psi.ch where a complete list of publications can be reviewed.

-

9

-

It has been paid due attention to possible support from within PSI, e.g. the expertise of ENE on aerosols. It
turns out that the competence built by ENE on aerosols ha
s been principally based on measurement
campaigns of air pollutions in form of aerosols, NOx and SOx, and CO
2

coming from industry,
transportation and farms in various locations (mainly in or influencing Switzerland) to characterize gaseous
and particulate

emissions with an aim at determining the impact on the ecosystem. This approach does not
include the physical modelling of aerosol processes, especially not in the range of interest for reactor safety.
Therefore, due to the heavily physical and computatio
nal nature of the work proposed in this project, there
are very limited grounds for collaboration between the NES and ENE groups in this specific proposal.


References

[16]

S. Güntay, D. Suckow, A. Dehbi, R. Kapulla,


ARTIST: Introduction and first results
, Proceedings of ICONE 12, paper ICONE12
-
49553, 12
th

International Conference on Nuclear Engineering, Arlington, VA, April 25
-
29, 2004.

[17]

J. Jokiniemi¹, A. Lähde
1
, A. Auvinen
1
, H. Tuomisto
2
, T. Routamo
2
, P. Lundström
2
, J. Dienstbier
3
,

S. Güntay
4
, D. Su
ckow
4
, A. Dehbi
4
, M. Slootman
5
, L. Herranz
6
, V. Peyres
6
, J. Polo
6
,


Steam Generator Tube Rupture (SGTR) Scenarios, Shared Cost Action / FIKS
-
CT1999
-
00007,

FISA 2003, Nov. 10
-
13, 2003.


1) VTT Processes, Espoo (FIN)

4) PSI, Villigen
-
PSI, Switzerland


2) Fo
rtum Nuclear Services, Vantaa, Finland

5) NRG, Arnhem, Netherlands


3) NRI Rez, Prague, Czech Republic

6) CIEMAT, Madrid, Spain

[18]

L.E
1
. Herranz, V
1
.
Peyres, J
1
. Polo, S. Güntay, D. Suckow, A. Dehbi,

On the source term scrubbing within a steam generator

under dry conditions of a SGTR Accident
Sequence, Proceedings of ICAPP’03, Cordoba, Spain, May 4
-
7, 2003, paper 3202.

1
CIEMAT, Spain

[19]

SARNET: Network of Excellence for a Sustainable Integration of European Research on Severe
Accident Phenomenology”,

2004
-
2006, Work Package “
Aerosol Behaviour impact on source term
(AEROB)

“, Task 15.1, 2003, EU
-

Contract: FI6O
-
CT
-
2004
-
509065.

[20]

S. Güntay,

Description of de
-
agglomeration process of aerosol particle agglomerates, PSI
-
4
-
081a, June 2004.

[21]

Cortesi
, A.,
Yadigaroglu, G.,

Banerjee
, S., Numerical investigation of the formation of three
-
dimensional structures in stably
-
stratified mixing layers
, Physics of Fluids 10(6), 1449

1473 (1998).

[22]

Cortesi, A., Smith, B,
Yadigaroglu, G., Banerjee
, S.,
Numeric
al investigation of the entrainment and
mixing processes in neutral and stably
-
stratified mixing layers, Physics of Fluids 11(1), 162

185
(1999).

[23]

S. Güntay,

Bubble hydrodynamics, research proposal (PSI
-
4
-
024) for a PhD, Nov. 1995.

J. H. Kubasch,

Bub
ble hydrodynamics in large pools, Diss. ETH No 14398, 2001.

[24]

Dehbi A., Suckow D., Guentay S., The Effect of Liquid Temperature on Pool Scrubbing of Aerosols,
J. of Aerosol Science
, Vol. 28., Suppl. 1 pp. S707
-
S708, 1997.


1.3

R & D Plans for the Futur
e

(Main problems/questions to resolve / to answer. Innovations in the approaches of problems / questions. What outcome
do you expect? Criteria for project success or failure.)

The mechanisms of aerosol removal inside an enclosure with prevailing turbulent

natural circulation flow is
not well understood, although it is of central importance in many applications, in particular nuclear safety.
This investigation aims at studying the effects of turbulence on particle removal inside a model cavity using
-

10

-

direct
numerical simulation. This will help elucidate the dominant mechanisms responsible for particle
deposition, and provide direction to develop future models of the interaction between turbulence and
particles that can be incorporated in fast running, CFD
-
typ
e computer codes.


