the control, design and performance of a helium phase ...ž—明泉-20131021-002.pdf · ghe vent...

5
ID:31 The Control, Design and Performance of a Helium Phase Separator HsingChieh Li * , ChaoPin Liu, FengZone Hsiao, HuangHsiu. Tsai, and MeiHsia Chang, NSRRC, Taiwan A 100L helium phase separator with a cryocooler of cooling capacity 1.5 W is under test and operation standing alone at NSRRC. Three cryogenic valves and one 30W heater regulate the level and pressure in this phase separator; its pressure can be operated at 1.5 bara with fluctuation ±3 mbar The level of liquid helium in the inner vessel can be Abstract Measurement and calculation of the heat load 1. Calculation of the heat load by the Rate of volume flow of helium vapour 2. Calculation of the heat load from the liquid level of liquid helium in the inner vessel mbar . The level of liquid helium in the inner vessel can be controlled at 82 % within fluctuation ±2 %. The results of control of liquid helium level and the pressure in the inner vessel are discussed; the entire electrical configuration of the control system is also presented in this paper. Configuration of the phase separator Rate of volume flow of helium vapour from the inner vessel Rate of decrease of liquid helium in the inner vessel Description of the control component and the control design (2) (1) (3) (4) (5) (6) (7) (18) (19) (10) (15) (16) (17) (21) (20) (20) (8) (14) (16) (15) (1) (7) (8) (10) (14) (17) HMI & Datalogging Program IO Hardware 1.5W Heater at 2nd stage of cold head AEG controller Dewar Level Sensor Level Moniter Level Controler LHe supply valve Openning Dewar Pressure Sensor Valve Controller GHe Vent valve Openning Heater Controller Dewar Heater (30W) Lakeshore Cryogenic Temperature Sensor * 3 Temperature Moniter CLTS-2B Cryogenic Temperature Sensor * 8 (1) cryocooler; (2) first stage of cryocooler; (3) second stage of cryocooler; (4) 1.5W heater;(5) 30W heater;(6) level meter;(7)pressure transmitter;(8) relief valve;(9) (9) (13) (12) (11) (10) (14) (13) LHe Out valve Openning GHe Vent Flow Meter Thermalcouple Temperature Sensor * 2 Control system of the phase separator 1.45 1.50 1.55 ara) 70 80 90 Pressure and performance of the level control condenser; (10) condenser housing; (11) vacuum; (12) copper thermal shield; (13) 100L inner vessel; (14) outer vessel; (15) liquid He supply valve; (16)gaseous He vent valve; (17) outlet valve for liquid He; (18) location of CLTS2B temperature sensor; (19) Lakeshore cryogenic temperature sensor; (20) pumping port; (21) flow meter for gaseous helium. Condenser fin OFHC plate 0 50 100 150 200 250 300 350 400 1.15 1.20 1.25 1.30 1.35 1.40 Dewar Pressure (ba Pass Through Time (minutes) 0 20 40 60 80 100 120 140 160 180 200 10 20 30 40 50 60 Dewar level(%) Pass Through Time (minutes) Performance of the level control Performance of the pressure control Conclusion Condensercover Returning flow pipe for condensed liquid helium Guided pipe for boiling gaseous helium VCR connector Condenser We completed a system for measurement and control of a helium phase separator, with a standalone test with liquid helium also performed at the end of 2012. From that test the result is a total static heat load less than 0.939 W; the pressure stably operated at 1.5 bara with a fluctuation ±3 mbar. The level stably operated at 82 % ± 2 %. With this control and measurement system, we obtained many valuable data; we use these experience and data to improve our simulation result. In the near future we can improve the performance of the phase separator. Conclusion

Upload: hoangthuy

Post on 04-Apr-2018

221 views

Category:

Documents


3 download

TRANSCRIPT

Page 1: The Control, Design and Performance of a Helium Phase ...ž—明泉-20131021-002.pdf · GHe Vent Flow Meter Thermalcouple ... differential pressure of the Venturi-type ... Through

