Severe accident assessment of a small lead cooled reactor

DEGREE PROJECT, IN NUCLEAR ENERGY ENGINEERING , SECOND LEVEL STOCKHOLM, SWEDEN 2015

Severe accident assessment of a small lead cooled reactor

TIMOTHY EKELUND

KTH ROYAL INSTITUTE OF TECHNOLOGY

Akademisk uppsats f¨ or avl¨ aggande av civilingenj¨ orsexamen inom ¨ amnesomr˚ adet maskinteknik.

Scientific thesis for the degree of Master of Science in Engineering in the area of Mechanical Engineering.

TRITA-FYS 2015:73 ISSN 0280-316X

ISRN KTH/FYS/–15:73–SE

Abstract

The computer codes SAS4-A and SIMMER have been used to study the resilience of a small lead

cooled reactor, the SEALER concept, during severe accident conditions. With SAS4-A the reshaping

of fuel pins was studied during steady state and an UTOP. Due to low operating temperature the

reshaping was small and damage to fuel rods prevented. SIMMER was used to simulate blockage in

the highest power sub-assembly. Results indicate fuel damage can be avoided during a total blockage,

since all heat are transferred radially to neighbouring sub-assemblies.

Acknowledgments

I would like to thank my supervisors Janne Wallenius, Alessandro Del Nevo and Marica Eboli for

making it possible for me to undertake this exciting project, and for all the guidance and help along

the way. Also a special thanks to my family for all their support throughout the years.

Table of contents

Abstract i

Acknowledgments i

Table of contents iii

Nomenclature v

List of figures xiii

List of tables xiii

1 Introduction 1

1.1 Background . . . . 1

1.2 Objective . . . . 1

2 SEALER Design 3 3 SAS4-A overview and input 7 3.1 General overview . . . . 7

3.2 DEFORM-4 overview and input . . . . 8

3.2.1 Fuel pin mechanics . . . . 8

3.2.2 Mitigation of fabricated porosity . . . . 11

3.2.3 Grain growth . . . . 12

3.2.4 Fission gas release . . . . 12

3.2.5 Fission product swelling . . . . 13

3.2.6 Irradiation induced cladding swelling . . . . 14

3.2.7 Fuel pellet gap conductance . . . . 15

4 SIMMER-III overview and input 17 4.1 Fluid-dynamics model . . . . 18

4.1.1 Interfacial area model . . . . 19

4.1.2 Momentum exchange functions . . . . 20

4.1.3 Heat-transfer coefficients . . . . 20

4.1.4 Heat and mass transfer model . . . . 21

4.1.5 Inter-cell heat transfer . . . . 22

4.1.6 Equation of state model . . . . 22

4.2 Structure model . . . . 23

4.2.1 Fuel Pin Configuration and Heat-Transfer Model . . . . 23

4.2.2 Can Wall Configuration and Heat-Transfer Model . . . . 24

4.3 Fluid-dynamics cell initialization . . . . 25

4.4 Boundary conditions . . . . 25

4.5 SIMMER-III input . . . . 26

4.5.1 Inlet plenum . . . . 26

4.5.2 Core . . . . 27

4.5.3 Outlet plenum . . . . 28

4.5.4 Pump, heat-exchanger and cold leg . . . . 29

4.5.5 Vessel and barrel . . . . 30

4.5.6 Mass flow . . . . 31

4.5.7 Power profile . . . . 31

4.5.8 Pressure nodalisation . . . . 31

4.6 Fuel blockage . . . . 32

5 Results 34 5.1 SAS4-A steady state . . . . 34

5.2 SAS4-A transient BOL . . . . 36

5.3 SAS4-A transient EOL . . . . 37

5.4 SIMMER steady state . . . . 38

5.4.1 Non-adiabatic model . . . . 38

5.4.2 Adiabatic model . . . . 46

5.5 SIMMER transient . . . . 47

5.5.1 Total blockage of sub assembly channel . . . . 48

5.5.2 Adiabatic total blockage . . . . 50

5.5.3 Partial adiabatic blockage . . . . 51

6 Discussion and conclusion 53 6.1 SAS4-A model . . . . 53

6.2 SIMMER model . . . . 53

7 References 55

A

DEFORM theory and input i

B

Extended SIMMER theory iv

C

SIMMER results vii

Nomenclature

Roman Symbols

V ¯ ¯ M Virtual mass [

]

¯

v

Velocity field vector [

]

β Generation rate of fission gas inside a grain [

]

δC

δt

Change in fission gas concentration inside a grain per time step t [

] A Interfacial area [m

]

a Contact area per unit volume [m

] A

Fraction of axial expansion to be used

a

accommodation coefficient of either helium or xenon A

Calibration constant for pore velocity [

]

A

Calibration constant for heat conductivity in closed gas gap [

] A

Pre-exponential constant for pressure in fission gas bubble [Pa]

A

Calibration constant for pore velocity A

Sub channel flow area [m

]

C

Calibration constant for roughness in gas gap size c

Amount of trapped gas at time step i [kg]

C

Heat capacity at constant volume for plenum gas [

] C

Orifice coefficient

d Fuel rod outer diameter [m]

D

Maximum grain size [m]

E Modulus of elasticity [Pa]

e Specific internal energy [

]

E

Mass averaged modulus of elasticity in the cracked fuel zone [Pa]

E

Energy per fission [MeV]

F

Force on fuel from cladding [N]

F

Number of fissions in axial segment i

F

Force applied axially to the fuel column, usually from the pressure in fission gas plenum [N]

F

Force in central void [N]

f

Fraction of fission gas that is in grain boundaries

g Standard gravity [

]

g

Thermal jump distance of the cladding surface [m]

g

Thermal jump distance of the fuel surface [m]

G

Mass of fission gas in fuel matrix [kg]

G

Mass of fission gas in grain boundaries [kg]

G

Fission gas generated in radial cell i [kg]

G

Pre-exponential grain growth constant [

]

