Comparison between RELAP5 and TRACE for modelling different loads on pipe systems during transient conditions

UPTEC F10035

Examensarbete 30 hp Oktober 2010

Comparison between RELAP5 and TRACE for modelling different

loads on pipe systems during transient conditions

Karl Bjorklund

Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

Postadress:

Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Abstract

Comparison between RELAP5 and TRACE for modelling different loads on pipe systems during transient conditions

Karl Bjorklund

This is a M. Eng. degree project at Uppsala University carried out at the Forsmark nuclear power plant in Sweden. The purpose of it is to compare the two codes RELAP5 and TRACE during transient changes in mass flow against experiment. The change in mass flow will create a pressure wave and generate pipe loads. RELAP5 is a transient analysis code used to model thermal hydraulic systems. TRACE is an effort to combine the previous codes TRAC-B, TRAC-P, RAMONA and RELAP5.

Both RELAP5 and TRACE has been compared to experiments. These comprise two abrupt valve closures, the closure of an inertial swing check valve (a flapper disc which closes when the flow is reversed) and a pump start and stop.

Both RELAP5 and TRACE conforms well to the experiments with the abrupt valve closures. The check valve closes faster in the calculations compared to the

experiment, both for RELAP5 as with TRACE. The amplitude of the pressure wave from the closure of the inertial swing check valve is lower compared to the experiment in both RELAP5 and TRACE. Numerical disturbances become visual as very high amplitudes in the time history diagram of the force in TRACE. The check valve oscillates between its open and closed position in RELAP5, but not in TRACE.

Both RELAP5 and TRACE conforms well to the pump start. The mass flow decreases faster in both RELAP5 and TRACE compared to the pump stop.

ISSN: 1401-5757, UPTEC F10035 Examinator: Tomas Nyberg

Ämnesgranskare: Michael Österlund Handledare: Hans Lindqvist

Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

Postadress:

Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Abstract

Comparison between RELAP5 and TRACE for modelling different loads on pipe systems during transient conditions

Karl Bjorklund

Det här är ett examensarbete vid Uppsala universitet utfört vid kärnkraftverket i Forsmark. Syftet är att jämföra de två koderna RELAP5 och TRACE vid snabba förändringar av massflöde mot experiment. Snabba förändringar av massflöde skapar en tryckvåg och ger upphov till laster på rör. RELAP5 används för att göra

termohydrauliska systemanalyser. TRACE är en strävan att kombinera de tidigare koderna TRAC-B, TRAC-P, RAMONA och RELAP5.

Både RELAP5 och TRACE har jämförts mot experiment. Dessa är två snabba ventilstängningar, stängningen av en klaffbacksventil (en ventil som består av en fritt hängande klaff som stänger när flödet går bakåt) och en pump som sätts på och stängs av.

Både RELAP5 och TRACE överensstämmer bra jämfört med experimenten med de snabba ventilstängningarna. Klaffbacksventilen i RELAP5 och TRACE stänger snabbare i beräkningarna jämfört med experiment. Amplituden på tryckvågen efter stängningen av klaffbacksventilen är lägre i både RELAP5 och TRACE jämfört med experiment.

Numeriska störningar blir synliga som höga amplituder i de uträknade lasterna i TRACE. Klaffbacksventilen oscillerar mellan sin öppna och stängda position i RELAP5 men inte i TRACE. Både RELAP5 och TRACE överensstämmer bra jämfört med pumpstarten. Massflödet minskar snabbare i både RELAP5 och TRACE jämfört med pumpstoppet.

ISSN: 1401-5757, UPTEC F10035 Examinator: Tomas Nyberg

Ämnesgranskare: Michael Österlund Handledare: Hans Lindqvist

Contents

1 Introduction 2

2 Literature study 2

2.1 Time step size and Courant number 2

2.2 Calculation of pipe loads 3

2.3 Theory of the inertial swing check valve 4

2.4 Theory of pipe junction loss coefficients 6

2.5 Theory of centrifugal pumps 7

3 Experimental set up and simulations 9

3.1 Case 1 abrupt valve closure 9

3.2 Case 2 abrupt valve closure with an area change 10

3.3 Case 3 and 4 closing of inertial swing check valve 11

3.4 Case 5 start and stop of pump 323P4 13

3.5 Data for pump 323P4 14

4 Results 15

4.1 Case 1 15

4.2 Case 2 16

4.3 Case 3 17

4.4 Case 4 22

4.5 Case 5 25

5 Conclusion and discussion 27

6 References 28

Appendix A – Converting a model from RELAP5 to TRACE and options used in TRACE 29 Appendix B – Orifice and valve diameters and hydraulic resistance models used in system 323 30

1 Introduction

This is a M. Eng. degree project at the Uppsala University carried out at the Forsmark nuclear power plant in Sweden. The purpose of the project is to compare and evaluate the two codes RELAP5 and TRACE during transient changes in mass flow rate against experiment. The change in mass flow rate may originate from the opening and closing of valves, or pipe ruptures etc.

An abrupt change in mass flow rate will create a water hammer. A water hammer is a change in pressure that will propagate as a wave with the speed of sound, reflect whenever it hits an obstacle and eventually vanish due to reflection and friction losses. Water hammers are a major concern when designing pipe systems.

RELAP5 is developed for the U.S. Nuclear Regulatory Commission (NRC) and is a transient analysis code used to model thermal hydraulic systems. TRAC/RELAP Advanced Computational Engine (TRACE) is an effort to combine the capabilities of NRC’s four main system codes TRAC-B, TRAC-P, RAMONA and RELAP5, with the intention to eventually replace them.

The models in RELAP5 and TRACE are built from predefined components such as pumps and valves. The components are connected through pipes, in a one dimensional flow path. The pipes are split into a number of cells, with a junction between each cell. RELAP5 and TRACE solves the continuity equation, momentum equation and energy equation, for each of the two phases liquid and vapour. These are partial differential equations solved using finite volume methods.