ID:31

The Control, Design and Performance of a Helium Phase Separator Hsing‐Chieh Li*, Chao‐Pin Liu, Feng‐Zone Hsiao, Huang‐Hsiu. Tsai, and Mei‐Hsia Chang, NSRRC, Taiwan

A 100‐L helium phase separator with a cryocooler of coolingcapacity 1.5 W is under test and operation standing alone atNSRRC. Three cryogenic valves and one 30‐W heaterregulate the level and pressure in this phase separator; itspressure can be operated at 1.5 bara with fluctuation ±3mbar The level of liquid helium in the inner vessel can be

Abstract Measurement and calculation of the heat load

1. Calculation of the heat load by the Rate of volume flow of helium vapour

2. Calculation of the heat load from the liquid level of liquid helium in the inner vessel

mbar. The level of liquid helium in the inner vessel can becontrolled at 82 % within fluctuation ±2 %. The results ofcontrol of liquid helium level and the pressure in the innervessel are discussed; the entire electrical configuration ofthe control system is also presented in this paper.

Configuration of the phase separator

Rate of volume flow of helium vapour from the inner vessel

Rate of decrease of liquid helium in the inner vessel

Description of the control component and the control design

(2)

(1)

(3)

(4)

(5)

(6) (7)

(18) (19)

(10)

(15)(16) (17)

(21) (20)(20)(8)

(14)

(16)(15)

(1)

(7)

(8)

(10)(14)

(17)

HMI & DataloggingProgram

IOHardware

1.5W Heaterat 2nd stage of cold head

AEG controller

DewarLevel Sensor

Level Moniter

LevelControler

LHe supply valve Openning

DewarPressure Sensor

Valve Controller

GHe Vent valve Openning

Heater Controller

Dewar Heater (30W)

Lakeshore CryogenicTemperature Sensor * 3

Temperature Moniter

CLTS-2B CryogenicTemperature Sensor * 8

(1) cryocooler; (2) first stage of cryocooler; (3) second stage of cryocooler; (4) 1.5‐W heater; (5) 30‐W heater; (6) level meter; (7) pressure transmitter; (8) relief valve; (9) 

(9)

(13)

(12)(11)

(10)(14)

(13)

LHe Out valve Openning

GHe Vent Flow Meter

ThermalcoupleTemperature Sensor * 2

Control system of the phase separator

1.45

1.50

1.55

ara)

70

80

90

Pressure and performance of the level control

; ( ) ; ( ) ; ( ) p ; ( ) ; ( )condenser; (10) condenser housing; (11) vacuum; (12) copper thermal shield; (13) 100‐L inner vessel; (14) outer vessel; (15) liquid He supply valve; (16)gaseous He vent valve; (17) outlet valve for liquid He; (18) location of CLTS‐2B temperature sensor; (19) Lakeshore cryogenic temperature sensor; (20) pumping port; (21) flow meter for gaseous helium.

Condenser finOFHC plate 0 50 100 150 200 250 300 350 4001.15

1.20

1.25

1.30

1.35

1.40

Dew

ar P

ress

ure

(ba

Pass Through Time (minutes)0 20 40 60 80 100 120 140 160 180 200

10

20

30

40

50

60

Dew

ar le

vel(%

)

Pass Through Time (minutes)

Performance of the level controlPerformance of the pressure control

Conclusion

Condenser‐cover

Returning flow pipe for condensed liquid helium

Guided pipe for boiling gaseous helium

VCR connector

Condenser

We completed a system for measurement and control of a helium phase separator, witha stand‐alone test with liquid helium also performed at the end of 2012. From that testthe result is a total static heat load less than 0.939 W; the pressure stably operated at 1.5bara with a fluctuation ±3 mbar. The level stably operated at 82 % ± 2 %. With this controland measurement system, we obtained many valuable data; we use these experienceand data to improve our simulation result. In the near future we can improve theperformance of the phase separator.