G

Pre-exponential calibration constant for maximum grain size [m]

H Hardness of the softer material of fuel and cladding [Pa]

h Heat transfer coefficient [

] H(T ) Heaviside unit function

h

Conduction heat transfer coefficient through gas in gas gap [

] i Specific enthalpy [

]

K Momentum exchange function [

] k

Microscopic thermal conductivity [

]

k

Thermal conductivity of the cladding at the inner surface[

] k

Thermal conductivity of the fuel at the outer surface [

] k

Thermal conductivity for the gas in the gap [

]

k

Thermal conductivity of helium [

] k

Turbulent thermal conductivity [

] k

Thermal conductivity of xenon [

]

m

Calibration constant for heat conductivity in closed gas gap M

Atomic weight of helium [kg]

M

Fuel mass in radial cell i [kg]

M

Atomic weight of xenon [kg]

M

Moles of fission gas in a bubble [mole]

p Pressure [Pa]

P

Gas plenum pressure [Pa]

P

Power in axial segment i [W]

p

Pin pitch [m]

P

Pressure in central void [Pa]

P

Pressure in fission gas plenum[Pa]

q Heat transfer rate [

]

Q

Calibration constant for probability of fission gas release [K]

Q

Calibration constant for probability of fission gas release Q

Calibration constant for probability of fission gas release Q

Calibration constant for probability of fission gas release [K]

Q

Calibration constant for probability of fission gas release Q

Energy interchanging rate for melting or freezing [

] Q

Nuclear heating rate [

]

Q

Calibration constant for pore velocity [

] Q

Fluid and cladding heat exchange rate [

] Q

Energy interchanging rate for heat transfer [

] Q

Calibration constant for maximum grain size [

] Q

Energy transfer rate due to nuclear heating of cladding[

] Q

Calibration constant for pressure in fission gas bubble [

] Q

Grain growth activation energy [

]

R Universal gas constant [

] R

Outer fuel radius [m]

r

Inner radius [m]

r

Outer radius [m]

S Interfacial area source term [m

s]

S

Power shape factor T Temperature [K]

T

cladding temperature [K]

T

Fuel temperature [K]

T

Reference temperature [K]

T

Lead temperature [K]

T

Surface temperature of structure [K]

T

Temperature [C]

u Displacement in radial direction [m]

u

Radial displacement from external force [m]

u

Radial displacement from thermal effects [m]

V

Equilibrium volume of a fission gas bubble [m

] V

Fission gas bubble volume [m

]

V

Volume of fission gas bubbles in a cell [m

] w Displacement in axial direction [m]

X

Mole fraction of helium X

Mole fraction of xenon

z

Radially constant axial strain [m]

z

Radially constant axial strain from force effects z

Radially constant axial strain from thermal effects Abbreviations

ADS Accelerator driven system B

C Boron carbide

BC Boundary condition BU Burn-up

DBA Design basis accident EOS Equation of state F A Fuel assembly HX Heat exchanger

IAEA International Atomic Energy Agency LBE Lead-Bismuth eutectic

LF R Lead fast reactor LW R Light water reactor N P P Nuclear Power Plant SA Subassembly

SEALER Swedish Advanced Lead Reactor SG Steam generator

U Uranium

U LOF Un-protected loss of flow U O

Uranium dioxide

U T OP Un-protected transient over power ZrO

Zirconium dioxide

Greek Symbols

(∆r)

Total effective fuel-cladding gap size [m]

αT Mean linear thermal expansion coefficient [K

] α Volume fraction

α

Calibration constant for density change in cladding α

Volume fraction of structure material in a mesh cell

¯

ρ Macroscopic density [

]

δ

Mean surface roughness of the cladding surface [m]

δ

Mean surface roughness of the fuel surface [m]

∆

Fractional volume change associated with the changes in the radial boundaries of the cell by the constant displacement u

∆

Fractional volume change from radial cracks

∆

Fractional volume change associated with fission product swelling in the cell



Circumferential strain of the cracked fuel cell [m]



Elastic strain from applied boundary forces



Fuel emissivity



Radial strain



Strain from solid and volatile fission products or irradiation created voids



Total strain at a cell boundary



Axial strain



Circumferential strain



Cladding emissivity



Solid fission product swelling rate parameter [

]



Strain from thermal expansion

Γ Total mass transfer rate per unit volume [

] γ Surface tension of fission gas bubble [

]

γ

Ratio of heat capacity at constant pressure and heat capacity at constant volume

ν Poission’s ratio

φ Fast neutron flux [

]

ρ Inner radius of fuel annulus or density [m][

] Σ Negative fractional density change for cladding σ

Radial stress [Pa]

σ

Axial stress [Pa]

σ

Circumferential stress [Pa]

σ

Stress at cladding fuel interface [Pa]

σ

Stefan-Boltzmann constant [

] τ

Fuel creep time constant [s]

τ

Incubation parameter

υ Component specific volume [

] Subscripts

Crt Critical point F G Fission gas G Vapor mixture

Gm Gas density component LCW Left can wall

M Energy component m Density component q Velocity field q

Velocity field

qS Terms existing at interface between velocity field q and structure RCW Right can wall

Superscripts

I Interface quantity

List of Figures

1 Overview of the primary system flow scheme created in SAS4-A . . . . 7

2 Pore velocities[19][20] . . . . 11

3 Fission gas behavior. Experimental data from BWR fuel[29] . . . . 14

3a Surface tension pressure. . . . 14

3b Average fission gas bubble radius, from the pressure in figure 3a . . . . 14

4 Interaction between SIMMER models[37] . . . . 17

5 Diagram of four step method[37] . . . . 19

6 SIMMER pool flow regime map[37] . . . . 19

7 Heat and mass transfer paths in SIMMER-III[37]. V/C=Vaporization/condensation and M/F=Melting/Freezing. The black areas illustrate the invalid transition of e.g gas to gas phase . . . . 20

