Deliverable title: Description of the sloshing effects in ...

EUROPEAN COMMISSION 7th EURATOMFRAMEWORK PROGRAMME 2007-2013

THEME [Fission-2011-2.3.1][R&D activities in support of the implementation

of the Strategic Research Agenda of SNE-TP]

SILERSeismic-Initiated events risk mitigation

in LEad-cooled Reactors

Grant Agreement N°: 295485

Deliverable title: Description of the sloshing effects inLFR system

WorkPakage

Deliverablenumber

Lead contractor Date

WP3 D3.1 IDOM 16/December/2013

Responsible person detailsname: telephone: email:

Starting date Due date Actual date Delay* Nature1/January/2013 31/Oct/2013 1/March/2014 Three months Input dataDescription of the activities:In this report, the sloshing effects in the isolated LFR concept are analyzed. Detailed models of the vessel internals components are included. Seismic input is introduced through acelerograms obtained in WP2 .In the first part (by IDOM), the report includes the models, procedures and results obtained using the FLUENT code for the dynamic displacements study of the liquid lead. In this approach no fluid structureinteraction is considered. ANSYS code is used for the stress evaluation in vessel and internal components. Furthermore, the ABAQUS code is used with the objective to evaluate the fluid structure interaction. A first step with no-interaction is analysed and a second step with iteraction is developed in order to have data for the interaction magnitude. From the examination of the obtained results,some recommendations are given on the design of the reactor vessel and its internal components.In the second part (by KTH), simulation of the dynamic phenomena in which local equipment response could undergo significant coupling with the overall motion of the reactor is carried out. KTH has studied the sloshing in terms of gas entrapment and fluid structure interaction within the vessel of the ELSY LFR configuration.SIGNATURESAuthors: A. Moreno, IDOMG. Barrera, IDOMA. Guerrero, IDOMM. Jeltsov, KTHW. Villanueva, KTHP. Kudinov, KTH

WP Leader: P. Kudinov, KTHCoordinator: M. Forni, ENEA

A.M.

FP7-295485-SILER

1

G.B.

A.G.

M.J.

W.V.

P.K.

FP7-295485-SILER

2

EUROPEAN COMMISSION 7th EURATOM FRAMEWORK PROGRAMME 2007-2013

THEME [Fission-2011-2.3.1] [R&D activ ities in support of the implementation

of the Strategic Research Agenda of SNE-TP]

SILERSeismic-Initiated events risk mitigation

in LEad-cooled Reactors

Grant Agreement N°: 295485

Foreword

In this report, the sloshing effects in the isolated LFR concept are analyzed. Detailed models of the vessel internals components are included. Seismic input is introduced through acelerograms obtained in WP2. Este document contiene dos partes: la primera realizada por IDOM y la segunda por KTH

Description of the activities:

1st PART: In the first part developed by IDOM, the report includes the models, procedures and results obtained using the FLUENT code for the dynamic displacements study of the liquid lead. In this approach no fluid structure interaction is considered. ANSYS code is used for the stress evaluation in vessel and internal components. Furthermore, the ABAQUS code is used with the objective to evaluate the fluid structure interaction. A first step with no-interaction is analysed and a second step with iteraction is developed in order to have data for the interaction magnitude. From the examination of the obtained results,some recommendations are given on the design of the reactor vessel and its internal components.

2nd PART: In the second part developed by KTH, simulation of the dynamic phenomena in which local equipment response could undergo significant coupling with the overall motion of the reactor is carried out. KTH has studied the sloshing in terms of gas entrapment and fluid structure interaction within the vessel of the ELSY LFR configuration.

3rd PART: Three annexes of the first part, developed by IDOM, are included in the third part. The second part, developed by KTH, doesn’t have annexes.

Seismic-Initiated ev ents risk mitigation in LEad-cooled Reactors

Analy sis of Seismic Sloshing of Coolant in the ELSY-LFR

16962 CD 3.1/01 Rev. 0 FP7-295485-SILER D3.1 - PART I Page 1 of 68

Part I: Analysis of Seismic Sloshing of Coolant in the

ELSY-LFR(IDOM)




TABLE OF CONTENTS

1. INTRODUCTION ........................................................................................................6

1.1. Preamble ............................................................................................................6

1.2. Purpose ..............................................................................................................6

1.3. Scope .................................................................................................................6

1.4. Organization of the document ...............................................................................7

2. INPUT DATA ..............................................................................................................8

2.1. Reactor vessel description....................................................................................8

2.2. Seismic input .......................................................................................................9

2.3. FLUENT methodology........................................................................................11

2.3.1.CFD ANALYSIS .......................................................................................12

2.4. ABAQUS methodology.......................................................................................13

3. DESCRIPTION OF THE MODEL.............................................................................13

3.1. FLUENT model..................................................................................................13

3.1.1.2D ANALYSIS ..........................................................................................13

3.2. FLUENT 3D ANALYSIS .....................................................................................14

3.2.1.Model ......................................................................................................14

3.2.2.Fluid properties ........................................................................................17

3.2.3 Load cases ..............................................................................................17

3.2.4 Reference points ......................................................................................18

3.3. ABAQUS model.................................................................................................20

3.3.1.Abaqus model with rigid components .........................................................21

3.3.2.Abaqus model with deformable components ..............................................23

4. ASSESSMENTS OF FLUENT RESULTS ...............................................................24

4.1. 2D MODEL........................................................................................................24

4.2. FLUENT 3D MODEL RESULTS .........................................................................27

5. ASSESSMENTS OF ABAQUS RESULTS .............................................................38

5.1. Seismic asse ssments.........................................................................................38

5.1.1.ABAQUS model with rigid components ......................................................38

5.1.2.ABAQUS model with deformable components: ...........................................39

5.1.3.Displacement comparison .........................................................................41

5.2. Pressure distribution ..........................................................................................42

5.2.1.ABAQUS model with rigid components ......................................................42

5.2.2.ABAQUS model with deformable components ............................................45

5.3. Fluid-Structure Interaction ..................................................................................47

6. ASSESSMENTS OF STRESSES RESULTS..........................................................49

6.1. ANSYS RESULTS ON STRUCTURAL ANALYSIS...............................................49

6.1.1.MODEL ...................................................................................................49




6.1.2.Finite Element model ................................................................................50

6.1.3.Material properties....................................................................................51

6.1.4.Boundary conditions .................................................................................52

6.1.5.Load cases ..............................................................................................53

6.1.6.RESULTS ................................................................................................54

6.2. ABAQUS RESULTS ..........................................................................................56

7. RESULTS EVALUATION ........................................................................................61

7.1. FLUENT ANSYS RESULTS ...............................................................................61

7.1.1.Fluid pressures.........................................................................................61

7.1.2.Stresse s re sults........................................................................................61

7.2. ABAQUS ANALYSIS RESULTS .........................................................................62

7.2.1.Fluid pressures re sults..............................................................................62

7.2.2.Stresse s re sults........................................................................................63

8. CONCLUSIONS .......................................................................................................63

9. REFERENCES .........................................................................................................65

ANNEX I: ALE Method v alidation. Slosh height in a rectangular tank

ANNEX II: FLUID AND STRUCTURAL ANALYSIS WITH FLUENT-ANSYS

ANNEX II.1: FLUID ANALYSIS

ANNEX II.1.1: ELSY GEOMETRY

ANNEX II.1.2: FLUID DOMAIN. GEOMETRY AND MESH

ANNEX II.1.3: ACCELERATION TIME HISTORIES

ANNEX II.1.4: RESULTS

ANNEX II.2: STRUCTURAL ANALYSIS

ANNEX II.2.1: MODEL

ANNEX II.2.2: RESULTS

ANNEX III: ABAQUS FLUID STRUCTURE ANALYSIS

ANNEX III.1: ACCELEROGRAMS: INPUT LOADS

ANNEX.III.2. PRESSURE TIME HISTORIES

ANNEX III.2.1: PRESSURE TIME HISTORIES: RIGID CASES

ANNEX III.2.2: PRESSURE TIME HISTORIES: FLEXIBLE CASES

ANNEX III.3: TIME HISTORIES ANALYISI: FRECUENCY CONTENTS

ANNEX III.3.1: FRECUENCY CONTENTS: RIGID CASE

ANNEX III.3.2: FRECUENCY CONTENTS: FLEXIBLE CASE

ANNEX III.4: CONTACT FORCES

ANNEX III.4.1: CONTACT FORCES: RIGID CASES

ANNEX III.4.2: CONTACT FORCES: FLEXIBLE CASES

ANNEX III.5: VON MISES STRESSES: FLEXIBLE CASES

ANNEX III.6: FREE SURFACE VERTICAL DISPLACEMENTS




LIST OF TABLES

Table 3-1 Load cases............................................................................................................18

Table 3-2 Location of the reference points ..............................................................................19

Table 4-1 Data corresponding with part a for CASE_1.............................................................29

Table 4-2 Data corresponding with part b and c for CASE_1....................................................29





Table 4-7 Data corresponding with part a for CASE_12 ...........................................................32

Table 4-8 Data corresponding with part b and c for CASE_12..................................................32

Table 4-9 Maximum percentage of surface lid wet by molten lead and time it occurs .................35

Table 5-1 Maximum pressures obtained in the four load cases in both models..........................47

Table 6-1 Maximum displacements and Von Mises stresse s (MPa).........................................55

Table 6-2 Maximum Von Mises stresses obtained for all cases for the inner and external vessel ................................................................................................................57

LIST OF FIGURES

Figure 2-1 Main components of the ELSY/LFR reactor ..............................................................9

Figure 2-2 Horizontal response spectra – Cases 1, 3, 6, 12 .....................................................10

Figure 2-3 Vertical response spectra – Cases 1, 3, 6, 12 .........................................................11

Figure 3-1 2D model .............................................................................................................14

Figure 3-2 ELSY reactor geometry .........................................................................................15

Figure 3-3 Fluid domain geometry..........................................................................................16

Figure 3-4 Fluid domain mesh ...............................................................................................16

Figure 3-5 Geometrical distribution of the reference points ......................................................19

Figure 3-6 Abaqus model with rigid components. Shell elements .............................................22

Figure 3-7 Abaqus model with rigid components. Molten lead elements....................................23

Figure 4-1 Pressure ..............................................................................................................24

Figure 4-2 Volume fraction: Red – Lead; Blue-Argon...............................................................25

