Transient Thermal-hydraulic Simulation of a Small modular Reactor in RELAP 5

This thesis analyzes and evaluates relevant thermal-hydraulic features of the integral pressurized water reactor for a new design of nuclear power plant. The chosen design is the NuScale small modular reactor. This reactor has a thermal power of 160 MW and operates usually with more reactors of its kind in a common power plant. The NuScale design is currently in the licensing process from the Nuclear Regulatory Commission. The first part of this thesis deals with basic knowledge about nuclear fission, SMR technology, and the power plant steam cycle. The second part is about the simulation software RELAP 5, which uses a one-dimensional model to simulate nuclear power systems. It describes how to program the different components, which are needed to simulate the NuScale system. In addition, the two fluid model is introduced which is the basis for the RELAP 5 thermal hydraulic simulations. The final part is about the simulation and the evaluation of the SMR. The NuScale design criteria were looked up in the final safety analysis report, which is used for licensing at the NRC. The results show that the steady state values of the simulation matches with the data from the FSAR of the NuScale design. Therefore it can be said that a reactor, which only runs via natural circulation, works and all the heat which is produced by the core is transferred to the secondary cycle of the SMR. The findings of this thesis confirm the benefits of the NuScale SMR design and suggest further theoretical and later experimental investigations.


7.2
T-S-diagram of an ideal Rankine cycle [21] .  Energy and energy availability are two important topics for the future. Above all is the ever increasing public need for long-term economic and ecological energy supply which has become an ever greater challenge for scientists and engineers in many parts of the world in recent years. Nuclear fission energy production has ensured efficient and clean energy supply in many parts of the world for over 70 years. But even this technology continues to evolve and so in addition to ever larger nuclear power plants, so-called small modular reactors (SMR) are being developed. Not only are these SMRs much smaller in size, they also have much more application potential.
They are also affordable in terms of startup Gst. The goal of these developments are safe and efficient small modular reactors which are designed for much improved safety. These reactors are tested and further developed in thermal-hydraulic simulation models. RELAP 5 is one such of these thermal-hydraulic simulation models and is used worldwide to test many types of nuclear reactors in a cost-effective manner and, importantly, without security risk. In order to perform these simulations, a 1 basic understanding of nuclear energy, SMRs, and thermal-hydraulic must first be aquired in order to analyse the results calculated by RELAP 5. After that, the reactor model is analyzed by comparing RELAP 5 calculated results to design data, hand calculations, and experimental data when available. When the simulations start, the first required series of tests are carried out in order to see how the reactor model behaves in steady state. Then based on these results, various accident scenarios can be carried out and subsequently evaluated. The aim of the simulations are to gain insignt into the behavior of the small modular reactor. ing. Because of their small size, small modular reactors can be used to produce energy in low populated regions like islands, deserts or jungles. These reactors are also an opportunity for developing countries because of the lower investment costs. Also, a well-developed infrastructure is unnecessary for SMRs which is usually needed to run a conventional nuclear power plant. Therefore SMRs are a good, long-term solution to the general energy production for the future. Small modular reactors can be distinguished into four different types: • Integral Pressurized Water Reactors, IPWRs • High Temperature, Gas-cooled Reactors, HTGRs

Integral Pressurized Water Reactors, IPWRs
The neutrons in an integral pressurized water reactor are moderated with light water.
In addition to that, the light water is also used as cooland in the reactor primary cycle.
An IPWR operates at a temperature level of about 300 • C depending on how high the vapor pressure is in the cooling circuit. Enriched uranium (U 235 ) must be used as fuel because of the higher neutron absorption cross section of the water. The enriched uranium causes a greater number of nuclear fissions of the uranium which leads to a higher production of neutrons in the nuclear process. This balances the absorption losses. As shown in Figure 2.1 the reactor includes the reactor core, steam generators, pressurizer and cooling supply lines. All of these components are inside a large reactor pressure vessel. The cooling cycle of an IPWR is powered either from a pump inside the reactor pressure vessel or from natural circulation

Liquid Metal-Cooled Reactors, LMRs
Liquid metal-cooled reactors are cooled by metals such as sodium or lead bismuth as the primary coolant. These metals have high boiling-points and high thermal conductivity, thus they operate at high temperatures of approximately 750 • C and at ambient pressure. The circultion of the metal inside the reactor is powered by electromagnetic pumps or natural circulation. A second cooling system which also uses liquid metal as coolant is installed between the primary cooling system and 5 the stream generators. This safety system is installed so that only non-radioactive metal can react with water in the case of steam generator leakage. All LMRs are fast neutron-reactors thus a moderator is not needed in this system. Liquid metal-cooled reactors use the full energy potential of uranium compared to conventional power reactors which use only one percent of the uranium energy [1] [2][3] [4].