Conclusion

Page 2: The Control, Design and Performance of a Helium Phase ...ž—明泉-20131021-002.pdf · GHe Vent Flow Meter Thermalcouple ... differential pressure of the Venturi-type ... Through

ID:78

Calculation of the Pressure Drop of Long Cryogenic Transfer Lines M. H. Chang*, Ch. Wang, M. C. Lin, F. T. Chung, Y. H. Lin, M. S. Yeh, L. H. Chang, T. T. Yang, C. H. Lo, T. C. Yu, L. J. Chen, and Z. K. Liu, NSRRC, TaiwanM. H. Tsai and L. L. Han, NTUT, Taiwan 

Cryogenic Configurations 

Theoretical Modelling on Various Pressure Drops

Frictional pressure drop:

Static pressure drop:

Valve pressure drop:

Steady, one-dimensional, incompressible and homogenous flowx = 0: pure liquid; x = 1: pure gas; 0 < x <1: saturated gas-liquid phase

Measurement Results

IntroductionFor a cryogenic helium transfer system, after the operating pressure of the cryogenic equipment is decided, the maximum allowablepressure drops on the LHe and CGHe transfer lines are determined, and vice versa.When the pressure drop of either the LHe line or the CGHe line is greater than the allowable value, the LHe vessel of the terminalcryogenic equipment correspondingly suffers from insufficient LHe supply or a pressure increase.A computational approach is developed to estimate the pressure drops of long cryogenic transfer lines for LHe and CGHe; the frictionof flow, resistance of valves and elevation head are all taken into account.The 200-m flexible cryogenic-transfer system in NSRRC is taken as an example to test this computation approach.

( )22)2()2(),2( 2

1φφφφ ρ u

dLfP f =Δ

( )12)2(),2( zzgP s −=Δ φφ ρ

2

⎟⎞

⎜⎛ Vx &

Gas:

Liquid:

Heat Loads of the Cryogenic Transfer SystemTwo‐phase LHe transfer line

Overall heat load correction factor:

q

Table 2 Operating conditions and ranges of the applied heaterpower for five test cases

09.51 1

max,

)3.101,273(1,1

2,

)3.101,273(=

⎟⎟⎟

⎜⎜⎜

⎛+Δ−Δ

−GkPaK Lv

kPaKg

gvGvG RK

VxTPPP ρ

2

1max,

,

)1(1000 ⎥

⎤⎢⎣

⎡ −=Δ

−LLv

LLvL RK

VxP&ρ

calcL

measLB q

qF

,

,= ,

Vapor quality:

, j = 1 ~ 4

, j = 5 ~ 11

,

Fig. 1 Schematic diagram and piping path of the 200‐m cryogenic transfersystem for operating the testing SRF module S0 at NSRRC.

Table 1 List of type, length, inner diameter and heat load specification foreach element of the LHe and CGHe transfer lines.

)0(,

)(,,

SmeasL

totalmeasLmeasL qqq −=

( )( ) )1(,

)(,

1

)(,

1 SmeasLh

totalmeasL

j

i

icalcLB

j qqqX

qFx

++−

⎟⎠⎞⎜

⎝⎛

≅∑=

( )( )htotal

measL

j

i

icalcLB

j qqX

qFx

+−

⎟⎠⎞⎜

⎝⎛

≅∑=

)(,

1

)(,

1

)0()0(

)0()1#(

SL

SG

SL

MDL

hhhhX

−−

=

Assumption and working parameters CGHe transfer line

Properties ρ and ν = func(h P ) (using HEPAK)

The pressure properties of fluid areapproximated as constant value in theLHe and CGHe transfer lines forcalculating the viscosity and density ateach cryogenic piping element.

Total pressure drop:

Enthalpy rise:

Calculation Results 

Fig. 2 The accumulated static heat load along the LHe transfer linefrom main Dewar #1 to the testing SRF module S0 is thus derivedfrom the linear fit for these five test cases.

vi

is

i

ifcalcL PPPP ),2(

11

4

)(),2(

11

4

)(),2(, φφφ Δ+Δ+Δ=Δ ∑∑

==

T

j

i

igB

SGT

j m

qFhmh

&

& ∑=

+= 1

)(calc ,

)0(

Properties (ρL, ρG) and (ν L, νG) = func((PMD#1+PS0)/2) (using HEPAK)

(ρL, ρG, ν L, νG, xj) Properties ρ(2φ) and Re(2φ)

A simple calculation procedure only using analytic formula but introducingan overall heat load correction factor to estimate the pressure drops of longcryogenic transfer lines, with promising predictions relative to themeasured results of the existing 200-m flexible cryogenic transfer system inNSRRC.