Five different cases have been simulated and compared against experiment. Case 1 an abrupt valve closure, case 2 an abrupt valve closure with an area change in the main pipe, case 3 and 4 the closure of an inertial swing check valve and case 5 a pump start and stop.

2 Literature study

2.1 Time step size and Courant number

RELAP5 is primarily designed for non-steady processes with a time scale of seconds. It is not designed for extreme events with abrupt changes in mass flow rate. If such extreme events are considered it is recommended by the developers to choose an appropriate time step size. If the time step size is too small, errors occur in the discrete spectrum. If the time step size is too large there is an unphysical numerical damping. Experience has shown that choosing a time step size so that the pressure wave travel one tenth of a cell length during a time step, creates the best balance between these two errors [15], thus the time step size is calculated from:

c t ∆x

=

∆ 0.1 (1)

where ∆t is the time step size, ∆x is the cell length and c is the speed of sound.

2.2 Calculation of pipe loads

According to Newton’s second law of motion, a force is equal to the change in momentum [16]

∫

=

V

dt dV

d v

F ρ (2)

where the momentum per volume unit is defined as vρ , whereρis the density of the fluid and v is the velocity of the fluid and the momentum per volume unit is integrated over the volume of interest. The objective is to provide an expression of the force as a function of mass flow rate.

Because only one dimension is considered, the densityρ and the velocityv will only depend on the coordinate directed along pipe. Thus the integral in (2) can be written:

) , ( ) , ( ) , ( )

, ( ) , (

0 0

x t A x t v x t dt dx

dA d x t v x t dt dx

F d

L

A L

ρ

ρ

∫ ∫

∫

= (3)

where L is the length of the pipe and A is the inner area of the pipe. From the definition of mass flow, for a steady state flow m& =ρAv, this can be written [15]:

) , (

0

x t m dt dx F d

L

∫

= & _{. (4)}

A pipe load is calculated through control blocks in each time step by taking the average of all mass flows, differentiating this average with respect to time and multiplying it with the length of the pipe. By convention, only half of the mass flow is included at the endpoints. The other half is considered to contribute to the load in the adjacent pipe. This means that the two endpoint

junctions will count as one when taking the average.

In RELAP5 and TRACE the mass flows and forces are scalar quantities, they are either positive or negative depending on the direction of the flow and alignment of the junctions. Therefore, each straight pipe section needs to be considered separately since the only defined direction is along a straight pipe.

Figure 1: A pipe where mass flow is measured at n junctions.

For example, a pipe where the mass flow is calculated at n junctions including the endpoints as shown in Figure 1, the pipe load is calculated from:



 





−

+ + +

= + ⁻

1

5 . 0 5

.

0 _{1 2 1}

n

m m

m m dt L d

F & & K &ⁿ &ⁿ

. (5)

A major concern when calculating pipe loads is the use of numerical differentiation.

Differentiation is a noisy process and discontinuities in the input signal may create spikes in the derivative. The discontinuities may originate from numerical issues. According to the developers numerical differentiation should be avoided if possible [2].

2.3 Theory of the inertial swing check valve

An inertial swing check valve is made up of a flapper disc that swings around a hinge pin inside of a pipe structure, as shown in Figure 2. The pressure difference over the valve governs the position of the flapper disc. When the pressure is higher upstream of the valve compared to downstream, there is a forward flow and the flapper disc is pushed towards its open position.

Likewise, when the pressure is higher down stream of the valve, the flow is reversed and the flapper disc is pushed towards its closed position. This is the purpose of the inertial swing check valve. It should stay open to allow forward flow, and close to prevent backflow. Its usage in nuclear power plants is for example to protect pumps from reverse flow during unexpected pump stops.

Figure 2: The inertial swing check valve, where the torques are shown during a proposed backflow.

The motion of the valve is governed by the angular version of Newton’s second law of motion in both RELAP5 and TRACE. It states that the sum of all torques is equal to the change in angular momentum. For a rigid body rotating around an axis of symmetry, the moment of inertia is a scalar constant and the law can be expressed as

∑

where

∑

rotational axis. In RELAP5 and TRACE only the pressure difference, coulomb friction and weight contributes to the total torque, hence considering only the motion along the rotational axis,

Newton’s second law can be expressed as:

ω^&

I T T T

T_Pj−1+ _Pj + _F + _w= (7)

where a positive angular acceleration will push the valve towards its fully open position and a negative angular acceleration will push the valve towards its fully closed position. When each individual contribution is considered the law can be written as

ω θ θ

θ PA L P A L gmL I ^&

L A

P_{j−1 R} cos − _{j R} cos ±∆ _{Add R} − sin = (8) where θ is the flapper angle, L is the length between the hinge pin and the centre of mass, AR is the flapper area and the cosθ term is due the torque being applied on the projected area of the flapper.

The individual contributions in equation 8 are:

• T_Pj−1 =P_j−1A_RLcosθ the torque due to the pressure in the cell just upstream of the swing check valve, which will push the valve towards its open position.

• T_Pj =−P_jA_RLcosθ the torque due to the pressure downstream the swing check valve, which will push the valve towards its closed position, hence the minus sign.

• T_F =±∆P_AddA_RL the additional torque required to initiate movement due to coulomb friction or other forces acting in the hinge pin. It is assumed that the torque will act in the opposite direction of the movement and be positive when the valve is closing and negative when the valve is opening.

• T_w =−gmLsinθ is the torque due to gravity.

An inertial swing check valve that closes slowly, allows a larger back flow to establish before the flow is stopped, thus creating larger pipe loads. The inertial swing check valve in RELAP5 is from experience known to close too fast, thus underestimating the pipe loads.

2.3.1 Calculation of the moment of inertia for the inertial swing check valve The flapper moment of inertia has been estimated from shapes with known moment of inertias.