1.3.1 Flow Modelling

The geometry of the problem is idealized as a Differentially Heated Cavity (DHC). The flow obeys the
Navier
-
Stokes equations, subject to the usual simplifying Boussinesq approximation which ignores the
changes in flu
id density except in the gravity term of the momentum equation. The fluid flow equations can
be written in the compact, vectorial form as follows:


,
)
(
2
z
T
Pr
Ra
Pr
p
t
e
v
v
v
v

















(2)

,
0
)
(



v




(3)

,
Pr
)
(
2
T
T
t
T







v



(4)

where
v

is the flu
id instantaneous velocity vector,
T

the temperature,
p

the pressure, and
z
e

the unit vector in
the direction of the gravity force. The cavity dimensions and

T will be chosen so as turbulence is well
established within the cavity, but the turbulence level will not be so great as to make the DNS computations
prohibitive. The best solution algorithms for equations (2) through (4) needs to be determined, because
broadly speaking, the fluid dynamics of buoyancy driven flow and turbulence in confined cavities or
enclosures has still only be partially explored. The parameter space is large and a variety of unforeseen
phenomenon can arise based on the specific geometr
y and parameter range of interest. It is therefore
important to first clearly characterize the fluid dynamics before analysing aerosol dispersion in enclosures.
Some recent developments in solution algorithms as applied to lid
-
driven cavity flow [25] could

be
incorporated to improve the overall numerical scheme and convergence of the DNS computations.

1.3.2
Numerical Method

The numerical method to be used for the spatial approximation of the equations of fluid motion is based on
the use of expansions in Ch
ebyshev polynomials along every space direction. This high
-
order method
eliminates diffusion and dispersion errors in the solution, the latter being common with low
-
order methods
(finite difference or finite element) currently used in three
-
dimensional num
erical simulations of bounded
flows.

More precisely, the space discretisation proceeds by expanding the velocity and pressure fields in tensor
product of Chebyshev polynomials, of order (N,M,L) for the (x,y,z) dependencies, respectively. The
Chebyshev coll
ocation method consists of exactly enforcing the differential equations and the boundary
conditions at the Gauss
-
Lobatto points [26,27,28].

A number of different methods have already been tried to enforce the incompressibility constraint. A
cheaper approac
h was recently proposed by Batoul et al. [29] and
analysed

in [30,31]
-

called projection
-
diffusion method
-

in which the pressure is expanded into polynomials of the same order as the velocity,
while intermediate velocity results are truncated in
a way that enforces continuity without any contamination
by spurious pressure modes. Indeed at the boundaries, only the boundary conditions are imposed on the
velocity, but not the vanishing divergence [32]. The pressure is therefore evaluated in a relativ
e sense.

A DNS code (DNSBDTC) of the DHC cavity was developed at the EPFL and is available for this PhD
project. A complete numerical analysis of the decoupling method may be found in [30,31]. The code has
been tested on two
-
dimensional problems and its a
ccuracy checked against problems with known analytical
-

11

-

solution and with published numerical data. Moreover, it is compared, first with the splitting scheme
proposed by G. Karniadakis et al. [33] and with the unique grid
P
N
-
P
N
-
2

Uzawa approach (which consi
sts in
expanding the pressure field in polynomials two orders less than those of the velocity field, avoiding the
pressure spurious modes [30]) for the space accuracy and computational costs. The DNS code has been
validated in the range of Ra up to 10
6

(se
e schematic in Figure 2 and sample results in Figure 3, which
reproduces well known isotherms found in the literature). The agreement with published data is very good.
With this code, the time step limits are less stringent and it is therefore possible to
tackle higher Ra numbers.
This will allow simulations into the turbulent regime (Ra of order 10
9
), which is the object of this
investigation. An adaptation of the code (e.g. time
-
stepping algorithm) could arise when the turbulent effects
start to dominate,

and this will be treated as the need arises. The coupling of the particle tracking modelling
with the DNS results will be done by starting at low enough Ra numbers so that the CPU requirements are
still modest. Once the coupling is well assessed, one move
s gradually to higher Ra numbers (10
9
or even
higher)

where turbulence is well established.





