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Heat transfer crisis during liquid nitrogen cooling of high temperature superconductor
Heat transfer crisis during liquid nitrogen cooling of high temperature superconductor Yu.A. Kirichenko, S . M . Kozlov, K.V. Rusanov and E.G. Tyurina Institute for Low Temperature Physics and Engineering, Ukr.SSR Academy of Sciences, 47 Lenin Avenue, Kharkov, 310164, USSR
Received 3 April 1991 The maximum heat flux density and the corresponding temperature drop during nucleate boiling of liquid nitrogen on the surface of high temperature superconductor ceramic samples were studied over a wide range of pressures. The experiments were performed during pool and narrow gap channel boiling. The stability of nucleate boiling and the dynamics of temperature rise of the ceramics were studied during heat transfer crises.
Keywords: heat transfer; pool boiling; ceramics
Nomenclature
Greek letters
c Heat capacity D Heating surface diameter d Thermoinsulating plate diameter g Acceleration due to gravity G Temperature gradient in autowave front K, [ ()~cp)H/(~cp)]] 0.5 L Heat of evaporation I Channel length p Pressure q Heat flux density Q Heat flux T Temperature AT Temperature drop w Velocity of autowave front
6 k p a z
The transfer of heat between a superconductor with a transport current and the coolant is an important factor which is responsible for the stability of superconductivity during thermal and other disturbances. The characteristics of stationary and non-stationary heat transfer between metallic surfaces and liquid helium have been considered previously as part of a study of the cooling of low temperature superconductors and composites ~. In a number of instances the allowed heat release is limited by the onset of the liquid boiling crisis. Therefore particular attention was given to the determination of qmax and ATmax. The discovery of high temperature superconductors (HTS) cooled with liquid nitrogen gives a new outlook to the problem of stabilizing the superconducting state. Firstly, the heat transfer occurs at considerably higher temperature and secondly, HTS ceramics have different thermophysical properties and a more porous structure compared with metals.
Gap width of channel Thermal conductivity Density Surface tension coefficient Time
Subscripts H 1 max min v
HTS sample Liquid Heat transfer crisis in nucleate boiling Heat transfer crisis in film boiling Vapour
These features must be taken into account when calculating the stability of HTS ceramics which are to be used in solenoid windings and cables. No data have been reported on the characteristics of heat transfer between HTS samples and liquid nitrogen. The heat transfer crises during the pool boiling of nitrogen and its boiling in narrow gap channels 2-5 have been studied experimentally at this institute and the results are presented in this paper.
Sample characteristics and experimental technique HTS ceramic samples of YBa2Cu307 composition were prepared by cold pressing. The temperature of the onset of superconductivity varied from 90.6 to 94.0 K. The characteristics of the samples are given in Table 1, The
0011 - 2 2 7 5 / 9 1 / 1 1 0 9 7 9 - 0 6 © 1991 Butterworth- Heinemann Ltd
Cryogenics 1991 Vol 31 November
979
Heat transfer crisis: Yu. A. Kirichenko et al. Table 1
Characteristics of HTS samples
Sample No. 1 2 3 4
Geometry
Heat transfer surface size (mm)
Thickness (mm)
Porosity (%)
Thermal c o n d u c t i v i t y at T = 150 K (W m - 1 K - l )
Disc Disc Plate Plate
Diameter 2 2 . 0 Diameter 2 0 . 0 29.5 x 8 . 0 29.7 x 8.0
3.1 2.0 2.0 3.7
16.8 28.7 22.0 22.0
3.55 1.87 3.05 2.73
disc end and the wide face of the plate served as heat transfer surfaces; the opposite surface was heated by an electrical element. Except for the heat transfer surface, all the surfaces were placed within a thermoinsulating plastic foam case. The polyvinyl chloride foam (volume density 69 kg m -3 and thermal conductivity two orders of magnitude lower than that of the ceramics) provided a heat leak to the liquid nitrogen which was not higher than 5 % of the total heat flux. The bores in the sample contained the junctions of one to six copper-constantan thermocouples which measured the temperature drop between the ceramic and the liquid. The thermoelectromotive force of the thermocouples was measured with a digital microvoltmeter. The heat transfer surface temperature was found from the measured temperature of the ceramics, taking into account the corrections for thermal conductivity. At more intensive heat fluxes the calculated error in AT was large due to the low thermal conductivity of the HTS 6, e.g. it was about 40% at q = 150 kW m -2. The error in the heat flux density at this level is not more than 8 %. The temperature of the liquid was measured with germanium resistance thermometers, the uncertainty being 4-0.1 K. The experiments were performed in saturated liquid nitrogen; the pressure varied from 0.013 to 1.4 MPa. Samples 1 and 2 were fixed so that the heat transfer surface was horizontal and faced upwards. Samples 3 and 4 were studied with both horizontal and vertical orientations of the heat transfer surface. The latter orientation was used to study the heat transfer crisis in the gap channel. A flat channel (length 30 mm and width 8 mm) was formed by the sample heat transfer surface, the unheated fibre glass plate parallel to it and two spacers representing the channel sides. The size of the gap with a rectangular cross section was defined by the spacer thickness ~ = 0 . 2 0 - 2 . 5 5 mm; a similar construction was used previously 7. The heat transfer crisis was investigated by the quasistationary method; the measurement of qm, and ATma~ was repeated two to six times and showed a satisfactory reproducibility. Samples 3 and 4 had a six-channel recorder attached to them to measure the temperature variation during the heat transfer crises. The stability of nucleate boiling against local temperature disturbance was studied on sample 1; in this instance the crisis was initiated using the thermoinsulating plate applied to the heating surface. The plates were 1 mm thick and were made of fibre glass.