High-Temperature, Gas-Cooled Reactors, HTGRs
High-temperature, gas-cooled reactors are operated with pressures greater than 7 MPa and tempeatures up to 1000 • C, which is higher than in other reactor types. This is possible by the use of gas as the coolant and graphite as the moderator inside the reactor core. The fuel elements consist of graphite into which the uranium, in the form of many smaller coated particles, is embedded. The ceramic coating of uranium particles serves to retain the fission products. Usually Helium is used as the coolant because of high temperatures in the primary reactor system.

Molten Salt Reactors, MSRs
In molten salt reactors, a molten salt which consists of fuel, cooling liquid and fission products, is used to run the nuclear reaction and to transport the produced heat. The molten salt circulates between the core and a heat exchanger. Only in the core is the nuclear moderation triggered by the existing moderating graphite and thus heat 8 energy released. Outside the core the molten salt is subcritical. A second cooling cycle which also uses molten salt is used to transport the heat to the steam generator. MSRs can be operated at temperatures up to 1400 • C. At higher temperatures, the molten salt is unstable [1] [2]. The principle of nuclear energy generation is based on the capture of a neutron by a fissle heavy atomic nucleus (e.g. uranium). By this capture, the nucleus is excited resulting in fission. Products of fission include two fragments (e.g. krypton and barium) and two to three new neutrons. In addition energy is released during the fission process, which is ultimately used to generate electrical energy. This chapter will deal with the basic topics of nuclear energy generation [10][11] [12].

Structure of Atomic Nuclei
To begin with, it is important to consider the components of an atomic nucleus.
Atoms consist of a nucleus and an electronic shell. While the core consists of positively charged protons and neutral neutrons, the shell consists exclusively of negatively charged electrons. Protons and electrons have a mass and an electrical charge, as can be seen in Table 3 The Z-number (number of protons) determines the position of the atom in the periodic table of elements. In the symbol 3.1, it is seen how the numbers of an element can be read [10][11] [12].

Binding Energy
The components of the nucleus are held together with the strong force which works between the nucleons (protons and neutrons) in the nucleus. Between proton and proton, neutron and neutron and neutron and proton, the nuclear strong force is about equally strong. Nuclear strong forces only work at very short distances of less than 2·10 -15 m, but then these are much stronger than all other interaction mechanisms. Binding energy is the energy required to separate the nucleons from the nucleus. The separation of the nucleons requires energy, that means, the sum total 11 mass of nucleons is larger than the mass of the nucleus. As can be seen clearly in Figure 3.1, the binding energy per nucleon in the heaviest atomic nuclei (e.g. uranium) is about 7.5 MeV. It can also be seen that the binding energy per nucleon of uranium is less than the binding energy per nucleon of medium-heavy atomic nuclei, which corresponds to approximately 8 MeV (e.g, Fe-56). For example, if uranium is split into two medium-heavy atomic nuclei, the binding energy per nucleon of the fission products is larger than the uranium nuclus binding energy per nucleon. That means, energy must be released, as shown in Equation From this example, it is seen that energy must be released on the product side of the equation 3.2 to satisfy the equation. On the other hand, it can also be seen that 13 the binding energy has a direct influence on the mass of atomic nuclei. The required energy can now be determined by the theory of relativity [10][11] [12].

Neutron Reactions
In a nuclear reactor, many different neutron-nucleus nuclear reactions occur. In this section, however, only the four most important reactions will be discussed.
• Neutron absorption with nuclear fission Binding energy + Kin. Energy of the last neutron > Critical energy (3.8) In the case of fissile atomic nuclei, the required critical energy is smaller than the binding energy of the last neutron. In the case of atomic nuclei which are fissionable, the binding energy of the last neutron is smaller than the critical enery at the compound nucleus Therefore, the neutron kinetic energy must be larger then the differnce, in order for fission to occur [10] [11] [12].

