Evaluation of the thermal-hydraulic software GOTHIC for ...633796/FULLTEXT01.pdf · Evaluation of the thermal-hydraulic software GOTHIC for nuclear safety analyses Linn Bydell The

UPTEC-ES13013 Examensarbete 30 hp Juni 2013

Evaluation of the thermal-hydraulic software

GOTHIC for nuclear safety analyses

Linn Bydell

i

ABSTRACT

Evaluation of the thermal-hydraulic software GOTHIC for nuclear

safety analyses

Linn Bydell

The aim of this master theses was to evaluate the thermal-hydraulic

calculation software GOTHIC for the purpose of nuclear

containment safety analyses. The evaluation was performed

against some of the Marviken full scale containment experiments

and a comparison was also made against the two codes RELAP5 and

COPTA. Models with different complexity were developed in

GOTHIC and the parameters pressure, temperature and energy in

different areas of the enclosure was investigated.

The GOTHIC simulations in general showed a good agreement with

the Marviken experimental results and had an overall better

agreement then RELAP5. From the results it was possible to

conclude that the developed GOTHIC model provided a good

representation of the Marviken facility.

Supervisor: Robert Larsson

Project carried out for: Vattenfall Research & Development AB in collaboration with KTH Royal Institute of Technology

Financed by: Vattenfall Research & Development

Subject reviewer: Henrik Sjöstrand

Examiner: Kjell Pernestål

ii

POPULÄRVETENSKAPLIG SAMMANFATTNING

Utvärdering av det termohydrauliska beräkningsprogrammet GOTHIC för nukleära

säkerhetsanalyser

Linn Bydell

Kärnkraft har potential att producera stora mängder el till låga produktionskostnader och

klimatpåverkande utsläpp. Kärnkraftens baksida är den överhängande risken för olyckor med

omfattande skador till följd. Att skapa en god säkerhetskultur är nyckeln till en fungerande

produktion. Säkerhetssystemen vid svenska kärnkraftverk består av flera skyddsbarriärer och

reaktorinneslutningen är en barriär som, i händelse av en olycka, ska stå emot tryckökningar och

förhindra spridning av radioaktiva ämnen. Inneslutningen måste dimensioneras att tåla de höga

tryck och temperaturer som kan uppstår och termohydrauliska beräkningsprogram används för

att beräkna dessa laster. För att utvärdera beräkningsprogramens överensstämmelse mot

verkligheten valideras de mot experiment. Ett av fåtaliga fullskaliga inneslutningsexperiment som

utförts skedde i den Svenska Marviken anläggningen på 1970 talet.

Två program som idag används för nukleära säkerhetsanalyser är RELAP5 och COPTA, vilka båda

har utvärderats mot Marviken experimenten. COPTA som används för säkerhetsanalyser av

reaktorinneslutningen är en relativt gammal kod som jämfört med modernare programvaror har

en begränsad komplexitet. Ett program som har potential att ersätta eller komplettera de

program som idag används är GOTHIC. GOTHIC är ett generellt termohydraulisk

beräkningsprogram med förmåga att analysera system av komplexa geometrier. Till följd av att

GOTHIC är modernare och mer komplex jämfört med program som används idag är Vattenfall

Research and Development AB intresserad av att utvärdera GOTHIC som möjlig ersättare.

Utvärderingen av GOTHIC utfördes framförallt gentemot mätningar från utvalda experiment

utförda i Marviken, men även mot RELAP5 och COPTA. Modeller av Marviken inneslutningen med

olika komplexitet utvecklades i GOTHIC och parametrarna tryck, temperatur och energi

studerades. Simuleringarna i GOTHIC visade generellt en god överensstämmelse med mätningar

från Marviken och låg oftast närmare mätningarna än vad RELAP5 simuleringarna gjorde.

iii

ACKNOWLMENTS

Great thanks to Robert Larsson from Vattenfall Research and Development AB who has answered

all my questions and been a good and dedicated supervisor.

Thanks to Vattenfall Research and Development AB and KTH for providing the opportunity for me

to perform the thesis. Also thanks to Pavel Kudinov, Walter Villanueva, and Hua Li from KTH at

the Department for Nuclear Power Safety for their commitment and opportunity to use the KTH

GOTHIC license during the thesis.

GOTHIC is developed and maintained by the Numerical Applications Division of Zachry Nuclear

Engineering under EPRI sponsorship. I would like to thanks NAI for providing access to the

program for educational and research purposes. Also, great thanks to Donald Todd at Numerical

Applications, for his advices regarding GOTHIC related questions which was a totally new software

for me at the beginning of the project.

I would also like to thank Henrik Sjöstrand from Uppsala University at the Department of Physics

and Astronomy for the input and guidance on my master thesis.

iv

iv

TABLE OF CONTENT

ABSTRACT ....................................................................................................................................... i

POPULÄRVETENSKAPLIG SAMMANFATTNING .............................................................................. ii

ACKNOWLMENTS ......................................................................................................................... iii

1. INTRODUCTION ......................................................................................................................... 1

1.1 BACKGROUND ..................................................................................................................... 1

1.2 AIM OF THESIS ..................................................................................................................... 2

2. THEORY ...................................................................................................................................... 3

2.1 BWR CONTAINMENT AND PS-PRINCIPLE ............................................................................ 3

2.1.1 Sequences affecting PS-principle ................................................................................. 5

2.2 PRESSURE AND TEMPERATURE IN CONTAINMENT DURING PIPE BRAKE ........................... 6

2.2.1 Pressure before clearance of blowdown pipes ............................................................ 6

2.2.2 Pressure when steam and gas flows to wetwell .......................................................... 6

2.2.3 Pressure reduction in containment .............................................................................. 8

2.2.4 Temperature in containment ....................................................................................... 8

2.3 GOTHIC INTRODUCTION...................................................................................................... 8

2.3.1 Control volume ............................................................................................................. 9

2.3.2 Flow path .................................................................................................................... 10

2.3.3 Thermal conductor ..................................................................................................... 11

2.3.4 Boundary and initial conditions ................................................................................. 11

2.3.5 Resources and components ....................................................................................... 12

2.4 MARVIKEN TEST FACILITY DESCRIPTION ........................................................................... 12

3. METHOD .................................................................................................................................. 15

3.1 OVERALL MODEL APPROACH ............................................................................................ 15

3.2 MAIN MODEL STRUCTURE ................................................................................................ 15

3.2.1 Boundary and initial conditions ................................................................................. 18

3.2.2 Heat structures ........................................................................................................... 19

3.3 VESSEL MODEL .................................................................................................................. 22

3.4 3D WETWELL MODEL ........................................................................................................ 23

3.5 SIMULATED MODELS ......................................................................................................... 24

3.5.1 Experiment 4 .................................................................................................................. 25

3.5.2 Experiment 7 .................................................................................................................. 25

v

3.5.3 Experiment 10 ................................................................................................................ 25

3.5.4 Model 1 – Hydraulic model (without thermal conductor) ......................................... 26

3.5.5 Model 2 – Lumped GOTHIC model ............................................................................. 26

3.5.6 Model 3 – Vessel model ............................................................................................. 26

3.5.7 Model 4 – 3D wetwell model ..................................................................................... 26

4. RESULTS ................................................................................................................................... 31

4.1 EXPERIMENT 4 ................................................................................................................... 32

4.1.1 Pressure ...................................................................................................................... 32

4.1.2 Air transport ............................................................................................................... 34

4.1.3 Temperature .............................................................................................................. 36

4.1.4 Hydraulic model (without thermal conductors)......................................................... 40

4.1.5 Vessel model .............................................................................................................. 41

4.2 EXPERIMENT 7 ................................................................................................................... 42

4.2.1 Pressure ...................................................................................................................... 42

4.2.2 Air transport ............................................................................................................... 44

4.2.3 Temperature .............................................................................................................. 45

4.2.4 Hydraulic model (without thermal conductors)......................................................... 49

4.2.5 Vessel model experiment 7 ........................................................................................ 50

4.2.4.1 3D wetwell............................................................................................................... 51

4.3 EXPERIMENT 10 ................................................................................................................. 54

4.3.1 Pressure ...................................................................................................................... 54

4.3.2 Air transport ............................................................................................................... 56

4.3.3 Temperature .............................................................................................................. 57

5. DISCUSSION ............................................................................................................................. 61

5. 1 PRESSURE ......................................................................................................................... 61

5.2 TEMPERATURE .................................................................................................................. 62

5.2.1 Temperature in the wetwell compression space ....................................................... 62

5.2.2 Temperature in the drywell ....................................................................................... 63

5.2.3 Temperature in the wetwell water pool .................................................................... 64

5.2.4 Concrete structure temperature .................................................................................... 65

5.3 COMMENTS RELATED TO BLOWDOWN 10 ....................................................................... 65

5.4 VESSEL MODEL .................................................................................................................. 65

5.5 3D WETWELL MODEL ........................................................................................................ 66

vi

5.6 MAIN COMMENTS CONCERNING RELAP5 AND COPTA .................................................... 67

5.7 ACCURACY OF THE MARVIKEN MEASUREMENTS ............................................................. 67

6. CONCLUSIONS ......................................................................................................................... 69

8. REFERENCES ............................................................................................................................ 70

Appendix 1 .................................................................................................................................. 71

Appendix 2 .................................................................................................................................. 72

Appendix 3 .................................................................................................................................. 73

Appendix 4 .................................................................................................................................. 75

Appendix 5 .................................................................................................................................. 78

Appendix 6 .................................................................................................................................. 80

Appendix 7 .................................................................................................................................. 82

Appendix 8 .................................................................................................................................. 84

1

1. INTRODUCTION

1.1 BACKGROUND

Nuclear power is a reliable technology for large scale electricity generation, with low production

cost and during operation it is nearly free from climate changing emissions. However, nuclear

power production also entails a risk of accidents with major damages potentially affecting large

areas. Due to the two-faced background the key to a good production culture is to also provide a

good safety culture. A reliable safety culture is based on knowledge and supported by extensive

safety regulations, it is an engineering work and responsibility to assure the safety.

One of the approaches to nuclear safety is to use several physical safety barriers, preventing

distribution of radioactive material. One of these barrier is the reactor containment, which

contains the reactor vessel and the radioactive fuel. The containment plays a vital role in several

accident scenarios where it might be the last barrier left preventing large releases of radioactive

material, as was the case in the recently seen Fukushima accident. Requirements regarding the

containment are formed from government regulations and fulfilments of the requirements must

be verified with safety analyses.

Today modelling codes are used to model the accident sequence to ensure that the nuclear

power plant are safe. The codes used to perform the safety analyses needs to be validated against

experiments in order to show that they can predict the reality in an adequate way. During the

years 1972-1973 a series of full scale containment experiments simulating pipe-breaks were

performed in the Swedish plant Marviken. These experiments has been widely used in order to

validate codes used for safety analyses. Two codes presently used for safety analyses in Sweden

are COPTA and RELAP5. Both RELAP5 and COPTA has been compared with the containment

experiments performed in Marviken [10] [12]. Today several of the safety analyses performed for

the reactor containments are carried out with COPTA, which is a relatively old code and have a

limited complexity. Limitations in the currently used codes generate interest among companies

to evaluate the code strategy for the future. A calculation software with potential to replace or

complement the currently used codes is GOTHIC, which is a general thermal hydraulic calculation

software with the potential to analyse system of complex geometry.

2

1.2 AIM OF THESIS

The aim of the thesis is to evaluate the thermal-hydraulics calculation software GOTHIC for

nuclear containment safety analyses. The evaluation are performed against some of the

experiments performed in Marviken power plant and also compared against the two codes

RELAP5 and COPTA. Models of the Marviken containment are developed in GOTHIC and the

parameters pressure, temperature and energy in different areas of the enclosure are

investigated.

3

2. THEORY

This chapter contains a description of the reactor containment function relevant to the thesis.

The chapter also provides an introduction in how to use GOTHIC and a description of the Marviken

facility.

2.1 BWR CONTAINMENT AND PS-PRINCIPLE

The reactor containment contains the reactor vessel and the radioactive fuel. Inside the reactor

vessel the hot fuel produces steam at a high pressure which is transported to the turbine through

the steam lines. The purpose of the containment is that, in case of an accident, it shall act as a

protective shield preventing distribution of radioactive substances into the environment. During

a pipe break causing loss of essential coolant medium (blowdown), the containment need to

resist high pressures. The typical containment can in general be described as a cylindrical building

made out of reinforced concrete. In order to limit the containment volume, needed in order to

cope with the pressure rise during a pipe break, it can be constructed according to the pressure

suppression principle (PS-principle). The containment is then divided into a primary space (the

drywell) and a secondary space (the wetwell). The Drywell contains the reactor vessel including

all pressurized parts and the wetwell consists of a condensation pool and a compression space.

