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IRW REPORT NASA CR 16515334129-600- W1-00
DEPRIfffiNG OF ARC IAA.HEAT PIPES: AN INV, E"i GATIONOF CTS THEIRM AL EXCURSIONS
(NASA-C-U-165153) DEPRIMIVG OF ARTERIAL EZAT 180-32688PIPES: AN INVESTIGATION OF CTS THERMAL
.EXCURSIONS Final Report, Sept. 1978 - Aug.1980 (TRW Defense and Space Systems Group) Unclas214 p HC AlD/MF A01 CSC.L 20D G3/34 28773
F'NW ALREFOU
1AUGUI ST 2Q, 1980
D. AntonfiLikD. lK. Edwards
TTRW SALES NO- 34129-000CONTRACT INAS 3-217410
Prepared for
NASAAMMS RESEARCH CENUR
CLEVELAND, Of-410,,",135
04P '0
TR, 1 W.DEFENSEAND SPACVSVSTFMS GROUP
r mm MlP.A,rE MWRA -- MlE-t),0'N.0',0 lf3 fF A:C-H _J
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1. Report 'No.
CR 1'65153i
2. Government :Accession 'No. 3. !Recipient s .Catalog 'No.
A. Title and :Subtitle 15. 'Report :Date
DEPRIMING OF ARTERIAL HEAT :PIPES August '19806. !Performing Organization'CodeAn Investigation of CTS Thermal Excursions
7.:Author(s)
D. Antoniuk and D. K. :Edwards
Z. !P.erforming Organization Report'No.34129-6001-UT-00
1U. Work Unit 'No.V. Performing Organization Name and Address
TRW .Defense and Space Systems Group:One :Space Park 11. Contract or ;Grant 'No.
Redondo Beach., California 90278 NAS3 21'740'13. Type of 'Report and Period Covered
Final (978 to 8/80)i
12. Sponsoring Agency 'Name and Address
NASA Lewis 'Research Center14. 'Sponsoring Agency code21000 .Br.00kpark Road
Cleveland, Ohio 44135 6133'15. 'Supplementary Notes
1B. Abstract
This :final report describes the 'analyses .and expe.r ment•ation performed todetermine the cause(s) :and/or contributing factor(s) responsible for :four :(4)thermal Fexcursions of the Transmit'te:r Experiment :Package (UP) on the Communi-zati_ns Technology Satellite (CTS) during its eclipse season in 1977. Thesezo-called ".anotrol-tes" were the result of the depriming .of the arteries in allthree (3) heat pipes in the variable Conductance ;Heat Pipe ,System ;(VCHPB)Which cooled the TEF. The determined .cause of the depriming of the heat pipes-was the :formation of bubbles of the nitrogen/helium control gas mixture in Thearteries during the thaw portion of .a froeze/thaw:cycle of the inactive regionof the condranear section of the heat pipe;. Conditions such as ;suction freezeo.utor heat :pipe turn-on, which moved these bubbles into the .active region of the.heat pipe, contributed to the depriming mechanism. 1-lethods for precluding„ orreducing the probability of,, this type of failure mechanism in :future applicationsof :arterial heat 'pipes are also included in the report,.
'17. Key Words (Suggested by Author(s)) 18.:Distributk;,; Statement
Arterial heat pipes., thermal control; Unc1a,=5sified - unlimited
artery depri'min'a mochanisms; STAR category
Communications Tecluiology Satellite(Hermes)..
'19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. 'No. of 'Pages 22. Price"
Unclassified [rnclassi'fied 216
'' For'sale.ti the 'National Technical Information Service, Springfield, Virginia 22161
'NASA=C-168 (Rev. 10-75)
e
CONTENTS
Page
1. 0 INTRODUCTION 1
1.1 CTS Thermal Anomali,e:s 1
1,.2 :Revi.ew of Previous Mork 5
1..3 Phase I Studies 10
1,.4 O.bjectives of Phase II Studies 23
:2.0 ANALYSIS OF BUBBLE LIF;ETI'ME'S I'N HEAT PI!P:E .ARTERIES 25
2.1 The 'Spherical Bu'.bbItc Model 25
2..2 Governing Equations for the Spherical 'Bub'ble 27
2,.3 Transformation and Numerical 'Solution 29
2.4 The Elongated Bub'bl a Model 32
2..5 Properties Used in Calculations 33
2,.6 Results for the Spherical Bubble 33
2.7 Results for the Elongated ;Bu'b'ble 40
2.8 Significance of Analytical/Numer;ical 'Results 46
,.0 CYCLIC FREEZE-THAW TESTS ON SNO09 ,HEAT 'PIP,E 48
3,.1 Test Objectives 48
3..2 Apparatus and Procedure 48
3,.3 Test Results 54
3.4 Significance of Test Results 72
4.0 CONCEPTS TO AVERT ARTERY.DERRIMING 75
4.1 Noncondensi.ble Control Gas 'Selection 75
4.2 Operational Procedure for Start-Up, of ,a Frozen 76Condenser
4.3 Mechanical Modifications 77
5,.0 CONCLUSIONS 79
6,.'0 REFERENCES 80
APPENDICES
A.. PHASE I STU.DIiES
A.1 Excess 'S'kew ry 4^ Load "Parti ti oni',ng A-1
A..2 :Sudden Cooing 'Mechanisms
A.2,.1 Instantaneous iHeat !Flow After 'Heat PipeReservoir :Eclipse A-4
-iii
CONTENTS (Continued)
Page
A.2.2 Instantaneous Heat Flow After Heat PipeRadiator Eclipse A-11
A.2.3 Condenser and/or Reservoir Shadowing Testson SNO09 .Heat Pipe A-19
A.3 Freezing :Blowby Tests on SNO09 Heat Pipe A-21
A.4 TEP Thermal Analysis
A.4.1 Brief Review of LeRC Thermal Studies A-23A.4.2 Generalized 'Variable Conductance Heat Pipe
Modeling A-26
A.5 Bubble Studies
A.5.1 Potential for Bubble Formation in CTS HeatPipes: Fundamentals A-80
A.5.2 Potential for Bubble Formation in CTS HeatPipes: Sample Claculations A-86
A.5.3 Bubble Nucleation Experiments A-95A.5.4 Glass Heat Pi,pe :Bubble Nucleation/Migration
Experiments A-99
B. PHASE II STUDIES
B..1 Spherical Bubble.Model Computer Program Listing B-1
B..2 SNO09 Heat Pipe Cyclic Test Data B-17
tf
iv
1.0 INTRODUCTIONS
1.1 CTS THERMAL ANOMALIES
The Communication Technology Satellite (CTS) was launched into an
equatorial geosynchrouous orbit in January, 1976 and is stationed at 1160
longitude. After completing nearly four years of operation, the CTS mis-
sion has recently been terminated.
The major payload on the CTS is the Transmitter Experiment Package
(TEP) which consists of a high power travelling wave tube (TWT), a power
processing system (PPS) and a variable conductance heat pipe system (VCHPS)
shown schematically in Figure 1-1. Heat produced in the tube collector is
directly radiated to space, whereas power dissipated in the PPS is first
conducted to the TEP saddle and the spacecraft south panel from where it
is radiatively rejected.
The temperature control of the TWT is provided primarily by a variable
conductance heat pipe (VCHP)/Radiator system which transports and rejects
most of the heat dissipated in the tube body. Mounting details of the tube
body to heat pipe evaporator saddle and the spacecraft south panel are
sketched in Figure 1-2. As shown there are several interfaces through which
the heat must flow to reach the heat pipes. Normally, heat reaching the
aluminum baseplate is mostly absorbed by the heat pipes and is transported
axially to the VCHP radiator. A fraction of it, however, is conducted to
the spacecraft south panel where it is radiated to space.
The VCHP system, shown in Figure 1-3, consists of three stainless
steel/methanol dual artery heat pipes whose variable conductance is achieved
with the help of external cold wicked reservoirs loaded with a 10 percent
helium/90 percent.nitrogen gas mixture. Figure 1-3 shows the six positions
in the VCHP/radiator system at which temperatures are measured in flight.
The Transmitter Experiment Package is instrumented with four additional
temperature sensors, two located on the Multistage Depressed Collector (MDC)
and two sensors located on and near the tube body.
The CTS is the first spacecraft to rely on heat pipes to control the
thermal performance of a major onboard system. The Transmitter Experiment
Package has performed sl,tisfactorily except on four occasions in 1977,
March 16, March 23, April 11, and September 10 when measured tube body
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temperatures displayed sudden, rapid increases not normal for the TEP
operating conditions and inconsistent with the design of the thermal con-
trol systems. The anomalous behavior of the TEP in these four occasions
are referred to as the "CTS Thermal Anomalies" of days 75, 82, 101, and
253 respectively.
During all the anomalies, the continuous increase of the tube body
temperatures was reversed by reducing the output power without damage to
TEP. Operation of the TWT at the reduced power resulted subsequently in
the recovery of the thermal control system with no evidence of degradation
or changes in its performance.
After the fourth anomaly (day 253), the TEP was successfully operated
at somewhat reduced power (below the open artery capacity of the heat pipes),
and no further anomalies were detected.
1.2 REVIEW OF PREVIOUS WORK
Following the first occurrence (day 75), the CTS anomalies were the
subject of investigations both at NASA Lewis Research Center (LeRC) and at
TRW in an effort to understand the cause of the thermal failures, focussing
particular attention on the VCHPS since it is in the thermal path from the
tube body to space. The work performed at LeRC and preliminary studies
conducted at TRW are documented in References 1 and 2, respectively.
LeRC's investigation included the use of flight-type TEP components
in ambient and vacuum ground tests, analytical studies, flight data review,
and CTS on-orbit tests. The objectives were to determine the most probable
cause of the anomalies and to identify procedures or TEP operating modes
which would preclude damage to the TWT in the event of recurring anomalies
or of continuous degraded capacity of the thermal control system.
From the review of flight data for both normal and anomalous days the
following observations about the anomalies were made:
1) All occurred after relatively long periods at constant,although differing, TWT RF power 'levels or heat rejectionrates from the tube baseplate.
2) All the anomalies took place near the Spring and Fall equinoxperiods during which sun angle with respect to the VCHPSradiator is relatively small and during the orbit quadrantwhere the CTS is almost directly between Earth and Sun inwhich case the VCHPS surface becomes increasingly shadowed bythe spacecraft itself.
-5-
i J
i
3) All the anomalies, except on day 253, were characterized by beingpreceded by temperatures measured at the extremity of heat pipenumber 1 (HP1 with sensor HPT5. See Figure 1-3) being a lL orbelow -98 C, the methanol freezing point.
4) All the thermal anomalies were preceded or accompanied by asudden abnormal but small increase in the difference inmeasured temperatures between the adiabatic sections of heatpipe number 3 and 1, oT1 - 3. This increase in A171-3 wasfollowed by a second increase, and at the outset of unstabletube body temperature rise, o173 -1 was observed to drop to alower level.
Tests were performed with a TWT almost identical to the one outboard
CTS. The results indicated that the anomalies could not have been caused
by thermal interface failure inasmuch that: a) it is improbable that a
failed interface could recover its integrity completely after an anomaly,
and b) it was demonstrated that an interface failure results in tube body
temperature rates higher than those observed during the anomalies.
Vacuum tests that most closely approximated anomalous temperature
profiles were those in which the tube base plate cooling was abruptly
reduced from that required for thermal equilibrium at normal operating
temperatures. These test results suggested that the reduction in heat
transfer capability of the variable conductance heat pipe system is, to
a high degree of certainty, the cause of the thermal anomalies.
Room-ambient tests at LeRC with a flight-type VCHPS indicated that
o173-1 increases are caused by depriming of heat pipe 1 (HP1) or heat pipe
(HP1) and heat pipe 2 (HP2). The temperature difference between the adia-
batic sections of heat pipe 3 (HP3) and HP1 was found to depend on the
priming states of the heat pipe arteries. The measured temperature dif-
ferences oT3-1 were:
a) AT 3-1 1.1C, all heat pipes are primed
b) oT3-1 5.1C, HP1 is deprimed
C) AT 3-1 7.8C, HP1 and HP2 deprimed
d) AT 3-12.3C, all heat pipes deprimed
-6-
t
d
These values for eT3-1 are consistent with the temperature levels observed
during anomalous days and tend to confirm the postulate that the anomalies
are initiated by depriming of HP1, followed by dep•,im •ing of HP?., and the
onset of tube body unstable temperature rise caused finally by depriming
of HP3.
On day 253, while LeRC personnel were performing experiments on-board
CTS, the fourth anomaly occurred. This event gave the unique opportunity
to establish the stable VCHPS heat rejection capacity beyond which the
tube body temperature becomes unstable. Ix was found the open artery
capacity of the VCHPS is approximately 106 watts.
The comprehensive investigative work performed at LeRC made signifi-
cant contributions to the understanding of the CTS thermal anomalies. The
most significant contribution is the fact that convincing evidence was
made available to establish that the thermal anomalies were caused by
unexpected reductions in the VCHPS heat transfer capability resulting from
depriming of the heat pipe arrteries.
The first preliminary investigation of the CTS thermal anomalies con-
ducted at TRW is documented in Reference 2. This investigation, performed
in direct support of LeRC efforts, focussed particular attention at the
identification and analysis of potential artery depriming mechanisms.
Selection of depriming mechanisms was based on the premise that they
must be consistent with three key observations:
1) All the anomalies occurred during the eclipse season.
2) These anomalies are sporadic. Similar conditions on successivedays can yield an anomaly one day but not the next.
3) The anomalies are triggered by depriming of arteries in HP1.
In the early study, among a number of postulated mechanisms, only
three were identified which could be associated with eclipse seasons:
I) Condenser freezing
II) Marangoni flow
III) Gas evolution in the arteries due to rapid chilling
-7-
ed
It was argued that under certain conditions freezing of CTS arteries could
lead to depriming. Arterial failure could result from the transfer of mass
from the evaporator to the frozen condenser where it would freeze and not
be available for circ!+ation. This transfer of mass could be effected by
vapor diffusion, by liquid pumping in fillets due to reduction of specific
volume as it cools and/or by Marangoni flow. The fact that the CTS-type
heat pipes will not fail due to condenser freezing when operated under no
load or at high heat loads, led to the argument that the condenser freez-
ing mechanism will work if the pipe is operated at the right load, not too
high, not too low. However, several factors implied that, although con-
denser freezing can lead to artery depriming, it could not be the primary
cause of the anomalies.
These factors are the fact that on day 253 an anomaly occurred before
the radiator portion of HP1 approached freezing conditions, and the fact
that with all pipes primed HP3 should freeze and deprime first since it
carries least load and its radiator portion radiates from both sides, how-
ever, HP1 failed first. An additional factor is the fact that after the
anomalies the VCHPS recovers before the radiator begins to warm up. It
was thus argued that if sufficient excess fluid was frozen to cause artery
depriming 'there would be none available to rewet the evaporator. There-
fore, condenser freezing was ruled out.
Marangoni Flow (surface tension flow due to temperature gradients
along the a VCHP gas-blocked region) could induce a flow along fillets and
excess fluid reservoirs toward the condenser end along the vapor-liquid
interfaces. No flow, however could be induced in the wick and arteries
which have structure to support the surface tension gradient. It was
argued that Marangoni Flow could influence the VCHP in two ways:
1) If the condenser end is frozen, Marangoni Flow toward thatend would increase freezing under load. However, condenserfreezing was argued not to be the primary mechanism fordepriming.
2) If the heat pipe is not frozen, Marangoni Flow will cause apressure drop along fillets and natural reservoirs reducingtheir pumping capacity. However, the reduction must besmall, otherwise anomalies due to Marangoni Flow effectswould occur on consecutive days under Limilar conditions,not sporadically. It was argued, however, that once deprimed,
-8-
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the open artery capacity could be measurably influencedby Marangoni Flow.
In view of the fact that the control gases helium and nitrogen, par-
ticularly helium, have solubilities in methanol decreasing with decreasing
temperature a',id pressi.ire, it was argued that this behavior could give rise
to a potential depr;. , ng mechanism which is consistent with sporadic occur-
rences during the eclipse seasons. This mechanism is gas evolution within
the arteries during heat pipe chilldown.
It was postulated that when TEP ceases to operate several hours before
an eclipsa, the gas blocks the entire length of the heat pipes. During
this off period, liquid in the arteries becomes saturated with gas surround-
ing the arteries at the gas-blocked condenser temperature and evaporator
pressure. When the CTS enters eclipse, the heat pipes experienced rapid
chilldown which causes the temperature and pressure to drop rendering the
liquid in the arteries sufficiently supersaturated in dissolved gas to
cause gas bubble nucleation within the arteries.
In the early study, it was postulated that gas would evolve at unspe-
cified nucleating sites leading to numerous small bubbles, some of which
would coalesce to form fewer but larger bubbles with intrinsic longer life-
times. When the TEP is reactivated, the heat pipes would turn on leading
to the establishment of a gas/vapor front and a build-up of stress in the
active portion. It was postulated then that if the local liquid stress
exceeds a critical level for a bubble before this bubble is redissolved or
vented, the arteries would deprime. Of the three potential mechanisms for
artery depriming considered in this early study, gas evolution was argued
to be the most plausible inasmuch that it ties the anomalies to eclipse
seasons when the VCHP system experiences rapid chilldowns. Furthermore, it
also provided an explanation for the sporadic occurrences within eclipse
seasons since, it depends on the operating conditions before and after the
eclipse and on bubble nucleation and aglomeration which are statistical
phenomena.
Although no attempts were made at that time to analytically treat the
gas evolution scenario, a simple experiment was performed to determine
whether gas bubbles would be nucleated in the arteries under CTS conditions.
-9-
/ l
The experimental setup consisted of :a short section of CTS-type arterial
wick inserted into :a glass tube sealed at one end and valved at the other.
The tube was filled with appropriate amounts of 10 percent He/90 percent
l2 gas and methanol simulating CTS design parameters.. The tube was then
subjected to temperature reduction under hydrostatic stress in excess of
open artery capacity. The imposed stress was equivalent to increased
supersaturation which would er^`hance the probability of bubble nucleation.
Experiments at 'temperature reduction rates of -1.71 C/Min and -0.9 C/Min
yielded negative results even though the cooling rates were about twice
those observed in orbit, and the imposed hydrostatic stress enhanced the
probability of 'bubble nucleation.
The results of this experiment lead to the conclusion that the gas
evolution mechanism could not have caused artery depriming under conditions
experienceu by the CTS.
Thus, th's preliminary investigation at TRW was unsuccessful in its
quest for a single or sequential series of mechanisms for artery depriming
consistent with all flight data. However, depriming due to gas evolution
within the arteries was regarded as qualitatively consistent with all the
observed anomalies and warranted further investigation.
1.3 PHASE I STUDIES
In view of the fact that previous investigations of the CTS thermal
anomalies convincingly established depriming of the heat pipes in the VCHP
system as the cause of the anomalies but failed to identify the mechanism
or sequential serie. of mechanisms that led to depriming of the arteries,
TRW (under contract to NASA teRC - Contract NAS3-21740) undertook a two-
step investigation of the hydrodynamic characteristics of CTS-type heat
pipes
This section of the report summarizes the work performed during
Phase I and refers to attached appendices (documents generated during
Phase I) for further details.
The first task performed was to identify mechanisms which under a
wide range of feasible conditions could lead to depriming of the heat pipe
arteries. Ten mechanisms were postulated which are briefly described and
classified in four basic groups in Figure 1-4. Also shown are comments on
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the postulated mechanisms in It ht of .observed ,character sti;cs of the
anomalies and flight data,. The approach in 'Phase I to i nvesti,gate the
;potential of these mechanisms is shown in 'Figure 1-5,.
The .basic approach has been., for .a given deprim ng mechanism, to con-
duct analyses in the following sequential order with the implementation of
each succeeding task being contingent upon the results of the !previous .one
a) Analytical ,back-of-the-envelope" calculations and/or flight:datareview.
'b) Calculations with more realistic analytical models,.
C) Bench-scale experiments such as with glass heat .pipe..