Figure 2: Geometry of DHC


Figure 3: Temperature isosurfaces in DHC, Ra=10
6

(x=
-
1 face cooled, x=1 face heated)






-

12

-


1.3.3 Particle Tracking Modelling

Particle
tracking based on detailed flow field data calculated from DNS is the most physical approach to
simulate the turbulent dispersion of particles. Traditional Eulerian approaches, based on statistical Fickian
diffusion models, can treat particle dispersion on
ly in a time
-
averaged sense and cannot predict the highly
non
-
uniform distribution of phases giving a poor description of the true physics of the dispersion process.
Time dependent, Lagrangian approaches are required for a deeper understanding of the mecha
nisms for
particle dispersion, preferential concentration and deposition mechanisms.

For the practical implementation of the Lagrangian tracking approach, we propose to calculate the trajectory
of a large number of particles by integrating explicitly over
time the equations of motion for each particle.

The equations can be written as:


,
p
p
dt
d
v
x






(5)

,
f
v

dt
d
p




(6)

where
x
p

and
v
p

are the particle instantaneous position and velocity, respectively, and
f

the sum of the force
s
acting on the particle (per unit mass), given by:

mass
virtual
Basset
esis
thermophor
gravity
lift
drag







f
f
f
f
f
f
f

(7)


with:

),
(
18
2
v
v
f
p



p
p
drag
d



(8)

,
)
1
(
g
f
p
gravity






(9)

,
6
)
/
1
(
T
T
K
r
m
p
p
esis
thermophor










f


(10)

,
)
(
/
9
0






d
t
d
d
d
t
p
p
Basset





v
v
f
p


(11)


),
(
)
/
(
46
.
6
)
/
1
(
2
/
1
2
p
v
v
f







p
p
lift
r
m


(12)


).
(
2
v
v
f
p




dt
d
p
mass
virtual




(13)

In the above, m
p

is the mass of the particle,

p

its density, r
p

its radius, d
p

its diameter,


the dynamic gas
viscosity,


the kinematic viscosity,


the gas density, g the gravity acceleration, K the thermophoretic
coeffi
cient, and


the local fluid velocity gradient normal to the wall, t

the time. The Basset force represents
the history of the viscous effects on the particle.

The assumptions for particle modelling are: (1) all particles are non
-
interacting,
non
-
deformable

solid
spheres; (2) particle density is large compared to fluid density; (3) particle concentration is low enough to
neglect the effect of particles on the flow (
one
-
way

coupling assumption), and (4) particles and surfaces are
-

13

-

electros
tatically neutral
. In particle
-
laden flows, the key parameter controlling dispersion is the Stokes
number (St), which is the ratio between the particle aerodynamic response time and the relevant flow time
scale.

According to many previous reports [35,36] t
he study of the forces acting on particles based on the equation
of motion derived in [36] reveals the following order of magnitude: the drag force is of order St
-
1
(
O
(St
-
1
)),
the virtual mass is
O
[(

/

p
)
1
] and the Basset force is
O
[(

/

p
)
1/2
], where


and


p

are fluid density and
particle density, respectively. In our work,

/

p

is

O
(10
-
3
) and St based on the
reference timescale for the
fluid
, will be in the range [10
-
4

-

10
1
]. Therefore, for the specific flow systems to be examined here, virtual
mass and
Basset forces can be neglected, and hence the equation of motion reduces to a balance of Stokes
drag, gravity, thermophoresis and the lift. The drag force will be evaluated by calculating the fluid velocity
at each particle position using high order interp
olation techniques.

The equations of motion of the particles will be solved with a Runge

Kutta scheme, assuming that the gas
flow field remains constant during each time interval of the DNS simulation since the trajectory integration
time
-
step is much smal
ler than the smallest time scale (Kolmogorov scale). This calculation will be carried
out for a time long enough to obtain adequate results on deposition rates and Eulerian statistics. The initial
location of the particles in the cavity will be random, as
is traditionally done in Lagrangian particle studies.

