umu.diva-portal.org938553/FULLTEXT01.pdf · behavior of the centrifugal pump and swing check valve. In existing cal-culation tools, the system and components are modeled in one dimension

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�CFD study of a pump trip in a pump-check valve system

Elin Eriksson

Master’s Thesis in Engineering Physics, Department of Physics, Umeå University, 2016

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Abstract

Pressure waves can be caused by e.g. valve operations, pump trips, pipebreak and steam collapse. Therefore it is of interest to investigate thebehavior of the centrifugal pump and swing check valve. In existing cal-culation tools, the system and components are modeled in one dimensionalong the axis of the piping with the Relap5 code. There exist models forswing check valves and centrifugal pumps, but the models are insufficientfor accurate prediction of pressure wave phenomenons. In two previousMaster Thesis projects performed by D.Bragmark and E.Boqvist, the dy-namic behavior of a centrifugal pump and a swing check valve in transientflow have been investigated using CFD (Computational Fluid Dynamics).

The model of the centrifugal pump from the previous thesis work byD.Bragmark was improved by including leakages and flow correcting ge-ometries that had been removed as well as surface roughness. Both acentrifugal pump and a swing check valve have been investigated during apump trip event. One dimensional simulations in Relap5 suggested thatthe pump is not noticeably affected by the valve closing before the valveis completely closed. Due to this, the centrifugal pump and the swingcheck valve were simulated separately during the pump trip. The CFDcode Ansys Fluent as well as the one dimensional code Relap5 are usedto simulate the pump during the pump trip. The swing check valve wassimulated in the two CFD codes Ansys Fluent and Star-CCM+.

The pump trip simulated in Relap5 showed similar characteristics as thepump trip simulation in Ansys Fluent. The main difference was that theRelap5 pump rolls out faster that the CFD pump, i.e the impeller of thepump comes to a stop faster. This means that the pump model in Relap5is conservative, i.e it overestimates the loads in the system. The valvesimulation in the two different CFD codes showed close to identical re-sults. For further valve simulations the Star-CCM+ code is preferred dueto more convenient dynamic mesh method and geometry handling. If theapproximation of separate simulation proves to be accurate, the pumptrip simulation of the valve could be used efficiently in future develop-ment. It is hard to take measurements of the valve during a pump tripand therefore no experimental values were available.

The valve model used in Relap5 is a newly developed model and might notbe fully tested yet. For further used one should make sure that the modelis properly tested. A better estimate of the surface roughness would bedesirable for further use of the CFD models.

Acknowledgements

I would like to express my gratitude to FS Dynamics for a rewarding springfilled with new experiences and talented colleagues. There has not beena day I was not happy to arrive at the office. I also thank FS Dynamicsfor giving me the opportunity to perform my master thesis at their Solnaoffice.

A special thank you to my two supervisors Ori Levin and Fady Ishaq,for lending me your time and for discussing my problems with me, withouttheir help I would not have come this far. I thank them also for our weaklymeetings and for the help with Relap5 and the CFD codes. A thank youalso to Emil Boqvist and David Bragmark for lending me your expertisewhen no one else knew the answers.

A thank you to Berakningsgruppen for funding the thesis and lastly Iwould like to thank KSB for allowing me to work with their real modelof the centrifugal pump as well as their experimental data to compare mymodels to.

Elin Eriksson June 16, 2016

Contents

1 Introduction 81.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Published work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Theory 132.1 The Realizable k − ε model . . . . . . . . . . . . . . . . . . . . . 152.2 Wall functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Impeller rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5 Valve closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.6 Homologous curves . . . . . . . . . . . . . . . . . . . . . . . . . . 192.7 Mesh motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.8 Dimensionless valve variables . . . . . . . . . . . . . . . . . . . . 20

3 Method 213.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.1 Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.2 Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.1.3 Pump system . . . . . . . . . . . . . . . . . . . . . . . . . 273.1.4 Pump-valve system . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Pump system . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 Pump-valve system . . . . . . . . . . . . . . . . . . . . . . 303.2.4 Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.1 Numerical set up . . . . . . . . . . . . . . . . . . . . . . . 313.3.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . 313.3.3 Impeller motion . . . . . . . . . . . . . . . . . . . . . . . 313.3.4 Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . . 323.3.5 Reproducing pump curves . . . . . . . . . . . . . . . . . . 32

3.4 Pump trip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4.1 Numerical setup . . . . . . . . . . . . . . . . . . . . . . . 333.4.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . 333.4.3 Impeller motion . . . . . . . . . . . . . . . . . . . . . . . 333.4.4 Sensitivity study . . . . . . . . . . . . . . . . . . . . . . . 343.4.5 Pump trip Relap5 . . . . . . . . . . . . . . . . . . . . . . 34

3.5 Pump trip with open valve . . . . . . . . . . . . . . . . . . . . . 343.5.1 Numerical setup . . . . . . . . . . . . . . . . . . . . . . . 343.5.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . 343.5.3 Impeller motion . . . . . . . . . . . . . . . . . . . . . . . 343.5.4 Sensitivity study . . . . . . . . . . . . . . . . . . . . . . . 343.5.5 Pump trip with valve Relap5 . . . . . . . . . . . . . . . . 35

3.6 Dynamic valve closing . . . . . . . . . . . . . . . . . . . . . . . . 353.6.1 Numerical setup . . . . . . . . . . . . . . . . . . . . . . . 353.6.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . 36

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3.6.3 Disc motion . . . . . . . . . . . . . . . . . . . . . . . . . . 363.6.4 Relap5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Result 374.1 Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1 Sensitivity study . . . . . . . . . . . . . . . . . . . . . . . 374.1.2 Reproducing pump curves . . . . . . . . . . . . . . . . . . 40

4.2 Pump trip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Pump trip with open valve . . . . . . . . . . . . . . . . . . . . . 43

4.3.1 Relap5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3.2 CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.4 Dynamic valve closure . . . . . . . . . . . . . . . . . . . . . . . . 45

5 Discussion 465.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.2.1 Reproducing pump curves . . . . . . . . . . . . . . . . . . 485.2.2 Pump trip . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2.3 Pump trip with valve . . . . . . . . . . . . . . . . . . . . 495.2.4 Dynamic valve closing . . . . . . . . . . . . . . . . . . . . 49

6 Conclusion 50

A Sensitivity study pump trip

B Pump trip UDF

C Dynamic valve UDFs

D Relap5 pump trip with dynamic valve code

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List of Figures

1 A typical centrifugal pump. Image from Bragmark [1]. . . . . . . 82 The valve model with disc in closed position. Image from Bo-

qvist [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 The experimental setup from the experiment performed by KSB.

The static pressure was measured in four points, two diametersfrom both inlet (pM1) and outlet (pM2) [1]. Image from Brag-mark [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 The Homologous curves representing (a) Pressure head and (b)impeller torque used in the Relap5 simulations. . . . . . . . . . . 22

5 The dimensionless coefficients defined in (a) (42), (43) and (b)(44) obtained by simulating the valve in Star-CCM+ with fixedvalve disc for varying opening angles and constant mass flow rate. 23

6 A cross section of the meshed (a) old pump geometry [1] and (b)new, full pump geometry. Notice the leakage clearances at theinlet and below the impeller at the shaft. The moving mesh zoneis highlighted with red. . . . . . . . . . . . . . . . . . . . . . . . . 24

7 A zoom in on the cross section of the leakage clearances at (a)the inlet and (b) the shaft as well as (c) one of the two stabilizinggeometries at the inlet . . . . . . . . . . . . . . . . . . . . . . . . 25

8 A side view of the valve showing opening angle, rotation center,center of mass and the distance between the two later. Imageobtained from Boqvist [1]. . . . . . . . . . . . . . . . . . . . . . . 26

9 The geometry used in the pump trip simulations. . . . . . . . . . 2710 The geometry used in the pump trip with open valve simulations. 2711 The leakage clearance at the inlet consists of two walls, i.e. inner

and outer part of the circle. This part is connected to the rest ofthe fluid zone by interfaces at the top and bottom of the clearance. 28

12 A stationary rotation of the impeller with the entire pump ge-ometry is compared to the previous thesis at nominal flow withregard to (a) pressure head normalized by nominal pressure head∆HR and (b) impeller torque normalized by nominal impellertorque τR. The flow rate is normalized by the nominal flow rateQR. There is no surface roughness applied, hence the 0 µm no-tation. The dashed line between the Bragmark simulation pointsis an interpolation of the simulated data. . . . . . . . . . . . . . . 37

13 Pump simulations were performed with surface roughness 600µm, 100 µm and 30-45 µm defined in table 9 at Q=190m3/h. Theresulting impeller moment and pressure head of these simulationsare compared to the previous thesis results and to experimentalvalues. (a) Pressure head normalized by nominal pressure head∆H and (b) the impeller torque normalized by nominal impellertorque τR are shown. The flow rate is normalized by the nominalflow rate QR. The dashed line between the Bragmark simulationpoints is an interpolation of the simulated data. . . . . . . . . . . 38

14 A comparison of the result of pump simulations at nominal flowrate with meshes P1 and P2, defined in table 6. . . . . . . . . . . 39

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15 The normalized experimental pump curves for head rise and im-peller moment are compared to the result of simulations at thefour flow rates Q = 0, 60, 120, 190 m3/h. In the simulations thesurface roughness is set to 25 µm for all surfaces in contact withthe fluid. The mechanical loss has been added to the moment.The curves are normalized by nominal values ∆HR, τR and QRof head rise, impeller torque and volumetric flow rate. . . . . . . 40

16 The pump trip simulations in Fluent and Relap5 are comparedfor (a) pump head, (b) impeller moment, (c) volumetric flow rateand (d) radial velocity of the impeller. . . . . . . . . . . . . . . . 41

17 A comparison between taking away the motor torque in onetimestep (sharp) and over ten time steps (smooth) in Ansys Flu-ent for (a) pump head, (b) impeller moment, (c) volumetric flowrate and (d) radial velocity of the impeller. . . . . . . . . . . . . 42

18 The Resulting flow rate from the Relap5 pump trip simulationsare shown. The three simulations include the piping system infigure 10 without valve, with fully open valve and with dynami-cally closing valve. The deviation of the closing valve simulationstarts when the valve is completely closed. . . . . . . . . . . . . . 43

19 Pump trip simulations without valve and with valve implementedin both Ansys Fluent and Relap5 are compared for (a) pumphead, (b) impeller moment, (c) volumetric flow rate and (d) theradial velocity of the impeller. o.p stands for only pump and w.vstands for with valve. . . . . . . . . . . . . . . . . . . . . . . . . . 44

20 The dynamic valve closing simulated in both Star-CCM+ andAnsys Fluent. The result of the simulations are represented by(a) the total pressure drop over the valve, (b) the moment on thedisc produced by pressure and viscous forces, (c) The volumetricflow rate and (d) the opening angle θ of the disc over time, alsosimulated in Relap5 with both new valve model and original valvemodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

21 Surface roughness 25 µm and 45 µm implemented in Ansys Flu-ent are compared for (a) pump head, (b) impeller moment, (c)volumetric flow rate and (d) the radial velocity of the impeller. .

22 Meshes P3 and P4 implemented in Ansys Fluent are comparedfor (a) pump head, (b) impeller moment, (c) volumetric flow rateand (d) the radial velocity of the impeller. . . . . . . . . . . . . .

23 Pump trip with time step 0.0002 and 0.00046 implemented inAnsys Fluent are compared for (a) pump head, (b) impeller mo-ment, (c) volumetric flow rate and (d) the radial velocity of theimpeller. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24 The designed UDF and the Ansys Fluent 6DOF solver imple-mented in Ansys Fluent are compared for (a) pump head, (b)impeller moment, (c) volumetric flow rate and (d) the radial ve-locity of the impeller. . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Tables

1 Definition of the near wall regions [8]. . . . . . . . . . . . . . . . 162 The definition of the different homologous curves used to model

the pump in Relap5. . . . . . . . . . . . . . . . . . . . . . . . . . 223 Pump values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Scaled valve values . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Clearance mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Pump meshes used in various simulations . . . . . . . . . . . . . 297 Valve meshes used in a sensitivity study . . . . . . . . . . . . . . 308 Solution settings in Ansys Fluent. . . . . . . . . . . . . . . . . . 319 Surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . 3210 Solution settings in Ansys Fluent and Star-CCM+. L-S is an ab-

breviation of Least Squares and p-v is an abbreviation of pressure-velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

11 Comparison between simulation and experimental pressure headand moment results. The experimental value at nominal flow ofthe impeller moment is 113 Nm and of the head rise 25.7 m. . . . 38

12 The result of the leakage clearance sensistivity study. . . . . . . . 3913 Comparison between simulation, experimental and previous sim-

ulation pressure head and moment results. . . . . . . . . . . . . . 4014 Result of sensitivity study of valve mesh with stationary disc. . . 43

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Nomenclature

αR Rotational speed at nominal operation [rpm or rad/s]

δij Kronecker delta

µ Dynamic viscosity [Pa·s]

µt Turbulence viscosity [m/s]

ν Local kinematic viscosity [m2/s]

ω Rotational velocity of impeller [rad/s or rpm]

ρ Density [kg/m3]

τ Torque [Nm]

τR Impeller torque at nominal operation [Nm]

τw Wall shear stress [kg/(m·s2)]

τb Buoyancy torque [Nm]

τfr Friction torque [Nm]

τh Hydraulic torque [Nm]

τtot Total torque on the valve disc [Nm]

τw Weight torque [Nm]

τw external torque [Nm]

θ Opening angle of valve disc [deg]

ε Dissipation rate of turbulence kinetic energy [m2/s3]

CM Coefficient that expresses the ratio between measured torque and torquecalculated from the measured static pressure difference [-]

Cq Dimensionless flow coefficient [-]

Dimp Impeller diameter [m]

e internal energy [J]

f Force [N]

g Gravitational accelleration [m/s2]

H Pressure head [m]

h Height [m]

HR Pressure head at nominal flow [m]

I Moment of inertia [kg·m2]

K Pressure loss coefficient [-]

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k Turbulent kinetic energy [m2/s2]

Ks Roughness height [m]

K+s Dimensionless roughness height [-]

L Length scale [m]

Ld Length of valve disc torque arm [m]

m Mass [kg]

p Static pressure [Pa]

Q Volmetric flow rate [m3/s or m3/h]

QR Nominal flow rate [m3/h]

r Distance from rotation axis [m]

RCG Distance from rotation axis to center of gravity [m]

Rec Reynolds number for centrifugal pump [-]

U Mean velocity of fluid [m/s]

u Velocity of fluid [m/s]

u′ Velocity fluctuations [m/s]

U∗ Dimensionless velocity [-]

uτ Friction velocity [m/s]

W Work [J]

y+ Dimensionless wall distance [-]

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1 Introduction

In this master thesis two components common in nuclear piping systems willbe studied, a centrifugal pump and a swing check valve. Both componentshave been studied in previous thesis work, thus this will be a continuing andconnecting work. Figure 1 shows a typical centrifugal pump and figure 2 showsthe geometry of the swing check valve when the valve is closed.

Figure 1: A typical centrifugal pump. Image from Bragmark [1].

Figure 2: The valve model with disc in closed position. Image from Boqvist [2].

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1.1 Background

FS Dynamics has a well-developed cooperation with Swedish and Finnish nu-clear power industry where FS Dynamics contributes with experience and deeptheoretical knowledge within various simulations. The nuclear power plants arerequired to verify that piping systems can withstand the loads that the systemsare exposed to. Due to this, it is of high interest to investigate the behavior ofa centrifugal pump and a swing check valve during a pump trip.