8 Fuel pin geometry for a simplified pin[37] . . . . 23

8a Axial fuel pin geometry . . . . 23

8b Radial fuel pin geometry . . . . 23

9 Can wall configuration in SIMMER-III[37] . . . . 24

10 Overview of SEALER model in SIMMER . . . . 26

11 Overview of inlet plenum in SIMMER . . . . 26

12 Overview of reactor core in SIMMER . . . . 28

13 Overview of SEALER model in SIMMER . . . . 29

14 Overview of cold leg in SIMMER . . . . 30

15 Blockage propagation in fuel bundle with wire- or grid spacer[44] . . . . 32

16 Radial location of outer fuel and inner cladding. The effective gap sizes are observable in Figure 17a. The denomination ”w/o R-S” refer to a simulation where DEFORM was implemented, but the Ross - Stoute solution of gap conductance was neglected . . . . 34

17 Evaluation of fuel cladding gap size and gap conductance . . . . 35

17a Fuel-Cladding gap size . . . . 35

17b Gap conductance . . . . 35

18 Steady state fuel pin temperatures at BOL for the three different models, all measured in the central SA . . . . 36

18a Steady state peak fuel temperature at BOL . . . . 36

18b Steady state peak cladding temperature at BOL . . . . 36

19 Steady state fuel pin temperatures at EOL for the three different models . . . . 36

19a Steady state peak fuel temperature at EOL, for the central SA . . . . 36

19b Steady state peak cladding temperature at EOL, for the central SA . . . . 36

20 TOP fuel pin temperatures at BOL . . . . 37

20a Transient fuel temperature at BOL . . . . 37

20b Transient cladding temperature at BOL . . . . 37

21 Gap size before and after BOL transient . . . . 37

22 TOP fuel pin temperatures at EOL . . . . 38

22a Transient fuel temperature at EOL . . . . 38

22b Transient cladding temperature at EOL . . . . 38

23 Gap size before and after EOL transient . . . . 38

24 Volume vs. height curves . . . . 42

24a Lead volume from vessel bottom up to heat exchanger, inside barrel . . . . 42

24b Lead volume from heat exchanger start to vessel bottom, outside barrel . . . . 42

25 Comparison between axial power profile in SAS4A and SIMMER model . . . . 43

26 Fuel rod temperatures during steady state . . . . 44

26a Steady state fuel temperature comparison . . . . 44

26b Steady state cladding temperature comparison . . . . 44

27 Lead temperatures during steady state . . . . 45

27a Lead in core temperature comparison . . . . 45

27b Lead over HX temperature comparison . . . . 45

28 Steady state pressure drop in channel 1,3 and 5 . . . . 45

28a Total pressure drop . . . . 45

28b Wrapper pressure drop . . . . 45

29 Lead temperatures during steady state for adiabatic model . . . . 46

29a Lead in core temperature comparison . . . . 46

29b Lead over HX temperature comparison . . . . 46

30 Comparison between fuel and coolant densities[22][51] . . . . 47

31 Fuel rod peak temperatures during the total blockage . . . . 48

31a Fuel temperatures . . . . 48

31b Cladding temperatures . . . . 48

32 Coolant peak temperatures and mass flow . . . . 49

32a Lead temperatures during the total blockage . . . . 49

32b Mass flow in top of peak SA. Values below zero indicates mass flow in negative axial direction . . . . 49

33 Radial heat transfer regarding central fuel SA. Data from 500 seconds after transient initiation . . . . 49

33a Heat transfered through cladding and can wall . . . . 49

33b Heat transfered in bypass outside channel 1 . . . . 49

34 Fuel rod temperatures in blocked SA . . . . 50

35 Lead temperatures . . . . 50

35a Liquid lead temperature in the middle of the central SA . . . . 50

35b Lead temperature in the middle of Channel 2 and 3 . . . . 50

36 Volume fractions in central SA . . . . 51

36a Solid fuel volume fraction in different parts of central SA . . . . 51

36b Liquid lead volume fraction in the middle of central SA . . . . 51

37 Pressure in blocked SA . . . . 51

38 Comparison of fuel rod temperatures after blockage in active region and at the inlet . 52 38a Fuel temperatures . . . . 52

38b Cladding temperatures . . . . 52

39 Comparison of lead behavior after blockage in active region and at the inlet . . . . 52

39a Coolant temperatures . . . . 52

39b Mass flows after blockage . . . . 52

40 Maximum allowed grain size . . . . iii

41 Fuel thermal conductivity and specific heat[51] . . . . iii

41a Fuel specific heat . . . . iii

41b Fuel thermal conductivity . . . . iii

42 Densities of fuel and cladding . . . . iv

42a Fuel theoretical density[51] . . . . iv

42b Cladding density[14] . . . . iv

43 Cladding thermal conductivity and specific heat . . . . iv

43a Cladding specific heat[54][14] . . . . iv

43b Cladding thermal conductivity[14] . . . . iv

44 Fuel rod temperatures during steady state for adiabatic model . . . . vii

44a Steady state fuel temperature comparison . . . . vii

44b Steady state cladding temperature comparison . . . . vii

List of Tables 1 Fuel rod design parameters[12] . . . . 3

2 Control rods design parameters[12] . . . . 4

2a Burn-up rod design parameters . . . . 4

2b Shut down rod design parameters . . . . 4

3 Radiation protection rods[12] . . . . 4

3a Reflector rod design parameters . . . . 4

3b Shield rod design parameters . . . . 4

4 Hexcan wrapper dimensions[12] . . . . 4

5 Reactor design parameters[12] . . . . 5

5a Reactor core design parameters[12] . . . . 5

5b Thermal hydraulics of average and peak sub assembly . . . . 5

6 Primary system design parameters[12] . . . . 6

7 Steam generator design parameters[12] . . . . 6

8 Parameters conserved in design of Pump, HL, HX and CL . . . . 30

9 EOL parameter for SAS4-A models with DEFORM implementation . . . . 34

10 Acceptability criteria for thermal-hydraulics nodalization qualification at steady state[48] 39 11 Primary circuit volumes. Colored cells indicate values design against . . . . 40

