Abstract
Analytical expressions are obtained for the longitudinal temperature profiles of the wall and the stream of cryogen during the cooling of a cryogenic pipeline. A comparison of the calculated data with experiment gives their good agreement.
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Abbreviations
- T:
-
temperature, °K
- ρ:
-
density, kg/m3
- α:
-
heat-transfer coefficient between wall and stream, W/m2·°K
- Π:
-
perimeter wetted by stream, m
- c:
-
heat capacity, J/kg·°K
- F:
-
cross-sectional area, m2
- G:
-
flow rate of cryogen, kg/sec
- t:
-
time, sec
- x:
-
longitudinal coordinate, m
- λ:
-
coefficient of thermal conductivity of cryogen, W/m·°K
- μ:
-
coefficient of dynamic viscosity, m2/sec
- Pr:
-
Prandtl number
- η:
-
dimensionless time
- ξ:
-
dimensionless longitudinal coordinate
- χ:
-
dimensionless longitudinal coordinate in the moving coordinate system
- Δη:
-
width of zone of heat exchange
- θ:
-
dimensionless temperature
- P:
-
pressure of cryogen, N/m2
- R:
-
gas constant, J/kg·°K
- ε:
-
dimensionality of temperature
- v1 :
-
dimensionless velocity of movement of steady temperature profile
- ¯cw :
-
integral-mean heat capacity of wall, J/kg·°K
- a :
-
b, m, constant coefficients in the approximating equations. Indices: 0, initial value
- w:
-
wall
- g:
-
cryogen
- r:
-
relative value
Literature cited
V. K. Koshkin, É. K. Kalinin, G. A. Dreitser, and S. A. Yarkho, Non-Steady Heat Exchange [in Russian], Mashinostroenie, Moscow (1973), pp. 24, 161.
A. M. Baron, V. M. Eroshenko, and L. A. Yaskin, “Studies on cooldown of cryogenic cables,” Cryogenics,3, 161–166 (1977).
M. C. Jones, “Cool-down of superconducting power transmission lines with single phase helium,” in: Superconducting Power Lines [in Russian], Izd. Énerg. Inst. Moscow (1979), pp. 139–165.
V. E. Keilin, I. A. Kovalev, and S. A. Lelekhov, “On the cooling time of circulating cryogenic systems,” Inzh.-Fiz. Zh.,27, No. 6, 1081–1085 (1974).
N. T. Bendik, S. K. Smirnov, and E. (Ye.) L. Blinkov, “Calculation of stationary heat transfer zone in conduits under cooldown,” Cryogenics,8, 477–482 (1979).
R. B. Scott, Cryogenic Engineering, Van Nostrand, Princeton, New Jersey (1959).
R. D. McCarty, “Thermophysical properties of helium-4 from 2 to 1500°K with pressures to 1000 atm,” Nat. Bur. Stand. (U.S.), Tech. Note 631 (1972), pp. 78–79.
N. T. Bendik and N. E. Komissarzhevskii, “Determination of the temperature of a section of core under nonsteady conditions of operation of a superconducting power cable,” Informénergo, B. U. (Vses. Inst. Nauch. Tekh. Inform.), Deposited manuscripts, No. 2, 69 (1979).
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 524–531, September, 1981.
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Azarova, L.G., Bendik, N.T., Blinkov, E.L. et al. An analytical investigation of the longitudinal temperature profile developing during the cooling of a cryogenic pipeline. Journal of Engineering Physics 41, 1023–1029 (1981). https://doi.org/10.1007/BF00821816
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DOI: https://doi.org/10.1007/BF00821816