Verification of LHP Verification of LHP Stability Theory Part IStability Theory Part Iy yy y

Triem T. HoangTriem T. HoangTTH R h ITTH R h ITTH Research Inc.TTH Research Inc.

Robert W. BaldauffRobert W. BaldauffGSFC· 2015 U.S. Naval Research LaboratoryU.S. Naval Research Laboratory

Outline

• Loop Heat Pipe (LHP) Stability Theoryp p ( ) y y

• Instability Criterion for Low-Frequency Oscillations

• Theory Verification Process

• Model Predictions vs Test DataModel Predictions vs. Test Data

• Summary / Conclusion

Loop Heat Pipe

(E)T

EG

(E)WT

EQ

EPMc

Heat Source

(E)

Attached Payload

( )SATT

(R)WT

)W(RPMc

Evaporator Pump

ReservoirTSAT, PE

(E)

TL(IN)

EPMc

1

VQm

2Q

PrimaryWick

(R)SATT

(L)RG

(W)RG

W

(R) )W(

Evaporator Pump

VapoLiqu

id m

L

TSAT, PR(R)

PLOOP PE PR Non-wickFlow PathSecondary

Wi k(R)LT )W(

RPMcCondenser

or mV

Wick

Metal Casing

Secondary

Heat Sink

TSAT, PLVI(LVI)

TSAT(C)

Secondary Wick

Not Shown

LHP is a capillary-pumped device having no mechanical moving part

LHP Linear Stability Theory

Is LHP state x capable of reaching steady state xSS ?

tk

ke(t) Axx SS2050

/K)

TSINK = 10oC and TAMB = +23oC

x

k

ke(t) Axx SS

10

12

14

16

18

25

30

35

40

45

mpe

ratu

re (o C

)

ance

1/R

LHP

(W/

1/RLHPPoint 1xSS x xSS

2

4

6

8

10

5

10

15

20

25

Satu

ratio

n Te

m

herm

al C

ondu

cta

TSAT

Point 3

02 4

000 100 200 300 400 500 600 700

ThPower Input (Watts)

Point 3

)CRIT(

)L(RP

)W(RP

)E(W 11McMcT

Instability Criterion for Low-Frequency/High-Amplitude Oscillations

)CRIT(LFHAINPEPSSE GQcMcQ

LHP Linear Stability Theory

Is LHP state x capable of reaching steady state xSS ?

tk

ke(t) Axx SS2050

/K)

TSINK = 10oC and TAMB = +23oC

x

k

ke(t) Axx SS

10

12

14

16

18

25

30

35

40

45

mpe

ratu

re (o C

)

ance

1/R

LHP

(W/

1/RLHPPoint 1

TW(E)

QIN/GE

xSS x xSS

2

4

6

8

10

5

10

15

20

25

Satu

ratio

n Te

m

herm

al C

ondu

cta

TSAT

Point 3

02 4

000 100 200 300 400 500 600 700

ThPower Input (Watts)

