1

2010 IRUG MeetingRELAP5-3D

Flexible Wall ComponentFluid Property Improvements

Glen A. MortensenDoug Barber

Dan Prelewicz

Nuclear Systems Analysis DivisionInformation Systems Laboratories (ISL), Inc.

Rockville, Maryland, USAIdaho Falls, Idaho, USASeptember 20-23, 2010

2

Recent Additions to RELAP5-3D

• Flexible walls– Single flexible wall component– Multiple flexible wall component

• Fluid Property Improvements– Metastable liquid extrapolation– Mass error edits for

• Total• Liquid• Vapor• Noncondensables• Boron

– Transport properties => TPF tables

3

Flexible Walls

• Couples fluid and structure response– Models pressure relief effect of structural deflection

• Presently limited to elastic deflection

• Mass of the wall is not included in the model

• Nonlinear stiffness can be modeled (input table)

– Allows more realistic prediction of structural loadings

– Pressure wave propagation speed more accurately predicted

– Typical applications• Core barrel deflection in LBLOCA

• Valve closure loading (check valve slam)

• Condensation induced water hammer loadings

4

Flexible WallsGeometry

• Flexible walls– Between two volumes (like a junction)

– Added two new components• Single flexible wall (SNGLFW)• Multiple flexible wall (MTPLFW) (e.g., core barrel)

FromVolume

ToVolume

Wall

5

Flexible Wall

• The wall separating two volumes acts like a spring-mass system responding to the differential pressure force between the volumes, where X = volume displacement

M d2X/dt2 + C dX/dt + K X = P1 – P2

• In this implementation inertia and damping are neglected

(M = C = 0)– Reasonable since response of structure is generally much

faster than pressure difference changes, i.e. structures are stiff and structure response is quasi-static

• Stiffness (K) is determined from pressure versus volume displacement calculations or data

6

Flexible WallsInput – Single Flexible Wall Component

• Card CCC0000, Component name and type– W1(A) Component Name– W2(A) Component type, use SNGLFW for flexible walls

• Cards CCC0101 through 109, Geometry– W1(I) From connection code to a component– W2(I) To connection code to a component– W3(R) Flexible wall area (m2, ft2)– W4(I) Flexible wall stiffness general table number

• Card 202TTT00, General table type and data– W1(A) Table type, use FWSTIF for flexible walls (words 2-5

are not used)• Card 202TTT01 through 99, General table data

– W1(R) Argument value, use volume displacement (m3, ft3)– W2(R) Function value, use flexible wall stiffness (Pa/ m3,

psi/ft3)

7

Flexible WallsInput – Multiple Flexible Wall Component

• Card CCC0000, Component name and type– W1(A) Component Name– W2(A) Component type, use MTPLFW for multiple flexible walls

• Card CCC0001, Number of flexible walls with this geometry– W1(I) Number of flexible walls, nfw (0<nfw<100)

• Cards CCC0NNM, Geometry– W1(I) From connection code to a component– W2(I) To connection code to a component– W3(R) Flexible wall area (m2, ft2)– W4(I) Flexible wall stiffness general table number

• Card 202TTT00, General table type and data– W1(A) Table type, use FWSTIF for flexible walls (words 2-5 are not

used)• Card 202TTT01 through 99, General table data

– W1(R) Argument value, use volume displacement (m3, ft3)– W2(R) Function value, use flexible wall stiffness (Pa/ m3, psi/ft3)

8

Flexible WallsNew Plot Variables

• Plot variables are available using 2080 cards– FWDVOL

• Flexible wall incremental volume displacement for this time step on the “FROM” side of the wall. The “TO” volume incremental volume displacement is the negative of the “FROM” side displacement (m3)

– FWSTIF• Flexible wall stiffness (Pa/m3)

– FWVOL• Flexible wall volume displacement from the “FROM” side of

the wall. The “TO” volume displacement is the negative of the “FROM” side displacement (m3)

– FWDX• Flexible wall linear displacement on the “FROM” side of the

wall. The “TO” volume linear displacement is the negative of the “FROM” side displacement (m)

9

Flexible WallsTheory

• The original RELAP5-3D equations had the volume pulled outside the time partial derivative terms in the partial differential equations because the volume was independent of time

• The five partial differential equations are for the conservation of– Liquid, vapor, and noncondensable mass– Liquid and vapor energy

• With a flexible wall, the volume is now a function of time, so the volume has to remain inside the time partial derivative terms– This adds an additional term to each equation that contains

the partial derivative of volume with respect to time– These partial derivative of volume with respect to time terms

are converted to partial derivative of pressure with respect to time terms by using the equation that equates a volume change to a pressure change divided by the wall stiffness (K)

t

P

Kt

V

1

10

Flexible WallsEquation Modifications

• Addition of variable volume to mass, energy, and noncondensable equations results in a new term in each equation that multiplies the increment in pressure in the cell

• For the “FROM” volume, these additional terms add to the existing terms in column 5 of the 5x5 “A” matrix– They are added when the matrix is built in PRESEQ

• For the “TO” volume – two cases are possible– “TO” volume pressure is constant, i.e., TDV, no more

modifications are required– “TO” volume pressure is part of the system, handled

like the velocities are in PRESEJ in a new subroutine called PRESEJW

11

Flexible WallsColumn 5 “A” Matrix Modifications

12

Flexible WallsDocumentation and Examples

• Documentation was added to Volume I as Appendix B• Two examples follow

– Edwards pipe – solid and flexible wall (shows effect on decompression wave speed)

– G3 pressure pulse test – solid and hollow test section (shows pressure relief effect on structural loading; peak load reduced from ~8,000 kPa to ~6,000 kPa)

• Semi = semi-implicit solution method

13

Edwards Pipe

14

G3 Pressure Pulse Test

Test ProcedureHammer was dropped on top of the piston which created a pressure pulse in the water between the inner square test section wall and the outside cylinder.

