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#### Visual observation of high temperature profiles during startup in lithium heat pipeTélécharger gratuit NASA Technical Reports Server (NTRS) 19710001519: Reexamination of heat pipe startup pdf

NASA TM X-52924

N

NASA TECHN ICAL

MEMORANDUM

CASE FI L

CORX

NASA TM X-52924

RE-EXAMINATION OF HEAT PIPE STARTUP

by Peter M. Sockol and Ralph Forman

Lewis Research Center

Cleveland, Ohio

TECHNICAL PAPER proposed for presentation at

1970 Thermionic Conversion Specialist Conference sponsored

by the Institute of Electrical and Electronics Engineers

Miami, Florida, October 26-29, 1970

RE-EXAMINATION OF HEAT HIE STARTUP

Biter M, Sockol and Ralph Forman

NASA-Lewis Research Center

Cleveland, Ohio 44135

Abstract

In a lithium heat pipe high operating tempera-

tures permit visual observation of the temperature

profile during startup. Cotter's model of the startup

process is reassessed in the light of these observa-

tions. The model is modified by moving the sonic

point to the end of the hot zone and including the

* opposing effects of wall friction and condensation on

the flow. Transient measurements have been made on a

lithium heat pipe for startup to temperatures in the

o range 1000 to 1400° C. As predicted by the theory,

m the temperature of the hot zone is fairly independent

of the power input to the evaporator until the hot

zone reaches the end of the pipe. The hot zone

temperature predicted by the theory is 50 to 80° C

higher than the measured value with up to 30° C of the

discrepancy attributable to the measurement.

Introduction

Most of the interest in heat pipe startup is

limited to the conditions under which a pipe can or

cannot be started. Nevertheless, when the heat pipe

is part of a structure designed to operate at a high

temperature and composed of materials with different

coefficients of expansion, it may be necessary to have

detailed information about the performance of the pipe

during startup. In the case of a heat -pipe -cooled

fast reactor, where the reactivity is dependent on the

temperature of the materials, the performance of the

heat pipes during startup Is especially important.

In a lithium heat pipe high operating tempera-

tures permit visual observation of the temperature

profile during startup. At sufficiently high heat

inputs the temperature Is seen to rise to some inter-

mediate level and remain almost constant as a steep

temperature front moves down the pipe . When the

uniform hot zone fills the pipe, the temperature

increases to Its steady state value. In Cotter's

model of the startup process 1 it is assumed that the

vapor flow is sonic at the end of the evaporator.

This, however, would require a substantial temperature

drop at this point 2 which is not observed. It is more

logical to assume a sonic point at the end of the hot

zone near the sharp temperature front.

In the present work a modified version of Cotter's

analysis is applied to the startup of a radiation-

cooled heat pipe. Particular attention is focuBed on

the vapor flow in the evaporating and condensing

sections of the hot zone. To check the analysis

transient measurements were made on a lithium heat

. pipe during startup to temperatures of 1000 to l400°C.

Temperature vs time histories were recorded at equally

spaced points on the condensor. Numerical calcula-

tions of the temperature and length of the hot zone vs

<. time are compared with the experimental values.

fere a is the evaporator length, .£ is the length

of the hot portion of the condensor, Q is the heat

input to the evaporator, and q is the radiation per

unit length from the hot zone.

Energy balances on the evaporator and condensor

give

cje s %( r - r ‘) -* «- (1)

C -- ** h f3 - (2)

where w e is the mass flow. rate of vapor leaving the

evaporator, hfg the heat of vaporization, and C the

heat capacity per unit length of the wall, liquid

and wick. The heat capacity of the vapor is negli-

gible, despite the large heat of vaporization,

because the vapor density is very small. In addition

the heat of fusion is neglected even though this

produces a noticeable effect for values of Tj below

the melting point.

When the hot zone fills the pipe and £ = £ c ,

Eqs. (l) and (2) give

CMe (T- T.)- Q- Me ^c). (3)

This describes the final approach to the steady

state .

In evaluating the flow rate w e it Is assumed

that the vapor velocity becomes sonic at the end of

the hot zone. In the condensing portion of the hot

zone wall friction increases the Mach number and

condensation decreases it. 3 Hence, the above

assumption requires that the effects of wall friction

predominate. This is probable if most of the con-

densation occurs Just down stream of the sonic point

where the wail is cold. As T is approximately

constant while the temperature front moves down the

pipe, the condensation rate per unit length m is

given by q/hf g . From Eq. (l) with T constant

w e hfg = Q - q^e • Thus, the present model imposes

the requirement that Q» q(£ e + £) for £ <£ c ;

this is true when the steady state temperature is

well above the intermediate value of T during the

motion of the front. In addition it is assumed

that the difference between the stagnation tempera-

ture of the flowing vapor and the temperature of

the evaporating or condensing vapor is everywhere

small relative to the vapor temperature and that

heat conduction to or from the vapor is negligible.