Figure 4-3 Volume fraction at rest ..........................................................................................25

Figure 4-4 Velocity ................................................................................................................26

Figure 4-5 Horizontal velocity.................................................................................................26

Figure 4-6 Vertical velocity ....................................................................................................27

Figure 4-7 Percentage of reactor vessel lid in contact with molten lead for case 1 .....................33






Figure 4-10 Percentage of reactor vessel lid in contact with molten lead for case 12 .................35

Figure 4-11 Maximum seismic loads pressure versu s the pressure at rest for case 1 ................36



Figure 4-14 Maximum seismic loads pressure versu s the pressure at rest for case 12...............37

Figure 5-1 Vertical displacement of the free surface for the case 1 and the rigid model..............38

Figure 5-2 Vertical displacement of the free surface for the case 6 and the rigid model..............39

Figure 5-3 Vertical displacement of the free surface for the case 1 and the flexible model..........40

Figure 5-4 Vertical displacement of the free surface for the case 6 and the flexible model..........40

Figure 5-5 Comparison rigid vs flexible model of the vertical displacement for the case 1 ..........41

Figure 5-6 Comparison rigid vs flexible model of the vertical displacement for the case 6 ..........41

Figure 5-7 Distribution and location of the reference elements .................................................42

Figure 5-8 Step time 11.20 s in the model with rigid components case 1. (P=1.74 MPa) ............43

Figure 5-9 Step time 13.60 s in the model with rigid components case 6. (P=10.25 MPa) ..........44

Figure 5-10 Step time 13.60 s in the model with rigid components case 6. (P=10.25 MPa) ........44




Figure 6-1 ELSY Reactor geometry for structural analysis .......................................................50

Figure 6-2 ELSY Reactor mesh for structural analysis .............................................................51

Figure 6-3 Distribution and location of the reference elements to obtain stresses in the inner and external vessel .............................................................................................56

Figure 6-4 Stresses obtained for the inner vessel in the case 1 for the model with deformable components........................................................................................................58

Figure 6-5 Stresses obtained for the external vessel in the case 1 for the model with deformable components ......................................................................................59

Figure 6-6 Stresses obtained for the inner vessel in the case 6 for the model with deformable components........................................................................................................59

Figure 6-7 Stresses obtained for the external vessel in the case 6 for the model with deformable components ......................................................................................60

LIST OF ACRONYMS AND ABBREVIATIONS

DHR Decay Heat Removal

IV Inner Vessel

LFR Lead cooled Fast Reactor

RV Reactor Vessel

SG Steam generator

SILER Seismic-Initiated events risk mitigation in LEad-cooled Reactors




1. INTRODUCTION

1.1. Preamble

SILER is a Collaborative Project within the seventh Framework Programme of the European

Commission, aimed at studying the risks associated to seismic initiated events in Gen IV Heavy

Liquid Metal reactors and developing adequate protection measures. The attention is focused on

the evaluation of the effects of earthquakes, with particular regards to unexpected (beyond de-

sign) events, and the identification of mitigation strategies like seismic isolation, acting on both

structures and components design.

In this context, task 3.1 of SILER includes the study of sloshing in seismic isolated reactors. In

order to study the sloshing effects in the LFR concept, detailed and refined models of key com-

ponents inside the reactor vessel have been realized, moving for the response spectra pro-

duced in WP2 (S.R.S. Servizi di Ricerche e Sviluppo Societa a Responsabilita Limitata). The

purpose is to identify if there is contact between the lead free surface and the lid during the

earthquake and the significant loads in the internal components due to the lead displacement.

During the study, solid-structure interaction has also been analysed.

The present report gathers the work carried out within task 3.1 regarding sloshing.

1.2. Purpose

The purpose of the work described in this document is the study of the sloshing effect in ELSY

reactor by seismic loads. The first part is a CFD (Computational Fluid Dynamics) analysis with

ANSYS_FLUENT program in order to calculate: free surface displacement, pressure on

components, etc. With the results from the first analysis a structural analysis is made with

ANSYS_MECHANICAL in order to obtain the stresses, displacement, etc. on considered

components

The second purpose of the study is to analyse the fluid-structure interaction between the lead

and the exterior and cylindrical inner vessel. In this study, the rest of internal components have

been modelled as rigid solids. These activities have been developed with ABAQUS software.

1.3. Scope

The purpose above has been met by the following scope of activities:

Detailed models of the reactor vessel and the main internal components have been made




for studying sloshing effects, moving for the response spectra at component locations produced

in WP2. These models behavior have been evaluated with FLUENT approach.

1. Fluid and structural analysis in order to obtain the fluid and solid solution fields. For the

structural analysis ANSYS code has been used.

2. In order to evaluate the fluid structure interaction, two models of the ELSY/LFR reactor

have been developed. In the first one, the reactor has been modelled as a rigid body,

and in the second one, the main components (heat exchangers and steam generators)

have been modelled as rigid bodies, but the external and the cylindrical inner vessel

have not been modelled like that. Those models have been processed with ABAQUS.

3. Run the four seismic load scenarios of the different seismic inputs for all cases

described above. The object was to obtain information on the sloshing of the free

surface and on the fluid-structure interaction, with both approaches..

4. Conclusions and recommendations: From the examination of the studies described

above, responses from the two models will be compared to conclude with the significant

loads on the vessel and vessel l id and on the internal components.

These activities are described in detail in the following chapters.

1.4. Organization of the document

The present proposal includes eight additional chapters and three appendixes.

Chapter 2 gives the description of the input data used for analysis and a description of the

FLUENT and ABAQUS methodologies used.

Chapter 3 describes with detail the developed finite element models used for the analysis in the

two used approaches.

Chapter 4 is the assessment of the FLUENT results. Includes a description of the evaluation

performed with these approach. Contains a description of main results obtained for the seismic

loads cases.

Chapter 5 gives the assessment of the ABAQUS results. Includes a description of the evaluation

performed with these approach. Contains a description of main results obtained for the seismic

loads cases. Both analysis results with rigid component and with flexible vessels are included.

Chapter 6 gives a description of the stresses analysis results obtained with both approaches

ANSYS and ABAQUS with flexible vessels.

Chapter 7 deals with a comparative analysis of the results obtained with both approaches.




Finally, chapter 8 is devoted to the conclusions and suggestions for future works.

Chapter 9 is a l ist of the main references.

ANNEX I contains the ALE method validation.

ANNEX II contains all the results obtained with the FLUENT methodology

ANNEX III contains all the results obtained with the ABAQUS methodology

2. INPUT DATA

2.1. Reactor vessel description

The geometry of ELSY/LFR,used in these analysis, has been supplied by Ansaldo Nucleare

(Ref. 3). In essence, the reactor consists of the reactor vessel (RV), the lid, a cylindrical inner

vessel (IV), eight steam generators (SG) and four Decay Heat Removal (DHR) exchangers,

together with the connection pipes of internals. Figure 2-1 shows a sketch of the main

components.

The reactor vessel is shaped as a cylindrical vessel with hemispherical bottom head and the lid.

The diameter of the vessel is 12.30 m and the height, 8.40 m. The vessel is fi l led with 7.91 m of

molten lead at 480ºC. The distance between the molten free surface and the bottom surface of

the reactor roof is 0.490 m at rest. The reactor vessel is supported by a forged Y-piece, the outer

leg of which is supported directly by the ring beam anchored to the reactor pit and the inner leg

is supporting the roof.

The lid consists of an annular thick plate with penetrations for the dip components and for the

cylindrical inner vessel. The thickness of the roof is 200.0 mm.

The cylindrical inner vessel contains the above core structures, including the upper heads of fuel

elements. It provides for lateral restraint of the core, but it does not have a core support plate.

The outer diameter of its circular cross section is 5.95 m. This vessel has ducts branching out

from its lower part, each of one connected with one SG. The vessel is supported on the upper

part by the roof.

The SGs are vertical, circular cross-section units that hung from the reactor vessel roof and are

immersed in the molten lead. They contain the primary pumps. They are axisymmetrically

positioned by pairs and are located in the annular space between the cylindrical inner vessel and

the reactor vessel wall.




The DHR exchangers also hung from the reactor vessel and are immersed in the molten lead.

They are not connected to the inner vessel.

Figure 2-1 Main components of the ELSY/LFR reactor

2.2. Seismic input

The seismic input for all the analyses consists of three acceleration time histories which are

obtained from the seismic analysis of the ELSY Reactor Building model with and without seismic

isolators (Ref.5). The following cases are analysed:

a) Case 1: Hard soil, no isolators, and Design Base Earthquake;

b) Case 3: Hard soil, with isolators, and Design Base Earthquake;




c) Case 6: Hard soil, with isolators and Beyond Design Base Earthquake; and

d) Case 12: Soft soil, with isolators, and Design Base Earthquake.

These cases are assumed to be the most significant load cases in the horizontal and vertical

directions. The acceleration time histories are shown in Figure 2-2 and Figure 2-3.

For every analysis, the seismic action is prescribed simultaneously in the three global directions

for the reactor by means of three acceleration time histories. The total simulation time for which

results are to be computed is 20.0 seconds (total duration of the seismic time histories).

Figure 2-2 Horizontal response spectra – Cases 1, 3, 6, 12

0

10

20

30

40

50

60

70

80

90

100

0.1 1.0 10.0 100.0

PS

A (m

/s2)

Frequency (Hz)

AX- Case 01 - 5%

AX- Case 03 - 5%

AX- Case 06 - 5%

AX- Case 012 - 5%

AY- Case 01 - 5%

AY- Case 03 - 5%

AY- Case 06 - 5%

AY- Case 012- 5%




Figure 2-3 Vertical response spectra – Cases 1, 3, 6, 12

2.3. FLUENT methodology

In order to solve the sloshing problem, by using a fluid dynamic analysis, the ANSYS FLUENT

computational fluid program was used, which solves the Navier-Stokes equations using the finite

volume numerical technique based on cell center.

Being a free surface simulation, we have used one of the many formulations of the program for

solving multiphase flow.

FLUENT analysis is based on the Eulerian approach. In the Euler-Euler approach, the different

phases are treated mathematically as a continuum. Since the volume of a phase cannot be oc-

cupied by the other phases, the concept of volume fraction is introduced. These volume frac-

tions are assumed to be continuous functions of space and time and their sum is equal to one.