A) Experiments ,wit'h .CTS 'SN009 'heat !pipe which is similar to(heat pipe '1 on the 'CTS.
,e;) Correlations of experimental data with thermal (SINDA') andheat ;pipe (UCHPDA;) analytical models results.
Tasks a., ',b., c., and d were P erfo:rmed by 'TRW., whereas task ^e was the result
of a point effort :with 'LeRC in which the experimental data ,generated at
TRW facilities :werecorrelated :with the results of steady state ,and tran-
sient thermal analyses of TEP per-Formed at 'LeRC.. The ILeRC study is briefly
reviewed in Appendix A.4.. L
'Mechanisms Exceeding Heat Pipe Capacity
The arteries in a heat pipe can certainly be ,caused to deprme if
the imposed 'heat load ex:_eeds the designed 'heat transfer capacity of the
heat pipe. 'Exceeding the heat ,pipe ,capacity can be the result of increased
dissipation by TEP,, excess skew in load partitioning on the VCHPS, and high
transient heat pipe load due to condenser and/or reservior shadowing.
Increased Dissipation (Col:umn'D of Figure 1-4). This is clearly not
t"he,cause ,of artery depriming since:
1) TEP power dissipation exceeding designed levels is notsupported by flight power data
2) The !heat loads are well 'below the system capacity whenall three heat ;pipes are ;primed. in fact a single ;primedbeat pipe can carry the maximum designed dissipation 'heatload.
-12-
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3) On many days preceding and/or following the anomalies, higherheat loads were accommodated without difficulty.
Excess Skew in Load Partitioning (Column E of Figure 1-4). The three
heat pipes of the VCHPS on CTS are designed to turn on sequentially so as
to balance the load between them at full-on design conditions. However,
very low sink temperatures during equinox conditions could result in the
load of heat pipe HP1 exceeding transiently its capacity before HP2 and
HP3 take up a significant share of the load. Failure of HP1 by the above
mechanism or by any other could then result in a rapid transfer of load to
.HP2 which, due to inertial effects associated with rapid load transfer,
could fail leading to a rapid transfer of load to HP3, yielding, perhaps,
a "domino effect" failure of the whole system.
Failure of HP1 due to excess skew in load partitioning is discounted
since LeRC transient thermal results for periods preceding the four anoma-
lies indicate the maximum load on HP1 never exceeds 80 watts, a load that
is well below its primed heat transfer capacity.
In Appendix A.1 flight data are analyzed to determine whether there
exists a regularity in the depriming sequence associated with the anomalies,
and the possibility of a "domino effect" failure of the system is investi-
gated experimentally.
The analysis of flight data showed that these exists some regularity
in the depriming sequence as follows: HP1 deprimes first, HP2 deprimes
next followed by depriming of HP3. (On days 89 and 253 the temperature
data suggest that heat pipe 2 or 3 was deprimed, while HP1 carried the
load.) Experimentally, attempts were made to deprime the SN009 heat pipe
with rapid increases of load, simulating, under more stringent conditions,
rapid sequential load transfer as heat pipes deprime.
Tests performed for both high (-18C) and low (-96C) sink temperatures
and at 2.5 cm evaporator tilt, indicated no measurable rate effect attribut-
able to fluid inertia and thus argued against a "domino effect".
High Transient Heat Pipe Load Due to Condenser and/or Reservoir
Shadowing (Column F of Figure 1-4). Sudden shadowing cools the heat pipe
F reservoir which causes the vapor/gas front to move toward the reservoirt
end of the radiator increasing the active portion of the condenser which
F.
-14-
causes the heat load on the pipe to increase. In addition, shadowing of
the VCHPS radiator increases the load on the heat pipes due to a drop in
the effective environment temperature.
Although both effects will eventually lead to cooling of the heat
source, movement of the gas/vapor front reducing the active condenser sec-
tion, and reequilibration at the dissipation load, the transient peak may
be sufficient to exceed the heat pipe capacity and deprime the arteries.
An examination of flight data corresponding to periods preceding and
including the onset of the four anomalies shows a scenario of decreasing
temperatures of the gas reservoirs and on sections of the VCHP system
radiator. Telemetry data for temperature sensors HPT5 and HPT6 (see Fig-
ure 1-3) show that at these locations the temperature drop monotonically
prior to the anomalies.
In order to explore the potential if this postulated mechanism for
artery depriming, the transient loads possible under typical orbital con-
ditions were estimated using a simplified analytical model of the VCHP
system. The description of the model and the basis for the transient loads
calculations are presented in Appendices A.2.1 and A.2.2, which address the
effects of shadowing of the reservoir and condenser, respectively. The
analytical estimates show, that under some assumed cooling rates, the
instantaneous heat loads may be as much as 45 percent larger than steady
state conditions would indicate. These analytical results were found sig-
nificant enough to warrant further tests on the SNO09 heat pipe.
Appendix A.2.3 describes a series of tests performed on the SNO09
heat pipe during which the condenser or the gas reservoir was cooled at
various rates while the evaporator was maintained at a constant heat load.
In tests loads of 100 and 150 watts and cooling of the condenser at
approximately 2.8 C/Min produced no depriming. No depriming was observed
either in tests with 125 watts and at a condenser cooling rate of approxi-
mately 3.9 C/Min. Thus, depriming due to rapid chilldown of the condenser
was not demonstrated.
During tests in which the gas reservoir was cooled repeatedly at suc-
cessively higher rates depriming was observed. With 100 watts at the
evaporator and the inactive condenser at -18 C, depriming occurred when the
reservoir was cooled at the threshold rate of approximately -3.2 C/Min.
-15-
r.
FQ
Although depriming due to rapid chilldown of the reservoir was
demonstrated, the required rates were substantially higher than those
observed during the anomalies. This fact eliminates the postulated sudden
cooling mechanism as a potential cause of the CTS anomalies.
Mechanisms for Depletion of Liquid Inventory
Another possible cause of artery depriming in a heat pipe is depletion
of liquid inventory, either depletion of total heat pipe inventory such as
that resulting from a leak, or depletion of liquid from the active portion
of the pipe such as could result from diffusion freezeout, suction freeze-
out or freezing blow by. Suction freezeout is the loss of liquid from
freezing. Freezing blowby is the loss of liquid from the thawing of an
ice plug allowing a high pressure evaporator to blow liquid from the active
pipe into a low pressure gas reservoir.
Loss of inventory due to leaks will cause permanent changes in heat
pipe performance, an event that is not supported by the observed complete
recovery of the system following an anomaly. Diffusion freezeout is the
transfer of inventory in the vapor phase from the active pipe into the
frozen section where the vapor condenses and freezes. It is too slow a
transfer process to have been effective during the time available prior to
the anomalies.
Suction Freezeout (Column B of Figure 1-4). Suction freezeout has
long been recognized as an artery depriming mechanism. Depriming occurs
due to depletion of evaporator liquid because of the local density increase
as a freezing front moves toward the evaporator end of the pipe. It is
necessary, however, that the condenser freeze while the heat pipe is under
load so that the natural liquid reservoirs in the evaporator do not contain
excess liquid. Such excess liquid would satisfy the demand of the freezing
process without stressing the arteries to failure. Suction freezeout is a
viable explanation for depriming on anomaly days 75, 82, and 101. But not
on day 253, since the results of steady state and transient calculations on
the CTS model performed at LeRC indicate no freezing on this day at the
time of the anomaly.
This depriming mechanism was investigated analytically in the previous
TRW's study (2)
where the mechanism is referred to as "Condenser Freezing".
-16-
a .rr
The results of this investigation made in light of flight data and
observation about the anomalies were summarized in Section 1.2 of this
report.
In Phase I of this program, suction freezeout was subjected to experi-
mental investigation with tests on the SNO09 heat pipe. Several attempts
to deprime the arteries by freezing the condenser while the SNO09 heat pipe
was under hydrostatic and thermal load were unsuccessful.
The experimental results support the conclusion of the previous inves-
tigation (2) which states that although suction freezeout or condenser
freezing can and may lead to artery depriming, it is not the primary cause
of the anomalies.
Freezing Blowby (Column C of Figure 1-4). The CTS heat pipes contain
substantial amounts of excess liquid. Such excess inventory is requiredfor successful priming of the arteries in earth gravity testing. In zero
gravity a slug of excess liquid generally bridges the condenser vapor
spaces, acting as a moving membrane between portions of the non-condensible
control gas. Subfreezing radiator temperatures can cause the slug of
liquid to become an immobilized plug of ice separating the active section
of the pipe from its gas reservoir. If during a transient a pressure dif-
ferential develops across the ice plug, with the pressure higher on the
evaporator side, and then the plug partially thaws, this pressure difference
can blow liquid from the evaporator to the reservoir side and deplete the
active pipe inventory causing the arteries to deprime.
Because freezing blowby requires freezing, this mechanism can not be
the cause of the fourth anomaly, since freezing had not occurred immediately
preceding the anomaly on day 253. However, freezing blowby could account
for some of the anomalies during which freezing occurred.
To explore experimentally the depriming potential of this mechanism,
it was first necessary to develop means of forming an ice plug in the
laboratory in the absence of the natural slugging of excess liquid expected
in zero gravity. Appendix A.3 describes a successful technique that was
developed to form an ice plug in the SNO09 heat pipe, and the procedure
followed during the blowby tests. Three tests were performed during which
depriming occurred each time. The results of these tests clearly establishedFgt
-17-j
i
that freezing blowby is a bonafide depriming mechanism and a candidate to
explain at least some of the anomalies.
The latter statement is supported, to a certain extent, by some results
from the CTS model analyses which showed that ice plugs formed in all the
heat pipes on day 82 several hours prior to the onset of the anomaly. In
addition, the results showed that the pressure on the evaporator side
would have been higher than on the reservoir side when the plugs thawed
forty five minutes before the last heat pipe deprimed. The significance
of these calculated results is that they show conditions for freezing
blowby may have existed on at least one day of -the anomalies.
Mechanisms for Bubble Nucleation
The presence of gas inside the arteries of the heat pipe has long been
recognized as detrimental to the stable operation of the pipe. Because the
solubilities of nitrogen and, particularly, helium in methanol, decrease
with decreasing temperature and pressure, there exists the potential of
bubble nucleation within the arteries in CTS-type heat pipes as they
undergo rapid temperature reduction. This potential is compounded by the
decrease in pressure that results from temperature reduction in the closed
heat pipe environment. Liquid methanol saturated with gas can become
supersaturated with gas when undergoing rapid temperature and pressure
reduction, an event that enhances the potential of bubble nucleation.
Bubbles that might nucleate inside the arteries during the transient
cooldown of the heat pipes after the power is turned off and the spacecraft
enters into eclipse, can coalesce to form fewer but larger bubbles. If,
as the result of their size and the rather slow process of gas diffusion
back into surrounding liquid, the bubbles survive until the heat pipes are
once again activated under load, some bubbles might be convected into high-
stress liquid regions where they can grow in size and consequently deprime
an artery.
The process of bubble coalescence and migration is recognized as
statistical in nature.
The above postulated mechanism was examined during a previous TRW
investigation; (2) however, experiments under simulated anomaly conditions
failed to induce bubble nucleation.
-18-
Rr^
7.
Despite these results, this mechanism was reexamined during the
current program due to the fact that the postulated conditions for the
mechanism to be activated can be supported by flight data corresponding
to all the anomalies, and the probabilistic nature of the mechanism bears
positive correlation to the sporadic occurrences of the anomalies. In
addition, a thorough examination required the performance of experiments
simulating more realistically the operating characteristics and anomaly
conditions of the CTS heat pipes and investigation of the potential of
other mechanisms, particularly freezing-thawing, to induce bubble nucleation.
Bubble Nucleation Due to Temperature and Pressure Reduction (Columns G
and H on Figure 1-4). An analysis of the potential for bubble formation
was performed based on fundamentals described in Appendix A.5.1. Sample
calculations were made for two cases (1) a condenser depressurization case
where the evaporator temperature is dropped at constant gas-blocked con-
denser temperature and (2) a condenser chilldown case where the gas-blocked
condenser is cooled at constant total pressure.
The sample calculations presented in Appendix A.5.2 showed the possi-
bility for bubble formation upon (1) depressurization by reduction in heat
pipe loading and reservoir chilling and (2) condenser chilldown. Depres-
surization showed greater potential, for approximately 500,000 bubbles/cm3
were found possible, compared to only one of equal size resulting from
condenser chilldown. The above calculations, based on two hypothetical
cases, were followed by a number of calculations for various anomaly con-
ditions. The predicted number of bubbles of varying critical size was
found substantial for all anomaly conditions considered in the analysis.
In order to verify qualitatively the above analytical results, a
series of simple experiments were formulated which are described in Appen-
dix A.5.3. Tests were performed with a glass vessel half filled with
liquid methanol containing a short section of mesh screen artery laying on
its bottom. The vessel was instrumented to permit continuous monitoring
of temperature and pressure. The liquid methanol was saturated with either
helium or nitrogen at room temperature subsequent to which three series of
tests were performed. In the first two series of tests the saturated
methanol was subjected to various rates of temperature and/or pressure
reduction. During the tests bubble nucleation in the bulk of the liquid
-19-
i.
or on the surface of the artery mesh screen was never observed. These
results suggested that temperature and pressure reduction are not potential
mechanisms for bubble generations in CTS-type heat pipes. In the Ust
series of tests with the glass vessel, the saturated methanol was subjected
to several freeze/thaw cycles. Large numbers of bubbles were observed
streaming from the ice surface.
Bubble Generation Due to Freezing (Column I of Figure 1-4). The
results of the glass vessel tests were of paramount importance, for they
identified freezing and thawing of gas-saturated methanol in the arteries
as a potential mechanism for bubble formation in the arteries. The fact
that freezing occurred preceding three of the four anomalies and sometime
during the 24 hours before all of them, the involvement of ice-generated
bubbles in the four thermal anomalies was shown to be a distinct
possibility.
To explore this bubble nucleation mechanism in a realistic heat pipe
environment, a series of tests were performed with an existing glass heat
pipe. The pipe contains a slab wick with a CTS-type artery attached to
one side and permits observations on the behavior of the artery in an
operational heat pipe. For the tests the heat pine was gas loaded with
a 90 percent N 2/10 percent He gas mixture at a pressure equivalent to that
in the CTS heat pipes. The experiments performed on the glass heat pipe
are documented in Appendix A.5.4.
The results of bubble nucleation experiments showed that each time
the artery in the condenser section underwent freezing and thawing bubbles
were observed inside the arteries although the number of bubbles, their
size and location along the artery varied from test to test. The time
required for the bubbles to disappear by diffusion was found to vary enor-
mously depending on their size. Small spherical bubbles dissolved within
hours, while elongated bubbles required up to several weeks.
Additional experiments were conducted with this heat pipe during
which the gas/vapor front was forced to move into the previously frozen
condenser section in attempts to incorporate ice-generated bubbles into
the active condenser and cause depriming. A number of deprimings were
observed, but they were sporadic, probabilistic in nature. These results
-20-
f
I!i
ii
conclusively demonstrated that: 1) Control gas is liberated from
sai*,urated methanol every time the heat pipe goes through a freeze/thaw
csjcle, 2) the number, size, and durability of gas bubbles generated within
the arteries have a statistical variation and are influenced by bubble
coalescence, and 3) arterial bubbles can lead to depriming if they migrate
or are convected into the active region of the pipe under normal load con-
` ditions. Thus, it is clear that freezing and thawing of the condenser can,
but does not necessarily, lead to artery depriming, depending on subsequent
history.
Attempts to induce arterial failure in the SNO09 heat pipe due to the
ice-generated-bubble mechanism were partially successful. Depriming was
not observed in several tests when the heat pipe was brought under a heat
load immediately after the condenser had gone through a freeze/thaw cycle.
However, depriming was discovered on two occasions after the SNO09 heat
pipe had been left unattended under hydrostatic load for several hours
during which time the condenser froze following the termination of a normal
freeze/thaw cycle.
The results of tests with the SNO09 and glass heat pipes clearly indi-
cated that in order to establish the statistics of this artery failure
mode, repeated experiments would be required.
SUMMARY
In the course of Phase I of this program, numerous depriming mechanisms
were postulated and subjected to analytical and experimental investigation.
Several mechanisms were convincingly rendered highly improbable causes of
artery failure on CTS. Four mechanisms, however, were identified as poten-
tial candidates to explain the anomalies and are listed in decreasing like-
lihood in Table 1.
It was argued during this Phase of the study that potential depriming
mechanisms must be consistent with three key observations about the
anomalies:
1) The anomalies occur only during the radiator eclipse seasonwhen condenser freezing may be realized.
2) The anomalies are sporadic. Similar conditions on successive dayscan yield an anomaly on one day and not on any of several similardays.
-21-
Table 1. Summary of Potential Depriming Mechanisms from Phase I.
ARTERY DEPRIMING ANALYTICALLY EXPERIMENTALLYRESULTS FROM: FLASK GLASS H.P SN•009 H.P
I. BUBBLE NUCLEATIONDUE TO:a) FREEZE/THAW — YES YES 7b) PRESSURE REDUCTION YES NO NO --C) TEMP REDUCTION YES NO NO --
11. FREEZING BLOW-BY YES -- -- YES
111. RADIATOR/RESERVOIRRAPID COOLING
YES — -- YES
IV. SUCTION FREEZE-OUT YES -- -- NO (7)
3) On day 253 condenser freezing did not occur immediatelyprior to the onset of the anomaly.
In light of the above observation, the following comments can be made on
the mechanisms listed on Table 1.
Suction freezeout is not a statistical depriming mechanism and cannot
account for the anomaly on day 253. Artery depriming due to suction
freezeout was not demonstrated with the SN009 heat pipe which seems to
indicate that none of the other anomalies could have been caused by this
mechanism alone. This mechanism can only be considered a potential contrib-
uting factor to some of the anomalies.
The sudden cooling nechanisms could account in principle for all the
anomalies, however, they are not statistical in nature. Furthermore:, tests
with the SN009 heat pipe showed that the cooling rates required to fail the
arteries far exceed those indicated by flight data. Thus, this artery fail-
ure mode can be assigned a low probability of success and only be consid-
ered a contributing factor to some of the anomalies.
Artery depriming due to freezing blowby was verified in repeated
experiments with SN009 { peat pipe, establishing freezing blowby as a
bonafide potential depriming mechanism. Analyses of the CTS thermal model
{
-22-
for day 82 predicted the formation of ice plugs in the CTS heat pipes and
calculated pressure differential acc,oss the barrier (pressure higher on
evaporator side) which were sustained until the ice plugs thawed. These
predicted results tend to indicate that conditions for blowby may be
present on some of the anomaly days. Although freezing blowby is not a
statistical mechanism and can not be the cause of the anomaly on day 253,
it can not be totally discounted.
In view of the results of glass flask and glass heat pipe experiments,
the ice-generated bubble mechanism appears to be a prime candidate for
explaining all four CTS anomalies. It is consistent with (1) their sea-
soned occurrence (eclipse conditions are necessary to cause condenser
freezing), (2) their sporadic occurrence (due to the statistical nature of
bubble population and behavior), and (3) the lack of freezing on day 253
(bubbles were generated by a freeze/thaw process during day 252).
1.4 OBJECTIVES OF PHASE II STUDIES
The Phase I studies demonstrated that bubbles are generated each time
liquid methanol containing dissolved gas undergoes freezing and thawing,
and that these bubbles may result in artery depriming if inducted into the
active portion of the heat pipe. This depriming mechanism was demonstrated
on the glass heat pipe. However, depriming due to ice-generated bubbles
was not conclusively demonstrated on the SNO09 heat pipe. Because the
SNO09 heat pipe is similar in overall dimensions and performance charac-
teristics to heat pipe number 1 onboard CTS, the need to demonstrate
depriming on the SNO09 due to bubbles became apparent in order to demon-
strate beyond a reasonable doubt that the postulated bubble mechanism is
the cause of the thermal anomalies.