Cross Section
The cross section is a quantity which determines the probability of a particular reaction of an atomic nucleus upon capture of a neutron. The cross section is dependent on the neutron energy. In Figure 3.2 and 3.3 it is very easy to see the magnitude of a given cross section when a neutron with a certain energy excites an atomic nucleus. As can be seen clearly from the figures, a fission occurs at 235 U even at low neutron energies. For 238 U, a certain neutron energy (velocity) is necessary to trigger a fission or to improve the probability of a fission [10][11] [12].

Moderation
The neutrons generated during nuclear fission have initial energies of approximatly 2 MeV and thus are fast neutrons. Since the fission cross section, is higher in the thermal energy range by several orders of magnitude than the fast range, a moderator is used to slow down the new, fast neutrons by about 7 orders of magnitude on the energy-scale before they trigger new fissions. In the various reactors, graphite and water (light or heavy) are used as moderators. Figure 3.4 shows the three energy ranges in which a neutron can be found [10][11] [12].

Neutron Life Cycle
On the subject of safety it is necessary to consider the neutron generation cycle and the so-called multiplication factor, k, in a nuclear reactor. . This also decreases the number of neutrons. In the end, N·f · η · ε · p · P f · P t neutrons remain in the reactor. The multiplication factor, k, is defined as k=f · η · ε · p · P f · P t and represents the generation cycle of all neutrons present in the reactor. Thus, the power of the reactor is dependent on the multiplication factor k, since when k > 1 more neutrons are available for fission than in the previous cycle. Through different values of k, a nuclear reactor can be divided into three states. In addition to that the so-called reactivity, ρ, represents the deviation from the critical state and is calculated with ρ = 1 − 1 k .
• subcritical: k < 1, ρ < 0 At the various values of the reactivity (ρ), the power of the reactor may either rise (ρ > 0), fall (ρ < 0), or remain at a steady level (ρ = 0). The neutron population is the key factor for control and safety in the nuclear reactor. This is achieved by the control rods in the reactor. The control rods are arranged between the individual uranium fuel elements and can be retracted and extended as required. The control rods are made of cadmium, boron or a similar material that has a high thermal neutron absorption cross section. Thus depending on how far the control rods are extended or retracted into the core of the nuclear reactor, the multiplication factor, k, and the reactivity, ρ, are influenced. In the same way the power of the reactor is influenced.
The energy released during nuclear fission is released as heat energy. This must be transported through the various cooling cycles from the core to the turbine, where it is finally converted into electrical energy via a generator. The control rods regulate the released energy and thus also the total electrical energy production of the nuclear reactor [11] [12].

Conventional Pressurized Light Water Reactors
Pressurized water reactors are the world's most widely used types of nuclear power plants. More than 70 percent of all nuclear power plants are designed as pressurized water reactors. A pressurized light water reactor is a nuclear reactor type which uses water as a coolant and as a moderator. As implied from the name of the reactor, the used water is under high pressure, which has an effect on its thermodynamic properties. In the case of light water reactors, normal water (H 2 O) is used as a coolant, compared with deuterium in heavy water reactors. The rated power of a pressurized water reactor is between 700 MW el and 1400 MW el . The most important component of a pressurized water reactors is the reactor core in which the nuclear reaction takes place. The core is made out of different fuel assemblies, some of  As can be seen very clearly from the figure, the reactor has a total of three circuits for converting the heat energy from the uranium into electrical energy. These three circuits are called: • Primary circuit The primary circuit is located exclusively in a safety container. The separation of primary and secondary cycle is the task of the radioactive contaminated water exclusively within a safety container in the primary circuit. The advantage of this design compared to the boiling water reactor is that no radiation protection measures are necessary in the machine house where the turbines and the generator are located [14][15] [16].

Primary Circuit
The primary circuit consists of the reactor core vessel in which the uranium fuel rods are located, the steam generators, the circulating pumps and connecting pressure pipes between these components. The entire primary circuit is surrounded by a protective cover made of reinforced concrete. The nuclear fission in the reactor core vessel produces heat energy and thereby heats the cooling water of the primary circuit. This heat energy is transported to the steam generator by means of the pumps and the high pressure water. There, the heat energy is transferred to the secondary circuit and the primary cooling water is thereby cooled. Afterwards, the water is fed back into the reactor core and the process begins again.