The drywell and the wetwell are connected via pipes, referred to as blowdown and vent pipes,

which opens up under the surface of the water in the condensation pool. Figure 1 provides a

description of the main areas in a boiling water reactor containment [1].

Figure 1: Reactor containment description of the main components discussed in the section [1].

4

The PS-principle suppress the pressure in the containment by diverting steam released during a

pipe break into the condensation pool. The principle is a passive pressure relief system activated

due to the division of the containment. An easy understanding of the principal can be achieved

by following an example explained in figure 2 [1].

Figure 2: Explanation of the PS-principle [1].

1. During a pipe rupture steam and/or water will flow into the drywell and the pressure and temperature in the area will rise.

2. Due to the fact that the wetwell and the drywell are separated, only connected through the blowdown and vent pipes, a differential pressure will arise. When the pressure in the drywell exceeds the pressure in the wetwell and the pressure corresponding to the water column in the pipes, the water column will be pressed out. Gas and steam will start to flow to the condensation pool providing a pool swell. The steam will condense and limit the pressure rise in the containment.

3. The non-condensable gases flowing through the pipes will transport to the compression space and rise the pressure in the area. The maximum pressure will occur when all gas has been transported to the compression space

4. Pressure in the drywell starts to decrease when the condensation rate exceeds the provided steam from the break flow. Often spray system are introduced to increase the condensation rate.

5. When the pressure in the wetwell exceeds the pressure in the drywell gas will flow back to drywell via pressure dependent valves referred to as vacuum breakers. This equalizes the pressure in the containment and the pressure drops .

5

Demands regarding pressure relief of the containment are formed from government regulations.

Requirements particular includes the maximum allowed pressure in the containment and allowed

water level and temperature in the condensation pool. Threats to the containment are all

phenomena that can lead to damages of the containment tightness [1].

2.1.1 Sequences affecting PS-principle

If the separation surface between the drywell and the wetwell is not completely tight, steam from

the drywell can transport directly to the compression space avoiding the condense face in the

condensation pool. The consequences are that the PS-principle is bypassed and the pressure

reduction process will be less effective [1] [2].

During a large pipe break the reactor vessel can be water drained within a time scale of seconds.

The blowdown pipes submergence is important to limit the time before the pressure starts to

decrease. A small submergence limits the time before the water column is blown out. However,

the submergence must be deep enough to not risk being exposed during the pipe break, providing

a degradation of the PS-principle [1] [2].

If providing external water to the condensation pool, for example via spray systems, the

compression space volume will be reduced and provide an increased submergence for the pipes.

This will increase the containment pressure [1] [2].

Heating of the wetwell compression space will occur due to the fact that the blowdown pipes are

in contact with the compression space. Conduction through the pipes will heat the gas in the

compression space and provide a pressure increase in the wetwell [1] [2].

Large pipe breaks will cause large scale level increases providing loads on equipment in the

wetwell. This can lead to a pressure rise in the compression space exceeding the pressure in the

drywell and provide opening of the vacuum breakers. This will provide a risk of leakage from the

drywell to the wetwell during the blowdown [1] [2].

6

2.2 PRESSURE AND TEMPERATURE IN CONTAINMENT DURING PIPE BRAKE

2.2.1 Pressure before clearance of blowdown pipes

Before the blowdown pipes are cleared pressure only increases in the drywell due to steam

and/or water from the break flow. The period is in magnitude of one to teen seconds depending

on the drywell volume, break flow size and type and the submergence depth of the blowdown

pipes [1].

2.2.2 Pressure when steam and gas flows to wetwell

The pressure in the containment when steam and gas flows to the wetwell can be calculated

according to

𝑃𝑊𝑊 = 𝑃å𝑊𝑊 + 𝑃𝑔𝑊𝑊 = 𝑃å𝑊𝑊 +𝑀𝑔𝑊𝑊𝑅𝑇𝑔𝑊𝑊

𝑀𝑉𝑘 (1)

𝑃𝐷𝑊 = 𝑃𝑤𝑤 + 𝜌𝑔ℎ (2)

where PWW is the wetwell pressure, PDW the drywell pressure, PåWW the steam partial pressure in

wetwell, PgWW the gas pressure in the wetwell, MgWW the amount of non-condensable gas in

wetwell, R the universal gas constant, TgWW the absolute gas temperature in wetwell, Vk the

compression space gas volume, ρ the density, g the gravity and h the submergence depth [1].

The steam partial pressure (Påww) is largely dependent on of the condensation pool water

temperature. The steam partial pressure in the wetwell can be approximated at different

temperatures according to figure 3 [3].

Free gas volume (Vk) in the compression space is affected by the water level in the condensation

pool. A higher level will decrease the free gas volume and thereby increase the maximum

pressure during a break. The free gas volume during a blowdown can be calculated according to

𝑉𝑘 = 𝑉𝑔𝑊𝑊 ± 𝑉𝐻2𝑂𝑇𝑊𝑊 (3)

where VgWW is the initial water volume in the wetwell and VH2OTWW is the amount of water

transported to or from the wetwell during the blowdown [1].

7

Figure 3: Steam partial pressure [3].

The amount of gas accumulated in the compression space (MgWW) is the most important

parameter affecting the pressure in the containment. The total amount of gas transported to the

wetwell depends on the initial amount of gas in the drywell, containment design, break flow size

and type, spray flow and possible additional supply of gas [1].

The initial amount of gas in the drywell (MgDW0 ) can be calculated according to

𝑀𝑔𝐷𝑊0 =(𝑃𝐷𝑊−𝑃å𝐷𝑊)𝑀𝑉𝑔𝐷𝑊

𝑅𝑇𝑔𝐷𝑊 (4)

where PDW the total pressure in the drywell, PåDW the steam partial pressure in the drywell, M the

gas molar mass, R the universal gas constant, TgDW the absolute gas temperature in the drywell

and VgDW the drywell gas volume [1].

During a blowdown it is likely that gas will remain in some areas of the drywell, due to small

mixture between gas and steam and absence of flow opportunities in the containment design. In

analyses it is often assumed that the steam and gas in the drywell is homogeneously mixed. A

consequence from the assumption is that if the blowdown continues all gas will accumulate in

the wetwell providing the highest possible pressure. With the assumption the gas mass in the

wetwell (MgWW) space during a blowdown can be calculated from

1500

3500

5500

7500

9500

11500

13500

15500

17500

15 20 25 30 35 40 45 50 55 60

Tryc

k (P

a)

Temperature (°C)

8

𝑀𝑔𝑤𝑤 = 𝑀𝑔𝑊𝑊0 + 𝑀𝑔𝐷𝑊0 =(𝑃𝑊𝑊−𝑃å𝑊𝑊)𝑀𝑉𝑔𝑊𝑊

𝑅𝑇𝑔𝑊𝑊+ 𝑀𝑔𝐷𝑊0 (5)

Where MgWW0 is the initial amount of gas in the wetwell, MgDW0 is the initial amount of gas in the

drywell, PWW the total pressure in the drywell, PåWW steam pressure in wetwell, M the air molar

mass, VgWW the gas volume in wetwell, R the universal gas constant and TgWW the absolute gas

temperature in the wetwell [1].

2.2.3 Pressure reduction in containment

When more steam condenses in the containment than provided from the break the pressure

decreases. Water introduced via spray system provides an increased condensation rate and a

faster depressurisation rate. When the drywell pressure falls behind the wetwell pressure the

vacuum breakers opens, providing a flow of gas from the wetwell to the drywell [1].

2.2.4 Temperature in containment

Temperature in the containment during a pipe break includes temperature changes in the

drywell, compression space and in the condensation pool. The drywell temperature generally

follows the saturation temperature at the current vapour pressure curve. During steam line

breaks the steam can theoretically be overheated before the spray system starts. Energy content

of the superheated steam is relatively small and is likely to be accumulated by the containment

area. The compression space temperature depends on initial temperatures, gas flow rate, heat

transfer through blowdown pipes and the spray system. The condensation pool water

temperature is affected by initial temperature, amount of steam that condenses, water flow to

the pool, initial water mass and cooling capacity [1].

2.3 GOTHIC INTRODUCTION

GOTHIC is a thermal-hydraulic software which can be used for design and analyse of nuclear

power plants. GOTHIC is developed and maintained by the Numerical Applications Division of

Zachry Nuclear Engineering under EPRI sponsorship.

Creating models in GOTHIC involves work in a graphical user interface where the user draw a

schematic picture of the model. GOTHIC solves equations for mass, momentum and energy for

the created model. Results from GOTHIC may include graphs and tables representing for example

temperature and pressure within different areas of the containment [4].

9

2.3.1 Control volume

The main object used when creating GOTHIC models is the control volume, representing a limited

volume that contains fluid. It is possible to create lumped and subdivided volumes. A lumped

modelling approach can be described as a black-box model where spatial variations are ignored.

The actual geometry and shape of a lumped volume is not set by the user, an arbitrary volume is

calculated by GOTHIC. Subdivided volumes can also be created by the user in one, two or three

dimensions and provides the ability to model a volume of a certain shape. As an example the

temperature in a lumped volume are calculated as an average value for the whole volume while

a subdivided volume can capture the temperature variations in the volume. All control volumes

are mainly represented by providing the volume, height, location and hydraulic diameter.

The hydraulic diameter (Dh) for a control volume should, according to the GOTHIC manual, be

defined according to

𝐷ℎ =4𝑉

𝐴𝑤 (6)

where V is the fluid volume and Aw is the wetted area which is the structure surface area exposed

to the fluid [4].

The lumped parameter approach is suitable if the conditions are homogeneous and one is not

concerned about local conditions. This is due to that lumped volume is single noded and GOTHIC

uses volume average in the calculations of the dependent variables like pressure and

temperature. Variables in a subdivided volume are calculated at the centre of each cell and

thereby provides a distribution of parameters across the modelled region. In additional a

subdivided model needs a longer calculation time. The calculation time are strongly influenced

by the complexity of the control volumes, as an example a 3D subdivision of the wetwell can

change the time needed for a simulation from minutes to hours. Subdivided volumes are defined

by dividing the x, y and/or z direction of a volume within a desired amount of grid lines. Blockages

can be defined for subdivided volumes to model objects that displace fluid within the volume.

Blockages can also be defined to displace the solid. The flow through a cell can be adapted to be

more or less permeable to the fluid (porosity adaption).

Within a single model it is possible to include combinations of lumped parameter and subdivided

volumes.

10

2.3.2 Flow path

Flow paths are used to link control volumes to each other. Volumes may be connected by one or

several flow paths and momentum equations for multiple phases are solved for each flow path.

All flow paths are mainly represented by position, flow area, hydraulic diameter, loss coefficients,

inertia length and friction length. The parameters are used to calculate the flow through a flow

path. No mass or energy can be stored in a flow path, so if a flow path represents a significant

volume it should be modelled as a control volume [4].

The loss coefficients should be obtained from a handbook [5]. Recommended value for a sharp-

edged orifice in a wall that is much larger than the orifice opening is 2.78 [4].

The hydraulic diameter in a flow path (Dh) should, according to GOTHIC manual, be defined as

𝐷ℎ =4𝐴

𝑃𝑤 (7)

where A is the flow area and Pw is the wetted perimeter [4].

If a single junction is used to model parallel connections with several flow losses, the effective

loss coefficient (total loss coefficient) and effective hydraulic diameter for the connection should

be used to represent the connection in GOTHIC. The effective loss coefficient and effective

hydraulic diameter are in the GOTHIC manual recommended to be calculated according to

𝐴

√𝐶𝑒𝑓𝑓= ∑

𝐴𝑖

√𝐶𝑖𝑖 (8)

where A is the total flow area, Ai are the individual junction area, Ci represents the loss coefficient

or hydraulic diameter for the individual connections and Ceff represents the effective loss

coefficient or effective hydraulic diameter [4].

Inertia length (LI) depends on the geometry of the two regions connected by the junction. The

product of inertia length and the junction flow area defines an effective junction volume. The

general recommendation for calculation of inertia length from the GOTHIC user manual is

11

𝐿𝐼 = 𝑀𝑖𝑛 (𝐿1, 𝐿1𝐴𝐽

𝐴1+

0.45𝐷ℎ

1+𝐴𝐽

𝐴1

) + 𝐿0 + 𝑀𝑖𝑛 (𝐿2, 𝐿2𝐴𝐽

𝐴2+

0.45𝐷ℎ

1+𝐴𝐽

𝐴2

) (9)

where AJ is the junction area, Dh the junction hydraulic diameter, Lo the orifice wall thickness, L1

and L2 are the distances from the attached cell centers to the area change and A1 and A2 are the

expanded areas on either side of the junction opening [4].