1.3.4 Goals of the investigation

The main outcome of this investigation will be a more rigorous understanding of particle settling in a
turbulent flow cavity. The study would help elucidate why inertial

particles in turbulent, circulating flow
tend to settle more rapidly than under quiescent conditions, as well as uncover other inter
-
relationships
between settling rates, turbulence and particle inertia. In addition, the investigation would show the exact

role of each contributing force in the transport of particles towards and away from the walls. In terms of
application of DNS to practical problems such as aerosol deposition in nuclear reactor containments, future
work should concentrate on judicious use

of dimensional analysis and scaling to complement basic DNS
results of this current work.

[25]

Leriche E., Deville M., An Uzawa pressure solver for the Chebyshev spectral method: Application to
the lid
-
driven cavity, Computers and Fluids (2002).

[26]

Gott
lieb, D. and Orszag, S.A.,

Numerical Analysis of Spectral Methods: Theory and Applications
,
SIAM
-
CBMS

(
1977
).

[27]

Deville, M.O., Fischer, P.F. and Mund, E.H.
,
High
-
Order Method for Incompressible Fluid Flow
,
Cambridge University Press

(2002).

[28]

Canuto,

C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A.,

Spectral Methods in Fluid Dynamics
,
Springer
-
Verlag

(
1988
).

[29]

Batoul, A., Khallouf, H. and Labrosse, G.
,
Une Méthode de Résolution Directe (Pseudo
-
Spectrale) du
Problème de Stokes 2D/3D Instationnaire.

à la Cavité Entrainée Carrée
,
C.R. Acad. Sci. Paris
,

Vol.:
319(I), 1455
-
1461,

(
1994
).

[30]

Leriche, E. and Labrosse, G.
,
High
-
order direct Stokes solvers with or without temporal splitting:
numerical investigations of their comparative properties
,
SIAM J.

Scient. Comput.,

Vol.:
22(4),1386
-
1410,

(
2000
).

[31]

Leriche E., Perchat E., Labrosse, G., and Deville M.,
Numerical evaluation of the accuracy and
stability properties of high
-
order direct Stokes solvers with or without temporal splitting
, to appear in
J
ournal of Scientific Computing,

(2005).

[32]

La
brosse, G.
,
Compatibility Conditions for the Stokes System Discretized in 2D Cartesian Domains
,

Meth. Appl. Mech. Eng., Vol.: 106, 353
-
365,
(
1993
).

[33]

Karniadakis, G.E.M., Israeli, M. and Orszag, S.A.,

H
igh
-
Order Splitting Methods for the
incompressible Navier
-
Stokes Equations
,
J. Comput. Phys.,

Vol.: 97, 414
-
443,
(
1991
)

-

14

-

[34]

Leriche, E. and Gavrilakis, S., Direct Numerical Simulation of the Flow in a Lid
-
Driven Cubical
Cavity
, Vol.:
12(6), 1363
-
1376, Ph
ys. Fluids,

(
2000
).

[35]

Chung, J.N. and Troutt, J.J., Simulation of particle dispersion in an axisymmetric jet,


J. Fluid Mech. 186, 199
-
222 (1988).


[36]

Loth, E.,
Numerical approaches to dilute two
-
phase flow,


Prog. Energy Combust. Sci. 26, 161

223 (
2000).

[37]

Maxey, M.R., Riley, J.,

Equation of motion for a small rigid sphere in a no uniform flow,

Physics of Fluids 26(4), 883

889 (1983).

[38]

Picciotto M., Marchioli C, Reeks M., Soldati A., Statistics of velocity and preferential accumulation
of

micro
-
particles in boundary layer turbulence, to be published, Nuc. Engr. Design. (2005)

1.4

Relevance of Work

(Potential for development of new technologies. Possible implications to processes, technologies of today.
Recognition of the PSI
-
contribution
by the international community; influence of the PSI
-
results on the overall
trends of the international research in this field.)