The moment of inertia is defined as a rotation around the hinge pin through the parallel axis theorem. A cylinder represents the flapper disc and its moment of inertia is

flapper flapper

flapper

flapper m R m L R L m

I 



 



 +

= +

= ^{2 2 2 2}

4 1 4

1 (9)

where mflapper is the mass of the flapper disc, R is the disc radius and L is the distance between the hinge pin and the centre of mass for the flapper disc.

A rod represents the arm which the flapper disc hangs on, and its moment of inertia is

2 2

2

3 1 2

12 1

arm arm arm

arm arm arm

arm L m L

m L m

I  =



 

 + 

= (10)

where m_arm is the mass of the arm and L_arm is the length of the arm. The numerical values used in both equation 9 and 10 are:

6 . 1

flapper =

m kg

077 . 0

=

L m

051 . 0

=

R m

8 . 0

arm =

m kg

08 . 0

arm =

L m

The total flapper moment of inertia is the sum of flapper and arm moment of inertia.

2.4 Theory of pipe junction loss coefficients

At area changes, pipe bends and orifices, energy is irreversibly lost. This is known as hydraulic resistance, and is not possible to model in one dimension. Both RELAP5 and TRACE provides special models and the possibility to specify loss coefficients. Hydraulic resistance will affect mass flow and thus pipe loads. Loss coefficients are determined by comparing the shape of the obstacle with predefined shapes where loss coefficients have been determined from

experiments [2].

In RELAP5 there are three options when specifying hydraulic resistance. These are a smooth area change, abrupt area change and partial abrupt area change. For a smooth area change, the

hydraulic loss coefficient is entirely specified by the user. For an abrupt area change a loss coefficient is calculated internally by RELAP5 with a possibility to specify additional losses through loss coefficients. The smooth area change has the advantage of giving the user a total control over what loss coefficients to use and the abrupt area change model is suitable for orifices.

The loss coefficients calculated internally by RELAP5 depends on the area of the junction. The partial abrupt area change gives the user the opportunity to use this dependency through the equation

2

min







= 

A Kloss A

Kloss_{jun user} ^jun . (11)

where Kloss_useris the loss coefficient input by the user,A_jun is the area in the junction andA_minis the minimum area of the two nearby cells.

In TRACE it is possible to specify whether additive loss coefficients (FRIC) or K-factors should be used. FRIC coefficients are a left over from the earlier development of TRAC, it is

recommended to use K-factors when a new model is created [3, vol2]. Options available when specifying hydraulic losses are shown in Table 1. The different options in the TRACE manual are described using the FRIC additive loss coefficients rather than K-factors, a convention used here as well.

Table 1: The different hydraulic loss options available in TRACE

0 Constant friction based on FRIC input.

1 Homogenous flow friction factor plus FRIC additive loss coefficient. This is the default option.

-1 Homogenous flow friction plus FRIC input plus a form loss due to an abrupt area change calculated internally by TRACE.

-100 FRIC additive loss coefficient plus form loss from abrupt area change calculated internally by TRACE.

The homogenous flow friction factor is due to wall friction and structure drag and the FRIC additive loss coefficients are specified by the user. The default option is option 1, a homogenous flow friction factor plus FRIC additive loss coefficient. Option -1 is the same as option 1 except for an extra form loss calculated internally by TRACE. The remaining options omit the

homogenous flow friction factor and are recommended when approaching chocking conditions Choked flow occurs when the mass flow becomes independent of the downstream condition. If TRACE and RELAP5 are compared, it is reasonable to believe that option 1 is the TRACE counterpart for a smooth area change and option -1 is the TRACE counterpart for an abrupt area change.

2.5 Theory of centrifugal pumps

This section contains a brief description of a centrifugal pump. The pump contains a rotating impeller located inside a casing. The fluid is forced into the centre of the impeller which discharges the fluid at a higher velocity at the impeller’s periphery through centrifugal force.

Some important pump characteristics include the head H (m), the capacity Q (m³/s), the power P (W), the efficiency η (-), torque τ (Nm) and the impeller rotational speed Ω (rad/s). The head H is the work done by the pump and the capacity Q is the volume of liquid per unit time passing through the pump. The power is given by

gHQ

P=ρ (12)

where ρ is the density of the fluid and g is the standard gravity. The torque is the power divided by the rotational speed of the impeller.

= Ω

= ΩP ρgHQ

τ . (13)

The efficiency is the output power divided by the power of the pump motor

Peng

= P

η . (14)

The pump can operate in four different quadrants; normal, dissipation, turbine and reverse, shown in Figure 3. The quadrant of operation depends on the impeller rotational speed and the mass flow through the pump. When the pump is operating in the normal quadrant both mass flow and

rotational speed are positive and the pump adds energy to the fluid. During the dissipation mass flow is negative while rotational speed is positive and energy is lost. In the turbine quadrant both mass flow and rotational speed are negative and the pump acts as a turbine, withdrawing energy from the fluid. In the reverse quadrant mass flow is positive and rotational speed is negative.

Usually only data for the normal operation quadrant is provided. Data for the other quadrants can be obtained through scaled-down pump tests.

The centrifugal pump is designed to be as efficient as possible at a certain mass flow. In RELAP5 and TRACE the four quadrant curves are input as homologous curves which are dimensionless quantities. They are the actual head, capacity, torque and rotational speed divided by rated values, which correspond to the design point of the pump. The design point is usually (but not

necessarily) where the pump is most efficient. Homologous pump curves are used to avoid two- dimensional arrays and two-dimensional interpolations during computation.

Figure 3: The four quadrants of operation, divided into eight regimes. The horizontal axis is the mass flow Q and the vertical axis is the impeller rotational speed Ω. The design point is indicated by



.

Values at the design point are provided with the pump data. The design point is in the normal quadrant, indicated in Figure 3 with
. The homologues data in RELAP5 is inserted by mirroring the design point in each quadrant, creating eight regimes shown in Figure 3. In total, sixteen homologues pump curves can be inserted, eight for the head and eight for the torque. The curves are based on the normalized head and torque and the normalized rotational speed divided by the normalized mass flow or the normalized mass flow divided by the normalized rotational

speed. [2, 3, 5]

TRACE uses four curve segments rather than eight regimes, these are shown in Figure 4, the difference is simply that the independent value is in the range [-1,1] rather than [0,1]. [3]

Figure 4: The four regions in TRACE. The oblique lines are the same as in Figure 3.

