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Comparison of heat transfer to hydrogen, deuterium, and neon boiling with free convection at atmospheric pressure
Experimental results on thermal exchange by free convection at atmospheric pressure are described. They have been measured in the same experimental arrangement for liquid neon, deuterium, and hydrogen. The exchange surface consists of a platinum wire of 0.015 cm diameter and 49 cm effective length, heated by a direct current. For all three fluids, the region of free convection without boiling (heat flow less than approximately 0.2 W/cm 2) is described fairly well by the classical relation Nu = a(GrPr) n. The nucleate boiling region
appears between 0.2 and 0.4 W/cm 2 for all three fluids. For deuterium, and especially for neon, the Kutateladze relation, useful in this region of heat exchange, gives temperature steps between fluid and wall, which are greater than the experimentally observed values. The experimental values of critical heat flux in the three fluids as well as the corresponding temperature steps are comparable to each other, (Ne: 6 W/cm z and 2.8 K; D2: 6.2 W/cm 2 and 2.4 K; H2: 5.2 W/cm 2 and 2K).
COMPARISON OF HEAT TRANSFER TO HYDROGEN, DEUTERIUM, AND NEON BOILING WITH FREE CONVECTION AT ATMOSPHERIC PRESSURE J. M. ASTRUC, A. LACAZE, and P. PERROUD
M E A SU R E ME N T S of heat transfer by free convection in boiling liquids are difficult. Often they yield results of poor reliability, depending strongly on the measuring technique. When care is taken to ensure strictly identical measuring technique and identical heat exchange surface, the comparison of heat transfer data in different fluids gains more reliability. Such experiments yield results which allow for a serious comparison of the various existing relations. The comparison of results from liquid hydrogen, deuterium, and neon are of special interest. Indeed their normal boiling temperatures lie in the same range (20.4, 23.6, and 27.1 K respectively) while certain of their other physical properties are markedly different. It should also be emphasized that there are relatively few experimental results on the heat exchange in liquid neon 1, 7, s, and as far as we know there are no such publications on liquid deuterium.
Apparatus and experimental method The experimental arrangement and technique used in this work is strictly the same as those used before. 1 A heating element consisting of a platinum wire of 0.15 mm diameter and 49 cm effective length is arranged in a plane spiral of 9.5 cm outer diameter. This is mounted horizontally in a cryostat of 10 cm inner diameter, J. M. Astruc and P. Perroud are with the Centre d'Etudes Nucl6aires de Grenoble, France, and A. Lacaze is with the Centre National de la Recherche Scientifique de Grenoble, France. Received 10 December 1968.
248
shown in Figure 1. The heat to be exchanged is generated by direct current Joule heating, and the value of the average temperature of the wire is obtained by a measurement of its electrical resistivity. This has been previously calibrated against the vapour pressure of the liquid. The thermal exchange values are obtained by a stepwise
NOMENCLATURE
C~ specific heat at constant pressure, J/g K g gravity, cm/s 2 Gr Grashof number h heat exchange coefficient, W/cm 2 K k thermal conductivity, W/cm K Nu Nusselt number P static pressure, dynes/cm2 Pr Prandtl number ATsat wall temperature minus fluid temperature at saturation point, K 2 heat of evaporation, J/g /t dynamic viscosity, g/cm s p density, g/cm 3 a surface tension, dynes/cm Subscripts
v l c nucl
vapour liquid critical in the state of nucleate boiling
C R Y O G E N I C S • A U G U S T 1969
increase of the heating power. Voltage, current, and electrical resistivity of the wire (using a Kelvin bridge) are registered up to the point where the critical heat flow for nucleate boiling is reached.
Measured values
H2 D2 Ne
÷ A o
Salculated H2
Results
values
/
D2 . . . . Ne
Figure 2 summarizes the experimental results obtained with identical conditions for liquid hydrogen, deuterium, and neon. Two regions are clearly discernible for all three fluids: the region of free convection without boiling and the nucleate boiling region. In all three fluids the transitions take place between 0.2 and 0.4 W/cm z.