Fundamental understanding and description of turbulence effects on aerosol removal in cavities with DNS is
one of six research
areas either being conducted in association with the international ARTIST project or
planned for the near future. The other 5 areas are:

a)

Modelling of aerosol motion and de
-
agglomeration in highly turbulent pipe flows,

b)

Stochastic description of aer
osol motion within turbulent boundary layers and integration in the
CFD code FLUENT.

c)

Large Eddy Simulation (LES) of particle
-
turbulence interactions in closed volumes

d)

Experimental investigation of particle
-
turbulence interactions in closed volum
es

e)

Synthesis of DNS/LES/experiments and development of simplified model of particle
-
turbulence
interactions in closed volumes

Topic a) is being conducted through a PhD investigation (collaboration between PSI and the University of
Newcastle). Its objec
tives are to i) identify, locate and measure the de
-
agglomeration in a steam generator
tube under very high flow velocities ii) develop models for break
-
up of agglomerates by turbulent shear
flows at very high Reynolds numbers (of order 5.10
5
).

Topic b) is

being conducted jointly by our PSI group and the FLUENT code developers, with the aim of
producing a better stochastic model for the turbulence effects on inertial particles. The model will be linked
to FLUENT (summer of 2005) and can be used by the ARTIS
T project partners for their pre
-

and post
-
test
simulations of the ARTIST tests.

Topic c) is a planned PhD investigation involving Large Eddy Simulations (LES) to study the same
phenomena as in the DNS research. This will however allow the simulation of hi
gher turbulence levels
(Rayleigh numbers) to extend the DNS database. In addition to PSI, this project would involve the EPFL,
the University of Newcastle as well as the University of Udine.

Topic d) is a planned experimental investigation which would asse
ss the DNS/LES results and confirm their
main predictions (aerosol removal rates, preferential concentrations, etc.).

Topic e) is a planned Post
-
doc study which will provide the synthesis of the information collected so far and
develop realistic CFD
-
type
models for particle
-
turbulence interactions in closed volumes, which will lead to
simplified yet accurate lumped
-
parameter models that can easily be incorporated in safety system codes such
as MELCOR.

These topics together with the proposed PhD project co
nstitute an advanced treatment of aerosol physics in
conjunction with the thermal
-
hydraulics and have a large potential for application, not only in the nuclear
safety domains, but also chemical, environmental, and occupational areas. The approaches in the

six areas
-

15

-

are conformable with the new trends which are followed in a few centres in Europe and will open our doors
to further academic institutions.


1.5

Time Table

(Start of work, implementation phase, research phase, end of work)

The details of the a
ctivities and the
timetable

are described in the table and GANNT diagram below.



Activity

Man Months

1

Review of literature on turbulence modelling, DNS, spectral methods,
differentially heated cavity driven flow, particle tracking.

4

2

Famil
iarization with typical DNS calculation using the EPFL DNS code.
Adaptation of the code to cover higher Ra numbers (as required).

8

3

Familiarization with typical DNS calculation involving Lagrangian
particle tracking for channel/pipe flow. Adaptation of

the method to
differentially heated cavity driven flow at low Ra number to minimize
CPU times. Implementation of coupling between flow and particle
modules.

6

4

Parametric coupled DNS
-
Lagrangian tracking studies. Effects of Ra
number, particle inertia.

8

5

Development of understanding of dominant mechanisms of aerosol
removal in DHC. Elucidation of experimental observations. Directions
for future work.

6

7

Write
-
up of PhD dissertation

4


Total

36


Activity

Nr.

Calendar months

1
-
4

5
-
8

9
-
12

13
-
16

17
-
20

21
-
24

25
-
28

29
-
32

33
-
36

1










2










3










4










5










6










It is expected that the student will spend 30 % of the time at EPFL, depending on his/her under
graduate/master program, to attend a number of courses
, learn mathematical modelling of DNS, and perform
actual flow computations. He/she will spend 20 % of the whole duration at the University of Udine to
develop and apply particle turbulent dispersion inside a DHC. He/she will spend the rest of the time at
PSI
(50 %) to learn about the applications areas of the work and make sure the scope of the problem and the
parametric studies will fit in the overall research undertaken here. While at PSI he/she will run the codes and






-

16

-

make analysis as well as receive com
puter support for the
HORIZON

machine in Manno, and Merlin cluster
of PSI.


1.6

Boundary Conditions

(Prerequisites for success, critical path)

The PhD student will get his/her degree from the Ecole Polytechnique Fédérale de Lausanne (EPFL). At
EPFL he/sh
e will start working with the modelling team under Professor Deville of the Laboratory of
Computational Engineering (LIN) to get familiar with the DNS fundamentals and methods as applied to
DHC. The PhD student will be part of the powerful LIN team which i
s involved in a wide range of basic as
well as applied research topics in fluid mechanics, from a computational and theoretical point of view.
Whenever enough DNS background is achieved, the student will move as frequently as needed to the
University of Ud
ine, where Professor Soldati’s group within the framework of general DNS research, is very
active in particular the study of turbulent dispersion of inertial particles.