The centrifugal pump is one of the most common pumps and has been usedto transport fluid for over a decade. The centrifugal pump is a thoroughlytested and robust device. When the pump is operating, the fluid is sucked fromthe suction side in to the pump at the center of the impeller, the impeller eye.The pressure of the fluid is increased from inlet to outlet, or from suction topressure side. This is done by transforming mechanic energy to kinetic energythrough the rotating impeller. The fluid is accelerated along the impeller bladesby the centrifugal force and thus transforming kinetic energy into pressure andthis results in a higher pressure at the pressure side than at the suction side.The fluid flow inside a pump is a three dimensional, turbulent flow which isoften complicated to analyze. [3].

Losses in a centrifugal pump can be divided into two main groups; hydraulic-and mechanical losses. Among mechanical losses we have losses in bearings andin the shaft seals. The mechanical losses cause the power consumption to risesince they give a resisting torque. Bearing life, which is dependent of axial,radial and hydraulic thrust can also affect the mechanical losses [4].

The hydraulic losses contain flow friction, mixing, recirculation, incidence,impeller friction and leakage. The impeller friction will lead to a higher powerconsumption due to its resisting torque, leakage leads to a reduced flow throughthe pump and the rest of the hydraulic losses cause a lower head rise [3].pressure-to-suction leakage flows in shrouded centrifugal pumps also substan-tially contribute to the fluid induced rotor dynamic forces. These forces inverselyproportional to the clearance between impeller and casing [5], from here on ref-erenced by leakage clearances.

Reverse flow can occur in the pipe system due to for example a pipe rupture or apump trip. It is not desirable to have back flow since it might damage the pumpand other components. This can be prevented by having check valves build into the pipe system. Although back flow can still occur, it will be restrictedby the check valve. There are a number of different check valves available, forexample swing, lift and tilting disc. The most represented type in the nuclearindustry, which is also the type that causes the most failures is the swing checkvalve. This valve is beneficial since it gives a low pressure loss compared toother mentioned models, has a simple design and comes in many different sizes.One drawback of the swing check valve is that it is known to have one of thelongest closing times, which may increase the maximum back flow compared toother valve types.

Today’s method of obtaining preliminary results is to simulate the system in1D along the axis of the piping. The nuclear system code Relap5 (Reactor

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Excursion and Leak Analysis Program) developed at Idaho National Labora-tory for the U.S Nuclear Regulatory Commission in the 1980s is one of themost widely used 1D codes in the nuclear industry. An interesting question isweather the code is conservative or not, i.e. if the code overestimates loads inthe system. A new model of the swing check valve has recently been createdfor Relap5 by W.Baltyn [6]. The new valve model can be used with differentcalculation models for the hydraulic torue data. The model of interest for thisthesis work is a model called the cmcq model [7]. The new valve model is anempirical model, but one should have in mind that it has not been completelytested yet. One of main the problems with the original swing check valve modelin Relap5 is that it is known to close too fast.

In this Thesis, the centrifugal pump and swing check valve will be simulatedin 3D using the CFD (Computational Fluid Dynamics) codes Ansys Fluent16.2 ans Star-CCM+ 11.2. CFD is the analysis of system including fluids, heattransfer and associated phenomenons through computer aided simulation. CFDcodes are structured around numerical algorithms that can solve fluid problemsand it can be advantages to experiments since it can shorten development timeand costs [8].

A model of the pump created by David Bragmark [1] will be used togetherwith an existing model of the swing check valve created by Emil Boqvist [2].

1.2 Problem description

Pressure waves can be caused by e.g. valve operations, pump trips, pipe breakand steam collapse. Therefore it is of interest to investigate the behavior of thecentrifugal pump and swing check valve. In existing calculation tools, the sys-tem and components are modeled in one dimension along the axis of the pipingwith the Relap5 code. There exist models for swing check valves and centrifugalpumps, but the models are insufficient for accurate prediction of pressure wavephenomenons. In two previous Master Thesis projects, the dynamic behavior ofa swing check valve and a centrifugal pump in transient flow have been investi-gated using CFD. The idea of the present Master Thesis is to model a centrifugalpump and a swing check valve with appropriate boundary conditions to studythe scenario of a pump trip and how the pump rolls out as well as how the valvecloses during this event.

1.3 Aim

An existing pump model is to be improved by including losses that have notyet been considered. The aim of the project is to simulate a pump trip scenarioboth with 1-dimensional (1D) modeling and 3-dimensional (3D) CFD analysisand compare the results. The main focus will be to see how the centrifugalpump impeller rolls out and how the swing check valve closes. It is of highinterest to see how the one dimensional calculations compare to CFD and if theone dimensional calculations are conservative as well as if valve and pump canbe simulated separately without making a too rough of an estimate.

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1.4 Published work

This Master thesis is a continuing work of David Bragmarks thesis [1] regardinga centrifugal pump during a water hammer event. The same centrifugal pumpwill be used in this project. In Bragmark [1] a valve closure was modeled inAnsys Fluent 16.0 by decreasing the mass outflow of the pump, which was set asthe outlet boundary condition. Both transient and stationary simulations wereperformed, where the simulation was stationary with regard to the mass outflow.A mesh with 2 prism layers was used, although more prism layers could givebetter results. two turbulence models were tested, the realizable k − ε and theSST k−ω model. The SST k−ω model was found to be more mesh dependentthan the realizable k − ε model. The resulting pressure head and moment ofthe 3D simulation did not quite match the experimental values from the pumpmanufacture. The pressure head curve had a percentage error between 3-4%and the moment curve had a percentage error between 3-16% when comparedto experimental data. The deviation from the experimental curves could be dueto ignoring some losses from motor to pump.

URANS equations together with the two equation k− ε turbulence model werefound by S.R.Shah et.al. [9] to be appropriate and considered to give a good es-timation of the overall performance of the centrifugal pump. The typical errorsof the result using this approach was found to be below 10 % of the experimen-tal values. The study concludes that the impeller has been extensively studied,while the volute of the centrifugal pump is a field with few studies, and thusstudies in this field may be promising for pump performance. Although CFDis promising in many regards, it is still recommended to compare the result ofCFD simulations to experimental results.

In an article written by Wen-Guang Li [10] the impact of the surface roughness,viscosity and design of the impeller was investigated by CFD computation. Thequantities were investigated using the CFD code Ansys Fluent. The standardk − ε model was used in the CFD computations to evaluate turbulent stresses.Non-equilibrium wall functions were applied to include stress on the walls ofthe pump. Water and three different oils with varying viscosity were used toinvestigate the importance of viscosity. The sand roughness height 0, 50 and 100µm were used to investigate importance of surface roughness. The roughnesscoefficient in Fluent was set to 0.75. It was concluded that the results for theperformance of the CFD simulation were qualitative compared to observations.

In an article from 2007 by R. Spence and J. Amaral-Teixeira [11] a model ofthe complete geometry of a double inlet centrifugal pump, including the leakagefrom pressure to suction side. The simulations were performed in 3D using CFX-TASCflow which is a Navier-Stokes code. In the article, it was concluded thatprevious studies had suggested that the area where the leakage flow meets theinlet flow requires careful modeling. It was also suggested that the grid designwas improved by grid interfaces in complex regions having one-to-one connec-tions. Scalable wall functions were used in the model. The study resulted in asuccessful model of the entire geometry. The largest pressure pulsations werefound at the impeller outlet and the CFD-analysis agreed well with experimen-tal results at most locations.

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A doctoral thesis by Eskil Storteig [12] suggests that leakage from pressureto suction side through the seal in a centrifugal pump can be important forpump performance. In the article the importance of the geometry of the sealsare investigated. It was concluded that inlet and exit conditions of seals affectboth seal leakage and rotor dynamic coefficients to some extent. The clearancewas modeled with a grid of square cells. For clearances between 0.0031 and 0.10mm the number of layers for the minimum clearance was set to 8. For clearance0.15, 0.20 and 0.40 the number of layers were set to 18, 25 and 40 respectively.

In a former thesis paper by Emil Boqvist [2] a swing check valve was inves-tigated. The swing check valve investigated was used to transport pressurizedwater to a reactor tank. The aim of the project was to simulate both stationaryand transient cases to later improve a 1D model. Two important parameterswhen investigating the fluids impact on the disc are the torque on disc and massflow. The turbulence model used in the final simulation was the Realizable k−εmodel and sclalable wall functions were used for wall treatment. The valve wastested for different deaccelerations of the flow and it was found that the closingtime varies with the deacceleration. It was also found that back flow occursbefore the valve is completely closed. There were however noticeable differencesin torque on the disc for different turbulence models for the steady state simu-lations and the turbulence models were not tested for the transient simulations.There were no experimental values available for determining which turbulencemodel was best suited for the CFD simulations. A model of the same swingcheck valve is also available in Star-CCM+, although there are no sensitivitystudies performed on this model and the existing mesh is currently to coarse.

In an article written by A. R. D. Thorley [13] a review of check valves un-der transient flow conditions is made. In this paper it is stated that the systemsthat are most at risk are those with pumps that deliver high pressure heads. Ifa pump is protected with a badly fitted check valve it can result in problemswith check valve slam, line vibration and failure. A basis for valve dynamicresponse from measurements taken under laboratory conditions has been cre-ated. The use of this basis is most efficient in pipeline designs when used innon-dimensional representation of the important terms.

12


2 Theory

Centrifugal pumps are used to increase the pressure of a fluid for it to be trans-ported to a higher level. The process that takes place when the fluid passesthrough the pump can be assumed to be adiabatic, since the heat exchangebetween the fluid and the surroundings is so small that it can be neglected. Wecan also assume that the external leakage is negligible, since this is normallyvery small. For the described case, the energy equation for stationary flow perpumped unit mass according to

W = eo − ei +po − piρ

+c2o − c2i

2+ g(ho − hi), (1)

where W is the work performed by the pump, ei and eo are the inlet andoutlet internal energy, pi and po are the inlet and outlet static pressure, g is thegravitational acceleration, hi and ho are the inlet and outlet heights and ci andco are the inlet and outlet absolute velocity.

It is desirable that as much as possible of the work added by the electricmotor results in an increase of static energy in the fluid, since internal energy ishard to utilize. An increase of internal energy would increase the temperatureof the fluid and is considered to be a loss [14]. The increase of pressure head isthus the useful part of the fluids change of state and is defined by

∆H =po − piρg

+c2o − c2i

2g+ ho − hi. (2)

When the Reynolds number of a flow rises above the critical Reynolds number,the flow goes from the laminar to turbulent regime. The flow goes from be-ing smooth and predictable, to containing random and chaotic motions. Thereynolds number in the centrifugal pump can be defined by

Rec =ρnD2

imp

µ, (3)

where n is revolutions per second, Dimp is the diameter of the impeller and µis the dynamic viscosity of the fluid. The flow in a centrifugal pump is in theturbulent region since the Reynolds number in the volute is Rec ∼ 106, whichis in the turbulent region [1].

The governing equations needed to model the turbulent flow, written in Einsteinnotation, are the continuity equation

∂ui∂xi

= 0 (4)

and Navier-Stokes equations

∂ui∂t

+ uj∂

∂xjui =

1

ρfi −

1

ρ

∂p

∂xi+

1

ν

∂2ui∂xj∂xi

, (5)

where fi are the external forces, p is the static pressure, u is the velocity ofthe fluid and ν is the local kinematic viscosity. The fluctuations in a turbulentflow are always in 3D and makes the flow costly to describe. We need to apply

13


numerical methods and turbulence models to predict the flow. When usingCFD, the finite volume method (FVM) is used, where the fluid is discretized onto a grid of control volumes that contain the flow variables. To account for theturbulence, velocity and other flow properties are divided into fluctuating andmean values e.g

u = U + u′, (6)

where u is the velocity of the fluid, U is its mean value and u′ its fluctuations(also applicable on fi, p,...). This method is called Reynolds decomposition. Weconsider time averaging the fluctuating properties u = U + u′ and v = V + v′

defined by

〈u′〉 = 〈v′〉 = 0 〈U〉 = U 〈∂u∂s〉 =

∂U

∂s〈∫uds〉 =

∫Uds (7)

〈u+ v〉 = U + V 〈uv〉 = UV + 〈u′v′〉〈uV 〉 = UV 〈u′V 〉 = 0.

The time average of the governing equations (5) and (4) used together with (7)can be written

∂ui∂xi

=∂Ui∂xi

= 0 (8)

and∂Ui∂t

+ Uj∂

∂xjUi =

1

ρ

[Fi −

∂P

∂xi+

∂

∂xj

(2µSij − ρ〈u′iu′j〉

)], (9)

where Fi are the external forces and

Sij =1

2

(∂Uixj

+∂Uj∂xi

)(10)

is the mean strain rate tensor. The last term in (9) is the Reynolds stressRij = −ρ〈u′iu′j〉. In 1877 Boussinesque proposed that the Reynolds stress isproportional to the rates of deformation, that is

− ρ〈u′iu′j〉 = 2µtSij −2

3ρkδij , (11)

where µt is the turbulent viscosity and k = 12 〈u′iu′j〉 is the turbulence kinetic

energy [8].

To numerically model the RANS equation (9) it can be beneficial to write thepressure on the form

P = P + ρ0gixi (12)

where ρ0 is a reference density and P is a non-physical pressure variable. Thus(9) can be written

∂Ui∂t

+ Uj∂

∂xjUi −

1

ρ

∂

∂xj

(2µSij − ρ〈u′iu′j〉

)=

1

ρ

[Fi −

∂P

∂xi

]=

1

ρ

[Fext + ρg − ∂P

∂xi

]=

1

ρ

[Fext + g(ρ− ρ0)− ∂P ′

∂xi

], (13)

where Fext are the average external forces excluding gravity. If the referencedensity is set equal to the constant density it may improve convergence [15] [16].

14


The k− ε equations are based on mechanisms that affect the turbulent kineticenergy. The standard k− ε model has two model equations, one for turbulencekinetic energy k, and the second for dissipation rate ε. The standard k−ε modelis empirically based on the understanding of relevant fluid processes, since theexact k − ε equations contain many unknown parameters and constants. Thismodel can be used for a large number of turbulent applications, but is not wellsuited for rotating flows or flows with large adverse pressure gradients. For thestandard k − ε model the turbulent viscosity is defined by

µt = ρCµk2

ε, (14)

where Cµ = 0.09 [15].

2.1 The Realizable k − ε model

The realizable k − ε model differes from the standard k − ε model in twoimportant ways,

First Cµ in the turbulent viscosity is not a constant.

Second The transport equation for the dissipation rate ε is derived from anexact equation for transport of mean square vorticity fluctuation.