12 Active structure heat transfer area . . . . 40

13 Non-active structures heat transfer volumes comparison . . . . 41

14 Active structure heat transfer volumes comparison . . . . 41

15 Comparison between elevation of components . . . . 42

16 Comparison between flow areas . . . . 43

17 Steady state mass flow comparison . . . . 44

18 Pressure drops in primary system . . . . 45

19 Channel velocities in steady state . . . . 46

20 Comparison between lead inventories . . . . 46

21 Conditions for blockage transients in central FA . . . . 47

22 Mass flow during total blockage transient . . . . 49

23 DEFORM-4 specific parameters . . . . ii

1 Introduction

1.1 Background

For licensing NPP a safety assessment is required to evaluate accident conditions both from internal and external events[1]. The safety assessment has to include an analysis and assessment of safety dur- ing normal operation, anticipated operational occurrences and accident condition. Severe accidents are defined as accidents with less likelihood than design basis accidents (DBA). Accident conditions may arise due to multiple failure of safety equipment and result in significant core degradation[2].

IAEA requires severe accidents to be considered, with a combination of the probability and engineer- ing judgement, assess reasonable mitigation measures. A severe accident assessment also helps in identifying necessary procedures in the required accident management. The objectives for accident management are[2]:

1. Preventing significant core damage.

2. Terminating the progress of core damage once it has started.

3. Maintaining the integrity of the containment as long as possible.

4. Minimize the releases of the radioactive inventory.

5. How to achieve a long term stable state.

Lead cooled reactors are one of the main candidates for the Generation IV NPP. To this day Generation IV is many different concept reactors, all with the objectives to meet certain requirements.

The idea is to generate nuclear energy sustainably by transmutation and reduce the amount of high- level waste. Further they should excel in safety by a very low possibility of core damage and accident progression, and eliminate the need of off-site response. In competition with other energy sources they should provide life cycle cost advantage and have an equal financial risk for the investors. As a last goal they should provide a very unattractive route for dispersion and theft of nuclear material, in light of proliferation resistance[3].

One aspect making lead a candidate for coolant is the low moderating effects, helping to achieve a fast spectrum in order to fission trans uranium elements. It also provides excellent coolant capabilities with high density and heat capacity. In aspects of safety the high boiling temperature provides a significant advantage. With the ability of natural circulation sufficient to cool of decay heat, the safety aspects of lead as coolant are superb. Lead being inert with air provides another advantage, e.g. to another Generation IV candidate, a sodium cooled fast reactor.

The lead cooled reactor design to be studied, SEALER (”Swedish Advanced Lead Reactor”), is a concept developed by LeadCold, a spin-off company from KTH Stockholm. It embraces parts of the goals for Generation IV. The purpose of this thesis is to study the behaviour of SEALER during severe accidents. To find relevant initiating events, experience from previous analyses of lead cooled fast reactors (LFR) is utilized. For design such as ELFR, ELSY and ELECTRA, previous simulations, have shown highest fuel and cladding temperatures for ULOF- and UTOP accidents[4][5][6]. Hence part of the simulations will consider local blockage of a sub assembly, resulting in loss of flow. The blockage material can for example be metal, metal oxides or foreign material. Idea with the analysis is to study the behaviour and conclude the consequences, to determine the accident progression to neighbouring SAs. Another simulation will consider the UTOP accident with mechanical deformation of fuel rods. Previously such simulation have not considered deformation of fuel rods.

1.2 Objective

The thermal hydraulic system code SAS4-A/SASSYS was used to identify the reshaping behaviour

of fuel rods. A possibility by implementing the module DEFORM-4[7]. This was done in order to

compare the result of a previous study of SEALER during steady state and UTOP conditions, where the fuel and cladding were treated as solids, with no allowance of swelling etc. Focus was to evaluate how the conditions changed when the gas gap was not constant. Effects such as reconstructing, mechanical stresses and swelling during the reactor life were also simulated. Two different models of gap conductance were considered. One with linear dependence of the gap size and one considering radiative heat transfer, conductance through fill and fission gas and the possible solid-to-solid heat transfer.

In the second part the severe accident code SIMMER-III were utilized. A computer code capable of simulating postulated accident and degradation of the core[8]. It holds the advantage of SAS4-A of being able to simulate two-dimensional flow[9]. One scenario was chosen as candidates for severe accident. The previously described local loss of flow by blockage of a fuel channel. In competition with UTOP, ULOF and loss of heat zink. UTOP will be studied by the SAS-4A code and SEALER is designed for ULOF. For the last accident, loss of heat zink, data of secondary side is not present at this date. Hence local blockage was screened out.The scenario will be subdivided into three different scenarios for the central fuel SA, a blockage in the active region reducing the flow area by 32 % of the sub channel flow area, the same amount of blockage at the inlet and a total blockage at the inlet. These percentage was in line with safety analysis of another heavy liquid metal cooled reactor concept, MYRRHA[10]. To have a conservative approach the scenarios was treated as unprotected.

The detection system of the core is otherwise expected to notice the decreased flow and initiate a

SCRAM within a second from the blockage[11].

2 SEALER Design

SEALER is a lead cooled open pool type reactor, with the purpose of serving as a nuclear battery.

Therefore it embraces an extreme long operational life. The goal is 30 years with an availability of 90 %[12]. With uranium oxide as fuel it lack the generation IV objective of sustainability. Uranium dioxide however, as the main fuel of LWR reactors, provides a existing manufacturing industry and experience. In terms of safety it requires that no off-site accident response should be needed. Hence to avoid accident progression is of great importance. With a low thermal gradient the parts of the accident corrosion problems of lead reactors can be handled. In contrast with the generation IV concept reactors it operates with a lower fuel temperature than todays water-cooled reactors.