Secondary Circuit
The secondary circuit is a current clausius rankine power plant process. The water pressure is increased by a feed water pump. Thereafter, the water is directed into the steam generator, in which primary and secondary flow meet. There, the water changes its aggregate state from liquid to gaseous. This steam now drives turbines that are connected to a gernerator, which finally generates electrical energy. In the turbines, the steam is expanded to a lower pressure and is passed into a further heat exchanger in which the steam is again liquefied. The water is then returned to the feed water pump and the process starts again.

Cooling Circuit
The cooling circuit is used to ensure the liquefaction of the cooling water in the secondary circuit and to remove the waste heat which is not usable from the secondary circuit. Cooling circuit and secondary circuit meet at the second heat exchanger.
For this last cycle, cooling water is required, depending on the location of the nuclear power plant, either from the sea or from a river. With the aid of a pump, the cooling water enters the second heat exchanger of the secondary circuit and is subsequently passed into the cooling tower. By this, it is then possible to dissipate the waste heat, which is not usable, into the environment [10] [14][15] [17].

Power Plant Example
The following Table 4.1 shows technical data of a typical pressurized water reactor as it is built around the world.

NuScale Systems
An example of a manufacturer of SMRs is the US-company NuScale. This enterprise is specialized in the design and development of integral pressurized water reactors (IPWRs). The company, founded in 2007, predicts that its technology will be commercially available by the year 2025, and will contribute a large share to clean energy generation [19][20].

NuScale Small Modular Reactor
A NuScale SMR is a integral pressurized water reactor that can operate as a standalone unit or in a system of up to twelve SMR modules. All SMR units of the reactor system are enclosed in a high-strength containment vessel and work in a common pool filled with water, which contributes a great part to the safety of the reactors.
Each vessel is called module and is equipped with its own steam turbine-generator.

33
Due to the small size of the components of the reactor system compared to conventional light water reactors, the reactor, pumps and turbines are easy to transport, install and maintain. The NuScale SMR uses two cooling cycles to convert the heat energy of the core into electrical energy through generators. Each module consists of a reactor core, in which the fission reaction takes place. The reactor core is sur- (ECCS). Generally, the passive safety systems provide for cooling the core, using natural convection, to remove the core decay heat when the normal feedwater sys-35 tem is not available.

Decay Heat Removal System
The decay heat removal system or short DHRS is one of the two passive safety systems of the NuScale SMR. If the normal feedwater system of the secondary cycle is not available, it is possible to cool the reactor using the DHRS. For this purpose, capacitors, which are located on the outer wall of the high-strength containment vessel, are used. It is also necessary to close the valves, which connect the steam generators of the primary cycle to the secondary cycle, and to open the DHRS valves. After opening, the cooling water of the DHRS cycle is able to transfer the 36 decay heat to the capacitors via the steam generators of the primary cycle. These then give the decay heat to the pool, into which the entire reactor vessel has been immersed. Natural convection also plays an important role in this process, since the primary cycle is driven by this process. The DHRS is able to remove decay heat for a minimum of 3 days without pumps or power. Figure 5.2 illustrates the discribeld process of the decay heat removal system in a NuScale SMR works [19][20].

Emergency Core Cooling System
The emergency core cooling system or short ECCS is the second passive safety system of the NuScale SMR. If the normal feedwater system of the secondary cycle or the decay heat removal system (DHRS) are not available, it is possible to cool the reactor using the ECCS. In the head of the core reactor vessel, ventilation valves are installed, which can be opened if necessary and thus lead to a pressure drop in the core reactor vessel. It is also necessary to close the valves, which connect the where it evaporates. Thus, the process can begin anew. This process makes use of natural convection, since it also works without pumps. The difference to the natural convection in normal primary cycle is that here a phase change of the cooling water takes place. But in general, the driving force is the density difference in the different phases of the process. Figure 5.3 illustrates the discribeld process of the emergency 39 core cooling system in a NuScale SMR works [19][20].

Behavior of the Pool
As previously described, each reactor module of an SMR system is submerged in a common pool of water. In this pool, there is water to cool the reactors in accident scenarios for another 30 days after the incident. This is only possible if the water pool is not refilled during this time, which is possible without any problems. For this 40 purpose, it is possible to use rotary pumps. One of the advantages of this design is that the water needed for cooling is present at all times and does not have to be first transported to the reactor. Furthermore, the pool is underground, which is an advantage in terms of extreme events and offers significant protection against earthquakes, floods, tornadoes and aircraft impacts.