980
Cryogenics 1991 Vol 31 N o v e m b e r
Heat transfer crisis during nucleate pool boiling It is seen in Figure Ia that q~x increases with increasing pressure; the relationship q ~ = q~.~(p) is similar to that observed during nitrogen boiling on metals and can be approximately described by the known Kutateladze's equation
qr~, = KLpp.S [ og(p]
- Pv) ] 0.25
(1)
with K = 0 . 1 3 5 . Under atmospheric pressure the sample-averaged t/,= is about 140 kW m -2. This is lower than the mean ~mx = 180 kW m -2 typical of horizontal copper plates °. In contrast, the critical temperature drop is on average higher during boiling on HTS samples than during boiling on metallic surfaces (for copper at p = 0.1 MPa, ATm~x = 6.3 K, Reference 8) and has a qualitatively different pressure dependence (Figure lb). Below atmospheric pressure AT~x is almost invariable; at
c~
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a
2
o O19 19 i
~
.o / ~ /
~
A
I
I
102 i
l
I
I
I
6 3E
~o
._b
o O •
2 •
•
•
•
•
Z _
/k
Ozx
0 0 A
i0 ~
o 4
I0 -2
l
I
2
4
I
I
I
I()-a Pressure (MPo)
I
l
2
4
Figure 1 Dependence of heat transfer characteristics during nucleate boiling of nitrogen upon pressure. ( z= ) 1, ( O ) 2, ( • ) 3, ( • ) 4 correspond to sample numbers in Table 1 ; ( ) calculations by Equation (1); ( . . . . ) relationship &Tma x = ATmax (p) for metallic heaters 8
Heat transfer crisis: Yu. A. Kirichenko et al.
p > 0.1 MPa the critical temperature drop increases rapidly with pressure, reaching 4 0 - 5 0 K, i.e. it exceeds the limiting superheat of the liquid ( = 33 K). This can be explained by the hypothesis that in the precrisis range of q values there are zones of film boiling on the heat transfer surface ('dry patches') with locally increased temperature. These do not disturb the stability of nucleate boiling on the rest of the surface. Therefore the average temperature of the non-isothermal surface determined by distant thermocouples can exceed the thermodynamic limit of liquid nitrogen superheat. Similar values of ATm,x exceeding the limited liquid superheat are often observed during helium boiling 1. The significant discrepancy between ATmx on different samples can be accounted for by the large error in the temperature of the heat transfer surface. The critical heat flux density estimated more accurately shows no regular data separation dependent on sample thickness or porosity. A growth of qm,x was observed 9 on porous metal coatings during nitrogen boiling when the porosity increased from 50 to 93 %. Ceramic samples used in this work have a lower and less variable porosity; they are less permeable to liquid and vapour than the structures described previously 9 and are thermally and hydrodynamically more similar to a solid. The characteristics of the nitrogen film boiling crises on the HTS ceramic surface are approximately calculated from the decrease in temperature in the samples recorded during their cooling under atmospheric pressure; this gives qm~, = 22 - 36 kW m-2, mTmi n = 1 0 0 - 1 4 0 K for different samples. For HTS samples the qmin values coincide with the maximum magnitudes on copper plates, whereas the critical temperature drops are four to five times higher than those for metals '. The main difference between HTS ceramics and metallic surfaces is therefore the significantly higher temperature at which the boiling regimes change. It is known that ATmax and mTmi n a r e a function of the ratio of the thermal properties of the material and
:I"
,,.10
the liquid, the critical temperature drops decreasing with increasing K,. Figure 2 shows the dependence of critical temperature drops on the thermal properties of various metals, non-metals (PTFE, Pyrex) and ceramics.