For junctions that represent parallel openings, the effective junction inertia length (LJ) should be

set to

𝐴𝐽

𝐿𝐽= ∑

𝐴𝐽𝑖

𝐿𝐽𝑖𝑖 (10)

where AJ is the sum of AJi, AJi and LJi represents the specific area and inertia length for the

individual junction [4].

The frictional length is defined to calculate the wall frictional force and should be set to the flow

path length [4].

2.3.3 Thermal conductor

Conductors represents thermal effects in solid structures. Heat can be stored in the conductor or

be transferred to or from the fluid at the conductor surfaces. Conductors can be modelled as

external and internal. An external conductor permits heat transfer between different volumes.

Internal conductors are used to model a conductor where both sides are connected to the same

volume. The properties of a conductor in GOTHIC are defined by heat transfer coefficient type,

conductor type, surface area and initial temperature. The definition of the heat transfer

coefficient type includes choices between models which compute the heat transferred between

the conductor and the surrounding steam or liquid. Definition of a conductor type includes

geometry, material type and nodding of the conductor. Nodding involves dividing the conductor

thickness into a number of regions.

2.3.4 Boundary and initial conditions

Users can define flow to and from a volume through boundary conditions. It is possible to define

conditions determined by flow-, pressure- or coupled boundaries. A flow boundary condition is

12

defined by a mass and energy source and a pressure boundary condition by a pressure source. A

coupled boundary condition allows fluid to be extracted from a volume and then be distributed

to another volume or excluded from the model.

In GOTHIC it is necessary to set the initial conditions for the fluid in a control volume and for the

thermal conductors. Fluid initial conditions include pressure, temperature, humidity and the

composition of the fluid (fraction of liquid and gas). Thermal conductor requires an initial

temperature.

2.3.5 Resources and components

To control the sequence of events during a transient a number of different resources are

available. The resources include forcing functions, control variables, trips and material properties.

The three first can all be used to control the scenario of a transient. Material properties are used

to define materials. As an example a trip resource may be used to open a valve at a certain

overpressure and a forcing function to control the mass flow into a volume. In additional GOTHIC

includes several opportunities for modelling mechanical components like pumps, valves and heat

exchangers.

2.4 MARVIKEN TEST FACILITY DESCRIPTION

The facility in Marviken was initially built in order to be used as a boiling heavy water reactor, but

was never used for this purpose. The plant has instead played a role as a test facility and it has

been used for full scale containment response experiments. The experiments were performed to

study the containment response to different simulated ruptures in pipe systems connected to

the vessel. There is a design report available describing the conditions of the facility during the

experiments performed in August 1972 to May 1973 [6].

The Marviken containment is of pressure suppression type (PS-principle). In the design report the

drywell and the wetwell is subdivided into several rooms and components assigned with different

reference numbers. The wetwell condensation water pool consists of room 105 and all rooms

except this and the reactor vessel constitutes the drywell, see appendix 1. A complete description

of the facility can be found in the design report [6] where information about surfaces, contents

and volumes of all the 14 rooms in the facility are included. The design report also contains

information about 31 connections between the volumes. An example of the available information

for the volumes and connections used in the developed GOTHIC model, can be seen in table 1.

13

In addition the design report also contains information about the position of the rooms, the

thickness of the walls and about surfaces shared by rooms and connections. The containment is

of a complex geometry and in appendix 1 and 2 one can see a schematic picture and a description

of the nodal representation of the facility.

Before the safety experiments were carried out adaptations were made in the facility. Some

internal parts of the reactor vessel were removed and a special heating device was installed.

Devices to simulate different pipe ruptures were mounted in the reactor vessel cupola, in the

main steam line and in the feed water line, see appendix 5. To enable measurements during the

experiments various types of equipment were fixed in the containment. Due to building design

and to reduce the risk for damages the equipment was placed near the walls. Marviken is

equipped with a spray system in order to cool the atmosphere in the containment. The system

takes water from the condensation pool. For the experiments it was possible to spray in room

124 only, in the drywell or in the drywell and the wetwell. See appendix 3 for an illustration of the

spray system. The plant also has vacuum breakers between the drywell and the wetwell. The

vacuum breakers are three parallel valves between the ceilings in the wetwell and room 110. The

valves opens when the pressure in the wetwell exceeds the pressure in the drywell with 0.22 bar

[6].

Table 1: Description of available information for room 124 and the connection between room 124 and

room B in the Marviken containment [6]. The data was used in the developed GOTHIC model.

Room 124

Volumes [m3]

Gross volume 297.3

Insulated pipes with aluminium sheets 24.1

Miscellaneous sheets 1.3

Constructional steel 0.5

Net volume 271.4

Surfaces Thickness [m]

The ceiling (z=143.7 m)

1 concrete with 6 mm steel lining 1.1

2 Cast steel 0.4

The walls (z=138.4 m - 143.7 m)

14

3 PS-wall with 4 mm steel lining -

The floor (z=138.4 m)

4 Steel plate 0.4

5 Steel plate 0.05

6 Concrete with 15 mm steel lining 1.3

7 Steel plate 0.3

Contents Area [m2]

Mass [ton]

Aluminium 196 0.3

Constructional steel 77 3.8

Miscellaneous steel 12 0.6

Spray water pipes 60 3.0

Connection between room 124 and room B

Minimum cross-section area [m2]

3 pipes, diameter 0.7 m, length 5.9 m 1.2

1 pipe, diameter 0.8 m, length 6.5 m 0.5

Total area 1.7

Volumes [m3]

3 pipes, diameter 0.7 m, length 5.9 m 6.8

1 pipe, diameter 0.8 m, length 6.5 m 3.3

Total volume 10.1

Surfaces [m2]

Steel lined concrete 55.3

Total volume 10.1

15

3. METHOD

3.1 OVERALL MODEL APPROACH

The project goal was to evaluate GOTHIC against the Marviken full scale containment

experiments. Selected experiments for validation were number 4, 7 and 10. The experiments

differ in the total amount of energy released to the containment as well as in the type of break

flow (steam, water or both) and the location of the break (further information of the experiment

characteristic will be provided later in this report). The results from the model in GOTHIC was

compared with measured data from the experiments as well as with simulations performed in

RELAP5 and COPTA. References from the experiments performed in Marviken were provided

from Vattenfall [6], [7], [8] and [9] as well as results from simulations in RELAP5 [10] and COPTA

[12].

Different main models of the containment with different complexities were developed for the

three selected experiments. The models were developed in agreement with the description of

the facility and experiments performed in Marviken given in [6], [7], [8] and [9]. In the

development process the nodal representation presented in the facility description, seen in

appendix 2, was used as a base. This was chosen to simplify the model and validation work.

Initially a model was evolved for experiment 7 and then adaptations were made from this model

to generate models with conditions characteristic to experiment 4 and 10. Description regarding

modelling method for experiment 7 is therefore the same also for experiment 4 and 10.

3.2 MAIN MODEL STRUCTURE

Included in the GOTHIC model were control volumes, flow paths, thermal conductors, vacuum

breakers, spray system and a boundary condition representing the break flow. All rooms in the

facility was modelled as lumped volumes. The hydraulic diameters for the volumes were

calculated in accordance with equation 6. Table 2 provides an explanation of the relationship

between the facility room representation and the GOTHIC volume number representation. The

lumped volume representation means that a general geometry is given to the room and therefore

provides a simplification of the represented room. The physical location of the room and the

representative volume is preserved while the actual geometry and shape is lost. Figure 4 shows

the structure for one of the main models developed for Marviken during this thesis.

16

Figure 4: The developed lumped model of the Marviken facility. Number in yellow squares represents

volumes, number in green squares represents flow paths and number in red squares represents thermal

conductors. Numbers in blue squares represents boundary conditions and those in white squares are

different components.

Before the start of the experiments one of the 58 vent pipes were blocked. In GOTHIC this was

modelled by subdividing volume 17, which represents the vent pipes, and adjust the flow areas.

Sometimes the modelling approach created wide connections between volumes. This occurred

when a large room was represented by several smaller volumes. In the real facility large rooms

permits a quite free flow path for the fluid with well mixed conditions. The modelling approach

to obtain good mixture of the atmosphere between connected volumes was to include at least

two flow paths between the volumes.

17

Table 2: Marviken room representation and GOTHIC volume number representation.

Room Volume Description

124 1 Upper drywell

B 2 Region around reactor vessel

A 3 Region around reactor vessel

123 4 Drywell

123.1 5 Drywell

123.2 6 Drywell

123.3 7 Drywell

122 8 Drywell

121 9 Drywell

114 10 Drywell

113 11 Drywell

112 12 Drywell

111 13 Drywell

111.1 14 Drywell

110 15 Drywell

108 16 Blowdown pipes

107 17 Vent pipes

106 18 Header

105 19 Wetwell

104 20 Blowdown channels

124-122 21 Drywell

As volumes not can store mass and energy the connection volumes were in the model accounted

for in the adjacent room volumes. The resistance provided to the connections was calculated in

agreement with equations 7 – 10. Loss coefficients were obtained from [5] and recommendations

provided in the GOTHIC user manual [4]. Volume 21 which represents the connection between

room 124 and 122 in the facility description was modelled as a volume due to the significant size.

In cases where the connection flow area was affected during the experiment the area used in the

simulations was the one reported after the experiment.

18

Vacuum breakers were included by placing an initially closed valve between the drywell and the

wetwell. The valve starts to open when the differential pressure exceeds 0.22 bar, this was

achieved by using trips with pressure as the sense variable.

Between wetwell and lower drywell a drainage pipe were installed in agreement with the facility

description.

Coupled boundary conditions were included to model the spray water system for experiment 7.

A flow boundary condition draws water from the wetwell and divides it into 6 coupled boundary

conditions. Flow drawn from the wetwell was in GOTHIC controlled with an initially closed valve

using trips to open and close the valve. Appendix 3 provides information about the spray flow in

the simulated experiment. The flow paths assigned to the coupled boundary conditions and

discharge volumes was equipped with spray nozzles. Drop diameter formed by the nozzles was

in agreement with the reference set to 0.07 cm [6].

3.2.1 Boundary and initial conditions

Boundary conditions for the mass- and enthalpy flow from the vessel during the time of the break

was included with a flow boundary condition. Measurements from the Marviken experiment used

as boundary condition in the simulation for experiment 7 are shown in figure 5 and 6 [8].

Appendix 4 shows the curves used as boundary conditions for experiment 4 and 10 [7] [9].

Initial parameters in the model for experiment 7 are presented in table 8. Table 9 and 10 present

the initial information for experiment 4 and 10. Rooms not represented in the design report were

given an average value of the adjacent rooms. Rooms represented with more than one

temperature value were given an average temperature of the reported values. Since the

Marviken design reports did not include any information of the temperature history of the

containment prior to the beginning of the experiments, the heat structures were assigned the

same initial temperatures as the room containing the structures. Possible implications of this is

further discussed in section 5.2.4. The humidity was never measured during the experiments, but

an estimation of the humidity was provided in the experimental report for each experiment. The

estimation of the humidity was used in the model.

19

Figure 5: Break enthalpy used as boundary condition in the simulations for experiment 7 [8].

Figure 6: Break flow used as boundary condition in the simulations for experiment 7 [8].

3.2.2 Heat structures

Material in the containment consists of concrete, steel and aluminium. The amount of aluminium

in the containment is small and has been ignored. Properties used to define the concrete and

steel material types were density, thermal conductivity and specific heat in accordance with table

3 [6].

0

500

1000

1500

2000

2500

3000

0 200 400 600 800 1000 1200 1400

Spec

ifik

en

thal

ph

y (K

J/kg

)

Time (s)

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200 1400

Flo

w (

kg/s

)

Time (s)

20

Table 3: Material properties for concrete and steel used in the simulation [6].

Materials Density [kg/m3] Specific heat [kJ/kg°C] Thermal conductivity [W/m°C]

Concrete 2400 0.9 1.6

Steel 7800 0.5 55

If a conductor models a wall shared by more than one room heat can be transferred between the

rooms. In the Marviken experiments the rooms are in several cases thermally isolated, due to

transient time and thickness of material with low conductivity. Knowledge about the thermal

isolated rooms was obtained by performing simulation tests on the concrete material. The test

involved the same boundary and initial conditions, materials, transient time and heat transfer

coefficients as intended to be used in the Marviken model, but only one volume and one

conductor. The intended heat transfer coefficient was assigned to one side of the conductor

surface and a zero-heat-flux boundary condition to the other side. The test provides a

temperature profile of the conductor during the transient time, giving information about the heat

penetration depth in the conductor. A temperature profile for concrete obtained from the test is

shown in figure 7. The profile views a concrete wall where the left side has been exposed to heat

from the room. Heat has penetrated about 11 cm of the wall at the end of the transient time. The

conclusion was that all concrete walls thicker than 22 cm could be considered as thermally

isolated on the side not facing the fluid.