Fig. 4 The calculated total pressure drop of the 200‐m CGHetransfer line between VB #1 and VB #2 in NSRRC approaches themeasured results with an overall correction factor FB = 1.274applied.

Fig. 3 With an overall correction factor FB = 1.274 applied, thecalculated pressure drop of the 200‐m LHe transfer line betweenVB #1 and VB #2 in NSRRC approaches the measured results muchbetter when gravity effect is neglected.

Properties ρ and ν = func(hj, PCB#1) (using HEPAK) y g p p gThe average pressure of main Dewar

#1 and SRF module S0 is assigned to alltwo-phase LHe transfer lines; the returnpressure of CB #1 is assigned to allCGHe transfer lines.

The friction factor for the corrugatedtubes is assumed to be 0.08; the surfaceis assumed to be smooth for the non-corrugated tubes.

A pressure drop 15 % of the measureddifferential pressure of the Venturi-typeflow meter at VB #2 is used to simulatethe pressure drop across the Vernturi-t fl t t VB #1

Total pressure drop:

Conclusions

vgi

isg

i

ifgcalcg PPPP ,

10

3

)(,

10

3

)(,, Δ+Δ+Δ=Δ ∑∑

==

A overall heat load correction factor 1.274 was assigned to thecomputational approach based on the measured static heat load of the liquidhelium transfer lines. The discrepancies between measured and calculatedfor both LHe and CGHe transfer lines are less than 1 kPa (10 mbar).To apply this computational approach in the design phase of a longcryogenic transfer system, a factor 1.5 as commonly adopted for acryogenic system is hence strongly suggested as a conservative estimate.After commissioning of cryogenic transfer system, a more precise overallheat load correction factor can be obtained after calibrating the calculatedstatic heat load with the measured values.

Fig. 5 With an overall correction factor FB = 1.274 applied, thecalculated total pressure drop for the two‐phase LHe lineapproaches the measured results much better, but helps little theresults for the CGHe transfer line.

type flow meter at VB #1.Two smooth 900 elbows are

considered, while effects of the bendswith large radius are neglected.

Total  heat load

274.11.73

371.130

,

, =−

==calcL

measLB q

qF

Overall heat load correction factor

qT = accumulated heat load + appliedheater power + flash loss

Fig. 6 The calculated pressure drop of each component and thecalculated pressure drop per unit length at a total heat load of 210W.

Page 3: The Control, Design and Performance of a Helium Phase ...ž—明泉-20131021-002.pdf · GHe Vent Flow Meter Thermalcouple ... differential pressure of the Venturi-type ... Through

National Synchrotron Radiation Research Center

The Comparison Between Experimental and Numerical Simulation, and Concept Improvement of Helium Phase Separator

C. P. Liu, H. C. Li, F. Z. Hsiao, H. H. Tsai, and M. H. Chang101 Hsin-Ann Road, Hsinchu Science Park, Hsinchu 30076, Taiwan.

ID 1258National Synchrotron Radiation Research Center

IntroductionThe prototype of helium phase separator had been built up completely in NationalSynchrotron Radiation Research Center (NSRRC). The main original purpose is toestablish a device which could re-condense the vaporized liquid helium from the liquidhelium transfer line, and the experimental prototype would be tested by filling theliquid helium into the inner vessel. Then the inner vessel would be vaporized liquidhelium into vapour helium due to that there are heat loss in the separator. Through thistest process we could find out the condensed capability of the prototype

ID-1258

Concept Improvement of Helium Phase SeparatorIt could be found that the modified of newconcept of improving the pre-cooling methodwhich is to use the oxygen-free high-conductivity cooper (OFHC) to connectcryocooler first stage and the top of the innervessel. The reasons to do this are : (1) Using thehigh conductivity of OFHC, the pre-cooling ratetest process, we could find out the condensed capability of the prototype.