Under these conditions the stagnation temperature

is approximately constant. Finally, since the

velocity of the front is small relative to the

vapor velocities, it is assumed that steady flow

equations are applicable.

Theory

Following Cotter, 1 it is assumed that the wall

temperature T in the hot zone is uniform and the cold

zone remains at the initial temperature T*. The state

of the heat pipe at time t is pictured in figure 1.

Upstream of the sonic point the equation for

the Mach number M, in the one-dimensional approxi-

mation, is written3

AT / - M 2 4 o 1 ' " J)

( 4 )

Prepared for the 1970 Thermionic Conversion Specialists Conference, October 26 through 29, 1970

Miami, Florida.

1

where k is the ratio of specific heats, f the friction

factor, D the passage diameter, w the mass flow rate,

and. x the axial coordinate. If the flow is 1 ami nar

and the wall Reynolds number , where fx is the

viscosity, is of order one or. less, the velocity pro-

file is essentially parabolic^ and f is given by

f = &4/R* =• f&rr/AO/vs, ( 5 )

apart on the condensor end of the pine. The quartz

tube is evacuated by a turbomolecular pump and the

thermocouple leads are taken out through a side arm

connected to the quartz tube. Black body holes are

machined in the evaporator and condensor end caps.

These are used to obtain independent temperature

measurements and estimates of the spectral emissivity

of the heat pipe surface.

where R x is the axial Reynolds number. For constant

m, w = w e - mx. Elimination of f and w from Eq. 4

gives

We - m X *

(6) it is seen

/--«« ' We - rnx * ( 6 )

with b = k(8 fT/U /m-l). From Eq

that it is necessary to have bNP > 1 at the end of

the evaporator if M is to increase in the condensor.

Integration of Eq. (6) from x = 0 to £ , where

M = 1, gives -/

~L b + tik-D]

.[(*>- oj»o - & N ) r ‘W’ fci N )] }

(7)

with N = 1 -

In the evaporator it is assumed that the effects

of wall friction are negligible compared to those of

evaporation. The one-dimensional flow equations can

be integrated to give3

w* ~ / + L ,r J ?

(8)

where w is the value of w at M = 1. From the

definitions of w and M, w/M = /O a A where /O and

a are the density and speed of sound of the vapor

and A is the cross-section of the passage. Thus,

Eq. (8) at M = 0 gives

a

3

w*~ /° a 0 A [2-lk+i)]

(9)

where fi 0 and a Q are values at the beginning of the

evaporator. At the end of the evaporator, where

M 8 = = 1 - If, Eq. (8) gives

*e * **(‘ - fe' ")*0~ (io)

Note that /° a Q = p Q i/ k/RT 1 where p Q is the vapor

pressure at temperature T and R is the gas constant

per unit mass of vapor. Thus v* is a very strong

function of T.

Equations (l) and (2) are integrated numerically

to obtain T and -S as functions of t. At each point

in time Eqs. (7) and (10) must be solved simultane-

ously to obtain N and w 8 .

Experiment

A 14 in. long, 0.5 in. diameter lithium filled

heat pipe has been designed and fabricated for

experiments on startup characteristics. The con-

tainment envelope for the pipe is Trill, an alloy of

90# Ta, 8# W, and 2$ Hf . The wick structure is a

composite made of Ta screen (150 mesh and 0,002 in.

diam, wire) and fabricated as an 0.008 in. thick

porous tube by swaging techniques. The wick is

employed in a concentric annulus design as described

in ref, 5. The annular gap is 0,017 in.

A sketch of the experimental apparatus is shown

in figure 2. The heat pipe is supported in a quartz

tube by lucalox spacers, and the evaporator is heated

over 5 in. of its length by induction heating. Three

thermocouples (W, 5 $- Re,* W, 26^-Re) are spaced 0,5 in.

Experimental data on the startup characteristics

are obtained as follows. With the quartz tube

evacuated to the range of 2 x 10" 7 torr, the induction

heater is switched on to a constant power level

(e.g. 1 kw). As the temperature of the pipe increases,

the thermocouple readings at positions 1 to 3 (fig. 2)

are recorded on a four-pen strip chart recorder.