Point 3

)CRIT(

)L(RP

)W(RP

)E(W 11McMcT

Instability Criterion for Low-Frequency/High-Amplitude Oscillations

)CRIT(LFHAINPEPSSE GQcMcQ

Criterion for Low Frequency Oscillations

)CRIT(

LFHAINPEP

)L(RP

)W(RP

SSE

)E(W

G1

Q1

cMcMcMc

QT

For Unstable LHP Operation:ESS

0e

Zone 1 Zone 2Zone 3

(E)WT

0

SSIN

)E(W

QT

nduc

tanc

e

13

)CRIT(G/1ture

or C

on

)3(INQ)1(

INQ

for large attachedLFHAG/1

Tem

pera

t for large attached thermal mass

Criterion for Low Frequency Oscillations

)CRIT(

LFHAINPEP

)L(RP

)W(RP

SSE

)E(W

G1

Q1

cMcMcMc

QT

For Unstable LHP Operation:ESS

0e

Zone 1 Zone 2Zone 3

(E)WT

0

SSIN

)E(W

QT

nduc

tanc

e

13

)CRIT(G/1ture

or C

on

)3(INQ)1(

INQ

for decreasingLFHAG/1

Tem

pera

t for decreasingthermal mass

Criterion for Low Frequency Oscillations

)CRIT(

LFHAINPEP

)L(RP

)W(RP

SSE

)E(W

G1

Q1

cMcMcMc

QT

For Unstable LHP Operation:ESS

0e

Zone 1 Zone 2Zone 3

(E)WT

0

SSIN

)E(W

QT

nduc

tanc

e

13

)CRIT(G/1ture

or C

on

)3(INQ)1(

INQ

for decreasingLFHAG/1

Tem

pera

t for decreasingthermal mass

Criterion for Low Frequency Oscillations

)CRIT(

LFHAINPEP

)L(RP

)W(RP

SSE

)E(W

G1

Q1

cMcMcMc

QT

For Unstable LHP Operation:ESS

0e

Zone 1 Zone 2Zone 3

(E)WT

0

SSIN

)E(W

QT

nduc

tanc

e

13

)CRIT(G/1ture

or C

on

)3(INQ)1(

INQ

for decreasingLFHAG/1

Tem

pera

t for decreasingthermal mass

JPL TES Loop Heat Pipe

(o C)

20

30

40

20

25

30

Wat

ts)

JPL TES/LHP EDU 12/08/1999 TSINK = 10oC

TC8

TC6

Tem

pera

ture

(

0

10

20

10

15

20

Hea

t Inp

ut (W

TC8

TC23 TC24

10

Elapsed Time (hours)0 1 2 3 4 5 6 7 8 9 10

H

0

5TC31TC32

20

With Large Attached Thermal MassTests with Heater Block

Rodriguez, J. and A. Na-Nakornpanom, “Investigation of Transient Temperature Oscillations of a Propylene Loop Heat Pipe,” Paper No. 01ICES-74, International Conference on Environmental Sciences (ICES), 2001.

JPL TES Loop Heat Pipe

Evaporator P i Wi k C i /S ddl 1st Wi k d A h d Th l M

Dimensions and Properties of LHP Components

Primary Wick Casing/Saddle, 1st Wick, and Attached Thermal Mass Material: Sintered Powder Nickel Attached Thermal Mass: 9,080J/K Outer Diameter: 24.21mm (0.950”) Thermal Mass-to-Vapor Inner Diameter: 9.525mm (0.375”) Conductance GE: 8.16 W/K Active Length: 0.1524m (6”) Saddle: 7.62cm x 15.24cm x 1.91cm Al 6061 Max. Pore Radius: 1.2m Vapor Grooves Permeability: 4.0x10-14m2 Number of Channels: 4 Effective Conductivity: 7.8W/m-K Hydraulic Diameter: 0.05” Transport LinesTransport Lines Vapor Line Liquid Line Outer Diameter: 5.54mm Outer Diameter: 5.54mm Wall Thickness: 0.508mm Wall Thickness: 0.508mm Length: 1.0m Length: 1.2264m (incl. bayonet) C d R iCondenser Reservoir Number of Parallel Passes 1 Outer Diameter: 43.94mm Heat Exchanger Tubing Wall Thickness: 2.20mm Inner Diameter: 3.99mm Active Length: 0.08023m Length: 3.81m (200”) Thermal Mass (McP)R: 190J/K

)MAX( Conductance :G )MAX(C 25W/K Conductance GR: 22W/K

LHP Steady State Model

35JPL TES LHP Steady State (w/o Large Thermal Mass)

20

25

30at

ure

(o C) Predictions

JPL TES/LHP Data

5

10

15

on T

empe

ra

‐10

‐5

0

Satu

ratio

‐150 20 40 60 80 100 120 140 160 180 200

Power Input (W)

LHP Saturation Temperature

35JPL TES LHP Steady State (w/o Large Thermal Mass)

20

25

30

ture

(o C) Predictions

JPL TES/LHP Data

5

10

15

n Te

mpe

rat

‐10

‐5

0

Satu

ratio

n

‐15

10

0 20 40 60 80 100 120 140 160 180 200

Power Input (W)

Thermal Mass Temperature

30JPL TES LHP Steady State (w/o Large Thermal Mass)