But due to lack of liquid helium supply at recent days in the world, the condensedefficiency could not be tested by buying liquid helium to fill the inner vessel and tofinish the test. So the direction of condensed efficiency testing should be changed :from re-condensed the vaporized liquid helium from inner vessel to produce the liquidhelium from vapour on the separator. This is a big design modification. So the papernot only introduce the concept of original design and simulation, experiment results,but also discussed the modification of the separator which is modified to produceliquid helium from the vapour helium.

Configuration of Helium Phase SeparatorThe tested prototype of height 1854 mm and diameter 956 mm is composed of

g y , p gof inner vessel would be increased by the cooperwire. (2) Due to there must be thermal gradientin the inner vessel between the top and bottomside. But we still could storage the liquid heliumin the inner vessel at a certain level.

Results and DiscussionsSteady Distribution of Temperature of the Helium Phase Separator without LiquidHelium in Inner VesselThe simulation and experimental temperature data with no liquid helium in the innervessel are shown in table below. The temperature difference between simulation andexperiment is within 20 %The tested prototype, of height 1854 mm and diameter 956 mm, is composed of

cryogenic valves, a sustaining rod, meters to measure the level of helium liquid and thepressure of the inner vessel and a testing sample port

experiment is within 20 %.

Component name Simulation result /K

Experiment result /K

Difference between simulation and experiment /%

LHe-in cryogenic valve thermal anchor 39.6 42.3 6.4LHe-out cryogenic valve thermal anchor 40.1 45.9 12.6GHe-out cryogenic valve thermal anchor 41.2 43.9 6.2

Inner vessel 155.3 176.6 12.1Thermal shield 50.04 61.6 19.1

Results of Inner Vessel Pre-cooling with vapour helium inside the Inner Vessel

The figure above is the appearance and components of the helium phase separator.(a): the whole phase separator with the outer vessel; (b): outer vessel has beenremoved to reveal the thermal shield; (c): components after removal of the thermalshield; (d): the prototype of helium phase separator

Steady-State Simulation Model and Boundary ConditionsBoundary conditions of simulation of helium phase separator where the inner vessel

g p

In the figure it could be found that the temperature of innervessel is 13.854K, which matches the experiment data closely.The error between simulation and experiment is 0.01%. Afterthis test, not only we could re-verify the simulation model couldbe used to predict the heat transfer condition of phase separatoraccurately, but obtain the pre-cooling rate of inner vesselconnecting with the new condenser module.

The steady-state simulation result of pre-cooling the innervessel

It could be found that when the number of connectedcooper wire are 16, the averaged temperature of the

The simulation model isbuilt according to the realexperimental equipment.The ambient temperaturewas assumed to be 293 K;the temperatures of thecryocooler first stage andthe top surface of thecondenser are set to be 32K and 3.6 K, obtainedfrom the experimental

Boundary conditions of simulation of helium phase separator where the inner vesselis with vacuum condition

p , g pinner vessel without vapour helium inside is about 45K,the pre-cooling effect is much obvious than the originaldesign. According this result, we could cut the pipe forliquid helium flowing-out than connected to thecondenser. By this way, the bottom could be cooled bythe liquid helium which is condensed from thecondenser gradually. After a period of time, the bottomof inner vessel would be at the saturated temperature ofliquid helium and the temperature area would be biggerand bigger since the liquid helium level is getting higher,until the liquid helium height level reached at thethermal equilibrium level.

assumed to be 293 K.The figure above is the boundary conditions of thesimulation model without liquid helium in the inner vessel. (a): simulation modelwithout thermal shield; (b): simulation model with thermal shield; (c): perspectiveview of thermal shield

from the experimentalresult. As the experimentwas initiated at 293 K, theinitial condition of thissimulation is

Verification of new condenser module at pre-cooling condition

The changing of new condenser module is where theconnecting pipe is larger than before, from outer diameteris 5 mm to 48.26 mm. Due to the simulation results ofpredict the temperature distribution of separator is within

The relation between the liquid helium level and the pre-cooling effectThe relation between the liquid helium level and thepre-cooling effect is very important in this condition. Ifthe number of cooper wire increased, the temperaturearea near the first-stage of the cryocooler would alsobe increased. Thus the storage liquid helium could befilled in the inner vessel which would be decreased. Inthe other words, the less cooper wires, the storageliquid helium level would be increased.

