Chatter of Safety Valve - My Committeesmycommittees.api.org/standards/cre/scprs/Shared Documents/2008... · 3 Purpose of Study Safety valve chatter would result in (1) Mechanical

1

Chatter of Safety Valve

Hisao IZUCHI

PLE Technology Center

Chiyoda Advanced Solutions Corporation

April, 2008

@CHIYODA/ChAS All rights reserved 2007

2

Contents

1. Purpose of Study

2. Chatter Test at Test Facility

3. Dynamic Simulation

4. Stability Analysis

5. Future Plan


3

Purpose of StudySafety valve chatter would result in (1) Mechanical failure of the valve and related piping system (risk of failure would increase for large size of the safety valve)(2) Reliving flow rate reduction caused by insufficient valve opening due to chatterSince there is no publication which clearly explains the mechanism of chatter, Chiyoda executed to study safety valve chatter for the following purposes:(1) Investigate mechanism of chatter(2) How to prevent chatter


4

Study Program(1) Chatter test at a manufacturer test facility

(2) Dynamic simulation taking valve disc motion and fluid dynamics in the connected piping system into account （to simulate actual valve motion)

(3) Stability Analysis based on Professor Hayama’s theory recently published for pressure-open-type valve which is similar to safety valve (to investigate valve stable condition)


5

Possible Cause of Chatter

(1) Excessive pressure drop of inlet or outlet pipe (well known characteristics)

(2) Interaction between valve disc motion and pressure wave propagation into piping system (acoustic phenomena)

(3) Effect of outlet area ratio to orifice area（Increase of valve body pressure in case of small outlet area ratio)


6

Outlet Area Ratio to Orifice Area API A Manufacturer

1D2 27.7 22.31.5D3 62.2 50.11E2 15.5 10.8

1.5E3 34.9 24.31.5F2 9.9 8.11.5F3 22.3 18.22G3 13.6 11.52H3 8.7 7.42J3 5.3 4.63J4 9.5 8.23K4 6.6 5.73K6 14.9 12.93L4 4.3 3.74L6 9.6 8.34M6 7.6 6.64N6 6.3 5.44P6 4.3 3.76Q8 4.4 3.76R8 3.0 2.66R10 4.8 4.18T10 2.9 2.6

SizeOutlet Area / Orifice Area

Orifice area ratio tends to decrease as SV size becomes larger


7

V = cW = ρ1A1cP = P1

V = cW = ρ2A2cP = P2

1

21

1

212 /

AAPPP =⋅=

ρρ

P2 becomes larger as area ratio, A2/A1 decrease.Increase of P2 affects to close the valve and might result in chatter except balance type safety valve. This instability is similar to the excessive inlet pipe pressure drop.

V : velocityc : sound speedW : weight flow rateρ : densityA : flow areaP : pressure suffix 1 : orifice (nozzle)suffix 2 : outlet


8

Safety Valve Chatter Test

1st Day Lift Force Measurement (1)2nd Day Lift Force Measurement (2)3rd Day Chatter Test (1)4th Day Chatter Test (2)5th Day Chatter Test (3)@ a test bench of a manufacturer

No. of Tests135139506272

458Total


9

Lift Force Measurement （to obtain basic characteristic of safety valve）

Compressor Vessel（0.5m3）

20barG

Lift Force was measured by load cell(Spring is removed and position of disc is adjusted)

Investigate effect of outlet area1. With no attachment2. With reducer and effuser 2” > 1-1/2” < 2”3. With reducer and effuser 2” > 1-1/4” < 2”4. With reducer and effuser 2” > 1” < 2”5. With reducer and effuser 2” > 3/4” < 2”

Ball Valve

P1

P2

P3

Pn Pressure Sensor

P4Minimum inletPipe length

（Corresponding to larger size of safety valves)

Test Valve1E2 & 1.5F2


10

コンプレッサ Vessel（0.5m3）

20barG

Ball Valve

P1

P2

P3

Pn Pressure Sensor

Investigate effect of outlet pipe length1. No pipe 3. 10m2. 5m

Investigate effect of Inlet pipe length1. 1m 4. 10m2. 3m 5. 15m3. 5m 6. 20m

P4

Ball Valve

P5

Chatter Test

Investigate effect of outlet area1. With no reduce2. With reducer and effuser 2” > 1-1/2” < 2”3. With reducer and effuser 2” > 1-1/4” < 2”4. With reducer and effuser 2” > 1” < 2”5. With reducer and effuser 2” > 3/4” < 2”