Size
The difference in size is one of the main reasons why SMRs have an advantage compared to typical conventional reactors.

Manufacturing Process
Each conventional nuclear reactor is individually planned, licensed, tested and subsequently built, with great effort in a building. This building has to be planned and

Transportation
Another advantage of the small modular reactors is that they can be transported easily. This is made possible by the low weight and the demountability of the SMRs.
In some regions of the world, it is difficult to produce energy or transport energy to

New Applications
In addition, new applications for nuclear reactors are possible with small modular reactors. Large conventional light water reactors have hitherto only been used to generate large scale energy for large cities, densely populated regions and aircraft carriers. In other words, only where there is enough space to build a large reactor.
In addition to that a large body of water has to be near the conventional nuclear power plant due to it large decay heat. Due to the considerably smaller size of an SMR, machines or small regions whose energy requirements are not so high can be supplied in the future. Examples of this are tunnel boring machines, large production plants or countries in Africa whose energy requirements are generally very low. Another factor for these new applications is the lower price of a small modular reactor compared to a conventional reactor [

Safety
Small modular reactors are safer than conventional pressurized water reactors due to their passive safety systems. One of the most important features of the passive safety of an SMR is the natural convention cooling cycle which continues to function even in the event of power or secondary systems failing, to cool the nuclear core of the reactor. In addition, the reactor core of the SMR is surrounded by several safety vessels and the entire reactor is placed in a water pool below the ground level. If an accident occurs during which the pool is completely emptied by the passive safety systems, but the reactor still needs to be cooled with water, the pool can be easily refilled with mechanical pumps and the cooling process can be The Rankine basic cycle can be divided into four primary components.

• Condenser
The construction scheme of the cycle can be seen in Figure    • 1-2, adiabatic isentropic pressure increase by the feed pump Subsequently, the remaining vapor is liquefied again in the condenser so that the working medium again assumes its initial state (point 1). After that the medium is again passed into the feedwater pump. The work done can be read directly from the T-S diagram. The area enclosed by the working curve of a cycle represents the work gained during the cycle. In order to be able to quantitatively evaluate the work achieved, the efficiency (η) of the cycle has to be considered. The efficiency of an ideal Rankine Cycle is defined as follows.
From the given work of the turbine (w 4-3 ), the required work of the feedwater pump (w 2-1 ) has to be deducted in order to determine the net work (w t ) of the process. The advantage of the rankine cycle is the large specific cycle work that results from the high specific volume difference between liquid and vapor.

Real Cycle
In the real Rankine cycle, the feed water pump and the steam turbine are not working ideally. Now these components have an inner efficiency like the rest of the process.
This means that not all the work that these components require is converted. Part of the work involved in operating the feed water pump and the steam turbine is lost inside these components. The losses can be seen in the following T-S diagram 7.3 with an increase of the thermodynamic value entropy. The relationship between ideal and real work of the components is described in the following equations 7.3 and 7.2. water pump must now compress a higher volume resulting in a higher workload and thus a lower efficiency. For turbines on the other hand more volume is available for expansion due to the higher specific volume and thus more work can be generated.
As a result of these processes, the surface area of the area enclosed by the working curve of the cyclic process and thus also the work won and efficiency change. All this can be seen from

Optimization
The rankine cycle can be improved by various operational and design steps. These steps can not only gain more work but also increase the efficiency of the entire cycle.
One of the operational steps is the increase in steam parameters. So the increase of temperature and pressure at the highest point of the cycle. Constructive steps include reheating and regenerative feedwater preheating [23][24].