Test SectionsTwo square test sections were used: solid and hollow

15

G3 Pressure Pulse TestSolid Test Section

16

G3 Pressure Pulse TestHollow Test Section

17

G3 Pressure Pulse TestHollow Test Section

18

Fluid Property Improvements Metastable extrapolation at constant temperature

• Example using Edwards pipe blowdown using h2o fluid– 20 volume pipe (component number 3)– Break volume is volume 3-20– Closed-end volume is volume 3-01– Decompression wave travels from 3-20 to 3-01 where it tries to

double down– Pressure in volume 3-01 drops below saturation, so the liquid

in this volume goes into the metastable region (superheated liquid)

– RELAP5-3D extrapolates from the saturation pressure at constant pressure to get the metastable liquid properties

– This results in a relatively large mass error in this volume as shown on the next slide

• Mass error at 0.25 milliseconds comes from the break volume (3-20) as will be shown later

• Mass error at 3.6 milliseconds comes from volume 3-01

19

Fluid Property Improvements Metastable extrapolation at constant temperature

20

Fluid Property Improvements Metastable extrapolation at constant temperature

• Reason for the mass error is a bad liquid density extrapolation at constant pressure

• Decided to try extrapolation at constant temperature– New capability was added via Card 1, Option 71

• Comparisons of these two methods is shown on next slide for the closed-end volume 3-01– Saturation and liquid temperatures

– Liquid densities• Notice that the constant pressure extrapolation (base) case

computes a liquid density that increases instead of decreases as the liquid becomes more superheated

• In fact, it is even greater than the saturation value• This is the source of the mass error at 3.6 milliseconds

21

Fluid Property Improvements Metastable extrapolation at constant temperature

22

Fluid Property Improvements Metastable extrapolation at constant temperature

• The h2on fluid has metastable properties and it looks better on the previous plots – maybe it is the one to use

• Ran typ1200n for the three cases: h2o, h2o with option 71, and h2on

• First slide shows the system mass error in 0-40 second time span for primary and secondary systems– System 1 is the primary system (top figure)– System 2 is the intact secondary system (bottom figure)– Note that h2on fluid does not give a smaller mass error

• Second slide shows the same info in the 0-1200 second time span– Not sure what is going on with the h2on fluid

23

Fluid Property Improvements Metastable extrapolation at constant temperature

24

Fluid Property Improvements Metastable extrapolation at constant temperature

25

Fluid Property Improvements Mass error edits

• Additional mass error edits were added for– Total (liquid plus vapor)

– Liquid

– Vapor (includes the noncondensables)

– Noncondensables

– Boron

• Total for each volume as well as for each system • Volume number in each system that has the maximum

volume total mass error (vnmaxvme)• Maximum total mass error of all the individual volume

total mass errors in each system (maxvme)

26

Fluid Property Improvements Mass and mass error variables for each Volume

Type of edit Continuity-eq. mass (state)

State-eq. mass (statep)

Mass error = cont eq.– state eq.

Total volmas tmassv volmer

Liquid volmasf tmassfv volmerf

Vapor volmasg tmassgv volmerg

Noncondensable volmasn tmassnv volmern

Boron volmasb tmassbv volmerb

27

Fluid Property Improvements Mass and mass error variables for each System

Type of edit Continuity-eq. mass (state)

State-eq. mass (statep)

Mass error = cont eq.– state eq.

Total systmc systms sysmer

Liquid systmfc systmfs sysmerf

Vapor systmgc systmgs sysmerg

Noncondensable systmnc systmns sysmern

Boron systmbc systmbs sysmerb

28

Fluid Property Improvements Mass error edit example

29

Fluid Property Improvements New plot edits using 2080 cards

• Can now use -1 for the parameter for volumes and junctions– When -1 is used as a parameter instead of the volume

number or junction number, all the volume or junction data for that variable will be written to the plot file

• Added a new volume variable– ALLVOLS with a -1 for the parameter

• ALL the volume data will be written to the plot file

• Added a new junction variable– ALLJUNS with a -1 for the parameter

• ALL the junction data will be written to the plot file

• These new plot edits are very useful for debugging

30

Fluid Property Improvements Transport properties added to TPF tables

• Transport properties are being added to the thermodynamic property tables for all the fluids

• The transport property subroutines are used to generate values at the same pressure-temperature points that are used for the thermodynamic properties– Surftn for surface tension– Thcond for liquid and vapor thermal conductivity– Viscos for liquid and vapor dynamic viscosity

• Thermodynamic TPF files will be expanded to add these five additional transport properties

• Eventually, the expanded TPF files will be converted to XDR files so that they are portable between computers– Future installations would not require generating the fluid

property files or converting an ASCII file to a binary file