The term realizable means that the model satisfies certain mathematical con-straints on the Reynolds stress which is consistent with turbulent flows. Thestandard k − ε model does not satisfy these constraints and is therefore notrealizable. The transport equation for k in the realizable k− ε model is definedby

∂k

∂t+∂kujxj

=1

ρ

{∂

∂xj

[(µ+

µtσk

)∂k

∂xj

]+Gk +Gb − ρε+ YM + Sk

}(15)

and the transport equation for ε is defined by

∂ε

∂t+∂εujxj

=1

ρ

{∂

∂xj

[(µ+

µtσε

)∂ε

∂xj

]+

ρC1Sε− ρC2ε2

k +√νε

+ C1εε

kC3εGb + Sε

}. (16)

Gk represents the generation of turbulence kinetic energy due to mean veloc-ity gradients, Gb represents the generation of turbulence kinetic energy due tobuoyancy and YM is the contribution of fluctuating diliation due to compress-ibility. C2 and C1ε are constants, Sk and Sε are user defined source terms andC3ε is the degree of which the dissipation rate is affected by the buoyancy. C3ε

can be defined by

C3ε = tanh |u⊥u‖|, (17)

where u‖ is the velocity component parallel to the gravitational vector and u⊥is the velocity component perpendicular to the gravitational vector [15]. Theturbulent viscosity is defined by

µt = ρCµk2

ε(18)

15


as in the standard k − ε model. The difference is in the definition of Cµ whichfollows

Cµ =1

4.04 +√

6 cosφ(19)

where

φ =1

3cos−1

(√6W), W =

sijsjkskis3

, s =√sijsji (20)

and

sij =1

2

(∂uj∂xi

+∂ui∂xj

). (21)

The constants in the model are set to [15]

C1ε = 1.44, C2 = 1.9, σk = 1.0, σε = 1.2. (22)

2.2 Wall functions

Semi empirical formulas called wall functions can be used to model the flownear the wall when that region is not resolved. Instead of resolving the nearwall region, wall functions bridge the viscous sublayer between the wall andthe log layer, without having to modify the turbulence model to consider thepresence of the wall. The dimensionless wall distance and friction velocity aredefined by

y+ =uτy

ν, uτ =

√τwρ

(23)

where τw is the wall shear stress and y is the wall distance. When y+ of the firstwall adjent cell is below 15 the solution gradually deteriorates and the accuracyof the solution is not be maintained [15].

Table 1: Definition of the near wall regions [8].

Layer RegionViscous sublayer y+ < 5Buffer layer 5 < y+ < 30Log-layer 30 < y+ < 500

The three near wall regions are defined in table 1. In the log layer the law ofthe wall for mean velocity is used, which is defined by

U∗ =1

κln(y+)

+B (24)

where κ = 0.4187, B = 5.4494 and

U∗ =U

uτ. (25)

The layer closest to the wall is the viscous sublayer. In this layer the dimen-sionless velocity is related to y+ by

U∗ = y+. (26)

16


In the buffer layer it can be hard to determine an equation for the dimensionlessvelocity [8]. Ansys Fluent’s standard wall function uses (24) when y∗ > 11.225and (26) when y∗ < 11.225. Note that in Ansys fluent,

y∗ =ρC

1/4µ k

1/2P

τw/ρ(27)

is used instead of y+ in (26) and (24), where kP is the turbulence kinetic energyat the wall-adjacent cell centroid. These two variables are approximately equalin equilibrium turbulent boundary layers [15].

Scalable wall functions are chosen to get consistent results when the gridrefinement is arbitrary and can be used when y∗ < 11.225 to avoid deteriorationof the standard wall functions. For the case when y∗ > 11.225 the scalable wallfunction is equal to the standard wall function. The limiter

y∗ =

{y∗lim if y∗lim > y∗

y∗ otherwise(28)

where y∗lim = 11.225. y∗ will be used instead of y∗ [15], when using scalable wallfunctions.

2.3 Surface roughness

The surface roughness affects the drag on the walls and can therefore have aconsiderable effect on the flow, depending on the non-dimensional roughnessheight,

K+s =

ρKsU∗

µ, (29)

where Ks is the roughness height in meters. In Ansys Fluent [15], surfaceroughness heights are divided into three regimes:

Hydraulic smooth: K+s ≤ 2.25,

Transitional: 2.25 < K+s ≤ 90,

Fully rough: 90 < K+s .

The hydraulic smooth region is considered to be negligible, while the importanceof the roughness height increases in the transitional region and having full effectin the fully rough region. The wall roughness is added to the simulation throughthe law-of-the-wall modified for roughness [15]

U∗ =1

κln(y+)

+B −∆B. (30)

In the three regions, the constant ∆B [15] [16] takes the values

∆B = 0 (31)

in the hydraulic smooth region,

∆B =1

κln

[K+s − 2.25

87.75+ CsK

+s

]sin{0.4258(lnK+

s − 0.811)} (32)

in the transition region and

∆B =1

κln(1 + CsK

+s ) (33)

in the fully rough region.

17


2.4 Impeller rotation

When the pump is tripped the driving torque from the motor driving the im-peller rotation will be set to zero. Thus only the torque arising from fluid andmechanical losses will be present. The mechanical losses can be considered con-stant with rotational speed, while the fluid forces will vary with both mass flowrate and rotational speed. The moment of inertia is the resistance of a bodyagainst change in rotation rate and depends on how the mass is distributedaround the rotational axis. The moment of inertia, Iφ around axis φ is calcu-lated by

Iφ =

∫∫∫r2 dm (34)

where r is the orthogonal distance from the axis and dm = ρdV [15]. If weperform a dimension analysis of the mass and moment of inertia we get

[m] ∼ [ρ]L3, [I] ∼ [m] · L2 ∼ L5, (35)

where L is the length scale. Since the density of the material will not be affectedby scaling, the moment of inertia scales with L5, according to (35).

Given the torque around the rotation axis on the impeller from the fluid, theradial acceleration of a rigid body rotation can be then calculated by

ω = τi/Ixx, (36)

where Ixx is the moment of inertia around the x-axis and τi is the torque aroundthe rotation axis on the impeller. The rotational velocity of the impeller canthen be calculated by [15]

ω(t) =

∫ t

t0

ω dt. (37)

Given the rotational velocity of the impeller, the impeller passing frequency fip,i.e. the frequency of impeller blades passing a fixed point, can be calculated by

fip =6ω

2π, (38)

since there are 6 impeller blades in the centrifugal pump we will use in thepresent work.

18


2.5 Valve closing

The torque that controls the position of the valve disc is a sum of the torquescaused by the weight of the disc τw, the buoyancy of the disc τb, friction at thehinge pin τfr and the surrounding fluid τh. It might also exist external torqueτe, thus the total torque can be written

τtot = τw + τb + τfr + τh + τe. (39)

The total torque can also be written

τtot = IAθ (40)

where IA is the inertia moment around axis A and θ is the angular accelerationof the disc [2]. IA can be calculated by (34) by letting r be the distance fromaxis A.

2.6 Homologous curves

To simulate the pump trip in the 1D code Relap5, homologous curves need to beprovided to describe the behavior of the pump. Homologous curves in Relap5are described by the dimensionless variables

α =ω

ωR, v =

Q

QR, h =

H

HRand β =

τ

τR, (41)

where αR, HR, QR and τR are the values of rotational speed, head, flow rateand torque at nominal operation. The relationship between the four parametersdefined in (41) are displayed in a four quadrant representation. For a full pumprepresentation, all four parameters need to be represented for both positive andnegative values [17].

2.7 Mesh motion

In this thesis, three types of mesh motions will be used, dynamic mesh withsmoothing, layering and overset mesh.

Smoothing retains the original cells and only moves cell common nodes. It istherefore suitable for boundaries with small deformations [15].

Layering allows cells to compress or expand. In this case, the mesh may onlyconsist of hexahedra and prism cells. If a cell is too compressed/expandedthe cell will merge with the neighboring cell/split into two cells. Thismethod is useful when having large movements [15].

Overset is a dynamic mesh option that is available in Star-CCM+. Thismethod used overlapping meshes and is useful when working with movingbodies. It does not require mesh modification after initialization. Thesolutions in the overlapping mesh zones are interpolated, the cell size ofthe two meshes should thus be similar [16].

19


2.8 Dimensionless valve variables

To model the swing check valve in Relap5 the cmcq model [7] presented inW.Baltyn [6] is used. This model needs measurement data from stationaryexperiments, or in our case simulations. To use this model three dimensionlessvariables are needed for different opening angles with stationary flow. The firstvariable is the coefficient that expresses the ratio between measured torque andtorque calculated from the measured static pressure difference. This coefficientis calculated by

CM =τH

A∆pLd, (42)

where τH is the hydraulic torque, A is the seat area of the disc, ∆p is thepressure drop over the valve and Ld is the length of the torque arm. The secondvariable is a flow coefficient defined by

CQ =

√ρQ|Q|2∆pA2

, (43)

where Q is the volumetric flow rate. Finally, the third coefficient is a losscoefficient that can be written

K =1

C2Q

. (44)

To model the valve, a model called the sr model [18] could also be used.This model requires measurements from transient experiments or simulationsto calculate the necessary variables.

20


3 Method

In an experiment performed on the centrifugal pump by KSB, the static pressureof the fluid was measured at four points around the wall of the pipe, all fourpoints the same distance from the inlet/outlet. The measurements were takentwo diameters from the inlet and two diameters from the outlet. The mean valueof these measurements was considered to be the static pressure at that point.The total pressure was calculated by (2), assuming no height difference betweenthe measurements, that is hi = ho. In figure 3 we can see the experimentalsetup of the experiment performed by KSB. To mimic the experiment and geta model close to reality, the pressure head produced by the pump was obtainedby calculating an area weighted average of the static pressure at the inlet andoutlet of the pump. The average of the static pressure was calculated twodiameters from the inlet and two diameters from the outlet. The total pressurewas calculated by (2) assuming hi = ho. Since the flow is assumed to beincompressible, the absolute velocity is calculated from the volumetric flow rateand cross sectional area by u = Q/A.

Experimental values provided by KSB were also used to produce the ho-mologous variables defined in (41). These variables were used to model thepump in Relap5. Since there were no experimental measurements for back flowthrough the pump, some values had to be estimated for the homologous curves.The estimations were based of the experimental values together with resultsfrom articles by Jung Yoon, Tae-Ho Lee, Hwi-Seob Park [19] and I.K Madni, E.Cazzoli [20].

Figure 3: The experimental setup from the experiment performed by KSB. Thestatic pressure was measured in four points, two diameters from both inlet (pM1)and outlet (pM2) [1]. Image from Bragmark [1].

21


The curves presented in figure 4 are the homologous curves that were used tomodel the pump in Relap5. The six curve types HAD, HVN, HAN, BAD, BVNand BAN are defined in table 2 with α, h, v and β defined in (41).

Table 2: The definition of the different homologous curves used to model thepump in Relap5.

Curve x-axis y-axis quadrant

HVN α/v h/v2 1stHAD v/α h/α2 2ndHAN v/α h/α2 1stBVN α/v β/v2 1stBAD v/α β/α2 2ndBAN v/α β/α2 1st

-1 -0.5 0.5 1

v/ α or α/v

0.5

1

h/α

2 o

r h/

v2

HANHVNHAD

(a)

-1 -0.5 0.5 1

v/ α or α/v

0.5

1

β/α

2 o

r β

/v2

BANBVNBAD

(b)

Figure 4: The Homologous curves representing (a) Pressure head and (b) impellertorque used in the Relap5 simulations.

22


The pressure difference over the valve was measured directly in total pressuredrop, by calculating the surface average of the total pressure at inlet and outlet.The input variables (42) - (44) were calculated for 7 different disc opening anglesbetween minimum and maximum angle using a CFD model, the valve modellater defined for Star-CCM+. The values were taken from steady state solutionswith fixed valve positions. This was done since there were no experimentalvalues available. The values of the coefficients for completely closed valve wereestimated.

0 20 40 60

angle [deg]

0

0.5

1

1.5

2

[-]

Cq

CM

(a)

0 20 40 60

angle [deg]

0

5

10

15

20

25

K [-

]

(b)

Figure 5: The dimensionless coefficients defined in (a) (42), (43) and (b) (44)obtained by simulating the valve in Star-CCM+ with fixed valve disc for varyingopening angles and constant mass flow rate.

23


3.1 Geometry

In this thesis, four different geometries were used. The pump and the swingcheck valve were two of these geometries. The third geometry was a systemdesigned for the pump trip and the last geometry is the pump trip system withthe valve inserted.

3.1.1 Pump

The geometry from the previous master thesis [1] did not consider the clear-ance between impeller and casing at the inlet. As suggested by previous work,the leakage clearances might be of importance when modeling the centrifugalpump [11], [12]. These parts were included in this thesis work to model theleakage from pressure to suction side of the pump as well as the shaft leakage.A stabilizing geometry feature at the inlet that had also been omitted in theprevious thesis work was added for higher precision. In the former model, it wasconcluded that an entrance and exit pipe length equal ten times the entrance orexit diameter, respectively, is appropriate for the stationary simulations. There-fore this is what was used for the current geometry as well.

(a)

(b)

Figure 6: A cross section of the meshed (a) old pump geometry [1] and (b) new,full pump geometry. Notice the leakage clearances at the inlet and below theimpeller at the shaft. The moving mesh zone is highlighted with red.

24


(a) (b) (c)

Figure 7: A zoom in on the cross section of the leakage clearances at (a) the inletand (b) the shaft as well as (c) one of the two stabilizing geometries at the inlet

A CAD model of the pump was provided by KSB and the geometry was strippedof unnecessary parts in Ansa 15.2. The pump specific data that is used for thepump simulations are specified in table 3. Water at 22◦C with density ρ = 998.2kg/m3 and viscosity 1.003e-3 kg/ms was used throughout the simulations. It isassumed to be no heat flux through the walls.

Table 3: Pump values

Rotational speed n 1450 rpm, or 151.8 rad/sNominal flow QR 190 m3 /hOptimal head HR 25.7 mOptimal moment τR 113 NmSpecific speed nq 29.3Impeller diameter Dimp 300 mmInlet diameter Din 142 mmOutlet diameter Dout 100 mmMoment of inertia Ixx 0.276 kgm2

Impeller weight mimp 12.4 kg

25


3.1.2 Valve

The geometry used in the present work was the same as the one in the formermaster thesis by Emil Boqvist [2]. This geometry is shown in figure 8, noticethat the disc geometry was simplified by removing the part of a disc at theaxis of rotation, A. The only alteration from the previous work was that thegeometry was scaled to obtain an inlet pipe diameter of 100 mm instead of 367.9mm for the valve inlet to match the pump outlet dimensions. In table 4 themeasurements of the valve are scaled according to (35).

Figure 8: A side view of the valve showing opening angle, rotation center, centerof mass and the distance between the two later. Image obtained from Boqvist [1].

Table 4: Scaled valve values

Original valve Scaled valveMass 62.2 kg 1.2498 kgIyy,CG 0.786 kg·m2 0.0012 kg·m2

RCG 255.3 mm 69.4 mmIyy,A 4.841 kg·m2 0.0072 kg·m2

Buoyancy weight of disc 7.0 kg 0.14 kgMaximum angle, θmax 59.74◦ 59.74◦

Minimum angle, θmin 10.37◦ 10.37◦

Seat angle, θs 4.0◦ 4.0◦

26


3.1.3 Pump system

To simulate a pump trip, typical piping at inlet and outlet of the pump wasadded. The pipes were extruded from inlet and outlet of the pump and thus thediameter of the inlet and outlet were retained. The dimensions of the pipingsystem used are shown in figure 9.

Figure 9: The geometry used in the pump trip simulations.

3.1.4 Pump-valve system

To obtain the correct pressure drop that the fully opened valve will introduceto the pipe system of the pump the valve geometry was inserted in the pipingsystem. The valve was placed horizontally after the pipe bend. Apart fromthe insertion of the valve, the pump system geometry remained unaltered. Theposition of the valve in the piping system is shown in figure 10.

Figure 10: The geometry used in the pump trip with open valve simulations.

27


3.2 Mesh

The meshes for the four different geometries as well as corresponding sensitivitystudy meshes are presented in this section.