3 Experimental set up and simulations

3.1 Case 1 abrupt valve closure

The first experiment consists of a 100 m long pipe with an inner diameter of 1.09 cm connected in a 90 degree angle to a water reservoir. The experimental setup is shown in Figure 5 and the

geometrical data and boundary conditions are shown in Table 2. The water level in the reservoir was 135 m above the pipe inlet and the pressure above the water surface was atmospheric at 101 kPa. In the other end of the pipe there was a valve with an area of 20 cm². During the experiment it was shown that the pressure measurement had an effect on the result. Therefore a pressure outlet was used during the experiment, modelled as a 2 m long pipe with an inner diameter of 1.09 cm. This pipe was connected in a 90 degree angle to the 100 m long pipe just prior to the valve. The valve faced atmosphere at 101 kPa. The pipes and reservoir were filled with water, the temperature in the system was 293 K. The valve was initially open and closed 0.05 s prior to the initiation of time measurement at 0 s. The valve was modelled as a motor valve and the valve change rate was set to 11 s^-1, which is equivalent to a closing time of 0.091 s. The cell length was roughly 1 m. see ref [6].

Figure 5: The experimental setup for the first experiment. The pressure is measured just prior to the valve.

Table 2: Geometrical data and boundary conditions for the first experiment with an abrupt valve closure

Pipe length (m) 100

Pipe inner diameter (cm) 1.09

Water level in reservoir tank (m) 135

Valve area (cm²) 20

Valve closing time (s) 0.091

Pressure at outlet (bar) 1.01

Temperature (K) 293

3.2 Case 2 abrupt valve closure with an area change

The second experiment consists of two 100 m long pipes. The experimental setup is shown in Figure 6 and the geometrical data and boundary conditions are shown in Table 3. The first pipe was connected in a 90 degree angle to a water reservoir, and the second pipe was connected in series with the first pipe. The first pipe had an inner diameter of 1.09 cmand the second pipe had an inner diameter of 0.78 cm. The water level in the reservoir was 133 m above the first pipe inlet and the pressure above the water surface was atmospheric at 101 kPa. A valve was placed in the other end of the second pipe with the area 10 cm². The pressure outlet was modelled as a 2 m long pipe with an inner diameter of 1.09 cm.This pipe was connected in a 90 degree angle to the second pipe just prior to the valve. The valve faced atmosphere at 101 kPa. The pipes and

reservoir were filled with water, the temperature in the entire system was 293 K and the valve was initially open and closed 0.05 s prior to the initiation of time measurement at 0 s. The valve was modelled as a motor valve and the valve change rate was set to 17 s^-1, which is equivalent to a closing time of 0.059 s. The cell length was roughly 1 m. see ref [6].

Figure 6: The experimental setup for the second experiment. The pressure is measured just prior to the valve.

Table 3: Geometrical data and boundary conditions for the second experiment with an abrupt area change on the main pipe

Total pipe length (m) 200

The first pipe, inner diameter (cm) 1.09 The second pipe, inner diameter (cm) 0.78 Water level in reservoir tank (m) 133

Valve area (cm²) 10

Valve closing time (s) 0.059 Pressure at outlet (bar) 1.01

Temperature (K) 293

3.3 Case 3 and 4 closing of inertial swing check valve

Two different experiments considering closing of an inertial swing check valve was performed at Westinghouse in 1973 see ref [7,9]. The purpose of the experiments was to see and understand the behaviour of a swing check valve during a pipe break. These experiments have been compared with calculations. The difference between the two cases was the pressure in the tank, 75 bar and 10 bar respectively. The experimental set up is shown in figure 7. The pipe break exposed the system towards the outside atmosphere reducing the pressure upstream of the valve and closed it.

Inertial check valves in RELAP5 have shown inaccurate results where the valve closes too fast and shows oscillating behaviour. The purpose with the simulations is to confirm if TRACE provides more accurate results than RELAP5.

Figure 7: The experimental procedure for inertial swing check valve. The pressure is measured 1.3 m prior to the valve.

The experimental model consists of a 18.3 m long main pipe connected to a 1.8 m long bended pipe. The bended pipe was connected to a 0.5 m³ large tank that was filled with water to 2.66 m above the main pipe. The space above the water level was filled with nitrogen. The check valve was located 17.3 m from the tank. To simulate the pipe break, two rupture discs where

implemented upstream the check valve. These were broken by increasing the pressure between the discs. This was modelled in the simulation with a trip valve (a valve which opens abruptly at a certain predefined time), located one meter from the inertial swing check valve. After the rupture discs, there was a pool-like structure modelled as a three meter long pipe, which discharged into atmosphere at 101 kPa. All the pipes had the inner diameter 0.1053 m, the inertial swing check valve had the diameter 0.0954 m, and the trip valve had the same diameter as the pipe 0.1053 m.

The entire system was at the temperature 293 K. The pressure difference or the additional pressure∆P_Add required to move the valve was calculated from an experimentally known Coulomb friction using the last term in equation 8. The cell length was roughly 0.5 m. The geometrical data and boundary conditions are shown in Table 4 and the properties used for the inertial swing check valve are shown in Table 5.

Table 4: Geometrical data and boundary conditions for the experiments with the inertial swing check valve.

Pressure in tank (bar) 75 and 10^*

Tank volume (m³) 0.5

Pipe length (m) 18.3

Water level (m) 2.66

Inner pipe diameter (m) 0.1053 Pressure at outlet (bar) 1.01

Temperature (K) 293

* Two experiments have been simulated. The experimental setup was identical but the pressure in the tank differed.