Conservation equations for each phase are derived in order to obtain a set of equations, which

have similar structure for all phases. These equations are closed constitutive relations obtained

from empirical information.

The FLUENT program has three different Euler-Euler multiphase models: the volume of fluid

(VOF), the mixture model, and the Eulerian model. In this analysis, VOF (Direct method of pre-

dicting interface shape between immiscible phases) multiphase model was used.

0

20

40

60

80

100

120

140

160

180

200

0.1 1.0 10.0 100.0

PS

A (m

/s2)

Frequency (Hz)

AZ- Case 01 - 5%

AZ- Case 03 - 5%

AZ- Case 06 - 5%

AZ- Case 12 - 5%




The VOF model is a surface tracking technique applied to a fixed Eulerian mesh. It is designed

for two or more immiscible fluids where the position of the interface between the fluids is of in-

terest. In the VOF model, a single set of momentum equations is shared by the phases, and the

volume fraction of each of the phases in each computational cell is tracked throughout the do-

main.

Applications of the VOF model include stratified flows, free-surface flows, fi l l ing, sloshing, the

motion of large bubbles in a l iquid, the motion of l iquid after a dam break, the prediction of jet

breakup (surface tension), and the steady or transient tracking of any liquid-gas interface.

2.3.1. CFD ANALYSIS

The basic problem of fluid structure interaction (FSI), when a fluid flow interacts with a solid

structure, involves the evaluation of the hydrodynamic pressure distribution. The hydrodynamic

pressure of l iquids in moving rigid containers could be split into two hydrodynamic components

namely:

• Impulsive component due to rigid-body motion of the liquid. Under dynamic loading, part

of the liquid moves synchronously with the vessel as an added mass and is subject to the same

acceleration levels as the vessel.

• Convective component due to sloshing of the liquid at the free surface. Under lateral exci-

tation, oscil lations of the fluid occur and this results in the generation of pressures on the walls,

base and roof of the vessel.

A CFD analysis with ANSYS-FLUENT solver, with appropriate 3-D FEM model, has been ap-

plied in order to obtain the induced hydrodynamic pressures from sloshing effects due to the

fluid motion.

The analysis is transient and the solution is obtained through an iterative process due to the non

linear nature of the problem.

In a first approximation it considers that the contour of the both fluids, coolant and cover gas, is

rigid. The fluid and solid structure fields are solved separately. The pressure exerted by the fluid

on the structure may cause structural deformations significant enough to change the fluid flow

itself (2 way interaction), or the deformations may be neglected on the fluid side (1 way). 1 way

or 2 way analysis depends on the results of structural analysis.




2.4. ABAQUS methodology

This methodology solves the fluid structure interaction problem with ABAQUS/Explicit (Ref.6) by

using the ALE (Arbitrary Lagrangian-Eulerian) method to represent the fluid response. The

reactor vessel and its main components are first represented as a rigid body in order to obtain

the fluid response without taking into account the vessel and internals deformation contribution.

At a later stage, the reactor vessel is no longer considered rigid and fluid structure interaction is

assessed and compared with the results from the rigid body assumption.

The ALE method of space discretization is a hybrid of the Lagrange and Euler methods. This

method makes it possible to maintain a high-quality mesh throughout an analysis, by allowing

the mesh to move independently of the material. The method redefines the mesh continuously

as the calculation proceeds. The advantage of ALE is the ability to reduce difficulties caused by

severe mesh distortions encountered by the Lagrange method and allows a calculation to

continue efficiently.

In order to validate the application of the ALE method with Abaqus Explicit to determine the

sloshing in the ELSY reactor, a simplified model is analysed by applying this method. Results

are then compared to a reference solution obtained by the analytical approach given by Housner

(Ref. 8). Appendix 1 shows the analysis performed for validation. Several parameters : bulk

modulus, viscosity and mesh size have been checked to validate convergency and results.

3. DESCRIPTION OF THE MODEL

3.1. FLUENT model

3.1.1. 2D ANALYSIS

Previous to the 3D analysis, it has performed a 2D analysis in order to confirm that fluids can

displace properly inside the reactor vessel and internals: main pipes, steam generators, core

and core upper internals.

With this model the following has checked: porosity, head pump, free surface displacement, etc.

These will be used in the 3D analysis. The 2D model has got 74000 nodes and 69000 elements.

Figure 3-1 shows the geometry and mesh of the 2D model




Figure 3-1 2D model

3.2. FLUENT 3D ANALYSIS

Five independent CFD analyses have been carried out. The first one only concerns about the

dead load, which means the weight of the molten lead and argon fluids.

The other ones allow to determine the fluid response undergoing the seismic excitation. The

main results from these analysis are the hydrodynamic pressure distribution into the reactor

vessel and the internal components as well as the free surface displacement, due to the molten

lead motion.

The pressure distribution will be used in order to check the structural integrity of the reactor

vessel and the internal components.

3.2.1. Model

The analysis requires of two models: the first one allows to determine the fluid response

(velocity, pressure, free surface displacement, etc) by using a fluid dynamic analysis with

FLUENT code and the second one uses the results obtained from the first analysis at several

times in order to perform a static structural assessment of the vessel (stresses, displacements,

etc) with ANSYS code. Both of them are 3D.

The CFD (Computational Fluid Dynamics) model is performed from ELSY Reactor geometry.

The geometry considered includes the following main components:

• REACTOR VESSEL (RV)

• INNER VESSEL (IV)

• LID




• STEAM GENERATOR (SG)

• DECAY HEAT REMOVAL (DHR)

• FUEL ASSEMBLY (FA)

In this analysis, all of them are considered rigid.

Appropriate 3-D finite element models were set up and implemented in FLUENT code

Figure 3-2 shows the ELSY Reactor geometry:

Figure 3-2 ELSY reactor geometry

The fluid domain has been generated from Elsy Reactor geometry considered, which consists of

a two-phase model composed of a coolant fluid (molten lead at 480ºC) and a cover gas (argon).

The fluid domain has been created fi lling the ELSY Reactor geometry and using as fluid bounda-

ry condition, the reactor vessel and the main internal components (IV, LID, SG, DHR, and FA).

The interface between the molten lead and the gas is located, at rest, 0.490 m below the reactor

vessel l id.Figure 3-3 and Figure 3-4 show the fluid domain geometry and mesh:




Figure 3-3 Fluid domain geometry

Figure 3-4 Fluid domain mesh

The grid in the interface between the molten lead and the argon has been refined, because the free surface displacement is critical

The numbers of nodes and elements used for this 3D analysis are:

• 1300000 nodes




• 1900000 elements

The objective of these high node numbers is twofold. The first one is to have a good description

of the vessel internal which could impair the fluid displacement. The second one is to avoid the

loss of convergence it has been experienced with smaller models, especially for the seismic

loads with high accelerations.

3.2.2. Fluid properties

The fluids considered in the analysis are molten lead and argon (modelled as an ideal gas). The

properties at 480ºC are the following:

a) Molten lead

Density: 10470.0 kg/m3

Specific heat: 145.4 j/kg-K

Thermal conductivity: 17.5 w/m-K

Viscosity: 0.0018820 kg/m-s

b) Argon


Specific heat: 520.64 j/kg-K

Thermal conductivity: 0.0158 w/m-K

Viscosity:2.125x10-5 kg/m-s

3.2.3 Load cases

Five independent CFD analyses have been carried out. The first only takes into account the

dead load. The others corresponds with the four load cases shown in Table 3-1.




CASE CASE redu. SOIL ISOLATORS EARTHQUAKE

1 1 HARD NO DBE

3 3 HARD YES DBE

13 6 HARD YES BDBE

23 12 SOFT YES DBE

Table 3-1 Load cases

In all cases shown in the Table 3-1, for each load case, the seismic action is prescribed

simultaneously in the three global directions for the reactor by means of three acceleration time

histories. See paragraph 2.2.

The seismic input for all the analyses are three acceleration stories, with a total duration of 20.0

seconds. The time increment is of 0.01 seconds, and they are shown in ANNEX-II.1.3.

3.2.4 Reference points

It has fixed 49 points, denominated control points or reference points, for these points the pres-

sure on the external vessel is saved in time step each 0.01 seconds. They are grouped in sever-

al height with respect to the global coordinate system. Each group has got eight points, situated

in circumferential direction, each 45º, except P_H0_1 point. This point is located at the bottom of

the reactor vessel. Table 3-2 shows axial an d radial position of each group. Figure 3-5 shows

the position and numbering of the point situated in XZ plane.




Figure 3-5 Geometrical distribution of the reference points

Reference points group

Z (m) R (m)

H0 - 8.380 0.000

H1 - 7.750 2.970

H2 - 7.095 4.130

H3 - 4.530 5.900

H4 - 0.490 6.120

H5_EXT 0.000 6.050

H5_INT 0.000 3.000

Table 3-2 Location of the reference points




3.3. ABAQUS model

Two 3D finite element models are created using Abaqus/Explicit (Ref.6). Both represent the

reactor vessel and the outer shells of its main components: the roof, the cylindrical inner vessel,

the eight SG and the four DHR exchangers. The molten lead located in the annular space

between the reactor vessel and the cylindrical inner vessel is represented by using a single

adaptive mesh domain that follows the ALE technology.

Using the ALE method, the molten lead response is intended to be analysed in both models in

terms of its free surface sloshing and in terms of the hydrodynamic pressure applied by the fluid

on the wall interfaces during the seismic motion.

In order to represent more adequately the hydrodynamic pressure applied by the molten lead

during the earthquake at the bottom of the reactor vessel, the molten lead located inside the

cylindrical inner vessel is also represented in both models. As the inner vessel does not have a

bottom plate the molten lead from the inside and the outside of the inner vessel are

communicated. Since lateral movement of the molten lead located inside the inner vessel is

restricted by the presence of the fuel components, additional vertical elements are placed in the

interior of the inner vessel model. These vertical elements limit the horizontal molten lead flow

inside the inner vessel and do not allow the fluid to impact laterally onto the inner vessel walls.

Since fuel elements placed inside the inner vessel are no represented in the models, the height

of the molten lead column inside the inner vessel is lower than it should be, as it has been

decided to conserve the original mass of molten lead inside the inner vessel.

On the other hand, since the sloshing effect of the molten lead located inside the inner vessel is

considered not to be significant, an auxiliary l id close to this fluid free surface is modelled. The

purpose of putting this extra l id is to avoid excessive distortion of the free surface of the molten

lead mesh located inside the inner vessel during computation.