Heat transfer crisis during boiling in a vertical gap channel The boiling of nitrogen in a vertical channel 30 mm long and 8 mm wide with one heated side was studied during the natural circulation of the liquid. The critical heat flux density and the temperature drop decreased as the gap became narrower. In Figure 3 the data for samples 3 and 4 at atmospheric pressure are compared with the results of Reference 7. The latter were obtained during nitrogen boiling in a gap channel 40 mm long and 10 mm wide with a copper heated wall. The similarly sized channels show a good quantitative agreement of the relationship qmax = qmax(~) (Figure 3a). This relationship can be described empirically as qm,x = 1.6 X 10511 + 3.97
×
10 -3
(1/~)1.44] -1
(2)
For critical temperature drops the dependences ATma, = ATmax(6) of HTS ceramics and copper agree only qualitatively (Figure 3b). The absolute values of ATmax are on average twice as high for HTS ceramics. The data can be described by the equation ATmax = 2011 + 5.88 X
10 -3
(l/t~) 1"30] -1
(3)
2 I
E ~
10 2
4
/ "E
i
*
~
iO t
v
iO I
B4
o~
/t
E ~2
I
I
I
t
t
*
I
~
2
4
t
J
*
t
i
I
I
t
x3
-
A A
-E o iO I 6
8
AA
4
10 °
L
L
2
4
I
L
i
101
2
L~
I
21/2
4
10 2
K~ = [(;kCP)H/(XCP)L] 0.5
Figure 2 Dependence of critical temperature drops during nitrogen boiling under atmospheric pressure on the ratio of thermal properties of the heater and liquid. Circles, HTS; triangles, metals; squares, non-metals. Open symbols, &Tmax; solid symbols, ATtain
i0 ° tO- t
i
I
i
I0°
2
4
I
I0 I
G a p size (mm)
Figure 3 Dependence of characteristics of heat transfer crisis during nucleate boiling of nitrogen under atmospheric pressure on the gap size of the channel. ( • ) HTS, sample 4; ( O ) HTS, sample 3; ( z~ ) copper (Reference 7). ( , 1) Calculation by Equation (2); ( , 2) calculation by Equation (3)
C r y o g e n i c s 1 9 9 1 V o l 31 N o v e m b e r
981
Heat transfer crisis: Yu. A. Kirichenko et al. The experimental data of this work for qm.x obtained over the range p = 0 . 0 1 3 - 1 . 4 MPa and & = 0 . 2 2.55 mm were approximated by the empirical relationship 0.0995Lp °5 [ a g ( # , - p j ] 0.2, (p,~0.0638
qmax=
I 7"~-
X l~/~-~
"4~
(4)
\Pv/
Equation (4) is developed using Equations (1) and (2) as the base; the maximum deviations from the calculation from Equation (4) do not exceed 35%. The critical temperature drop is increased as the pressure rises; however, the pressure dependence of ATn~ appears to be weaker when the channel gap is smaller. Thus at = 1.0 mm the AT~,x value increases with pressure from 12 to 13 K at p = 0.015-0.05 MPa to 2 0 - 2 2 K at p = 0 . 4 - 1 . 4 M P a , whereas at 5 = 0 . 3 m m , ATm,x = 5 - 6 K at p = 0 . 0 1 3 - 0 . 2 MPa and 7 - 8 K at p = 0 . 6 - 1 . 4 MPa. An approximating equation, similar to Equation (4) was not obtained for the critical temperature drop.
Stability of nucleate boiling against temperature disturbances During the continuous or short-term deterioration of the heat transfer a superheated region is formed on the heat transfer surface; the temperature disturbance may either change the boiling regime (crisis of boiling) or leave it unchanged, depending on the size d, the superheat value and the lifetime of the superheated region. The dependence of Q~,x on the immovable thermoinsulating plate diameter was studied for sample 1: local superheating occurs under the plate, which simulates the constant disturbance region. Figure 4a shows that the decrease in critical heat flux with increasing plate diameter is faster on HTS ceramics that on a similar copper sample for
41 b
a
zl
5(
loll 1 41 "¢ ,C
21
0
#1 I
~5
g8
30
,
o \
' 0-0 5 I0 15 Diameter of applied disc(turn}
I 9i
40
l
I
I
45
I
50
Heat flux (W)
Figure 4
D e p e n d e n c e o f (a) critical heat f l u x during nitrogen boiling on t h e r m o i n s u l a t i n g plate d i a m e t e r and (b) the critical disturbance time on heat flux. ( 0 ) Experimental results; ( , 1) relationship Qmax = Qmax(d) f o r copper; ( , 2) calculation by Equation (6)
982
Cryogenics 1991 Vol 31 N o v e m b e r
which the following equation holds Qmax(d) = Q=~(O) [ 1 - (d/D) 2]
(5)
The dependence of the critical heat flux on the disturbance time was studied using an electronic circuit with an electromagnetic actuating mechanism pressing the thermoinsulating plate with d = 6 nun to the centre of the surface of sample 1 during a given time r. At small values of r and Q = constant, the temperature disturbance relaxes after the thermoinsulating plate has been removed, but as the time of contact increases, a critical value of rm.x is reached at which an irreversible crisis of heat transfer develops. Figure 4b presents data on the relationship r~x = rmax(Q) which may be approximated by IOgrmax = 8.593 -- 0.179Q
(6)
Extrapolation of this dependence to Q~x = 52.5 W ('natural' heat transfer crisis) would allow the time scale of the 'intrinsic' disturbances of nucleate boiling to be found at r~x ~- 0.164 s. The dependence of the critical disturbance time on the heat flux is much stronger for HTS ceramics than for copper; for copper the factor before Q is 0.0526, i.e. more than three times lower than in Equation (6). Therefore the nucleate boiling of nitrogen is more sensitive to temperature disturbances on a high Tc superconductor than on a similar metallic surface.