Figure 7: Temperature profile at 1500 s for a concrete wall with 4 mm steel lining.

0

50

100

150

200

250

300

0 20 40 60 80 100

Tem

per

atu

re (

°C)

Conductor thickness (cm)

21

Marviken containment includes a great number of individual conductors and it would be a

significant amount of work to represent them all separately. The approach for the model has been

to provide a few conductor types for each material. The amounts of represented types were

decided from the demand of the situation regarding simulation time and presence of different

thicknesses for the same material. This approach means that several conductors of same material

was represented with one conductor and thickness.

Concrete in the containment had a low conductivity and a thickness usually exceeding 0.5 m. Due

to this it has been considered most important to preserve the surface area, which was the part

of the conductor participating in the heat transfer. The penetration depth during the transient

time was 11 cm and due to the thermal isolation concrete walls were modelled with 25 cm

thickness in each room. Even walls shared by several rooms are independent and were modelled

with 25 cm thickness. With this modelling approach all concrete surfaces are preserved without

losing any heat sinks participating during the transient time. Steel lined concrete in the

containment was also modelled to a 25 cm concrete thickness while the steel lining was modelled

in agreement with the actual lining thickness.

Steel in the containment, with high conductivity and thinner thickness compared with the

concrete, will be fully heated during the transient time and the total amount will be involved in

the heat transfer. Due to this it has been considered important to preserve the total amount of

steel in the containment. Steel conductor types of several thicknesses were defined. The

approach has been to use the conductor thickness that best represented the steel conductors in

a room and then adjust the total surface area to a value preserving the total steel mass in the

room.

The blowdown pipes consisted of steel and was in direct contact with the wetwell compression

space. To model the heat transfer between the adjacent rooms, external conductors were used.

GOTHIC includes several models regarding heat transfer, the user need to decide between

different heat transfer coefficient options. Film, Direct, Tagami, Correlation Set and Sp Cond HTC

are examples of condensation options and additional choices must be done between UCHIDA,

GIDO-KOESTEL, MAX and four variations of DLM (Diffusion Layer Model). For additional

information regarding the different models see reference 4. In the user manual for GOTHIC it is

mentioned that all but one of the qualification cases used the direct heat transfer coefficient

22

option, providing good results for containment analyses. The direct option was therefore used in

the Marviken model for the exposed surfaces. Heat transfer option for surfaces in contact with

liquid was set to correlation Set. The recommended and also chosen condensation option was

DLM-FM.

3.3 VESSEL MODEL

The vessel model simulates the initial vessel conditions and break pipe positions and was

developed with a simple design. The vessel and discharge pipes were modelled with initial

conditions in agreement with table 4. A vessel model was developed for experiment 4 and 7.

Experiment 4 simulates a steam line break in room 124 [7] and blowdown 7 a break on the feed

water system in room 122 [8]. In short the feed water line system consists of 21 channels

positioned inside the pressure vessel penetrating through the bottom of the vessel connecting to

the feed water line [8]. The 21 channels and feed water line were each modelled by a control

volume. The steam line break consists of a short pipe mounted on the top cupola [7] of the vessel

and was modelled by a control volume. A schematic description of the break positions can be

seen in appendix 5. Figure 8 views a picture of the developed GOTHIC vessel model for

experiment 7.

Figure 8: Description of the developed GOTHIC vessel model for experiment 7.

• Reactor vessel

• 21 channels

• Feed water line

•t

• Break room 122

•

•

23

Table 4: Conditions in the vessel and discharge pipes, used in the developed vessel model [7] [8].

Room Vessel conditions

Pressure 49.0 bar

Temperature steam region 261°C

water level in vessel 8.0 m

Amount of water 114 ton

Amount of steam 6.8 ton

Top steam line break

Location of break room 124

Diameter of discharge orifice 200 mm

Area of discharge orifice 0.314 m2

Feed water line break

Location of break room 122

Diameter of discharge orifice 150 mm

Area of discharge orifice 0.0177 m2

Length of 21 channels 6-9 m

Diameter 21 channels 68.9 mm

Feed water line diameter 220 mm

Total length of discharge orifice 28 m

3.4 3D WETWELL MODEL

The 3D wetwell model developed during the thesis can be seen in figure 9. The model was divided

into a grid pattern represented by 1386 cells. Subdivided volumes in GOTHIC are initially

represented by a rectangular mesh. Blockages were used to adapt the rectangular mesh to the

containment design and exclude areas positioned inside the wetwell volume. Areas excluded with

blockage were regions outside the cylindrical containment, the header, the fuel channel and the

two fuel channel pedestals. The 4 blowdown pipes and 58 vent pipes positioned in the wetwell

volume was represented by reduced volume porosity. Blockage were not used for the vent and

blowdown pipes due to that a blockage completely blocks the cells, and the area representing

vents and blowdown pipes are only partly blocked.

24

The vent pipe volume was divided into 20 channels with the intention to distribute the flow from

the vent pipes out into the wetwell. Each channel represents 2.9 vent pipes with the

corresponding cross section flow area. The channels were connected by individual flow paths

from the header to the wetwell volume.

Figure 9: The subdivided wetwell model. The left picture shows a front view of wetwell where the top

heavily shaded region represents the blowdown pipes and the bottom the vent pipes. The oblong light

shaded plate in the middle represents the vent pipe header and the remaining light shaded regions

represents the fuel channel. The middle picture shows a top view of the header. The right picture is a top

view showing the vent pipes and fuel channel pedestals. The heavily shaded region represents the vent

pipes and the light shaded region the fuel channel pedestals.

Initial conditions were set in each cell to fit the surrounding medium. Setting initial condition can

be tricky and provide a not functioning model. To limit possible errors it can be convenient to

remember that completely blocked cells are not affected by the initial conditions.

3.5 SIMULATED MODELS

The simulations for all developed lumped models has been performed with a time step and

plotting frequency according to table 5. Pool swell in the experiments are violent and provides

numerical problems for the subdivided model. To avoid the problem an additional time domain

was added between 2 and 5 s including a smaller minimum time step of 0.000001. The

calculations for the subdivided model have been performed according to table 6.

Table 5: Time interval and plotting frequency used in all the developed lumped models.

Min time step Max time step End time Print interval Graphical interval

0.001 0.01 1500 1000 0.5

25

Table 6: Time interval and plotting frequency used in the developed 3D wetwell model.

Min time step Max time step End time Print interval Graphical interval

0.00001 0.1 2 10 0.5

0.00001 0.001 5 10 0.5

0.00001 0.1 1500 10 0.5

3.5.1 Experiment 4

Experiment 4 simulates a steam line break in room 124 with a preheated wetwell condensation

pool, see appendix 5 for a reminder of the break position in the vessel. The experiment was

carried out according to the conditions reported in reference 7. Mass and specific enthalpy flow

from the break position are presented in appendix 4. The containment conditions used in the

simulation are summarized and presented in table 7.

3.5.2 Experiment 7

Experiment 7 simulates a break in the feed water system in room 122, see appendix 5 for a

reminder of the break position in the vessel. Initially the break flow was water and at 270 s the

flow started to consist of steam. The experiment was carried out according to the conditions

reported in reference 8 and the mass and specific enthalpy flow from the break position are

presented in figure 5 and 6. The containment conditions used in the simulation are summarized

and presented in table 8.

3.5.3 Experiment 10

Experiment 10 simulates a massive waterline break in room 122 obtained by two break positions,

one on the main steam line and one on the feed water line. See appendix 5 for a reminder of the

break position in the vessel. The experiment was carried out according to the conditions reported

in reference 9 and the mass and enthalpy flow from the break position are presented in appendix

4. The containment conditions used in the simulation are summarized and presented in table 9.

26

3.5.4 Model 1 – Hydraulic model (without thermal conductor)

Model 1 was a lumped model which excluded the thermal conductors, simulations was

performed for experiment 4 and 7. The intention with the model was to illustrate the impact from

the thermal conductors. Additional purpose was to early in model work obtain knowledge about

the results.

3.5.5 Model 2 – Lumped GOTHIC model

Model 2 was built from a copy of model 1, in addition all the heat structures described in the

design report [6] has been included. Lumped models was developed for all three experiments.

The intention with the case was to create a model closer to reality.

3.5.6 Model 3 – Vessel model

Model 3 was an expansion of model 2 including a vessel model as described in chapter 3.3. The

intention with the model was to create the opportunity to simulate the input boundary conditions

(mass and enthalpy flow). Additional purpose was to be able to observe differences in the

outcome given boundary conditions in a table or with a vessel model. A vessel model was

developed for experiment 4 and 7.

3.5.7 Model 4 – 3D wetwell model

Model 4 was built from a copy of model 2. In model 4 the wetwell volume has been subdivided

as described in section 3.4. The intention with model 4 was to obtain knowledge about the

possibilities with 3D modelling and be able to observe local variations in parameters like

condensation pool temperature and condensation pool surface swell. Model 4 also includes

additional subdivision of the volume representing the vent pipes. Model 4 was developed for

experiment 7.

Table 7: Initial conditions used in the developed models for experiment 4 [7].

Containment conditions

Drywell pressure 1.01 bar

Wetwell pressure 1.00 bar

Drywell temperatures Room No Temperature °C

104 30

106 26

27

110 18

111 20, 23, 29

112 19

113 20

114 18

121 24

122 26

123 30

124 61, 74, 53

Wetwell air temperature 105 46.5 maximum

43.9 average

41.3 minimum

Wetwell water temperature 105 33.8 maximum

31.6 average

30.6 minimum

Depth of wetwell pool 4.60 m

Water pool volume 572 m3

Wetwell air volume 1572 m3

Drywell volume 1934 m3

Vent pipe submergence 2.9 m

Number of open vent pipes 57

Vent pipe flow area 4.07 m2

Estimated humidity of the air in:

wetwell 100 %

room 124 2-5 %

drywell 17 -30 %

The sequence of events

Initiation of blowdown 0 s

Termination of blowdown 780 s

28

Table 8: Initial conditions used in the developed models for experiment 7 [8].





104 19

106 19

110 19

111 19, 27, 31

112 20

113 20

114 19

121 28

122 27, 30

123 40

124 56, 72, 64


17.3 average

16.0 minimum


18.6 average

17.3 minimum









wetwell 100 %

room 124 4 %

drywell 12 - 37 %

29


Initiation of blowdown 0 s

Termination of blowdown 835 s

Start of spray cooling 970 s

Table 9: Initial conditions used in the developed model for experiment 10 [9].





104 14

106 16

110 14

111 54, 29, 13

112 15

113 15

114 14

121 23

122 51, 56

123 97

124 78, 96, 87


16.6 average

15.7 minimum


15.7 average

14.4 minimum






30




wetwell 100 %

room 124 1 %

drywell 5 - 40 %


Start of blowdown by opening main steam line rupture disc 0 s

Star of discharge flow through feed water system 4 s

Closing of steam line valve

(still a leakage) 53 - 57 s

Closing of feed water line valve, termination of blowdown 480 – 486 s

Opening of the valve in the drain pipe between drywell and wetwell 900 s

31

4. RESULTS

This chapter presents the results from the GOTHIC simulations of the three experiments under

consideration (experiment 4, 7 and 10). The result chapter mainly consists of a comparison

between GOTHIC simulations and Marviken experimental measurements. However, a

comparison between results from simulations performed with RELAP5 [10] and COPTA [12] has

also been included in several of the result graphs. The main lumped model has been developed

for all tree experiments and has the advantage of a shorter calculation time. Due to this most of

the results has been calculated with the lumped model. In several graphs results from the vessel

model are also included in order to allow a comparison. A few results from the 3D wetwell model

are presented with the purpose to see local variation in some parameters.

Each graph comes with a legend, the legend structure can be clarified by an example: XX:YY-Z,

where XX represents the simulated parameter, YY the simulated room and Z the code/model used

to provide the curve. Table 10 provides explanations for some of the legend structures. Measured

results from the Marviken experiments are referred to as just experiment and curves from the

GOTHIC lumped model simulations just as the simulation in the result and discussion chapter. The

time when the pipe break was open, providing steam and water flow to the drywell, are referred

to as the time for the blowdown.