3.2.1 Pump

In a sensitivity study in Bragmark [1] the final pump model proved to be verystable with regard to changes in the mesh. Both number of prism layers andelement size were considered and proved to have little to no affect on the result.Due to this, the mesh generation followed the method described in Bragmark [1].Some modifications were made to the mesh due to the new geometry. A separatesensitivity study was performed for the leakage clearances in the geometry. Themesh was created in Ansa by

First creating to shell mesh for the entire geometry,

Second creating a prism layer for the inlet, outlet, volute and impeller,

Third auto generating a volume with a tetrahedral element type,

Fourth extruding the inlet and outlet and

Fifth repairing mesh cells with bad quality.

Triangular elements were used for the major part of the surface mesh, withexception of the most outer part of the inlet and outlet as well as the leakageclearances where quads were used. Prism elements were used in the inflationlayers with a first cell thickness that is set so that y+ > 30. It is however notguaranteed that the first prism layer will always satisfy the specified thicknesssince the layers are squeezed in problematic areas. The number of prism layerswas set to 3 due to previous recommendations.

The volume mesh in the leakage clearances was created with varying numberof quad layers between the leakage walls. The geometry of the inlet leakageclearance is shown in figure 11. Interfaces were placed to separate the leakageclearances from the inlet and the volute. This enables the possibility to meshneighboring zones separately.

Figure 11: The leakage clearance at the inlet consists of two walls, i.e. inner andouter part of the circle. This part is connected to the rest of the fluid zone byinterfaces at the top and bottom of the clearance.

28


A new sensitivity study was performed for the clearances to decide the numberof layers needed between the inner and outer wall. The meshes used are definedin table 5. Mesh C2 was used in the pump simulations.

Table 5: Clearance mesh

Mesh # of layers # of cellsC1 7 190771C2 8 218024C3 9 245277C4 10 272530

A rotating fluid region was defined by inserting interfaces in the volume betweenimpeller and volute as well as between impeller and inlet highlighted with redin figure 6b.

The inlet was extruded by offsetting the interface to the pump in outwardsnormal direction. The length of the inlet was set to be more than 10 diameters.The outlet was created in the same manner. The remaining volume mesh wascreated, as mentioned above, by using auto-generation in Ansa. The meshesused are defined in table 6. The finer pump mesh, P2 was used to control thatthe result from the previous thesis correctly stated the mesh independence, andthat it is also applicable to the new geometry.

Table 6: Pump meshes used in various simulations

Mesh # prism layers # cells afterconversion

Max tet.cell length

P1 (pump) 3 4.47 mn 10.68 mmP2 (pump) 3 5.49 mn 9.19 mmP3 (system) 3 6.06 mn 10.68 mmP4 (system) 3 6.62 mn 10.22 mmP5 (system with valve) 3 6.25 mn 16.02 mm

3.2.2 Pump system

The mesh was extruded from inlet and outlet of the pump to obtain the geometrydimensions in figure 9. A suitable growth rate smaller than 2% was used toensure that the transitioning elements size ratio at inlet and outlet was not toolarge. The sizes of the two meshes, P3 and P4, used for the pump system aredefined in table 6

29


3.2.3 Pump-valve system

All meshes used for the valve in this system are defined in table 7. Mesh V1-V6were created in the current thesis for the pump trip with open valve simulations,since it was desired to have as course mesh as possible. The pump valve systemwas created by using pump mesh P3 and inserting valve mesh V5 for fixed valvesimulations. The valve meshes were inserted according to figure 10. The outletwas extruded from the valve outlet in the same manner as for the pump. Thesize of the mesh, P5, is defined in table 6.

3.2.4 Valve

Mesh V7 was created by Emil Boqvist [2] and scaled down to match the pipedimension of the pump outlet. A mesh had been created in Star-CCM+ asa result of the previous thesis by Boqvist [2], which was also scaled down.Since this mesh was too coarse it was also refined, resulting in mesh V8. V7was created in Ansa for Ansys Fluent and V8 was created in Star-CCM+ forsimulations in the corresponding codes. The mesh extended 0.8 m from bothinlet and outlet.

Table 7: Valve meshes used in a sensitivity study

Mesh # prismlayers

# cells Max celllength

comment

V1 2 1.35 mn 20.36 mm Same shell as V2, V3V2 3 1.43 mn 19.05 mm Same shell as V1, V3V3 4 1.56 mn 19.02 mm Same shell as V2, V1V4 3 1.20 mn 18.82 mm Coarser shell at top of

valve than V2V5 3 1.49 mn 16.24 mm Finer shell mesh than V4V6 3 1.80 mn 15.08 mm Finer shell mesh than V5V7 5 6.65 mn 8.87 mm From former thesis work

[2]V8 5 2.16 mn - Stat-CCM+

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3.3 Pump

The stationary rotation case is a simulation of the pump mesh in section 3.2.1where only the impeller is rotating at a constant radial velocity of 1450 rpm.The simulation was run until a steady flow state is reached. This model wassimulated using Ansys Fluent. The gravity was not activated in this simulationand thus no reference density had to be set.

3.3.1 Numerical set up

In the previous work regarding the pump, it was concluded that RANS (9)together the realizable k − ε model defined in (15)-(22) is suitable for the sim-ulation of the pump [1]. Therefore this was the model that was used in allsimulations. Since it could not be guaranteed that the first layer has a thicknessthat will satisfy y+ > 30, scalable wall functions were used. The solver setupfor the simulations in this thesis is shown in table 8. This was chosen basedon the recommendations and sensitivity studies performed in the former masterthesis [1].

Table 8: Solution settings in Ansys Fluent.

Turbulence model Realizable k − εWall treatment scalable wall functionsPressure velocity coupling scheme SIMPLEGradient Least squares cell basedPressure Second orderMomentum Second order upwindTurbulent kinetic energy Second order upwindTurbulent dissipation rate Second order upwindTransient formulation Second order implicit

3.3.2 Boundary conditions

Inlet To avoid cavitation, a high gauge pressure is set at the inlet. The suctionside pressure used in all simulations is 20 bar.

Outlet A mass flow outlet was set to 0, 60, 120 or 190 m3/h, constant overtime.

Walls The wall boundaries of the pump are defined with a no-slip conditionand also given a surface roughness. The roughness coefficient was set to0.75. The rotating walls outside the moving mesh zone was given themoving wall condition with rotational speed 151.8 rad/s.

Interfaces Interfaces had to be created between the moving and stationarymesh zones, as well as where we want different grid sizes in neighboringzones. The zones restricted by interfaces are the clearances and the movingmesh impeller zone.

3.3.3 Impeller motion

The impeller motion was set by assigning the fluid around the impeller as amoving mesh zone. A sliding mesh can be described as a rigid rotation in

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the given mesh zone. The rotating mesh zone is connected to other cell zonesthrough interfaces. The rotational speed was set to ω = 151.8 rad/s. Not allrotating walls of the impeller were included in the moving mesh zone. Therotating walls outside the moving mesh zone were given moving wall boundarycondition with rotational velocity ω = 151.8 rad/s.

3.3.4 Sensitivity Study

At nominal flow the existing pump model [1] showed that the torque due to shearstress was well above 10 percent of the momentum caused by pressure forces.Due to this, a surface roughness was added to the existing model on all walls.The stationary solution was used with a roughness height of Ks = 600 µm, 100µm and 30-45 µm. 600 µm and 100 µm are high values surface roughness sincecast surfaces usually lie within 15 − 300 µm [10]. Since 45 µm is a standardvalue for pipes, it is also a quite high value. The treatment of the inside of thepump is thought to be quite close to hydraulic smooth. The high roughnessheights were used to see if the transition from smooth to rough surface wouldimpact the flow significantly and thus motivate a continued inclusion of surfaceroughness. The three cases of surface roughness tested are further described intable 9.

Table 9: Surface roughness

Ref. by Ks,Impeller[µm] Ks,V olute[µm] Ks,Inlet [µm] Ks,Outlet [µm]30-45 µm 30 45 45 45100 µm 100 100 100 100600 µm 600 600 600 600

A sensitivity study of the leakage clearance was performed to determine a suit-able number of layers between the clearance walls. Inlet- and outlet pressureboundaries were set to produce the pressure difference between volute and inlet,this pressure difference was found in the simulation from the former thesis byBragmark [1]. The tested clearance meshes are defined in table 5. The sensitiv-ity was investigated with regard to resulting moment coefficient on the rotatingimpeller wall and with regard to the volume flow rate through the clearance. Achange in moment coefficient or volume flow rate less than 1% was considered tobe mesh independent for the clearances. This since the flow through the clear-ance will be small compared to the flow through the pump. The two meshes P1and P2 were compared at nominal flow to assure mesh independence.

3.3.5 Reproducing pump curves

Four simulations were performed to reproduce data measured during experi-ments. The decision of which parameters were to be used in the pump modelwas based on the result from the sensitivity study. The experimental data fromKSB produces two curves, from here on referred to as pump curves. The pumpcurves consist of the two curves obtained by plotting pressure head rise andimpeller moment against volumetric flow rate respectively. To reproduce thecurves constant rotation rate of the impeller was used. A mechanical loss of 1%of the impeller moment at nominal flow was added to the resulting moment.

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3.4 Pump trip

Before the pump was tripped, i.e. before the external torque was removed,the pump was allowed to reach a steady state as in the pump simulation. Thissteady state was later used as initial conditions in further pump trip simulations.When the steady state was reached the motor torque was removed and the pumpwas allowed to roll out.

The pump trip was simulated in both 3D and 1D, in Ansys Fluent andRelap5. These two simulations were later compared to see how the 1D simulationcompared to the CFD simulation. To compare the two types of simulations,the system simulated needed to be the same for both simulation methods, thegeometry is specified in figure 9. The gravity was activated in this simulationand the reference density in (12) was set to ρ0 = ρ.

3.4.1 Numerical setup

The numerical setup for the transient pump trip was achieved by using thenumerical setup described in section 3.3.1. When removing the driving torquefrom the motor, the torque is gradually removed over 10 time steps. This wasdone to get a smooth transition.


Inlet To avoid cavitation, a high gauge pressure is set at the inlet. The suctionside pressure used in all simulations is 20 bar.

Outlet Pressure outlet of 21.837 bar was set to obtain nominal flow throughthe pump at impeller radial velocity ω = 151.8 rad/s.

Walls The wall boundaries of the pump are defined with a no-slip conditionand also given a surface roughness. The roughness coefficient in was set to0.75. The walls outside the moving mesh zone was given the moving wallcondition with rotational speed specified by an UDF available in appendixB.

Interfaces Interfaces had to be created between the moving and stationarymesh zones, as well as where we want different grid sizes in neighboringzones. The zones restricted by interfaces are the clearances and the movingmesh impeller zone.


The rotating mesh approach is replaced by a dynamic mesh motion controlled bythe UDF in appendix B. The UDF controlled the radial velocity of the impellerusing (36) and (37). When a stable nominal flow was reached, the driving torquefrom the motor was removed by the UDF. The mechanical loss was added tothe fluid moment on the impeller as a constant. This constant was set to 1% ofthe moment on the impeller at nominal flow and with active motor. The UDFused was a designed 1DOF (one degree of freedom) function.

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3.4.4 Sensitivity study

Simulations with two different values of surface roughness and two differentmeshes were run to investigate how it would impact the behavior of the pump. Acomparison between time steps 0.0002 s and 0.00046 s was perform for the steadyflow state and a comparison between the designed UDF and Ansys Fluent’s6DOF (6 degrees of freedom) solver was performed as well.

3.4.5 Pump trip Relap5

The 1D pump trip simulation was performed in Relap5. The surrounding pipingused in the 1D simulation had the same dimensions as for the 3D CFD simu-lations. The homologous curves calculated by (41) shown in figure 4 were usedin Relap5 to model the pump. Before performing the pump trip, a script wasused to set the outlet pressure to obtain nominal flow through the pump, in thesame manner as for the pump.

3.5 Pump trip with open valve

The pump trip with open valve was simulated in the same manner as the pumptrip, with the only difference that a valve with the disc fixed at the maximumangle was inserted according to figure 10. The gravity was activated in thissimulation and the reference density in (12) was set to ρ0 = ρ.


The Numerical setup is identical to the one presented in section 3.4.1.


The same boundary conditions as presented in section 3.4.2 with the exceptionof an added interface are used. The new interface is between the inlet of thevalve and the outlet piping of the pump. This was done to be able to meshthe pump and the valve separately and later merge the meshes. The outletboundary pressure was adjusted to 21.501 bar to maintain nominal flow beforetripping the pump.


See section 3.4.3


To use as rough a mesh as possible on the valve for a stationary valve pumptrip a sensitivity study was performed on the valve alone. The nominal massflow Q = 190m3/h was set at the outlet and the pressure 22 bar was set at theinlet. The meshes tested are described in table 6.

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3.5.5 Pump trip with valve Relap5

The pump trip with valve was simulated in Relap5 in two ways. First the valvewas kept open throughout the pump trip and second, the valve was allowed toclose due to the flow conditions produced by the pump. These two simulationswere performed to see how and if the pump trip was affected by the closing ofthe valve. The dimensionless variables (42)-(44) were used as earlier specified.The Relap5 code for the pump trip with closing valve is available in appendix D.

3.6 Dynamic valve closing

The dynamic valve closing is a simulation of the valve geometry only, of howthe valve closes depending on the volumetric flow produced by the pump tripwith open valve. The dynamic valve closing was simulated using only the valvemodel, instead of simulating the entire pump-valve system. This was donesince the pump-valve system is very large and a valve closing would be timeconsuming with the entire geometry. If the Relap5 simulations show that thedifference between the pump trip with open valve and pump trip with closingvalve is small, this approach will be considered justified. The Ansys Fluentmodel was not investigated further from the former thesis work, since extensivesensitivity studies already had been made on the model. The mesh of the Star-CCM+ model was refined, but there was no further mesh study performed onthe model. The Star-CCM+ model was the model used to simulate steady statefor varying opening angles to obtain the coefficients (42) - (44).

In both Star-CCM+ and Ansys Fluent, a steady state solution was reachedbefore letting a 6DOF solver release the valve disc. In Star-CCM+ the anglecan be restricted so that the valve is not able to be pushed above the maximumangle. In Ansys Fluent, this restriction had to be written in an UDF. The twoUDFs used in Ansys Fluent are available in appendix C


The numerical setup from the previous master thesis by Boqvist [2] was partlyused, but altered to match the numerical set up of the pump trip. The turbu-lence model in Star-CCM+ was set to realizable k− ε model to match all othersimulations in this thesis.

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The numerical setup for the valve in Ansys Fluent and Star-CCM+ are shownin table 10. The reference density in (12) was set to ρ0 = 0 to include thebuoyancy forces on the valve. For the valve closing in Star-CCM+ the originalmesh created by Boqvist was first used. Since this proved to give pressure dropresults far from the simulation in Ansys Fluent, mesh V8 was created and usedin the final simulation.

Table 10: Solution settings in Ansys Fluent and Star-CCM+. L-S is an abbrevi-ation of Least Squares and p-v is an abbreviation of pressure-velocity.

Settings Ansys Fluent Star-CCM+Turbulence model Realizable k − ε Realizable k − ε two layerWall treatment scalable wall functions All y+p-v coupling SIMPLE – (Segregated flow)Gradient L-S cell based Hybrid Gauss-L-SPressure Second order Second orderMomentum Second order upwind Second order upwindTurb. kinetic energy Second order upwind Second order upwindTurb. dissipation rate Second order upwind Second order upwindTransient formulation Second order implicit First order Implicit


Inlet The time-dependent mass flow rate obtained from the CFD pump tripwith open valve simulation was set at the inlet.

Outlet A reference pressure of 0 Pa was set at the outlet.