Table 1: Fuel rod design parameters[12]

Parameter Value

Fuel composition UO2

235U enrichment 19.9 wt %

Fuel density 10.39 g/cm³

Fuel pellet porosity (cold) 4.00 % Fuel pellet diameter 13.384 mm Cladding inner diameter 13.520 mm Cladding outer diameter 14.520 mm

Cladding thickness 0.50 mm

Fuel column height 1100 mm

Insulation pellet height 2 x 10 mm Insulation pellet composition ZrO₂ Insulation pellet porosity 10.00 % Upper end cap height 20 mm Lower end cap height 50 mm

End cap material 316L

Lower shield height 50 mm

Lower shield material ¹⁰B4C Lower shield boron enrichment 96.00 % Lower shield porosity (cold) 10.00 % Upper gas plenum height 350 mm

Fuel pin length 1 590 mm

Cladding material 12R72 (15-15Ti)

The fuel of SEALER consists of 19 FAs. Each contains 91 fuel rods. The design specifications of

the fuel rods is specified in table 1. Around the central FAs is the burn-up rods, table 2a, and shut

down rods, table 2b. Their numbers equal 12 and 6 assemblies. Burn-up rods have the purpose to even

out the reactivity swing, during the long radiation cycle of the fuel. Next is 24 reflector rods, used

to improve neutron economy and limit radiation damage to vessel and structure material. Specifics

of the reflector rods is seen in table 3a. In the outermost hexagonal are the shield rods, which sole

purpose is to limit radiation doses to outer structure. Shield rod parameters are seen in table 3b.

Table 2: Control rods design parameters[12]

(a) Burn-up rod design parameters

Parameter Value

Rods per assembly 19

B₄C pellet diameter 27.97 mm Cladding inner diameter 28.70 mm Cladding outer diameter 31.89 mm Boron enrichment 19.9 % (natural) Absorber density 2.25 g/cm³

(b) Shut down rod design parameters

Parameter Value

Rods per assembly 7 B₄C pellet diameter 49.96 mm Cladding inner diameter 50.22 mm Cladding outer diameter 55.80 mm Boron enrichment 96.00 % Absorber density 2.14 g/cm

Table 3: Radiation protection rods[12]

(a) Reflector rod design parameters

Parameter Value

Pellet diameter 17.75 mm Cladding inner diameter 19.26 mm Cladding outer diameter 21.40 mm

Yttrium fraction TBD

Pellet density 5.68 g/cm³

(b) Shield rod design parameters

Parameter Value

Pellet diameter 24.77 mm Cladding inner diameter 26.87 mm Cladding outer diameter 29.86 mm Boron enrichment 96.00 % Pellet density 2.14 g/cm³

Table 4: Hexcan wrapper dimensions[12]

Parameter Value

Hex-can inner flat-to-flat 160.0 mm Hex-can outer flat-to-flat 164.0 mm

Hex-can pitch 166.0 mm

Hex-can material 12R72

Height above fuel pin 200 mm

Height from upper diagrid to pin bottom 100 mm Height of section converging to foot 50 mm

Foot outer diameter 120 mm

Foot inner diameter 40 mm

Foot height at constant diameter 400 mm

Table 5a shows dimensioning between core elements together with the power of the core. Hexcan wrapper tubes, table 4, are used to guide the coolant flow. Wire spacer are used to support and separate rods in the different assemblies. Outside the shield rods is the core barrel where support structure is mounted. The barrel also has the purpose of separating the cold leg from the hotter part of the core. A fuel rod start with the lower end cap. Above is the lower shield, used to absorb neutron and limit the damage doses in structure material. A insulation pellet separates the hot fuel from the lower shield. The height of the fuel is 1.10 m, significant smaller than for todays commercial LWR.

Above the fuel there is another insulation pellet, used to protect the pin in the fission gas plenum

above the core. Ending the fuel rods is the upper end cap. Some thermal hydraulic data specific for

fuel assemblies can be seen in Table 5b.

Table 5: Reactor design parameters[12]

(a) Reactor core design parameters[12]

Parameters Value

Fuel assemblies 19

Fuel pins per assembly 91

Fuel pin pitch 16.37 mm

Fuel pin P/D 1.1265

Wire spacer diameter 1.84 mm

Core power 8.0 MW

Average linear power 4.21 kW/m

Grid plate thickness 50 mm

Diagrid vertical (internal) distance 300 mm Number of BU-control elements 12

B4C rods per BU- 19

BU-control rod pitch 32.92 mm Number of shutdown elements 6 (2 x 3)

B4C rods per shutdown 7

Shutdown rod pitch 49.26 mm

Number of reflector elements 24

ZrO2 37

Reflector rod pitch 25.07 mm Number of shield elements 24 B4C rods per shield element 19

Shield rod pitch 34.75 mm

Core grid plate material SS316L

(b) Thermal hydraulics of average and peak sub assem- bly

Parameter Average SA Peak SA

Power 0.42 MW 0.66 MW

Mass flow 78.5 kg/s 108 kg/s

Interior channel velocity 1.06 m/s 1.46 m/s Edge channel velocity 1.15 m/s 1.57 m/s Corner channel velocity 0.79 m/s 1.08 m/s Bundle pressure drop 38 kPa 86 kPa Inlet pressure drop 1.3 kPa 2.5 kPa Outlet pressure drop 7.5 kPa 20 kPa Orificing pressure drop 61 kPa - Assembly pressure drop 108 kPa 108 kPa

When the coolant exits the core it enters the upper plenum above the core, located inside the barrel.

Above this hot plenum is cover gas, separating lead from the reactor lid. Also devices responsible for insertion of control rods will be placed here later in the design. From the upper plenum lead is dragged into the hot leg, either by forced circulation (pumps) or by natural circulation. The coolant then enters the eight different pumps. With eight different pumps high redundancy and availability is obtained. Each pump contributes with a mass flow equal of 164 kg/s. The reactor can even operate with one or two faulty pumps. With heat exchangers and pumps being an integrated unit the coolant exit horizontally from the pump shaft into the spiral heat exchanger. A design similar to ELSY, another lead cooled fast reactor concept[13]. Spiral heat exchanger gives a very compact solution, in regard of heat exchange power per unit length. The coolant flow path and spiral heat exchangers are perpendicular to each other. Out of eight different heat exchangers six is assumed to be in operation.