Table 10: Explanation of the legend structure used in the result graphs.

Legend Parameter Room Code/Model

PR:122-GOTHIC Pressure 122 GOTHIC lumped model

TV:122-RELAP Temperature 122 RELAP5 model

LL:WW-GOTHIC (vessel) Liquid level Wetwell GOTHIC vessel model

PR:122-GOTHIC (3D) Pressure 122 GOTHIC 3D wetwell model

PR:122-Marviken Pressure 122 Marviken experiment

ST:124-GOTHIC Steam temperature 124 GOTHIC lumped model

TV:WWLIquid-Marviken Temperature Wetwell water phase Marviken experiment

TV:WWVapor-RELAP Temperature Wetwell vapor phase RELAP5

32

4.1 EXPERIMENT 4

4.1.1 Pressure

All the rooms in the drywell show the same pressure behaviour during the experiment. See

section 3.5.1 in order to refresh the conditions for experiment 4. The pressure in room 124, where

the break was located, room 122 and the wetwell are presented in appendix 6. In figure 10 a

comparison between the experiment and simulation results can be seen for the pressure in the

drywell and the wetwell during the transient time. Refer to chapter 2.1 and 2.2 for a reminder of

the pressure event during a blowdown. Maximum pressure in the drywell as well as in the wetwell

was with the GOTHIC simulation predicted in agreement with the experiment. The initially rapid

pressure increase in the drywell was due to the steam and water flow from the break. The initial

wetwell increase was due to transport of air from the drywell into the wetwell. After 80 s from

the start of the blowdown the simulated pressure dropped, this was not measured during the

experiment. After the pressure drop the simulated drywell pressure increased until the end of

the blowdown. At 780 s the containment pressure decreased rapidly due to that the blowdown

was terminated. At 830 s the experimental drywell pressure fell below the wetwell pressure

providing the opening of the vacuum breaker at 880 s, allowing air to return to the drywell. In the

simulation the valve opened at 920 s, when the wetwell overpressure exceeded 22 kPa. The

depressurization rate from the end of blowdown was not predicted in agreement with the

experiment, providing a higher pressure in both the drywell and the wetwell at the transient end.

Se section 5.1 for further discussion of the pressure in the containment.

The vent pipes are the connection between the drywell and the wetwell, refer to appendix 1 and

figure 2 for a reminding understanding of the vent pipes position in the Marviken facility and the

events during a blowdown. The water plug inside the pipes was blown out during the first seconds

of the experiment, initial water level inside the pipes was at 4.6 m from the wetwell floor. The

vent pipes outlet was positioned at 1.7 m from the wetwell floor and had a height of 5.3 m. Figure

11 and 12 views the clearance of the vent pipes during experiment 4. Vent pipes was cleared after

2.9 s in the experiment and at 2.0 s in the simulation. When the flow through the vent pipes

stopped the level inside the pipe started to rise again, when water re-entered the vent pipes due

to a wetwell overpressure.

33

Figure 10: Pressure in the drywell and the wetwell during experiment 4.

Figure 11: Liquid level in the vent pipes during the first seconds of experiment 4, simulated with the

GOTHIC lumped-model.

0

40

80

120

160

200

240

280

320

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:124-GOTHICPR:WW-GOTHICPR:WW-MavikenPR:124-MarvikenPR:124-RELAPPR:WW-RELAPPR:124-COPTAPR:WW-COPTA

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5

Liq

uid

leve

l in

ven

t p

ipes

(m

)

Time (s)

34

Figure 12: Liquid level in the vent pipes for experiment 4, simulated with the GOTHIC lumped-model.

The differential pressure between the drywell and the wetwell can be seen in figure 13. The

variability during the first second was provided by the vent pipe clearance. After the clearance

the difference remained fairly constant at 30 kPa, corresponding to the vent pipe submergence,

until the end of the blowdown. The small variations were due to the increased vent pipe

submergence, related to the increased pool surface. The pool surface rises due to steam

condensation and water drained into the wetwell pool from the drywell. After the blowdown

ended the differential pressure dropped as a result from the drywell depressurization. The

differences are negative due to that the wetwell pressure was above the drywell pressure.

4.1.2 Air transport

It was first of all the amount of air (non-condensable gas) transported from the drywell to the

wetwell that provided the pressure increase in the containment. In the Marviken result report

the total amount of air present in the drywell and the wetwell where calculated from the

measured pressure, temperature, partial pressure and humidity in accordance with the equations

1 - 5 discussed in the theory chapter of this report. According to the calculations the initial amount

of air in the drywell was 2200 kg [7], which was the same amount as reproduced by the simulation.

The mass of air in the wetwell during the blowdown are presented in figure 14. According to the

calculations 95-98 % (2090-2160 kg) was transported to the wetwell during the experiment. From

figure 14 it can be seen that 2060 kg was transported to wetwell during the simulation.

0

1

2

3

4

5

6

7

8

0 200 400 600 800 1000 1200 1400

Liq

uid

leve

l in

ven

t p

ipes

(m

)

Time (s)

35

Figure 13: Differential pressure between the drywell and the wetwell during experiment 4.

Figure 14: Air mass in the wetwell during experiment 4.

From figure 14 it can also be seen that 1790 kg was transported to the wetwell during the first 60

s of the simulation and 1500 kg in the calculation, this is further discussed in section 5.1. The

reason for the difference was probably related to a more rapid air flow rate in the simulation than

in the experimental calculation. The air flow into the wetwell during the first 60 s of the simulation

is presented in figure 15.

-40

-30

-20

-10

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400

Dif

f.p

ress

ure

(kP

a)

Time (s)

Differential pressure - GOTHIC

Differential pressure - RELAP

Differential pressure - Marviken

Differential Pressure - COPTA

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

Air

mas

s (k

g)

Time (s)

Mass of air in ww-GOTHIC

Mass of air in ww-Calculated in result report

36

Figure 15: Simulated mass flow into the wetwell during experiment 4. The reason that the calculated air

flow is not included in the graph is that the data was only available as a graph in the Marviken result

report. The graph had many heights and lows, which would provide an error in an attempt to reproduce it.

4.1.3 Temperature

The temperature in room 122 and 124 are presented in figure 16 and 17. The simulation reached

a higher temperature earlier than in the experiment. In figure 18 it can be seen that after the

blowdown ended the simulated temperature in room 124 dropped to the saturation

temperature, while the measured temperature stayed above until the end of the transient. In all

rooms, except room 124, there were no superheated steam measured during the experiment. In

the simulation a higher temperature was predicted providing superheated steam in some of the

drywell rooms. The superheated steam is further discussed in section 5.2.2.

Data from the experiment provided a temperature profile for the concrete block in room 111.

The block has a 4 mm steel lining. A comparison between the temperature profile of the concrete

structure in the experiment and simulation can be seen in figure 19. Note the difference that the

25 cm depth are being compared with 22 cm depth. In the figure it can be seen that heat was

transported into the thermal structure. The graph also views the temperature in room 111. The

simulated temperature in room 111 reached a higher temperature earlier than in the experiment,

just as seen for room 124. The initial concrete temperature was not the same in the experiment

and simulation which are further discussed in section 5.2.4.

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60

Mas

s Fl

ow

(kg

/s)

Time (s)

37

Figure 16: Temperature in room 124 during experiment 4.


0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:124-RELAPTV:124-MarvikenTV:124-GOTHICTV:124-GOTHIC (vessel)TV:124-COPTA

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:122-RELAPTV:122-MarvikenTV:122-GOTHICTV:122-GOTHIC (vessel)TV:124-COPTA

38

Figure 18: Temperature in room 124 during experiment 4. Views that the simulated vapour temperature

drops to the saturation temperature after the blowdown ended.

Figure 19: Temperature in the concrete block with 4 mm steel lining positioned in room 111 during

experiment 4. The 0 mm notation means that the temperature was measured at the concrete block

surface. 25 mm that the temperature was measured at a depth of 25 mm into the concrete structure and

200 mm that it was measured at a 200 mm depth.

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:124-Marviken

TV:124-GOTHIC

ST:124-GOTHIC

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C

)

Time (s)

0 mm - GOTHIC 22 mm - GOTHIC 200 mm - GOTHIC0 mm - Marviken 25 mm - Marviken 200 mm - Marviken0 mm - RELAP 25 mm - RELAP 200 mm - RELAPTV:111-GOTHIC

39

The wetwell water pool and compression space temperatures are presented in figure 20 and 21

and the differences between the experiment and simulation are further discussed in section 5.2.3

and 5.2.1. Figure 22 views that heath was transferred from the air to the heat structures in the

wetwell compression space.

Figure 20: Temperature in the wetwell condensation pool during experiment 4.

Figure 21: Temperature in wetwell compression space during experiment 4.

0

20

40

60

80

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWLiquid-RELAP

TV:WWLiquid-GOTHIC

TV:WWLiquid-GOTHIC (vessel)

TV:WWLiquid(4m)-Marviken

TVWWLiquid (1 m)-Marviken

TV:WWLiquid-COPTA

0

20

40

60

80

100

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWVapor-RELAP

TV:WWVapor-Marviken

TV:WWVapor-GOTHIC

TV:WWVapor-GOTHIC (vessel)

TV:WWVapor-COPTA

40

Figure 22: Heat was transferred from the wetwell air to the thermal structure during experiment 4.

4.1.4 Hydraulic model (without thermal conductors)

The simulation without thermal conductors views the effect of the heat structures in the

containment. In this case all energy was stored in the fluid and transported from the drywell to

the wetwell, providing higher pressures and temperatures. Figure 23 and 24 views the effect of

the thermal conductors in the simulation.

Figure23: Pressure in the wetwell when introducing the thermal structures in the model for experiment 4.

0

20

40

60

80

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV Concrete-GOTHIC

TV Steel-GOTHIC

TV:WWVapor-GOTHIC

0

40

80

120

160

200

240

280

320

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:WW-GOHIC

PR:WW-Maviken

PR:WW-Without thermal conductors

41

Figure24: Temperature in the wetwell compression space when introducing thermal structures in the

model for experiment 4.

4.1.5 Vessel model

The mass flow rate and enthalpy from the break in the steam line were used as boundary

conditions in all GOTHIC models except for the vessel model. The discharge flow was obtained

from measurements performed during the Marviken experiments. A comparison between the

mass flow rate and enthalpy used in the original GOTHIC simulations and the one predicted by

the vessel model can be seen in figure 25 and 26.

Figure 25: Mass flow rate from the break during experiment 4.

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWVapor-MarvikenTV:WWVapor-GOTHICTV:WWVapor-Without thermal conductors

0

20

40

60

80

100

120

140

160

180

0 100 200 300 400 500 600 700

Mas

s fl

ow

rat

e (k

g/s)

Time (s)

Mass flow from boundary condition

Mass flow from vessel

42

Figure 26: Enthalpy from the break during experiment 4.

4.2 EXPERIMENT 7

4.2.1 Pressure

All the rooms in the drywell show the same pressure behaviour during the experiment. The

pressure in room 124, 122 and the wetwell are presented in appendix 7. In figure 27 a

comparison between the experiment and simulations can be seen for the pressure in room 122

and the wetwell. See section 3.5.2 in order to refresh the conditions for experiment 7.

The initial pressure increase follows the same pattern already seen for experiment 4.

Experimental maximal pressure in the drywell occurred before the blowdown ended, as the

condensation rate equalled the discharge flow. At 910 s the pressure difference was above 0.22

bar providing the opening of the vacuum breakers. The spray cooling introduced at 970 s

increased the depressurization in the containment. The simulated pressure was predicted in

agreement with the experiment for both the drywell and the wetwell. Differences that can be

noted was that the initial pressure build up was predicted to occur earlier and the pressure

decrease to start later in the simulation related to the experiment. The later pressure decrease

provided that the drywell pressure fell behind the wetwell pressure at 890 s and a later valve

opening at 980 seconds. The pressure sequences are further discussed in section 5.1.

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600 700

Spec

ifik

en

thal

ph

y (k

J/kg

)

Time (s)

Enthalphy flow from vessel

Enthalphy from boundary condition

43

Figure 27: Pressure in the drywell and the wetwell during experiment 7.

The clearance of the vent pipes for experiment 7 followed the same sequence already mentioned

for experiment 4. According to the experiment it took 3.5 s to clear the vent pipes while it took

2.0 s in the simulation.

The differential pressure between the drywell and the wetwell can be seen in figure 28. The

differences between the simulated and the experimental curve are related to the same

phenomena mentioned for experiment 4.