Since the main objective of this analysis is evaluating the importance of the fluid-structure

interaction this modelling issue is not significant.

The difference between both models is that the first one does not take into account the effect of

the flexibility of the external and internal vessel in the fluid response and the second one does,

i.e., the second model is the one that considers the fluid-structure interaction.

Although the reactor components elements are defined differently in both models for the reason

explained above, the definition of the molten lead is the same for both. To model the molten lead

material it is used a simple Newtonian viscous shear model and a linear volumetric equation of

state for the bulk response. The bulk modulus functions as a penalty parameter for the

incompressible constraint. Since sloshing problems are unconfined, it can be chosen a bulk




modulus lower than the actual value for molten lead in order to avoid an overly stiff response

and the molten lead will sti l l behave as an incompressible medium. The following parameters are

taken into account to represent the molten lead material:


Linear volumetric response (Equation of State)

Speed of sound: 800.0 m/s (obtained from the reduced bulk modulus)

Shear behaviour (Newtonian fluid)

Viscosity: 1.882x10-3 Pa·s

No turbulence or l imit layer effects

Additionally, for computation stabil ity purposes, a very low coefficient of friction (i.e., 0.05) is

taken into account between every fluid-wall interfaces.

Gravity and seismic loads are considered to act simultaneously in the models. To represent the

gravity loading, an initial geostatic stress field is defined to equilibrate the stresses caused by the

self-weight of the molten lead. The four seismic case loads described above are analysed with

these two models.

Regarding the gravity action in the molten lead located inside the inner vessel, an additional

pressure load is needed to be applied on its free surface because the height of molten lead

column inside the inner vessel does not coincide with the real one. The value of the applied

pressure is directly proportioned to the difference of height between the originally projected and

the finally modelled molten lead. This additional pressure load allows that, at the same level,

every point of molten lead located either inside or outside the inner vessel could have the same

hydrostatic pressure due to gravity.

3.3.1. Abaqus model with rigid components

The objective of the first Abaqus model is to obtain the fluid response without taking into account

the effect of the reactor flexibility. For this purpose, the model represents the reactor vessel and

its components as a rigid body using shell elements. The elements of the molten lead mesh are

hexahedral elements (C3D8R, Ref.6). Figure 3-6 and Figure 3-7 show different views of the

whole model, which consists of 138104 elements.

Since the reactor vessel and its components are represented as a rigid body, all of them move

accordingly to the seismic motion.




Figure 3-6 Abaqus model with rigid components. Shell elements




Figure 3-7 Abaqus model with rigid components. Molten lead elements

3.3.2. Abaqus model with deformable components

In this second Abaqus model, the fluid-structure interaction is taken into account. In particular,

the effect of the flexibil ity of the reactor vessel, its roof and the cylindrical inner vessel are taken

into consideration. On the other hand, the eight SG and the four DHR exchangers are sti l l

represented as rigid bodies because the effect of their flexibil ity is considered negligible.

In this model, the forged Y-piece that supports the reactor vessel is also represented and its

flexibil ity is also considered. At the ending points of this piece, boundary conditions are

prescribed. Specifically, the seismic motion is prescribed at this set of points simultaneously in

the three global directions.

The whole model consists of 135396 elements. The elements of the molten lead mesh are

hexahedral elements (C3D8R, Ref.6). Every component whose flexibility is taken into account is

represented in the model with S4 and S4R elements (Ref.6).

Original thicknesses of all of the deformable components outer shells are considered in the

model except for the cylindrical inner vessel. For this component, the represented thickness is

the sum of the thicknesses of the two outer shells, which are connected by stiffeners.

The material of the deformable components of the reactor vessel is SA 240 TP 316 LN steel. In

the model, the material is assumed to be linear elastic with a Young's modulus of 200.0x109 Pa,

a Poisson's ratio of 0.3 and a density of 7850.0 kg/m3.




In order to include the mass of the internal components of the inner vessel that are not

represented in the model, an additional equivalent mass is distributed over the inner vessel

elements. The mass distribution is made by maintaining the original centre of mass.

Regarding the SG and the DHR exchangers, an additional mass for each component is added to

its centre of mass in order to take into account the masses of their non-modelled internal

components.

In relation with the loads applied to the model, in this model an additional pressure load is

applied to the walls of the cylindrical inner vessel. This triangular pressure load represents the

effect of the hydrostatic pressure of the part of molten lead that is located in the inner vessel and

that is not represented in the model.

4. ASSESSMENTS OF FLUENT RESULTS

4.1. 2D MODEL

Figure 4-1 to Figure 4-6show the main results of the 2D model. Figures show the fluid velocity

which demonstrates that it can be displaced in all directions. The main conclusions are that

displacements are strongly l imited by the internal surfaces and that these surfaces should be

correctly located.

Figure 4-1 Pressure




Figure 4-2 Volume fraction: Red – Lead; Blue-Argon

Figure 4-3 Volume fraction at rest




Figure 4-4 Velocity

Figure 4-5 Horizontal velocity




Figure 4-6 Vertical velocity

4.2. FLUENT 3D MODEL RESULTS

The results, when only considered dead load, are pressure in reference points and pressure

distribution in the reactor vessel and internals. These results are shown in the ANNEX-II.1.4,

where pressure distribution at the vessel and internal components is shown. Maximum internal

pressure is located in the external vessel bottom with 0.8 MPa.

The main results, corresponding with the seismic loads, cases: 1, 3, 6 and 12 are the following:

1. Temporal evolution of pressure in reference points

2. Pressure distribution in the reactor vessel and internals

3. Free surface position

4. Percentage of the lid surface in contact with the molten lead

ANNEX: II.1.4 present results for case 1, case 3, case 6 and case 12.

It would be desirable to have the results for the post-processing every 0.01 seconds, time step

coinciding with the time step of the acceleration stories. The only results stored every 0.01 sec-

onds, are the pressures at reference points. For the other ones, there is only information every

0.2 seconds. The reason is that the size of the fi les to store the pressure in the reference points

is relatively small. In return, to store the other ones, very large fi les are necessary. The problem

with this is the loss of information needed to know what and at what time the worst situation




occurs. The estimation of the requirements for a fluid storage of information each 0.01 seconds

for each case is about 20 Tb.

For each of the load cases analysed is showed graphically the position of the free surface and

pressure distribution in the reactor vessel and internals, The results are shown for the final time

of the process, t = 20.0 s, and those corresponding with the following situations:

• The time when the pressure distribution in the reactor vessel is considered

like the most un-favourable.

• The time when the surface of the reactor vessel l id, wet by molten lead, is

maximum

The most unfavourable situation for the reactor vessel is determined from records of pressure in

the reference points, as follows:

a. For each of the heights where the reference points are grouped, the point of max-

imum pressure and the time at which it occurs are taken.

b. From the fi le with results each 0.2 seconds, time close to the previous time is

considered. For this time, the pressure in the same points of the previous part is

read.

c. The average value of the ratio between pressure in part a an part b, is calculated.

d. It is considered as most unfavorable situation the pressure obtained in part b mul-

tiplied by the value calculated in part c. This pressure will be used in structural

analysis in order to check the reactor vessel.

The following tables show the time and factor which multiplies the pressure for the different ana-

lyzed cases.

.




CASE_1

Reference points

Pressure (Pa) Time (sec)

P_H0_1 1388330.0 15.44

P_H1_4 1541898.0 15.44

P_H2_4 1522937.0 15.44

P_H3_4 1290202.0 15.45

P_H4_2 609822.0 15.36

P_H5_EXT_2 696689.0 15.36

P_H5_INT_2 634809.0 16.98

Table 4-1 Data corresponding with part a for CASE_1

CASE_1 (TIME = 15.8 sec)

Reference points Pressure (Pa) P (table 3.3)/P (t=15.8 s)

P_H0_1 1129466.5 1.229

P_H1_4 898309.0 1.716

P_H2_4 763234.0 1.995

P_H3_4 400715.0 3.219

P_H4_2 96910.0 6.292

P_H5_EXT_2 96910.0 7.189

P_H5_INT_6 194924.0 3.256

Av erage v alue 3.55

Table 4-2 Data corresponding with part b and c for CASE_1




CASE_3

Reference points Pressure (Pa) Time (sec)

P_H0_1 1585307.0 3.86

P_H1_4 1481062.0 3.86

P_H2_4 1352589.0 3.86

P_H3_4 874565.0 3.86

P_H4_6 260265.0 16.81

P_H5_EXT_3 228206.0 7.60

P_H5_INT_6 187511.0 17.00




P_H0_1 1257329.0 1.261

P_H1_4 1174748.0 1.261

P_H2_4 1073647.0 1.260

P_H3_4 698601.0 1.252

P_H4_6 67700.0 3.844

P_H5_EXT_3 68074.0 3.352

P_H5_INT_6 61525.0 3.048






CASE_6

Reference points


P_H0_1 3289981.7 13.68

P_H1_4 3123347.2 13.68

P_H2_4 2947532.5 4.36

P_H3_4 2302257.5 4.36

P_H4_2 1316391.7 9.70

P_H5_EXT_2 1884037.6 3.35

P_H5_INT_2 1606643.9 13.01




P_H0_1 2441657.5 1.3474

P_H1_4 2300620.2 1.3576

P_H2_4 2130498.0 1.3832

P_H3_4 1382724.4 1.665

P_H4_2 226356.2 5.8156

P_H5_EXT_2 154592.3 12.187

P_H5_INT_6 154569.0 10.394






CASE_12

Reference points


P_H0_1 1027357.0 13.99

P_H1_4 970366.0 13.99

P_H2_4 890725.0 13.99

P_H3_4 594835.0 16.30

P_H4_3 142783.0 16.46

P_H5_EXT_4 134482.0 16.40

P_H5_INT_1 153105.0 9.88



Reference points Pressure (Pa) P (table 3.9)/P (t=14.0s)

P_H0_1 989210.0 1.04

P_H1_4 934746.0 1.04

P_H2_4 858400.0 1.04

P_H3_4 563084.0 1.06

P_H4_3 28651.0 5.00

P_H5_EXT_4 35742.0 3.77

P_H5_INT_1 35846.0 4.28



Table 4-1 to Table 4-8 show the time and factor to be applied to the pressure for the analyzed

cases.