Walls The walls were given a no-slip condition with roughness height 25 µm.The roughness coefficient was set to 0.75.

Interfaces An interface was set between the rotating zone around the disc andthe surrounding fluid for the Ansys Fluent simulations. An overset meshwas region was defined around the disc in Star-CCM+.

3.6.3 Disc motion

The disc motion is a rigid body rotation controlled by a 6DOF solver accordingto (36) and (37) with rotation only about the rotational axis of the disc. InAnsys Fluent an UDF that controls the 6DOF solver was provided, this wasnot needed in Star-CCM+. In Ansys Fluent, a dynamic mesh with layering wasused. In Star-CCM+ overset mesh was used for the zone around the valve.

3.6.4 Relap5

The swing check valve was simulated separately with the same boundary condi-tions in Relap5, using both the new and the original swing check valve model.The new valve model [6] was simulated using the cmcq model defined in (42)-(44). The sr model mentioned in section 2.8 was not used since it would befar more complicated due to the need of variables from transient measurements.This was the only simulation where the original Relap5 swing check valve modelwas used.

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4 Result

The 4 types of simulations were successfully run, i.e. pump, pump trip, pumptrip with open valve and dynamic valve closing. The results of these simulationsand associated sensitivity studies are presented in the following sections.

4.1 Pump


As we can see in figure 12 the pump curve at nominal flow rate 190 m3/h ismarginally improved by using the new geometry. The relative difference betweenthe experimental and simulation moment is -5.56 % and between simulation andexperimental head rise it is 2.8 %.

0.6 0.8 1Q/Q

R [-]

0.8

0.9

1

1.1

1.2

1.3

∆H

/∆H

R [-

]

ExperimentBragmark 0 µmleakage 0 µm

(a)

0.6 0.8 1Q/Q

R [-]

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

τ/τ

R [-

]

ExperimentBragmark 0 µmleakage 0 µm

(b)

Figure 12: A stationary rotation of the impeller with the entire pump geometry iscompared to the previous thesis at nominal flow with regard to (a) pressure headnormalized by nominal pressure head ∆HR and (b) impeller torque normalizedby nominal impeller torque τR. The flow rate is normalized by the nominal flowrate QR. There is no surface roughness applied, hence the 0 µm notation. Thedashed line between the Bragmark simulation points is an interpolation of thesimulated data.

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As we can see in figure 13a, the pressure head given by the stationary simulationis decreased by applying surface roughness. In figure 13b it is shown that thepresence of surface roughness increases the impeller moment. In table 11 therelative difference between the experimental and simulated values are specified.

Table 11: Comparison between simulation and experimental pressure head andmoment results. The experimental value at nominal flow of the impeller momentis 113 Nm and of the head rise 25.7 m.

Roughness [µm] ∆HSim [m] Rel. Diff to experiment [%]30-45 23.0 -2.7100 24.2 -5.8600 29.8 -10.7Roughness [µm] τSim [Nm] Rel. Diff to experiment [%]30-45 109.6 -3.0100 115.4 2.1600 125.3 10.9

0 0.5 1Q/Q

R [-]

0

0.2

0.4

0.6

0.8

1

1.2

∆H

/∆H

R [-

]

ExperimentBragmark 0 µm30-45 µm100 µm600 µm

(a)

0 0.5 1Q/Q

R [-]

0

0.2

0.4

0.6

0.8

1

τ/τ

R [-

]

ExperimentBragmark 0 µm30-45 µm100 µm600 µm

(b)

Figure 13: Pump simulations were performed with surface roughness 600 µm,100 µm and 30-45 µm defined in table 9 at Q=190m3/h. The resulting impellermoment and pressure head of these simulations are compared to the previous the-sis results and to experimental values. (a) Pressure head normalized by nominalpressure head ∆H and (b) the impeller torque normalized by nominal impellertorque τR are shown. The flow rate is normalized by the nominal flow rate QR.The dashed line between the Bragmark simulation points is an interpolation ofthe simulated data.

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Table 12 shows the result of the sensitivity study of the clearance mesh. Defi-nitions of meshes C1-C4 are found in table 5. The moment on the rotating walland leakage flow are presented in table 12 as well as the percentage differencewith increasing mesh size.

A comparison between simulations with meshes P1 and P2 defined in table6 is shown in figure 14. As we can see, there is almost no visible differencebetween the two meshes and the solution is considered mesh independent.

Table 12: The result of the leakage clearance sensistivity study.

Mesh Leakage flow [kg/s] Rel. Diff [%] Moment [Nm] Rel. Diff [%]C1 0.6139 - 0.2474 -C2 0.6181 0.65 0.2454 -0.81C3 0.6250 1.13 0.2451 -0.1C4 0.6292 0.64 0.2443 -0.35

0.5 0.6 0.7 0.8

Time [s]

25

25.5

26

26.5

27

∆H

[m]

P2P1

(a)

0.5 0.6 0.7 0.8

Time [s]

105

110

115

τ [N

m]

P2P1

(b)

Figure 14: A comparison of the result of pump simulations at nominal flow ratewith meshes P1 and P2, defined in table 6.

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In figure 15 we can see the result of the stationary simulations using the newgeometry and surface roughness 25 µm. In the same figure the experimentalmeasurements from KSB are shown as well.

In table 13 the experimental, previous (Bragmark [1]) and current simu-lation results are prescented in numbers. The relative difference between theexperimental values and the current simulation results are also calculated andpresented in the table. We can see that the new model is closer to the experi-mental values.

Table 13: Comparison between simulation, experimental and previous simulationpressure head and moment results.

Q [m3/h] ∆HExp [m] ∆HSim [m] Rel. Diff [%] ∆HBragmark [m]0 31.8 31.2 1.95 33.260 31.7 31.6 0.38 32.8120 29.6 29.8 -0.74 30.8190 25.7 26.1 -1.4 26.6Q [m3/h] τExp [Nm] τSim [Nm] Rel. Diff [%] τBragmark [Nm]0 33.5 30.6 8.69 28.060 59.3 59.5 -0.27 54.9120 85.5 87.2 -2.04 83.0190 113 110.1 2.58 106.2

0 0.5 1Q/Q

R [-]

0

0.2

0.4

0.6

0.8

1

1.2

∆H

/∆H

R [-

]

ExperimentSimulation

(a)

0 0.5 1Q/Q

R [-]

0

0.2

0.4

0.6

0.8

1

τ/τ

R [-

]

ExperimentSimulation

(b)

Figure 15: The normalized experimental pump curves for head rise and impellermoment are compared to the result of simulations at the four flow rates Q =0, 60, 120, 190 m3/h. In the simulations the surface roughness is set to 25 µm forall surfaces in contact with the fluid. The mechanical loss has been added to themoment. The curves are normalized by nominal values ∆HR, τR and QR of headrise, impeller torque and volumetric flow rate.

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4.2 Pump trip

In figure 16 the CFD simulation of the pump trip performed in Ansys Fluent iscompared to a corresponding simulation in Relap5. All Relap5 curves except theimpeller moment shows the same characteristic behavior as the behavior in theCFD simulation, even though the Relap5 pump rolls out faster than the CFDpump. Sensitivity studies related to the pump trip are found in appendix A.

(a) (b)

(c) (d)

Figure 16: The pump trip simulations in Fluent and Relap5 are compared for (a)pump head, (b) impeller moment, (c) volumetric flow rate and (d) radial velocityof the impeller.

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In figure 17 a comparison between taking away the motor torque in one timestep (sharp) and over ten time steps (smooth) in Ansys Fluent is shown. Aswe can see in figures 17a and 17b, the discontinuities that arise when usingthe sharp method are not present when using the smooth method. Additionalsensitivity studies were performed regarding the surface roughness, the designedUDF, the time step and the mesh size. These four studies are presented in detailin appendix A. A surface roughness of 25 µm and 45 µm only shows a smalldifference at low flow rates, where the pressure head showes the largest relativedifference of 6% smaller pressure head for 45 µm relative to 25 µm surfaceroughness. The mesh study was performed comparing meshes P3 and P4. Thisstudy showed no visible difference in moment, head, flow rate or radial velocity.

-0.02 0 0.02 0.04 0.06

time [s]

19

20

21

22

23

24

25

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27

∆ H

[m]

Sharpsmooth

(a)

-0.02 0 0.02 0.04 0.06

time [s]

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85

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115τ [N

m]

SharpSmooth

(b)

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time [s]

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186

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191

Q [m

3/h

]

SharpSmooth

(c)

-0.02 0 0.02 0.04 0.06

time [s]

1250

1300

1350

1400

1450

ω [r

pm]

SharpSmooth

(d)

Figure 17: A comparison between taking away the motor torque in one timestep(sharp) and over ten time steps (smooth) in Ansys Fluent for (a) pump head, (b)impeller moment, (c) volumetric flow rate and (d) radial velocity of the impeller.

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The designed UDF is compared to Ansys Fluents 6DOF solver in appendix A,which shows close to no difference. The time step 0.0002 was compared to timestep 0.00046 for the steady state of the pump trip, before the motor torque wasremoved. This to showed close to no difference in result and ∆t = 0.0002 wascontinued to be used.

4.3 Pump trip with open valve

The difference of pressure drop for increasing valve mesh sizes are shown intable 14, the definition of the meshes are found in table 7. Mesh V5 was used tosimulate the pump trip with open valve in Ansys Fluent. The resulting flowratefrom that simulation was later used as the inlet boundary condition for thedynamic valve closing.

Table 14: Result of sensitivity study of valve mesh with stationary disc.

Mesh Rel. pressure drop changeV1 -V2 -0.91 %V3 0.21 %V2 -V4 0.35 %V4 -V5 2.6 %V6 1.2 %

4.3.1 Relap5

The simulations of the pump trip with a valve was performed with both closingand completely opened valve in Relap5. The flow rates of the Relap5 pumptrip simulations without valve, with valve and with closing valve are shown infigure 18. The pump impeller torque, head rise and rotational velocity of theimpeller showed no difference before complete valve closure between pump tripswith open and closing valve.

0 0.5 1

time [s]

-50

0

50

100

150

200

Q [m

3/h

]

No valveClosing valveOpen valve

Figure 18: The Resulting flow rate from the Relap5 pump trip simulations areshown. The three simulations include the piping system in figure 10 withoutvalve, with fully open valve and with dynamically closing valve. The deviationof the closing valve simulation starts when the valve is completely closed.

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4.3.2 CFD

In figure 19 we can see a comparison of a pump trip with open valve and pumptrip without valve. As seen in figure 19c the flow rate through the pump-valvesystem is noticeably affected by the presence of the valve. The moment on theimpeller, the head rise and radial velocity of the impeller seems to be somewhataffected when the flow rate reaches values close to zero and below, which isshown in figures 19b, 19a and 19d. The pump during the pump trip seems tobe affected in the same manner for CFD and Relap5 when a valve is inserted.For the CFD simulation with valve, back flow occurs 0.92 s after the pump istripped and in Relap5 back flow occurs 0.73 s after the pump is tripped.

0 0.5 1

time [s]

0

5

10

15

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∆H

[m]

CFD o.pCFD w.vRelap5 o.p.Relap5 w.v.

(a)

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100τ [N

m]


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]


(c)

0 0.5 1

time [s]

200

400

600

800

1000

1200

1400

ω [r

ad/s

]


(d)

Figure 19: Pump trip simulations without valve and with valve implemented inboth Ansys Fluent and Relap5 are compared for (a) pump head, (b) impellermoment, (c) volumetric flow rate and (d) the radial velocity of the impeller. o.pstands for only pump and w.v stands for with valve.

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4.4 Dynamic valve closure

Since Relap5 showed no difference in mass flow rate between pump trip withopen valve and closing valve before the valve was completely closed in figure18, it was concluded that it is a reasonable approximation to simulate the valveseparate from the pump. Successful simulations of the dynamic valve closingwere performed in both Fluent and Star-CCM+.

As we can see in figure 20 the simulations in Star-CCM+ and Ansys Fluentgive similar results, The Star-CCM+ simulation have a closing time that is0.0005 seconds longer than in Ansys Fluent. The Relap5 valve closes about0.033 s earlier than in Star-CCM+ and Ansys Fluent as we can see in figure20d. The total closing time in RELAP5 is 0.2158 s which is 0.0282 s fasterthan the valve simulated in Ansys Fluent. The closing time of the original valvemodel is 0.097 s.

0 0.5 1

time [s]

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1

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4

∆P

[Pa]

×10 4

StarFluent

(a)

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-5

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5

τh [N

m]

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(b)

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]

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0 0.5 1

time [s]

10

20

30

40

50

60

Ang

le [d

eg]

StarFluentRelap5Relap5 orig.

(d)

Figure 20: The dynamic valve closing simulated in both Star-CCM+ and AnsysFluent. The result of the simulations are represented by (a) the total pressuredrop over the valve, (b) the moment on the disc produced by pressure and viscousforces, (c) The volumetric flow rate and (d) the opening angle θ of the disc overtime, also simulated in Relap5 with both new valve model and original valvemodel.

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5 Discussion

5.1 Method

There are two potential leakage clearances that were added to the improvedpump model, i.e. leakage from pressure to suction side and leakage at the shaft.The clearances were modeled with 8 layers between the two walls due to theresult of the sensitivity study. This was also the number of values used inE.Storteig [12], which strengthens the choice of number of layers. The shaftleakage is assumed to be small and therefore the fluid is not allowed to flowout from this clearance. It was included to see if the clearance would affectthe flow through the pump. As we can see in figure 12 the updated geome-try did not take the model much closer to the experimental values. Due tothe small improvement using the new geometry, the simplified geometry used inthe previous master thesis by Bragmark [1] could be used in further simulations.

It is very hard to measure or estimate the surface roughness inside the pump. Itis often assumed to be close to hydraulic smooth, but surely it is not completelysmooth. Since it has a significant impact on the pump model according to figure13, it could be of interest to investigate this parameter further. 25 µm was setbecause it was thought by KSB to be close to hydraulic smooth, and thus itshould have a lower surface roughness than a standard pipe (∼45 µm).

In the previous master thesis regarding the pump [1], careful studies were madefor the mesh. Due to this, the mesh was created in the manner recommended byBragmark [1]. To see if the solution in fact is mesh independent, the stationarypump simulation was run at nominal flow with a finer mesh. As we can seein figure 14 the solutions are very close, and thus the stationary pump modelwas considered to be mesh independent. As mentioned in the previous masterthesis [1], it would be interesting to resolve the near wall region, but since thesimulations are in 3D, for a complex model the costs of the simulation would befar too large.

The mechanical loss was estimated to 1% of the moment on the impeller atnominal flow. This loss was also considered to be constant with radial velocity,which might not be exactly true in reality but was considered to be a goodestimation [3]. Further investigation of this parameter could be of interest if thepump model were to be used further.

The time step of the pump and pump trip simulations were chosen accord-ing to the former thesis work. The previous valve simulations [2] had a largertime step than the pump simulations, thus the smaller time step of 0.0002 s waschosen. Simulations with time step 0.00046 showed to comparable results andthus the time step of 0.0002 was accepted, this result can be found in appendixA, figure 23. With this time step, the impeller rotates ∼ 2 degrees per timestep, which is acceptable.

Since the impeller rotates, a transient solver was used to reach a steady statesolution. A rotating impeller can be modeled in a steady state environment, byusing a moving reference frame (MRF). This was done in some cases to reach a

46


more reasonable initial condition than zero velocity for the transient solver. Thereason to why MRF was not used to find the final steady state was that it gaveresults too far from the transient solution. Since the reason to have a steadystate solution in many cases was to set the correct outlet pressure, MRF wouldnot have been sufficiently accurate. In the Ansys Fluent user manual [15], italso states that MRF should not be used if walls are close to the region, whichis the case for the rotating mesh zone.