20

25

ratu

re (o C

)

15

20

ass T

empe

r

5

10

Ther

mal

M

00 20 40 60 80 100 120

T

Power Input (W)

Predicted Instability Map

80

90JPL TES LHP

W)

60

70

80

wer

Inpu

t (W

40

50 Predicted Region of Instability

Pow

10

20

30

Sink Temperature (oC)30 25 20 15 10 5 0 5 10 150

10

20

Sink Temperature (oC)

Predictions vs. Test Data

Test Without Oscillations

JPL TES LHP

80

90W

)

60

70

80

wer

Inpu

t (W

40

50 Predicted Region of Instability

Pow

10

20

30

Sink Temperature (oC)30 25 20 15 10 5 0 5 10 150

10

20

Sink Temperature (oC)

Predictions vs. Test Data

80

90Test Without Oscillations

JPL TES LHPW

)

60

70

80Test With Oscillations

wer

Inpu

t (W

40

50 Predicted Region of Instability

Pow

10

20

30

Sink Temperature (oC)30 25 20 15 10 5 0 5 10 150

10

20

Sink Temperature (oC)

Transient Model

Governing Equations for Large Attached Thermal Mass

)IN()E( )TT)(/c(QQdTQQdT

0 QQ and 0 QQ and QQQ 2SC)2(

C121E (1)

)L(RP

)W(RP

LSATP12SAT

EP

EINW

McMc)TT)(/c(QQ

dtdT

McQQ

dtdT

(2)

Solution of Eq. (1):

)Q(fT )Q(fQ )Q(fQ )Q(fT E4)IN(

LE32E21E1SAT

Integrate Eq. (2) with Runge-Kutta-Fehlberg (RKF45)method to obtain T and Q as functions of time t(E) .method to obtain TW and QE as functions of time t

Predictions vs. Test Data)

20 01/24/2000 TSINK = 10oC

Power Input

Pow

er (W

)

15Evaporator

(Data)

e (o C

) or P

10

empe

ratu

re

5

i

Reservoir(Data)

Evaporator

Te

0 1 2 3 4 5 60

Reservoir(Model)

p(Model)

Elapsed Time (hours)

Predictions vs. Test Datae

(o C)

15

20

15W/20W/30W Power Input TSINK = 10oCEvaporator

(Model)

25

Heat Input

25

30

35

ut (W

)

e (o C

)

20

30

02/14/2000 TSINK = 10oC

Reservoir(Data)

Evaporator(Data)

40

Heat Input

30

40

50

ut (W

)

Tem

pera

ture

5

10

15

15

20

25

Pow

er In

pu

Tem

pera

tur

0

10

20 ( )

10

20

30

Pow

er In

pu

0 5 10 15 20 25 300

Elapsed Time (hours)

Reservoir(Model) 10

0 4 8 12 16 20 2410

Elapsed Time (hours)28

0

360Prediction for TSINK=30oC

35

riod

(min

utes

)

180

240

300 TES/EDU Data for TSINK=30oC

Prediction for TSINK=20oC

TES/EDU Data for TSINK=20oC

Prediction for TSINK=10oC

TES/EDU Data for TSINK=10oC

P di i f T 0 C Am

plitu

de (o C

)20

25

30

Osc

illat

ion

Per

60

120

180 Prediction for TSINK=0oC

TES/EDU Data for TSINK=0oC

Peak

-to-P

eak

A

5

10

15

0 10 20 30 40 50 60 70 800

Power Input (W)

P 5

Power Input (W)0 10 20 30 40 50 60 70 80

0

Conclusion / Summary

• LHP Linear Stability Theory– low-frequency/high-amplitude oscillations are caused by large

thermal mass ratio between evaporator and reservoir– unstable range of power input is between those of two

extrema (Points 1 & 2) of TW vs. QIN curve, i.e. dependent on (E) .

environmental heating of liquid line and reservoir– theory is limited to single-pass condenser LHPs

• Theory Verification• Theory Verification– model predictions agreed very well with JPL TES test data– unfortunately, test data from only one LHP are available

• Path Forward– continue with verification when additional data available– add multiple parallel evaporators/condensers to theory