Temperature rise dynamics of HTS ceramics during heat transfer crisis It is known that during heat transfer crisis the temperature increase in long metallic samples proceeds with the motion of the temperature autowave front at a time-invariant velocity along the heated sample. The front velocity w is dependent, in addition to the heat flux density, on the thickness of the sample and its thermophysical properties. The same parameters determine the dependence T = T(r) at each point of the sample. The data for temperature rise in the centre of sample 3 at different critical heat fluxes are shown in Figure 5; the heating rate dT/dr has a maximum value which increases with qm,x" At qm,x = constant, similar curves are obtained at the other five points on the sample where the thermocouple junctions are located, although these are displaced with time. The velocity and the mean front steepness (the longitudinal temperature gradient) are estimated from the known distances between the junctions; the results are shown in Figure 6. The open symbols correspond to pool boiling nitrogen on sample 3; the solid symbols correspond to pool boiling in a gap channel on sample 4. The negative values of the velocity are indicative of the vapour film collapse, i.e. the heat transfer crisis during film boiling. The relationships w = w(q) and G = G(q) of HTS ceramics agree qualitatively with those for metals, although they display significant quantitative differences. The comparison in Table 2 shows that the propagation velocity of the film boiling region boundary on a HTS sample is four to five times lower than in steel and two orders of magnitude
Heat transfer crisis: Yu. A. Kirichenko et al. Table 2
Characteristics of temperature wave front q = 150kWm-2
q = 100 kW m -2
Thickness
Sample material
(mm)
W (ram s -1)
G (K m m -1)
W (mm S -1)
G (K m m -1)
HTS
2
0.10-0.12
22-26
0.4-0.7
17-23
Steel
3 6 10
O. 56 0.42-0.49 0.61
-3.1 --
-1.54 --
3.3
Brass
6
1 . 4 - 1.6
1.35
3.3
1.3
8 - 11 7.5-8.5 5.5
0.25 --
25-28 16.5 10-11
0.22 --
Copper
2.5 6 12
1.0
~
/
a
--
'E E
•
o 0.5
o
3c
b
•
_o 0
o
-0.5 30 -I.0
I0
0 0 0
~ -I.5
io
F--
~_-2.0 ~- ?
150
o
•
-2
5'o
20o
-3o
o
°° o o
5'0
,c o
,;o
200
Heot flux density ( kW m-2)
I00 0
20
40
60
'~ 20
Figure 6 Dependence o f (a) velocity and (b) mean steepness of t e m p e r a t u r e a u t o w a v e f r o n t during nitrogen boiling on heat flux density. ( O , •) $ = oo, ( • ) 1.5 ram, (|) 1 . 0 m m , (•) 0 . 7 5 ram, ( 0 ) 0 . 5 mm, ( I ) 0 . 3 r a m
~15
~lo o~
3
5
20
40 Time ( s ]
60
Figure 5 Dependence of (a) t e m p e r a t u r e and (b) rate of t e m p e r a t u r e increase on t i m e during nitrogen nucleate boiling crisis, qmax is 164 (1), 123 (2) and 102 kW m -2 (3)
lower than in copper. The temperature wave front is considerably steeper in HTS ceramics than in metals. It may be assumed that the small size of the normal zone formed during the thermal destruction of superconductivity in the HTS sample with a large transport current and its slow propagation would result in a release of all the stored energy within a small region. This would produce very rapid heating and the thermal destruction of this region of the superconductor.
Conclusions These experimental studies show that during nitrogen boiling on the surface of HTS ceramic samples both the
static and dynamic characteristics of the heat transfer differ from those observed on metal surfaces. Critical temperature drops on HTS ceramics are much higher than on copper; much smaller temperature disturbances are sufficient to initiate the heat transfer crises. The 'dry spot' propagation velocities are very low during heat transfer crisis on the HTS sample. These differences are mainly induced by the low thermal conductivity of HTS ceramics and must be taken into account when calculating the cryostabilization conditions of the current-carrying superconductor.
Acknowledgements The authors are grateful to V.V. Baranets, I.E. Bratchenko, K.E. Vlasenko and S.V. Nozdrin for assistance in the experiments and data processing and to V.T. Zagoskin for HTS sample preparation. The work was carried out under the terms of the USSR State Programme 'High temperature superconductivity'. References
1 Kirichenko, Yu.A.
and R u s a n o v , K.V. Heat Transfer in Helium-I Under Free Motion, Naukova Dumka, Kiev (1983) 156 (in Russian)
Cryogenics 1991 Vol 31 November 983
Heat transfer crisis: Yu. A. Kirichenko et al. 2 Kirichenko, Yu.A., Rusanov, K.V. and Tyurina, E.G. Preliminary results on heat transfer during nitrogen boiling on heater made of metal-oxide ceramic YBa2Cu307 Klmrkov (1989) 18-89 (preprint/ AN UkrSSR FTINT 20) 3 Baranets, V.V., Kirichenko, Yu.A., Kozlov, S.M., Nozdrin, S.V., Rusanov, K.V. and Tyurina, E.G. ln~-Flz Zh (1990) 59 772-775 4 Kirichenko, Yu.A., Kozlov, S.M., Nozdrin, S.V., Rusanov, K.V. and Tyurina, E.G. Vysoko-temperaturnaya Sverkhprov (1990) No 1 25-31 5 Baranets, V.V., Bratchenko, I.E., Vlasenko, K.E., Kirichenko, Yu.A., Kozlov, S.M., Nozdrin, S.V., Rusanov, K.V. and Tyurina, E.G. Thermal autowave front dynamics in cooled high-Tc supercon-
984
Cryogenics 1991 Vol 31 November
6
7 8 9
ductor on changes of nitrogen boiling regimes Kharkov (1990) 17"90 (preprint/AN UkrSSR FTINT 14) Kirichenko, Yu.A., Rusanov, K.V. and Tyurina, E.G. Superconductivity: physics, chemistry, engineering (1990) 3 1385-1410 Kirichenko, Yu.A., Rusanov, K.V. and Tyurina, E.G. Teploenergetica (1984) No. 3 23-25 Verkin, B.I., Kirichenko, Yu.A. and Rusanov, K.V. Heat Transfer During Cryogenic Liquid Boiling Naukova Dumka, Kiev (1987) 264 (in Russian) Levterov, A.I., Semena, M.G., Zaripov, V.K. and Gershuny, A.N. Teploenergetica (1983) No. 3 62-64
Received 3 April 1991 The maximum heat flux density and the corresponding temperature drop during nucleate boiling of liquid nitrogen on the surface of high temperature superconductor ceramic samples were studied over a wide range of pressures. The experiments were performed during pool and narrow gap channel boiling. The stability of nucleate boiling and the dynamics of temperature rise of the ceramics were studied during heat transfer crises.