The valve simulations were much simpler to set up and run in Star-CCM+ thanin Ansys Fluent. This was due to the availability of the overset mesh methodand convenient way of specifying the disc angle in Star-CCM+. It might havebeen easier to implement the entire model, including pump in Star-CCM+. Thiswas not done due to a limited access to Star-CCM+.

Since the valve used was scaled down from a real valve model, there were noexperimental results to compare the valve closing with. It would have beeninteresting to see if the closing of the simulations matched an experiment. Itwould also have been better to have experimental results of the stationary flowsat varying opening angles used to model the valve in Relap5, to confirm thevalve model. Since the new Relap5 model is empirically based on two valves,it should be closer to experimental values than the original Relap5 model. Oneshould have in mind though, that the new Relap5 model might not be fullytested yet.

In Star-CCM+ the mesh generated can be allowed, if not specified otherwise, tochange the boundaries of the valve geometry somewhat. In the case of the valve,it meant that the edges of for example the disc were rounded off. This provedto have a quite large impact on the resulting pressure drop and disc moment.Due to this, the mesh was set to keep the original geometry edges. Since thefinal model matched the Ansys Fluent model very well, although completelydifferent mesh methods were used, no further mesh studies were performed onthe Star-CCM+ valve model. Mesh studies would have been good to establishmesh independence of the Star-CCM+ model and to confirm that the model isreasonable. The second would however demand experimental values of a valveclosing.

An attempt was made to simulate both the centrifugal pump and the dynamicvalve closing in one model in Ansys Fluent. This simulation was never successfuland there was a lot of problems with the mesh movements and divergence. Itcould be due to a problem with the pressure boundary conditions at both inletand outlet, since this was never tested for the valve only. A compressible flowwas tested and did not produce better results.

When simulated separately, both impeller and valve had their axis of rotationcentered in the origin. If simulated in the same model, one of them has to bemoved from the origin to a suitable position in the piping system. This causedproblems regardless of which of the two parts were moved. If there was moretime available in the project, the source of the problem might have been foundand fixed. It would have been interesting to see if a CFD simulation confirmesthe result from Relap5 showing that the pump is not affected during the valveclosing.

47


5.2 Result


We can see in figure 12 that the updated geometry did not affect the resultmuch. The most noticeable difference is the change in pressure head rise, whichwas to be expected, since the pressure should drop due to the leakage flow frompressure side to suction side. From this result we can conclude that it would bea reasonable assumption to model the simplified geometry used in the previousmaster thesis [1] (figure 6a), even though the updated geometry in figure 6b wasused throughout this thesis.

In figure 15 the resulting pump curves using the improved pump model areshown compared to experimental values from KSB. The new model proves tobe closer to the experimental values than the model produced in the formermaster thesis [1], this is shown with numbers in table 13. The percentage errorof the impeller moment is changed from 3-16 % to 0.3-8.7 %. The percentageerror of the head rise is change from 3-4 % to 0.4-2 %. This was considered tobe a good improvement and thus the new model was used to move forward andsimulate the pump trip.

When reproducing the pump curves, the gravity is not included. This wasdone due to the exclusion of gravity in the former thesis work, so that themodels would be comparable. If gravity was included 0.5 m would be added tothe pressure head rise results, which would still be closer to the experimentalpump curves than the previous model.

5.2.2 Pump trip

In figure 16 the resulting pump trip simulation in Ansys Fluent is compared tothe Relap5 simulation. The two trip simulations display similar behavior, butthe Relap5 pump rolls out to a stop quicker than in the CFD simulation. Weneed to remember that the homologous curves for negative flow were estimatedand that it might have affected the result. The estimation of the torque curve islikely the reason to why the impeller torque from Relap5 deviates from the CFDresult so much. The homologous torque curve might have been estimated toolow for low negative flows. That said, all curves except the torque at negativeflows matched the homologous estimations quite well.

The faster the pump stops, the larger loads the system will be exposed to.For example if the pump stops faster, the faster reduction of flow rate will slamthe valve shut faster, which in turn will cause large pressure waves in the system.Since the Relap5 simulation stops the pump faster than the CFD simulation, itindicates that the Relap5 code is indeed conservative.

The smooth release of the motor torque is compared to a sharp release in figure17. As we can see, the discontinuities does not seem to affect the solution morethan instantaneously at the sharp release. The two solutions coincide quicklyafter the release and thus the sharp method could be used as well.

The pump trip was also run with surface roughness 45µm which showed adifference only at low flow rates. A comparison between 25 µm and 45 µm is

48


shown in appendix A. This is most likely due to the larger pressure drop thatis present due to the higher surface roughness. The difference is however verysmall and both surface roughness heights seems to be acceptable.

The designed 1DOF UDF and the 6DOF solver gives results very close to eachother. This verifies that the designed UDF gives reasonable values and that itcan be used for further simulations. The reason to why the designed UDF ispreferable is that it does not include any matrix operations, which the 6DOFsolver uses.

Notice in figures 16 and 17 that the solution oscillates. These oscillations havea frequency matching the impeller passing frequency defined in (38), which is areasonable result. The oscillations should in fact be present.

5.2.3 Pump trip with valve

The pump trip was also run with a fully open valve inserted in the pipe system.As we can see in figure 19 it takes a longer time for back flow to occur when avalve is present in the system. Notice that the outlet pressure had to be lowerthan for the pump trip simulation without valve, since the valve introduces ahigher pressure loss in the system. A lower outlet pressure would result in lowerretardation of the flow rate. The flow rate of this simulation was the time de-pendent flow rate that was used as input for the dynamic valve simulations.In figure 18, which shows flow rates resulting from Relap5 simulations without,with open and with closing valve, similar effects are shown when adding thevalve.

In addition to the flow rate shown in figure 18, the Relap5 curves for headrise, impeller torque and radial velocity showed no difference between simula-tions with open and with closed valve. From these results it was assumed thatthe separate simulations would be a reasonable assumption. It would however,as mentioned, be preferable to have a CFD simulation including both pump andvalve confirm this as well. Note that the flow rates shown in figure 18 are theresulting flow rates of pump trips. The valve closes completely earlier than infigure 20 due to the conservative pump model.

5.2.4 Dynamic valve closing

The method of simulating the valve and pump separately during the pumptrip can result in losing some swirling motion as an effect of the pipe bend.Also, since the flow rate is set at the inlet independent of the closing valve, thetime back flow occurs might not be completely correct. This could result inpushing the valve shut with the inlet boundary condition. Despite these facts,it was considered to be a reasonable assumption to simulate the valve closingseparately due to the amount of simulation time it saved. It would be of greatadvantage if this method proved to be a good approximation of a real pumptrip, since it could be used in future development.

49


In figure 20 we can see that the simulations in Ansys Fluent and Star-CCM+gives very similar results. The closing times of the valve only differed by 0.0005s. This implies that the valve can be simulated independent of software usingthe flow rate measured from a pump trip.

As we can see in figure 20d, the separated valve closing in Relap5 using thenew valve model shows comparable results to the CFD simulations. The closingtime of the new Relap5 valve model is however ∼0.028 s shorter than the CFDvalve models. This is though to be due to the use of the cmcq model, which usesstationary measurements to model the hydraulic torque. The sr model mighthave given results closer to the CFD simulations. In the former thesis performedby Boqvist [2], the stationary valve simulations showed a pressure distributionresulting in a longer torque arm than in the transient valve simulations. Thissuggests that the valve would be closed faster when using the cmcq model withstationary measurements instead of the sr model with transient measurements.

The new Relap5 valve model does indeed seem to be more accurate thanthe original valve model, since the original valve model closes more than twiceas fast as the Ansys Fluent valve. The short closing time of the original valvemodel is shown in figure 20d as well.

6 Conclusion

The pump curves produced in this thesis are closer to the experimental valuesthan in the previous master thesis. The simplified version of the geometry cre-ated by Bragmark [1] could be used without significant loss in precision. Thesurface roughness height of the pump walls is an important parameter that ifpossible should be measured if further improvements on the pump model are tobe made. The new model was considered to be close enough to the experimentalvalues to proceed and simulate the pump trip.

The pump trip was successfully simulated in both Relap5 and Ansys Fluentand the CFD simulations show that it takes a longer time for the CFD pump toroll out than the Relap5 pump. This proves that compared to CFD simulations,the Relap5 pump model is conservative, i.e. over estimates the moments andforces in the system due to faster stop of the pump.

According to Relap5, the valve closing does not affect the operation of thepump before the valve is completely closed. Based on this information, it wasdecided that is was a reasonable assumption to simulate the centrifugal pumpand swing check valve separately during the pump trip. If there are experimen-tal pump trip values available for the pump, the simulation of the valve will notbe very time consuming when using the separate approach.

The valve closing was simulated in both Ansys Fluent and Star-CCM+ withclose to the same results. This implies that the valve closing during a pumptrip can be simulated separate from the pump, independent of the CFD code.

50


References

[1] David Bragmark, CFD study of a centrifugal pump during a Water ham-mer event, 2015

[2] Emil Boqvist, Investigation of a swing check valve using CFD, 2013.

[3] Grundfos reasearch and technology, The centrifugal pump, accessed Febru-ary 2016.

[4] Vasant Godbole, Rajashri Patil, S.S. Gavade, Axial Thrust in centrifugalpumps - experimental analysis, International Conference on ExperimentalMechanics, 15, 2012.

[5] Robert V.Uy, Brian L.Bircumshaw and Christopher E.Brennen, Rotor-dynamic Forces from Discharge- to-Suction Leakage Flows in CentrifugalPumps : Effects of Geometry, JSME International Journal. Series B, Flu-ids and Thermal Engineering, 41 (1). pp. 208-213, 1998.

[6] Wojtek Baltyn, Development of models for swing and tilting disk checkvalves in RELAP5, Berakningsgruppen, 2016-06-01.

[7] Adamkowski, extraction of, Stany Przejsciowe w Ukladach WirowychMaszyn Wodnych. Zagadnienia Analizy i Sterowania w AspekcieOgraniczania Destrukcyjnych Skutkow Tych Stanow, IMP Gdansk 2004

[8] H.K. Versteeg, W. Malalasekera, An introduction to computational fluiddynamics, 2007.

[9] S.R. Shaha, S.V. Jainb, R.N. Patelb, V.J. Lakherab, CFD for centrifugalpumps: a review of the state-of-the-art, Procedia Engineering, 51:715-720,2013.

[10] Wen-Guang Li, Effect of exit blade angle, viscosity and roughness in cen-trifugal pumps investigated by CFD computation, Department of FluidMachinery, Lanzhou University of Technology, China, 2011.

[11] R. Spence and J. Amaral-Teixeira, Investigation into pressure pulsationsin a centrifugal pump using numerical methods supported by industrialtests, Computers & fluid 37 (2008).

[12] Eskil Storteig, Dynamic characteristics and leakage performance of liquidannular seals in centrifugal pumps, Doctoral thesis, NTNU, Fakultet foringenirvitenskap og teknologi, 2000.

[13] A. R. D. Thorley, Check valve behavior under transient flow conditions: astate-of-the-art review, ASME, Vol 111, June 1989.

[14] Bengt Algers, Alvar Andersson, Ingemar Andersson, Ivan Eriksson, Bror-Arne Gustafson, Lennart Hedenfalk, Yngve Hland, Arna Jonsson, AndersLfgren, Bengt Samuelsson, Olof Wikner and Nils gren, Pumphandboken,1979.

[15] ANSYS Fluent User Guide, ANSYS, Canonsburg, 16.2.0

51


[16] Star-CCM+ user guide, CD-adapco, 11.2.

[17] Relap5/mod3.3 code manual, volume 1: Code structure, system modelsand solution methods, October 2010, Information Systems Laboratories,Inc.

[18] Guohua Li, Jim C. P. Liou, Swing Check Valve Characterization and Mod-eling During Transients, Journal of Fluid Engineering, November 2003,Vol. 125, pp.1043-1050.

[19] Jung Yoon, Tae-Ho Lee, Hwi-Seob Park, Flow Characteristics of the PHTS Mechanical Pump in PGSFR, Transactions of the Korean Nucl earSociety Autumn Meeting, 2014.

[20] I.K Madni, E. Cazzoli, Single-phase pump model for analysis of LMFBRheat transport systems, United states, 1987

52


A Sensitivity study pump trip

The result of the sensitivity study for the pump trip is presented in this section.A comparison between two different roughness heights is shown in figure 21.The chosen roughness height 25 µm is compared to the roughness height 45µm.

0 0.5 1

time [s]

0

5

10

15

20

25

∆H

[m]

25 µm45 µm

(a)

0 0.5 1

time [s]

-20

0

20

40

60

80

100

τ [N

m]

25 µm45 µm

(b)

0 0.5 1

time [s]

-150

-100

-50

0

50

100

150

Q [m

3/h

]

25 µm45 µm

(c)

0 0.5 1

time [s]

200

400

600

800

1000

1200

1400

ω [r

ad/s

]

25 µm45 µm

(d)

Figure 21: Surface roughness 25 µm and 45 µm implemented in Ansys Fluentare compared for (a) pump head, (b) impeller moment, (c) volumetric flow rateand (d) the radial velocity of the impeller.


In figure 22 the two meshes P3 and P4 defined in section 3.2.1 are compared.

0 0.5 1

time [s]

0

5

10

15

20

25

∆H

[m]

P3P4

(a)

0 0.5 1

time [s]

-20

0

20

40

60

80

100

τ [N

m]

P3P4

(b)

0 0.5 1

time [s]

-150

-100

-50

0

50

100

150

Q [m

3/h

]

P3P4

(c)

0 0.5 1

time [s]

200

400

600

800

1000

1200

1400

ω [r

ad/s

]

P3P4

(d)

Figure 22: Meshes P3 and P4 implemented in Ansys Fluent are compared for(a) pump head, (b) impeller moment, (c) volumetric flow rate and (d) the radialvelocity of the impeller.


In figure 22 the time steps 0.0002 and 0.00046 are compared for the steady stateof the pump trip (before releasing the pump).

-0.02 -0.015 -0.01 -0.005

time [s]

25.5

26

26.5

27

∆ H

[m]

∆ t = 0.0002∆ t = 0.00046

(a)

-0.02 -0.015 -0.01 -0.005

time [s]

105

110

115

τ [N

m]

∆ t = 0.0002∆ t = 0.00046

(b)

-0.02 -0.015 -0.01 -0.005

time [s]

189

189.5

190

190.5

191

Q [m

3/h

]

∆ t = 0.0002∆ t = 0.00046

(c)

-0.02 -0.015 -0.01 -0.005

time [s]

1445

1450

1455

ω [r

pm]

∆ t = 0.0002∆ t = 0.00046

(d)

Figure 23: Pump trip with time step 0.0002 and 0.00046 implemented in AnsysFluent are compared for (a) pump head, (b) impeller moment, (c) volumetric flowrate and (d) the radial velocity of the impeller.


The designed impeller motion UDF is compared to Ansys Fluent’s 6DOF solver.As we can see the designed UDF gives the same pump behavior as the 6DOFsolver.