Table 5: Properties used for the inertial check valve

Additional pressure ∆P_Add (Pa) 15586

Leak fraction 0

Initial flapper angle (deg) 65

Minimum angle (deg) 0

Maximum angle (deg) 65

Flapper inertia I (kgm²) 0.0122335 Initial angular velocity (rad/s) 0

Moment length L (m) 0.077 Flapper radius (m) 0.051

Flapper mass (kg) 1.6

Area (m²) 0.0954

3.4 Case 5 start and stop of pump 323P4

Subsystem four of system 323 has been modelled for Forsmark 1 and 2. System 323 is an emergency core cooling system and is meant to protect the reactor core from overheating. It contains four independent subsystems, where each sub contains a pump with the ability to pump water from a condensation pool into the reactor vessel. Figure 8 shows a simplified flow chart of the modelled subsystem.

Figure 8: A simplified flow chart of system 323, as it is shown in SNAP, for a RELAP5 model.

There are several orifices and motor controlled valves throughout the system which will reduce and control the flow. Valve 401 and 409 are controllable valves that make it possible to isolate the condensation pool from the system. V402 is an inertial swing check valve meant to protect the pump P4 from reverse flow. K304 is a flow measurement device and V418 is an orifice that reduces the flow. Two pipelines are able to lead the fluid back into the condensation pool. One of the routes is through the valve V407, which is used during pump tests. The other route goes through the three orifices 410.93, 410.94 and 410.95, which are dimensioned so that the mass flow through this pipe is roughly 20 kg/s. The two pipelines reunite before valve V414, where the flow is lead through the orifice V408 into the condensation pool. The remaining pipeline leads into the reactor vessel, where V404 is a controllable valve and V405 is an inertial swing check valve. Details concerning the valves and orifices are shown in Table 7 in Appendix B.

Reactor vessel

Elevation is measured from a datum at sea level plus an additional 100 m, in order to avoid negative numbers. Some heights which might be of interest, to comprehend with the size of the system, the pump is at 98.550 m, valve V404 is at 126.217 m and V410.93 is at 106.490 m. Hence it is roughly 28 m between the pump and valve V404. The water level in the condensation pool was at 112.275 m. The space above the water level is filled with nitrogen. The pressure above the water level in the condensation pool was atmospheric at 101 kPa and the temperature in the entire system was 293 K. The cell length was roughly 0.3 m. [8, 10, 11]

3.4.1 Pump start

A pump start has been modelled based on a pump test made on September 19, 2007 in Forsmark.

This test did not include a pump stop. Thus an earlier pump test made on subsystem one was used to provide experimental data for the stop. The subsystems are assumed to be similar enough and the start and stop are independent of each other. Before the pump was started all the valves were open except valve V404 which was closed during the entire pump test, thus no flow was pumped into the reactor vessel.

3.4.2 Pump stop

When modelling the pump stop, the inertial swing check valve V402 located after the pump needs to be considered. It is assisted with a spring. A spring will usually make sure that the valve closes faster, preventing large backflows to establish and thus reducing the loads on pipes and other components. Neither the default configuration of RELAP5 nor TRACE provides the opportunity to model spring assisted inertial swing check valves. The closing characteristics of the valve have a major impact on the change of mass flow during the pump stop. Therefore the valve has been modelled as a motor controlled valve, with a prescribed closing time. An analysis of the drawing of the valve suggests that the valve might close linearly since the spring is attached behind the valve [14]. Therefore the controlled valve was modelled to close linearly with time.

3.5 Data for pump 323P4

The rated values used when modelling the pump in system 323 are shown in Table 2. The rated motor torque has been calculated from a known rated power output of 200 kW divided by the motor rotation speed 312.7 rad/s according to equation 13. The moment of inertia is the sum of the motor and the impeller moment of inertia obtained from the pump data. The pump curves and the pump motor start curve are shown in Figure 28 and 29 in Appendix C. [13]

Table 6: The rated values and the moment of inertia used for the pump

Rated velocity (rad/s) 311.54 Rated flow (m³/s) 0.126

Rated head (m) 117

Rated torque (Nm) 464.7

Moment of inertia (kgm²) 5.25 Rated motor torque (Nm) 639.8

4 Results

4.1 Case 1

Figure 9 shows the pressure wave from the first experiment, measured just prior to the valve. The black line is data from the experiment, the red line is the result from RELAP5 and the blue line is the result from TRACE. The valve is initially open and closes 0.05 s prior to the initiation of the time measurement at 0 s with a closing time of 0.091 s. The closing time was chosen to best predict the experimental result, since no closing time experimental data was available. Once the valve closes, mass flow is abruptly decelerated and a pressure wave is created. The wave will reflect in the tank and propagate back and forth between the tank and valve, with decreasing amplitude due to reflection and friction. It should be noted that a small difference in amplitude exists between RELAP5 and TRACE. In RELAP5, a full abrupt area change model has been used and the [-100] option has been used in TRACE. The amplitude difference is probably due to a difference in hydraulic losses between these two models. Using the default option [-1] including the homogenous flow friction factors resulted in a low mass flow, thus creating a pressure wave with a lower amplitude than experiment.

Figure 9: The pressure wave from the first experiment, the pressure is measured just prior to the valve.

Figure 10 shows the pipe load on the horizontal pipe for case 1. The higher amplitude in TRACE compared to RELAP5 is explained by the slightly higher mass flow through the valve in TRACE compared to RELAP5.

Figure 10: The pipe load as a function of time on the horizontal pipe in the experiment with an abrupt valve closure.

4.2 Case 2

Figure 11 shows the pressure wave from the second experiment, measured prior to the valve. The distinction compared to the first experiment is the area change, at the middle of the pipe. It will reflect some of the pressure wave back towards the valve. The valve is initially open and closes 0.05 s prior to the time measurement at 0 s with a closing time of 0.059 s. The closing time was chosen to best predict the experimental result, since no closing time experimental data was available. As shown in Figure 11 the reflected wave from RELAP5 and TRACE returns

approximately 0.023 s later than the experiment. This implies that there might be some difference in the speed of sound or pipe length between RELAP5, TRACE and the experiment.