（Corresponding to larger size of safety valves)


11

Test Valve1E2 1.5F2

Set Press. = 20 barg

Disk positionwas measured by non-contact displacement

meter with laser sensor


12

Test Bench

Vessel

Safety Valve

DisplacementMeter

Inlet Piping (5m)


13

Test BenchNo Inlet Pipe Inlet Pipe Length is 1m

14

Lift Force Measurement

Load Cell

15

0

200

400

600

800

1000

1200

0 1 2 3 4 5Lift (mm)

Lift

Forc

e (N

)

Area Ratio = 8.3 (outlet = 2inch)Area Ratio = 5.6 (outlet = 1-1/2inch)Area Ratio = 4.1 (outlet = 1-1/4inch)Area Ratio = 2.5 (outlet = 1inch)Area Ratio = 1.5 (outlet = 0.75inch)Spring Load

Max Lift4.4mm

Area Ratio = Outlet Area / Orifce Area0

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4 5Lift (mm)

Lift

Forc

e (N

)

Area Ratio = 11.2 (outlet = 2inch)Area Ratio = 7.5 (outlet = 1-1/2inch)Area Ratio = 5.5 (outlet = 1-1/4inch)Area Ratio = 3.3 (outlet = 1inch)Area Ratio = 2.0 (outlet = 3/4inch)Spring Load

Max Lift3.8mm

Area Ratio = Outlet Area / Orifce Area

Results of Lift ForceMeasurement

1E2 1.5F2

Lift Force > Spring Load=> Popping Action

Lift Force < Spring Loadwith Reducer of 1”or 3/4”=> Possibility of Unstable Characteristic

Lift Force > Spring Load=> Popping Action


16

1"/0m 1"/1m 1"/3m 1"/5m 1"/10m 1"/15m 1"/20m- 55-68Hz 71-111Hz 79-104Hz - - -

1-1/2"/0m 1-1/2"/1m 1-1/2"/3m 1-1/2"/5m 1-1/2"/10m74-92Hz 42-59Hz - - -

1-1/2"/5m-

Actual length is figure in table + 1.2m of safety valve stand Chatter occurs Both cases were observed with chatter and without chatter

Natural frequency of valve disc and spring is 75 Hz

1E2

1.5F2

1E2

Inlet Pipe Size / Inlet Pipe LengthChatter Frequency

1-1/2"/1m-, 43-52Hz

Results of Test / Effect of Inlet Pipe LengthChatter occurs

Inlet length < 5m No Chatter

Inlet Length >= 10m

Longer line length means larger pressure drop of pipe.Therefore, chatter could not be caused by excessive pressure drop of pipe.


17

Time History in Case of Chatter Occurrence試験Ｎｏ．3-39 チャタリング試験

---SVサイズ上流ボール弁

１Ｅ２全開管台＋１００ｃｍ ---上流配管下流絞り下流ボール弁下流配管

---

-0.50

0.50

1.50

2.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00

経過時間　(sec)

圧力

　(M

Pa)

圧力①

圧力②

-1.000.001.002.003.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00


弁リ

フト

　(m

m)

弁リフト

-0.050.000.050.100.15

0.00 1.00 2.00 3.00 4.00 5.00 6.00


圧力

　(M

Pa)

圧力③

圧力④

圧力⑤

2.5

1.5

0.5

-0.5Pre

ss. (

MP

aG)

1. Relatively Short length of inlet pipe, 1E2, Inlet pipe length = 1m

0 1 2 3 4 5 6

Time (sec,)

Point 1Point 2

0 1 2 3 4 5 6

Time (sec,)

Point 3Point 4Point 5

0.150.10

0.00-0.05P

ress

. (M

PaG

)

0.05

0 1 2 3 4 5 6

Time (sec,)

32

0-1Li

ft (m

m)

1


18

試験Ｎｏ．3-45 チャタリング試験

---SVサイズ上流ボール弁

１Ｅ２全開管台＋１０００ｃｍ ---上流配管下流絞り下流ボール弁下流配管

---

-0.50

0.50

1.50

2.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00


圧力

　(M

Pa)

圧力①

圧力②

-1.000.001.002.003.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00


弁リ

フト

　(m

m)

弁リフト

-0.05

0.00

0.05

0.10

0.00 1.00 2.00 3.00 4.00 5.00 6.00


圧力

　(M

Pa)