Free convection without boiling. The curves for q(ATsat) in Figure 2 have been calculated from the classical formula, which is valid for thermal exchange by free convection: Nu = a(Gr Pr) n. For a and n, we have used values which have given reasonable results for a great number of non cryogenic fluids 4: for 10 < Gr Pr < 100, a = 1.08 and n = 0"15, which gives a slope of log q/logATs~t = 1.15. These values give good agreement with our experimental results; the discrepancies between calculated and measured values lie within the margins of experimental error (q _+ 6% and ATsat _+ 0"2 C). Nucleate boiling. When the power exchange exceeds 1 W/cm z, the slope of the experimental curves becomes constant and all three fluids seem to have reached the region of nucleate boiling. From numerous relations
/
Kutetelo.dze relation "
0.5 O4
E
c~
U
tr
0,1 +
0.05
Relation Nu = 1.08(Gr Pr) 0"15 0
,
0.1
0
2 05
&&at,
~ 1
2
3
/+567
c
Figure 2. Heat exchange in free convection at atmospheric pressure. Results for liquid hydrogen, deuterium, and neon
existing in literature, we have chosen one established by Kutateladze z which has given fair agreement with experimental values obtained in cryogenic fluids such as 02, N2, Hz, and He 3,5. This relation can be written in the form hnuel~ (7 ]0.5
1~-~]
= 3"25 x
C ' 0- 0.5] 0-6 lO_4[qnuel(Cp)lPl[__~ [ ).pvk, ~gp,] j x p, 2 0-
Vottage
Platinum wire Vacuum
Support /
9
Current leads
10 P
~'=
~'~: 1 2
insulated feedthrough liquid nitrogen level control 3 liquid nitrogen pool 4 level control (diodes) 5 polyurethane foam insulation 6 vacuum insulation
9"5 c m - , , -
• AUGUST
7 thermal exchange element 8 copper 9 stainless shell 10 auxiliary heater 11 liquid level sensor (controlled condensation capillary)
1969
[
p
]0.7
The agreement between experimental and calculated values cannot be good apriori, for the experiment gives a value of 5 for the slope log q/log ATsat, compared with a calculated value of 2.5. It is well known that this slope depends mainly on the size of the nucleation sites which is given by the characteristics of the heating surface. 9 All the same, there is a certain interest in the comparison of measured and calculated curves, because both show the same sequence. For the same temperature difference ATsat, the heat flux q is greater in hydrogen than in deuterium and neon.
10cm~
Figure 1. Schematic view of experimental arrangement CRYOGENICS
1'5 0'125
leads
Critical heat flux (burn-out) in the nucleate boiling region. As soon as the heat exchange in the nucleate boiling region reaches a certain critical value, a vapour layer is gradually formed between the liquid and the wall. This layer has a poor heat conductivity. That is the moment when the critical heat flux qe at the upper end of the nucleate boiling region is reached. In our experimental arrangement, this moment manifests itself by a sudden increase of the electrical resistivity of the platinum 249
wire. An electronic circuit interrupts the current at this instant to protect the wire from melting. qc values determined experimentally for liquid neon under widely varying pressures ~ have been compared with Kutateladze's relation 2: qc = k 2(pv)°'S[ag (Pz
-
pv)l°'25
We were only able to fit this relation to our results for neon by taking K = 0.09 instead of K = 0.16 which is more generally used. The following table compares experimental qc values (measured' at atmospheric pressure) of neon as well as more recent values of deuterium and hydrogen with values calculated by the above formula, using K = 0.09. It may be realized that the agreement between calculation and experiment is fairly good, which seems to confirm our opinion that K depends only on the features of the experimental arrangement (nature o f exchange surface etc.). Neon Deuterium Hydrogen qc calculated, W/cm 2 qc measured, W/cm ~ ATsat measured critical value, C
6.5 6.0 2.8
6.6 6.2 2.4
4.9 5.2 2.0
The critical temperature difference ATsat, measured at the moment of the departure from nucleate boiling, is decreasing with the value of the normal boiling point.
250
This agrees with the theory based on the thermodynamical similarity. 6 Conclusion In conclusion, it can be said that a heating element consisting of a platinum wire, whose surface conditions are sufficiently reproducible from one experiment to the other, has turned out to be a good means for proving the similarity of thermal exchange characteristics exhibited by liquid hydrogen, deuterium, and neon. REFERENCES
1. ASTRUC,J. M., PERROUD,P., LACAZE,L., and WEIL,L. Advances in Cryogenic Engineering 12, 387 (1967) 2. KUTATELADZE,S. S. 'Heat transfer in condensation and boiling' Translation 3770 (Atomic Energy Commission Technical Information Service, Oak Ridge, Tennessee, 1959) 3. BRENTARI,E. G., GIARRATANO,P. J., and SMITH,R. V. 'Boiling heat transfer for oxygen, nitrogen, hydrogen and helium', NBS Technical Note 317 (1965) 4. MCADAMS, W. H. Heat Transmission, p. 176 (McGraw-Hilt, New York, 1954) 5. BRENTARI,E. G., and SMITH, R. V. International Advances in Cryogenic Engineering 10 (1965) 6. FREDERKING,T. H. Advances in Cryogenic Engineering 9, 71
(]964) 7. BEWILOGUA,L., KNONER, R., and WOLF, G. Cryogenics 6, 36 (1966) 8. LAPIN,A., WENZEL,L. A., and ToT'rEN,H. C. AIChEJourna111, 503 (1965) 9. WESTWATER,J. W. Theory and Fundamental Research in Heat Transfer, p. 61 (Pergamon, 1963)
CRYOGENICS - AUGUST
1969
appears between 0.2 and 0.4 W/cm 2 for all three fluids. For deuterium, and especially for neon, the Kutateladze relation, useful in this region of heat exchange, gives temperature steps between fluid and wall, which are greater than the experimentally observed values. The experimental values of critical heat flux in the three fluids as well as the corresponding temperature steps are comparable to each other, (Ne: 6 W/cm z and 2.8 K; D2: 6.2 W/cm 2 and 2.4 K; H2: 5.2 W/cm 2 and 2K).