Figure 11: The pressure wave from the second experiment, the pressure is measured just prior to the valve.

Figure 12 shows the pipe load on the horizontal pipe with an area change. The amplitude of the pressure wave conforms well between RELAP5 and TRACE.

Figure 12: The pipe load as a function of time on the horizontal pipe in the second experiment with an abrupt valve closure and an area change along the pipe.

4.3 Case 3

Figure 13 shows the pressure wave from the inertial swing check valve with a 75 bar tank during a 15 s. long calculation. At 6 ms the disc upstream of the valve is cracked, thus inducing a pressure difference over the pipe and allows a mass flow through the system. The pressure difference will

close the inertial swing check valve. Experimental data is only available for 0.18 s. The interesting information in Figure 13 is the difference between RELAP5 and TRACE. In RELAP5 new

pressure waves are created during approximately 5 s. with a frequency of 2 Hz. This behaviour is not seen in TRACE.

Figure 13: The pressure wave from the inertial swing check valve when time is measured for 15 seconds

The valve opening area is shown in Figure 14 with the experiment indicated with crosses. The inertial swing check valve oscillates between its open and closed position in RELAP5 but not in TRACE. It should be noted that both RELAP5 and TRACE provides the option to use a latched valve. That is imposing a constraint on the valve so that once it is closed it should never open again. This option has not been used, neither in RELAP5 or TRACE.

Figure 14: The valve opening area as a function of time, when time is measured for 15 seconds.

Figure 15 shows the pressure wave from case 3 compared to experiment. Some of this wave is reflected against the check valve; this is shown in figure 15 as a small step during the initial pressure drop.

Figure 15: The pressure wave from the closure of the inertial swing check valve, with a 75 bar tank. The pressure is measured 1.3 m prior to the valve.

Neither the results from RELAP5 nor TRACE conforms well to the experiment. This is due to the shorter closing time of the valve compared to the experiment. The closing time is shown in Figure 16. The short closing time will not allow the mass flow rate to increase enough for a pressure wave with the right amplitude to form. A modification to the closing time can be done by changing the moment of inertia of the valve, since an increase of the moment of inertia will decrease the valves angular acceleration according to equation 6. When a multiplying factor of approximately 8 for TRACE and 12 for RELAP5 was used on the moment of inertia, the closing time and pressure wave conformed better to experiment. The result from this modification is shown in figure 17 and the closing times from the modified moment of inertia are shown in figure 16.

The valve closes too fast because the model does not take into account the surrounding fluid.

Whenever an object is accelerated through a fluid the object will displace the fluid, since they cannot occupy the same space. Therefore the force accelerates both the object and the fluid. The additional inertia compared to if the object would have been accelerated through a vacuum is known as an added mass or virtual mass. [9, 16]

Figure 16: The valve closing time for both the unchanged and changed moment of inertia. The black line is the experiment, the blue and red line is obtained when using experimental data and the green and purple line is

the closing time with a changed moment of inertia.

Figure 17: The pressure wave from the closure of the inertial swing check valve, with a changed moment of inertia (note: this is a result based on unphysical data).

Figure 18 shows the pipe load on the horizontal pipe in case 3. The pipe loads calculated with RELAP5 and TRACE are in good agreement until around 0.065 s. At this time the loads come out of phase, but still have roughly the same amplitude. This may be explained by some difference in the tank between the two models that causes the wave calculated by TRACE to return earlier compared to RELAP5. This phase difference between the two codes is also shown in the pressure wave in figure 15. There are spikes in the pipe loads calculated by TRACE, spikes are usually explained by discontinuities in the input signal. No discontinuities have been found in the mass

flow, thus it is unclear why spikes occur in TRACE but not in RELAP5. It was possible to remove the second and the third spike by decreasing the time step size.

Figure 18: The pipe load as a function of time on the horizontal pipe

Figure 19 shows the first spike presented in Figure 18. Each time step is indicated by a circle. The large initial pipe load in TRACE occurs during more than one time step. The choked flow model in TRACE was set to the default multiplier, option 1. However the TRACE ASCII file exported from SNAP notes that no choked flow checking will be performed. Choked flow occurs when the mass flow becomes independent of the downstream condition. There might be some difference in the choking models that explains the large initial pipe load in TRACE compared to RELAP5.

Figure 19: The pipe load as a function of time on the horizontal pipe

Figure 20 shows the third spike in Figure 18. Each time step is indicated by a circle. The pipe load increases to around eight times in magnitude in one time step. This is a typical behaviour

whenever discontinuities are present in the mass flow. It should be noted that the pipe load is positive in TRACE and negative in RELAP5, this is because the different signals are out of phase as shown in figure 18.

Figure 20: The pipe load as a function of time on the horizontal pipe

4.4 Case 4

Figure 21 shows the pressure wave from inertial swing check valve with the 10 bar tank.

Figure 22 shows the closing time, both RELAP5 and TRACE closes faster than the experiment.

The rapid closing time explains why the amplitude of the pressure wave in both RELAP5 and TRACE is lower compared to the experiment, because not enough backflow has been established before the valve is closed. This also causes the pressure to increase earlier compared to

experiment for both RELAP5 and TRACE, which in turn causes the wave to return earlier. As shown in Figure 21, the pressure wave in TRACE is behind the pressure wave in RELAP5. This could be due to the different closing characteristic between RELAP5 and TRACE and a difference in the way the tank is modelled. Experimental data for the reflected wave was not available thus it was not possible to compare the reflected wave to the experiment. It should be noted that attempts have been made to modify the moment of inertia and increase the closing time. However the result was not as much in agreement with the experiment compared to the 75 bar tank, though a multiplying factor of approximately 25 would increase the closing time and a better resemble to the experiment. Thus, different pressure drops requires a different multiplying factor on the moment of inertia.