圧力③

圧力④

圧力⑤

Time History in Case of Normal Actuation 2. Relatively Long length of inlet pipe, 1E2, Inlet pipe length = 10m

2.5

1.5

0.5

-0.5Pre

ss. (

MP

aG)

0 1 2 3 4 5 6

Time (sec,)

Point 1Point 2

0 1 2 3 4 5 6

Time (sec,)

Point 3Point 4Point 5

0.150.10

0.00-0.05P

ress

. (M

PaG

)

0.05

0 1 2 3 4 5 6

Time (sec,)

32

0-1Li

ft (m

m)

1


19

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

時間　(sec)

圧力

　(M

Pa)

弁箱内

SV上流

0

1

2

3

1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

時間　(sec)

弁リ

フト

　(m

m)

Vibration Occurs

1. Relatively Short length of inlet pipe, 1E2, Inlet pipe length = 1m

SV InletSV Body

3

2

0

Lift

(mm

)

1

Time (sec.)1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

Time (sec.)1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

2.5

Pre

ss (M

PaG

)

2.01.51.00.50.0

-0.51.10


20

2. Relatively Long length of inlet pipe, 1E2, Inlet pipe length = 10m

0

1

2

3

1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78

時間　(sec)

弁リ

フト

　(m

m)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78

時間　(sec)

圧力

　(M

Pa)

弁箱内

SV上流

3

2

0

Lift

(mm

)

1

Time (sec.)1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78

SV InletSV Body

Time (sec.)1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78

2.5

Pre

ss (M

PaG

)

2.01.51.00.50.0

-0.51.38

Disc oscillating motion is attenuated

71 msec = Duration pressure wave propagates from safety valve tovessel and return back to safety valve

Nonlinear characteristics


21

0

1

2

3

1.19 1.24 1.29 1.34 1.39 1.44 1.49 1.54 1.59

時間　(sec)

弁リ

フト

　(m

m)

0

1

2

3

1.13 1.18 1.23 1.28 1.33 1.38 1.43 1.48 1.53

時間　(sec)

弁リ

フト

　(m

m)

0

1

2

3

1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

時間　(sec)

弁リ

フト

　(m

m)

0

1

2

3

1.38 1.43 1.48 1.53 1.58 1.63 1.68 1.73 1.78

時間　(sec)

弁リ

フト

　(m

m)

0

1

2

3

0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35

時間　(sec)

弁リ

フト

　(m

m)

0

1

2

3

1.04 1.09 1.14 1.19 1.24 1.29 1.34 1.39 1.44

時間　(sec)

弁リ

フト

　(m

m)

Time History of Valve Lift / Effect of Inlet Pipe Length

Duration of pressure wave propagation becomes longer as inlet pipe length increases

Inlet Pipe Length 1m - 5m ： ChatterInlet Pipe Length >= 10m ： No Chatter

30m2

1

0

Lift

(mm

)

1.13 1.18 1. 23 1.28 1.33 1.38 1.43 1.48 1.53Time (sec.)

3

2

1

0

Lift

(mm

)

1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

1m

Time (sec.)

3

2

1

0

Lift

(mm

)

1.13 1.18 1.18 1.23 1.28 1.33 1.38 1.43 1.59Time (sec.)

5m

3

2

1

0

Lift

(mm

)

1.38 1.43 1. 48 1.53 1.58 1.63 1.68 1.73 1.78

10m

Time (sec.)

71msec

95msec

123msec

3

2

1

0

Lift

(mm

)

0.95 1.00 1. 05 1.10 1.15 1.20 1.25 1.30 1.35Time (sec.)

3

2

1

0

Lift

(mm

)

1.04 1.09 1. 14 1.19 1.24 1.29 1.34 1.39 1.44Time (sec.)

15m

20m


22

Results of Test / Effect of Outlet Area Ratio

Outlet Area Ratio to Orifice Area < 5.5There is possibility of chatter

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

1.47 1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87

時間　(sec)

圧力

　(M

Pa)

弁箱内

SV上流

0

1

2

1.47 1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87

時間　(sec)

弁リ

フト

　(m

m)

1E2Outlet 1”

2

Lift

(mm

)

1

01.47 1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87

Time (sec.)

1.52 1.57 1.62 1.67 1.72 1.77 1.82 1.87Time (sec.)