The Phase I studies also warranted further study of the behavior of
bubbles inside arteries, particularly their lifetimes, owing to the fact
that the probability of arterial failure due to bubbles induction into
high stress regions is positively correlated to longer bubbles lifetimes.
As a result a second phase of this program was continued. The second
phase was necessary to bring the CTS-anomaly studies to the satisfactory
conclusion envisioned at the outset.
A
-23-
The objectives of Phase :I:I were:
1,. To :analyze the .diffusion ;process for non-condensi'bl,e °controlgases in arteries and to ;determine lifetimes of ibubbles ofvarious sizes at various temperature levels and rates of;change :of ' temperature bevel and for various selected control,gases,.
L. To run continuous cyclic freeze/thaw :tests on the `SN009 heat,pipe for five consecutive days in an effort to :produce :arterydeprimng Eby freeze-thaw ;bubble .formation. The isuccessfultriggering of a failure ,would ^establ i sh that freeze-thaw 'bubbl eformation i - the l o;gical cause of the CTS thermal anomalies.
3. To propose concepts to :avert artery dep.riming.
-24-
aa.
vapor aad
Bubble
Radius 'Rl
dies 'R2
r-coordinate
(quid ('Rl 5 r:sR2)
Z.0 ANALYSIS OF BUBBLE LIFETIMES IN 'HEAT !PIPE ARTERIES
2.1 THE SPHERICAL BUBBLE MODEL
Consistent with Phase II objectives 1 and 3, it is desired to calculate
'how fast vapor :bubbles in (heat pipe arteries might grow or collapse and
'how the 'kind of gas ,used ,affects the growth/collapse rates. The first
model selected for such calculations is the one-dimensional spherical
annulus., the domain 'R1 < ,r < ',R2 as shown in Figure 2-1.
External
Gas and Vapor (r z Rzd
Figure 2-1. Spherical Bubble Model
The vapor-and-gas-filled,bubb'',e (r < R 1 ) has uniform composition,
because gas-phase diffusiviti.es exceed liquid phase diffusivities by
several orders of magnitude,. The external gas r > R2 ;has known pressure
and composition. The interface at 'R 2 is considered to 'be a screen like
the wall of an artery so that the pressure difference across the interface
is uncoupled from that otherwise dictated by surface tension and R 2 . At
r=R1 no screen exists, so the vapor-to-liquid pressure difference is 2G/R1
where a is surface tension.
-25-
5
NA
The following 'heat pipe scenario is postulated: The heat pipe
,pictured in Figure 2-2 operates with an active section at 300K and a gas-
blocked condenser at 250K long enough for the artery liquid to saturate
with the gas. Then as pictured in Figure 2-3 the condenser is briefly
frozen and then thawed to 180K. Upon thawing of the gas-blocked condenser,
there are, as has been:observed experimentally, large .numbers of .minute
bubbles :released from the ice, but most diffuse back into solution. A few
are ;postulated to condense to form the bubble of prescribed size R1 0'
The .noncondens ble gas compositions in the bubble and in the liquid were
taken to be the same, the same as that i,n the saturated liquid at 250 :K..
The condenser then warms .up at a prescv'^bed rate as pictured in Figure 2-3,
affecting the vapor composition in the external gas. Because thermal
diffusion proceeds at a much higher rate than mass diffusion (Prandtl num-
ber is much smaller than Schmidt number, the artery liquid is assumed to
be in thermal equilibrium with the condenser temperature, and the vapor
composition of the internal gas is also affected.
ADIABATICEVAPORATOR^-- CONDENSER -- 1 SECTION H
GAS-BLOCKED I ACTIVE REGION
HEAT PIPE
TEMPERATURE iBEFOREFREEZING
TEMPERATURE AFTERFREEZING AND THAWING
e
300
250
Z180AXIAL DISTANCE
Figure 2-2. Axial Temperature Profile
-26-
0
250
I
w
o^W W
d.V EO W.-i F-CO1 C'In
CD Z 780WZCD F.P
0 TIME
t
R1)
dt
2 dR1
v = r (2-2)
k
4 •:
Figure 2-3. Postulated Gas-Blocked Condenser Temperature History
2.2 GOVERNING EQUATIONS FOR THE SPHERICAL BUBBLE
Within the liquid, conservation of mass species i takes the form.
ax. ax.(,2x• ax.
at + v are1
Di
ar2 + ,r ar
(2-1)
where i = 2 to n 0 =1 is reserved for the liquid). The quantity x i is the
mole fraction of species i, and r is the radius. The assumption has been
made that the solution is dilute and isothermal, so the molar concentration
c is constant at that of the liquid, and the diffusivity D i for species i
in the liquid is unaffected by the other dilute species present. The
radial velocity v is caused entirely by growth or collapse of the central
bubble, because the diffusion mass transfer rates are so low, conservation
of mass dictates
-27-
dw-dt, = -4,rRi Ni '1 (2-3)
Within the central bubble the gas is assumed to be unife-m in
composition and pressure, because the gas-phase diffusivities are high
compared to the liquid-phase values, and inertia forces are negligible for
the small changes in bubble growth or collapse rate. Accordingly the gas-
phase species equations equivalent to Eq. (2-1) are not used explicitly.
Rather, they rare replaced by the simple expression
where w is the molar content of species i within the bubble and N i 1 is
the molar flux for species i at r=R1 , given by Fick's Law on the liquid
side of the bubble meniscus as
ax
Ni,l = c Di ar i Ir=Ri=2,n (2-4)
1
where c is liquid molar concentration (g-moles/cm3).
The molar content of the bubble is given by
wi = 3 ,r R1 3 P i /R Tci=2,n (2-5)
where T is the condenser temperature, and R is the universal gas constant.
Similarly the conservation of momentum equation is replaced by a quasi-
hydrostatic balance equation
n
i=1 Pi = Pliq + 2a/R1
(2-6)
The partial pressures within the bubble are given by Raoult's and
Henry's Laws. Since x 1 is nearly unity, Raoult's Law gives simply
P1 = Pv(Tc)
(2-7)
while Henry's Law is
P i = Ci (Tc) x ii=2,n
(2-8)
Outside the liquid at r=R2 the total pressure of the vapor and gas is
Pv (Tev ) where Tev is the evaporator temperature. The gas pressure in the
-28-
f
__...,^. ._...rte
gas-blocked condenser is
Pg = P (Tev) - P
v (T c )
(2-9)
The gas composition is specified by Y i , i=2 to n, where Y i is the mole
fraction of species i in the noncondensible. For example, if 2 is helium
and 3 is nitrogen, Y2 might be 0.10 and Y 3 0.90 for a 10 percent helium,
90 percent nitrogen gas mixture. The saturation values of x i at r = R2 are
xi = Y i P g/G i (Tc ) (2-10)
The initial conditions at t=0 are specified by a uniform set of xi,
i=2 to n, for the initial liquid composition, a set of Y i in the gas bubble
and the initial radius R 1 of the bubble. From these there can be derived
the set of w i , i =2 to n. First, from Eqs. (2-6) and (2-7)
Pg = P liq + 2a (Tc)/R1 - PV (Tc ) (2-11)
Then from the gas law
Wg = 3 ,rR3 PgATc (2-12a)
where
nwg = L w i (2-12b)
i=2
Finally
w = Y i w (2-13)
2.3 TRANSFORMATION AND NUMERICAL SOLUTION
It is convenient to anchor the spatial coordinate to the bubble inter-
face and make the coordinate dimensionless with respect to R 2 - R1.
r - R (t)
'nR 2(t) R t^
(2-14)2 1
-29-
ax i - ax 1
ar - an AR(2-17)
where R2 (t) is given by
4 3 4 3 = 4 3 4 3 ( )3 f R2 - 3 7rR1 3 7rR2,0 - 3 7rR1,0 2-15
Velocity v given by Equation (2-2) becomes
R 2.
v = \R +nARk 1(2-16)
1
Partial derivatives with respect to r at constant t (and thus at constant
R1 and AR = R2 - R1 ) are given by
The partial derivative with respect to t at constant r must be transformed
to one with respect to t at constant n
a„^ i axi + ax an(2-18)
.
at = at an I at I rr n t
I
^t = - DR R1 - ( rR1 ) AR (2-19)
r AR
2
Hence Equation (2-1) becomes
ax iaxi1 . n R1 2 R 1 ax
at I + I+an AR R1 AR AR) + (F + ARj ER an
n
= D. (/ 1 92xi + 2 1 axi)
\oR2 a 2 R 1 + nAR AR an
TI
Collecting terms gives
axiR12 R1 ( 1+n)R1
2Di ax D i a2xi
at + 2 - AR R +nAR AR an - --j^ = 0 (2-20)
(R 1+nAR) AR 1 AR an
Since large values of ax i /9n are expected near n = 0, computational
efficiency is improved by transforming the n coordinate to z so as to
expand the region near n = 0 relative to the region near n=1. A negative
-30-
a{
value of the parameter y in the following coordinate transformation
achieves the desired result.
1-eynZ =
(2-21)1-ey
After transformation Equation (2-20) is in 'he form of
ax. ax. 92x.
at e + F az' + G
2^ = 0 (2-22)
az
where F and G are functions of z, R l , R19 D i , and y (recall that R2 and
hence AR is given by Equation (2-15)).
Equation (2-22) is solved numerically in finite difference form. Let
subscript j denote z location and superscript o and oo denote values at
t-at and t-tot respectively. The species subscript i is dropped to avoid
confusion. The temporal derivative is approximated as
9t- of tat xj + a2 xjo + a3 x ooj ^
(2-23)
where for constant time increment et, a l = 3/2, a2 = -2, and a 3 = 1/2.
The spatial derivatives are
ax __ xj+1 xj-15—z2AZ
(2-24)
a2xj __ xj+l + xj-1 - 2x
az2 (Oz)2
(2-25)
Equation (2-22) takes the form
x = A xj+1 + B xj-1 + Cj , j = 2,N (2-26)
where z2 = 0 and z = 1. The coefficients Aj . Bj , and C may be calculated
at any time step in terms of the previous known sets x o. and xj00 and the
known values of R11 R15 D i , y, and zj . The new set of x values is computed
by means of Gaussian elimination in which
-31-
xj = A xj+1 j
(2-27)
Equations (2-26) and (2-27) combine to permit the forward (j=2, 3, ...)
calculation of A j and Bj .
A2* = 0 , B2* = B2 x1 + C2(2-28a,b)
Aj* = Aj /(1 - B Aj * 1 ) (2-280
Bj* (Bj Bj-1
+ Cj )/(1 - B Aj*1 ) (2-28d)
Then Equation (2-27) allows the backward (j=N-1, N-2, ...) calculation of
x starting with the prescribed boundary value xn.
Appendix B.1 contains the listing of the program used to calculate
x(zj ,t) and R1(t).
2.4 THE ELONGATED BUBBLE MODEL
When a bubble grows so that its radius (R1 ) reaches the artery radius,
further growth occurs through elongation of the bubble within the artery.
In the absence of a priming foil, the artery wall prevents meniscus coales-
cence, and a sheath of liquid is retained about the elongated bubble.
Mass transfer of species i (i=2 to n) can occur through the sheath and into
or out of the end-cap liquid. Equations (2-5) and (2-12) become
wi = (3 w Ra+ wR2L) Pi/RTC (2-29)
wg = (3 ff Ra+ 7R2L) PgATC(2-30)
while Equations (2-6) through (2-11) and (2-13) remain unchanged.
Equation (2-3) and (2-4) are well approximated by
dwidt = cD i [(21TRaL c/TAR) + (F/Ra)J AX (2-31)
where AX
is the difference in mole fraction between that of the inside
liquid at the bubble-liquid interface and that of the outside liquid at
the condenser-gas-liquid interface. The quantity c is the artery screen
-32-
F't.
void fraction, T is its tortuosity, and F is the conduction shape factor
for a hemispherial bubble of radius R in a semi-infinite cylinder of
radius R + AR. Fcr the CTS heat pipe arteries R 0.0127 cm, c 0.37,
Ra/AR = 8, and F ='8.
Equation (2-31) was integrated numerically with Equation (2-30) used
to find L in a Runge-kutta type algorithm.
2.5 PROPERTIES USED IN CALCULATIONS
Figures 2-4 (Ref. 3) shows the solubility data used for the calcula-
tions. Shown versus temperature is the mole fraction in the liquid for a
partial pressure of 1 atm, that is the reciprocal of Henry's constant in
atm-1 . The variation with temperature will be shown to be quite signifi-
cant. For now, merely note that methane and argon become less soluble in
methanol with increasing temperature (as does air in water) while helium
becomes less soluble with decreasing temperature. The solubility of nitro-
gen in methanol is nearly independent of temperature. Helium is seen to
be only sparingly soluble while methane is quite soluble in methanol.
Figure 2-5 (Ref. 4) shows the diffusivity of argon and helium in
liquid methanol versus reciprocal temperature. The theory shown in the
figure agreed poorly with experimental data, and it was decided to fit the
experimental data with an Arrhenius relation. Since data were lacking and
theory seemed dubious, it was decided to use the experimental helium fit
for helium diffusivity and the experimental argon fit for the diffusivity
of argon, nitrogen, and methane. Thus the calculated results for the
latter two gases should be regarded as only qualitatively correct. When
reliable data for these latter two gases become available, a minor time-
scale expansion or contraction will be necessary to adjust for the approxi-
mate values of diffusivity used.
2.6 RESULTS FOR THE SPHERICAL BUBBLE
Figures 2-6 through 2-9 show the calculated results for the spherical
bubbles. Each of the four figures is for a different gas: helium, argon,
methane, and 10 percent He 90 percent N 2 , respectively. For a given con-
denser warmup rate and initial bubble size, helium bubbles are seen to
persist for very much longer times than argon bubbles. Methane bubbles
disappear much faster than even argon bubbles. The explanation is simply
2.25 2.3 2.35 2.4 2.45 2.•5
LOG 10OF TEMPERATURE (K)
10 2
10 52.2
}
i^
{
ZCD
10-3
WJO
F-JmJON
10-4
S .
Figure 2-4. Solubility of Various Gases in Methanol asFunction of Temperature (from Reference 3)
-34-
10-3
10-4
N
ItMH
3wO
10-5
EXPERIMENTAVEXTRAPOLATEDMODIFIED MILKE-CHANG THEORY-°- - --
ID-6L3.0 3.5 4.0 4.5 5.0 5.5 6.0
1000./T(K)
Figure 2-5. Diffusivity of Helium and Argon in Methanolas Function of Temperature (from Reference 4)
-35-
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-39-
that, despite its higher diffusivity, the solubility of helium in rethanol
is low; hence the values of cDi AX
are low for helium. Beciuse of the
helium component, the 90%N 2 - 10%He noncondensible gas mixture displ';ays
long bubble lifetimes.
For a given gas and condenser warmup rate, small bubbles disappear
.much faster than large bubbles. In the small bubble the gas pressure is
larger due to surface tension, so the values of xi are larger. The mass
transfer coefficient area product decreases with size as R1 , but the
volume of gas remaining decreases as R13.
With helium gas in a bubble of a certain initial size, increasing the
condenser warmup rate increases the solubility and diffusivity of the
helium and hastens the reabsorption of the bubble, despite a decreased
surface tension, and an increased pressure of methanol vapor which tends
to swell the bubble.
With argon the increase in diffusivity with increasing temperature
causes the same type of behavior as in the case of helium but to a lesser
degree. With methane, however, the increase in diffusivity offsets the
decrease in solubility and lessened surface tension, so that the time to
reabsorb small bubbles is nearly independent of condenser warmup rate. A
complex behavior is seen for the large bubble and high condenser warmup
rate. In that case, the fall in solubility of methane and the increase in
methanol vapor pressure combine to cause the methane gas and methanol vapor
bubble to swell before ultimately collapsing.
Table 2-1 summarizes t-s bubble lifetime results. Note the much
longer times necessary for helium-containing bubbles to be reabsorbed.
2.7 RESULTS FOR THE ELONGATED BUBBLE
Figures 2-10 through 2-13 show calculated results for the elongated
bubbles. Again each figure is for a different gas or gas mixture. Again
helium-containing bubbles are seen to persist to a much longer time, while
methane bubbles are most readily reabsorbed. Again an increase in conden-
ser warmup rate strongly hastens the reabsorption of helium bubbles and
weakly hastens the 'reabsorption of argon and methane bubbles. Bubble
swelling, elongation i-n this case, is seen in all cases, because reabsorp-
tion is initially slower than for small spherical bubbles. A final
-40-
i
Table 2-1. Calculated Spherical Bubbles Lifetimes
Condenser Warm-up Rate (K/sec)
Gas/GasMixture
InitialRadius(cm)
0.0 0.01 0.05
Time, in seconds, at whichbubble radius reaches 1/10of initial radius.
0.01 15 15 15Methane
0.02 68 68 68CH4
0.04 3775 4362 3712
0.01 10717 4055 1658Helium
0.02 64411 9998 6782He
0.04 3714138 38651 35409
0.01 208 204 194Argon
0.02 3614 2790 1884Ar
0.04 27890 10740 8460
0.01 1514 1216 782CTS Mixture
0.02 10777 4950 282390% N2/10% He
0.04 67520 16038 14150'
l
-41-
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-43-
41
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-44-
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-45-
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observation is that the helium in the helium-nitrogen gas mixture becomes
the residual gas in the bubble at long times and low condenser warmup rates
and requires a long time to diffuse out of the bubble.
Ta:)le 2-2 summarizes the calculations of the elongated bubble lifetimes.
Table 2-2. Calculated Elongated Bubbles Lifetimes
Condenser Warm-up Rate (K/sec)
Gas/GasInitial 0.0 0.01 0.05
MixtureLength
CM Time, in seconds, at which bubblelength reaches 1/10 of initiallength.
Methane 2.5 110,070 42,655 40,555CH
Helium 2.5 5',069,500 436,000 432,300He
ArgonAr
2.5 406,500 101,600 99,000
CTS Mixture90% N2/10% He
2.5 998,800 182,560 186,440
2.8 SIGNIFICANCE OF THE ANALYTICAL/NUMERICAL RESULTS
The CTS heat pipes contained 90%N 2 - 10%He control gas. The helium
was added to facilitate leak detection. In retrospect, that decision
appears to have been unfortunate. For should gas bubbles be created by
freezing in the gas-blocked condenser and should they coalesce into bubbles
approaching.0.8 mm in diameter, their lifetimes are seen to be on the
order of 20 hours when the condenser warmup rate is slow. Larger sausage
bubbles are seen to persist hundreds of hours, that is, some ten days or
more. Such bubbles, if present through cyclic freezing and thawing may be
enlarged through a fractionation process reminiscent of the making of New
England applejacn. With each freezing episode dissolved gas is forced out
-46-
of the ice into the bubble. A large bubble can persist many days even
after freezing no longer occurs provided it is in the gas-blocked region.
When the heat pipe is powered up, and the gas front approaches the bubble,
Marangoni Flow brings the bubble into the active condenser, and condensate
flow sweeps it up the pipe toward the evaporator to a location where the
local vapor-liquid pressure difference exceeds the capillary pressure of
the artery, and the artery deprimes.
The results suggest that methane would make a good control gas,
because methane bubbles up to 0.8 mm in diameter are reabsorbed in approxi-
mately one hour. Thus there is little likelihood that a 24 hour periodic
freezing and thawing could create a large bubble, and the small bubbles
released from thawing ice would be reabsorbed before the approach of the
gas front.
-47-
3.0 CYCLIC FREEZE/THAW TESTS ON SNO09 HEAT PIPE
3.1 TEST OBJECTIVES
Phase II objective 2 was to simulate an anomaly with the SNO09 heat
pipe by cyclic freezing and thawing of the condenser during a 5-day extended
continuous test period. The goals of the tests were (a) to demonstrate the
generation and collection of bubbles in the arteries and their migration
or induction into the active section of the heat pipe where their presence
could result in depriming of at least a single artery, and (b) to establish !
by test data analysis that freezing blowby or suction freezeout rather than
bubble formation was not the cause of the observed heat pipe failure.