ConclusionTh f h li h i b il i NSRRC A d f h fpredict the temperature distribution of separator is within

the acceptable error range, so we could catch the heat fluxdata of every component and to simulation the condition ofthe new condenser. After 36 hrs of testing the pre-coolingcapability with inner vessel filled with vapour at 1.5 bara,the temperature of cold head is stay at about 7.5K and theinner vessel is 14K with the initial condition 300K. Thisexperiment result could also be a referenced data to re-verified the simulation model is accurate or not.

The prototype of helium phase separator is built up in NSRRC. And after the many ofcomparing simulation and experiment results, a good agreement is obtained. Themaximum error between experiment and simulation is within 20%. And the simulationmodel is also could be used in predicting heat convection of inner vessel pre-cooling. Theerror between experiment and simulation is within 1%. So this simulation model could bea good predicted tool to use at modifying the phase separator in the future. Thepreliminary inner vessel pre-cooling concept is also be tested by the simulation andobtain a good efficiency of pre-cooling than the original model.

Page 4: The Control, Design and Performance of a Helium Phase ...ž—明泉-20131021-002.pdf · GHe Vent Flow Meter Thermalcouple ... differential pressure of the Venturi-type ... Through

ID:134

Dynamic Response of an SRF Module to Low-Frequency Vibration at Cryogenic Temperature

Ming‐Hsun Tsai, Chaoen Wang, Ming‐Chyuan Lin, et. al., NSRRC, Hsinchu, TaiwanLee‐Long Hang, NTUT, Taipei, Taiwan,    Tsing‐Tshih Tsung, CCU, Taipei, Taiwan

Ab t t

Tunner Spec. PSt1000/35/80 VS45, Piezo Mechanics. 

AbstractOperation of a superconducting radio-frequency (SRF) module would be unstable if its structure oscillation varies either the phase or the resonance frequency of the RFfield to a critical point. This becomes an issue since the low-frequency vibration are often triggered by the other accelerator devices nearby. . Illustrated herein is theKEK-type 500 MHz SRF module, the finite element models were established to study its overall dynamic behavior and to be compared to the measured results on anassembled SRF module; major contributors on the low-frequency modes were thus identified. Reinforcement ribs were then applied on the cavity structure to shift itsnatural vibration modes and frequencies, as well as to examine its effects on the SRF cavity’s dynamic responses to the low-frequency oscillation.

Measurement5

10

Amplitude

74.1Application of KEK‐type 500‐MHz SRF Module:KEKB, BECPII, TPS/NSRRC

St 000/35/80 S 5, e o ec a csOutput : 0~1000V                 Max. Force : 50000NMax. Pre‐load : 6000N         Max. Load :  70000N

Finite‐Element ModelGeometry of the 500‐MHz SRF cavity:

0 50 100 150 200 250 300-30

-25

-20

-15

-10

-5

0

Am

plitu

de (d

B)

Frequency (Hz)

100.6

143

177.5 231.9

241.6

299.2Analysis and experiment on nature Frequency modes Effective reinforcement with rings on cavity cell.

Simulation Result

Geometry of reinforcement

50

100

150

200

250

300

Freq

uenc

y (H

z)

Meassurement @ 273 K Simulation @ 273K

50

100

150

200

250

300

Freq

uenc

y (H

z)

Elongated 1 mm at 273K 273K

q y ( )

Thickness:      3 mmDiameter:  225 mmwidthness : 11 mm

Software: Solidworks Simulationtriangular shell element

Effects of turning elongationMeasurement vs. Simulation 

1 2 3 4 5 6 750

Mode

100

150

200

250

300

Freq

uenc

y (H

z)