Keywords: heat transfer; pool boiling; ceramics
Nomenclature
Greek letters
c Heat capacity D Heating surface diameter d Thermoinsulating plate diameter g Acceleration due to gravity G Temperature gradient in autowave front K, [ ()~cp)H/(~cp)]] 0.5 L Heat of evaporation I Channel length p Pressure q Heat flux density Q Heat flux T Temperature AT Temperature drop w Velocity of autowave front
6 k p a z
The transfer of heat between a superconductor with a transport current and the coolant is an important factor which is responsible for the stability of superconductivity during thermal and other disturbances. The characteristics of stationary and non-stationary heat transfer between metallic surfaces and liquid helium have been considered previously as part of a study of the cooling of low temperature superconductors and composites ~. In a number of instances the allowed heat release is limited by the onset of the liquid boiling crisis. Therefore particular attention was given to the determination of qmax and ATmax. The discovery of high temperature superconductors (HTS) cooled with liquid nitrogen gives a new outlook to the problem of stabilizing the superconducting state. Firstly, the heat transfer occurs at considerably higher temperature and secondly, HTS ceramics have different thermophysical properties and a more porous structure compared with metals.
Gap width of channel Thermal conductivity Density Surface tension coefficient Time
Subscripts H 1 max min v
HTS sample Liquid Heat transfer crisis in nucleate boiling Heat transfer crisis in film boiling Vapour
These features must be taken into account when calculating the stability of HTS ceramics which are to be used in solenoid windings and cables. No data have been reported on the characteristics of heat transfer between HTS samples and liquid nitrogen. The heat transfer crises during the pool boiling of nitrogen and its boiling in narrow gap channels 2-5 have been studied experimentally at this institute and the results are presented in this paper.
Sample characteristics and experimental technique HTS ceramic samples of YBa2Cu307 composition were prepared by cold pressing. The temperature of the onset of superconductivity varied from 90.6 to 94.0 K. The characteristics of the samples are given in Table 1, The
0011 - 2 2 7 5 / 9 1 / 1 1 0 9 7 9 - 0 6 © 1991 Butterworth- Heinemann Ltd
Cryogenics 1991 Vol 31 November
979
Heat transfer crisis: Yu. A. Kirichenko et al. Table 1
Characteristics of HTS samples
Sample No. 1 2 3 4
Geometry
Heat transfer surface size (mm)
Thickness (mm)
Porosity (%)
Thermal c o n d u c t i v i t y at T = 150 K (W m - 1 K - l )
Disc Disc Plate Plate
Diameter 2 2 . 0 Diameter 2 0 . 0 29.5 x 8 . 0 29.7 x 8.0
3.1 2.0 2.0 3.7
16.8 28.7 22.0 22.0
3.55 1.87 3.05 2.73
disc end and the wide face of the plate served as heat transfer surfaces; the opposite surface was heated by an electrical element. Except for the heat transfer surface, all the surfaces were placed within a thermoinsulating plastic foam case. The polyvinyl chloride foam (volume density 69 kg m -3 and thermal conductivity two orders of magnitude lower than that of the ceramics) provided a heat leak to the liquid nitrogen which was not higher than 5 % of the total heat flux. The bores in the sample contained the junctions of one to six copper-constantan thermocouples which measured the temperature drop between the ceramic and the liquid. The thermoelectromotive force of the thermocouples was measured with a digital microvoltmeter. The heat transfer surface temperature was found from the measured temperature of the ceramics, taking into account the corrections for thermal conductivity. At more intensive heat fluxes the calculated error in AT was large due to the low thermal conductivity of the HTS 6, e.g. it was about 40% at q = 150 kW m -2. The error in the heat flux density at this level is not more than 8 %. The temperature of the liquid was measured with germanium resistance thermometers, the uncertainty being 4-0.1 K. The experiments were performed in saturated liquid nitrogen; the pressure varied from 0.013 to 1.4 MPa. Samples 1 and 2 were fixed so that the heat transfer surface was horizontal and faced upwards. Samples 3 and 4 were studied with both horizontal and vertical orientations of the heat transfer surface. The latter orientation was used to study the heat transfer crisis in the gap channel. A flat channel (length 30 mm and width 8 mm) was formed by the sample heat transfer surface, the unheated fibre glass plate parallel to it and two spacers representing the channel sides. The size of the gap with a rectangular cross section was defined by the spacer thickness ~ = 0 . 2 0 - 2 . 5 5 mm; a similar construction was used previously 7. The heat transfer crisis was investigated by the quasistationary method; the measurement of qm, and ATma~ was repeated two to six times and showed a satisfactory reproducibility. Samples 3 and 4 had a six-channel recorder attached to them to measure the temperature variation during the heat transfer crises. The stability of nucleate boiling against local temperature disturbance was studied on sample 1; in this instance the crisis was initiated using the thermoinsulating plate applied to the heating surface. The plates were 1 mm thick and were made of fibre glass.