There will also be a number of courses at the EPFL that the PhD student, depending on
the past curriculum
during the undergraduate/master program and subjected to the approval of EPFL, will be invited to attend.
The student will also attend some aerosol
-
related courses, if needed, and workshops while at Udine.

Routine PhD review meetings w
ill be organized at PSI under the chairmanship of the project manager with
the attendance of two supervising professors to review the progress and provide recommendations. The local
(PSI) daily supervision will be assigned to Dr. Dehbi of the severe accide
nt team. Dr. Dehbi is a graduate of
MIT/USA and is also responsible for local
-
supervision of De
-
agglomeration
-
PhD and PhD’s assigned by the
ARTIST project partners for a few months of stay at PSI within the ARTIST project associated with the
modelling of C
FD/aerosol aspects in complex geometries. Dr Dehbi is also responsible for definition and
conduction of the collaboration work carried out to develop ‘Improved modelling of particle tracking in
turbulent fields’ and its implementation in the FLUENT code el
uted in Entry II of the work program
introduced in Sections 1.2 and 1.4. The CFD group of the Laboratory of Thermal
-
hydraulics, where the
severe accident research group is also located, will provide, as already indicated in Section 1.2, the scientific
supp
ort as needed.

The student will also make presentations of the results at a few key conferences on multiphase flow and
particle dynamics. The PhD student will be required to have a strong background in numerical methods,
with good programming skills, and f
ine knowledge of fluid mechanics and heat transfer. On top of the
necessary skills in these fields, it is very wishful if the student has certain experience in either the DNS or
aerosol science. This is important to eliminate the need for taking courses in

both fields.

2.

Resources, Partners

2.1

Special Equipment Needed

(State equipment purchased or planned especially for this project; use of previously existing facilities (indicate
annual use in hours).

DNS computations are very time consuming and requir
e state of the art computational resources. However,
there are excellent computer capabilities available to PSI for this investigation. There are currently three
possibilities to conduct the bulk of the computations for our project: 1) The
Nec
-
Sx5 vectoria
l
-
parallel
machine at the
Swiss National Supercomputer Centre (
CSCS in Manno), which the LIN group of EPFL has
been using extensively, and 2) The HORIZON
massively parallel processor (MPP), also at CSCS, which
will be available soon, and 3) The Merlin clus
ter at PSI, which
is a Linux cluster consisting of 56
computational nodes.

The LIN and PSI will apply jointly for computer time on the Nec
-
Sx5.

By the summer of 2005, the Swiss National Supercomputer Centre CSCS in Manno will install the high
performance
computing (HPC) Cray XT3 computer HORIZON, as a joint project between the CSCS and
-

17

-

PSI. HORIZON produces a peak performance of 5.9 Tflop/s and is made up of 1’100 2.6 GHz AMD
Opteron processors. A share of the system is to be used by PSI for various comple
x simulations.

As a back
-
up solution for the computations, we have foreseen the Merlin cluster at PSI, which, although
being slower CPU (1/2 the speed of the HORIZON CPU’s), has the advantage of being available for this
project, and this availability will

increase as more of the larger computational projects will migrate to the
HORIZON machine.

Besides heavy computations on supercomputer facilities, the student will require a high performance PC to
do post
-
processing particle tracking computations. The PC
will likely be a 2 a processor machine, with 4 or
more GB of memory.


2.1.1
CPU
-
Time Requirements for the DNS fluid part


An accurate estimation of the CPU
-
time needed to perform a direct numerical simulation of a turbulent flow
in a cubical differentiall
y heated cavity (DHC) at Rayleigh near or above 10
8

is difficult to give because the
longest time scales of this flow are not known a priori. However, an approximate estimate based on
dimensional analysis and published experimental and numerical data can b
e used for the present purposes.
For laminar flows the typical velocity scale within a side
-
heated cavity is given by V
lam

= L /


Ra
0.5

where L
is the size of the cavity, and


is the thermal diffusivity. This leads directly to a time scale of T
lam

= L / V
lam
.