With Rienforcement 273K

1 2 3 4 5 6 750

M ode

100

150

200

250

300

Freq

uenc

y (H

z)

4K 273K

Mechanical propertiesYoung’s modulus E0 : 105 GPa  @273KEC : 125 GPa  @4K

Poisson’s ratio ν : 0.38

Effects of Reinforcement Rings Effects of different temperature

1 2 3 4 5 6 750

100

Mode

1 2 3 4 5 6 750

100

ModeNatural Vibration Modes  

Page 5: The Control, Design and Performance of a Helium Phase ...ž—明泉-20131021-002.pdf · GHe Vent Flow Meter Thermalcouple ... differential pressure of the Venturi-type ... Through

ID:80

Measurement of Mechanical Properties Measurement of Mechanical Properties at Cryogenic Temperature by Microwave Technologyat Cryogenic Temperature by Microwave Technology

Ming-Chyuan Lin, Chaoen Wang, NSRRC, TaiwanMeng-Kao Yeh, Hao-Yu Wang, NTHU, Taiwan

Fundamentals1. Radial deflection of a circular cylindrical shell:

at central part of a long cylindrical shell( )xxAxxA

tRPP

ERR

ae ββββν coshcossinhsin12

1 *2

*1 ++⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −−=

Δ

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −−=

ΔtRPP

ERR

aem

21 ν

Pe and Pa : lateral and axial press.

Measured Results1. ε and α at room temperature:

at cryogenic temperature⎠⎝⎠⎝ tER 2

( ) CCaC

eC

mtRPP

ERR ααν

−−⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −−=

Δ 12

1

E : Young’s modulusν : Poisson’s ratioαC : thermal contraction

2. Ε and ν at room temperature:0.110916.2' 60 +×=

′= −

GNr Pffε 00 fTf

RRf T

i+Δ×××⎟⎟

⎞⎜⎜⎝

⎛−=′ α

αΤ = 1.536 ×10-5 vs. 1.51×10-5

2. Resonance frequency of a circular cylindrical cavity:

riRf

ε

8

01014822.1 ×

=( ) '

1014822.1'8

0rii RR

fεΔ+

×=

at cryogenic temperature

11'

11'0

−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ Δ

−⎟⎟⎠

⎞⎜⎜⎝

⎛=−⎟⎟

⎞⎜⎜⎝

⎛ Δ−⎟

⎟⎠

⎞⎜⎜⎝

⎛=

Δ

i

m

r

r

i

m

r

r

RR

RR

RR

ff

εε

εε

12

11'0

−⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

Δ

iae

r

r

RR

tRPP

Eff ν

εε

( ) 112

11'0

−⎟⎟⎠

⎞⎜⎜⎝

⎛+−⎟⎟

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

ΔCC

ia

Ce

Cr

r

RR

tRPP

Eff ααν

εε 3. αC, Ε, and ν at 77K:

10 2

11 mRR

RR

tR

EP

ff

iie ⎟⎟

⎞⎜⎜⎝

⎛=⎟⎟

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −=∂⎟⎟

⎞⎜⎜⎝

⎛ Δ∂

ν

( ) ( ) ( )21212 /and2 mmtREmmm −=−−=ν

20 2

1 mRR

RR

tR

EP

ff

iia ⎟⎟

⎞⎜⎜⎝

⎛=⎟⎟

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−=∂⎟⎟

⎞⎜⎜⎝

⎛ Δ∂

ν

tensile test:ν = 0.312±0.015E = 198.2±6.7 GPa

Measurement Setup

CavitiesSS304

(Ri = 30.08 ± 0.06 mm)

( ) Ci

CeC

C RR

tRP

Eff ααν

+⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−×⎟

⎠⎞

⎜⎝⎛ −=

Δ 12

11

0( ) ⎟⎟

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−−=∂⎟⎟

⎞⎜⎜⎝

⎛ Δ∂

iC

C

Ca R

RtR

EP

ff αν 1

21

0

( ) ( )43434 1and2 mmEmmm CC −=−−=νm3 m4

reference:αC = 2.935×10-3

νC = 0.278EC = 214 GPa