0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:WW-MarvikenPR:122-RELAPPR:WW-RELAPPR:122-GOTHICPR:WW-GOTHICPR122-MarvikenPR:WW-COPTAPR:122-COPTA

-40

-30

-20

-10

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400

Dif

fere

nti

al p

ress

ure

(kP

a)

Time (s)

Differential Pressure-RELAPDifferential pressure - GOTHICDifferential Pressure-MarvikenDifferential Pressure - COPTA

44

4.2.2 Air transport

It was first of all the amount of air transported from the drywell into the wetwell that provided

the pressure increase in the containment. According to the calculations in the result report the

initial amount in the drywell was 2180 kg [9]. The simulation predicted the initial amount in the

drywell to be 2200 kg. The air mass in the wetwell during the blowdown is presented in figure 29.

According to the calculations 82 % (1780 kg) of the initial air in the drywell was transported to

the wetwell during the blowdown. From figure 29 it can be seen that the same amount of air was

transported to wetwell during the simulated blowdown and during the experiment. From figure

29 it can also be calculated that during the first 60 s 1160 kg was transported to the wetwell in

the simulation and 850 kg in the calculation, the difference is further discussed in section 5.1. The

reason for the difference was probably related to a more rapid air flow rate in the simulation than

in the experimental calculation. Air flow into the wetwell is presented in figure 30.

Figure 29: Mass of air in wetwell during experiment 7.

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700 800

Mas

s (k

g)

Time (s)

Mass of air in wetwell-GOTHIC

Mass of air in wetwell-Calculated in experiment

45

Figure 30: Simulated mass flow rate into the wetwell for experiment 7. The reason that the calculated air

flow was not included in the graph is that the data was only available as a graph in the Marviken result

report. The graph had many heights and lows, which would give an error in an attempt to reproduce it.

4.2.3 Temperature

Temperature in room 122 and 124 are presented in figure 31 and 32. Figure 33 views that the

simulated temperature followed the saturation temperature, except during the period between

300 and 500 s where superheated steam was predicted. The superheated steam is further

discussed in 5.2.2.


0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25 30 35 40 45 50 55 60

Mas

s fl

ow

(kg

/s)

Time (s)

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:122-Marviken

TV:122-RELAP

TV:122-GOTHIC

TV:122-GOTHIC (vessel)

TV:122-COPTA

46


Figure 33: Views the overheated steam in room 122 during experiment 7.

A comparison between the temperature profile of the concrete structure in the experiment and

simulation can be seen in figure 34. The concrete structure presents the same behaviour already

seen for experiment 4.

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:124-MarvikenTV:124-RELAPTV:124-GOTHICTV:124-GOTHIC (vessel)TV:124-COPTA

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:122-Experiment

TV:122-GOTHIC

ST:122-GOTHIC

47

Figure 34: Temperature in a concrete block with 4 mm steel lining positioned in room 111. The 0 mm

notation means that the temperature was measured at the concrete block surface. The 25 mm that the

temperature was measured at a depth of 25 mm into the concrete structure and 200 mm that it was

measured at 200 mm depth.

Figure 35: Temperature in wetwell water pool for experiment 7.

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

0 mm - GOTHIC 22 mm - GOTHIC

200 mm GOTHIC 0 mm - Experiment

25 mm - Experiment 200 mm - Experiment

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWLiquid-RELAP

TV:WWLiquid-GOTHIC

TV:WWLiquid-GOTHIC (vessel)

TV:WWLiquid (1m) -Experiment

TV:WWLiquid (4m)-Experiment

TV:WWLiquid-COPTA

48

Wetwell water pool and compression space temperatures are presented in figure 35 and 36. The

figures shows the same behavior already seen for blowdown 4 and are further discussed in

section 5.2.3 and 5.2.1. Figure 37 shows the behavior of the heat structures in the wetwell gas

phase.

Figure 36: Temperature in the wetwell compression space during experiment 7.

Figure 37: Views the behaviour of the heat structures in the compression space during experiment 7.

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWVapor-MarvikenTV:WWVapor-RELAPTV:WWVapor-GOTHICTV:WWVapor-GOTHIC (vessel)TV:WWVapor-COPTA

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°c)

Time (s)

TV Steel

TV Concrete

TV:WWVapor-GOTHIC

49

4.2.4 Hydraulic model (without thermal conductors)

Figure 38 and 39 views the effect of the thermal conductors for experiment 7.

Figure 38: Views the effect on the pressure in the wetwell when introducing the thermal structures in the


Figure 39: Temperature in the wetwell compression space when introducing the thermal structures in the


0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:WW-MarvikenPR:WW-GOTHICPR:WW-without thermal conductors

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWVapor-Marviken

TV:WWVapor-GOTHIC

TV:WWVapor-without thermal conductors

50

4.2.5 Vessel model experiment 7

A comparison between the mass flow rate and enthalpy flow used in the original simulation,

measured during the Marviken experiment, and the one predicted by the vessel model can be

seen in figure 40 and 41. The difference in the time when the flow changes from water to steam

are further discussed in section 5.4.

Figure 40: Mass flow from vessel during experiment 7

Figure 41: Enthalpy flow from vessel during experiment 7.

0

500

1000

1500

2000

2500

3000

0 200 400 600 800

Spec

ifik

En

thal

ph

y (k

J/kg

)

Time (s)

Enthalphy-GOTHIC (vessel)

Enthalphy-Marviken

0

100

200

300

400

500

600

700

800

0 200 400 600 800

Flo

w (

kg/s

)

Time (s)

Mass flow - From boundary condtition

Mass flow:From vessel-GOTHIC (vessel)

51

4.2.4.1 3D wetwell

Figures 42 – 47 were obtained by simulations performed with the 3D wetwell model and contains

a comparison between the GOTHIC lumped model and GOTHIC 3D wetwell model. Figure 42 and

43 shows the pressure in room 122 and in the wetwell. In general the pressure follows the same

sequences discussed for the lumped model.

Figure 42: Pressure in room 122 during experiment 7, including the curve from the 3D wetwell model.

Figure 43: Pressure in the wetwell during experiment 7, including the curve from the 3D wetwell model.

0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:122-GOTHIC

PR122-Marviken

PR:122-GOTHIC (3D)

0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:WW-Marviken

PR:WW-GOTHIC

PR:WW-GOTHIC (3D) cell:354

52

The temperature in the drywell simulated with the 3D wetwell model are presented for room 122

in figure 44. The temperature from the 3D wetwell model follows the same curve obtained also

for the lumped model.

Figure 44: Temperature in room 124 for experiment 7, including the curve from the 3D wetwell model.

The wetwell temperature for two levels, measured from the wetwell floor, both in the

compression space and water pool are presented in figure 45 and 46. Note that the values in the

Marviken curve comes from readings of the measured values, which fluctuated a lot.

Figure 45: Temperatures at different levels in the wetwell compression space during experiment 7. The

legend indicates on which level from the wetwell floor the temperature occurred.

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:122-MarvikenTV:122-GOTHICTV:122-GOTHIC (3D)

0

10

20

30

40

50

60

70

0 500 1000 1500

Tem

per

atu

re (

°C)

Time (s)

15 m - GOTHIC (3D)

8 m - GOTHIC (3D)

15 m - Marviken

7 m - Marviken

53

Figure 46: Temperatures at different levels in the wetwell water pool during experiment 7. The legend

indicates on which level from the wetwell floor the temperature occurred.

The liquid level in the wetwell, representing the pool swell during the initial time of the blowdown

can be seen in figure 47. The 3D wetwell model are further discussed in section 5.5.

Figure 47: Liquid level in the wetwell during experiment 7, obtained from the 3D wetwell model.

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWLiquid (1 m)-GOTHIC (3D)TV:WWLiquid (4 m)-GOTHIC (3D)TV:WWLiquid (4m)-ExperimentTV:WWLiquid (1m) -Experiment

4,3

4,4

4,5

4,6

4,7

4,8

4,9

5

5,1

5,2

5,3

0 1 2 3 4 5

Liq

uid

leve

l in

wet

wel

l (m

)

Time (s)

LL:WW-GOTHIC (3D)

LL:WW-Marviken

54

4.3 EXPERIMENT 10

4.3.1 Pressure

For experiment 10 two different simulations was performed due to uncertainties regarding a

leakage in the steam line further discussed in section 5.3. One simulation included the leakage

and one excluded the leakage. The pressure in room 122 and the wetwell are presented in figure

48 and 49. Appendix 8 contains the results for the pressure in room 124 and a comparison

between the Marviken experiment and the simulation for the pressure events in room 122 and

the wetwell. See section 3.5.3 in order to refresh the conditions for experiment 10.

The initially pressure increase follows the same pattern already discussed for blowdown 4 and 7.

As noted earlier, the initial pressure build-up occured faster also for blowdown 10. The pressure

build-up, during the first 45 s, was due to a large transport of air from the drywell to the wetwell

when the main steam line break was open. The closing of the main steam line break provided the

initial pressure drop. The simulated pressure was not predicted in the same good agreement as

for the two earlier simulations which are further discussed in section 5.3. Differences that can be

pointed out was that the simulated wetwell pressure was higher and the pressure decrease after

the blowdown ended occurred faster than for the experiment. The opening of the vacuum

breaker occurred before the opening of the drainage pipe in the simulation but not in the

experiment.

Figure48: Pressure in room 122 during experiment 10.

0

40

80

120

160

200

240

280

320

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:122-Marviken

PR:122-RELAP, with leakage

PR:122-GOTHIC, without leakage

PR:122-GOTHIC, with leakage

PR:122-RELAP, without leakage

PR:122-COPTA, without leakage

55

Figure 49: Pressure in the wetwell during experiment 10.

The clearance of the vent pipes followed the same pattern already presented for blowdown 4

and 7. According to the experiment it took 1.0 s to clear the vent pipes and in the simulation it

took 1.3 s. The differential pressure between the drywell and the wetwell can be seen in figure

50. There was a large difference between the experimental and simulated pressure until the

closing of the main steam line break.


0

40

80

120

160

200

240

280

320

0 500 1000 1500

Pre

ssu

re (

kPa)

Time (s)

PR:WW-MarvikenPR:WW-RELAP, with leakagePR:WW-GOTHIC, without leakagePR:WW-GOTHIC, with leakagePR:WW-RELAP, without leakagePR:WW-COPTA, without leakage

-50

-30

-10

10

30

50

70

90

110

130

150

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

Differential Pressure - RELAP, with leakage

Differential Pressure - GOTHIC, without leakage

Differential Pressure - Marviken

Differential pressure - GOTHIC, with leakage

Differential Pressure - COPTA, without leakage

56

4.3.2 Air transport

It was first of all the amount of air transported from the drywell into the wetwell that provided

the pressure increase in the containment. According to the experimental calculation in the result

report the initial amount in the drywell was 2178 kg [10]. The simulation predicts the initial

amount to be 2200 kg. The air mass in the wetwell during the blowdown is presented in figure

51. According to the experimental calculations 90 % (1960 kg) of the initial air in the drywell was

transported to the wetwell during the experiment. From the figure it can be seen that

approximately the same amount was transported to the wetwell during the simulation.

Figure 51: Mass of air in the wetwell during experiment 10.

In figure 51 it can be seen that during the first 60 s 1850 kg air was transported into the wetwell

in the simulation and 1570 kg in the experimental calculation. The air transport is further

discussed in section 5.1. The reason for the difference was probably related to a more rapid air

flow rate in the simulation than in the calculation, which are presented for the simulation in figure

52.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 60 120 180 240 300 360 420 480

Mas

s (k

g)

Time (s)

Mass in wetwell - GOTHIC

Mass of air in wetwell - calculated in Marviken result report

57

Figure 52: Simulated mass flow rate into the wetwell for experiment 10. The reason that the calculated air

flow was not included in the graph is that the data was only available as a graph in the Marviken result

report. The graph had many heights and lows, which would provide an error in an attempt to reproduce it.

4.3.3 Temperature

Temperature in room 122 and 124 are presented in figure 53 and 54. When the main steam line

break was closed the temperature decreased and then increased slowly until the closing of the

feed water line break.


0

50

100

150

200

250

300

350

400

450

500

550

600

0 5 10 15 20 25 30 35 40 45 50 55 60

Mas

s Fl

ow

(kg

/s)

Time (s)

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:122-MarvikenTV:122-GOTHIC, without leakageTV:122-GOTHIC, with leakageTV:122-RELAP, without leakageTV:122-COPTA, without leakage

58


A comparison between the temperature profile of the concrete structure in the experiment and

simulation can be seen in figure 55. The figure views the same behaviour already presented for

experiment 4 and 7 and are further discussed in section 5.2.4.