Reheating
The maximum temperature increase is limited by the thermal capacity of the components, thus an increase in efficiency by increasing the steam parameters is limited.
Reheating can circumvent this fact. In this process the steam is first expanded in a

Nuclear Cycle
In the nuclear energy cycle, the heat generator is the core in which uranium is fis- Exposure to radiation must be reduced by very complex safety systems. In the event of an accident, no radioactive substances or radiation are released into the environment. Consequently, a nuclear power plant emits far less radioactivity than for example a coal power plant as coal contains natural radioactive isotopes that enter the environment from combustion. In addition a nuclear power plant produces After modelling the components for the chosen system or the chosen problem the code has to be input in RELAP. For starting RELAP, a bat-data was written to execute the RELAP5 program with the right input data. This input data is the written code. For example the "Pipe blowdown Problem" . Before the start of the simulation, RELAP checks the code for mistakes, and will not start until every line is correct. If the code is correct, RELAP will start the simulation. It starts with calculating the 64 steady state for the chosen system, or the chosen problem, until everything is in an equilibrium. After that, RELAP runs the code under the given boundaries and parameters. After RELAP has finished its simulations, it saves the data in three files.
One file shows how RELAP has done the simulation, and also contains all simulation errors. The second file is the plot file, which contains all measurement data. This file has to be opened by a special software, called "AptPlot" . This software is able to read the binary file and can create plots for the evaluation. Although, the plot was made in another software, called "Origin" , because this program is specialized to create very complex and exact plots [27][28] [29][30] [31].
9 Thermal-hydraulics in RELAP 5 RELAP 5 uses mathematical models to analyze operational and accident scenarios that can occur in a nuclear fission-based power plant. With RELAP 5, it is possible to describe the physical processes that take place in a nuclear power plant and to analyze and evaluate them at the end. As a model, RELAP 5 uses a set of partial differential equations that can describe and predict certain phenomena in a range of applicability. The prediction capability of the models can be considered as a compelling criterion, because the set of partial differential equations can only describe and evaluate certain scenarios.
The general solution of this set of partial differential equations is very complex and very difficult to solve. An analytic solution of the nonliniear partial differential equations is generally not possible. The most commonly used approach to solving partial differential equations is discretization, thus solving a discretized version of the system.
RELAP 5 simulates the thermal-hydraulic behavior of water and steam in the power 66 plant cycles for the transport of energy generated in the reactor. Despite the benefits of the discrete solution of these systems, some problems with this type of solution must be considered. The solution of discretized equations is subject to errors that must be monitored and solution steps controlled to reduce. Moreover, the interpretation of the results is a more notable problem. It should be noted that RELAP 5 is a mathematical model that is based on physics models to simulate nuclear power plants. As a starting point for the thermal-hydraulic calculations of the systems simulated in RELAP 5, the following space-time-dependent partial differential equations are considered.
• Conservation of Mass

Conservation of Energy
The model represented by these partial differential equations is called a two-fluid model. In this model, each phase (liquid or gaseous) is considered separately and for each phase one of the conservation equations can be established. The model evaluates, compared to other models, thermal-hydraulic non-equilibria between the different phases by its basic equations. As a result, the two-fluid model is precise and can easily solve and evaluate thermal-hydraulic problems very precisely. In general, for the two-fluid model, it can be said that each phase has its own velocity, temperature and pressure. While the different velocities of the phases are caused by density differences, temperature differences between the phases are generally caused by the time delay of the energy transfer between the phases. The pressure difference of the different phases of the two-fluid model is generated by three effects: • pressure differences due to surface energy of a curved interface • pressure differences due to mass transfer • pressure differences due to dynamic effects The first effect is generally caused by the phases, since the simple existence of an interface results in a pressure difference from the total mechanical equilibrium between these phases. The second effect is caused by large mass flows between the phases due to phase change (high evaporation or condensation) at the interface.
Due to the dynamics in which phase A has a greater pressure than phase B due to very rapid energy deposition or pressurization effects, the third effect is finally produced.
In most cases, however, it can be assumed that the pressure in the phases is the same and thus there are no pressure differences. RELAP 5 takes this case in its calculations. From RELAP 5 manual volume 1 "the phasic pressures are assumed equal" [27]. Thus it is assumed: values are Γ k and Γ k . Γ k and Γ k represent the mass transfer rate due to the phase change and the interaction force between the different phases. It can be assumed: The model provides for dividing the mass transfer rate Γ k into two different areas.
On the one hand, the mass transfer rate at the interface between vapor and liquid in the mass of the fluid Γ ik is considered. On the other hand, the mass transfer rate at the interface between vapor and liquid near the walls Γ wk is considered.
• AΓ k υ i = momentum transfer due to interface mass transfer The equation shows that all spatial derivatives of the momentum conservation have been removed, as described above. This special interface momentum balance results from the conservation of momentum for the different phases in equation 9.2.
In addition, for equation 9.7, it is assumed that the interfacial impulse transfer due to friction and due to the mass transfer add independently to zero.
The energy conservation equation represents the temporal and spatial evolution of energy in the simulated two phase system of RELAP 5. In the equation, the following simplifications are surpassed: • Reynolds heat flux is neglected The values for the heat transfer between the phases (Q ik & Q ik ) can also be The heat transfer between the phases in the fluid occurs at the interface between the phases. The heat transfer takes place at the saturation temperature T S and the total pressure P . In the equation for the interface heat transfer H ik represents the interface heat transfer coefficient and T k is the temperature of the phase.
Furthermore, it is assumed that the values of equation 9.9 on wall and between phases sum independently to zero. This can be seen from the next equations 9.12 and 9.13.
In order to determine the mass transfer rate near the walls, Q W ik = 0 is assumed for phase transitions from phase k to phase k and Q W ik = 0 for phase transitions from phase k to phase k. With the equation 9.13 and these assumptions, the mass transfer rates for the phases on the wall are: Through this new expression in equation 9.15 and equation 9.11, the equation 9.10 can be expressed in a new general form: The last value of the energy conservation equation is the phasic energy dissipation term DISS k . DISS k represents the sum of the energy dissipation effects through pumps, turbines or wall friction in the system. Equation 9.16 is shows how the phasic energy dissipation term expresses for wall friction losses. Dissipation effects due to mass transfer between the phases, friction between the phases, or virtual mass are neglected because these are very small in the energy conservation equation.
The losses of the different phases can be summed up again to a total value, as can be seen in equation 9.17.
As can be seen from these equations and the made assumptions, the description of the model that RELAP 5 uses is very difficult, and it is very clear that the phases and the system are interconnected and interact with each other through these partial differential equations [27][32] [33][34] [35].