0 0.05 0.1 0.15 0.2

time [s]

10

15

20

25

∆H

[m]

Designed UDF6DOF

(a)

0 0.1 0.2

time [s]

50

60

70

80

90

100

110

τ [N

m]

Designed UDF6DOF

(b)

0 0.1 0.2

time [s]

155

160

165

170

175

180

185

190

195

Q [m

3/h

]

Designed UDF6DOF

(c)

0 0.1 0.2

time [s]

900

1000

1100

1200

1300

1400

ω [r

ad/s

]

Designed UDF6DOF

(d)

Figure 24: The designed UDF and the Ansys Fluent 6DOF solver implementedin Ansys Fluent are compared for (a) pump head, (b) impeller moment, (c)volumetric flow rate and (d) the radial velocity of the impeller.


B Pump trip UDF

The UDF used to simulate a pump trip in Fluent is shown below.

1 #include "udf.h"

2 #include "stdio.h"

3

4 DEFINE_CG_MOTION(impeller_motion ,dt ,vel ,omega ,time ,dtime){

5

6 int impeller = 131;

7 int impeller_rotating =79;

8 int inlet_rotating =88;

9 int shaft_rotating =80;

10

11 Domain *domain = Get_Domain (1);

12

13 /* wall threads */

14 Thread *thread_impeller;

15 Thread *thread_impeller_rotating;

16 Thread *thread_inlet;

17 Thread *thread_shaft;

18

19 thread_impeller = Lookup_Thread(domain , impeller);

20 thread_impeller_rotating = Lookup_Thread(domain ,

impeller_rotating);

21 thread_inlet = Lookup_Thread(domain , inlet_rotating);

22 thread_shaft = Lookup_Thread(domain , shaft_rotating);

23

24 real x_cg[3], force_impeller [3];

25 real moment_impeller [3], moment_impeller_rotating [3],

moment_inlet [3], moment_shaft [3];

26 real moment_curr , omega_curr , domega , nr;

27

28 x_cg [0]=0.0;

29 x_cg [1]=0.0;

30 x_cg [2]=0.0;

31

32 /* Get current impeller moment from all rotating parts */

33 Compute_Force_And_Moment(domain ,thread_impeller ,x_cg ,

force_impeller ,moment_impeller ,TRUE);

34 Compute_Force_And_Moment(domain ,thread_impeller_rotating ,

x_cg ,force_impeller ,moment_impeller_rotating ,FALSE);

35 Compute_Force_And_Moment(domain ,thread_inlet ,x_cg ,

force_impeller ,moment_inlet ,FALSE);

36 Compute_Force_And_Moment(domain ,thread_shaft ,x_cg ,

force_impeller ,moment_shaft ,FALSE);

37

38 /* Motor torque */

39 real motor = 109.4312;

40 /* Mechanical torque */

41 real mechanical = 1.0901;

42 /* Total impeller moment */

43 moment_curr= moment_impeller [0]+ moment_impeller_rotating [0]

+ moment_inlet [0] + moment_shaft [0];

44 /* Set time trip of motor release */

45 real trip = 2.27;

46

47 /* Set radial velocity directly to stabalize in beginning */

48 if(time < 2.26){

49 NV_D(omega , =, -151.8, 0.0, 0.0);

50 NV_S(vel , =, 0.0);

51 }

52 /* start using moment equation to set radial velocity */


53 else{

54 /* motor in use */

55 if (time < trip){

56 moment_curr=moment_curr - motor;

57 }

58 /* ramp down motor in 5 timesteps */

59 else if( time < (trip + 10 * dtime) ){

60 nr = (time -trip)/dtime;

61 moment_curr=moment_curr - motor + 10.9*nr;

62 }

63 /* motor trips */

64 else{

65 moment_curr=moment_curr + mechanical;

66 }

67 /* calculate radial acceleration */

68 domega= moment_curr /0.276;

69 omega_curr = DT_OMEGA_CG(dt)[0];

70

71 /* New angular velocity */

72 NV_D(omega , =, omega_curr + domega*dtime , 0.0, 0.0);

73 NV_S(vel , =, 0.0);

74 }

75 }

76

77 DEFINE_EXECUTE_AT_END(execute_at_end){

78

79 /* **** set the radial velocity of the rotating walls in same

way as dynamic mesh zone **** */

80 int impeller = 131;

81 int impeller_rotating =79;

82 int inlet_rotating =88;

83 int shaft_rotating =80;

84 int FLUID_ID =76;

85


87 Dynamic_Thread *dt;

88

89 /* wall threads */

90 Thread *thread_impeller;

91 Thread *thread_impeller_rotating;

92 Thread *thread_inlet;

93 Thread *thread_shaft;

94

95 thread_impeller = Lookup_Thread(domain , impeller);

96 thread_impeller_rotating = Lookup_Thread(domain ,

impeller_rotating);

97 thread_inlet = Lookup_Thread(domain , inlet_rotating);

98 thread_shaft = Lookup_Thread(domain , shaft_rotating);

99

100 /* fluid threads */

101 Thread *thread_impeller_fluid;

102 thread_impeller_fluid = Lookup_Thread(domain , FLUID_ID);

103

104 /* definitions to calculate total impeller moment */

105 real x_cg[3], force_impeller [3];

106 real moment_impeller [3], moment_impeller_rotating [3],

moment_inlet [3], moment_shaft [3];

107 real moment_curr , omega_curr =-151.8, domega , nr;

108

109 x_cg [0]=0.0;

110 x_cg [1]=0.0;

111 x_cg [2]=0.0;


112

113 /* Get current impeller moment */

114 Compute_Force_And_Moment(domain ,thread_impeller ,x_cg ,

force_impeller ,moment_impeller ,TRUE);

115 Compute_Force_And_Moment(domain ,thread_impeller_rotating ,

x_cg ,force_impeller ,moment_impeller_rotating ,TRUE);

116 Compute_Force_And_Moment(domain ,thread_inlet ,x_cg ,

force_impeller ,moment_inlet ,TRUE);

117 Compute_Force_And_Moment(domain ,thread_shaft ,x_cg ,

force_impeller ,moment_shaft ,TRUE);

118

119 /* Total impeller moment , including mechanical loss */

120 real mechanical = 1.0901;

121 moment_curr= moment_impeller [0]+ moment_impeller_rotating [0]

+ moment_inlet [0] + moment_shaft [0];

122

123 real motor = 109.4312;

124 real time = CURRENT_TIME;

125 dt = THREAD_DT(thread_impeller_fluid);

126 real trip = 2.27;

127

128 real dtime =CURRENT_TIMESTEP;

129 /* set radial velocity */

130 /* constant first */

131 if (time < 2.26){

132 THREAD_VAR(thread_impeller_rotating).wall.omega =

-151.8;

133 THREAD_VAR(thread_inlet).wall.omega = -151.8;

134 THREAD_VAR(thread_shaft).wall.omega = -151.8;

135 }

136 /* start using moment equation to set radial velocity */

137 else{

138 /* motor in use */

139 if (time < trip){

140 moment_curr=moment_curr - motor;

141 }

142 /* ramp down motor in 5 timesteps */

143 else if( time < trip + 10 * dtime ){

144 nr = (time -trip)/dtime;

145 moment_curr=moment_curr - motor + 10.9*nr;

146 }

147 /* motor trips */

148 else{

149 moment_curr=moment_curr + mechanical;

150 }

151

152 /* calculate radial acceleration */

153 domega= moment_curr /0.276;

154 omega_curr = DT_OMEGA_CG(dt)[0];

155

156 THREAD_VAR(thread_impeller_rotating).wall.omega =

omega_curr + domega*dtime;

157 THREAD_VAR(thread_inlet).wall.omega = omega_curr +

domega*dtime;

158 THREAD_VAR(thread_shaft).wall.omega = omega_curr +

domega*dtime;

159 }

160

161 /* **** write radial velocity to file **** */

162 #if !RP_NODE

163 FILE *fp = NULL;

164 char filename []="impeller_motion.out";


165 #endif

166

167 #if !RP_NODE /* SERIAL or HOST */

168 if ((fp = fopen(filename , "a"))==NULL)

169 Message("\n Warning: Unable to open %s for writing\n

",filename);

170 else

171 Message("\nWriting radial velocity to %s...",

filename);

172 #endif

173

174 #if RP_HOST

175 fprintf(fp,"%E %E %E %E\n", CURRENT_TIME , -omega_curr *30/

M_PI , moment_curr , dtime);

176 #endif

177

178 #if !RP_NODE /* SERIAL or HOST */

179 fclose(fp); /* Close the file that was only opened if on

SERIAL or HOST */

180 Message("Done\n");

181 #endif

182 }


C Dynamic valve UDFs

For the dynamic valve closing in Ansys Fluent, two UDFs were used. The firstUDF controld the time dependent inlet boundary contiditon.

1 #include "udf.h"

2

3 DEFINE_PROFILE(transient_velocity , thread , position)

4 {

5

6 float time , velocity;

7 face_t f;

8 float ms ,A,rho;

9 A = 3.14159265*0.05*0.05;

10 rho = 998.2;

11 ms = 52.68/(A*rho);

12 float trip = 0.5;

13 time = CURRENT_TIME - trip;

14 if(time < 0){

15 velocity = ms;

16 }

17 else{

18 velocity = -6.9915 *pow(time ,6) + 35.413 * pow(time ,5)

-70.139 * pow(time ,4) + 69.129 * pow(time ,3) -

34.22* time*time - 0.45853* time + 6.7306;

19 }

20

21 begin_f_loop(f, thread){

22 F_PROFILE(f, thread , position) = velocity;

23 }

24 end_f_loop(f, thread)

25

26 #if RP_HOST

27 printf ("Inlet velocity = ");

28 printf ("%f", velocity);

29 #endif

30 }

The second UDF constrold the valve motion with the 6DOF solver.

1 #include "udf.h"

2 #include "f_wall.h"

3

4 DEFINE_SDOF_PROPERTIES(sdof_properties , prop , dt, time , dtime){

5


7 Thread *thread_a = Lookup_Thread(domain ,84);

8 Thread *thread_b = Lookup_Thread(domain ,77);

9 Thread *thread_c = Lookup_Thread(domain ,10);

10 real x_cg_a [3], f_glob_a [3], m_glob_a [3], x_cg_b [3], f_glob_b

[3], m_glob_b [3], x_cg_c [3], f_glob_c [3], m_glob_c [3];

11 float netmoment;

12 x_cg_a [0] = 0;

13 x_cg_b [0] = 0;

14 x_cg_c [0] = 0;

15

16 Compute_Force_And_Moment(domain ,thread_a ,x_cg_a ,f_glob_a ,

m_glob_a ,TRUE);

17 Compute_Force_And_Moment(domain ,thread_b ,x_cg_b ,f_glob_b ,

m_glob_b ,TRUE);

18 Compute_Force_And_Moment(domain ,thread_c ,x_cg_c ,f_glob_c ,

m_glob_c ,TRUE);


19

20 prop[SDOF_MASS] = 1.2498;

21 prop[SDOF_IXX] = 0.0015;

22 prop[SDOF_IYY] = 0.0072;

23 prop[SDOF_IZZ] = 0.0012;

24

25

26

27 prop[SDOF_ZERO_TRANS_X] = TRUE;

28 prop[SDOF_ZERO_TRANS_Y] = TRUE;

29 prop[SDOF_ZERO_TRANS_Z] = TRUE;

30

31 prop[SDOF_ZERO_ROT_X] = TRUE;

32 prop[SDOF_ZERO_ROT_Y] = FALSE;

33 prop[SDOF_ZERO_ROT_Z] = TRUE;

34

35 prop[SDOF_LOAD_M_Y] = -0.0693* prop[SDOF_MASS ]*9.8066* sin(

DT_THETA (dt)[1]);

36

37 netmoment = (m_glob_a [1] + m_glob_b [1] + m_glob_c [1] -

0.0693* prop[SDOF_MASS ]*9.8066* sin(DT_THETA (dt)[1]));

38

39 /* If the disc starts in the allowed fully opened state , -59

degrees ( -1.02974 rad), it will be forced to stay

there until the netmoment becomes larger than zero. If

the disc starts to close , and then reopenes to -59

degrees , it will crash. If it travels by the allowed

closing state , -11 degrees , it will be forced to stay in

that position and "Disc hit ..." will be displayed. */

40 if(( DT_THETA(dt)[1] <= -1.02974 && netmoment < 0) || (

DT_THETA(dt)[1] >= -0.19199)){

41 prop[SDOF_ZERO_ROT_Y] = TRUE;

42 printf ("Disc hit the seat/roof ");

43 }

44 else{

45 prop[SDOF_ZERO_ROT_Y] = FALSE;

46 }

47

48 printf ("6DOFvinkel = ");

49 printf ("%f", DT_THETA(dt)[1]);

50 printf ("Net Torque = ");

51 printf ("%f", netmoment);

52 printf ("\n updated 6DOF properties");

53

54 }


D Relap5 pump trip with dynamic valve code

The Relap5 script used to simulate the pump trip with dynamic closing valveis shown below.

1 =model.i

2

3 *==============================================

4 * Problem type and option (card 100)

5 *==============================================

6 0000100 new transnt

7

8 *==============================================

9 * Input check or run (card 101)

10 *==============================================

11 0000101 run

12

13 *==============================================

14 * Units selection (card 102)

15 *==============================================

16 0000102 si si

17

18 *==============================================

19 * Noncondensable gas species (card 110)

20 *==============================================

21 0000110 nitrogen

22

23 *==============================================

24 * Hydrodynamic System (card 120 -129)

25 *==============================================

26 0000120 100010000 0.000 h2o

27

28 *==============================================

29 * Timestep cards (201 -299)

30 *==============================================

31 * end min max ctrl minr -edt/plt majr -edt/plt rst -freq

32 0000201 100.0 1.0e-14 1.000e-002 7 10 1000000 1000000

33

34 *==============================================

35 * Trip cards , variable trips (401 -599)

36 * The logical statement is D o e s the quantity given by W1 and W2

37 * have the relationship given by W3 with the quantity given by

38 * W4 and W5 plus W6? W7 is the latch indicator where n=always , l

=once.