Figure 55: Temperature in the concrete block with 4 mm steel lining positioned in room 111. The 0 mm

notation means that the temperature was measured at the concrete block surface. The 25 mm that the

temperature was measured at a depth of 25 mm into the concrete structure and 200 mm that it was

measured at 200 mm depth.

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:124-RELAP, with leakageTV:124-GOTHIC, without leakageTV:124-MarvikenTV:124-RELAP, without leakageTV:124-GOTHIC, with leakage

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

0 mm - GOTHIC 22 mm - GOTHIC 200 mm - GOTHIC

0 mm - Marviken 25 mm - Marviken 200 mm - Marviken

0 mm - RELAP 25 mm - RELAP 200 mm - RELAP

59

The wetwell water pool and compression space temperatures are presented in figure 56 and 57.

The temperature in the water pool has the same trend as already seen for blowdown 4 and 7, the

simulations overestimate the temperature compared with the experiment. The temperature in

the compression space also shows the same behaviour already seen for experiment 4 and 7. The

wetwell temperatures are further discussed in section 5.2.1 and 5.2.3.

Figure 56: Temperature in the wetwell water pool during experiment 10.

Figure 57: Temperature in the wetwell compression space during experiment 10.

0

10

20

30

40

50

60

70

80

90

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWLiquid-RELAP, with leakageTV:WWLiquid-GOTHIC, without leakageTV:WWLiquid (4m) - MarvikenTV:WWLiquid (1m) - MarvikenTV:WWLiquid-RELAP, without leakageTV:WWliquid-GOTHIC, with leakage

0

10

20

30

40

50

60

70

80

90

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWVapor-MarvikenTV:WWVapor-RELAP, with leakageTV:WWVapor-GOTHIC, without leakegeTV:WWVapor-GOTHIC, with leakageTV:WWVapor-RELAP, without leakageTV:WWVapor-COPTA, without leakage

60

61

5. DISCUSSION

5. 1 PRESSURE

The simulated maximum pressure in the drywell as well as in the wetwell was in general predicted

in agreement with the experiment. The good pressure agreement was achieved due to the model

ability to simulate the transport of air from the drywell into the wetwell in similarity with the

experiment.

The simulations were able to reproduce the initially fast pressure increase in the drywell as well

as in the wetwell in rather good agreement with the experiment. However, all the GOTHIC

simulations presented a faster pressure increases in the wetwell as well as in the drywell during

the initial period of the blowdown. This was probably caused by the more open volumes (absence

of obstacle) in the models compared with the real containment facility. In the real facility the

room contents provided friction against equipment in the rooms and provided a delayed pressure

wave. It has been difficult to model and reproduce the inertia and friction of the rooms and

connections in agreement with the one present in the real containment. The open areas provides

the possibilities for a faster transportation of the pressure waves through the volumes and will

therefore transport the air from the drywell more effectively into the wetwell, leading to a faster

pressure increase than measured in the experiment.

The time for the vent pipe clearance agreed quite well with the measurements. But the difference

again points out the difficulties to model the inertia and friction of the system. In several cases it

was difficult to obtain an understanding of lengths etc. used to calculate the flow through the

flow paths. Further knowledge of the actual facility design (primarily regarding flow paths) would

possible provide the ability to create a model that better captures the inertia of the facility.

The simulated depressurization rate after the end of blowdown 4 and 7 was predicted to be lower

than the one in the experiments, providing a later opening of the vacuum breaker in the

simulations. It was not clear how fast the valve opened in the experiment and if it closes again

when the wetwell overpressure again falls below 22 kPa. When the simulated valve had opened

it stayed open until the end of the transient. It is likely that the valve opening sequence in the

simulation does not agree with the real opening process. This provides uncertainties in the

predicted drywell as well as wetwell pressure from the time where the valve opens. The lower

depressurization rate in the simulation, compared with the experiment, was probably related to

62

the condensation rate. The condensation model used in the simulation does not fully predict the

condensation rate in agreement with the one during the experiments. There is several

condensation models included in the GOTHIC code and it is possible that another model would

provide a result closer to the experiments. However, the condensation rate predicted in the

simulation was considered to be a quite good estimation of the one present in the experiments.

In additional the temperature of the structure in the containment affects the condensation rate.

As discussed in section 5.4 the initial temperature of the walls and other structures probably had

a lower value in the experiment than the temperature applied in the simulations.

The simulation for experiment 4 views a pressure drop 80 s from the blowdown start, see figure

10, this cannot be seen in the experiment. The drop can be related to the initial rapid temperature

rise in wetwell and subsequent temperature reduction.

5.2 TEMPERATURE

5.2.1 Temperature in the wetwell compression space

The initial temperature difference between the simulation and experiment in the wetwell

compression space during blowdown 4, see figure 21, are likely related to the accuracy of the

thermocouples used during the experiment. Steam condensation on the thermocouples before

the blowdown start, due to the preheated wetwell pool, provided wet thermocouples with a

delayed response time. It was discussed in the Marviken experiment result report that the wet

thermocouples at the beginning of the blowdown may view a temperature up to 30 °C too low.

The thermocouple assumed to indicate the actual air temperature (dry thermocouple referred to

as 105K537 placed at level 11 m from the wetwell floor) showed a maximum temperature of 78

°C after 90 s [7]. This implies that the temperature in the wetwell atmosphere likely followed a

curve more similar to the one predicted by the simulation. To support the discussed argument

figure 58 shows a comparison including the dry thermocouple measurements.

Experiment 7 and 10 did not contain a preeheated wetwell pool, but an initially higher

temperature then measured during the experiments was still calculated in the simulations, see

figures 36 and 57. In the result report for experiment 7 and 10 it was commented that the

thermocuples had a long response time, providing a to low measured temperature during the

first minute [8] [9]. This would imply that the initial temperature likely followed a curve more

similar to the one simulated also for experiments 7 and 10.

63

Figure 58: Temperature in the wetwell compression space during experiment 4. The blue curve represents

the experimental measurements from a dry thermocouple.

5.2.2 Temperature in the drywell

The overall differences between experimental measurements and simulations for the drywell

rooms was related to superheated steam. For some of the drywell rooms in experiment 4 a

superheated temperature was simulated, even though no superheated steam was measured in

the experiment. This phenomena was also noted for experiment 7, where superheated steam

was simulated during a period between 300 and 500 s in room 122. The superheated steam

phenomena are sensitive and it only takes a small source of water in a room to affect the

existence of the steam and cause a quite large jump in the temperature scale. A water source

may come from condensation providing water drops in a room or from other sources like

ventilation. By slightly adjusting the enthalpy boundary condition after 300 s used in the GOTHIC

simulation for blowdown 7, the superheated steam disappears as seen in figure 59. The slightly

adjustment was 50 kJ/kg. It is possible that the boundary conditions was slightly incorrect

represented for the model, but this seems unclear since the superheated steam was present in

the GOTHIC vessel model as well. Likely would be that a small amount of water was present in

the room leading to absence of superheated steam in the experiment measurements. The

superheated steam may also have occurred during the experiment but it is difficult to be curtain.

0

20

40

60

80

100

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:WWVapor-Marviken

TV:WWVapor-GOTHIC

105K537

64

Figure 59: Temperature in room 122 during experiment 7. The blue curve represents the simulated

temperature for the adjusted enthalpy boundary condition.

5.2.3 Temperature in the wetwell water pool

How well the simulation predicted the amount of steam that condensed in the drywell is

uncertain, it is possible that the simulation overestimated or underestimated the condensation

rate. An underestimation, compared with the experiments, would provide more heat to remain

in the gas phase and being transferred to the wetwell water pool. The consequences from an

underestimation would be a larger amount of energy collected in the wetwell providing a higher

temperature. The temperature rise in the wetwell water pool was mainly caused by the

condensation of steam, and a higher amount would provide a higher temperature. The

simulations calculated a higher water pool temperature than showed in the experimental

measurements, see for example figure 35, which gives the reason to believe that the

condensation rate was underestimated. But it is also important to be aware of that the

differences can be related to the accuracy of the temperature measurements.

Another reason for an underestimation of the condensation rate could be a difference in the

represented amount of thermal structures in the GOTHIC model and the structures present in

the Marviken facility. There is a possibility that all heat sinks present in the facility was not

represented in the design report and therefore not was included in the model. An under

representation of the amount of heat sinks would provide an underestimation of the amount of

steam that condensed in in drywell.

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:122-ExperimentTV:122-GOTHICLower enthalphy after 300 s

65

5.2.4 Concrete structure temperature

From the result of the concrete block temperature comparison a difference in the initial

temperature were noted between the Marviken measurements and the GOTHIC simulations, see

for example figure 19. In the simulations the initial temperature was set in accordance with the

initial room temperature. A lower initial temperature, as seen in the experiment, provided a

different temperature increase in the material. The initial temperature defined in the simulation

would preferably have been set to the temperature measured in the concrete block structures.

5.3 COMMENTS RELATED TO BLOWDOWN 10

After the end of experiment 10 a leakage was mentioned to have occurred in the main steam line

break. It has been difficult to get an exactly understanding of the leakage mass and enthalpy flow,

and due to this two simulations were performed for experiment 10. One case including the

leakage, as estimated in the result report [9], and one case excluding the leakage. The reason that

the simulations for experiment 10 was less consistence with the experiment, than for experiment

4 and 7, are likely related to a wrongly defined mass- and enthalpy flow after the closing of the

main steam line.

After the end of blowdown 10 the pressure descreased more rapidly in the simulation than in the

experiment. The decrease rate was mainly affected by the leakage flow. The experimental

pressure after the blowdown ended was often positioned between the simulated curves with-

and without leakage, see figure 48 and 49. It would probably be possible to find the mass- and

enthalpy leakage providing a better fit to the curve measured during the experiment. This has not

been perfomed, but it provides an explanation for the differences.

The rapid pressure descrease provided an earlier opening of the vacuum breaker at 750 s in the

simulation instead of the experiment opening time at 1060 s. The early opening provided an

increased difference between the simulation and experiment. In additional the simulated

pressure increased at 900 s due to an increased water level in the condensation pool when the

drainage pipe opened, this effect was not seen in the experiment.

5.4 VESSEL MODEL

In general the simple vessel model could reproduce the conditions during the pipe break,

providing results that followed the same pattern seen for the model with the boundary

conditions. For experiment 7 the simulated curve from the vessel model viewed an earlier change

66

of the break flow from water to steam, see figure 40. This was probably caused by the simple

design of the vessel model, not being able to reproduce the condition in the Marviken vessel.

Either the model design provided a faster flow of water out from the vessel or simulated a smaller

amount of water above the break pipe opening in the vessel. Both cases provides an earlier

exposition of the break pipes surfaces to the air in the vessel (see appendix 5 for the break

position) providing an earlier steam flow to the break room.

5.5 3D WETWELL MODEL

In general the 3D wetwell model followed the same pressure pattern as the lumped model, only

small differences were noted. The simulated pressure in the drywell as well as in the wetwell was

expected to show almost an identical behaviour, due to the same amount of air present in the

containment. However, the pressure was not predicted in exactly agreement between the

lumped and 3D model. The different pressure may be related to the difficulties in modelling the

subdivided volume. One cannot exclude that the cause for the difference may also be related to

the lumped modelling approach. A difference between the lumped and 3D wetwell model was

the representation of the thermal structures in the wetwell and also between the drywell and the

wetwell. This was due to different modelling possibilities between a subdivided and lumped

model and can be a reason for the differences.

It was not possible to capture the temperature increase across the different levels in the wetwell

air space with the lumped model approach. However, the 3D wetwell model made it possible to

study the temperature differences. The temperature in the wetwell air space were predicted in

agreement with the experiment, excluding the differences also seen and discussed for the

lumped model.

Only small temperature variations occurred in the simulated wetwell water pool, the

experimental measurements instead showed a more varied temperature between the bottom

and top of the wetwell water pool. The reason that the 3D wetwell model not predicted the

variation in the water temperature in agreement with the one measured in the experiment, was

likely related to an overestimation of the water mass mixture during the simulation.

The lumped model was not able to capture the initial pool swell due to that the whole wetwell

was represented by one node (one volume). The 3D wetwell model was able to reproduce the

pool swell. The height of the pool swell was predicted in good agreement with the measurements

67

from the experiment. The displacement seen between the experiment and simulation in figure

47 are due to the difference in the time for the vent pipe clearance. The simulated vent pipes was

cleared 1.5 s earlier than in the experiment. Shortly after the vent pipe clearance the wetwell

water pool starts to swell due to transport of air through the water.

5.6 MAIN COMMENTS CONCERNING RELAP5 AND COPTA

In general GOTHIC simulations showed a better agreement with the Marviken experimental

results than the RELAP5 simulations. RELAP5 was not able to capture the superheated steam

condition in any room and according to [10] the total amount of air transported from the drywell

into the wetwell was estimated to be greater in the experiments than in the RELAP5 simulations.