980
Cryogenics 1991 Vol 31 N o v e m b e r
Heat transfer crisis during nucleate pool boiling It is seen in Figure Ia that q~x increases with increasing pressure; the relationship q ~ = q~.~(p) is similar to that observed during nitrogen boiling on metals and can be approximately described by the known Kutateladze's equation
qr~, = KLpp.S [ og(p]
- Pv) ] 0.25
(1)
with K = 0 . 1 3 5 . Under atmospheric pressure the sample-averaged t/,= is about 140 kW m -2. This is lower than the mean ~mx = 180 kW m -2 typical of horizontal copper plates °. In contrast, the critical temperature drop is on average higher during boiling on HTS samples than during boiling on metallic surfaces (for copper at p = 0.1 MPa, ATm~x = 6.3 K, Reference 8) and has a qualitatively different pressure dependence (Figure lb). Below atmospheric pressure AT~x is almost invariable; at
c~
fE :>,
a
2
o O19 19 i
~
.o / ~ /
~
A
I
I
102 i
l
I
I
I
6 3E
~o
._b
o O •
2 •
•
•
•
•
Z _
/k
Ozx
0 0 A
i0 ~
o 4
I0 -2
l
I
2
4
I
I
I
I()-a Pressure (MPo)
I
l
2
4
Figure 1 Dependence of heat transfer characteristics during nucleate boiling of nitrogen upon pressure. ( z= ) 1, ( O ) 2, ( • ) 3, ( • ) 4 correspond to sample numbers in Table 1 ; ( ) calculations by Equation (1); ( . . . . ) relationship &Tma x = ATmax (p) for metallic heaters 8
Heat transfer crisis: Yu. A. Kirichenko et al.
p > 0.1 MPa the critical temperature drop increases rapidly with pressure, reaching 4 0 - 5 0 K, i.e. it exceeds the limiting superheat of the liquid ( = 33 K). This can be explained by the hypothesis that in the precrisis range of q values there are zones of film boiling on the heat transfer surface ('dry patches') with locally increased temperature. These do not disturb the stability of nucleate boiling on the rest of the surface. Therefore the average temperature of the non-isothermal surface determined by distant thermocouples can exceed the thermodynamic limit of liquid nitrogen superheat. Similar values of ATm,x exceeding the limited liquid superheat are often observed during helium boiling 1. The significant discrepancy between ATmx on different samples can be accounted for by the large error in the temperature of the heat transfer surface. The critical heat flux density estimated more accurately shows no regular data separation dependent on sample thickness or porosity. A growth of qm,x was observed 9 on porous metal coatings during nitrogen boiling when the porosity increased from 50 to 93 %. Ceramic samples used in this work have a lower and less variable porosity; they are less permeable to liquid and vapour than the structures described previously 9 and are thermally and hydrodynamically more similar to a solid. The characteristics of the nitrogen film boiling crises on the HTS ceramic surface are approximately calculated from the decrease in temperature in the samples recorded during their cooling under atmospheric pressure; this gives qm~, = 22 - 36 kW m-2, mTmi n = 1 0 0 - 1 4 0 K for different samples. For HTS samples the qmin values coincide with the maximum magnitudes on copper plates, whereas the critical temperature drops are four to five times higher than those for metals '. The main difference between HTS ceramics and metallic surfaces is therefore the significantly higher temperature at which the boiling regimes change. It is known that ATmax and mTmi n a r e a function of the ratio of the thermal properties of the material and
:I"
,,.10
the liquid, the critical temperature drops decreasing with increasing K,. Figure 2 shows the dependence of critical temperature drops on the thermal properties of various metals, non-metals (PTFE, Pyrex) and ceramics.