3.2 APPARATUS AND TEST PROCEDURE
The test assembly described in Figure 3-1 is similar to the one used
for tests on the SNO09 heat pipe during Phase I of this program. As shown,
the heat load is applied on the heat pipe over a 0.305 meter long section
by means of an attached 4.0 kg heated aluminum block.
The heat pipe condenser, 0.91 meter long, is mounted on an aluminum
plate whose area and thermal mass corresponds approximately to the effective
portion of the CTS radiator. This plate is coupled to the sink through 0.32
centimeters of cork over a 0.1045 square meter area. Tape heaters attached
along the plate allow changing the condenser temperatures even with a con-
stant temperature sink.
A cooling coil with tape heaters is attached to the gas reservoir for
purposes of controlling its temperature independently from the rest of the
heat pipe assembly.
The heat pipe test assembly is instrumented with seventeen temperature
sensors, the location of which are shown in Figure 3-2. The sensors are
connected to a 24-channel strip chart recorder which allows monitoring these
temperatures at 1.5 minute intervals.
The test procedure in Table 3-1 outlines the basic steps for conducting
the cyclic freeze/thaw tests on the SNO09 heat pipe. Steps 1 through 5
represent the original procedure for repriming the heat pipe and adjusting
the operating parameters in preparation for the commencement of a new cycle.
As indicated in the procedure, the selected evaporator elevation and heat
-48-
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-50-
Table 3-1. SNO09 Heat Pipe Freeze/Thaw Cyclic Test Procedure Outline
Using the test assembly described in SK80010 and SKE0011, perform the
cyclic tests for a period of 120 continuous hours in accordance with the
following procedure:
1. Level heat pipe to within 1.0 mm.
2. Isothermalize heat pipe to within 1°C and wait 30 minutes.
3. Elevate evaporator end 1.2 cm above condenser.
4. Apply 130 watts to evaporator heater and verify artery priming.If arteries are primed, proceed with Step 5, otherwise, repeatSteps 1 through 4.
5. Reduce sink plate, inactive condenser and gas reservoir tempera-tures to the following levels:
a) Sink plate: lower than -145°C (-229°F)
b) Inactive condenser: -40°C ±5°C
c) Gas reservoir: -95°C ±5°C (-139°F)
Reservoir temperature reduction rates should not exceed-2°C/min (-3.60F/min).
6. Simultaneously, reduce temperatures in inactive condenser sectionbelow -102°C (-152°F) and increase gas reservoir temperature to-40°C ±5°C over a period of approximately 25 minutes. Maintainsubfreezing condenser temperatures for at least 12 minutes. Ifheat pipe fails, repeat Steps 1 through 6.
7. Increase inactive condenser temperatures to -40°C ±5°C over aperiod of approximately 20 minutes and simultaneously startreducing gas reservoir,temperature to -95°C over a period of180 to 200 ininutes. At no time should the reservoir coolingrate exceed -2°C/min. If heat pipe fails, repeat Steps 1through 7.
8. Repeat Steps 6 through 8.
-51-
r
load onvthe heat pipe for the tests are 1.25 centimeters and 130 watts,
respErtively.
The tilt on the pipe is meant to minimize the contribution of excess
fluid inventory to the pumping capacity of the pipe and to compensate to a
certain extent for that component of the buoyancy force vector tending to
keep the bubbles ..against the upper walls of the arteries.
Although heat loads over 90 watts are known to be in excess of the
heat pipe one-artery capacity, the higher heat load of 130 watts is chosen
in order to enhance the migration of bubbles toward the evaporatc: ' r by vir-
tue of higher fluid flow rates inside the arteries.
Steps 6 through 8 of an idealized freezing/thawing test cycle are
shown graphically in Figure 3-3 where segments (B-C), (B-D), and (B-E)
represent different condenser warmup rates. These steps are described in
conjunction with the figure in what follows.
A — C E INACTIVE CONDENSER F
-70.^
UJ ° J
-
CL -^ r - MINIMUM 12 MINUTES
FREEZING POINT OF METHANOL
w BELOW FREEZING !POINTr
-130. <EVAPORATOR POWER 130 WATTS CONSTANT> END OF CYCLE
- SINK PLATEN --—
_
-160.30. 60. 120. 180. 240.
TIME ('Min )
Figure 3-3. idealized Freezing/Thawing Cycle "A"
-52-
By turning off the heaters on the condenser plate, the inactive
condenser section is allowed to cool from -40°C (Point A) to below the
freezing point of methanol (B) at a rate of approximately -40C/min.
Simultaneously, heat is applied to the gas reservoir to raise its tempera-
ture from about -95°C to -40°C in approximately 25 minutes. During this
period of the test cycle, the advancement of the gas front toward the
evaporator resulting from reduced condenser temperatures is furtiler enhanced
by the increasing temperature of the gas reservoir, the net effect of the
above being to inactivate temporarily a portion of the condenser to allow
the liquid in the arteries to freeze. Subfreezing temperatures in the
inactive condenser are maintained for ten minutes to ensure complete freez-
ing inside the arteries.
Failure of the heat pipe during condenser freezing could be attributed
to be the result of either suct*on freezeout or the bubbles mechanism. If
this event is repeatable in every cycle, then artery depriming will be,
with a .high degree of certainty, due to suction freezeout. On the other
hand, sporadic failure of the heat pipe during condenser freezing will be
consistent with the recognized statistical nature of the bubbles mechanism.
If no evidence of heat pipe burnout is observed through the end of the
freezing process, the test cycle continues with Step 7, otherwise, Steps 1
through 6 are repeated.
During Step 7, (e.g., B-C) power is applied to 'heaters on the conden-
ser plate to thaw the inactive condenser and raise its temperature in
approximately 25 minutes to -40°C where it is held within ±5°C for the
remainder of the 240-minute test cycle. About the time the inactive con-
denser starts to thaw (B+),, cooling of the gas reservoir is initiated and
allowed to continue through the end of the cycle (F) at an average rate of
0.3°C/min. Reservoir cooling rates are not permitted to exceed 2 0 C/min to
preclude the sudden cooling mechanism from taking place.
During this period of the test cycle, (e.g., B-C) .rising condenser
temperatures will cause the gas/vapor front to advance toward the reservoir
end of the condenser, thawing the previously inactive section of the pipe
and presumably engulfing into the active section bubbles that were gener-
ated during the freeze/thaw ,process. The simultaneous and continuous
reduction of the gas reservoir temperature will have t ,- ;o significant effects
-53-
on the bubbles mechanism. First, it will cause a continuous movement of
tie gas front toward the reservoir during which additional bubbles will be
induced into the active portion of the heat pipe where their migration
toward the evaporator is enhanced. Second, reservor cooling will tend to
diminish the pressurization of the heat pipe resulting from increasing
condenser temperatures and will cause subsequently, after the condenser
reaches a steady state, (e.g., C) a continuous decrease of the total pres-
sure in the heat pipe.
Exploratory analyses using the spherical bubble model indicate that
pressure reduction in the heat pipe environment can significantly increase
bubbles lifetimes. Longer bubble lifetimes are certainly a factor enhanc-
ing the potential of the bubble mechanism to deprime the arteries.
A heat pipe failure observed about the time the inactive condenser
undergoes thawing (B+) could be attributed to either the postulated freez-
ing blowby or the bubbles mechanism. The fact that artery depriming due
to freezing blowby is not statistical in nature requires in order to con-
sider the freezing blowby mechanism the culprit, that failures during the
thawing process (B+) occur at every cycle. Sporadic heat pipe failures
during the thawing process or at any other time during the test cycles will
be considered to be the result of bubble migration and growth in the
arteries. If no evidence of heat pipe burnout is observed by the end of
the 240-minute test cycle, (F) Steps 6 and 7 are repeated for the remainder
of the 120-'hour continuous test period.
3.3 TEST RESULTS
The cyclic tests on the SNO09 heat pipe were performed from April 14
to April 19, 1980. A total of twenty seven partial and complete cycles
were achieved during which seventeen burnouts or heat pipe failures were
observed. A summary of the test results is presented in Figure 3-4. It
shows the temperatures at nine different locations along the heat pipe at
the end of the cooling period (Condition-W ) and those observed near the
time of burnout or at the end of a cycle (Condition W).
The tests commenced at 0600 hours when the heat pipe was tilted
1.25 cm and 130 watts were applied to the evaporator block. After raving
established that both arteries were primed, cooling of the condenser was
-54-
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initiated by turning the radiator heaters off. This process continued
until subfreezing temperatures in the inactive condenser section, as indi-
cated by temperature sensors 10, 11 and 12, were realized. These sensors
showed minimum temperatures of -120C, -132; and -114C respectively prior
to the initiation of the condenser warm-up period. Approximately eleven
minutes after the radiator heaters were turned on, the heat pipe failed.
About the time of the failure, the condenser warm-up rate (CWR) was about
9F/min and the minimum temperature in the condenser section, shown by sen-
sor 11, was -790, which is 19C above the freezing point of methanol, thus
well past point B+ in Figure 3-3.
Subsequent to burnout, the heat pipe was leveled and allowed to reach
close to isothermal conditions over a period of two hours. The pipe was
then tilted 1.25 cm and 130 watts were applied to the evaporator, but the
heat pipe failed to sustain the load. The above priming procedure was
repeated with similar results.
The inability of the heat pipe to hold the load after two priming
attempts was postulated to be the result of the presence of residual
bubbles in the arteries. It was decided then to modify the procedure to
prime the pipe, by requiring that the evaporator end be raised 61 cm for
one minute before leveling the pipe. The high tilt would presumably eject
all the liquid and residual bubbles from the arteries. After the pipe was
leveled for thirty minutes, 130 watts were applied to the evaporator raised
1.25 cm. This time priming of the arteries was verified and the second
cycle was started. The latter procedure for priming the heat pipe was
followed through the rest of the test period with successful results.
Cycle number 2 was the first complete normal cycle and was followed
by three burnouts observed during the condenser warm-up periods of cycles 3,
4 and 5, at which times the CWR was, approximately 5C/min (9F/min).
The partial history of selected temperatures along the heat pipe dur-
ing normal cycle 2 is shown in Figure 3-5. It can be seen that prior to
condenser warmup the ice front almost reaches the locations of sensor 9,
i.e., approximately 18 inches of the condenser end were frozen. During
the warmup period of the cycle the figure shows the gas front moved close
to sensor 10 which indicates that a portion of the previously frozen con-
denser became part of the active condenser section.
-56-
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-57-
The large proportion of failures, four out of five, was attributed to
rapid thawing and warming of the inactive condenser, events which were
originally postulated to result in the formation of bubbles inside the
arteries and in their rapid induction into the active portion of the con-
denser before the bubbles could vent by diffusion. Once in the active
portion of the pipe, these bubbles would grow and deprime the artery.
A typical temperature history of the four cycles during which deprim-
ing was observed is that of cycle 4 shown in Figure 3-6. As shown, the
ice front was located somewhere between sensors 9 and 10 at the end of the
cooling period of the test cycle. During the warmup period depriming is
observed apparently at the time the gas front reached the previous location
of the ice front. The fact that depriming occurred approximately 9 minutes
after the inactive condenser completely thawed, the possible involvement of
freezing blowby in these heat pipe failures can be discounted, therefore
it can be argued that depriming can only be the result of bubbles.
In order to determine the effect of condenser warm-up rates on the
frequency of heat pipe failures, the CWR during the next six cycles was
reduced an average of fifty percent. The results were that the heat pipe
performed normally during two consecutive complete cycles, cycles 6 and 7,
at the reduced CWR of about 2.2C/min. The following four cycle,, however,
resulted in burnouts during condenser warmup at rates varying from 2.2C/min
to 3.6C/min. The variation in these CWRs was not intentional but rather
the result of the limited heater control capability of the test assembly.
The typical partial temperature history of normal cycles 6 and 7 is
that of cycle 6 shown in Figure 3-7. The temperature history of cycle 11
shown in Figure 3-8 is similar to that of cycles 8 and 10. As in most
previous cycles, the ice front can be seen located between sensor 9 and 10
at the end of the cooling period. Figure 3-8 shows however, that depriming
occurred under significantly different condenser conditions in most cycles
at the lower co y °denser warmup rate: 1) the inactive condenser was still
partially frozen (last 12 inches) and 2) temperatures of sensors 8 and 9
indicate the gas/vapor front never reached the previously frozen region.
Because the condenser was not completing the thawing process at the
time of burnout, freezing blowby can be discounted as the cause of pipe
-58-
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failure which, then can be attributed only to be the result of bubbles.
However, the fact that portions of the previously frozen condenser section
were never incorporated into the active heat pipe section, a condition that
was postulated to be necessary to induce bubbles into the evaporator,
seems to indicate that other mechanisms such as Marangoni Flow were involved
to move bubbles into the active portion of the condenser where further
growth or movement would be expected.
It was postulated that depriming due to bubbles released in the inac-
tive section occurred as follows. During the cooling period the freezing
front moves toward the evaporator expelling bubbles which are then locked
inside the ice and building stress on the arteries due to suction freeze-
out. This process continues until the end of the cooling period when the
imposed stress on the arteries due to freezeout reaches a maximum level.
This increase in stress is accompanied by a reduction of the hydrodynamic
stress which results from shrinkage of the effective length due to advance-
ment of the gas/vapor front toward the evaporator.
This imposed stress on the arteries due to suction freezeout is either
overcompensated by the reduced hydrodynamic stress or the unused pumping
capacity of the artery, for no heat pipe failures were observed during the
cooling periods of the test cycles. During the warmup period, the advance-
ment of the gas/vapor front toward the reservoir end results in increased
hydrodynamic stress as the effective length expands, and in the propaga-,
tion of a conduction heat wave which causes the ice front to recede and
release liquid and bubbles upon thawing. Although the release of the
liquid reduces the stress that came from suction freezeout, there remains
sufficient back stress on the arteries in the gas-blocked region to induce
growth of the released bubbles. These bubbles agglomerate and then reach
the active section due to continuing growth and/or Marangoni Flow.
Whereas depriming during cycles 8, 10, and 11 occurred 10 to 12 min-
utes into the warmup period before the gas/vapor front reached previously
frozen sections, depriming in cycle 9, as shown in Figure 3-9, occurred
approximately 45 minutes into the warmup period, 25 minutes after the con-
denser completely thawed. An interpretation of the data seems to indicate
that bubbles first released about the previous location of the ice front
somewhere between sensors 9 and 10 were subsequently incorporated into the
1'
-62-
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active portion and caused depriming when the gas/vapor front reached that
location 45 minutes later.
During test cycles 12 through 18, the heat pipe inactive condenser
was warmed up at even lower rates ranging from 0.4C/min to 1.7C/min.
Burnouts were observed in all these cycles, except in cycle 18 which had
the lowest CWR of 0.4C/min.
The temperature history of cycle 13 is shown in Figure 3-10. It can
be seen that depriming occurred before the gas/vapor reached previously
frozen sections and while the last 12 inches of the condenser were below
the freezing point. -Similar observations can be made of deprimings
observed during cycles 12, 14, 16 and 17.
Depriming ,during cycle 15, as shown in Figure 3-11, occurred under
different conditions. It can be seen that when the gas/front apparently
reached previously frozen areas a burnout was triggered. At this time the
condenser had been completely thawed for approximately 40 minutes.
Normal freezing cycle 18, was followed by three cycles during which
the inactive condenser was rapidly cooled to temperatures just above the
freezing point and then warmed at rates as high as 6.7C/min. The idealized
nonfreezing cycle is described graphically in Figure 3-12. These nonfreez-
ing test cycles were performed to support +he hypothesis that the frequency
of failures due to bubbles could be greatly diminished if freezing and
thawing did not occur in every cycle. The fact that the heat pipe evidenced
normal operation during these cycles tends to support the above. The typi-
cal temperature history of a nonfreezing test cycle is that for cycle 19
shown in Figure 3-13.
During test cycles 22 through 24, the inactive condenser was rapidly
cooled below the freezing point with the heat pipe operating under 130 watts.
Subfreezing condenser temperatures were maintained for at least ten minutes
subsequent to which the evaporator heaters were turned off and the inactive
condenser was rapidly warmed. When the inactive condenser temperatures
reached about -40C the evaporator heaters were turned on again. The
idealized cycle is described graphically in figure 3-14. A burnout was
observed during the second cycle, cycle 23, 15 minutes after the heat load
-64-
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-68-
-40. ^'"^INACTIVE CONDENSER
a
^ -70.
a -100. —.— — .—.—°--.—.--.—.FREEZING FOINT1HAITlSI '—•---• —
^+-- -MINIMUM 12 MINUTES
I BELOW FREEZING POINT
130 WATT EVAP.
-130. EVAP. POWER 130 WATT EVAPORATOR POWER
.POWER - OFF ' - - - ^ — E^ CYCLE
SINK PLATEN
-160.0. 30. 60. 120. 180. 240.
TIME ( Min )
Figure 3-14. Idialized Freezing/Thawing Cycle "C"
was reestablished. This can be seen in Figure 3-15 which shows that
depriming occurred apparently when the gas/vapor front reached the pre-
viously frozen condenser section.
In the last three cycles of the test program, the heat pipe, under a
continuous load of 130 watts, was sub,;ected to condenser warmup rates
ranging from 0.2C/min to O.4C/min. Cycle 25 with the higher CWR of O.4C/
min was normal. Burnouts were observed in the next two cycles. The last
heat pipe failure during cycle 27, however, is worth noting since it
occurred 165 minutes into the warmup period when the CWR was increased
from O.2C/min to 5C/min. The temperature history of this cycle is shown
in Figure 3-16. Although the cooling period of the cycle is not shown in
this figure, Figure 3-2 indicates the ice front prior to warmup was located
somewhere between sensor 9 and 10. Figure 3-16 shows the gas/vapor front
at the end of the slow warmup period was located between sensors 8 and 9.
As the warmup rate was increased, it can be seen that the gas front
rapidly moved between sensors 9 and 10 seemingly reaching the previously
frozen section and triggering a burnout.
-69-
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Following this final burnout, the heat pipe was leveled and left
undisturbed over the weekend. Fifty-five hours later, when 130 watts were
applied to the evaporator, the heat pipe failed to hold the load, an event
seemingly pointing to the survival of bubbles from the last freeze/thaw
cycle as the probable cause of artery depriming. The temperature histories
of cycles not shown in this section can be found in Appendix B.2.
3.4 SIGNIFICANCE OF TESTS RESULTS
The results of the cyclic tests on the SNO09 heat pipe clearly estab-
lished that thawing the frozen condenser of an arterial heat pipe under
high load is an operating mode that results in arterial failure with sig-
nificant frequency. Out of twenty one freezing and thawing cycles under
high load, sixteen cycles resulted in heat pipe failures. Although thaw-
ing the condenser under high load enhances the probability of artery
depriming, it is not a necessary condition. This proposition is supported
by the fact that out of three cycles in which the condenser was thawed
under no heat load one cycle (number 23) resulted in artery failure sub-
sequent to thawing when the heat load was reestablished on the pipe.
In twenty four freezing and thawing cycles no heat pipe failures
occurred during condenser freezing. The lack of failures during freezing
when the suction freezeout mechanism has its greatest potential to deprime
the arteries seems to indicate that none of the observed failures during
the test cycles can be solely attributed to this mechanism. Even though
bubbles are known to be released during freezing they are immobilized
inside the ice structure rendering a failure during freezing due to bubbles
an unlikely event.
All the observed anomalies occurred during or following condenser
warmup periods. The fact that the inactive condenser was either completely
thawed or still frozen along a considerable length when deprimings occurred,
it can be argued that the freezing blowby mechanism could not account for
any of the heat pipe failures observed during the cyclic tests.
Since neither suction freezeout nor freezing blowby were the sole
cause of any of the observed heat pipe failures, it can be concluded only
that all the anomalies during the cyclic tests on the SNO09 heat pipe were
the result of the freezing/thawing bubble mechanism.
G
-72-
The freezing and thawing process is required for bubbles to form
. inside the arteries. Periodic freezing and thawing replenishes the bub-
ble population which enhances the probability of artery depriming due to
bubbles. The results of three normal successive cycles without freezing
supports the above.