1.47Pre

ss. (

MP

aG)

2.52.01.51.00.50.0

-0.5

Small Area Ratio

Press at SV BodyIncrease

ChatterSV InletSV BodySV InletSV Body

2" 1-1/2" 1-1/4" 1" 3/4"Chatter No No No Yes*1 -

Press. at SV Body (MPag) 0.06 0.09 0.11 - -Outlet Area Ratio ( 11.2 ) ( 7.5 ) ( 5.5 ) ( 3.3 ) -

Chatter No Yes*2 Yes*2 Yes YesPress. at SV Body (MPag) 0.10 0.12 0.16 0.27 0.32

Outlet Area Ratio ( 8.3 ) ( 5.6 ) ( 4.1 ) ( 2.5 ) ( 1.5 )

*1 : Repeated popping action is observed*2 : Chatter occus before closure of SV

Reducer Size at Outlet

1E2

1.5F2


23

SV Size (1) OrificeArea

OutletSize

(2) OutletArea

Ratio(2) / (1)

1E2 1.82 cm2 2" 20.3 cm2 11.21-1/2" 13.6 cm2 7.51-1/4" 10.0 cm2 5.5

1" 6.0 cm2 3.31.5F2 2.43 cm2 2" 20.3 cm2 8.3

1-1/2" 13.6 cm2 5.61-1/4" 10.0 cm2 4.1

1" 6.0 cm2 2.54P6 47.80 cm2 6" 182.4 cm2 3.8

Chatter

Chatter

For larger size of safety valve such as 4P6, relatively small outlet area ratio would cause chatter

AlmostEquivalent

Safety valve size including outlet area is specified in API526

Results of Test / Effect of Outlet Area Ratio


24

Summary of Chatter Test

1. Safety valve chatter occurs under following conditions:- Excessive pressure drop of inlet or outlet piping- Inlet pipe length shorter than 5m (No chatter for inlet pipe length equal to or longer than 10m)

- Relatively small outlet area ratio

2. Chatter in case of inlet pipe length shorter than 5m is caused by interaction effect of valve disc motion and pressure wave propagation through inlet piping system.

3. For larger size of safety valves, chatter could occur because they have relatively small outlet area ratio. (theratio is specified by API526)


25

Simulation Model

Safety ValveEquation of Motion for Valve DiscOrifice Flow Equation at NozzleFlow Equation at OutletMass Conservation in Valve Body

Inlet / Outlet PipingEquation of Mass ConservationEquation of Motion for Gas FlowEquation for Energy ConservationEquation of State for Gas


26

Simulation Model / Safety Valve 1

( ) sc

HBVSS KZZfAPPKZZCZM −⎭⎬⎫

⎩⎨⎧

⎟⎠⎞⎜

⎝⎛+−=++

2

)(1 ψψ&&&

Equation of Motion for Valve Disc

Ms : Mass of Moving Part (kg) Cs : Damping Constant (Ns/m)K : Spring Constant (N/m)Z : Valve Lift (m)PV : Inlet Pressure of SV (Pa)PB : Pressure at SV Body (Pa)AH : Area of SV disc holder (m2)f : Lift Force Function (-)ψ : Flow Coefficient of Orifice (-)ψc : ψ at Critical Flow Condition (-)Zs : Initial Displacement of Spring (m)t : Time (sec.)

　

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=

+κ

κκ

κκψ

12

12

U

D

U

D

PP

PP

11

12 −

+

⎟⎠⎞

⎜⎝⎛

+=

κκ

κκψ c

1

12 −

⎟⎠⎞

⎜⎝⎛

+=

κκ

κUc PP

cD PP ≤

cD PP >

PU : Upstream Pressure (Pa)PD : Downstream Pressure (Pa)PC : Critical Pressure (Pa)κ : Specific Heat Ratio

Lift Force


270

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4 5Lift (mm)

Lift

Forc

e (N

)

MeasuredCalculated by Lift Force FunctionSpring Load Max Lift

3.8mm

0

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4 5Lift (mm)

Lift

Forc

e (N

)

MeasuredCalculated by Lift Force FunctionSpring Load

Max Lift3.8mm

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.00 1.00 2.00 3.00 4.00 5.00Lift z（mm)

1+f

Max Lift3.8mm

Simulation Model / Safety Valve 2

0

100

200

300

400

500

600

700

800

900

1000

0.00 1.00 2.00 3.00 4.00 5.00Lift z（mm)

Lift

Forc

e F（

N)