39 *==============================================

40 401 time 0 lt null 0 0.0 n * pump trip (running)

41 501 time 0 ge null 0 0.0 n * V1 not activated

42 520 time 0 ge null 0 0.0 n * table trip for tmdpvol 110, always

true

43 521 time 0 ge null 0 0.0 n * regulator trip , activated

44 513 mflowj 107000000 ge null 0.0 0.0 n

45 *==============================================

46 * Control variable numbers

47 *==============================================

48 20500000 9999

49

50 *==============================================

51 * time -dependent volume component 100 diameter 10.0 m length

10.0 m

52 * position x = 0.000 m, y = 0.000 m, z = 0.000 m

53 *==============================================

54 1000000 unnamed tmdpvol


55 * area length vol az -angle inc -angle dz

56 1000101 78.539816 10.0000 0.0 0.0 0.0 0.0

57 * rough hd vol_flags

58 1000102 0.000025 0.0 0

59 * ebt trip alpha idnum

60 1000200 103 0 time 0

61 * time press temp

62 1000201 0.0 20.000e+5 293.150

63

64 *==============================================

65 * single junction 101 inner diameter 122.5 mm

66 * position x = 0.000 m, y = 0.000 m, z = 0.000 m

67 *==============================================

68 1010000 junction sngljun

69 * from to area fwd. loss rev. loss jefvcahs

70 1010101 100000000 102010001 1.17859e-02 0.000 0.000 0

71 * cntrl flowf flowg veli

72 1010201 1 52.680 0.000 0.0

73

74 *==============================================

75 * pipe component 102 main inner diameter 122.5 mm length 5.000 m

76 *==============================================

77 1020000 unnamed pipe

78 * pipe component number of volumes

79 1020001 13

80 * pipe x-coord volume flow areas

81 1020101 1.17859e-02 13

82 * pipe x-coord volume lengths

83 1020301 0.384615 13

84 * pipe component volumes vertical angles

85 1020601 0.000 13

86 * rough hd vol. num

87 1020801 0.000025 0.0 13

88 * fwd. loss rev. loss junc. num

89 1020901 0.0 0.0 12

90 * tlpvbfe vol. num

91 1021001 0 13

92 * ef0cahs junc. num

93 1021101 0 12

94 * ebt press temp

95 1021201 103 20.000e+5 293.150 0.0 0.0 0.0 13

96 * cntrl word

97 1021300 1

98 * flowf flowg veli junc. num

99 1021301 52.680 0.000 0.0 12

100

101 *==============================================

102 * pump component 103 inner diameter 122.5 mm

103 * outlet position x = 5.260 m, y = 0.000 m, z = 0.315 m

104 *==============================================

105 * pump data are taken from:

106 * inner diameter of pump = 122.5 [mm]

107 * inner area of pump = 1.17859e-02 [m2]

108 * length of pump = 0.408 [m]

109 * vertical angle of the pump = 50.46 [deg]

110 * rated pump velocity = 1450 [rpm] (from pump curve)

111 * W1(R) rated pump velocity = 151.8 [rad/s] (1 rad/s = 30/pi

rpm)

112 * W2(R) initial pump velocity ratio = 1.0

113 * W3(R) rated pump flow = 0.05278 [m3/s] (from pump curve)

114 * W4(R) rated pump head = 25.6 [m] (from pump curve)

115 * W5(R) rated hydraulic torque = 113.0 [Nm] (RPP/W1)


116 * W6(R) pump moment of inertia = 0.276 [kgm2]

117 * W7(R) pump rated density = initial [kg/m3]

118 * W8(R) rated pump motor torque = 145.0 [Nm] (RMP/W1)

119 * W9(R) TF2 friction torque = 30.87 [Nm] (W8 - W5 - TF0)

120 * W10(R) TF0 friction torque = 1.13 [Nm] (friction at zero

speed)

121 * W11(R) TF1 friction torque = 0.0 [Nm]

122 * W12(R) TF3 friction torque = 0.0 [Nm]

123 * rated pump efficiency (eta) = 0.78 (from pump curve)

124 * rated pump hydraulic power (RPP) = 17.16 [kW] (from pump curve

)

125 * rated motor electrical power (RMP) = 22.0 [kW] (RPP/eta)

126 * motor synchronous speed = 1450 [rpm]

127 * motor synchronous speed = 151.8 [rad/s]

128 1030000 P1 pump

129 * area length vol az -angle inc -angle dz e

130 1030101 1.17859e-02 0.408442 0.0 0.0 50.464 0.315000 0

131 * from/to area fwd. loss rev. loss f0cah0

132 1030108 102130002 0.0 0.000 0.000 0

133 1030109 104010001 0.0 0.000 0.000 0

134 * ebt press temp

135 1030200 103 20.000e+5 293.150


137 1030201 1 52.680 0.000 0.0

138 1030202 1 52.680 0.000 0.0

139 * data indi 2ph multi 2ph diffi torque tab vel index trip rev

indi

140 1030301 0 -1 -3 -1 -1 401 1

141 * rated pvel velratio rated flow rated head rated torq mom inert

142 1030302 151.8 1.0 0.05278 25.6 113.0 0.276

143 * rated dens rtd mtr torq tf2 tf0 tf1 tf3

144 1030303 0 145.0 30.87 1.13 0.0 0.0

145 *** PUMPKURVOR ***

146 * HAN (pumpning , Flode < design)

147 1031100 1 1

148 * v/a h/a^2

149 1031101 0.0 1.2433828125

150 1031102 0.1112526316 1.256578125

151 1031104 0.1187952632 1.2574726563

152 1031105 0.2111915789 1.2430390625

153 1031106 0.2130773684 1.2427421875

154 1031107 0.2168489474 1.2421523438

155 1031108 0.3186731579 1.2366328125

156 1031109 0.3205589474 1.2364296875

157 1031110 0.4204978947 1.225515625

158 1031111 0.4223836842 1.224953125

159 1031112 0.5260942105 1.1939726563

160 1031113 0.5279789474 1.1934101563

161 1031114 0.5298631579 1.1927382813

162 1031115 0.6279210526 1.1577226563

163 1031116 0.6335736842 1.155703125

164 1031117 0.7354 1.1152929688

165 1031118 0.7391736842 1.113796875

166 1031119 0.8372263158 1.0648867188

167 1031120 0.8466526316 1.0615976563

168 1031121 0.8692789474 1.0537148438

169 1031122 0.9051052632 1.0467421875

170 1031123 0.9333947368 1.0383671875

171 1031124 0.9484789474 1.0316601563

172 1031125 0.9522473684 1.029984375

173 1031126 1.0 1.03

174


175

176 * HVN (pumpning , Flode > design)

177 1031200 1 2

178 * a/v h/v^2

179 1031201 0.5 0.0

180 1031202 0.632843934 0.2471579762

181 1031203 0.6335994451 0.2483867

182 1031204 0.6764334158 0.3216411798

183 1031205 0.6772966595 0.3231919512

184 1031206 0.6825276514 0.332645367

185 1031207 0.7024159411 0.3695612187

186 1031208 0.729467412 0.4194062289

187 1031209 0.7576059652 0.4756615319

188 1031210 0.7903494176 0.5413026138

189 1031211 0.7915281492 0.5437358301

190 1031212 0.8595184887 0.6803917269

191 1031213 0.8623154531 0.6863345739

192 1031214 0.8637188095 0.6893250645

193 1031215 0.9487002806 0.8817397707

194 1031216 1.0 1.03

195

196

197 * HAD

198 1031300 1 3

199 * v/a h/a^2

200 1031301 -1.0 1.8

201 1031302 -0.9 1.6

202 1031303 -0.8 1.48

203 1031304 -0.6 1.33

204 1031305 -0.55 1.3

205 1031306 -0.5 1.28

206 1031307 -0.4 1.26

207 1031308 -0.2 1.25

208 1031309 0.0 1.2433828125

209

210 * HVD

211 1031400 1 4

212 * a/v h/v^2

213 1031401 -1.0 1.8

214 1031402 0.0 0.7

215

216 * BAN

217 1031500 2 1

218 * v/a b/a^2

219 1031501 0.0 0.296602

220 1031502 0.1621652632 0.4115586561

221 1031503 0.2922742105 0.5056027633

222 1031504 0.4223836842 0.6100534765

223 1031505 0.5260942105 0.6884119097

224 1031506 0.6316894737 0.7563614055

225 1031507 0.7410578947 0.8295328543

226 1031508 0.8391105263 0.8922603973

227 1031509 0.9522473684 0.9758466114

228 1031510 1.0 1.0

229

230 * BVN

231 1031600 2 2

232 * a/v b/v^2

233 1031601 0.2 0.0

234 1031602 0.38 0.2

235 1031603 0.6799020941 0.5600465614

236 1031604 0.7304742316 0.624087267


237 1031605 0.7903494176 0.7043965944

238 1031606 0.8595184887 0.8021148963

239 1031607 0.9487002806 0.9253975618

240 1031608 1.0 1.0

241

242 * BAD

243 1031700 2 3

244 * v/a b/a^2

245 1031701 -1.0 1.02

246 1031702 -0.8 0.6

247 1031703 -0.6 0.3

248 1031704 -0.4 0.19

249 1031705 -0.3 0.18

250 1031706 -0.2 0.19

251 1031707 -0.00188564 0.29660168

252 1031708 0.0 0.296602

253

254 * BVD

255 1031800 2 4

256 * a/v b/v^2

257 1031801 -1.0 1.02

258 1031802 0.0 0.8

259

260 *==============================================


262 *==============================================



265 1040001 6


267 1040101 1.17859e-02 6


269 1040301 0.426667 6


271 1040601 90.000 6


273 1040801 0.000025 0.0 6


275 1040901 0.0 0.0 5


277 1041001 0 6


279 1041101 0 5


281 1041201 103 22.500e+5 293.150 0.0 0.0 0.0 6

282 * cntrl word

283 1041300 1


285 1041301 52.680 0.000 0.0 5

286

287 *==============================================


289 * position x = 5.260 m, y = 0.000 m, z = 2.875 m

290 *==============================================

291 1050000 bend sngljun


293 1050101 104060002 106010001 7.85398e-03 0.089 0.089 0


295 1050201 1 52.680 0.000 0.0

296

297 *==============================================



299 *==============================================



302 1060001 5


304 1060101 7.85398e-03 4

305 1060102 5.2224e-003 5


307 1060301 0.400000 5


309 1060601 0.000 5


311 1060801 0.000025 0.0 5


313 1060901 0.0 0.0 4


315 1061001 0 5


317 1061101 0 4


319 1061201 103 22.500e+5 293.150 0.0 0.0 0.0 5

320 * cntrl word

321 1061300 1


323 1061301 52.680 0.000 0.0 4

324

325 *==============================================


327 * position x = 7.260 m, y = 0.000 m, z = 2.875 m

328 *==============================================

329 1070000 V1 valve


331 1070101 106050002 108010001 5.2224e-003 0.000 0.000 200


333 1070201 1 52.680 0.000 0.0

334 * valve type

335 1070300 swcvlv * swing check valve

336 * latch min max init radius seat

337 1070301 2 4.0 53.0 53.0 0.049 0.041

338 * R leak inc -angle init mass dist

339 1070302 0.078 0.0 0.0 0.0 1.2498 0.0

340 * R dangle mass I volume

341 1071101 0.0693 10.0 1.2498 0.0072 0.00014085

342 * Hydraulic model

343 1071201 cmcq 550 540 560

344

345 * -----------------------------------------------

346 * Data from IFFM arch. No 378/2014 , Table 6 pp.38

347 * -----------------------------------------------

348 * Determine mass flow sign and multiply with valve angle

349 20505100 vlvfl_un tripunit 2.0 2.0 0 0

350 20505101 513

351 20505200 vlv_atr mult 1.0 1.0 1 0

352 20505201 vlvstem 107 cntrlvar 510

353 20505300 vlv_arg sum 53.0 53.0 1 0

354 20505301 0.0 1.0 cntrlvar 520 -1.0 vlvstem 107

355 * Table Cq

356 20201100 reac -t

357 20201101 -53.0 1.071789688592774

358 20201102 -48.0 0.997636291864619

359 20201103 -43.0 0.905425267157294

360 20201104 -38.0 0.834180350285793


361 20201105 -33.0 0.775968893168883

362 20201106 -23.0 0.666773528288052

363 20201107 -13.0 0.414912113506239

364 20201108 -4.0 0.212866861496991

365 20201109 4.0 0.212866861496991

366 20201110 13.0 0.414912113506239

367 20201111 23.0 0.666773528288052

368 20201112 33.0 0.775968893168883

369 20201113 38.0 0.834180350285793

370 20201114 43.0 0.905425267157294

371 20201115 48.0 0.997636291864619

372 20201116 53.0 1.071789688592774

373 20505400 CQ_cvar function 1.0 0.0 1 0

374 20505401 cntrlvar 530 11

375 * Table Cm

376 20201200 reac -t

377 20201201 -53.0 1.403779262195581

378 20201202 -48.0 1.622964200769869

379 20201203 -43.0 1.582770246769165

380 20201204 -38.0 1.486509025538848

381 20201205 -33.0 1.395085378220361

382 20201206 -23.0 1.363544777510245

383 20201207 -13.0 1.326051640344194

384 20201208 -4.0 0.882785350000598

385 20201209 4.0 0.882785350000598

386 20201210 13.0 1.326051640344194

387 20201211 23.0 1.363544777510245

388 20201212 33.0 1.395085378220361

389 20201213 38.0 1.486509025538848

390 20201214 43.0 1.582770246769165

391 20201215 48.0 1.622964200769869

392 20201216 53.0 1.403779262195581

393 20505500 CM_cvar function 1.0 0.0 1 0

394 20505501 cntrlvar 530 12

395 * Talbe Ck

396 20201300 reac -t

397 20201301 -53.0 0.870524204588190

398 20201302 -48.0 1.004744230600981

399 20201303 -43.0 1.219817276767964

400 20201304 -38.0 1.437077166408101

401 20201305 -33.0 1.660777209762752

402 20201306 -23.0 2.249278857450822

403 20201307 -13.0 5.808818022651023

404 20201308 -8.0 22.069062573104617

405 20201309 -4.0 500.0

406 20201310 4.0 500.0

407 20201311 8.0 22.069062573104617

408 20201312 13.0 5.808818022651023

409 20201313 23.0 2.249278857450822

410 20201314 33.0 1.660777209762752

411 20201315 38.0 1.437077166408101

412 20201316 43.0 1.219817276767964

413 20201317 48.0 1.004744230600981

414 20201318 53.0 0.870524204588190

415

416 20505600 CK_cvar function 1.0 0.0 1 0

417 20505601 cntrlvar 530 13

418 *

419 *==============================================


421 *==============================================




424 1080001 20


426 1080101 1.45068e-02 1

427 1080102 7.85398e-03 20


429 1080301 0.400000 20


431 1080601 0.000 20


433 1080801 0.000025 0.0 20


435 1080901 0.0 0.0 19


437 1081001 0 20


439 1081101 0 19


441 1081201 103 22.500e+5 293.150 0.0 0.0 0.0 20

442 * cntrl word

443 1081300 1


445 1081301 52.680 0.000 0.0 19

446

447 *==============================================


449 * position x = 15.260 m, y = 0.000 m, z = 2.875 m

450 *==============================================

451 1090000 junction sngljun


453 1090101 108200002 110000000 7.85398e-03 0.000 0.000 0


455 1090201 1 52.680 0.000 0.0

456

457 *==============================================

458 * time -dependent volume component 110 diameter 10.0 m length

10.0 m

459 * position x = 15.260 m, y = 0.000 m, z = 2.875 m

460 *==============================================

461 1100000 unnamed tmdpvol

462 * area length vol az -angle inc -angle dz

463 1100101 78.539816 10.0000 0.0 0.0 0.0 0.0

464 * rough hd vol_flags

465 1100102 0.000025 0.0 0


467 1100200 103 0 time 0


469 1100200 103 520 cntrlvar 8110

470 * cntrlvar press temp

471 1100201 20.5e+05 20.5e+05 293.150

472 1100202 21.5e+05 21.5e+05 293.150

473

474 * Proportional Regulation to set pressure boundary for given

mass flow

475 20511100 heviside tripunit 1.0 0.0 0

476 20511101 521

477 20521100 pkonst constant 100000.0

478 20531100 mfref constant 52.68

479 20541100 p110 sum 1.0 21.5 0

480 20541101 0.0 1.0 p 110010000

481 20551100 mf-mfref sum 1.0 0.0 0

482 20551101 0.0 1.0 mflowj 109000000 -1.0 cntrlvar 3110


483 20561100 mfref -1 div 1.0 0.0 0

484 20561101 cntrlvar 3110

485 20571100 product mult 1.0 0.0 0

486 20571101 cntrlvar 1110 cntrlvar 2110 cntrlvar 5110 cntrlvar

6110

487 20581100 newp110 sum 1.0 21.5 0

488 20581101 0.0 1.0 cntrlvar 4110 1.0 cntrlvar 7110

489

490 .end

Documents

umu.diva-portal.org938553/FULLTEXT01.pdf · behavior of the centrifugal pump and swing check valve. In existing cal-culation tools, the system and components are modeled in one dimension