Two
-
dimensional simulations which have noticeable large
-
scale structures, similar to those in
three
-
dimens
ional

ones, suggest that the integration time required for establishing a steady flow is of the order of
150 T
lam
. In a direct simulation there are two phases that need be simulated: the transient, (which is taken to
be the same as the above since the long
est lasting scales are determined by the size of the physical domain),
and the sampling period when a statistical steady state has been reached which is used for collecting the
database. The latter is estimated at 50 T
lam
. Thus the total flow time that wil
l be simulated is estimated at
200 T
lam
. The allowable time step is determined by the Courant numerical limits and Brunt
-
Väisälä
frequency restriction. These step restrictions will allow the minimum of 1400 steps per 1 T
lam
. Thus the total
number of steps
for the complete simulation will be 280000. Since the total number of collocation points
envisaged is 4
.
10
6

and the CPU time per grid is 12
.
10
-
6

(which includes the additional cost of solving for the
temperature equation) on a single processor of the Nec
-
S
x5 vectorial
-
parallel machine provided by CSCS,
the simulation will require a minimum of 500 CPU hours per month. This does not include the cost of
carrying the post
-
processing of data, and the particle tracking. Simple data analysis may be accomplished
wi
th an additional 10 CPU hours per month.

2.1.2
CPU
-
Time Requirements for particle tracking part

Computational requirements for particle tracking will be significant and at least of the same order of that
required for the flow field calculation.

CPU Time:
The main contribution to CPU time will be given by the i) flow field simulation; ii) particle
tracking. To take an example, the CPU time required to advance the last database in [36], on a last
generation Linux PC was:

-

10 sec for advancing one time step

of the flow field on a 128x128x128 grid;

-

15 sec to advance one time step of 100.000 small particles.

To have a statistically steady simulation for the particle dispersion field (hundreds of thousand particles),
the amount of time required is about the s
ame order of that required to reach a steady flow field. This means
CPU times on the order of 500
hours per month on the Nec
-
Sx5 machine.

2.1.3

The total CPU requirements

It is worth mentioning that one can split the required computations in two: DNS and particl
e tracking.

1) The DNS computations will ideally run on the Nec
-
Sx5 vectorial machine, where similar simulations are
currently being conducted. Total CPU requirements will be for most of the time of the PhD about 500 to 520
-

18

-

CPU hours per month. About 250
CPU hours per month on the Nec
-
Sx5 are already secured by EPFL
-
LIN
and PSI’s Merlin computer cluster is available to the project. Upon the acceptance of the proposal a certain
number of CPU hours on any one of the available three platforms will be applied
for.

2) The particle tracking is ideally suited for parallel machines, because it is very similar to Monte
-
Carlo
simulations and is easily parallelized. Based on initial estimates, particle tracking requires the same order of
magnitude CPU time as the DNS

calculation if one runs on a single processor machine (i.e. about 500 CPU
hours per month on the Nec
-
Sx5). However, this requirement will be considerably smaller if translated into
parallel CPU’s such as HORIZON or even Merlin. Thus, the strategy is to ru
n the DNS part on the Nec
-
Sx5,
and the particle tracking part on one or both of the parallel machines (HORIZON and Merlin).


2.2

Personnel



today (PY/y)

in about 3 years (PY/y)


PSI funding

External funding

PSI funding

External funding

Professional Sta
ff

Doctoral Students
2

Technicians

Others

0.08

0.5

0.4
1

0.5

0.08

0.5

0.4
1

0.5

1

Total of 6 MM from University of Udine in 3 years, the rest from EPFL

2

50% PSI, 50% Project own DM

.
2.3

External Partners

(Collaborations, Financial Supporters, Grants for R
esearch Work)

The Laboratory of Computational Engineering (LIN) group within the Institute of Energy Sciences (ISE) at
the EPFL, Lausanne, Switzerland.

The Laboratory for Environmental and Process Fluid Mechanics,
Department of Energy Technology,
Universit
y of Udine, Italy.


3.

Technology Transfer

3.1

Patent Search

(Search Results; Important Patents)


none applicable

3.2

PSI Patents

none planned

3.3

Potential for new Patents

none planned