Model of a cryogenic liquid-hydrogen pipeline for an airport ground distribution system

Int. J. Hydrogen Energy, Vol. 8, No. 8, pp. 623~30, 1983. Printed in Great Britain.

0360-3199/83 $3.00 + 0.00 Pergamon Press Ltd.

~) 1983 International Association for Hydrogen Energy.

MODEL OF A CRYOGENIC LIQUID-HYDROGEN PIPELINE FOR AN AIRPORT G R O U N D DISTRIBUTION SYSTEM

L. JONES,* C. WUSCHKEt and T. Z. FAHIDY:~§

* Envirocon Eastern Ltd., Mississauga, Ontario, Canada; t Gulf Canada Resources Inc., Stettler, Alberta, Canada; and ~: Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada

(Received for publication 7 January 1983)

Abstraet--A model for the estimation of liquid-hydrogen pressure and temperature along a pipeline equipped with cryogenic insulation is presented together with a numerical simulation scheme and the summary of a sensitivity analysis.

NOMENCLATURE

Ao External heat transfer area Cp Specific heat (isobaric) Cv Specific heat (isochoric) D Tube diameter dp Particle diameter f Friction factor fv Void fraction FT Factor defined via equation 25 G~ Thermal conductance of the ith element g Acceleration due to gravity h Heat transfer coefficient k Thermal conductivity k~,0 Gas thermal conductivity at ambient pressure L Pipe length Le Equivalent length m Rate of mass flow Nu Nusselt number (characteristic length: diameter) P Pressure Pr Prandtl number 0 Rate of enthalpy flow q Rate of enthalpy flow due to joints and supports Re Reynolds number (characteristic length: diameter) r Radius r 2 Square of correlation coefficient SSE Sum of squared errors (or residual) T Temperature u Velocity ui Internal energy v Volume Z Elevation o~ Accommodation coefficient /6 Coefficient of volumetric expansion y cdco ).g Mean free path in a gas

Viscosity p Density o Stephan--Boltzmann constant Special symbols

(Overbar) average * Equilibrium A Estimate via regression

§ Address all communications to this author.

INTRODUCTION

As the hydrocarbon supplies of the world are gradually depleted, the finding of alternative energy sources becomes a growing concern. Hydrogen has been proposed by numerous researchers as one fuel source for specific needs such as air transport. Liquid hydrogen [LH2] has been shown to be particularly attractive as aircraft fuel with respect to global availability, pollution control, noise level generated around airports, weight per unit volume, high performance in engines and caloric value per unit mass. There are a number of associated problems, however, e.g. the conversion/ modification of airports to service LHz-fuelled aircraft. A number of conversion proposals have been based on purely theoretical analyses and conceptual design stud- ies under NASA contracts [1-3]. Lockheed has also proposed a comprehensive technology development plan, including LH2-fuelled transport aircraft in international commercial cargo service [4]. In Canada discus- sions between the federal Government and Lockheed were recently started [5] on the possibility of linking directly Mirabel and San Francisco airports, which would have at their disposal full LH2 service in the future. There may be further Canadian initiatives forth- coming in this respect [6], although the rate of such development has not been firmly set. The airport-conversion process is still at an initial proposal stage, although industry has been encouraged [7] to consider relocating to an industrial park surrounding Mirabel airport, for the construction of a hydrogen liquefaction plant on airport premises could attract various LH2 consumers and secondary industries. It appears, therefore, that the design of large cryogenic transfer lines for the transport of LH2 from producing plant to essentially in-situ consumers is a timely subject matter of obvious technological implications in the near future.

The purpose of this paper is to summarize the results of a model-oriented simulation study of LH2 transport in a large pipeline equipped with appropriate cryogenic insulation [8].