In overall the GOTHIC simulations show a better match to the Marviken experimental

measurements than the COPTA simulations. Due to modelling limitations in COPTA the entire

drywell was modelled using only 4 separate nodes possibly influencing the amount of air trapped

in the drywell [12]. In general the COPTA simulations overestimate the maximum pressure

compared with the Marviken experimental measurements and the GOTHIC simulations.

5.7 ACCURACY OF THE MARVIKEN MEASUREMENTS The accuracy of the equipment used to perform different measurements during the experiments

were investigated before, during and after the experiments. Discussions regarding accuracy

related to all measurements can be found in reference 7, 8 and 9. The thesis purpose has not

been to carefully study the accuracy of the measurements during the Marviken experiments. It

has been considered important to obtain an idea of the accuracy of the measurements and due

to this some accuracy results are mentioned in this report.

Discussion regarding accuracy of the measured vessel and discharge pipe conditions are about

pressure, temperature, water level, mass flow and specific enthalpy. When thermal equilibrium

had been established ten of the eleven temperature channels agreed within a range of 1.3°C and

the error limits for the thermocouples were -0.8 to -3.1°C. The pressure measured had an error

limit of ±0.7 bar. The total mass escape from the vessel was calculated by various measurements

inside the vessel and discharge pipes. The mass escape were calculated by two methods and the

estimates for experiment 4 was 36.8 ±2.5 tons and 37.5 ±5 tons, which indicates a good

agreement. The total mass escape were considered to have been estimated quite well, but it is

68

also discussed that the mass flow rates were measured with an error of about 10 %. In the later

phase of the blowdown the error may have been greater due to a smaller discharge flow.

During the experiments a comparison between data from several pressure channels in the

containment, within periods when these data may be considered to represent the same quantity,

were performed to get an estimation of the random errors in the channels. Several comparisons

were performed for the drywell pressure channels after each experiment and most of the

channels showed an agreement around ±0.01 to ±0.05 bar during various times of the blowdown.

The uncertainties of the drywell temperatures are discussed to be within ±2°C. However, as

already discussed in this report for the wetwell temperature accuracy, the uncertainties may be

greater at the beginning of the blowdown due to that the response time of the thermocouples

were strongly dependent on the surrounding medium. The uncertainties of the temperature

channels measuring the water pool temperature were estimated to ±2°C.

The discharge flow measurements for experiment 10 were based primarily on the level probes in

the vessel and the differential pressure measured between the top and bottom of the vessel. The

two measurement system failed during different parts of the blowdown, but together they

covered the whole part of the blowdown. In the result report it was mentioned that the

determination of the discharge flow was more difficult for experiment 10, compared with earlier

experiments, and knowledge obtained from later tests were used to determine the discharge

flow. The discharge flow was anyhow considered to be determined with almost the same

accuracy as for earlier experiments. The estimation of the leakage in the main steam line was in

the result report mentioned to be based on quite unsafe data.

Measurement uncertainties during the Marviken experiments where carefully investigated and

the measurements can in most cases be considered to provide a good conformity with the

experiments reality. Excluding the uncertainties discussed earlier in this section.

69

6. CONCLUSIONS

In this work the thermal-hydraulic calculation software GOTHIC has been evaluated for nuclear

safety analyses. The evaluation has been performed against some of the Marviken full scale

containment experiments and comparison was performed also against the calculation software

RELAP5 and COPTA. Models of the Marviken containment with different complexity has been

developed in GOHIC and used for simulations. In general the GOTHIC simulations show a good

agreement with the Marviken experimental results and in overall a better agreement than the

simulations performed with the RELAP5 and COPTA. The pressures, temperatures and masses of

air were predicted in good agreement with the measured data from the Marviken experiments.

From the results it was possible to conclude that the developed GOTHIC model, according to the

GOTHIC manual, provided a good representation of the Marviken facility.

The GOTHIC model could predict the maximal pressure, which is the primary parameter to ensure

the containment function, in good agreement with the experimental measurements. GOTHIC

predicted the maximal pressure in better agreement than RELAP5 and COPTA.

In all simulations an initially faster pressure increase in the containment, compared with the

Marviken measurements, were obtained. The differences were quite small and are not

considered to affect the evaluation of the containment function significantly.

Differences between the Marviken measurements and the GOTHIC, RELAP5 and COPTA

simulations regarding superheated steam was noted. It was not clarified if the difference was due

to an error in the input data, absence of water sources in the model or in the capability of the

programs to predict the superheated steam. However, the superheated steam contains a

relatively small amount of excess energy and therefore the differences are of limited importance

regarding the containment function.

A significantly higher temperature in the wetwell air space was simulated in GOTHIC, RELAP5 and

COPTA during the first seconds of the blowdown, compared with the Marviken measurements.

However, the most likely reason for the differences were the uncertainty of the measurements

from the thermocouples in the wetwell air space during the Marviken experiments. The GOHIC

simulations were therefore considered to provide a credible picture of the temperature in the

wetwell air space.

70

8. REFERENCES

[1] Statens kärnkraftinspektion (2003). Störningshandboken BWR. 2003. Statens

kärnkraftinspektion. ISSN 1104-1374.

[2] Larsson, R. (2011). Forsmark 1 och 2 -3253 MWt Referens till säkerhetsredovisningen

Beräkningar av högt tryck och hög gastemperatur i reaktorinneslutningen. Forsmark. T-SEKV 05-

017.

[3] Alvarez, H. (2008). Energi Teknik. 3:3. ISBN 978-91-44-04509-2.

[4] Numerical Applications, Inc. (2010). GOTHIC CONTAINMENT ANALYSIS PACKAGE USER

MANUAL. NAI 8907-02 Rev 20.

[5] Blevins, R.D. (1984). Applied Fluid Dynamics Handbook.

[6] The Marviken Full Scale Containment Experiments Containment response to loss of coolant

accident Experiments. Description of the test facility. MXA-1-101.


accident Experiments. Blowdown 4 results MXA-1-204





[10] Facciolo, L & Almberger, T. (2009). RELAP5 Validation vs. Marviken Full Scale Containment

Experiment. T-CKS 08-025.

[11] Numerical Applications, Inc. (2010). GOTHIC CONTAINMENT ANALYSIS PACKAGE

QUALIFICATION REPORT. NAI 8907-09 Rev 12.

[12] Larsson, R. (2013). Simulations of the Marviken Full Scale Containment Experiment using

COPTA. NP-EN 13-34, ver 1.

71

Appendix 1

A containment description for Marviken is shown in figure 1-1 [6]. Room 108 represents the

blowdown pipes. The blowdown pipes are connected to room 106 representing the vent pipe

header which connect to the wetwell, room 105, via 58 nearly identical vent pipes represented

by room 107.

Figure 1-1: Containment description, Marviken facility.

72

Appendix 2

Nodal representation of the rooms in the Marviken containment [6]

Figure 2-1: Nodal representation, Marviken facility [6].

73

Appendix 3

Containment spray system can be seen in figure 3-1 [6].

Figure 3-1: Containment spray system.

The distribution of water to each volume from the main spray line was not directly measured. A

calculation in reference 6 provided a flow distribution according to table 3-1.

74

Table 3-1: Calculated spray water flow.

Spray-line Flow

A 6.3

B1;B2 2*11.7

C 11.7

D 11.7

124 10

During experiment 7 the spray was arranged to introduce water into room 124, 122, 121, 112

and 104. The total spray flow, taken from wetwell, was 52 kg/s and 6 kg/s were introduced in

room 124. The distribution in experiment 7 can be approximated from the distribution in table 3-

1 and are provided in table 3-2.

Table 3-2: Spray water flow in experiment 7.

Spray-line Flow

B1 11.4

B21 5.8

B22 5.8

C 11.5

D1 3.8

D2 3.8

D3 3.8

75

Appendix 4

Data from the Marviken experiment used as boundary condition for the break flows in the

simulations for experiment 4 and 10 are presented in figure 4-1 – 4-6.

Figure 4-1: Break mass flow used as boundary condition in the simulation for Marviken experiment 4 [7].

Figure 4-2: Break enthalpy used as boundary condition in the simulation for Marviken experiment 4 [7].

0

20

40

60

80

100

120

140

160

180

0 100 200 300 400 500 600 700 800

Mas

s fl

ow

rat

e (k

g/s)

Time (s)

2710

2720

2730

2740

2750

2760

2770

2780

2790

2800

2810

0 100 200 300 400 500 600 700 800

Spec

ifik

en

thal

ph

y (k

g/s)

Time (s)

76

Figure 4-3: Break mass flow rate for the feed water line, used as boundary condition in the simulation for

Marviken experiment 10 [9].

Figure 4-4: Break enthalpy for the feed water line, used as boundary condition in the simulation for


0

100

200

300

400

500

0 100 200 300 400 500

Mas

s fl

ow

rat

e (k

g/s)

Time (s)

0

200

400

600

800

1000

1200

0 100 200 300 400 500

Spec

ifik

en

thal

ph

y (K

J/kg

)

Time (s)

77

Figure 4-5: Break enthalpy for the steam line, used as boundary condition in the simulation for Marviken

experiment 10 [9].

Figure 4-6: Break mass flow rate for the steam line, used as boundary condition in the simulation for


0

200

400

600

800

1000

1200

0 10 20 30 40 50 60

Spec

ifik

en

thal

ph

y (k

J/kg

)

Time (s)

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500

Mas

s fl

ow

rat

e (k

g/s)

Time (s)

78

Appendix 5

Figure 5-1 and 5-2 views the break positions in the Marviken facility.

Figure 5-1: Break position in the Marviken facility [6].

79

Figure 5-2: Break positions in the vessel of the Marviken facility [6].

80

Appendix 6

Additional result graphs for experiment 4. Graph 6-1 – 6-3 presents the pressure in room 124,

room 122 and the wetwell. Graph 6-4 shows the saturation temperature in room 124.

Figure 6-1: Pressure in room 124 during experiment 4.


0

40

80

120

160

200

240

280

320

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:124-GOTHIC

PR:124-Marviken

PR:124-RELAP

PR:124-GOTHIC (Vessel)

PR:124-COPTA

0

40

80

120

160

200

240

280

320

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:122-GOTHICPR122-MarvikenPR:122-RELAPPR:122-GOTHIC (Vessel)PR:122-COPTA

81

Figure 6-3: Pressure in the wetwell during experiment 4.

Figure 6-4: Temperature in room 124 during experiment 4. Views that the simulated vapour temperature

drops to the saturation temperature after the blowdown ended.

0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:WW-GOTHICPR:WW-MavikenPR:WW-RELAPPR:WW-GOTHIC (Vessel)PR:WW-COPTA

0

20

40

60

80

100

120

140

160

180

0 200 400 600 800 1000 1200 1400

Tem

per

atu

re (

°C)

Time (s)

TV:124-Marviken

TV:124-GOTHIC

ST:124-GOTHIC

82

Appendix 7

Additional result graphs for experiment 7. Graph 7-1, 7-2 and 7-3 presents the pressure in room

124, room 122 and the wetwell.



0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:124-MarvikenPR:124-RELAPPR:124-GOTHICPR:124-GOTHIC (vessel)PR:124-COPTA

0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:122-RELAP

PR:122-GOTHIC

PR:122-GOTHIC (vessel)

PR122-Marviken

PR:122-COPTA

83

Figure 7-3: Pressure in the wetwell during experiment 7.

0

40

80

120

160

200

240

280

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:WW-Marviken

PR:WW-RELAP

PR:WW-GOTHIC

PR:WW-GOTHIC (vessel)

PR:WW-COPTA

84

Appendix 8

Additional result graphs for experiment 10. Graph 8-1 presents the pressure in room 124, and

graph 8-2 shows a comparison between the Marviken experiment and simulation for the pressure

events in room 122 and the wetwell.

Figure 8-1: Pressure in room 122 and the wetwell during experiment 10.

Figure 8-2: Pressure in room 124 during the transient time for experiment 10.

0

40

80

120

160

200

240

280

320

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kpa)

Time (s)

PR:WW-Marviken

PR:122-Marviken

PR:122-GOTHIC, with leakage

PR:WW-GOTHIC, with leakage

0

40

80

120

160

200

240

280

320

0 200 400 600 800 1000 1200 1400

Pre

ssu

re (

kPa)

Time (s)

PR:124-RELAP, with leakagePR:124-GOTHIC, without leakagePR124-GOTHIC, with leakagePR:124-MarvikenPR:124-COPTA

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