The presence of bubbles in the arteries is necessary for depriming
to occur. However, depriming does not necessarily occur when bubbles are
present. This statement is supported by the fact that out of 24 freeze/
thaw test cycles seven were normal (i.e., no failure occurred). These
test results indicate that the occurrence of the observed heat pipe fail-
ures is random, which is consistent with the demonstrated statistical
nature of the bubble mechanism.
During the freeze/thaw process bubbles are generated in the gas-
blocked condenser section. It was postulated at the outset of the cyclic
tests that the active condenser length had to expand into the previously
frozen section. However, in roughly half the failures the active conden-
ser length had not yet reached the previously frozen section.
The results of the tests seem to indicate that there exists some cor-
relation between the condenser warm-up rate and the incidence of heat pipe
failures. The reduction of the condenser warm-up rate used in the first
five cycles by approximately 50 percent was followed by the only two con-
secutive normal cycles observed during the tests. In addition, during
cycle 27 depriming occurred almost two hours into the warm-up period fol-
lowing a rapid and large increase in the condenser warm-up rate.
Deprimings observed during cycles with high warm up rates occurred
after the condenser had completely thawed and soon after the active con-
denser length reached the previously frozen section. On the other hand,
most heat pipe failures during cycles with low warm up rates occurred
while portions of the condenser were still frozen and before the active
condenser length ever reached the previously frozen section. The latter
failures are attributed to movement of bubbles into the active condenser
helped by suction f reezeout and/or Marangoni flow.
k
The results of several unsuccessful attempts to reprime the heat pipe
after the first freeze/thaw cycle indicate that a depriming does not clear
3
73
out all the bubbles. Consequently bubbles form during a single freeze/
thaw process can result in repeated successive failures due to residual
bubbles.
Numerous deprimings observed during the tests occurred 10 to 30 min-
utes after freezing conditions in the condenser ceased to exist. Follow-
ing the last freezing and thawing test cycle, the SNO09 heat pipe deprimed
52 hours later when the normal heat load was reestablished. This heat pipe
failure can only be attributed to be the result of bubbles generated during
the last freeze/thaw cycle of the test program.
These results indicate that ice-generated bubbles can last a long
time, and therefore freezing at the very time of the CTS anomalies was not
necessary. Thus the anomaly on day 253 can be attributed to ice-generated
bubbles from day 252 or earlier.
a
74F
tPkr
v
i
4.0 CONCEPTS TO AVERT ARTERY DEPRIMING
4.1 NONCONDENSIBLE CONTROL GAS SELECT?ON
Unquestionably the simplest and most effective concept to avert arte-
rial depriming is the selection of a control gas that would preclude the
formation of bubbles when the liquid methanol undergoes freezing and thaw-
ing. This concept is unfortunately unrealizable, for the freeze/thaw pro-
cess, being a degasifying process, will result always in the formation of
bubbles regardless of the noncondensible control gas selected.
Nucleation experiments performed during Phase I, showed that a large
number of minute bubbles are initially released during freezing and thaw-
ing. Most of them rapidly disappear owing to their size, but others coalesce
forming fewer but larger bubbles whose lifetimes strongly depend on their
sizes. Larger bubbles have longer lifetimes which enhance the probability
of further coalescence which results in bubbles of even longer lifetimes
which can then survive until the gas/vapor front moves into previously
frozen sections or until suction freezeout and/or Marangoni flow succeed
in making them grow and transporting them into the active section of the
heat pipe.
The above observations indicate that reducing bubble lifetimes by
proper selection of a control gas can decrease to a certain extent the
probability of bubble coalescence and of their induction into the active
section of the heat pipe. The results of the bubble lifetime analysis in
Section 2.0, show, for example, that a spherical CTS control gas bubble
(90% N2/10% He) of 0.8 mm in diameter (i.e., half the CTS artery diameter)
under some assumed conditions has a lifetime of about 19 hours compared to
a lifetime of less than one hour for a methane bubble of the same size.
The rapid dissolution of methane bubbles suggests the selection of methane
for the control gas.
Although the selection of a new control gas, such as methane, will
result in bubble lifetimes significantly shorter than in the CTS heat
pipes which will diminish to a certain extent the probability of deprim-
ing, this concept cannot guarantee that depriming will be averted. However,
the use of methane in conjunction with other steps to avoid depriming
should enhance the effectiveness of those steps.
75
4.2 OPERATIONAL PROCEDURE FOR START-UP OF A FROZEN CONDENSER
Since the bubbles leading to arterial depriming are formed by a
freeze/thaw process, the avoidance of freezing will avert artery deprim-
ing. Selection of sun angle and radiator radiation properties or the use
of heaters could prevent freezing in many missions. However, in missions
to outer planets, avoidance of freezing may be costly or even impossible.
Even when the condenser has been frozen, it is possible to thaw the heat
pipe and restore it to a primed and serviceable state, provided proper
procedure is followed.
The key to successful restoration of a previously frozen heat pipe is
dissolution or venting of the freeze/thaw generated bubbles. Venting is
discussed in Section 4.3„ Dissolution requires leaving the condenser in a
quiescent state somewhat above the freezing point for a time long enough
to allow the bubbles to collapse. This time depends upon the control gas,
the size of the largest bubble, and the pressure and temperature in the
gas-blocked condenser. The advantage of methane as a control gas has been
discussed. It has a high solubility-diffusivity product leading to more
rapid bubble dissolution.. Since the bubble agglomeration mechanism appears
to be statistical, and it is not clear that a laboratory test at 1-g is a
good indicator of agglomeration at zero-g, it is presently difficult to
predict with certainty the size of the largest bubble and thus the time
required for it to collapse. However, start-up can be attempted earlier.
than necessary merely to test whether a sufficiently long time has been
allowed to elapse. If depriming occurs, the heat pipe is returned to a
quiescent state for more time to pass. In the attempt at operation, at
least one bubble was vented. Thus successive attempts at start up contrib-
ute to the bubble clearing process.
High pressure during the bubble collapse period hastens it. With an
actively controlled heat pipe, the gas reservoir and evaporator could both
be heated somewhat to raise the gas-blocked condenser pressure. It should
be noted that the restart procedure would have to be used each time a seg-
ment of the gas-blocked condenser freezes and is thawed.
76
t4.3 MECHANICAL MODIFICATIONS
In a gas-controlled arterial heat pipe it has been found that a prim-
ing foil at the end of the evaporator is necessary for successful priming
[5]. Without it, gas in the pipe can be trapped inside the artery during
priming. With the priming foil and with a gentle heating of the evaporator
bubbles trapped in the evaporator are transported to the foil and vented.
The priming foil shown in Figure 4-1 consists of a very thin metallic
membrane with one or more holes no larger than the effective pumping pore
diameter needed for the capillary flow in the active pipe. The size of
the vent hole and the thickness of the foil must be such that the meniscus
of a bubble of arterial size contacts the meniscus attached to the outer
corners of the vent hole. Meniscus coalescence then ruptures the liquid
:^ ^ ^ •ter '^•.-^ ^^ f^w^r .^i
.y.A*,y^.rAvA^^
VV
i -0./ v ^! ;7 , t v ^^ ♦: !^ tea/ i
Fiugre 4-1. Segment of an Artery with aPriming or Venting Foil
77
1s
^f
film bridging the vent hole and allows the gas to be vented. It should be
noted that the heat load during venting must be less than the open-artery
capacity of the heat pipe.
The same principle can be applied to the condenser region or even to
the entire pipe [5] as long as the local stress does not exceed the capil-
lary pumping capability of the artery at that point and time. Thus a loca-
tion in the condenser (or perhaps even in the adiabatic section) can be
identified where under restart heat load the local stress is below this
limit. At that location a screen across the artery can be placed to fil-
ter out and collect small bubbles tending to move toward the evaporator.
On the condenser side of the screen a priming foil would be placed (venting
holes located one artery radius from the screen) to allow venting of the
collected gas should the gas volume reach arterial size.
The bubble-filter/venting-foil concept should allow a normal start up
from a frozen condenser state and permit continuous normal operation of
the heat pipe even though the gas-blocked condenser is undergoing
periodic freezing and thawing.
78
5.0 CONCLUSIONS
Evidence strongly suggests that bubbles generated through freezing
and thawing of methanol in the gas-blocked condenser arteries were respon-
sible for the CTS thermal anomalies. Out of the 24 freeze/thaw cyclic
tests with the SNO09 heat pipe, 17 deprimings were observed. While some
of the tests were conducted under conditions wi •iere probability of deprim-
ing was high, others were conducted where the pr^,bability was low, thus
emphasizing a statistical variation in the freeze-thaw bubble mechanism.
Most often depriming occurred while the gas-blocked condenser was
still frozen along a portion of its length but some occurred 10 to 30 min-
utes after thawing was completed. In one test depriming occurred 52 hours
after thawing.
Analytical-numerical studies of bubble collapse show bubble lifetimes
to be strongly dependent upon bubble size and control gas composition.
The helium in the CTS control gas mixture causes long bubble lifetimes
when the bubbles are of arterial size. Selection of methane as a control
gas would significantly shorten bubble lifetime for equal sized bubbles.
At the present level of understanding, selection of methane for control
gas cannot ensure avoidance of bubble depriming. Prevention of freezing in
the gas-blocked condenser by active or passive control should avert deprim-
ing. Should avoidance of freezing be inconvenient or not feasible, either
installation of a bubble-filter/priming foil element at the condenser-
adiabatic section interface or adoption of an appropriate thawing and bubble
clearing procedure would probably allow successful heat pipe operation.
79
........ . . .
6.0 REFERENCES
1. R.E. Alexovich and A.N. Curren, "Thermal Arwmalies of the TransmitterExperiment Package on the Communication Technology Satellite." NASATechnical Paper 1410, April, 1979.
2. B.D. Marcus, "CTS TEP Thermal Anomalies'—Heat Pipe System Perfor-mance," NASA Contract NAS3-21012, November 30, 1977.
3. E.W. Saaski, "Heat Pipe Temperature Control Utilizing a Soluble GasAbsorpton Reservoir," NASA Report CR 137,792, February 1976.
4. E.W. Saaski, "Investigation of Bubbles in Arterial Heat Pipes," NASAReport CR 114,531,, December 1972.
5. J.E. Eninger, "Menisci Coalescence as a Mechanism for Venting Gas fromHeat-Pipe Arteries," AIAA Paper No. 74-748, July 1974.
80
t
t
APPENDIX A.1
EXCESS SKEW IN LOAD PARTITIONING
The three heat pipes of the CTS VCHP system are designed to turn on
sequentially so as to balance the load between them at full-on design con-
ditions. However, a build up of tolerances on gas inventory during manu-
facture, and very low sink temperature during equinox conditions may result
in the load on heat pipe No. 1 exceeding its capacity before Nos. 2 and 3
take up a significant share. Failure of No. 1 by the above mechanism or
by any other could then result in a rapid transfer of load to No. 2, etc.,
perhaps yielding a "domino effect" failure of the whole system.
The first step in investigating this was to further review the flight
data to search for regularity in the depriming sequence associated with the
anomalies. Toward this end, NASA LeRC personnel provided computer plots of
pertinent flight data for subsequent review.
Experimentally, at ampts were made to deprime the SN009 heat pipe
with rapid load increases, simulating rapid sequential load transfer as
pipes deprime.
The tasks performed in this investigation are summarized below.
Flight Data Analysis to Determine Depriming Sequence
Computer plots and tabulations of CTS telemetered data were provided
for days 75, 82, 89, 101 and 253 of 1977. Day 39 was a so-called "normal"
day whereas the others were the four anomaly days.
Flight data had already been examined in a previous study effort.
However, the new data included overlay plots of all pertinent data on
single pages, and value; of AT 3-2and AT 2-1in
additiein to AT 3-1provided
earlier. It was hoped that this data format might shed additional light
on the system behavior, particularly the sequence in which the heat pipes
deprimed on the anomaly days.
Unfortunately, the telemetry increment in the temperatures was 1.8C
to 1.9C, which is of the same magnitude as the normal values of AT
between pipes as well as the changes in temperature which accompany
depriming. Consequently, it is very difficult to distinguish between
A-1
A-2
actual physical phenomena and.telemetry noise. In view of this limitation,
the data tentatively suggests the following:
Day 75: It appears that heat pipe No. 1 deprimed first, yielding
increased values for AT 2-1and AT3-1 . Several hours later
heat pipe No. 2 deprimed, followed almost immediately by
heat pipe No. 3 and the sudden rise in body temperature.
Day 82: The data is particularly unclear this day, but as with day
75, it appears that heat pipe No. 1 failed first, followed
by Nos. 2 and 3.
Day 89: No anomaly occurred on this day. However, the data sug-
gests that heat pipe No. 2 was deprimed, causing No. 3 to
carry a greater load.
Day 101: The data indicates the failure sequence was 1:2:3, as with
day '75.
Day 253: In this case, heat pipe No. 3 did not even "turn-on" until
the anomaly began, and apparently could not prevent it.
Thus, it had to be deprimed from the start. In fact, the
data suggests that heat pipes 2 and 3 deprimed first, with
the anomalous increase in body temperature corresponding to
the depriming of No. 1.
Specific interpretation of the depriming sequences is covered in the
SNO09 heat pipe test discussion that follows. However, one item of note
bears discussion. If bubble nucleation within the arteries is a cause of
the anomalies, then the statistical nature of the mechanism should yield
one heat pipe failed occurrences far more often than two or three heat
pipe failed occurrences. Day 89, in which No. 2 appears deprimed, while
Nos. 1 and 3 are primed, may be such a day.
Rapid Increases in Load Tests on SNO09 Heat Pipe
Extensive testing was performed wits the SNO09 heat pipe. The first
series of tests were to determine whether there exists significant iner-
tial effects on heat pipe capacity which could contribute to a "domino
effect" failure of all three CTS pipes. That is, if heat pipe No. 1
deprimed, most of the load it had carried would be suddenly transferred
to No. 2, etc. If the capacity of a heat pipe were substantially lower
for the sudden application of load than for gradual application (due to
fluid inertia), the probability of a sequential failure of all three pipes
would be enhanced.
In order to maximize the rate of load transfer into the heat pipe
evaporator, attached heater blocks normally used to simulate the thermal
mass of a heat source were removed and tape heaters were placed on the
heat pipe saddle over a 30-cm long section of the pipe which was then
properly insulated. Testing was done for both high (-'18C) and low (-95C)
sink temperatures with the heat pipe evaporator elevated 2.5 cm. Heat
loads ranging from 100 Ii,o 150 watts were rapidly applied resulting in no
heat pipe failures. The results indicated essentially no rate effect
attributable to fluid inertia. This argued against the postulated
"domino effect" failure of the whole VCHP system.
A-3
rt •ry ^ nR^
APPENDIX A.2.1
INSTANTANEOUS HEAT FLOW AFTER HEAT PIPE RESERVOIR ECLIPSE
p~ alaiONE i►ACE PY#K- MOONDO @E CM • CALWORNIA W278
INTEROFFICE CORRESPONDENCE
TO: E. E. Luedke cc. Distribution
:u..jacT: Instantaneous Heat Flow After HeatRipe Reservoir Eclipse
8715.10-78-6
DATE. 18 October 1978
FROM: D. K. Edwards*LDG 01 MAIL STA. 1230 ExT. 52850
INTRODUCTION
When a gas-controlled heat pipe's reservoir experiences an eclipse,
the gas partial density within the reservoir rises, and the gas front re-
treats until the evaporator temperature drops sufficiently to establish a
new equilibrium. During the transient, the evaporation from the warm end
may exceed the capacity of the axial wicking, and arterial depriming may
occur. It is desired to estimate the instantaneous heat flow during such
a transient for comparison to the burnout heat flow capacity.
RESERVOIR COOLING RATE
The reservoir temperature versus time may be known from measurement.
It is set by a heat balance between the surrounds and the thermal capacity.
Let the mass of the reservoir be M and its specific heat c. Conductive
coupling to the radiator is KA/L, and insulation is modelled with massless
radiation shielding.
-m c dT A R r [QT4 - a q ] - M[T -T c ] (1)
dt e L
Before eclipse q is high, and the quasi-equilibrium temperature is given
by setting the left-hand side to zero. After q - is reduce T, eoois at the
rate given by Eq. (1).
A-5
FLOW VELOCITY INTO RESERVOIR
When a wicked reservoir of volume V cools at a rate of -dT/dt, the
vapor partial pressure inside the reservoir falls. Since the total
pressure is fixed at the evaporator end (neglecting vapor flow pressure drop),
the partial pressure of the gas rises. Furthermore, the gas temperature falls
(assuming thermal equilibrium). These two effects increase the gas partial
density. The rate at which the partial density times the volume rises must
come from the flow of gas from the heat pipe radiator into the reservoir.
A (pg V) = pgc v Ac(2)dt
pg = P-Pv(T) (3)
R^
Differentiating Eq.(3) gives
dp P-Pv 1dT + 1 dPv+ 1 V
R9 fi\ cTt( -dl*^ t jR g T dt
Substituting into Eq.(2) then gives
V = V l P-Pv + dPv - dT + dP (4)p gcAc ( R9 dT fit, dt
Let dPv/dT be approximated from theiLlausius - Elapeyron equation
P = P e-(eh/RT0) (To/T-1)
v o
GhdPv = Pv - 1dT
A-5
S4
Then Eq.(4) becomes
v - V TOT l P + Pv (eh 1) dT + Q(5)Ac (P-P
vc I ^'T
7_ Rf J C cTt I TT
The total pressure P is the vapor pressure at the evaporator temperature Tv.
dP = dPv ( dTv) = - dPv (-dTv)HdTv dt dTv dt.
The evaporator temperature in turn is set by a heat balance upon it. The
worst case occurs when the evaporator is well-coupled thermally to a large
thermal mass. In this worst case dP/dt may fall only very slowly compared
to the other terms. Measured data may be used to evaluate dTv/dt. A crude
model is a one-capacity model.
MevOev dTv = Qelec. -Qelec. -Qhp -A; (QTv4 -aTs4 ) (7)dt
The last term in the equation models heat leak to surrounds at temperature
Ts
HEAT FLOW
The instantaneous heat flow through the pipe Qhp
is fixed by the
length of active condenser and the rate of advancement of the gas front.
Qhp = Qstatic + Qdynamic (8)
The static load is that caused by condensation on the gas-free condenser
wall
4Qstatic = cP Lc n (aT v - e gc ) (9)
c
t A-7
(6)
where the length Lc is fixed by a gas inventory mg
mg - P V + pgcAc (L -L c )
(10)
The dynamic load is proportional to the velocity v at which the front
advances
Rdynamic - pfcf fv n (Tv -Tc ) (11)
where pf is the condenser fin density, c f its specific heat, Af its area
(volume per unit length), and n is not the radiating fin effectiveness, be-
cause of the fourth power dependence of the black body radiosity. The
appropriate value of n is between the radiating fin effectiveness and the
fourth root of that value, depending upon the ratio of (Tc/Tvj4.
EXAMPLE
For example consider the CTS heat pipe 1 on Day 75. The following
data are available
Time Vapor Temp. Gas-Blocked Temp. Gas Reservoir Temp.
t TvT T
min °C °C °C
460 27.5 -93 -68
470 28 -94 -71
480 29 -95.5 -74
A-8
From these data one can estimate -dT/dt - 18 K/hr and dTv/dt = 4.5K/hr.