Figure 21: The pressure wave from the closure of the inertial swing check valve, with a 10 bar tank. The pressure is measured 1.3 m prior to the valve.

Figure 22: The valve opening area as a function of time

The experimental setup with the 10 bar tank has been modelled during a longer calculation time compared to the experiment, see Figure 23. Again the valve in RELAP5 oscillates rapidly between its open and closed position while TRACE does not. However the TRACE valve does actually open slightly just prior to 0.2 s. indicating that it is at least capable of opening once it has been closed. In Figure 23, each time step is indicated by a circle, this shows that the valve opening and closing proceeds over many time steps.

Figure 23: The valve opening area as a function of time

Figure 24 shows the pipe load from the experiment with the inertial swing check valve with a 10 bar tank.

Similar to the experiment with the 75 bar tank, there is initially a large load on the pipe in TRACE but not in RELAP5. After this initial difference the load conforms well to each other until the valve closes where the waves are out of phase. The amplitude of the pipe loads is similar. The strange behaviour after 0.1 s.

might be due to something occurring during the reflection in the tank.

Figure 24: The pipe load as a function of time on the horizontal pipe in the experiment with the inertial swing check valve with the 10 bar tank.

4.5 Case 5

Figure 25 shows the mass flow as a function of time from the pump start and stop. The pump is started at 195.07 s. and valve V404 is closed during the entire test, thus no flow is pumped into the reactor vessel. Valve V407 is initially open and closes at 262.71 s. with a closing time of four seconds. Once valve V407 is closed the entire flow is lead through the orifices 410.93, 410.94 and 410.95. until the pump is stopped at 354 s. The inertial swing check valve v402 is closed at 354 s.

with a closing time of 0.73 s. The mass flow in the experiment is measured at the measurement device K304, unlike RELAP5 and TRACE where it is measured through the pump. This is not a concern, since there are no diverging flow paths between the pump and the point of measurement.

Figure 25: The mass flow through K304, measured during a pump test.

There is a relationship between motor torque and impeller rotational speed, which is used in RELAP5 to govern the acceleration of the pump during the pump start. When data for this relationship was used, the pump did not accelerate as fast as the experiment. Therefore an extra factor of approximately 2.3 was used too increase the acceleration and better predict the

experimental result. In TRACE there are restrictions in the current version of the pump (TRACE 5.0p1) [3, vol2]. There is currently no relationship between motor torque and impeller rotational speed included in the TRACE pump. The rotational speed is instead assumed to be input by the user when the pump is started. Thus data for the impeller rotational speed has been taken from the result provided by RELAP5 and used in TRACE. This explains why the impeller rotational speed in TRACE is identical to RELAP5 as shown in Figure 26. It also explains why the mass flow in TRACE is in such good agreement with that of RELAP5 in Figure 25. There is a deviation in mass flow between the start of the pump and the closing of valve V407; this is explained by a difference in the modelled pipe junction losses between RELAP5 and TRACE, but it is not possible to draw any conclusion from this difference.

Figure 26: The rotational speed of the pump impeller.

Figure 27 shows the mass flow through the flow measurement device K304 during the pump stop.

It is the same pump test as shown in Figure 25 but with an emphasis on the pump stop. The pump is stopped at 354 s. The inertial swing check valve is closed at 354 s. with a closing time of 0.73 s.

RELAP5 and TRACE conform well to each other, explained by the identical pump impeller rotational speed. However neither RELAP5 nor TRACE conforms well to experiment. The mass flow from the pump test decreases much slower compared to RELAP5 and TRACE. This might be explained by a larger inertia in the real pump compared to RELAP5 and TRACE.

Figure 27 The mass flow through K304, measured during the pump stop.

5 Conclusion and discussion

A comparison between RELAP5 and TRACE against experiment has been made. These are two abrupt valve closures, the closure of an inertial swing check valve and a pump start and stop. The conclusions from the comparison are:

• Both RELAP5 and TRACE conform well to the experiments with the abrupt valve closure.

• The inertial swing check valve closes faster compared to the experiment in both RELAP5 and TRACE. The closing time is similar between RELAP5 and TRACE.

• The amplitude of the pressure wave from the check valve closure is lower in both RELAP5 and TRACE compared to the experiment. The amplitude is similar between RELAP5 and TRACE.

• Numerical disturbances become visual as very high amplitudes in the time history diagram of the force in TRACE.

• The check valve oscillates between its open and closed position in RELAP5 but not in TRACE.

The inertial swing check valve in RELAP5 oscillates rapidly between its open and closed position but not in TRACE. The following attempt to explain it is only speculative. It is possible to use pressure difference as an input signal to govern the opening and closing of valves in TRACE.

When doing so, rapid pressure fluctuations might cause the valve to “chatter” [3, vol2]. A recommended procedure to avoid this behaviour is to specify set point delays. That is a certain time that the condition has to remain at its value before the status of the trip, governing

movement, is changed. It is possible that there are set point delays built into TRACE. If this is the case, rapid pressure fluctuations may not affect the movement of the inertial swing check valve.

The inertial swing check valve closes faster than experiment in both RELAP5 and TRACE

because the model governing its movement is too simplified. A more detailed analysis of the fluid condition in the valve is required in order to implement an improved model. This could be

obtained through three dimensional CFD calculations, or experiments, or a combination of both.

Although it should be possible to present a model that is able to predict the closure of one inertial swing valve. An inertial swing check valve is only one component in a larger system, therefore it might be of interest to test a system with many inertial swing check valves for further validation.

Things that could be considered during future studies of TRACE include:

• A more detailed analysis comparing the hydraulic resistance models in RELAP5 and TRACE. Correctly modelling hydraulic resistance is important when calculating pipe loads, since it will affect mass flow. This report does not include any precise answers concerning the behaviour and difference of the hydraulic resistance between the codes.

• Investigating the possibly to find alternative ways to calculate pipe loads using a safer numerical differentiation or avoiding differentiation altogether.