When the pumps are operating the pressure head gives a rise of coolant in the hot leg compared to the

outlet plenum. The difference in height is 1.46 m. And the elevation of the steam generators thermal

centre compared to the thermal centre of the core is 2.5 m. Designed to achieve a pressure head,

driving the natural circulation. Some data of the pump and steam generator are found in Table 6

respectively Table 7. After exiting the steam generator the now cold lead will enter the cold leg, going

vertically down. It will flow to an elevation below the core. From there lead will flow towards inlet

plenum, located below the core. Located in the inlet plenum are the foot of the wrappers. Openings

on the side of the foot allow lead to enter into the hex-can wrapper, and hence into the core. The

wrapper foot are mounted in two diagrids, separated with an internal distance of 300 mm.

Table 6: Primary system design parameters[12]

Parameter Value

Core barrel inner diameter 1708 mm Core barrel outer diameter 1748 mm Primary vessel inner diameter 2648 mm Primary vessel outer diameter 2748 mm

Barrel and vessel material SS316L

Number of steam generators 8

Outer diameter of SG shell 400 mm

Height of SG shell 300 mm

Elevation of SG thermal centre 2.5 m Steam generator material Fe-10Cr-4Al-Zr

Number of pumps 8

Pump shaft length 1800 mm

Pump shell diameter 420 mm

Elevation of lead free surface (steady state) 1000 mm

Cover gas plenum height 1800 mm

Reactor lid thickness 500 mm

Vessel total height 5500 mm

Table 7: Steam generator design parameters[12]

Parameter Value

Number of tubes per SG 10

SG tube inner diameter 20.0 mm SG tube outer diameter 24.0 mm

SG tube pitch 25.0 mm

SG spiral initial radius 99 mm SG spiral terminal radius 174 mm SG spiral number of turns 5 SG tube exchanging length 4280 mm

SG tube bundle height 250 mm

Exchanging power 1.33 MW

Internal pressure 13.0 MPa

Steam inlet temperature 330^◦C Steam outlet temperature 400^◦C

SG total flow rate 1.08 kg/s (ideal Rankine cycle) Steam generator material Fe-10Cr-4Al-Zr

SG tube Hoop stress 71 MPa

3 SAS4-A overview and input

SAS4-A is a thermal hydraulic and neutronic code originally developed for a sodium cooled fast reactor.

Further development have expanded the code into different types of heavy liquid metal coolants.

3.1 General overview

Fuel pin channels create the core, where one channel represents an average pin of a SA. Multiple channels can then be created to represent different SAs. In axial direction the whole structure of a fuel pin can be defined with shields, blankets, gas plenum and active region. Nodalization provides the options to design primary system components as pump, pipes and HX beside the reactor core itself. The thermal hydraulic model in SAS4-A is one dimensional, where the can walls are estimated to be intact, allowing only axial flow[9]. Simulating two-dimensional flow is not possible. In the fuel pin radial heat transfer is present in many different nodes.

For neutronics the code uses a point kinetic model for the thermal dependent feedbacks. With this model it is possible to determine the power level of the reactor and hence the deposited energy in fuel.

The power shape is assumed to be independent of time, therefore changes in the reactor environment does not effect the neutron flux shape[7]. In nodalization the worth of different type of feedbacks are specified.

The created model consists of four channels, one representing the central SA, the second the six SA in the second fuel circle and two channels in the third fuel circle. The third circle was divided between SA facing shut down elements and SA not facing shut down elements. In SAS4-A compressible volumes are used to simulate the main inventories of coolant. Then liquid segments are used to connect compressible volumes. Liquid segments consist of one or more liquid elements. Liquid elements can be pipes, pumps, HXs, steam generators etc. The core is connected directly to the upper/lower outlet/upper/lower/inlet plenum. Hence the core is a liquid segment and a liquid element. In the present model isolation gas, in the gas plenum, is absent. From the upper plenum there is a pipe providing a connection to a heat exchanger. Note how only one HX is present, and it is positioned before the pump. An artefact not present in the current model of SEALER[12].

Upper plenum

Lower plenum Core

Cold leg

+0.0 +2.9

+2.9

+0.3 L.S

L.S

L.S L.E

L.E

L.E

L.E

L.E

L.E

L.E

+2.3

+2.3

+0.0 +0.0

C.V

C.V C.V

C.V=Compressible volume L.S=Liquid segment

L.E=Liquid element

Pump Heat exchanger

Figure 1: Overview of the primary system flow scheme created in SAS4-A

Between the HX and cold leg there is another pipe, as well between cold leg and the pump. Similar

to the HX there is only one pump here. Studying Figure 1, one will notice how also elevations differ

from the SEALER description in Section 2. The main outcome of different positioning and elevation

will be a different pressure in some components. Pressure drop in the core is controlled by a different input parameter and will not be affected.

3.2 DEFORM-4 overview and input

With the DEFORM-4 model the pre-transient behavior and plastic deformation of fuel pins in SAS4A is implemented. For steady state and transients DEFORM-4 is able to simulate the mechanistic behavior of fuel rods by

1. Thermal expansion

2. Mitigation of fabricated porosity by vapor transport.

3. Grain growth.

4. Fission gas release. It affect the radial distributed porosity and swelling by fission gas bubbles.

5. Fission product swelling. It includes swelling by solid fission together and fission gas bubbles.

Hence it also affect the porosity.

6. Irradiation induced cladding swelling. Radiation damage to cladding causing swelling and den- sification.

It allows the code to take into consideration reconstructing of the fuel, e.g. movement of pores and built up of columnar grains, fission gas retention, size of fuel-clad gap etc. In order to implement DEFORM-4 a certain number of parameters defining reactor/material behaviour have been specified.