Natural Circulation
In conventional nuclear power plants, the circulation of the coolant of the primary cycle and the secondary cycle is operated by reactor coolant pumps or by feedwater pumps. The NuScale SMR uses the natural circulation of water in its primary cycle to dissipate its core heat. The natural circulation is generated exclusively by the arrangement of the core (heat source) and the steam generator (heat sink). Natural circulation, in comparison to the principles of conventional circulation methods, has the advantage that no external energy is needed to maintain the cycle. This is a particularly strong safety aspect of a NuScale small modular reactor. This chapter deals with the physical principles of natural circulation [19][36] [37][38].

Physical Principle
The driving force of natural circulation is the density difference of the fluid present in the system. These density differences in the fluid are produced by heat removal on one side and heat supply on the other side of the circuit. The density differences 80 result in a pressure difference in the system, which is also referred to as the driving pressure. In the following equation 10.1, the pressure difference generated by the different densities is shown.
As can be seen very clearly from the equation, the pressure difference depends only on the height to be overcome, as well as the temperature at heat source and heat sink, which leads to the density difference in fluid. By this pressure difference, the heated fluid flows from the heat source to the heat sink. When the natural circulation comes to a closed circuit, there is talk of gravity circulation. With gravity circulation, it should be noted that the heat source must be located lower than the heat sink in the circuit. This is one of the prerequisites that the cycle needs to work.
As the fluid enters the heat source its density decreases. As a result, it rises by static buoyancy in a gravitational field up to the heat sink. At the heat sink heat is removed from the fluid, which leads to a decrease in temperature and thus to higher density. The denser fluid now sinks from the heat sink to the heat source and the cycle begins again.  It is both possible to create a naturally circulating circuit in which the fluid undergoes a phase change, as well as a cycle without phase change. In addition to that, natural circulating circuits can be generated with different materials (e.g. water, liquid metal or gas). Therefore, natural circulation is used in various applications, for example: solar water heaters or furnaces [40][41] [42].

Application in the SMR
As an application example, a small modular reactor with natural water circulation has been selected. In this reactor, the cooling of the core is guaranteed exclusively by natural circulation, that means no pumps are present in the primary circuit. Suppose

RELAP 5 Model of the NuScale SMR
This chapter discusses the exact structure and specific parameters to model the NuScale SMR in RELAP 5. All the important components and parameters needed for the operation of the NuScale SMR will be explained in this chapter. These include: • Core         value is the heat structure number. The card 1CCCG701 determines whether there is a source term in the heat structure or not. The first value is the source type term.