623

624 L. JONES, C. WUSCHKE AND T. Z. FAHIDY

The major objective was to develop a mechanistic model of LH2 flow, based on mass, momentum and heat balances, which a design engineer can use, via a computer, to study the sensitivity of the transport system to arbitrarily chosen design parameters (e.g. flow rate, pipe diameter, thickness of the cryogenic insulation, etc.). The underlying philosophy of the approach is that the prime criterion for an LH2 pipeline is its ability to deliver H2 fully in the liquid phase to its exit ports; in order to forestall partial evaporation the temperature profile along the pipeline must be below the saturated vapor temperature corresponding to the absolute pressure anywhere in it. This criterion may be met only by a stringently designed cryogenic insulation surrounding the LH2 flow pipe inasmuch as a local temperature in the pipe may differ only by one degree Celsius or less from the saturation temperature, at a given local pressure. Thus the heat balance component of the model is rather critical and its development requires particular precision. In the Lockheed study [4] the operating loop pressure of 241.3 kPa and the aircraft interface pressure of 193.1 kPa are considerably higher than the saturated vapor pressures of 106.4 and 137.9 kPa related to the operating temperature limits 20.4 and 21.4Kelvin, respectively, but a lower pressure profile may be speci- fied, in principle, without the danger of two-phase flow, on the basis of a reliable model. The model described in this paper allows a systematic search for this danger zone when operating parameters are varied in simulat- ing the temperature profile in the pipeline, and the relative scale of parameter sensitivity can be easily established. Such a model-based simulation is a first step in the rational design of LH2-supported aircraft facilities and airports.

MODEL CONSTRUCTION

The pipeline model incorporates the following major constituents: the physical and chemical parameters of hydrogen, the momentum equation, the energy balance equation, the thermal resistance relationships and the iteration algorithms which permit the stepwise computation of the temperature and pressure profile in sequential pipe-segments. The temperature and pressure dependence of the physical and chemical par-

ameters is incorporated via regression equations. The saturated vapor pressure/temperature relationship is also entered as a regression relationship whose accuracy, as shown in the sequel, is very important.

1. Physical and chemical parameters of LH2

At cryogenic temperatures of interest here (T < 30 K) hydrogen is essentially para-hydrogen [9]. Inspection of numerical data [10] indicates that the pressure dependence of density, thermal conductivity, viscosity and specific heat is very small over a 250 kPa range, but the effect of temperature is much more pronounced. Table 1 summarizes pertinent regression relationships in the computer simulation; except for thermal conductivity, these properties can be related to temperature by linear equations of acceptable statistical accuracy. However, the use of the linear relationship for k intro- duces only a small error into the numerical value of the overall thermal conductance.

2. The momentum equation

Since the pressure dependence of LH2 density is negligible, and anticipating a very small increase in temperature along the pipe (about 2 Kelvin) incompressible Newtonian flow may be postulated to compute the pressure drop upon integrating Bernoulli's equation:

P (u 2 - u 2) ~ 2fP u2Le AP = pg(Z2 - Z , ) + ~ O (1)

The friction factor f for cryogenic liquid flow can be obtained as in the case of conventional fluids from Moody diagrams when the pipe roughness and Reynolds number are known. The effective length L, comprises the length of the straight pipe sections and the equivalent lengths related to pipe entrance, fittings, valves, flow meters etc. inserted in the pipeline. Standard meth- ods of computing L, values, e.g. [11], have been pro- grammed into the computer simulation model to this effect.

3. The energy equation

If the pipe is divided into a number of segments

Table 1. Regression relationships for physicochemical properties of LH2 in the 15-24 Kelvin range

r 2 Property Regression Units* (%)t

Density Specific heat

Dynamic viscosity Thermal conductivity

p = 93.4074 - 1.1198T kg/m 3 99.2 Cp = -2.3106 + 0.6000T J/g.k 99.2 Co = 3.0165 + 0.1328T J/g.k 97.6 /.~.107 = 403.5620 - 13.0335T Pa.s 96.4 k.103 = 55.762 + 2.101T W/m.K 88.0 k.103 = 26.8225(T) 04326 W/m.K 95.6

* The unit of T is the Kelvin in each relationship. t Square of correlation coefficient, or coefficient of determination.