The main conclusion of this data is that in order to have a real estimation of the pressures

effects on the vessel the results obtained for each 0.2 seconds should be multiplied by a factor

of 3.55 for case 1, 2.18 for case 3, 4.87 for case 6, and 2.46 for case 12.




The second point of interest is the evolution of the fluid loads on the lid. The following graphics

results show the percentage of surface lid in contact with molten lead versus time. This value

has been obtained from the fi le with results every 0.2 seconds. Be aware that these means that

the real results if we were able to store data each 0.01 seconds will be higher. This percentage

versus time is showed in the following figures for all cases analyzed.

Figure 4-7 Percentage of reactor vessel lid in contact with molten lead for case 1

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

16,0

18,0

20,0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(%)

TIME (s)

CASE_1Surface LID in contact with lead






0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(%)

TIME (s)


0,0

5,0

10,0

15,0

20,0

25,0

30,0

35,0

40,0

45,0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

(%)

TIME (s)






CASE

MAXIMUM VALUE OF SURFACE LID WET BY MOLTEN LEAD

(%)

TIME

1 17.50 17.40

3 8.40 17.00

6 41.9 13.40

12 3.70 17.80

Table 4-9 Maximum percentage of surface lid wet by molten lead and time it occurs

These results show that this is a significant load on the upper l id due to sloshing. It means that it

is a parameter that should be evaluated specifically. This is another issue that should be evalu-

ated also related with these load impact on the lid. It is the corresponding load associated with

the different temperature between the lid and fluid lead.

Finally, Figure 4-11 to Figure 4-14 bellow show the relationship between the maximum seismic

loads pressure and the pressure at rest, for all reference points. It can be seen a high pressure

step between reference levels PH-3 and PH-4. This step is due to the change of fluid displace-

ment from fluid impulsive behaviour in the lower part of the vessel to the convective one in the

upper part of the fluid. It means that there are also significant loads in the upper part of the ves-

sel due to these convective loads. See ANNEX-II.1.4

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(%)

TIME (s)





Figure 4-11 Maximum seismic loads pressure versus the pressure at rest for case 1


1,0E+00

1,0E+01

1,0E+02

1,0E+03

1,0E+04

1,0E+05P_H

0_1

P_H

1_8

P_H

2_8

P_H

3_8

P_H

4_1

P_H

4_8

P_H

5_EX

T_8

P_H

5_IN

T_8

Pm

ax/

Pat

rest

REFERENCE POINTS

CASE_1

1,0E+00

1,0E+01

1,0E+02

1,0E+03

1,0E+04

P_H

0_1

P_H

1_8

P_H

2_8

P_H

3_8

P_H

4_1

P_H

4_8

P_H

5_EX

T_8

P_H

5_I

NT_

8

Pm

ax/

Pat

rest

REFERENCE POINTS

CASE_3






In these figures, the impulsive component due to rigid-body motion of l iquid and the convective

component due to sloshing of the liquid at the free surface, can be checked. Transition from

impulsive to convective component occurs inside the control points range covered by H3 and H4

groups.

Those results show that the loads on the vessel upper part including the lid are significant due to

the sloshing lead displacements.

1,0E+001,0E+011,0E+021,0E+031,0E+041,0E+05

P_H

0_1

P_H

1_8

P_H

2_8

P_H

3_8

P_H

4_1

P_H

4_8

P_H

5_E

XT_

8

P_H

5_IN

T_8P

max/

Pat

rest

REFERENCE POINTS

CASE_6

1,0E+00

1,0E+01

1,0E+02

1,0E+03

1,0E+04

P_H

0_1

P_H

1_8

P_H

2_8

P_H

3_8

P_H

4_1

P_H

4_8

P_H

5_EX

T_8

P_H

5_IN

T_8

Pm

ax/

Pat

rest

REFERENCE PPOINTS

CASE_12




5. ASSESSMENTS OF ABAQUS RESULTS

5.1. Seismic assessments

5.1.1. ABAQUS model with rigid components

In this model, all internal and external elements, either cylindrical inner vessel and exterior

vessel, have been modelled as rigid bodies. It means that everything will move and respond

following the seismic input data.

The seismic input data has been described in chapter 2.2. It consists of three acceleration time

histories for each case analysed. Four different cases have been chosen to be analysed in this

report.

For every case analysed, the sloshing effect of the free surface has been studied.

As the 3D finite element model has been modelled as rigid body, the entire model responds

referred to a reference point, and the seismic input data has been applied to that reference point.

Figure 5-1 and Figure 5-2 show the evolution of the height of the lead free surface during the fulll

period of the earthquake for the cases 1 and 6. Note that only in cases 1 and 6 the free surface

reach the 0.49 m height in which is located the lid.

Figure 5-1 Vertical displacement of the free surface for the case 1 and the rigid model

0

0,1

0,2

0,3

0,4

0,5

0,6

0 5 10 15 20

Ver

tica

lDis

pla

cem

ent

(m)

Time (s)

Vertical Displacement Free SurfaceRigid Case 1

U3_Max_Env_Free_Surface_Rigid_Case1




Figure 5-2 Vertical displacement of the free surface for the case 6 and the rigid model

5.1.2. ABAQUS model with deformable components:

As it has been described previously, in this model, the mail components have been modelled as

rigid bodies, but the cylindrical inner vessel and the exterior vessel have been modelled as de-

formable components..

In this model, the support consists of a forged Y piece which is anchored to the roof. In the mod-

el, it has been created two reference points: one of them is created to determine the rigid body

movement between the main components. The second one is created to l ink all the support

points and to apply the seismic acceleration time history input data.

In all cases the calculus aborted in this before the end of the seismic acceleration time histories

due to element distortion. In cases 1, 3 and 12, the simulation aborted approximately in the in-

terval t=7.0 s, and in the case 6, in the interval t=4.0 s. These result mean that the model should

be developed in a more detailed way in order to be able to accommodate the big deformations

suffered by some fluid lead elements.

Analysing the sloshing of the lead free surface in all cases mentioned above, it can be observed

that during the time before the calculus aborts, the lead free surface does not reach the 0.490 m

height where is located the lid. Figure 5-3 and Figure 5-4 show the evolution of the height of the

free surface during the earthquake until the simulation aborts. Even though, looking at the evolu-

tion in the first seconds of the earthquake, it is probably that the lead could reach the lid in cases

0

0,1

0,2

0,3

0,4

0,5

0,6

0 5 10 15 20

Ver

tica

lDis

pla

cem

ent

(m)

Time (s)

Vertical Displacement Free SurfaceRigid Case 6





1 and 6. These results are coherent with the results obtained in the model with rigid compo-

nents.

Figure 5-3 Vertical displacement of the free surface for the case 1 and the flexible model

Figure 5-4 Vertical displacement of the free surface for the case 6 and the flexible model

As a conclusion of the seismic assessment, it has been observed that in the model with rigid

components, the free surface reaches the lid, located at the height of 0.490 m, in the cases 1

and 6. In the model with deformable components, the calculus aborts before ending all the peri-

od that defines the acceleration time history of the earthquake.

0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

0 5 10 15 20

Ver

tica

lDis

pla

cem

ent

(m)

Time (s)

Vertical Displacement Free SurfaceFlexible Case 1

U3_Max_Env_Free_Surface_Flex_Case1

0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

0 5 10 15 20

Ver

tica

lDis

pla

cem

ent

(m)

Time (s)

Vertical Displacement Free SurfaceFlexible Case 6





5.1.3. Displacement comparison

Looking at the evolution of the height of the free surface, comparing with the evolution of height

of the free surface measured in the model with rigid components, it is very probable that the free

surface could reach the lid, in cases 1 and 6, as well as in the model with rigid components.

Figure 5-5 and Figure 5-6 show the comparison of the sloshing produced between the model

with rigid components and the model with deformable components. Results for case 6 show that

fluid lead will impact on lid earlier , which means a higher interaction fluid lead/lid.

Figure 5-5 Comparison rigid vs flexible model of the vertical displacement for the case 1

Figure 5-6 Comparison rigid vs flexible model of the vertical displacement for the case 6

0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

0 5 10 15 20

Ver

tica

lDis

pla

cem

ent

(m)

Time (s)

Vertical Displacement Free SurfaceCase 1 Comparison rigid vs flexible



0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

0 5 10 15 20

Ver

tica

lDis

pla

cem

ent

(m)

Time (s)

Vertical Displacement Free SurfaceCase 6 Comparison rigid vs flexible






5.2. Pressure distribution

5.2.1. ABAQUS model with rigid components

In the ABAQUS model, it has been selected a total number of 41 elements to request the

pressure history output. They are distributed every 45º and in each angle, there are another 5

elements distributed in different heights, and another element located in the centre of the

external vessel and in the lowest point. Figure 5-7 shows the distribution of those points men-

tioned above.

Figure 5-7 Distribution and location of the reference elements

Pressure time history during all the period of the earthquake has been obtained. Those figures

are attached in the ANNEX.III.2.1

It has been checked that in the lowest element (P9) the mean of the pressure time history is

similar to the hydrostatic pressure obtained at rest.

It can also be observed that in the elements located in the free surface a very high pressure has

been measured in a very short time range, so it corresponds to impact loads.

The values of these pressures measured are approximately:

1.8 MPa at the interval t=12.29 s in the case 1.

12.0 MPa at the interval t=9.94 s in the axe 5 and at the interval t=14.98 s in the axe 8 in

the case 6.

P1-Y

P2-Y P3-Y P4-Y

P5-Y

P6-YP7-Y

P8-Y

PX-1 PX-2

PX-3

PX-4

PX-5

P9

P9




Note that in case 6, the spectrums have been multiplied by 3, it is well above the design bases

earthquake.

It is important to note that without taking into account the impact loads, the pressure time histo-

ries have been measured around the value of 3.0 MPa. It has been observed that the highest

pressure measured coincide in time with the spectrum peaks.

Figure 5-8 and Figure 5-9 show these impact and local loads which should be analysed in future

studies.

Figure 5-8 Step time 11.20 s in the model with rigid components case 1. (P=1.74 MPa)





Making a zoom in the time axe, it can be notice how the lead follows the seismic frequency,

because it is only measured high pressures coinciding in time with the acceleration time history

peaks.






5.2.2. ABAQUS model with deformable components

Remembering that the calculus of this model aborted before the ending of the seismic accelera-

tion time history input data (approximately at the interval of 7.0 s in cases 1, 3 and 12 and at the

interval of 4.0 s in case 6) the results obtained will be compared where possible with the results

obtained in the model with rigid components. Results can be seen in ANNEX.III.2.2.