22 barg21 barg20 barg19 barg18 bargSpring Load

Max Lift3.8mm

( )⎭⎬⎫

⎩⎨⎧

⎟⎠⎞⎜

⎝⎛+−=

2

)(1c

HDV ZfAPPF ψψLift ForceLift Force Function f(z)

Outlet Area Ratio =11.2 (Outlet = 2inch) Outlet Area Ratio = 3.3 (Outlet = 1inch)

Comparison with measured data

Safety valve characteristic can be expressed by lift force function


28

Safety Valve Characteristic API520 Part1


29

Simulation Model / Safety Valve 3Orifice Flow Equation ,

/0 w

VdSS MzRT

PCAW ψ=

Flow Equation at Outletw

BdDDD MzRT

PCAW/0

ψ=

Equation of MassConservation at Valve Body

,DsB WW

dtdM

−=w

BBB M

zRTP ρ=

( )OHS AZdA ,min π=

Ws : Inflow Rate (kg/s) WD : Outflow Rate (kg/s)As : Effective Orifice Area (m2)AO : Orifice Area (m2)Cd : Orifice Flow Coefficient (-) CdD : Flow Coefficient at Outlet (-)z : Compressibility Factor (-)Mw : Molecular Weight (kg/kmol)

R : Gas Constant (8314 J kg/kmol/K)T0 : Total temperature (K) dH : Diameter of disc holder (m) MB : Mass of gas in valve body (kg)PB : Pressure of gas in valve body (Pa)ρB : Density of gas in valve body (Pa) TB : Temperature of gas in valve body (K)VB : Volume of valve body (m3)

,B

BB V

M=ρ


30

Simulation Model / Pipe 1

Equation of Mass Conservation

outin WWdt

dM−=

wMzRTP ρ

=,xA

MΔ

=ρ M : Mass of Gas (kg)Win : Inflow Rate (kg/s) Wout : Outflow Rate (kg/s)ρ : Density of Gas (kg/m3) A : Flow Area in Pipe (m2)⊿x : Divided Length (m)P : Pressure of Gas (Pa)T : Temperature of Gas (K)U : Velocity of Gas (m/s)Cp : Specific Heat at Constant

Pressure (J/kg/K)

Equation of Energy Conservation

.2 0

2

constTC

UTp

==+

P, T

Δx

Win Wout


31

Simulation Model / Pipe 2

Equation of Motion

f : Friction Factor of Pipe (-)D : Pipe Internal Diameter (m)

21 UUD

fxP

xUU

tU ρ

ρ ⋅−∂∂

−=⎟⎠⎞

⎜⎝⎛

∂∂

+∂

∂

,11xPP

xPF ud

Δ−

−=∂∂

−=ρρ

xUUU

xUUF u

u Δ−

−=∂∂

−=2xUUUF d

Δ−

−=2or

U

Δx

Uu Ud

Pu , ρu Pd , ρd

321 FFFdt

dU++=

213

UUD

fF ⋅−=

Note : Loss of valves and fittings can be expressed by the following form

213

UUx

KD

fF ⋅⎟⎠⎞

⎜⎝⎛ +−=

Δ@CHIYODA/ChAS All rights reserved 2007

32

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Time(s)

Lift(

m)

SimulationExperiment

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Time(s)U

pstre

am P

ress

ure

(MP

aG)


0.00

0.05

0.10

0.15

0.20

0.25

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Time(s)

Body

Pre

ssur

e (M

PaG

) SimulationExperiment

Simulation Results / Chatter Test 1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Lift(

m)


1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Ups

tream

Pre

ssur

e (M

PaG

)


0.00

0.05

0.10

0.15

0.20

0.25

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Body

Pre

ssur

e (M

PaG


1E2, Inlet Pipe = 0mLi

ft (m

m)

Ups

tream

Pre

ssur

e(M

PaG

)

Val

ve B

ody

Pre

ssur

e(M

PaG

)SimulationExperiment

Simulation can reproduce chatter phenomena

1E2, Inlet Pipe = 1m


33

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Lift(

m)


1.50

1.60

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)U

pstre

am P

ress

ure

(MPa

G)


0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Body

Pre

ssur

e (M

PaG


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Lift(

m)


1.70

1.75

1.80

1.85

1.90

1.95

2.00

2.05

2.10

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Ups

tream

Pre

ssur

e (M

PaG

)


0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Body

Pre

ssur

e (M

PaG


Simulation Results / Chatter Test 2Li

ft (m

m)