A summary of relevant input parameters for DEFORM is presented in Table 23, Appendix A.

3.2.1 Fuel pin mechanics

For the treatment of the fuel pin mechanics the treatment is subdivided into six different radial zones.

The user can then subdivide these zones. Not all zones have to exist. The six zones are 1. The central void,

2. The molten fuel zone,

3. The solid continuous fuel zone, 4. The cracked fuel zone,

5. The fuel cladding gap, 6. The fuel-pin cladding.

The solution approach is to divide the calculation into a thermo elastic solution and put on the plastic deformation obtained from fuel swelling or cladding stress induced plastic creep and irradiation swelling[16].



= 

+ 

+ 

(1)



is the total strain at a cell boundary, 

is the elastic strain from applied boundary forces, 

is the strain from thermal expansion and 

is the strain from solid and volatile fission products or

irradiation created voids and stress induced plastic creep in the cladding. The cladding is assumed to

be an elastic-perfectly-plastic material. Once the circumferential stress on the cladding, from the fuel

cladding interface, exceed the flow stress on the cladding the cladding will follow the fuel deformation.

This stops when conditions bring the cladding back to its elastic region.

The solid fuel and cladding thermo elastic solution uses Hooke’s law generalized into three dimen- sions.



= du dr = 1

E (σ

− ν (σ

+ σ

)) + ∆(αT )



= u r = 1

E (σ

− ν (σ

+ σ

)) + ∆(αT )



= dw dz = 1

E (σ

− ν (σ

+ σ

)) + ∆(αT )

∆(αT ) = α(T

)(T

− T

) − α(T

)(T

− T

)

(2)



, 

and 

is the strain in radial, circumferential and axial direction. σ is the corresponding stresses, ν is the Poisson ratio, α(T ) is the mean linear thermal expansion coefficient and T

is the reference temperature. The reference temperature was set to 700 K. For cladding and fuel the Poisson ratio was found out to be 0.318 respectively 0.316[14][15]. u is the displacement in radial direction and w in axial direction z. Using the following boundary conditions the displacement can be obtained

σ

(r = ρ) = σ

σ

(r = η) = σ

(3)

η is the outer radius of the considered zone, σ

is the stress at the inner surface of the zone and σ

is the stress at the outer surface of the zone. The displacement u(r) are the sum of displacement due to external stresses, σ

and σ

, and from thermal expansion.

u(r) = u

(r) + u

(r) u

(r) = 1 + ν

(η

− ρ

)E

 η

σ



(1 − 2ν)r + ρ

r



− ρ

σ



(1 − 2ν)r − ν

r



− νz

r u

(r) =  1 + ν

1 − ν

 

rI(r) + I(η)η

η

− ρ



(1 − 2ν)r + ρ

r



− νz

r I(r) = 1

r

Z

ρ

∆(αT )r

dr

(4)

z

and z

is the axial displacement due to forces and thermal effects. The stresses are similarly divided into their thermal and external applied force components.

σ

(r) = σ

(r) + σ

(r) σ

(r) = 1

η

− ρ

 η

σ

 1 − ρ

r



− ρ

σ

 1 − η

r



σ

(r) = E 1 − ν

 ν

I(ν) ν

− ρ

 1 − ρ

r



− I(r)



(5)

The exact same equation can be applied for circumferential stress.

If circumferential stress exceeds fracture strength of the fuel at a cell boundary, the cell inside that boundary is assumed to crack. This is repeated until a stable solid boundary is reached, or cracking occurs to the central void or molten fuel boundary[16]. The radial stress σ(r), at any point in the cracked fuel zone, is a function of gas plenum pressure P

and the stresses due to the cladding-fuel interface σ

σ(r) = −P

+ R

r (P

+ σ

) (6)

R

is outer fuel radius. The radial displacement in the cracked fuel region is u

= u

+ (2ν − 1)(r − η) P

E

+ P

+ σ

E

ηln  r η



(7) u

is displacement of the outer surface of the continuous fuel zone and E

is mass averaged modulus of elasticity in the cracked fuel zone. As the dimension of cracked fuel changes, so will the fraction of the volume that is associated with the cracks. In DEFORM only the volume changes due to radial cracks is considered. It depends on three different factors. These are changes in the cell boundary locations, circumferential strain and fission-product-induced fuel swelling. So the fractional volume change due to radial cracks

∆

= ∆

(u) − 

− ∆

∆

(u) = 2u r

+ r



= 

+ 

= −(1 − 2ν) ∆P

E

− νR

E

r (∆P

+ ∆σ

) + ∆(αT )

(8)

∆

(u) origin from the displacement of the cell boundary, r

and r

is inner and outer cell radius. 

is the circumferential strain in the cracked fuel, ∆P

is the change in plenum pressure during a time step and ∆σ

is the change in fuel-cladding interface stress. ∆

is the fractional volume changed associated with fission products.

There can also be situations where the fuel is fully cracked. No solid annulus remains. The fuel- cladding interface stress, σ

then depends on the gas plenum pressure P

and the dimension and pressure in central cavity σ

σ

= −P

+ R

R

(σ

+ P

) (9)

The axial interfaces between segments are assumed to remain parallel, and a segment expands or contracts with a uniform strain, z

, over its entire radius. Since this factor is used in e.g. Equation 4, this solution must be obtained before the radial displacement is considered. A force balanced a created for the axial expansion

F

= F

+ F

+ F

F

= −2πEη

I(n) + 2πν η

σ

− ρ

σ

+ πEz

(η

− ρ

) F

= πρ

P

F

= πr

P

(10)

where F

is force from the solid fuel zone, F

is the force in central void or molten fuel cavity, F

is the force applied axially from the pressure in fission gas plenum and F

is the force from cladding.