The following vapor pressure data pertain
Temperature Pressure Latent Heat
K N/m2 J/kg
Tv 300 19500 1.15 x 106
T 205 ul3 1.2 x 106
TC
- 180 -.1 .5 1.2 x 106
For a 90% N2 10% He mixture the mean molecular weight is 25.6 and Rg =
8314.3/25.6 - 325 J/kg K. The density of the gas in the gas-blocked condenser
is
pgc = 19500 = 0.333 kg/m3
RT(325)(1-580Y)
Other parameters needed are
ah r 1.2 x 106 = 22.51RT I T = 205 206 (205)
ah 1.15 x 106TT_ O T - 300 = (260) (300) = 14.74
The pertinent parameters of the pipe itself are understood to be as
follows:
Reservoir Volume V 8.70 inch 1.426 x 10-4 m3
Pipe Vapor Area A c 0.1245 in 8.03 x 10-5 m2
A-9
Equation (5) then gives
v - 1.426 x 10-4
8.03 x 10-
Q801205) 19500
19500 - 1.5 L 205+ 13 (22.5 - 1)] (18)
DT
+ 19500 (14.74) (4.5)300
v = (1.78) (4.50 x 10-5 ) [95.1 + 1.361 (18) + (958) (4.5)
V = 8 x 10-51736 + 4311 - 0.484 m/hr = 1.59 feet/hr
Note that, in this example, the fall of the vapor pressure in the reservoir
was a negligible consideration but the rise of vapor pressure in the
evaporator was quite significant.
For purposes of an estimate nA F is taken to be 0.04 inches; by 12 inches.
Thus Equation (11) gives
Qdynamic S (174) (0.21) (.04/12) (12/12) (1.59) (300 -130) (1.8)
Qdynamic = 41.8 BTU = 12.25 Watts
hr
DISCUSSION
While a rapid decrease in reservoir temperature has the potential of
adding a significant dynamic heat flow to the static load, the example worked
here indicates that the decrease must be rapid, much greater than the 18K/hr
value used in the example.
A-10
APPENDIX A.2.2
INSTANTANEOUS HEAT FLOW AFTER HEAT PIPE RADIATOR ECLIPSE
T i0tsSYSYCANS :"Up
Oki SPACt PAM- M[DONOO IACN - CMLWOMMA =79
INTEROFFICE CORRESPONDENCE 8715.10.2-78-9
To E. E. Luedke CC: D. Antoniuk DATE 28 November 1978J. E. EningerB. D. MarcusD. J. Wanous
SUDJ«T: Instantaneous Heat Flow After FROM: D. K. EdwardsHeat Pipe Radiator Eclipse .LDS MAIL STA. sxT.
01 1230 52850
IntrcL&&tien
When a gas-controlled heat pipe's radiator experiences an eclipse,
the heat flow in the pipe increases until the evaporator cools to a new
equilibrium operating condition. During the transient, the evaporation
from the warm end may exceed the capacity of the axial wicking, and
arterial depriming may occur. It is desired to estimate the instantaneous
heat flow during this transient for comparison to the burnout heat flow
capacity. This memo is a companion to one that explored the instantaneous
heat flew after heat pipe reservoir eclipse.
A Simplified Thermal Model.
To explore the magnitude of the expected effect and to show the effect
of the major parameters, a simplified model is proposed. In this model the
heat loss out of the radiator is taken to be
Qr x FscrWL(aTv4 - aT e4) of (1)
where Fscr is the so-called script - F radiant transfer factor (equal to
emissivity for an isolated radiator) W is the width or perimeter of the
panel per pipe (including both sides if both sides radiate), L is the active
length of the vapor in the radiator, Tv is the vapor temperature, Te is the
environmental temperature
T [ ^. ]11
eFscra
and of is the fin efficiency. The vapor filled length is assumed to be
given by
Tv ToL . Ltofi IT—
(2)
where Ltot is the total length, To is the turn-on point, and AT is the control A-12
It
l'
band width. Equation (1) may be factored into the form
Q - eescrWLa (TV 2 + Te2) (TV + Te) (
Tv - Te)
and Eq. (3) may be introduced to write
T - TQ = ( v— ^) (Tv - Te) (4)
where
l (5)
efFscrWL
tot o(Tv2 + Te 2) Cry ♦ Te
This latter parameter is insensitive to mild excursions in Tv and Te
since the absolute tei- eratures appear. in contrast Eq.(4) varies rapidly
withTv, because (Tv-To) and (Tv-Te) change significantly when Tv changes,
particularly the former quantity, and (T v-Te) changes when Te changes.
Note that this simplified model neglects the thermal capacity of the
radiator on the grounds that it is small compared to that of the heat source.
This neglect leads to an overprediction of thermal shock on the heat pipe from
sudden changes in environmental temperature Te.
The heat source is modelled as a single Lmped capacity of mass m and
specific heat c.
me dTh
Qe - ]^ (Th - Tv) (6)e
where TH is the heat source temperature, Qe is the net electrical power
dissipation, and Re is the thermal resistance into the heat pipe evaporator.
It is the heat flow into the evaporator that concerns us
•Q ` 1 ^— (Th - Tv)
The heat source thermal capacity me is assumed to be sufficiently large
A-13
(7)
q
that Th remains constant during the time that the radiator and gas front
readjust. In this respect the heat transfer through the heat pipe is
ass-ned quasi-steady.
Analysis Based Upon the Simplified Model
The model in its bare essent y, is consists only of E,qs. (4) and (7) .
The heat pipe behavior is determined by the evaporator resistance Re,
the radiator resistance R r , the turn-on point To , and the control band
width QT. The parameters Re and Rr may be inferred from observed termper-
atures at, say, the full-on operating point. Equation (4) shows that
Tv, full - Te = To Te + AT (8)
RrQfull Qfull
and from Eq. (7)
R - TMull - Tv,full(9)Re
Qfull
Hence
Re _ Tai, full - Tv, full S r (10)
Tv 9full - Te
Equating Eqs. (4) and ^7) and rearranging gives
LT(Th - Tv) = r(Tv - To)(Tv - Te)
This quadratic equation may be, solved for Tv , and the result put into
Eq.(7). Equations (8) and (9) are also introduced =or convenience
® AT + AT/r_ ^ (To - Te) 2 + 2 (eT/r) AT -- (oT/r)
Q = Qfu11 2r (To - Te + AT)
(11)
A-14
where, to shorten notation,,
ATo = 2 (Th - Te) - (To - Te)
(12)
Note that in the form of Eq.(11) neither Re nor Rr -appear explicitly, but
only their ratio r.
Sample Parametric Calculations
To show the importance of the parameter r we show three sample calcula-
tions, one with r=1, one with r=4, and another r=1/8. he choose the following
nominal values:
To = 200C Te max = -200C
AT = 50C Te min = -1100C
Th4= 300C
r = 1, , 1/8
In order to keep the same nominal value of R r as Te is changed, one multiplies
by the ratio of (To - Te + dT)/(To - Te + Mnom. The following results are
obtained:
TABLE 1EFFECT OF EVAPORATOR-TO-RADIATOR RESISTANCE RATIO
ON HAT PIPE 0VERMAD UPON RADIATOR ECLIPSE
roe
[Q/QFull][(To - T e + AT)/(To - Te + AT )nom]C
1 -20 [0.1981][45/45] = 0.1981 8%-110 [0.0713][135/45] = Mr, 0
0.25 -20 [0.6074][45/45] = 0.6074 28%-110 [0.2571][135/45] = 0.7714
0 125 -20 [0.9384][45/45] - 0.9384 45%-110 [0.4550][135/45] = 1.3651
A-15k'
Nonlinear Effect
In the preceedilig the effect of radiator eclipse was explored in-
the linearized limit. When the sink temperature changes greatly, the
heat flow is affected by the nonlinear variation of T4 in the radiation
terms. A nwnerical calculation is -easily made despite the nonlinearity.
We had
. -Q = FSCR of WLtot
Tv AT
To— (QTv 4 3- QTe ) (13)
and
Q=T-(Th-Tv)e
with
r = Re ESCR of 'tot o(Tv2 + Te2)(Tv + Te) (15)
Equating (13) and (14) and introducing (15) gives
4 4
(Th - v) - r Tv--^ To —
Tv - Te (16 )
(Tv,1 + Te,l)(TyDl + TeDl)
Equation (15) is understood to apply to both the original condition before
eclipse when Tv = Tv 1 and Te = Tel and to the conditions after eclipseD D
when v and Te are colder.
Given the value of Th , the original sink condition Te 1 , the turn-on point To , the band width BT, and the value of, r based upon the
original conditions, Eq. (16) is used to find T v l and Ql from Eq. (14).Then when Te,l goes to Te e,, the equation is used again to find Tv,21
and Q2 is found from Eq.! (14) .
(14)
A-16
F-
N
Consider the example used before:
To W 200C Teel = -200C AT - So Th = 30'C
r = 1/4, Te 2 a -1100C
.In the linearized limit we obtained Q2/Ql = 1.28. Allowing for the non-
linearity gives the following values:
Condition 1, By Binary Search
Tv LHS RHF
oC 0 oC
30 0 2520 10 025 5 11.2522,5 7.5 5.3123.75 6.25 8.2023.125 6.875 6.73823.4375 6.5625 7.465623.2813 6.7188 7.100823.2031 6.7969 6.919323.1641 6.8359 6.828723.1836 6.8164 6.873923.1738 6.8262 6.851323,1690 5.8310 6.840123.1665 6.8335 6.8344
Condition 2, By Binary Search
Tv WS RHS
0 30 0 46.3520 10 0.0025 5 21.5522.5 7.5 10.3821.25 8.75 5.09521.875 8.125 7.71422.1875 7.8125 9.042222.0313 7.9688 8.376721.9532 8.0469 8.0455
Ratio of QA, - 8.046/6.834 - 1.18
f A-17
L
^c
This ratio differs appreciably from unity, but somewhat less so than -the
value obtained with the linearized equation.
Conclusion.
The importance of the ratio of the thermal resistance between the
equipment and the evaporator to the thermal resistance between the radiator
and the evironment is illustrated. When the ratio is large (near one),
the transient load is only a few percent of the base load. When the ratio
is small, the transient load is a significant fraction of the base load.
A-18
APPFNDIX A.2.3
CONDENSER AND/OR RESERVOTR SHADOWING TESTS ON SNO09 HEAT PIPE
SNO09 heat pipe tests were directed toward examining two potential
artery depriming modes: 1) rapid chilldown of the -ondenser, and 2) rapid
chilldown of the reservoir. A large evaporator mass was a requisite con-
tributor during these hypothesized depriming modes and, accordingly, four
kilograms of aluminum were attached to the SNO09 evaporator.
Two series of rapid condenser chilldown tests were run. In the first,
the heat in the condenser sink was cooled to -73C (-100F), while the con-
denser was heated to maintain -18C (OF). The sink and condenser were
coupled through 0.30 centimeters of cork over a 162 in (0.1045 m 2 ) area.
With the heat pipe operating at 100 watts (well above open artery capacity),
the condenser heater was turned off allowing the condenser temperature to
fall approximately 2.3C/min (5F/min). When no depriming occurred, the
tests were repeated with 100 and 150 watts. Depriming at 160 watts under
steady state was verified. Thus, cooling the condenser at approximately
2.8C/min (5F/min) produced no depriming.
In the second series, the sink was -129C (-200F). When the con-
denser heater was turned off, a cooling rate of approximately 3.9C/min
(7F/min) was achieved. When no depriming occurred, the test was
repeated with 125 watts, and again no depriming was observed. However,
when an attempt was made to raise the power level to 150 watts, depriming
occurred (at the steady condenser temperature of -18C (OF). The pipe
was reprimed, held 100 watts, but failed to retain prime at 125 watts. A
third attempt resulted in failure to reprime. It is thought that ice-
generated bubbles may have been formed in the earlier transient cooling
tests, and these bubbles caused the repeated deprimings. Depriming due
to rapid chilldown of the condenser was not demonstrated.
Rapid chilldown of the reservoir was achieved by blowing vapors from
boiling liquid nitrogen through a cooling coil block attached to the
reservoir. With 100 watts power at the evaporator and the condenser at
-13C (OF), the reservoir was cooled repeatedly at successively higher
M.
A-19
I
rates. Depriming did occur at a rate of -3.2C/min (-5.6F/min). Deprim-
ing did not occur at rates of -0.8, -1.2, -1.6 and -2.5C/min (-1.5, -2.1,
-2.8 and -4.5F/min, respectively).
Although depriming due to reservoir rhilldown was demonstrated, the
rates required were substantially higher than those indicated by flight
data. This argues against reservoir and/or condenser shadowing as the
cause of the CTS anomalies.
A-20
APPENDIX A.3
FREEZING BLOWBY TESTS ON SNO09 HEAT PIPE
Freezing blow-by was hypothesized as a possible depriming mechanism.
This requires the formation of an incompletely frozen slug bridging the
vapor core during a transient in which the pressure on the evaporator side
of the slug is increasing with respect to the reservoir side. The result-
ing pressure difference across the slug can blow liquid from the evaporator
to the reservoir side and deplete the evaporator inventory.
To explore this mechanism, it was first necessary to determine how to
perform a meaningful 1-g test in the absence of the natural slugging of
excess liquid which occurs in 0-g. A successful technique to form an ice
plug in heat pipe SNO09 was developed. The procedure is as follows:
a) Instrument the heat pipe with temperature sensors along itslength to -able monitoring the location of the gas front.
b) Apply sufficient power to turn the heat pipe on i.e., tomove gas front into the condenser section. Maintain thesink temperature a few degrees above the methanol freez-ing point.
c) Midway along the inactive portion of the condenser, locallycode a short (ti2.5 cm) section of the pipe to subfreezingtemperatures. Periodically raise the reservoir-end ofpipe to force excess liquid to pass over the frozen pipesection in order to enhance ice build-up.
d) Apply periodically, a power pulse to gas reservoir to inducea transient temperature/pressure increase in the reservoirwhile monitoring the temperature profile about the locationof the gas front. Formations of all ice plug will decouplethe reservoir from the evaporator side of the heat pipe.The presence of an ice barrier blocking the arteries andvapor spaces can then be determined from the temperatureprofile along the evaporator side of the plug which shouldnot respond to an induced temperature change in the gasreservoir.
Experiments were then directed toward investigating the hypothesized
freezing blow-by depriming mechanism. The SNO09 heat pipe test was modified
such that a small, independently chilled, ice plug heat sink was attached
A-21
to the condenser midway along its length. The basic test approach was as
follows:
a) The ice plug heat sink was employed to generate a solid plugmidway along the condenser.
b) The evaporator power was raised to a value in excess of theopen artery heat pipe capacity, raising the temperature andpressure on the upstream side of the ice plug.
c) The ice plug was thawed, allowing the pressure differentialto relieve itself by blowing liquid and gas through thethawed region.
If there is liquid communication between the region to thaw first and
the arteries, the above sequence of events was hypothesized to lead to
depriming of the arteries by pumping them dry. The experiment was run so
that this liquid communication condition existed and, in fact, the arteries
did deprime. The experiment was run three times, always with the same
result. Thus, it has been clearly established that freezing blow-by is a
bonafide depriming mechanism and a candidate to explain at least some of
the observed anomalies.
To enable modelling the blow-by mechanism, the variable conductance
heat pipe subroutine was expanded to include the effects of an ice plug
forming in the condenser section of the heat pipe and open or deprimed
artery performance. Such a plug decoupies the reservoir from the active
portion of the heat pipe and alters its control characteristics. It also
provides the basis for the freezing blow-by depriming hypothesis; i.e., a
pressure difference is established across the ice plug which blows the
liquid through as the plug begins to thaw resulting in artery depriming
which causes the heat pipe to continue operating with reduced or open
artery capacity.
In Appendix A.4.2 a transient thermal analysis of a simple VCHP/
radiator system model is described which shows the effects of an ice plug
formed in the heat pipe condenser and subsequent blow-by depriming of the
arteries on the performanc- of the sample VCHP system.
A-22
APPENDIX A.4.1
BRIEF REVIEW OF LeRC THERMAL STUDIES
In support of Contract NAS3-21740 (Study of Liquid Dynamics in CTS-
Type Heat Pipes), NASA LeRC performed thermal analyses on a 'lump' param-
eter thermal model of the Transmitter Experiment Package. These efforts
were conducted by Louis Gedeon of LeRC and are described in two NASA docu-
ments entitled "Comparison of Predicted Versus Measured Temperatures for
CTS Thermal Anomalies," dated October 1, 1979, and "Modifications to CTS
Thermal Model for TRW Contract NAS3-21740," dated January 9, 1980. A
review of this analytical task is presented in the sequel.
The CTS model includes the VCHP system, the traveling wave tube, a
power processing system baseplate, the spacecraft forward and part of the
south panels, the antenna covers and skirts, and the solar array pallet.
TRW's Systems Improved Numerical Differential Analyzer (SINDA) computer
program and a Variable Conductance Heat Pipe model subroutine (VCHP2) were
utilized to solve the CTS model.
During the first transient calculations with a modified VCHP system
model, it was found that the heat pipe model subroutine (VCHP2) was not
suitable for transient calculations. An analysis at TRW of the solution
algorithm in VCHP2 revealed that the solution scheme, in view of the non-
linear nature of the model, was inadequate since it was susceptible to
becoming numerically unstable. As a result of this analysis, a new solu-
tion method was formulated which proved to be successful in circumventing
numerical instabilities.
This solution approach was incorporated into a new version .)f the vari-
able ,onductance heat pipe model subroutine renamed VCHPDA. In addition,
two new features were introduced into this version which permit simulating
the effects of an ice plug formation in the heat pipes and open or deprimed
heat pipe capacity on the performance of the whole VCHP system. The
description of the ice plug and open artery analytical models and the solu-
tion scheme, as well as, a listing of VCHPDA written in FORTRAN IV computer
language are presented in Appendix A.4.2.
A-23
Subsequent transient runs of the CTS model using R,f.0new subroutine
VCHPDA were normal, except that the predicted temperat,ur-_6 wr ro lower than
flight temperature data. In order to improve the temperature predictions,
additional modifications of input parameters were introduced into the CTS
model. Among the changes made were:
1) The solar absorptance and total hemispherical emissivity onthe VCHP system radiator were increased and d^_zreasedrespectively.
2) The reflected sun heat load on the VCHPs radiator wasassumed diffuse and was multiplied by a factor varyingwith time.
3) The south panel emissivity was increased.
4) Numerous view factors and shadowing parameters weremodified.
Although some of the above chi,ges are deemed somewhat physically
unrealistic, they resulted in gener al, in temperature predictions remark-
ably close to flight data. Transient runs were made for normal day 89 and
for periods preceeding and including the anomaly of days 75, 82, 101, and
253. The initial conditions were those obtained from steady state calcula-
tions using the conditions prevailing prior to the start of a spacecraft
eclipse.
For each anomaly day a minimum of two transient runs were made, one
assuming normal heat pipe operation prior and during the period of the
anomaly, with considerations for ice plug formation, the other run assum-
ing open artery capacity conditions prior and during the anomaly. Addi-
tional calculations were made for day 75 and day 253. For day 75, lower
open artery capacity values were assumed, and for day 253 a third run was
.jWzrformed in which normal heat pipe operation was assumed from eclipse
until the observed time of the anomaly at which time the heat pipes were
set for open artery or deprimed capacity operation.
Some significant results from these transient analyses were:
1) On day 253 freezing was not predicted at the time of theanomaly.
2) The maximum calculated heat pi pe loads never exceeded80 watts.
A-24
3) The coldest calculated temperature for heat pipe number 1always occv ;-,,ed near the reservoir end of the condenserwhere temperature sensor HPT5 is located (see Figure 1-3in text). Temperatures for heat pipes HP2 and HP3 atsimilar condenser locations were predicted to be a frwdegrees colder.
4) Formation of ice plugs in the three heat pipes were calcu-lated on day 82 prior to the anomaly.
5) The profile of the tube body temperature excursion isclosely matched on day 253 when the heat pipes were setfrom normal to cpen artery capacity operation at theobserved time of the anomaly.
A-25
APPENDIX A.4.2
GENERALIZED VARIABLE CONDUCTANCE HEAT PIPE MODELING
This appendix presents analytical models, sample problem solution, and
listing of subroutine VCHPDA.