COMPARISON OF HEAT TRANSFER TO HYDROGEN, DEUTERIUM, AND NEON BOILING WITH FREE CONVECTION AT ATMOSPHERIC PRESSURE J. M. ASTRUC, A. LACAZE, and P. PERROUD
M E A SU R E ME N T S of heat transfer by free convection in boiling liquids are difficult. Often they yield results of poor reliability, depending strongly on the measuring technique. When care is taken to ensure strictly identical measuring technique and identical heat exchange surface, the comparison of heat transfer data in different fluids gains more reliability. Such experiments yield results which allow for a serious comparison of the various existing relations. The comparison of results from liquid hydrogen, deuterium, and neon are of special interest. Indeed their normal boiling temperatures lie in the same range (20.4, 23.6, and 27.1 K respectively) while certain of their other physical properties are markedly different. It should also be emphasized that there are relatively few experimental results on the heat exchange in liquid neon 1, 7, s, and as far as we know there are no such publications on liquid deuterium.
Apparatus and experimental method The experimental arrangement and technique used in this work is strictly the same as those used before. 1 A heating element consisting of a platinum wire of 0.15 mm diameter and 49 cm effective length is arranged in a plane spiral of 9.5 cm outer diameter. This is mounted horizontally in a cryostat of 10 cm inner diameter, J. M. Astruc and P. Perroud are with the Centre d'Etudes Nucl6aires de Grenoble, France, and A. Lacaze is with the Centre National de la Recherche Scientifique de Grenoble, France. Received 10 December 1968.
248
shown in Figure 1. The heat to be exchanged is generated by direct current Joule heating, and the value of the average temperature of the wire is obtained by a measurement of its electrical resistivity. This has been previously calibrated against the vapour pressure of the liquid. The thermal exchange values are obtained by a stepwise
NOMENCLATURE
C~ specific heat at constant pressure, J/g K g gravity, cm/s 2 Gr Grashof number h heat exchange coefficient, W/cm 2 K k thermal conductivity, W/cm K Nu Nusselt number P static pressure, dynes/cm2 Pr Prandtl number ATsat wall temperature minus fluid temperature at saturation point, K 2 heat of evaporation, J/g /t dynamic viscosity, g/cm s p density, g/cm 3 a surface tension, dynes/cm Subscripts
v l c nucl
vapour liquid critical in the state of nucleate boiling
C R Y O G E N I C S • A U G U S T 1969
increase of the heating power. Voltage, current, and electrical resistivity of the wire (using a Kelvin bridge) are registered up to the point where the critical heat flow for nucleate boiling is reached.
Measured values
H2 D2 Ne
÷ A o
Salculated H2
Results
values
/
D2 . . . . Ne
Figure 2 summarizes the experimental results obtained with identical conditions for liquid hydrogen, deuterium, and neon. Two regions are clearly discernible for all three fluids: the region of free convection without boiling and the nucleate boiling region. In all three fluids the transitions take place between 0.2 and 0.4 W/cm z.