It is zero if the fuel can expand freely. r

is the radius of central void or fuel melting and r

is the radius of gas plenum. F

is obtained on a similar way as F

but with cladding properties, thermal expansion and inner and outer boundary forces. Finally z

can be found and is divided into a thermal and forces part

z

= 2η

I(η) η

− ρ

z

= − 2ν

η

− ρ

η

σ

− ρ

σ

E − ρ

P

+ r

P

E(η

− ρ

) z

= (z

(thermal) + z

(forces))A

(11)

3.2.2 Mitigation of fabricated porosity

During operation certain temperature effect can arise and cause changes to the microstructure of the fuel. Pores can migrate along the thermal gradient on the fuel, which was assumed to be the dominating process. Evaporation condensation or pore surface diffusion is not considered in DEFORM-4. A drawback since surface diffusion is the dominating process at lower temperatures[16].

There is a risk that these migrating pores pull grain boundaries with them. It will result in local columnar shaped grains, usually present in the centreline of the fuel. DEFORM-4 uses the parameter RLEQ to define if columnar grains exist. It is a boundary condition, defined as a fraction of initial fabricated porosity. If the porosity falls below RLEQ the cell is assumed to contain columnar grains.

Hence if a certain fraction of pores have left the fuel cell, it is considered to have another structure.

It does not however affect calculations[16]. RLEQ was set to 0.6[17]. So a porosity of 2.4 % would result in columnar grains in the simulations.

Next parameter regards the shift to equiaxed from fabricated grains, the RUEQ subroutine. When a ratio have been exceeded the grains is considered to be equiaxed, the values used is 1.2[18]. Since the pores migrate up the thermal gradient, there is a unlikely risk that the a cell will be emptied of pores, therefore the parameter PRSMIN prevent the possibility. It is a minimum porosity allowed in a cell, equal to 0.02. It also prevent a situation where more pores leave the cell than the sum of pores entering cell together with the original amount of pores. The initial porosity, PRSTY is set to 4 %.

The pore velocity, U , as a function of temperature, traveling along thermal gradient dT /dr, is U = dT

dr A

T

× e

(12)

R is the universal gas constant, A

, Q

and A

are calibration constants. Recommended values were provided for MOX fuel. The pore velocity was evaluated against literature data of both MOX and UOX with U/M of 2.00. The results are presented in Figure 2. The difference between UOX and MOX by the data of C.F Clement is very similar. Hence, default parameters were changed to allow a better fit toward Clement. Low fuel temperature allows none or minimum pore movement, due to small thermal gradient. However the changes may be of importance during transients.

5000 1000 1500 2000 2500 3000

0.5 1 1.5 2 2.5x 10⁻³

Temperature [K]

[cm/s]

DEFORM−4 default MOX[cm/s]

C.F Clement MOX[cm/s]. O/M=2.00 C.F Clement UOX[cm/s]. O/M=2.00 Fitted velocity UOX[cm/s]. O/M=2.00

Figure 2: Pore velocities[19][20]

The mitigation of pores is also of importance considering fission gas mitigation. Since the pores

moves into the central part of the fuel, there can be a release of fission gas when the central void is

reached. A central void must exist in the beginning of a deform calculations[16]. Here the inner fuel

radius is set to have a radius of 1 µm, the minimal value, since this is an unwanted feature of the fuel.

3.2.3 Grain growth

At high temperature grains will grow. Atoms will move from smaller to larger grains, and effect arising due to the ambition to minimize the surface area, hence the surface energy. Regarding the grain size SAS4-A contains two different models. One, which allows unlimited grain growth, and another which consider limiting factors, such as inter granular pores, solid and gaseous fission products. The latter was chosen. Hence size of grains is limited. The maximum size as a function of temperature is

D

= G

× e

(13)

Where calibration constants G

and Q

was obtained from Ainscough[21]. A differential equation arises for the actual grain size

dD

dt = G

 1

D − 1

D



e

(14)

Values for the constants were yet again based on the work of Ainscough. The calibration was also used in MATPRO-10[27]. The calibration has a good fit for low temperature data(∼800 K). A plot of the maximum allowed grain size can be seen in Figure 40, Appendix A. Note how the low temperature of the fuel is expected to prevent grain growth during steady state. The grains will however not shrink, if the maximum value is lower that the current value, which equation 14 indicate[16].

3.2.4 Fission gas release

The generated fission gas is proportional to the number of fission. It is also subdivided into axial segment to consider the power profile. Basic equations are used and they are presented in Appendix A. Migration of intra-granular fission gas toward grain boundaries is heavily simplified in DEFORM-4.

The diffusion usually depends by the radius of the gas, in solution or as a bubble. The code however utilizes a simple factor to divide the mass of fission gas between grain boundaries and fuel matrix.

G

= G

× f

(15)

G

= G

(1 − f

) (16)

Where G

denotes the mass of fission gas in ground boundary respectively the fuel matrix of radial cell i. The parameter f

is the fraction of generated fission gas on grain boundaries. This parameter is of great importance. Only gases in grain boundaries are assumed to induce swelling. Inter-granular gas is also released immediately upon fuel melting, while there is a transition time for intra-granular gas. At temperatures above 1650 K intrinsic diffusion dominate the diffusion rate. In temperature range 1650 K > T > 1387 K radiation enhanced diffusion, due to vacancies, is the main contributor.

While at low temperature, < 1387 K, athermal diffusion is the important phenomena[23][24]. It is a radiation-induced diffusion from knock out and recoils. The standard value DEFORM-4 uses for f

is 0.1, but is for MOX fuel at 2000 K. Remember that SEALER is expected to have a fuel temperature of ∼800 K. TRANSURANUS uses a correlation reported by Hj. Matzke for the thermal diffusion part and a correlation from R.J White and M.O. Tucker for the athermal coefficient[25]. Both have a dependence on temperature T [K] and the effective diffusion coefficient D

is the sum of both contributors

D

= 5 × 10

e

D

= 1.086 × 10

e

D

= D

+ D

(17)