Ups

tream

Pre

ssur

e(M

PaG

)

Val

ve B

ody

Pre

ssur

e(M

PaG


Simulation can reproduce pressure wave propagation in pipe

1E2, Inlet Pipe = 10m 1E2, Inlet Pipe = 20m


34

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Lift(

m)


1.70

1.75

1.80

1.85

1.90

1.95

2.00

2.05

2.10

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)U

pstre

am P

ress

ure

(MPa

G)


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Body

Pre

ssur

e (M

PaG

)


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Lift(

m)


1.70

1.75

1.80

1.85

1.90

1.95

2.00

2.05

2.10

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Ups

tream

Pre

ssur

e (M

PaG

)


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.10 0.20 0.30 0.40 0.50

Time(s)

Body

Pre

ssur

e (M

PaG

)


Simulation Results / Chatter Test 3Li

ft (m

m)

Ups

tream

Pre

ssur

e(M

PaG

)

Val

ve B

ody

Pre

ssur

e(M

PaG


Simulation can reproduce chatter caused by relatively small outlet area ratio

1E2, Outlet = 1-1/4inch 1E2, Outlet = 1 inch


35

Simulation Results / Chatter Test 4

75.8 Hz-1.5F2 / 3m (+1.2m)74.8 Hz-1.5F2 / 5m+(1.2m)

76.9 Hz59.0 Hz1.5F2 / 1m (+1.2 m)91.8 Hz104.3 Hz1.5F2 / 0m (+1.2 m)80.3 Hz78.8 Hz1E2 / 5m (+1.2m)77.1 Hz76.5 Hz1E2 / 3m (+1.2m)79.2 Hz68.7 Hz1E2 / 1m (+1.2m)

SimulationChatter TestSV Size / Inlet Pipe Length

Natural Frequency of valve disc and body = 75Hz

(+1.2m) is length of flow pass in safety valve stand


36

Summery of Simulation Results 1. Simulation results have good agreement with test results on chatter caused by the following phenomena:

- Interaction between valve disc motion and pressure wave propagation through inlet piping system

- Relatively small outlet area ratio of safety valve

2. Damping Problem (Mechanical Friction at Moving Part)- Nonlinear characteristics are observed in measured data- Possibility of difference in mechanical damping due to

manufacturing accuracy for guide and disc holder of safety valve

==> Additional tests with other parts of guide and disc holder show similar results on the effect of inlet pipe length


37

Professor Hayama published “stability analysis of a piping system equipped with a pressure-open-type valve at the exit”As “Pressure-open-type valve ” is similar to safety valve, the stability of safety valve is investigated based on Hayama’s Theory.Professor Hayama mentioned that conventional method cannot succeed to obtain stability condition for this type of the valve because of complexity of the stability equation. He could succeed to investigate the stability condition by introducing additional virtual negative damping to the valve motion and assuming a neutral stability condition.

Stability Analysis 1

Model for Hayama Theory

Pipe

Pressure-open-type valve


38

Stability Analysis 2Consider small disturbance from stable state

,~ZZZ += ,~PPP += ,~WWW +=

( ) ZdZdfAPfAPZKZCCZM HHSVSS

~1~~~)(~ ++=+++ &&&Equation of motion for valve disc

ZdZdfffff ~~

+=+=

Change of variables, etc.,ηω =tn ,/2

sn MK=ω,2/)( nsSVSSVS MCC ωζζζ +=+=

PPK

ZZ

dZdf

ZZ

ZZ ~~

1~

2~

1=⎟⎠⎞

⎜⎝⎛ −++ βζ

&&&

,KAP H=β

ZZZ

K f+=1

CSV : virtual damping coefficient to satisfy neutral stability condition (Ns/m)

df/dz affects to decrease natural frequency

(Choke flow is assumed at orifice : )cψψ =

Equation of motion can be transformed using above relations


39

Stability Analysis 3Flow Rate Equation

,PZW ∝ZZ

PP

WW ~~~

+= Substitute into equation of motion

Appling Laplace transformation

PPK

dZdf

PP

PP

WW

dZdf

WW

WW ~

1~

2~~

1~

2~

1 ⎟⎠⎞

⎜⎝⎛ +−++=⎟

⎠⎞

⎜⎝⎛ −++ βζβζ

&&&&&&

PsPK

dZdfss

WsW

dZdfss )(12)(12 1

22⎥⎦

⎤⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛ −++=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −++ βζβζ