In that short period of time, the comparison between the model with rigid components and that

model , in a similar time interval, show that pressures measured in the model with deformable

components are higher than the model with rigid components. The multiplication factor range

between 1 and 2. But a full time description is required for the flexible case.

Making a zoom in the pressure time history obtained it can be observed that there is a significant

interaction between the deformable structure of the vessel and the lead, because the pressure

distribution has different frequencies than in the model with rigid components. Figure 5-12 shows

that difference. Results can be seen in ANNEX.III.3.1., and III.3.2..






In the pressure time histories obtained in these models, it has also been observed a high in-

creasing of the pressure in a very l ittle interval of times, which are related with impact loads.




Table 5-1 shows the maximum pressures obtained with four load cases using the model with

rigid components as well as the model with deformable components.

Case Model Reference point Pressure (Pa) Time (s)

Case 1 Rigid P4-2 1.84 E6 12.29

Case 1 Flexible P8-4 3.05 E6 4.7

Case 3 Rigid P4-3 1.40 E6 13.44


Case 6 Rigid P5-4 1.26 E7 9.94

Case 6 Flexible P9 7.63 E6 2.88

Case 12 Rigid P6-3 1.61 E6 13.54


Table 5-1 Maximum pressures obtained in the four load cases in both models

In the load cases 1, 3 and 12, the pressures measured in the model with deformable by the time

before the calculus abortion are higher than in the model with rigid components. Only in the load

case 6 the pressure measured is lower in the model with deformable components than in the

model with rigid components.

So in general, the pressures registered in the model with deformable components are higher

than in the model with rigid components. Notice that the pressures in the model with deformable

components could be higher in the period after the calculus abortion.

5.3. Fluid-Structure Interaction

As it has been explained previously, the 3D finite element model with deformable components

calculus aborted in the first third of the seismic acceleration time history. The abortion was pro-

duced because of an element distortion.

By looking at the previous Figure 5-10 to Figure 5-13, it is thought that a significant effect of

fluid-structure interaction exists, due to the different tendencies in the pressure distribution and




pressure time histories measured compared to the pressure time histories obtained in the model

created with rigid components.




6. ASSESSMENTS OF STRESSES RESULTS

6.1. ANSYS RESULTS ON STRUCTURAL ANALYSIS

An structural analysis has been made in order to evaluate the effects of both, the fluid pressure

at rest and hydrodynamic pressures induced by the fluid motion due to the seismic loads. In

order to get it, five independent static analyses have been carried out using the pressure results

which have been got from the Computational Fluid Dynamics (CFD) analysis.

3-D finite element model with ANSYS_MECHANICAL has been made in order to obtain the

stress, displacement, etc. on considered components.

6.1.1. MODEL

A detailed 3-D finite element model has been made from ELSY Reactor geometry. The geome-

try considered includes the following main components:

REACTOR VESSEL INNER VESSEL LID STEAM GENERATOR DECAY HEAT REMOVAL REACTOR VESSEL SUPPORT

The next figure shows the considered geometry




Figure 6-1 ELSY Reactor geometry for structural analysis

6.1.2. Finite Element model

The mesh was performed from the previous geometry with 670000 nodes and 200000 elements.

The next figure shows the mesh generated




Figure 6-2 ELSY Reactor mesh for structural analysis

6.1.3. Material properties

The Reactor Vessel and internals are made of SA 240 316LN and the Reactor Vessel Support is

made of SA 516 Gr 70 carbon steel.

The properties of these materials are the following:

a. SA 240 316 LN


Moduli of elasticity: 1.95x1011 Pa

Poisson's ratio: 0.31

Tensile strength: 512.0x106 Pa (422.0x106 at 450oC)

Yield strength: 205.0x106 Pa (111.0x106 at 450oC)

b. SA 516 Gr 70 carbon steel





Moduli of elasticity: 2.10x1011 Pa

Poisson's ratio: 0.30

Tensile strength: 485.0x106 Pa

Yield strength: 260.0x106 Pa

6.1.4. Boundary conditions

The imposed boundary conditions are the following:

Null displacement in the bottom of reactor vessel support

Rigid junction between Y-piece and reactor vessel support

Rigid junction between lid and reactor vessel




Rigid junction between lid and inner vessel

Rigid junction between steam generator and heat decay removal with l id

Rigid junction steam generator and inner vessel

6.1.5. Load cases

Structural analysis have been carried out using the pressures which have been got from the

Computational Fluid Dynamics (CFD) analyses. The pressure used in the first analysis is got as

a consequence of the fluid weight at rest. The rest of analyses use hydrodynamic pressures

induced by the fluid motion due to the seismic loads. For each of the four seismic loads consid-

ered, results for 20.0 s are available, that is the time in which the seismic loads are working,

which are saved each 0.2 s. Pressures which have been used for each of the four seismic loads

considered, are the following:

Time for the most unfavourable situation. Two analyses are done, the first one using the

pressure saved in the results fi le for the time corresponding to the most unfavourable

situation, and another one using this pressure but being increased using the specific




average coefficient obtained to take in account the lack of storage space . Note: the time

and coefficient stated before are calculated later in the point 3.2.5 of this report.

Time in which the wet l id surface percentage is maximum. This time and percentage are

shown in the table 4.9

Final time, t=20.0 s.

Finally 17 different load cases have been analysed. Taking as a reference the first structural

analysis (with dead load), the results of the following structural analysis allow to evaluate the

effect of the seismic loads.

6.1.6. RESULTS

This work only checks the integrity of the vessel reactor, and that’s why it only takes into account

the vessel, the lid and the vessel support. However, pressure results are available each 0.2 s for

the next components:

REACTOR VESSEL INNER VESSEL LID STEAM GENERATOR DECAY HEAT REMOVAL

It would be possible to check just as it is done for the vessel, the integrity for each of these com-

ponents due to seismic loads used.

Graphical results are shown in the annex-II.2.2

Next table 6.1 includes a results summary:




COMPONENTS

REACTOR VESSEL LID SUPPORT

CASE TIME DISPLACEMENT (mm)

VON_MISES STRESS (MPa)

DISPLACEMENT (mm)


DISPLACEMENT (mm)


1

15.8 9.34 143.6 3.7 44.5 3.2 285.3 (* *)

17.4 6.6 100.0 2.5 20.1 2.1 159.8 (* *)

20.0 5.7 98.7 2.0 12.5 1.35 131.0 (* *)

15.8(*) 33.17 509.9 13.1 158.1 11.4 1013.0 (* *)

3

4.0 7.8 139.2 2.7 18.2 1.6 166.9 (* *)

17.0 3.1 74.1 1.5 26.6 1.2 92.6 (* *)

20.0 5.4 93.9 1.9 8.1 1.2 101.0 (* *)

4.0(*) 17.1 303.8 6.0 39.6 3.6 364.1 (* *)

6

13.8 15.35 272.4 5.5 59.8 3.7 367.1 (* *)

13.4 8.5 171.3 3.4 51.16 2.5 242.1 (* *)

20.0

13.8(*) 74.7 1326.5 26.6 291.1 17.9 1787.7 (* *)

12

14.0 6.2 106.6 2.1 11.0 1.3 133.4 (* *)

17.8 5.4 94.6 1.9 17.8 1.3 129.2 (* *)

20.0 5.2 88.7 1.7 5.6 1.1 108.2 (* *)

14.0(*) 15.3 262.2 5.2 26.9 3.2 328.2 (* *)

AT REST 5.1 85.2 1.7 0.76 0.95 104.5 (* *)

Table 6-1 Maximum displacements and Von Mises stresses (MPa)

(*) Results include the multiplication coefficients calculated in the point 3.2.5 to take in account

the time step recording value of 0.2 s.

(* *) Local stresses




The results show that the seismic loads produce stress exceeding the yield strength in localized

parts of the reactor vessel , therefore, locally impair its integrity.

6.2. ABAQUS RESULTS

In the ABAQUS simulation stresses have been obtained also in the model with deformable

components. As it has been explained before, in the chapter 3.3.2, only the external and the

inner vessel have been modelled as deformable components. It has allowed obtaining the

stresses reached in the external and inner vessel because of the lead movement.

Stresses time histories have been obtained in the reference elements shown in Figure 6-3 in the

inner and external vessel. The field output could not be obtained due to the fi le size. It is im-

portant to remember that the simulation aborts before the ending of the acceleration time history,

so the stresses obtained should be multiplied by the same factor that increases the pressure in

the model with deformable components respect to the model with rigid components.

Figure 6-3 Distribution and location of the reference elements to obtain stresses in the inner and

external vessel

Figure 6-3 show the reference points where it has been measured the maximum values of Von

Mises stresses. Table 6-2 shows the maximum values of the stresses obtained and the time

when it occurs.




Reference point Case Von Mises stress (MPa)

Time (s)

Inner vessel 8-5 Case 1 430.654 5.46

External vessel 11-4 Case 1 200.794 5.8







Table 6-2 Maximum Von Mises stresses obtained for all cases for the inner and external vessel

The materials considered in the model are SS-SA 240 316LN (Symin = 190.0 MPa (20ºC);

Symin = 103.0 MPa (450ºC)) for the reactor vessel and carbon steel SA 516 Gr 70 for the

reactor support.

In the model the Young modulus has been defined temperature-independent, with a value of

200.0x109 Pa.

Looking at the Table 6-2, the Von Mises stresses obtained in the cases 1 and 6 are up to 4 times

higher than the yield strength of the material at 450ºC.

It is important to note that those values obtained have been measured in the only first 4 and 7

seconds of the simulation, because the calculus aborted at the 7th second in the load cases 1, 3

and 12, and at the 4th second in the load case 6.




Figure 6-4 Stresses obtained for the inner vessel in the case 1 for the model with deformable

components

The main raison for calculus abortion is the high strain of some fluid elements. Several modifica-

tions have been tented to avoid this loss of convergence, including the increment on the element

numbers, but the size of the elements should be much lower. The number of elements used in

this calculus is around 140000 and it should be multiplied by a significant factor. In the case of

FLUENT a factor of 13 was used to obtain fluid solution. But including this huge number of ele-

ments requires also a huge data storage device which is not the calculations scope of this mo-

ment.