Heat transfer crisis during boiling in a vertical gap channel The boiling of nitrogen in a vertical channel 30 mm long and 8 mm wide with one heated side was studied during the natural circulation of the liquid. The critical heat flux density and the temperature drop decreased as the gap became narrower. In Figure 3 the data for samples 3 and 4 at atmospheric pressure are compared with the results of Reference 7. The latter were obtained during nitrogen boiling in a gap channel 40 mm long and 10 mm wide with a copper heated wall. The similarly sized channels show a good quantitative agreement of the relationship qmax = qmax(~) (Figure 3a). This relationship can be described empirically as qm,x = 1.6 X 10511 + 3.97
×
10 -3
(1/~)1.44] -1
(2)
For critical temperature drops the dependences ATma, = ATmax(6) of HTS ceramics and copper agree only qualitatively (Figure 3b). The absolute values of ATmax are on average twice as high for HTS ceramics. The data can be described by the equation ATmax = 2011 + 5.88 X
10 -3
(l/t~) 1"30] -1
(3)
2 I
E ~
10 2
4
/ "E
i
*
~
iO t
v
iO I
B4
o~
/t
E ~2
I
I
I
t
t
*
I
~
2
4
t
J
*
t
i
I
I
t
x3
-
A A
-E o iO I 6
8
AA
4
10 °
L
L
2
4
I
L
i
101
2
L~
I
21/2
4
10 2
K~ = [(;kCP)H/(XCP)L] 0.5
Figure 2 Dependence of critical temperature drops during nitrogen boiling under atmospheric pressure on the ratio of thermal properties of the heater and liquid. Circles, HTS; triangles, metals; squares, non-metals. Open symbols, &Tmax; solid symbols, ATtain
i0 ° tO- t
i
I
i
I0°
2
4
I
I0 I
G a p size (mm)
Figure 3 Dependence of characteristics of heat transfer crisis during nucleate boiling of nitrogen under atmospheric pressure on the gap size of the channel. ( • ) HTS, sample 4; ( O ) HTS, sample 3; ( z~ ) copper (Reference 7). ( , 1) Calculation by Equation (2); ( , 2) calculation by Equation (3)
C r y o g e n i c s 1 9 9 1 V o l 31 N o v e m b e r
981
Heat transfer crisis: Yu. A. Kirichenko et al. The experimental data of this work for qm.x obtained over the range p = 0 . 0 1 3 - 1 . 4 MPa and & = 0 . 2 2.55 mm were approximated by the empirical relationship 0.0995Lp °5 [ a g ( # , - p j ] 0.2, (p,~0.0638
qmax=
I 7"~-
X l~/~-~
"4~
(4)
\Pv/
Equation (4) is developed using Equations (1) and (2) as the base; the maximum deviations from the calculation from Equation (4) do not exceed 35%. The critical temperature drop is increased as the pressure rises; however, the pressure dependence of ATn~ appears to be weaker when the channel gap is smaller. Thus at = 1.0 mm the AT~,x value increases with pressure from 12 to 13 K at p = 0.015-0.05 MPa to 2 0 - 2 2 K at p = 0 . 4 - 1 . 4 M P a , whereas at 5 = 0 . 3 m m , ATm,x = 5 - 6 K at p = 0 . 0 1 3 - 0 . 2 MPa and 7 - 8 K at p = 0 . 6 - 1 . 4 MPa. An approximating equation, similar to Equation (4) was not obtained for the critical temperature drop.
Stability of nucleate boiling against temperature disturbances During the continuous or short-term deterioration of the heat transfer a superheated region is formed on the heat transfer surface; the temperature disturbance may either change the boiling regime (crisis of boiling) or leave it unchanged, depending on the size d, the superheat value and the lifetime of the superheated region. The dependence of Q~,x on the immovable thermoinsulating plate diameter was studied for sample 1: local superheating occurs under the plate, which simulates the constant disturbance region. Figure 4a shows that the decrease in critical heat flux with increasing plate diameter is faster on HTS ceramics that on a similar copper sample for
41 b
a
zl
5(
loll 1 41 "¢ ,C
21
0
#1 I
~5
g8
30
,
o \
' 0-0 5 I0 15 Diameter of applied disc(turn}
I 9i
40
l
I
I
45
I
50
Heat flux (W)
Figure 4
D e p e n d e n c e o f (a) critical heat f l u x during nitrogen boiling on t h e r m o i n s u l a t i n g plate d i a m e t e r and (b) the critical disturbance time on heat flux. ( 0 ) Experimental results; ( , 1) relationship Qmax = Qmax(d) f o r copper; ( , 2) calculation by Equation (6)
982
Cryogenics 1991 Vol 31 N o v e m b e r
which the following equation holds Qmax(d) = Q=~(O) [ 1 - (d/D) 2]
(5)
The dependence of the critical heat flux on the disturbance time was studied using an electronic circuit with an electromagnetic actuating mechanism pressing the thermoinsulating plate with d = 6 nun to the centre of the surface of sample 1 during a given time r. At small values of r and Q = constant, the temperature disturbance relaxes after the thermoinsulating plate has been removed, but as the time of contact increases, a critical value of rm.x is reached at which an irreversible crisis of heat transfer develops. Figure 4b presents data on the relationship r~x = rmax(Q) which may be approximated by IOgrmax = 8.593 -- 0.179Q
(6)
Extrapolation of this dependence to Q~x = 52.5 W ('natural' heat transfer crisis) would allow the time scale of the 'intrinsic' disturbances of nucleate boiling to be found at r~x ~- 0.164 s. The dependence of the critical disturbance time on the heat flux is much stronger for HTS ceramics than for copper; for copper the factor before Q is 0.0526, i.e. more than three times lower than in Equation (6). Therefore the nucleate boiling of nitrogen is more sensitive to temperature disturbances on a high Tc superconductor than on a similar metallic surface.