RELAP 5 Pipe/Annulus
A source term is necessary if for example a fuel rod is simulated because in the rod heat is generated due to nuclear fission. If the heat structure simulates a steam generator or a vessel wall no source term is necessary and the value is zero. If the heat structure has a source, the first value is a special table which determinates how much energy over time is generated from the heat structure. The second value of the card is the multiplication factor for every heat structure part. If the generated energy in the whole heat structure has an heterogeneous distribution, with this value it

Valve Junction
In general valve junction components have the capability to vary the flow area. Each valve type has its own input rules, which will not be discussed here. Eight valves out of six types can be chosen in RELAP 5. The types are: • check valves (CHKVLV) • trip valves (TRPVLV) • inertial swing check valves (TRPVLV) • motor valves (MTRVLV) • servo valves (SRVVLV) • relief valves (RLFVLV)

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The input text at the end of this section shows an example for a modeled trip valve.
The first card of a valve junction component is the card CCC0000. The CCC stands again for the junction number and can be chosen variably. The card requires two inputs. The first junction input is the name of the junction, which is also variable, and the word valve, which defines the junction type. The card CCC0101 deals with the     The next sections show the measured values at the specific volumes over the simulation time.

Core
The core in the model is located between component 100 (lower plenum) and com-

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The result is 158.69 MW. This shows the model works and the correct power level is reached.

Steam Generator Primary
The  in the produced power in the core. Therefore the reactor has reached steady state.

Steam Generator Secondary
The steam generator secondary in the model is located between component 760

Optimization
The important parameters for the model are the parameters of the primary cycle.
These are the hot leg temperature, the cold leg temperature, the primary mass flow rate and the primary system pressure. In the model, the secondary mass flow rate, the firctional losses and the steam generator surface had the most impact on the important values. In this section, a variation of the input parametes and their influence on the important output parameters will be presented.
As seen in table 12.2, the manipulation of the input parameters lead to an improvement of the output parameters. The most significant discovery was the relationship between primary system mass flow rate and frictional losses in the primay cycle. One big change, which is not seen in the table, is the rise of the roughness in the riser and in the downcomer of the model. This can be seen in the appendix where the input model is located. The calculated pressure and the hot leg temperature at the last case are exactly the same as in the final safety analysis report of NuScale.
The calculated cold leg temperature and the primary mass flow rate are still higher than expected, especially the mass flow rate is higher than in the final safety analysis report of NuScale.
In addtion to that, it is possible to look up the enthalpies in the thermodynamic steam tables for the exact pressure and temperatures from the NuScale FSAR. Together with the exact mass flow rate from the FSAR, it is possible to calculate the transferred heat in the system. This value is only approximatly 154 MW, expacted was 160 MW. This is a reason why the mass flow rate in the developed model is higher than expected. In RELAP 5 there are plenty of optional cards which could be used to reach the final and expected steady state of the system, but this would be too complicated for this simple model and for this reason the eighth case is the final steady state of the model for the futher development of the model.

Conclusions
The goal of this research was to develop a thermal hydraulic model to simulate the NuScale design small modular reactor with RELAP 5. The first step for this work was to survey design of small modular reactors (SMRs) and technology aspects.
Furthermore, since the simulated NuScale SMR is an integral PWR, the operation of pressurized water reactors needed to be exammed to develop the model. The of this verification was that it was proven that this reactor design works, also when it is only viewed from a physical-mathematical point. The steady state is the basis for all other following accident simulations. In the steady state simulation, it could be verified that the NuScale SMR design as described in the final safety analysis report is consistent. However, it was also discvered that frictional losses play a significant role in the NuScale system balance of mass flow and heat transfer. Also, it was shown that natural circulation only is enough to operate this kind of reactor.
These basis simulations showed the great potencial of the NuScale design and the corresponding developed RELAP 5 model. For future work it will be necessary to improve the RELAP 5 model and program more parts of the whole NuScale SMR system. An example could be the two passive safety systems, DHRS and ECCS.
The addition of these system would give the model a greater complexity and would improve the scope of application. At the end the model could be used to predict and analyse several operation and accident scenarios, which is significant because it would be not necessary anymore to wait for experimental data from hardware reactor models. This would lead to a fast development and would safe time and money. This work will be part of further development of the RELAP 5 Nuscale SMR model.