0,00E+00

5,00E+07

1,00E+08

1,50E+08

2,00E+08

2,50E+08

3,00E+08

3,50E+08

4,00E+08

4,50E+08

5,00E+08

0 5 10 15 20

Str

ess

(Pa)

Time (s)

Von Mises Stresses Cyl Vessel Flexible Case1

PCV1 5

PCV2 5

PCV3 5

PCV4 5

PCV5 5

PCV6 5

PCV7 5

PCV8 5

PCV9 5

PCV10 5




Figure 6-5 Stresses obtained for the external vessel in the case 1 for the model with deformable

components

Figure 6-6 Stresses obtained for the inner vessel in the case 6 for the model with deformable

components

0,00E+00

5,00E+07

1,00E+08

1,50E+08

2,00E+08

2,50E+08

0 5 10 15 20

Str

ess

(Pa)

Time (s)

Von Mises Stresses Ext Vessel Flexible Case1

PEV1 4N

PEV1 4P

PEV2 4N

PEV2 4P

PEV3 4N

PEV3 4P

PEV4 4N

PEV4 4P

PEV5 4N

PEV5 4P

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

7,00E+07

8,00E+07

9,00E+07

1,00E+08

0 5 10 15 20

Str

ess

(Pa)

Time (s)

Von Mises Stresses Cyl Vessel Flexible Case6

PCV1 4

PCV2 4

PCV3 4

PCV4 4

PCV5 4

PCV6 4

PCV7 4

PCV8 4

PCV9 4

PCV10 4




Figure 6-7 Stresses obtained for the external vessel in the case 6 for the model with deformable

components

0,00E+00

5,00E+07

1,00E+08

1,50E+08

2,00E+08

2,50E+08

3,00E+08

3,50E+08

0 5 10 15 20

Stre

ss(P

a)

Time (s)

Von Mises Stresses Ext Vessel Flexible Case6

PEV1 4N

PEV1 4P

PEV2 4N

PEV2 4P

PEV3 4N

PEV3 4P

PEV4 4N

PEV4 4P

PEV5 4N

PEV5 4P




7. RESULTS EVALUATION

7.1. FLUENT ANSYS RESULTS

7.1.1. Fluid pressures

1. The maximum vessel pressure loads obtained for the dynamic cases are: 1.4 MPa for

case 1, 1.6 MPa for case 3, 3.3 MPa for case 6 and 1.0 MPa for case 12

2. The total number of elements require to get the results is of 1.9 Mill ions of elements.

With a lower number a convergence problem erased, specially in the case of a very

high loads such as case 6.

3. So far, only have been processed seventeen seconds of the case 6.

4. To manage the high amount of data generated a huge storage device is required. That

is why only the time history in specific points is stored, while the full set of results are

stored only each 0.2 s. From the comparison of he pressure peaks for 0.01 s and 0.2 s.

some multiplication factor have been obtained in order to evaluate the effect of the data

losses because the lag of storage capacity. Those factors have been applied to the cal-

culated stresses.

5. In ANNEX II.1.4 Pressure time histories and vessel pressures in 3D distribution in spe-

cific time can be review. This 3D pressures represent the behaviour at specific time not

when the time peak pressure is obtained.

7.1.2. Displacements and stresses results

1. Displacements in the reactor vessel are relatively small. Therefore one way analysis is

acceptable for fluid displacements.

2. In all studied cases, the elastic l imit of the vessel material is exceeded in some points

3. There is a significant contact area between the lid and fluid lead. These means signifi-

cant loads on the lid.

4. There is a significant effect between the impulsive and the convective area. More points

should be placed between the H3 and H4 in order to describe precisely the transition be-

tween impulsive to convective components.

5. As is indicated in Table 6.1 maximum stresses appear in case 6 at the external vessel

with a value of 272.0 MPa. While at the lid it is of 60.0 MPa. These stresses are consid-




ering the pressures stored every 0.2 seconds and applied statically. If applied afeccted

by the factor calculated in the point 3.2.5 of this report, the values of these stresses are

1326.0 MPa in the external vessel and 291.0 MPa at the lid.

6. The results should be stored for each time step defined in the seismic loads. This allows

for a detailed dynamic structural analysis and thus take into account the amplifying ef-

fect due to dynamic loads evaluated in this study.

7. Since fluid lead enters in contact with the lid, it would be suitable to analyse the temper-

ature effects on the lid.

7.2. ABAQUS ANALYSIS RESULTS

7.2.1. Fluid pressures results

1. Maximum pressures in the lower part of the external vessel are: For the rigid case, 1.15

MPa for case 1, 1.2 MPa for case 3, 12.7 MPa for case 6 and 0.9 MPa for case 12. For

the flexible case these values are, 1.8 MPa for case 1, 1.4 MPa for case 3, 7.6 MPa for

case 6 and 1.5 Mpa for case 12.

2. The impact loads on the lid can be as higher as 1.6 MPa for case 1 and 1.2 MPa for

case 6.

3. The above results show a significant fluid structure interaction. That can be higher be-

cause the calculations for the flexible cases was aborted before the end time. The multi-

plication factor for pressures can range between 1 and 2. See ANNEX.III.3.1 and 3.2.

4. Table 5.1 show that pressure peaks can be of the order of 12.7 MPa for the rigid case.

See ANNEX III.2.1 and III.2.2

5. In figures 5.8 and 5.9 can be seen that peak pressures are local loads acting in very

short time intervals.

6. There is a significant fluid structure interaction, figures 5.10 and 5.13, show significant

differences on the peak pressures and on the pressure time histories.

7. The calculus abortion in the flexible cases was produced by the distortion excess of

some fluid elements. More detailed models should be developed to evaluate properly

the fluid structure interaction.




8. There is a significant contact pressure between fluid lead and the vessel l id for cases 1

and 6. For case 1 the contact starts around the second 14.0 s. and for case 6 around

the second 9.0 s.

9. This contact will start earlier for the flexible vessel cases as is indicated in figure 5-6.

Where vertical surface displacement is described for both cases rigid and flexible.

7.2.2. Stresses results

1. As is indicated in table 6.2 maximum stresses appear in case 1 at the inner vessel with

values of 430.0 MPa. While at the external vessel maximum values are of the order of

324.0 MPa for case 6. These values could be higher because the flexible case calcula-

tions was aborted because the fluid element distortions.

2. The internal loads transmitted to the vessel l id have been obtained. This information was

gathered in the ANNEX.III.4. The results show that very high loads are transmited to the

lid and sent to the vessel supports This transmission mechanism should be evaluated in

detail. ANNEX III.4.

8. CONCLUSIONS

1. In order to ensure the stabil ity of the calculation is necessary to develop models with a

high number of elements. The instability also depends on the load level. It means that it

is required to have a high capacity of data storage and, to avoid long calculation times,

work with high capacity computers.

2. The case number 6 by generating a high strain on the elements of lead, led to the nu-

merical instability that has led to the abortion of the ABAQUS calculations for the case.

With the FLUENT model, convergence has been solved but calculation time has been

significantly multiplied (For every second of the seismic time histories, about two or

three days of process).

3. The maximum pressure in the inner and outer vessel reaches values several times

higher than the pressure associated with the hydrostatic pressure. This implies high

stresses on the internal components of the vessel.

4. During seismic response, high specific pressures in small areas and for short time inter-

vals are generated. These pressure pulses are responsible for the identified peaks in the

pressure histograms.




5. In the process of dynamic response calculations it has been shown that the liquid lead

was in contact with the upper cover, thus generating significant areas with big loads on

the vessel l id.

6. The interaction between the refrigerant and the internal components generates signifi-

cant loads on the upper cap of the vessel. These loads and their transmission mecha-

nisms should be evaluated in detail.

7. The comparison of the calculations with rigid vessel and with flexible vessel, shows that

there is an effect of fluid structure interaction that must be taken into account.

8. The high pressures on the vessel show that local stresses can be very high. This gener-

ates a major impact on the design of the reactor vessel, which may require, well a ge-

ometry change with a thickness modifications or a material change in order to modify

mechanical capabilities.




9. REFERENCES

1. SMO12000005. “Seismic re-evaluation of EMO 1&2 NPPs – Seismic adequacy assessment

of mechanical and electrical equipment for the Seismic re-evaluation of EMO 1&2 NPPs”,

Rev. 02. Purchasing Technical Specifications. ENEL. January 2013.

2. SMO12000256. “Seismic re-evaluation of EMO 1&2 NPPs – Tender Participation

Requirements. Seismic adequacy assessment of mechanical and electrical equipment for

the Seismic re-evaluation of EMO 1&2 NPPs”, Rev. 00. ENEL. January 2013.

3. Ansaldo Nucleare. E-mail from Luigi Mansani (Ansaldo) to Francisco Beltran (IDOM), dated

on 10/Apr/2013.

4. Empresarios Agrupados. “SILER - Description of Systems, LFR”. Document 092-260-F-C-

00101, Issue 2. SILER Project, Work Package 2, deliverable D2.1a. July 2012.

5. SILER. WP2. Reactor Building Seismic Analysis. RPV seismic time histories.

6. ABAQUS. Release 6.10.

7. ANSYS_FLUENT. Release 14.0.

8. G. W. Housner. "Dynamic Pressures on Accelerated Fluid Containers". Bull.Seismol. Soc.

Am., 47(1). January 1957.

FP7-295485-SILER D3.1 Part II

Part II: Sloshing Maps and Parametric Sensitivity Analysis

(KTH)










•oo

•oo

•o


o






•••





































Part III: ANNEXES

ANNEXES PART I: ANNEX I: ALE Method validation. Slosh height in a rectangular tank ANNEX II: Fluid and Structural analysis with FLUENT-ANSYS ANNEX III: ABAQUS Fluid Structure analysis

ANNEXES PART II: (No Annexes)

Seismic-Initiated events risk mitigation in LEad-cooled Reactors

Analysis of Seismic Sloshing of Coolant in the ELSY-LFR

16962 CD 3.1/01 Rev. 0 ANNEX I Page 1 of 9

ANNEX I:

ALE METHOD VALIDATION




ALE METHOD VALIDATION

Slosh height in a rectangular tank

Table of contents

1. Objective and scope

2. ALE method

3. Description of the FEM model

4. Results

5. Conclusions

6. References

Annex - “Maximum slosh height in a rectangular tank - Housner procedure”

1. Objective and scope

The objective of the present document is to validate the application of the ALE

method to determine the sloshing in the ELSY reactor, in the context of the SILER

project.