Temperature rise dynamics of HTS ceramics during heat transfer crisis It is known that during heat transfer crisis the temperature increase in long metallic samples proceeds with the motion of the temperature autowave front at a time-invariant velocity along the heated sample. The front velocity w is dependent, in addition to the heat flux density, on the thickness of the sample and its thermophysical properties. The same parameters determine the dependence T = T(r) at each point of the sample. The data for temperature rise in the centre of sample 3 at different critical heat fluxes are shown in Figure 5; the heating rate dT/dr has a maximum value which increases with qm,x" At qm,x = constant, similar curves are obtained at the other five points on the sample where the thermocouple junctions are located, although these are displaced with time. The velocity and the mean front steepness (the longitudinal temperature gradient) are estimated from the known distances between the junctions; the results are shown in Figure 6. The open symbols correspond to pool boiling nitrogen on sample 3; the solid symbols correspond to pool boiling in a gap channel on sample 4. The negative values of the velocity are indicative of the vapour film collapse, i.e. the heat transfer crisis during film boiling. The relationships w = w(q) and G = G(q) of HTS ceramics agree qualitatively with those for metals, although they display significant quantitative differences. The comparison in Table 2 shows that the propagation velocity of the film boiling region boundary on a HTS sample is four to five times lower than in steel and two orders of magnitude
Heat transfer crisis: Yu. A. Kirichenko et al. Table 2
Characteristics of temperature wave front q = 150kWm-2
q = 100 kW m -2
Thickness
Sample material
(mm)
W (ram s -1)
G (K m m -1)
W (mm S -1)
G (K m m -1)
HTS
2
0.10-0.12
22-26
0.4-0.7
17-23
Steel
3 6 10
O. 56 0.42-0.49 0.61
-3.1 --
-1.54 --
3.3
Brass
6
1 . 4 - 1.6
1.35
3.3
1.3
8 - 11 7.5-8.5 5.5
0.25 --
25-28 16.5 10-11
0.22 --
Copper
2.5 6 12
1.0
~
/
a
--
'E E
•
o 0.5
o
3c
b
•
_o 0
o
-0.5 30 -I.0
I0
0 0 0
~ -I.5
io
F--
~_-2.0 ~- ?
150
o
•
-2
5'o
20o
-3o
o
°° o o
5'0
,c o
,;o
200
Heot flux density ( kW m-2)
I00 0
20
40
60
'~ 20
Figure 6 Dependence o f (a) velocity and (b) mean steepness of t e m p e r a t u r e a u t o w a v e f r o n t during nitrogen boiling on heat flux density. ( O , •) $ = oo, ( • ) 1.5 ram, (|) 1 . 0 m m , (•) 0 . 7 5 ram, ( 0 ) 0 . 5 mm, ( I ) 0 . 3 r a m
~15
~lo o~
3
5
20
40 Time ( s ]
60
Figure 5 Dependence of (a) t e m p e r a t u r e and (b) rate of t e m p e r a t u r e increase on t i m e during nitrogen nucleate boiling crisis, qmax is 164 (1), 123 (2) and 102 kW m -2 (3)
lower than in copper. The temperature wave front is considerably steeper in HTS ceramics than in metals. It may be assumed that the small size of the normal zone formed during the thermal destruction of superconductivity in the HTS sample with a large transport current and its slow propagation would result in a release of all the stored energy within a small region. This would produce very rapid heating and the thermal destruction of this region of the superconductor.
Conclusions These experimental studies show that during nitrogen boiling on the surface of HTS ceramic samples both the
static and dynamic characteristics of the heat transfer differ from those observed on metal surfaces. Critical temperature drops on HTS ceramics are much higher than on copper; much smaller temperature disturbances are sufficient to initiate the heat transfer crises. The 'dry spot' propagation velocities are very low during heat transfer crisis on the HTS sample. These differences are mainly induced by the low thermal conductivity of HTS ceramics and must be taken into account when calculating the cryostabilization conditions of the current-carrying superconductor.
Acknowledgements The authors are grateful to V.V. Baranets, I.E. Bratchenko, K.E. Vlasenko and S.V. Nozdrin for assistance in the experiments and data processing and to V.T. Zagoskin for HTS sample preparation. The work was carried out under the terms of the USSR State Programme 'High temperature superconductivity'. References
1 Kirichenko, Yu.A.
and R u s a n o v , K.V. Heat Transfer in Helium-I Under Free Motion, Naukova Dumka, Kiev (1983) 156 (in Russian)
Cryogenics 1991 Vol 31 November 983
Heat transfer crisis: Yu. A. Kirichenko et al. 2 Kirichenko, Yu.A., Rusanov, K.V. and Tyurina, E.G. Preliminary results on heat transfer during nitrogen boiling on heater made of metal-oxide ceramic YBa2Cu307 Klmrkov (1989) 18-89 (preprint/ AN UkrSSR FTINT 20) 3 Baranets, V.V., Kirichenko, Yu.A., Kozlov, S.M., Nozdrin, S.V., Rusanov, K.V. and Tyurina, E.G. ln~-Flz Zh (1990) 59 772-775 4 Kirichenko, Yu.A., Kozlov, S.M., Nozdrin, S.V., Rusanov, K.V. and Tyurina, E.G. Vysoko-temperaturnaya Sverkhprov (1990) No 1 25-31 5 Baranets, V.V., Bratchenko, I.E., Vlasenko, K.E., Kirichenko, Yu.A., Kozlov, S.M., Nozdrin, S.V., Rusanov, K.V. and Tyurina, E.G. Thermal autowave front dynamics in cooled high-Tc supercon-
984
Cryogenics 1991 Vol 31 November
6
7 8 9
ductor on changes of nitrogen boiling regimes Kharkov (1990) 17"90 (preprint/AN UkrSSR FTINT 14) Kirichenko, Yu.A., Rusanov, K.V. and Tyurina, E.G. Superconductivity: physics, chemistry, engineering (1990) 3 1385-1410 Kirichenko, Yu.A., Rusanov, K.V. and Tyurina, E.G. Teploenergetica (1984) No. 3 23-25 Verkin, B.I., Kirichenko, Yu.A. and Rusanov, K.V. Heat Transfer During Cryogenic Liquid Boiling Naukova Dumka, Kiev (1987) 264 (in Russian) Levterov, A.I., Semena, M.G., Zaripov, V.K. and Gershuny, A.N. Teploenergetica (1983) No. 3 62-64