UPTEC-ES13013 Examensarbete 30 hp Juni 2013
Evaluation of the thermal-hydraulic software GOTHIC for nuclear safety analyses
Linn Bydell
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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
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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.
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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 Lifrom 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.
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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
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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
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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
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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.
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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.
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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].
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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 .
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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].
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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].
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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
Tryck (Pa)
Temperature (°C)
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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].
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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=𝐴4𝑉
𝑤 (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.
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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
√𝐶𝑖
𝑖 (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
𝐿𝐽𝑖
𝑖 (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
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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.
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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)
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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
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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.
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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.
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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.
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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.
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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
Specifik enthalphy (KJ/kg)
Time (s)
0 100 200 300 400 500 600 700 800
0 200 400 600 800 1000 1200 1400
Flow (kg/s)
Time (s)
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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
Temperature (°C)
Conductor thickness (cm)
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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
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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
•
•
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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.
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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
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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.
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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
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Table 8: Initial conditions used in the developed models for experiment 7 [8].
Containment conditions
Drywell pressure 1.01 bar
Wetwell pressure 0.99 bar
Drywell temperatures Room No Temperature °C
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
Wetwell air temperature 105 18.2 maximum
17.3 average
16.0 minimum
Wetwell water temperature 105 20.8 maximum
18.6 average
17.3 minimum
Depth of wetwell pool 4.50 m
Water pool volume 560 m3
Wetwell air volume 1584 m3
Drywell volume 1934 m3
Vent pipe submergence 2.8 m
Number of open vent pipes 57
Vent pipe flow area 4.03 m2
Estimated humidity of the air in:
wetwell 100 %
room 124 4 %
drywell 12 - 37 %
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The sequence of events
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].
Containment conditions
Drywell pressure 1.03 bar
Wetwell pressure 1.03 bar
Drywell temperatures Room No Temperature °C
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
Wetwell air temperature 105 17.5 maximum
16.6 average
15.7 minimum
Wetwell water temperature 105 16.9 maximum
15.7 average
14.4 minimum
Depth of wetwell pool 4.50 m
Water pool volume 560 m3
Wetwell air volume 1584 m3
Drywell volume 1934 m3
Vent pipe submergence 2.8 m
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Number of open vent pipes 57
Vent pipe flow area 4.03 m2
Estimated humidity of the air in:
wetwell 100 % room 124 1 %
drywell 5 - 40 %
The sequence of events
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