40

Stability Analysis 4General solution for wave equation at pipe (constant pressure at x=0 with length of L)

)()(),( πφξηπφξηηξ +−−= FFP

Laplace Transformation

[ ])()(),( πφξηπφξηηξ ++−= FFcAW

,/ Lx=ξ ,2/2/

cL

Lcff nn

p

n

πωπωφ ===

)()sinh(2),( sFssP πφξξ −=

)()cosh(2),( sFscAsW πφξξ =

c : sound speed (m/s)

at X=L (ξ=1), i.e. condition at pipe end = safety valve inlet

)coth()()( s

cA

sPsW πφ−=


41

Stability Analysis 5Using equations for safety valve and pressure wave in pipe

Under neutral stability condition, since root of s shall be purely imaginary number, the relation of s =iν can be introduced. And both of real and imaginary parts in above equation shall be zero simultaneously. Thus ν and ζ can be obtained as follows:

H

H

AA

cWAP

cWAP

==μ

0)coth(1212 21

2 =⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+++⎥

⎦

⎤⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛ −++ s

dZdfssK

dZdfss πφβζμβζ

)(cot11 22

1

πφνμβν

++⎟

⎠⎞

⎜⎝⎛ −=

KdZdf

))(cot1(2)cot(

221

πφνμνπφνμζ

+−=

K

Here,


42

Stability Analysis 6The following two functions Y1 and Y2 are assumed:

)(cot11)( 22

12 πφνμ

βν+

+⎟⎠⎞

⎜⎝⎛ −=

KdZdfY,)(1 νν =Y

)()( 21 νν YY =

Safety Valve Data for 1E2Z 0.0006 0.001 0.002 0.003

K 1 10.8 6.9 3.9 3.0P 1.90E+06 1.95E+06 2.10E+06 2.30E+06

df/dZ 180 100 50 25β 5.56E-03 5.71E-03 6.15E-03 6.73E-03W 0.16 0.28 0.60 0.98μ 19.5 11.7 5.9 3.9

1- β df/dz 0 0.43 0.69 0.83

(m)

(Pa)(1/m)(m)(kg/s)

At neutral stability condition, Point of intersection for Y1 and Y2 shows neutral stability condition


43


0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ν

Y1,

Y2

Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m

1E2, L=1m (φ=0.429)

ζ<0, stable ζ<0, stableζ>0, unstable

ζ>0, Unstable


44

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ν

Y1,

Y2

Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m

Stability Analysis 81E2, L=5m (φ=2.15)

ζ>0, Unstable


45

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ν

Y1,

Y2

Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m

Stability Analysis 91E2, L=5m (φ=2.15), Comparison between inlet pipe size of 2inch and 4inch

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ν

Y1,

Y2

Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m

No apparent difference is observed on stability

Inlet Pipe = 2inch

Inlet Pipe = 4inch


46

0

1

2

3

4

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

ν

Y1,

Y2

Y1Y2, Z=.0006mY2, Z=.001mY2, Z=.002mY2, Z=.003m

Stability Analysis 101E2, L=0.355m (φ=0.152)

No unstable point

12 KcL

nωπ

<Stable Condition :


47


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7

φ

ν

1st

2nd

3rd

4th

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6 7

φ

ζ

1st

2nd

3rd

4th

Non

-dim

ensi

onal

Freq

uenc

y

Lift 1mm

Dam

ping

Rat

io


48

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6

φ

ν

1st

2nd

3rd

4th

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6

φ

ζ

1st

2nd

3rd

4th

Stability Analysis 12Lift 2mm

Non

-dim

ensi

onal

Freq

uenc

yD

ampi

ng R

atio


49

Test Results, 1E2, L=1m（inlet pipe length)

-0.50

0.50

1.50

2.50

0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000


圧力

　(M

Pa)

圧力①

圧力②

0.0E+00

5.0E-02

1.0E-01

1.5E-01

2.0E-01

2.5E-01

0 20 40 60 80 100 120 140 160 180 200

周波数　(Hz)

0.0E+00

1.0E-01

2.0E-01

3.0E-01

4.0E-01

0 20 40 60 80 100 120 140 160 180 200

周波数　(Hz)

0.0E+00

5.0E-02

1.0E-01

1.5E-01

2.0E-01

2.5E-01

3.0E-01

3.5E-01

0 20 40 60 80 100 120 140 160 180 200

周波数　(Hz)

1.25 secLift 1.73 mm



Time History of Valve Inlet Press.