In order to perform the validation, the maximum slosh height of a water-filled tank

shacked by a horizontal seismic motion is determined applying the ALE method by

using Abaqus Explicit (Ref. 1). Results are compared to a reference solution ob-

tained by the analytical approach given by Housner (see annex).




2. ALE method

The ALE (Arbitrary Lagrange Euler) method of space discretization is a hybrid of

the Lagrange and Euler methods. It allows redefining the mesh continuously as the

calculation proceeds. The advantage of ALE is the ability to reduce difficulties

caused by severe mesh distortions encountered by the Lagrange method and al-

lows a calculation to continue efficiently. However, compared with Lagrange, an

additional computational step of rezoning is employed to move the mesh and

remap the solution onto a new mesh.

The nodes at the boundary in an ALE mesh cannot leave the boundary because its

tracking is “Lagrangian”. After deformation of the boundaries takes place, the inter-

nal domain is remeshed in order to prevent excessive element distortion. The

remeshing is performed by transporting the “Eulerian” material across the mesh.

3. Description of the FEM model

The 2D-model is created in Abaqus Explicit (Ref. 1) and it consists of a rectangular

tank filled with water. The tank measures 12.3 x 12 m, and it is filled with 8 m of

water. The top of the tank is not modeled because the water is not expected to

come into contact with it. The tank is modeled as a rigid body and is meshed with

R2D2 elements. A graded mesh of CPE4R elements is used for the water. Friction-

less contact is defined between the water and the tank. The finite element model is

shown in Figure 1.

Figure 1 - Finite element model




The material model for water is defined by the following parameters:

- Density: 983.2 kg/m3

- Linear volumetric response (Equation of State)

- Speed of sound: 451 m/s

- Shear behaviour (Newtonian fluid)

- Viscosity: 1.4 10-3 Pa s

- No turbulence or limit layer effects

The wave speed is determined based on the bulk modulus, which has been chosen

one order of magnitude less than the actual bulk modulus of water (2 GPa) in order

to avoid an overly stiff response. On the other hand, since sloshing problems are

unconfined, the bulk modulus chosen can be reduced and the water will still behave

as an incompressible medium.

The water is subjected to gravity loading. Consequently, an initial geostatic stress

field is defined to equilibrate the stresses caused by the self-weight of the water.

In addition, an acceleration time history is prescribed for the tank in the horizontal

direction in order to represent the seismic motion corresponding to case 07, X-

direction (see figure 2). The sloshing analysis is performed for 20 seconds.

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 5 10 15 20

Acc

ele

ratio

n (

m/s

2)

Time (s)

Horizontal accelerogram (X direction)

Ax - case 07

Figure 2 - Horizontal accelerogram (X direction), case 07




4. Results

Figure 3 shows the pressures of the fluid in the deformed mesh at various times. As

the figure shows, there is significant sloshing of the water.

Figure 4 shows a time history of the envelope of the maximum vertical displace-

ments of the water free surface. As shown in the figure, the maximum vertical dis-

placement is 0.530 m and it is reached after 17.5 seconds of seismic motion. Fig-

ure 5 shows the vertical displacements of the water material at this time.

Figure 3 - Pressure at various times




Figure 4 - Water free surface maximum displacement

Figure 5 - Vertical displacements of the water material.




5. Conclusions

Maximum vertical displacement of the water free surface is obtained from a finite

element model created in Abaqus Explicit using the ALE technology. Its value is

0.530 m.

The reference solution, obtained from the Housner procedure, gives a maximum

vertical displacement of 0.547 m.

Comparing both methods, there is a difference between them of 3.2%, which is

considered acceptable.

Hence, the application of the ALE method is considered suitable to determine the

sloshing in the ELSY reactor.

6. References

1. Simulia. “ABAQUS User’s Manual”. Version 6.10.




ANNEX

“Maximum slosh height in a rectangular tank - Housner procedure”












16962 CD 3.1/01 Rev. 0 Annex II.1 Page 1 of 163

ANNEX-II

FLUID AND STRUCTURAL ANALYSIS WITH FLUENT-ANSYS

ANNEX-II.1

FLUID ANALYSIS

ANNEX-II.1.1

ELSY GEOMETRY










ANNEX-II.1.2

FLUID DOMAIN

(GEOMETRY AND MESH)




GEOMETRY




MESH




MESH




ANNEX-II.1.3

(ACCELERATION TIME HISTORIES FOR CASES 1,3,6 AND 12)
















ANNEX-II.1.4

RESULTS

FLUID ANALYSIS

ANNEX-II.1.4.1

RESULTS AT REST




ANNEX-II.1.4.1.1

PRESSURE IN REFERENCE POINTS




Reference points Pressure (Pa) Reference points Pressure (Pa) Reference points Pressure (Pa)

P_H0_1 808118,25

P_H1_1 746053,56 P_H2_1 P_H3_1

P_H1_2 742203,93 P_H2_2 P_H3_2

P_H1_3 742027,25 P_H2_3 P_H3_3

P_H1_4 746498,43 P_H2_4 P_H3_4

P_H1_5 739975,5 P_H2_5 P_H3_5

P_H1_6 742991,37 P_H2_6 P_H3_6

P_H1_7 745301,81 P_H2_7 P_H3_7

P_H1_8 748579,37 P_H2_8 P_H3_8

P_H4_1 P_H5_EXT_1 P_H5_INT_1











ANNEX-II.1.4.1.2

PRESSURE IN REACTOR VESSEL AND INTERNALS




Pressure

Pressure




Pressure




ANNEX-II.1.4.1.3

FREE SURFACE POSITION




Free surface

Red : Lead Blue : Argon




ANNEX-II.1.4.2

(RESULTS CASE-1)




ANNEX-II.1.4.2.1

(PRESSURE IN REFERENCE POINTS)




















































ANNEX-II.1.4.2.2

(RESULTS FOR TIME =15.8 sec)




ANNEX-II.1.4.2.2.1

(PRESSURE IN REACTOR VESSEL AND INTERNALS)










ANNEX-II.1.4.2.2.2

(FREE SURFACE POSITION)







ANNEX-II.1.4.2.3





ANNEX-II.1.4.2.3.1











ANNEX-II.1.4.2.3.2








ANNEX-II.1.4.2.4





ANNEX-II.1.4.2.4.1











ANNEX-II.1.4.2.4.2








ANNEX-II.1.4.3

RESULTS CASE-3




ANNEX-II.1.4.3.1
























































ANNEX-II.1.4.3.2











ANNEX-II.1.4.3.2.2








ANNEX-II.1.4.3.3





ANNEX-II.1.4.3.3.1











ANNEX-II.1.4.3.3.2








ANNEX-II.1.4.3.4





ANNEX-II.1.4.3.4.1











ANNEX-II.1.4.3.4.2








ANNEX-II.1.4.4

(RESULTS CASE-6)




ANNEX-II.1.4.4.1
























































ANNEX-II.1.4.4.2





ANNEX-II.1.4.4.2.1











ANNEX-II.1.4.4.2.2








ANNEX-II.1.4.4.3





ANNEX-II.1.4.4.3.1











ANNEX-II.1.4.4.3.2








ANNEX-II.1.4.3.4





ANNEX-II.1.4.3.4.1


PROCESSING PENDING




ANNEX-II.1.4.3.4.2


PROCESSING PENDING




ANNEX-II.1.4.5

(RESULTS CASE-12)




ANNEX-II.1.4.5.1
























































ANNEX-II.1.4.5.2





ANNEX-II.1.4.5.2.1











ANNEX-II.1.4.5.2.2








ANNEX-II.1.4.5.3

(RESULTS FOR TIME =17.8sec)




ANNEX-II.1.4.5.3.1











ANNEX-II.1.4.5.3.2








ANNEX-II.1.4.5.4





ANNEX-II.1.4.5.4.1











ANNEX-II.1.4.5.4.2







16962 CD 3.1/01 Rev. 0 ANNEX II.2 Page 1 of 75

ANNEX-II.2

STRUCTURAL ANALYSIS




ANNEX-II.2.1

3-D MECHANICAL MODEL: GEOMETRY AND MESH




Geometry

Geometry




Mesh

Mesh




Mesh

Mesh




ANNEX-II.2.2

RESULT




ANNEX-II.2.2.1

RESULTS AT REST




Total deformation (m)

Von Mises Stress (Pa)














ANNEX-II.2.2.2

(RESULTS CASE-1)




ANNEX-II.2.2.2.1




















ANNEX-II.2.2.2.2




















ANNEX-II.2.2.2.3




















ANNEX-II.2.2.2.4

RESULTS FOR TIME 15.8 s With the pressure increased by the coefficient

calculated in the point 3.



















ANNEX-II.2.2.3

(RESULTS CASE-3)




ANNEX-II.2.2.3.1




















ANNEX-II.2.2.3.2




















ANNEX-II.2.2.3.3




















ANNEX-II.2.2.3.4


calculated in the point 3.2.5



















ANNEX-II.2.2.4

(RESULTS CASE-6)




ANNEX-II.2.2.4.1




















ANNEX-II.2.2.4.2




















ANNEX-II.2.2.4.3





ANNEX-II.2.2.4.4





















ANNEX-II.2.2.5

(RESULTS CASE-12)




ANNEX-II.2.2.5.1




















ANNEX-II.2.2.5.2




















ANNEX-II.2.2.5.3




















ANNEX-II.2.2.5.4




















16962 CD 3.1/01 Rev. 0 ANNEX III Page 1 of 64

ANNEX III:

ABAQUS FLUID/STRUCTURE

ANALYSIS




ANNEX III.1:

ACCELEROGRAM INPUT LOADS













ANNEX III.2:

PRESSURE TIME HISTORIES

ANNEX III.2.1: RIGID VESSEL CASES
















ANNEX III.2.2:

FLEXIBLE VESSEL CASES
















ANNEX III.3 :

TIME HISTORY ANALYSIS














ANNEX III.3.2: FLEXIBLE VESSEL

CASES










ANNEX III.4 : CONTACT FORCES















































ANNEX III.4.2:

FLEXIBLE VESSEL CASES














































ANNEX III.5:

VON MISES STRESSES FLEXIBLE

VESSEL CASES






















ANNEX III.6:

FREE SURFACE

VERTICAL DISPLACEMENTS

RIGID AND FLEXIBLE VESSELS













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