Free convection without boiling. The curves for q(ATsat) in Figure 2 have been calculated from the classical formula, which is valid for thermal exchange by free convection: Nu = a(Gr Pr) n. For a and n, we have used values which have given reasonable results for a great number of non cryogenic fluids 4: for 10 < Gr Pr < 100, a = 1.08 and n = 0"15, which gives a slope of log q/logATs~t = 1.15. These values give good agreement with our experimental results; the discrepancies between calculated and measured values lie within the margins of experimental error (q _+ 6% and ATsat _+ 0"2 C). Nucleate boiling. When the power exchange exceeds 1 W/cm z, the slope of the experimental curves becomes constant and all three fluids seem to have reached the region of nucleate boiling. From numerous relations
/
Kutetelo.dze relation "
0.5 O4
E
c~
U
tr
0,1 +
0.05
Relation Nu = 1.08(Gr Pr) 0"15 0
,
0.1
0
2 05
&&at,
~ 1
2
3
/+567
c
Figure 2. Heat exchange in free convection at atmospheric pressure. Results for liquid hydrogen, deuterium, and neon
existing in literature, we have chosen one established by Kutateladze z which has given fair agreement with experimental values obtained in cryogenic fluids such as 02, N2, Hz, and He 3,5. This relation can be written in the form hnuel~ (7 ]0.5
1~-~]
= 3"25 x
C ' 0- 0.5] 0-6 lO_4[qnuel(Cp)lPl[__~ [ ).pvk, ~gp,] j x p, 2 0-
Vottage
Platinum wire Vacuum
Support /
9
Current leads
10 P
~'=
~'~: 1 2
insulated feedthrough liquid nitrogen level control 3 liquid nitrogen pool 4 level control (diodes) 5 polyurethane foam insulation 6 vacuum insulation
9"5 c m - , , -
• AUGUST
7 thermal exchange element 8 copper 9 stainless shell 10 auxiliary heater 11 liquid level sensor (controlled condensation capillary)
1969
[
p
]0.7
The agreement between experimental and calculated values cannot be good apriori, for the experiment gives a value of 5 for the slope log q/log ATsat, compared with a calculated value of 2.5. It is well known that this slope depends mainly on the size of the nucleation sites which is given by the characteristics of the heating surface. 9 All the same, there is a certain interest in the comparison of measured and calculated curves, because both show the same sequence. For the same temperature difference ATsat, the heat flux q is greater in hydrogen than in deuterium and neon.
10cm~
Figure 1. Schematic view of experimental arrangement CRYOGENICS
1'5 0'125
leads
Critical heat flux (burn-out) in the nucleate boiling region. As soon as the heat exchange in the nucleate boiling region reaches a certain critical value, a vapour layer is gradually formed between the liquid and the wall. This layer has a poor heat conductivity. That is the moment when the critical heat flux qe at the upper end of the nucleate boiling region is reached. In our experimental arrangement, this moment manifests itself by a sudden increase of the electrical resistivity of the platinum 249
wire. An electronic circuit interrupts the current at this instant to protect the wire from melting. qc values determined experimentally for liquid neon under widely varying pressures ~ have been compared with Kutateladze's relation 2: qc = k 2(pv)°'S[ag (Pz
-
pv)l°'25
We were only able to fit this relation to our results for neon by taking K = 0.09 instead of K = 0.16 which is more generally used. The following table compares experimental qc values (measured' at atmospheric pressure) of neon as well as more recent values of deuterium and hydrogen with values calculated by the above formula, using K = 0.09. It may be realized that the agreement between calculation and experiment is fairly good, which seems to confirm our opinion that K depends only on the features of the experimental arrangement (nature o f exchange surface etc.). Neon Deuterium Hydrogen qc calculated, W/cm 2 qc measured, W/cm ~ ATsat measured critical value, C
6.5 6.0 2.8
6.6 6.2 2.4
4.9 5.2 2.0
The critical temperature difference ATsat, measured at the moment of the departure from nucleate boiling, is decreasing with the value of the normal boiling point.
250
This agrees with the theory based on the thermodynamical similarity. 6 Conclusion In conclusion, it can be said that a heating element consisting of a platinum wire, whose surface conditions are sufficiently reproducible from one experiment to the other, has turned out to be a good means for proving the similarity of thermal exchange characteristics exhibited by liquid hydrogen, deuterium, and neon. REFERENCES
1. ASTRUC,J. M., PERROUD,P., LACAZE,L., and WEIL,L. Advances in Cryogenic Engineering 12, 387 (1967) 2. KUTATELADZE,S. S. 'Heat transfer in condensation and boiling' Translation 3770 (Atomic Energy Commission Technical Information Service, Oak Ridge, Tennessee, 1959) 3. BRENTARI,E. G., GIARRATANO,P. J., and SMITH,R. V. 'Boiling heat transfer for oxygen, nitrogen, hydrogen and helium', NBS Technical Note 317 (1965) 4. MCADAMS, W. H. Heat Transmission, p. 176 (McGraw-Hilt, New York, 1954) 5. BRENTARI,E. G., and SMITH, R. V. International Advances in Cryogenic Engineering 10 (1965) 6. FREDERKING,T. H. Advances in Cryogenic Engineering 9, 71
(]964) 7. BEWILOGUA,L., KNONER, R., and WOLF, G. Cryogenics 6, 36 (1966) 8. LAPIN,A., WENZEL,L. A., and ToT'rEN,H. C. AIChEJourna111, 503 (1965) 9. WESTWATER,J. W. Theory and Fundamental Research in Heat Transfer, p. 61 (Pergamon, 1963)
CRYOGENICS - AUGUST
1969