Spectrum

Pre

ss.

(MP

aG)

2.5

1.5

0.5

Time (sec.)0

-0.51 2 3 4 5 6

Point 1Point 2

0

Frequency (Hz)

20 40 60 80 100 120 140 160 180 200

0

Frequency (Hz)

20 40 60 80 100 120 140 160 180 200

0

Frequency (Hz)

20 40 60 80 100 120 140 160 180 200


50

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Lift (mm)

νTheory, 1st ModeTheory, 2nd ModeExperiment

L=2.17m

Comparison between stability theory and measured data, L=1m (2.17m)


51

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Lift (mm)

νTheory, 1st ModeTheory, 2nd ModeTheory, 3rd ModeTheory, 4th ModeExperiment

L=4.17m



52

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Lift (mm)

νTheory, 2nd ModeTheory, 3rd ModeTheory, 4th ModeTheory, 5th ModeTheory, 6th ModeExperiment

L=6.17m



53

Summary of Stability Analysis

1. Stable condition is

2. Frequency obtained by stability analysis agrees well to those obtained by chatter test

3. Size of inlet pipe size has no effect on stability

4. In case of relatively long length of inlet pipe, chatter cannot be excited since oscillating motion of the valve disc can be attenuated before the arrival of reflecting pressure wave as shown from the results of chatter test. These phenomena could not be solved by stability analysis because the steady amplitude of disc motion is assumed in the stability analysis though it decreased transiently by the damping effect.

12 KcL

nωπ

<


54

Case StudyOutlet Area Ratio >= 6 SV Size : 1E2, 2J4, 4P8 Inlet Pipe Size

1E2 :1-2 inch2J4 : 2-4 inch4P8 : 4-10 inch

Gas : Air, Methane, HydrogenSet Pressure : 2barg, 20barg, 60barg, 100bargDamping Ratio : 20% (Mechanical Friction)


55

Non-dimensional Parameters

( ) ZZZK f /1 +=

H

H

AA

cWAP

cWAP

==μ

cUM ach /0=

[ ] achMKDLfF += )/(

KMC

s

s

2=ζ

Mach Number, less than 0.5

Pressure Term / Momentum Force (Effect of Inlet Pipe Size)

cLfff npn /2/ ==φ SV Natural frequency / Acoustic natural frequency for 1st mode

Pressure drop of pipe and fitting

Damping ratio (20%)

Constant on SV Characteristic

κ Specific heat ratio of gas


56

2 - 502 – 25

2.2 - 2.62.3 - 2.8

0.01 - 0.340.3 - 0.5

Case StudyRange in Design

cUM ach /0=

WcPA

=μ

max

max1 Z

ZZK f+

=

Range of Parameters


57

cLfff npn /2/ ==φ

φ : Duration pressure wave propagate and return / Natural period of disc and spring

Pipe length increases => φ increasesSet pressure increases => Spring constant increases

=> fn increases => φ increasesMw increases => c decreases => φ increases

Longer pipe length tends to be stable= Large φ tends to be stable= Higher set pressure tends to be stable= larger Mw tends to be stable


58

Safety Valve Stability Characteristics

0

2

4

6

8

10

12

0 0.5 1 1.5 2F = {f(L/D)+K)}Mach

φ =

2fnL

/c

Pulsation Rateless than 1%1% - 2%2% - 5%5% - 10%larger than 10%

Stable

Unstable


Non

-Dim

ensi

onal

Inle

t Pip

e Le

ngth

Non-Dimensional Pressure Drop of Inlet Piping System

59

Conclusion and Future Plan / Approach 1

As the results of the study, the instability of the safety valve can be classified into the following three types:

(1) Excessive pressure drop of inlet/outlet piping system (well known phenomena)

(2) Interaction between disc motion and pressure wave propagation of inlet piping

(3) Relatively small out let area of safety valve

The safety valve chatter can be predicted by the dynamic simulation which is verified throughout the comparison to the test data for the small safety valves.


60

Conclusion and Future Plan / Approach 2

Further investigation including the chatter test for larger sizes of the safety valves shall be required so as to confirm the cause of chatter more quantitatively and establish a reliable design method to prevent the chatter occurrence.

API is requested to execute the further study as a public organization. In this study the effects of inlet pipe length and outlet area ratio shall be confirmed for the safety valves made by several manufacturers. After the study, the method to prevent chatter will be discussed and determined on API committee.