• The pump should be tested when or if a relationship between torque and angular velocity is included in the model. The model of the pump is not enough to validate the pump in TRACE since it was modelled using data from RELAP5.

6 References

[1] G.K. Batchelor, An introduction to fluid dynamics, Cambridge University Press, 1973.

[2] RELAP5/MOD3.3 Code Manual. Volumes 1-8. December 2001 Information Systems Laboratories, Inc. Rockville, Maryland, Idaho Falls, Idaho. Prepared for Division of Systems Research, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, Washington, DC 20555.

[3] TRACE V5.0 USER’S MANUAL, Division of Risk Assessment and Special Projects Office of Nuclear Regulatory, Research U. S. Nuclear Regulatory Commission Washington, DC 20555-0001.

[4] Frederick J. Moody, Introduction to unsteady thermofluid mechanics, John Wiley &

sons, 1990.

[5] Igor J. Karassik, William C. Krutzsch, Warren H. Fraser, Joseph P. Messina, Pump Handbook second edition, McGraw-Hill International Editions, 1986.

[6] Lennart Jönsson, Peter Larsen, Kompendium i instationär strömning, Institutionen för teknisk vattenresurslära Lunds Tekniska Högskola, 1975.

[7] Nordgren, Experimental investigation of pressure transients, created by a closing check valve, in the reactor auxiliary systems after a postulated pipe break outside the containment, ASEA-ATOM, 1973.

[8] Anders Surén, Forsmark 1 och 2 - system 323. Borttagande av härdstril -

Dimensionering av strypningar 323V118-418. FT-2002-784FT-2002-784, 2003.

[9] Baltyn Wojtek, Modifiering samt validering av RELAP5s modell för klaffbackventil mot experiment KVB 73-473, FT-2010-0047, 2008.

[10] Isometries, Babcock, Teilstück/Part of 323-BCA,BAA,EBB,EDB,FDB-4 1975.

[11] Forsmark 1 FSAR/323-4.

[12] Andrew Pytel, Jan Kiusalaas, Engineering Mechanics Statics & Dynamics, 1996.

[13] ASEA-ATOM nr 5 LQ 1949/323 p 1-4, KS 77-TS 057 K/1, Motor specification, Pump specification, 1975.

[14] Persta Stahl-Armaturen Persta GmbH, Ruckschlagkluppe PN 40. DN 200 mit Schliessfeder-Vorrichtung ongeschraubt am Gehause.

[15] Olof Björndal, Adam Letzter, Jerzy Marcinkiewicz, Peter Segle, Inspecta

forskningsrapport – Rekommendationer för analys av spänningsrespons i rörsystem utsatta för termohydrauliska transienter, Rapport nr: 11559001-1 revision 0, Inspecta Nuclear AB, 2007.

[16] Vladimir. P. Pavlenko, Lisa Rosenqvist, Department of Astronomy and Space Physics, Uppsala University, Version 2, 2007.

Appendix A – Converting a model from RELAP5 to TRACE and options used in TRACE

The models used in this report have been modelled as RELAP5 models in the Symbolic Nuclear Analysis Package (SNAP), a graphical user interface that may be used when creating RELAP5 and TRACE models. The RELAP5 models have been converted from RELAP5 to TRACE using the converting tool built into SNAP. Each component used in RELAP5 during this project had a counterpart TRACE. SNAP has been updated throughout this thesis and the latest version used was 1.2.2. Using the latest version of SNAP is highly recommended especially for the

improvements during the conversation process. The pipe junction loss coefficients do not agree very well between the original RELAP5 model and the converted TRACE model. Thus

adjustments where required to achieve similar mass flow rate in the comparison.

There are two different steam tables available in TRACE, one based on the formulation used in TRAC and the other one is based on the formulation used in RELAP5. The TRAC formulation is described as faster but less accurate [3, vol1]. The table based on the RELAP5 formulation is mainly the same as the one in RELAP5, aside from possible bug fixes or other improvements [3, vol1]. It should be noted that unlike RELAP5, which relies on an external file for its steam table, the steam tables are hard coded into the TRACE executable, although it is possible to use external steam tables if desired. All the models shown in this report have used the steam table based on RELAP5 included in the TRACE executable.

TRACE version 5.0p1 (patch 1) was used. This version had an inertial swing check valve that closed much faster than the one in RELAP5, so a modified version received from the NRC, with an improved check valve was used instead. The RELAP5 version used was 3.3gl.

It is possible to choose between two different numerical solvers in TRACE, one is called the stability-enhancing two-step (SETS) numerics, which allows the Courant limit to be exceeded, allowing the use of very large time steps during steady state conditions and slower transients. The other solver is called semi-implicit, and limits the maximum time step to the Courant limit, that is some cell length divided by the sound velocity of the fluid. The default option is the stability- enhancing two-step (SETS) numeric, and this is the solver that has been used in all TRACE models.

Appendix B – Orifice and valve diameters and hydraulic resistance models used in system 323

Table 7: Orifice and valve diameters and hydraulic resistance models used in system 323

Area change option Component Description Diameter [m] RELAP5 TRACE

V401 Valve 0.296 Smooth [-1]

V409 Valve 0.194 Smooth [-1]

P4 The pump Smooth

V402 Inertial check valve 0.2 Full

Abrupt

[-1]

V403 Orifice 0.146 Smooth [-1]

V418 Orifice 0.0751 Full

Abrupt K=1.8

[1]

K=2.15

V410.93 Orifice 0.0326 Full

Abrupt

[1]

K=3.13

V410.94 Orifice 0.039 Full

Abrupt

[-1]

V410.95 Orifice 0.0467 Smooth [-1]

V407 Valve 0.1615 Full

Abrupt

[-1]

V408 Orifice 0.0753 Full

Abrupt

[-1]

V404 Valve 0.1487 Full

Abrupt

[-1]

V405 Inertial check valve 0.145 Full

Abrupt

[-1]