A-26
r6f^mSEAAOSf►toFSYS7EMS IYIOt.F
ONE SPACE PARK REDONDO BEACH • :ALIFORNIA 90276
INTEROFFICE CORRESPONDENCE 3 7 15 10 1- 7 9_ 0 3
TO; Bruce Marcus ce: J. T. Bevans DATE: 6/11/79D. K. EdwardsJ. E. EningerE. E. Luedke
SUBJECT: Generalized Variable Conductance ,:ROM; David AntoniukHeat Pipe Modeling
BLDG MAIL ST A. EXT.
01 12 30 52 85 0
As the result of efforts carried out under the 1973 IR&D
Advanced Thermal Control program, a method to analytically simu-
late a gas loaded, variable conductance heat pipe (VCHP) was
developed and is documented in Reference 1.
A FOPIRAN IV computer code was implemented to numerically
solve the analytical model. This code which is suitable to
interface with general thermal models involving heat pipes, has
been used successfully in steady state thermal simulation of
systems, e.g., the transmitter experiment package (TEA) variable
conductance heat pipe system (VCHP) in the Canadian Technology
Satellite (CTS). Subsequent attempts, however, to utilize the
VCHP2 subroutine for transient thermal analyses yielded unsuc-
cessful results due to numerical instabilities arising during
the gas-vapor front location/vapor temperature calculations.
Recently, as part of the efforts to investigate the thermal
anomalies in the CTS spacecraft, the solution scheme in VCHP2
was analyzed in order to uncover the source of the numerical
problems. The analysis revealed that the iterative approach
of the subroutine to obtain a converged solution starting from
an initial guessed gas length/vapor temperature, was inadequate
in view of the non-linear natureof the model.
As the result of this analysis, a new analytical method
was formulated which under most physically realizable operating
modes, unconditionally circumvents numerical instabilities.
A-27
In addition, two new features were introduced into the VCHP
model which permits simulating the effects of an ice plug for-
mation and open artery capacity on the performance of a VCHP
system. The appropriate FORTRAN IV logic to solve the analytical
model was incorporated into a revised version of the VCHP2 sub-
routine, now identified as VCHPDA. A logic flow chart and listing
of the computer program are attached.
Basic Analytical Model:
Referring to the configuration of a typical, wicked-reservoir,
VCHP in Figure 1, and invoking the ideal gas law and the "flat
front" gas theory, the cumulative distribution of -the number of
moles of non-condensible gas along the length of a VCHP can be
written as:
z _
Ng(z) = (P T (z) - P v,R ) R.TR + PT(R)T z Pv(z) A(z) dz (1)
R o
for z < Lg
where
Lg - location of gas-vapor front or "gas length"
V - reservoir volume
T and T(z) - temperatures at vapor-liquid
interface in reservoir and along pipe, respectively.
R - universal gas constant
A(z) - gas/vapor space cross sectional area
P v,R and P v (z) - partial vapor pressure of working
fluid at T and T respectively.
P T (z) - total pressure in the VCHP defined in Eq. (2).
P T ( z ) = P v ( T V ( z ))
(2)
where T V (z)is the vapor temperature in the active section of
the pi pe.
A el
A-28
c
roW2
U^ Cco O.0 •rM i-)
•r U'L7 f]1< N
a.SC3
r
U•r2
f'-
4—O
r_
•r4J
iO
•r4-COU
ri-)OO
41 QfCQJ
NiO•r
LLS
A-29
L TLT
Tv(z) = f h(z') T(z') P(P) dz/f h(z') P(P) dz' (3)
z z
where h(z) is the local heat transfer coefficient and P(z), the
wetted perimeter. Equations 1, 2 and 3 form a complete non-linear
coupled set of equations which enable the calculation of the
length of the gas-blocked region and the vapor temperature in
the active portion given the temperature distribution along the
wall of a VCHP whose configuration conforms to the one sketched
in Figure 1.
Solution Scheme:
In order to illustrate the solution procedure incorporated
into the current version of subroutine VCHPDA, it is convenient
to rearrange Equation (1) as follows:
where
Ng(z) = P T (z) F(z) - N v (z) (4)
z
F( z ) = RRT + f T R((z' dz' (5)
R 0
P • V z P V • A(z')
Nv(z) = vRR• T R
+f
vR -- Z-7 -dz' (6)
R 0
Resorting to a numerical method to evaluate the integrals F(z),
Nv(z) and P T (z) are calculated stepping out from the reservoir
in Az increments. At each step, Ng(z) is evaluated and compared
to the total gas inventory, N T . The above procedure is continued
until Ng(z) ? N T at which point a quadratic binary search scheme
is applied to find the root of the transcendental equation
A-30
Ng(z) - N T = 0
(7)
which is satisfied when z = Lg.
To initiate this iterative process, a gas length is approxi-
mated by linear interpolation, i.e.,
Ng(z+Az) - NTLg = z +
Ng z+Az - Ng(z)Az
The search is terminated when a prescribed convergence criterion
is met, which in the current VCHPDA version is defaulted to
Ng(z) -N 10
NT < -4
— - T
Solution to Equation (7) allows the performance of the partially
gas-blocked VCHP to be quantified.
The thermal conductance between the vapor and the pipe
walls, G(z), can be calculated,
G(z) = U(z -Lg) h(z) P(z) (8)
where U is a Heavyside-type function defined as
0.0 for (z-Lg) 0.0
1.0 for (z - Lg) > 0.0
and the heat load on the VCHP
LT
= f G(z') - (T v (Lg) - T(z')) • H( T v ( Lg ) - T ( z ')) • dz'
Lg
where H is similarly defined as
0.0 for T v (Lg) - T(z) < 0.0H=
1.0 for T v (Lg) - T(z) > 0.0
(9)
Is
A-31
The heat load on the heat pipe in terms of power-length can
readily be calculated
QL = Q - Leff
(10)
where
_ (L c - Lg) LeL eff 2 + L
a + -f—
The above solution scheme holds provided the VCHP is under load.
In the event that Ng(z) < N T for z ^ L T , the gas length Lg = LT
and the total pressure in the VCHP is calculated by either
Equation (1) or (4). Using the latter Equation, the pressure
P T is given by
PT = { N1 - Nv(LT)) / F ( L T ) (12)
Ice Plug Modelling
Owing to excess fluid inventory, usually present in a VCHP,
operation of the heat pipe under subfreezing sink condictions
can result in the formation of an ice barrier in the condenser
section effectively decoupling the active portion of the pipe
from the gas reservoir. Formation of such an "ice plug" can
have a significant effect on the performance characteristics of
a VCHP. Furthermore, it can, under certain operating conditions,
lead to depriming of the arteries by what is referred to as the
"freezing blow-by" mechanism. In order to enable to simulate
the consequences of such an event, the ice plug model has been
developed and is incorporated as an optional operating VCHP mode
in subroutine.
It is assumed that in zero-gravity the bulk of the excess
fluid resides as a liquid mass in the gas reservoir and as a
slug blocking the vapor spaces in the pipe section at and near
the coupling between pipe and reservoir. During a transient
R-32
analysis, formation of an ice plug in the condenser is subject
to the following constraints: a) the gas reservoir temperature
must be above freezing conditions, b) the history of the VCHP
must show a net decrease of the gas inventory in the reservoir,
i.e., gas front and, presumably liquid slug, movement toward
the evaporator, and c) subfreezing temperatures at some point
along the condenser and/or adiabatic sections.
These conditions for ice plug formation can be stated
mathematically,
T > TF.P (Freezing temperature of working fluid) (14)
BNg R /at < 0 (15)
T(z) < T F.P. (16)
Provided conditions given by Equations (14) and (15) are met,
the solution procedure subsequently involves stepping out from
the reservoir end of the pipe in Az increments in the search of
subfreezing temperatures. The point at which conditions,
Equation (16), is first satisfied establishes the location of
the ice plug which is, currently modelled as a barrier of negli-
gible thickness. The location of the ice plug, L p , is defined by
L p = z where T(z) < T P. and T(z-dz) > TF.P.
(17)
Concurrent calculation of the cummulative gas inventory up to
z = L (Equation (1)) enables to determine the distribution of
the gas on the reservoir and evaporator side of the ice plug
which respectively are:
N g R = Ng(L p ) (18)
Ng E = N T - Ng R(19)
A-33
A
These parameters are stored and used at subsequent times to
analyze the characteristics of the two decoupled regions in
the VCHP. The solution procedure is then as follows:
I. Calculate total pressure on reservoir side of the
plug using Equation (12)
PT,R = N 9 - Nv(L p ) /F(L p ) (20)
II. Perform analysis on the evaporator side of the ice
plug resorting to Equations (1) through (12) and
appropriately changing the limits of integration
and reservoir volume in order to account for the
decoupling of the two regions, i.e., set V = 0
and evaluate the integrals fro ,! L to z ^ LT.
In addition, calculation of the effective length by Equation
(11) requires the condenser length, L c , be reduced by Lp.
L' c = L c - L (21)
The above procedure yields an estimate of a significant new
parameter: the pressure differential across the ice plug, which
can result in depriming of an arterial VCHP when liquid contact
is established between the two regions.
Open-Artery Capacity Modelling
If a mechanism such as the one described above leads to
depriming of an arterial VCHP, the designed capacity of the
heat pipe will deminish to what is usually referred to as "open-
artery" capacity. In such an operating mode, capillary pumping
pressure is substantially reduced and continuous operation of a
VCHP at high loads after depriming will generally result in
partial evaporator dry-out.
In order to simulate the performance of a VCHP with
A-34
open-artery capacity, a model was
incorporated in subroutine VCHPDA
mode. To exercise this option, a
into the overall VCHP model. The
heat pipe, defined in Equation (1
scribed capacity (QL) l , i.e.,
developed and is currently
as an operational operating
new constraint is introduced
power-length capacity of the
0), cannot now exceed a pre-
Q L ( z ) ' (QL) o(22)
The effective length, Leff, is calculated by
L'
L + L + Lc (23)
eff = 2 a e
where, L' es is the evaporator length reduced by the length
of the dry section of the pipe, Ld.
'Le
= L e - L (24)
L = L T - L w (25)
where, L w , is the length of the wet portion of the pipe measured
from the reservoir end.
Rearranging Equation (22) as
QL(z) - (QL) o = 0.0
(26)
the solution procedure involves finding the root of the above
Equation which establishes the length of the wet section of the
pipe and hence, the dry portion of the evaporator.
The general procedure which requires a double-iterative
scheme is as follows:
I. Initialize L w = L T (i.e., L d = 0.0) and Lg = LT
II. Calculate gas length, Lg, and vapor temperature, T ,such that Equation (7) is satisfied
v
A-35
4
III. Calculate QL(z) for z = L and check whether constraint(Equation (22)) is met. If the cneck is positive, thesolution to the model has been attained and the procedureis terminated; otherwise, perform step IV.
IV. Holding Lg fixed, and stepping out from the evaporatorend of the pipe in (-Az) increments, recalculate thevapor temperature using
z z
T v (z) = f h(z') T(z') P(z') dz'/ f h(z') P(z') dz' (27)
Lg Lg
and subsequently calculate QL(z).
Repeat steps III and IV until QL(z) ' (QL) 0 at which point
a quadratic binary search is performed to find the root of Equation
(26). To initiate the iterative process, the wet length, Lw,
is approximated by linear interpolations as follows:
(QL) o - QL(z)L w = z + QL z+Az - QL z
^z (28)
The search is terminated when a prescribed convergence
criterion is satisfied which is defaulted in VCHPDA to
Q L ( z ) - (QL)0 <10
-4I QL -
0
With the wet length, L w = z, held fixed a new gas length and
vapor temperature are calculated confining the calculations to
the wet section of the pipe. Steps II through IV are repeated
until
Wk+l - W k <4W K+1
- 1 0
where W k is either the gas length, Lg, or wet length, L w , and
superscript 'k' is the ite..^ation number.
A-36
0
Having established the domain of the active section of the
pipe, i.e., Lg ^ z ^ L w , the local thermal conductance, G(z),
between the vapor and adjacent pipe walls can now be redefined
to reflect the reduction of effective heat transfer area resulting
from gas blockage and wall dry-out.
G(z) = H(z) h(z) P(z) (29)
where H(z) is defined as
0.0 for (z-Lg) < 0.0 or (L -z) < 0.0H = ^
w> (30)
1.0 for (z-Lg) - 0 and (L w - z) c 0.0
VCHPDA: Computer Program Subroutine Usage
This subroutine solves numerically the analytical VCHP
model described in preceeding sections of this report. Its
solution logic is written in FORTRAN IV language which is com-
patible with current Control Data Corporation (CDC) compilers.
As a program subroutine, VCHPDA is meant to interact with
general lumped parameter thermal systems. In its present form,
however, VCHPDA is only suitable for usage in conjunction with
TRW's Systems Improved Numerical Differencing Analyzer (SINDA).
The subroutine must be called in VARIABLES 1. In the
process of generating a thermal model which involves a VCHP sub-
system, the following convention must be followed.
a) Heat pipe wall nodes are numbered and input sequentially
stepping out from reservoir end.
b) Wall to vapor conductors are numbered and input sequen-
tially as in a).
c) The vapor of each heat pipe must be declared a boundary
node.
A-37
Initial Temperatures
Calculate Wall to VaporConductor Values
Calculate Vapor Temperature
Calculate.Non-Condensable Gas Loading
1 Update Gas Length andRe-calculate VCHPDA
Vapor Temperature
Set Conductors
Determine Reservoir Heat Rate
UpdateTemperatures
Solve Nodal Network
Check Transient or S.S.? Advance T'.^eConvergence S.S.
Yes
Output
Figure 2, VCHPDA Solution Flowchart
A-38
The calling sequence is:
VCHPDA (Al, TN, A3, GN, A2, TJ, TK, QN, Kl , K,2, TL, A4)
where:
Al = Working fluid saturation pressure vs temperature array
TN = First node in wall temperature array
A3 = Array of vapor to wall conductors values with nogas input in order starting from the reservoirend (Btu/hr-°F)
GN = First conductor in vapor to wall conductor array
A2 = Heat pipe characteristics array (see below)
TJ = Reservoir temperature node
TK = Control temperature node (for a heated reservoirsystem)
QN = Reservoir heat input identification (for a heatedreservoir system).
Kl = Constant set to zero, fixed point
K2 = Usage flag; 1 = normal calculation usage
-1 = printout of heat pipe data only,used in output calls
TL = Vapor temperature node
A4 = Array of node lengths starting from reservoirend (inches)
Inputs for the heat pipe characteristics array are:
A2(1) = Total heat pipe length (inches)
A2(2) = Number of heat pipe wall nodes (FloatingPoint Number)
A2(3) = Heat pine free volume to length ratio (in 3/in)
A2(4) = Reservoir volume (in 3)
A2(5) = Gas NR value (Ft-lb/°R)
A2(6) = Reservior wick flag: 1.0 wicked reservoir
-1.0 un-wicked reservoir
A2(7) = 1.0
A2(8) = Reservoir heater power (Btu/Hr), -1.0 if unheated
A2(9) = Upper temperature setting (°F), (Heatedreservoir system)
A2(10) = Lower temperature setting (°F), (Heatedreservoir system)
A-39
A2(11) = 0.0
A2(12) = Heat pipe identification number (FloatingPoint Number)
A2(13) = A flag, 0.0 for steady state, 1.0 fortransient solutions
A2(14) = Working fluid freezing temperature
A20 5) = A flag, 1.0 to activate ice plug option,0.0 otherwise
A2(16) = Length of adiabatic section between evaporatorand condenser
A2(17) = Specified open artery (deprimed) power-lengthcapacity
A2(18) = A flag, 1.0 to consider deprimed capacity,0.0 for unrestricted capacity
A209) = Length of evaporator section.
Sample Problem
To illustrate the usage of subroutine VCHPDA, the steps
involved in solving a simple problem are described in what
follows. Consider the heat pipe radiator system sketched in
Figure 3. The heat source is a 0.32 Kg aluminum block in which
power is uniformly generated. The block is mounted on a 2.5 cm
wide saddle that is attached to the heat pipe over a 30 cm-long
section. The VCHP is a 1.25 cm O.D., 1.0 meter long aluminum/
ammonia heat pipe with a 0.1 litter gas reservoir. Short
Al/SS/Al and Al/SS transition sections minimize the coupling
by conduction between evaporator and condenser and between
reservoir and condenser respectively. Power generated in the
heater block is transported by the heat pipe to a radiator panel
from which is radiated to a sink.
The system is nodalized as shown in Figure 4. A listing
of this model is shown in pages 45 through 47. The FORTRAN
version of subroutine VCHPDA is listed in pages 48 through 67.
Steady state, followed by transient solutions were obtained
using SINDA. Selected solution outputs are shown in pages 68
through 79. The results are summarized in Figure 5.
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FIGURE 5 VCHP Model Transient Response
50 300
Y•
4-3 i-- - - - - -- -
Power: °'J
rLSink Temp ^-
0 : 1500 1.0 4.0 5.0 80
Time (Ftr.)3 20. :.
/4 • X0.0 o .1s
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Vapor Temp 5G.0°300
..
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0 1 .0 4:.0 5.0 80.T^ime^ (Hr)
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A-43
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For the first hour after steady state conditions were
reached, the VCHP system is shown to transfer 40 watts from
the heat source to a sinK at 190°K. The vapor temperature
remains constant at 296°K and the gas blocks about 3/5 of the
condenser section. When the power is turned off, the vapor
temperature can be seen to drop resulting in increase gas
blockage of the pipe. At 1.5 hours the entire length of the
pipe is gas blocked. Although the rate of heat leak from the
evaporator is of only one percent of peak power (i.e., 0.40
watt), the vapor, and consequently, the source temperatures
undergo a substantial drop during the off period. This is
the result of the rather small mass (0.32 Kg) of the source
modelled in this problem.
Continuous operation at low sink conditions, causes the
inactive condenser to reach subfreezing temperatures and, as
shown on the bottom of Figure 5; an ice plug forms at 2 hours,
0.10 meters from the reservoir end of the pipe. The center
sketch on the figure shows that a pressure differential de-
velops across the ice plug. This barrier effectively decouples
the evaporator from the gas reservoir and causes a large tem-
perature overshoot when the power is turned on at 4.0 hours.
Between this time and 5.0 hours, a large pressure differential
is sustained across the ice plug. Following a step increase
in sink temperature (5.0 hours) simulating a change in solar
view factor, the ice plug thaws giving rise to the freezing
blow by mechanism which is postulated to cause wicking failure.
Continuous operation of the VCHP at 40 watts and deprimed ca-
pacity (7.5 watt-meter) is seen to result in partial evaporator
dry-out as the heatpipe adjusts its effective length to satisfy
the imposed capacity constraint.
References:
Wanous, D. J., "Variable Conductance Heat Pipe Analysis Sub-routine, 1973 IR&D Project; Advanced Thermal Control",TRW IOC 8263.135-73-04.
A-44
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A-79
APPENDIX A.5.
POTENTIAL FOR BUBBLE FORMATION IN CTS HEAT PIPES:
FUNDAMENTALS
A-80
i' R1 r wIOVqW AAV 94OU saga
OM,( SPACI PARR- RFOONOO /[LC N • CALIFORNIA 9=70
INTEROFFICE CORRESPONDENCE
TO E. E. Luedke CC- D. Antoniuk
J. E. Eninger
B. D. Marcus
SUBJEfT. Potential for Bubble Formationin CTS Heat Pipes: Fundamentals
8715.10.2-78-7
.ATE: 27 October 1978
f^-i4rFROM. D. K. Edwards
OLDG 01 MAIL STA. 1230 EX T . 52850
INTRODUCTION
In the Anomalies Review and Program Plan of 19 October 1978, there
is promised the following analysis: "Calculate number of critical
size bubbles which can be generated due to supersaturation in rapid
chilldown. Consider both temperature and pressure effects". In
what follows the basis for making such a calculation is reviewed.