These readings are complemented hy visual observation

of the temperature profile along the pipe as a function

of time. The temperature of the evaporator is

observed to rise to the range of 800 to 900° C and

then remain relatively constant as a temperature front

moves down the pipe, In approximately one minute the

whole pipe reaches this intermediate temperature and

then behaves isothermally as the temperature increases

to a steady state value determined by a balance

between the heat input and the radiation losses. When

a steady state is reached, the recorder measurements

are checked with a standard potentiometer. A com-

parison between thermocouple and optical pyrometer

readings (corrected for emissivity) shows a deviation

of up to 30° C with the pyrometer readings consis-

tently higher.

Figure 3 shows some typical data obtained at a

heat input in the range of 1 kw. as the temperature

front moved hy the thermocouple positions. The origin

of the time scale is arbitrary. The curves go through

a small hump corresponding to the melting of lithium

at l80° C and then remain fairly parallel as they rise

to the intermediate temperature of 850° C. The final

increase of the Joined curves is quite marked and

corresponds to the assymptotic approach to the steady

state temperature of 1235° C.

From the spacing of the curves, in both distance

and time, the velocity x of the temperature front is

estimated as l.l cm/s. Since the curves are parallel

to each other, it can be inferred that the shape of

the front is constant and that a point moving with the

front remains at the same temperature. Hence, at a

fixed point x on the surface of the pipe,

il/i) t + i c)t/J j » 0, and the curves of figure 3

can he used to construct the temperature profile of

the front. In particular the maximum temperature

gradient of the front is 260° c/cm which indicates the

steepness of the front .

Comparison of Theory and Experiment

Figure 4 shows the theoretical values of the

temperature T and length ( J e + £ ) of the hot zone

for the case represented hy the data of figure 3. As

the heat input from the induction heater is not known,

the measured steady state temperature (1235° c) and an

assumed total emissivity of 0.3 were used to obtain an

approximate value of 1.25 kw. for Q. The intermediate

temperature of 905° C obtained from the theory exceeds

the experimental value hy 55° C. As much as 3O 0 C of

this difference may, however, be due to errors in the

thermocouple readings. The remaining 25 0 C is quite

acceptable when the approximate nature of the theory

is considered. From the plot of ( 2 ^ + J ) vs time

a mean velocity of 0.95 cm/s is obtained for the front.

This compares favorably with the value of 1.1 cm/s

estimated from the data. Finally, the theoretical

values of the intermediate temperature are compared

2

with the measured values for three other cases in the

following table.

Steady state temp. (°C)

1080

1190

1290

Calc, heat input (tor. )

0.80

1.10

1.43

Intermediate temp.

theory (°C)

875

895

915

experiment (°C)

810

830

840

Note that, while the intermediate temperature pre-

dicted by the theory is consistently high, the weak

variation of this temperature with heat input obtained

from the theory is in close agreement with experiment.

Concluding Remarks

On the basis of the satisfactory agreement

between theory and experiment obtained in the present

work we conclude that the theory provides an adequate

description of the heat pipe startup process. In

addition from analysis of temperature profiles

extracted from data similar to that of figure 3, it is

hoped that the local condensation rate down stream of

the temperature front can be obtained. This informa-

tion is needed before the present theory can be used

for heat transfer calculations during the startup of

a complex structure like a heat-pipe- cooled, fast

reactor.

STATE OF HEAT PIPE AT TIME t

k —

•

T

T|

TTTTTTTn TTTT

Q-q^ qi cs-56300

Fig. 1

References

1. T. P« Cotter, IEEE Therm. Conv. Spec. Conf., Palo

Alto (1967), p. 3W-.

2, J.. E* KemroSy IRFifi Therm* Conv. Spec. Conf.,

Framingham (1968), p* 266.

3» A. He Shapiro, M The Dynamics and Thermodynamics of

Compressible Fluid Flow',” Rondald Press, I few York,

1953* Vole I, Ch. 8.

k* F* M. White, Jr., B« F. Barfield, and M* J. Goglia,

J. Appl. Mech. 25, 613 (1958).

5* Los Alamos Scientific laboratory, quarterly status

report LA- 1*109- MS, Feb. 19^9 •

MEASURED TEMPERATURE VS TIME AT CONDENSER

1235° C

Fig. 3

CALCULATED TEMPERATURE AND LENGTH OF HOT ZONE VS TIME

EXPERIMENTAL APPARATUS

r BLACK

BODY

HOLE

ZflQQQaBQQaQfl-.

BLACK

BODY

HOLE j JO

/ VAC

II ' SYST

bbbUbbOTBb 1

HUCALOX

SPACER

L INDUCTION

HEATING

COIL

L QUARTZ

TUBE

Fig. 2

12 3 \

THERMOCOUPLES \

TANTALUM PIN

3

NASA-Lewis

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