GAS SATURATION
For dilute solutions of gas in liquid, Henry's Law can be invoked:
The partial pressure gas i in the vapor phase P i and the mole
fraction X i or concentration c of gas i in the liquid phase are
linearly related
P i = C (T) X i=
C C i (T)/c 1 c i , i > 2 (1)
In the vapor phase the total pressure P is given by Dalton's Law
for an ideal gas mixture
nP _ Pi (2)
i=1
where the vapor pressure of the solute species is given by
Raoult's Law
P1 = Psat (T) X 1 = C 1 (T) X 1(3)
A-81
n VSTEMGOIIC 14E V.0-70
t
Often Henry's contant C i (T) is so large that all XiIs
other than X 1 are very small, and X 1 = I. The mole
fractions in the liquid sum to unity, of course.
n n
1 = g' Xi cc
(4)
i=1 i-1
If the liquid contacts a gas mixture of specified total pressure P
and specified ratios of noncondensible gas mole fraction,
n
Y.; = P i / 2: Pi = P i /P g(5)
i=2
First, one finds ti.e mole fraction of noncondensibles in the
liquid
nE (Y i /C i ) (P - Cl)
(6)
X9 =
i = 2 n
1 - E (Yi/Ci) Cli=2
The partial pressures in the vapor phase are
P i = Y C
P - C 1 (1 - X g ) ]
(7)
The mole fractions in the liquid phase are
X i(Yi/Ci )
C P - C 1 (1 - Xg)
(8)
R- 82
CRITICAL BUBBLE SIZE
The proceeding relations are assumed to apply to gas at
equilibrium within a critically-sized bubble when the total
pressure in the bubble exceeds that in the surrounding
liquid by an amount related to the surface tension a and bubble
size r
P - P t = 2 a_2)r
(9)
Given a value of P,, a (T), and r one can find P from
Eq. (9) and then proceed as before to establish the set of
X i mole fractions in the liquid immediately surrounding the
bubble (the effect of X i on a is neglected). Conversely
given a set of X i , one can use Eqs. (1), (2), and (3) to
find P and Eq. (9) to find r.
PREVIOUS AND PRESENT STATE VARIABLES
For convenience we choose to set the composition of a (bubbly)
liquid by its "Previous state variables" T1 and T' c plus the Y
ratios. The quantity T' e is the "Previous evaporator temperature".
It sets the previous total pressure P'
P' = P sat (T e)
(10)
The "Previous (gas-blocked) condenser temperature is T- c
11 It sets
the previous vapor pressure according to Eq. (3) and, as explained
below Eq. (4) in Eqs. (5) - (8), with P' and P' 1 one can find
the previous liquid composition X'i.
A- 83
Present state variables are T and T c . The quantity
T is understood to fix pressure P R by the relation
Pp = Psat (Te )(i1)
The quantity T fixes a and P1.
CRITICAL BUBBLE SIZE IN AN INFINITE LIQUID
Specification of the previous state variables, present state
variables, and nonisothermal gas composition leads immediately
to the critical size of a single bubble in contact with an
infinite liquid. Variables T e ', Tc ', and Y' i leads to a set of
X1 which, in an infinite liquid, are identical to X i . Then,
as explained below Eq. ( 9), one can find P and r using the set
of X i and PQ ( from T e ) and a and P 1 ( from T
2 a (T c)
rcr P - P Q (12)
Where P R comes from Eq. (11) and P from Eq. (2) with P i from
Eqs. (1) and (^,.
NUMBER OF BUBBLES OF A SPECIFIED SIZE IN A FINITE LIQUID
Let the mole fractions in one mole of liquid mixture be
specified by the previous state variables. Imagine that
the 'liquid is supersaturated, that is, there exists a finite
rcr . Now choose a value o' r greater than rcr . Then Eq. (9),
with Pk fixed by T and a by sic , fixes total pressure P. Un-
fortunately the gas composition in the bubble is unknown so
that Eq. (7) cannot be directly applied. However, one can
write that the moles of species i remaining in the liquid plus
w
A-84
those in the gas sum to the original amount of species i.
X i (1 - N) + N Y = X i ` (13)
where N is the number of moles in the vapor phase.
Introducing Eqs. (1), (2), and (3) gives
X i + N P i /P = Xi'
X i + (N/P) C i X i = X i (14)
where C1 is understood to be Psat( Tc)• Solving for
X i gives
X i =
Xi
(15)1 + (N/P) Ci
Multiplying both sides by C i (Tc )/P and summing over i
gives a single equation which fixes the unknown N.
1 = ^` Ci Xis
(16)^..e P+NCi
i = 1
For a single-species noncondensible gas Eq. (16) may be
solved explicity via the quadratic equiation. For a
binary noncondensible gas mixture, one can employ a
computer-aided binary search for the normalizing value
of N. Once N is determined the number of bubbles follows
immediately
N N R
u T c Bubbles (17)
PP( Mole
where R is the universal gas constant.
A-85
APPENDIX A.5.2
POTENTIAL FOR BUBBLE FORMATION IN CTS HEAT PIPES:
SAMPLE CALCULATIONS
A-86
I
a & U w b'.SYSTEMS GROUP
ONE SPACE PARK - REDONDO SEACH - CALIFORNIA 50279
INTEROFFICE CORRESPONDENCE 8715.10.2-78-8
TO. E. E. Luedke CC: D. Antoniuk OATS: 28 November 1978J. E. EningerS. D. Marcus
SU13JF-CT: Potential for Bubble Formation in FROM: D. K. EdwardsCTS Heat Pipes: Sample Calculations BLDG MAIL STA. EXT.
01 1230 52850
INTRODUCTION
It is desired to calculate the number and size of critical size bubbles which
can be generated due to supersaturation. In Part I the fundamentals were developed.
Here sample calculations are made for two test cases (1) a condenser depressurization
case where evaporator temperature is dropped at constant gas-blocked condense:.~ .,
temperature and (2) a condenser chilldown where the gas-blocked condenser is cooled
at constant total pressure.
HENRY'S CONSTANTS
Henry's constants are calculated from extrapolations of a solubility curve
from Saaski. Saaski plots mole fraction of the gas in the liquid versus temperature
on a log-log scale. Presumably the gas pressure is one atmosphere. Thus one has
Xi for Pi = 1, and since Pi = CiXi , Ci = Pi/Xi = 1/Xi.
As a check, an Ostwald coefficient reported by Saaski for helium in methanol
at 250C is compared to the graphed value. Ostwald coefficient a at 250C is
reported to be 0.036. The graph shows Xi = 6 x 10-5 . Hence we expect from the
graph that Ci = 1/6 x 10 -5 = 16670 atm. Ostwald coefficient and Henry number
are related by
cRRUT p ZRUTCi = a
MCL'
C. (0.785) (82.0 (298.3.5) = 16670 atm
1 (32)(0.036)
The check is very satisfactory.
Table 1 gives Henry constant for helium and nitrogen at -100 oC and -400C.
The values are hypothetical and extrapoluted, hypothetical in that liquid is
A-87
freezes at a temperature of -98 0C, and extrapoluted in that Saaski's curves are
extrapoluted. The values are chosen merely to exemplify trends.
TEST CASES
Table 2 shows the test-case conditions selected. Table 3 shows the property
values needed for the test cases.
PREVIOUS STATE MIPOSITIONS
As detailed in Part I the calculation commences with Eq.(I-6) and proceeds
to Eq. (I-8) .
xg = [(Y2/C2) + (Y3/C3J[P-Cl]
'-[(y2/C2) + (Y3/C3 ) ]C1
xi= (yi/Ci) [P-Cl (1-xg)
Table 4 gives the values.
A-88
TABLE 1
Extraction of Henry's Constants From
A Solubility Curve
C = 1/xi atm
Gas Temperature Solubility Henry's Constant Cin Methanol atm
Helium
-1000 1 X 10-5100000
(Hypothetical)
-40C 2.6 X 10 -538500
(Extrapolated)
Nitrogen
-100C 2.82 X 10 -43550
(Hypothetical)
-40C 2.69 X 10-43720
(Extrapolated)
r
r 1
TABLE 2
Hypothetical Test Cases
Test Case 1 Depressurization from Drop in Evaporator Temperature
Previous State Variables
Evaporator Temperature, Te' 49C(120F)
Gas Blocked Condenser Temperature, Tc' -40C(-40F)
Noncondensible Gas Composition, yn'i 90% N2 - 10% He
Present State Variables
Evaporator Temperature, Te21C(70F)
Gas Blocked Condenser Temperature, Tc-40C(-40F)
Test Case 2 Chi]ldoum in Gas-Blocke- Condenser
Previous State Variables
Evaporator Temperature, T e ' 21C(70F)
Gas Blocked Condenser Temperature, Tc ' -40C(-40F)
Noncondensible Gas Composition, yn,i 90% N2 - 10% He
Present State Variables
Evaporator Temperature, T 21C(70F)
Gas Blocked Condenser Temperature, T -1000(-148F)
0
A-90
0
TABU 3
Vapor Pressure and Surface Tension
T PsatsClAsia
49 7.62
21 1.96
-40 0.02870
-100 0.00012
T a
C lbf/ft
-40 2.1 x 10-3
-100 2.4 x 10-3
A-91
vH .^O M
a o^v
K
%D ^o co KCoH OH r-1 Co o Nv L vX x
MM 914 M
r-i M '^ rO O
iO O GLr
Ni5 r„
!C ?CO
r-1 ON Ln n
X N M MM
O
brH et
V) ri O O ^.,.^ N N
.0 r-iH^
t^.^•H
Ln
U O O C U cd M Or-q9G YC , .1 •' Icdcd
Cn N O ON N N (14 r14 Ln^p0 • H U cd t, V5
M M
V)
Ar M O pMLA
^O
U
M M
U tdcno ?C
U
O
•H
-)O
N N•
U d U O NM M O O
,-i i-1
?C 5C
LOM
Mr-i ^ Cn Owl !C
Ucd O C ' MO O
ao^
G^ Ln r
C; Cs r. i OLnx N
O Q r"4 M
O O
O O x O O
Critical Bubble Size in an Infinite Liquid
As explained in Part I, to compute the ciritical bubble size, one computes
n
P xi Ci (T'c)i=1
and then
2a (Te)
cr - - sat e
Table 5 shown the results. For depressurization (case 1) the critical bubble
is small, 1.6 um in radius, the size of nuclei expected to be active in nucleate
surface boiling. However, the gas composition near the surface exposed to the
gas would be more nearly in equilibrium. That is contact with the wick might
be close to the composition assumed. For chilldown (case 2) the increase in
Henry's constant for helium results in supersaturation, but the potential for
nucleation is much less. A fifty-micron-radius nucleus would be required for
bubble formation.
Number of Bubbles of a Specified Size
From Part I the equation which governs the amount of gas N within bubbles
is
1 1 tC l xl
C2 x2
C3 x31 = P+ C1 ++NNCZ + F+AC7
where the total pressure within the bubble is
P e Psat
(Te). + 2cr
A-93
Q
For case 1 and r - 50.8 um the following values pertain:
P = 1.96 + 2(2.1 x 10-3/12 = 2.135 Asia - 0.1453 atm50.8/25400
C1 xlI = (0.001963)(1.000) - 0.001953 atm
C2 x2 T = (3720)(1.251 x 10 -4) = 0.465 atm
C3 x3 ' = (38500) (1.34 x 10 -6) = 0.052 atm
N = 8.96 x 10 -5 moles of bubbles/mole of original liquid
The number of bubbles per mole is then
"- N RiT^ _ (8.96 x 10 -5)(82.05)(233 15
Nb P(3 Wr3) (0.1453)( 0(50.8 x 10.4}
Nb = 2.15 X 10 7 Bubbles/g-mole of liquid
Taking c to be approximately 0.8 [g/cm 3]/32[g/g-mole] gives
N CL = 537000 Bubbles/cm3 of liquid
Conclusions
The sample calculations show the possibility for bubble formation upon
(1) depressurization by reduction in heat pipe loading and reservoir chilling
and (2) condenser chilldown. Depressurization shows greater potential, for
537000 bubbles/cm3 are found possible, compared to only one of equal size
from condenser chilldown.
A-94
APPENDIX A.5.3
d
BUBBLE NUCLEATION EXPERIMENTS
A-95
77Y ^7DIFEW AAAD SM1.651 S It 415 CA%"
ON( SPADE PAR*-WLMN00 BEACH - CAL IFOW41A X'270
INTEROFFICE CORRESRONDENCE
To: B. Marcus oo: D. K. EdwardsoATE: 8 December 1978J. EningerE. E. Luedke
9
SUBJECT, Bubble Nucleation .'ROM; D. AntoniukExperiments BLDG MAIL STA. EXT.
O1 1230 52850
As part of the experimental program to investigate the potential ofvarious mechanisms to cause artery depriming, a series of experiments havebeen conducted to examine bubble nucleation in methanol. The experimentswere to determine whether gas bubbles could be generated in the bulk ofliquid methanol saturated with either helium or nitrogen gas as it undergoestemperature and/or pressure reduction.
Prior to the experiments, a theoretical analysis of the potential forbubble formation in CTS heat pipes had sho1411 that large numbers of bubblescould be generated in methanol due to supersaturation resulting from temper-ature and pressure reduction tuider conditions similar to those prevailingprior to the anomalies. An objective of these experiments was to verify,at: least qualitatively, the theoretical results.
In addition the experiments considered the potential of a mesh screenartery to provide bubble nucleating sites.
The experimental set-up consisted of a glass flask half filled with50cc of spectral grade methanol and instrumented to allow continuousmonitoring of temperature and pressure. A sketch of the apparatus isattached. A needle valve located between the flask and a vacuum pumpwas used to control the pressure level or the rate of pressure reductionof the liquid. Cooling of the liquid was attained by immersion of thetest flask in liquid nitrogen. This technique, however, did not allowfor arbitrary control of the cooling rate. The liquid was saturated bybubbling either nitrogen or heliun gas through the liquid using a fritglass tube. This process was allowed to be continued for at least twohours.
A typical pressure reduction experimental sequence was as follows:
1. Saturate methanol with either nitrogen or helium at ambientconditions.
2. Reduce temperature at atmospheric pressure. Two temperatureLevels, 2100 and -40oC, were used.
3. Drop into the liquid a dry section of mosh screen artery.
A-96
.v , a .,ic n,— :I v.:-ie.
4. Reduce pressure from 14.7 psia to 4 psis. In some cases thispressure drop was accomplished in 10 seconds and in others in5 minutes.
A typical temperature reduction experimental sequence was as follows:
1. Saturate methanol at ambient conditions.
2. Drop isito the liquid a dry section of mesh screen artery.
3. Reduce pressure at ambient temperature. Pressure levels of14.7 psia, 10 psia, and 4 psia were used.
4. Reduce temperature. In some cases the temperature was reducedfrom 210C to -400C in approximately 20 minutes. Th;s was accom-plished by placing the flask near the liquid nitrog,.n surfacecontained in a Dewar flask where cooling of the methanol occurredby natural convection. In other cases, the liquid was rapidlychilled by immersing the flask in liquid nitrogen for approximately10 seconds at which point the liquid on the bottom of the test flaskand inside the artery froze.
The experiments were repeated several times and the results were foundreproducible. No bubbles were observed as the liquid, originally at a settemperature level, underwent pressure reduction. Similar results were obtainedfrom temperature reduction experiments provided the liquid temperature did notdrop below the freezing point (-550C).
Experiments in which the liquid partially froze however, yielded significantlydifferent results. A large number of small bubbles were observed streaming from thesurface of the thawing ice. As the melting process a gent to competion the bubbleswere reduced to a fcw originating from the bottom surface of the flask and from theoutter surface of the mesh screen artery. About a dozen small bubbles were observedtrapped inside the arteries after the ice melted. These bubbles were observed laterto coalesce forming f.Ftiver but larger bubbles which continue to grow. The ulti-natesize of these bubbles depended on the pressure of the system. For example, at 4 Asiathe remaining bubbles inside the artery continue to grow for approximately 10 minutesas the liquid temperature rose from -40 0C to OoC, ac which point the size of thebubbles was such that essentially all the liquid in the artery was displaced.
As the result of these experiments, freezing of supersaturated methanol in thearteries has been identified as a potential mechanism for bubble formation in hearteries owing to the i:act that the ice surface is an excellent source of nucleatingsi.tos.
1
A-97
TEMPERATURERECORDER
VACUUM PUMP
LIQUID TRAP
NEEDLEVALVE
MILLIVOLTRECORDER
PRESSURETRANSDUCER
He OR N. GAS
y v Lf-%j j f tRl
TUBE
METHANOLMESHSCREENARTERYSECTION
LN2
APPENDIX A.5.4
GLASS HEAT PIPE BUBBLE NUCLEATION/MIGRATION EXPERIMENTS
A series of experiments were performed with an existing 1.07 meter
long glass heat pipe. A cross section of this heat pipe is shown in Fig-
ure 1. The pipe contains a slab wick with a CTS-type artery attached to
one side. A heater and cooling loop are attached to the other side of the
wick in the evaporator and condenser sections, respectively. This arrange-
ment permits observations on the behavior of the artery in an operational
heat pipe.
The heat pipe was gas loaded with a 90% nitrogen — 10% helium mixture
at a pressure equivalent to the conditions in the CTS pipes. The experi-
ments simply involved visually observing the artery behavior as a result
of freezing the methanol within it by passing liquid nitrogen-through the
cooling loop, and subsequently thawing the methanol by terminating the LN2
flow.
The experiment was repeated several times with the following results:
• The methanol froze to an opaque white solid (frost), indi-cating it was full of gas bubbles.
® As the methanol thawed and warmed, numerous (up to 33) gasbubbles of varying size were observed along a 12-inch lengthof the artery.
• The bubbles slowly shrank and ultimately disappeared as thegas within them redissolved into the liquid and diffusedthrough the artery wall into the surrounds,,,q vapor coreunder the pressure gradient established by their curvatureand surface tension.
® The time required for the bubbles to disappear varied enor-mously, depending on their size. Very small bubbles(d ti1/4 artery dia) dissolved within a few hours, while alarge sausage-shaped bubble which filled the artery (2artery diameters long) required several weeks.
It was believed that incorporation of these ice-generated bubbles into
the active condenser could cause artery der y-iming. Accordingly, additional
tests°were conducted and a number of deprimings were observed, but they
were sporadic (probabilistic in nature). On some occasions, as the active
A-99
O CO ^-
E EW c
0% Cr
wco
P—
NN
Y JE ► : F-
n ^ zdN co ppJ^^ OO Vi V
A-100
NCO
a,
0o sa.•-+ o
CL
W jN WN pt!1 O
rd
V iaiN^QQ1'
N-o^W' cO o
w ..c
c•r
vQ
artfNSNNzo ^
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4
condensation front was brought into the previously gas-blocked condenser,
no depriming occurred. On two occasions, freezing generated a bubble in
the adiabatic section; on both these occasions, advancement of the front
to the bubble caused depriming. On another occasion, a rather large bubble
formed in the center of the condenser, and advancement of the front to this
bubble caused depriming.
These results conclusively demonstrated that: 1) control gas is
liberated from saturated methanol every time the heat pipe goes through
a freeze-thaw cycle, and 2) the number, size, and durability of gas bubbles
generated within the arteries is a statistical phenomena influenced by bub-
ble coalescence. Arterial bubbles are known to lead to depriming if they
are convected into the active region of the pipe under high load conditions.
Thus, it is clear that freezing and thawing of the condenser can, but does
not necessarily, lead to artery depriming, depending on subsequent history.
That is, do the bubbles dissolve and diffuse away before they are con-
vected into a high stress region where they would deprime the artery?
This mechanism appears to be a prime candidate for explaining the CTS
anomalies. It is consistent with their seasonal occurrence (eclipse sea-
sons may be necessary to experience condenser freezing), sporadic occur-
rence (statistical nature of bubble population) and the lack of freezing
prior to the anomaly on day 253 (bubbles were generated during day 252).
A-101
APPENDIX B.1
SPHERICAL BUBBLE MODEL COMPUTER PROGRAM LISTING
This appendix contains the main program and sample input.
B-1
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B-16
APPENDIX B.2
SNO09 HEAT PIPE CYCLIC TEST DATA
This appendix presents plots of temperatures along the SNO09 heat pipe
versus time for selected freeze/thaw test cycles not shown in Section 3.3.
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