A CRYOGENIC LIQUID-HYDROGEN PIPELINE

within which average values of the physical parameters (lumped parameters) can be assumed, the energy equation for a given segment may be written (balance form) a s :

= m2 ug + Pv + -~ + gZ z + O--t" (2)

The left-hand side of equation 2 expresses LH2 energy flowing into the section and heat leak-in, whereas the right-hand side consists of LH2 energy flowing out of the section and the net change in internal energy. Under steady state conditions, in single phase liquid flow and since ml = m2 = m, equation 2 can be simplified and rearranged to read

The rate of heat leakage into the pipe from the surroundings may be expressed in terms of thermal driving G2 - - - force (To - T~), the overall thermal conductance UoA0, and the rate of leakage through pipe joints, supports G3 = and valves, q:

Q = UoAo(To- "[%) + d t (4) G 4 - -

thence, the segment outlet temperature may be computed as G5 =

/'2 (UoA0/2) + rhO, ~

+ UoAoTo + Cl - thg(Z2 - Z,) ] (5) J

ho

al

Fig. 1. A sectional view of the pipeline and the cryogenic insulation.

625

if incompressible flow in the segment with a constant cross-sectional area is assumed. Note that Tb varies from segment to segment and, as discussed in the sequel, the estimation of Tz requires a successive approximation procedure for each segment.

4. The overall thermal conductance and its components

Figure 1 illustrates the individual components of the overall thermal conductance. The conductance of the cryogenic insulation shown in the enlarged view, may be considered as a composite of three effective thermal conductivities: gas phase, solid phase and radiation conductivity:

kc = ka + ks + kR. (6)

The individual conductances may, therefore, be written a s :

2:rrlLhi (inner pipe wall to LH2) (7a)

2zcklL ln(r2/rl) (inner pipe wall) (7b)

2zckcL ln(r3/r2) (cryogenic insulation) (7c)

2zck2L ln(r4/r3) (outer pipe wall) (7d)

2zrraLho

(surroundings to outer pipe surface). (7e)

Consequently, the overall thermal conductance is computed from equation 8:

U0A0 (8)

The estimation of individual conductivities is carried out by employing appropriate heat transfer relationships. For LH2 in turbulent flow several relationships have been proposed at cryogenic temperatures and supercritical pressure [12-14], of which equation 9 [12] was judged to be the most suitable:

2hirl = 0.0217 Re°i'SPr°i4 (Tw~-o.34 N u i = ki \ T b / " (9)

Heat transfer across the cryogenic insulation depends strongly on the type of insulation used (e.g. expanded foam, vacuum, gas space filled with powders and fibrous materials, opacified or evacuated powders, multilayer and "super" insulations etc.). In the case of evacuated powders [15, 16], the gaseous conductivity is estimated via: ka = ka,o

(1 -fv)[1 + ((2 - o0/a~)((9y-5)/(y+ 1))(3)~gfv/4d)]

where (10)

kc,o = ¼(97- 5)/ucv (11)


is the gas thermal conductivity at ambient pressure and 2g is the mean free path for an unconstrained gas mol- ecule. For solid conduction, experimental observations indicate that for particle sizes below 1000 #m, k, = 1.73 x 10 -4W/m.K. In the case of multilayer insulations

ka = kc.0 I + ((2 - cr)/oO(4)~gfo/~dp)" (12)

The contr ibution of solid-phase conduction depends on the stacking properties and empirical relationships are preferred to the theoretical. Thence, in the case of a crinkled-aluminized Mylar insulation (NRC-2)

k, = 6.8 x 10-6n °'184 W/m.K (13)

where n is the layer density (turns per length). The radiation component depends on the degree of scatter- ing and partial adsorption of radiant energy in the insulation layer. In evacuated powders, the radiation conductivity may be estimated via equation 14:

kR 4 aFr T]. (14) 3

where cris the Stephan-Boltzmann coefficient, Th is the "hot" temperature, ,8 is the radiation extinction coefficient and FT is computed as

Fr= [l +-~h] [l + (T--~:I\Th/ J" (15)

Here, T~ is the "cold" temperature.

The ambient to outer pipe surface conductivity may be estimated from the dimensionless heat transfer relationship (17)

2hor4 Nuo = k----~- = 0.0266 ReSS°Ser °73 (16)

where the velocity term in Reo is the average velocity

of the ambient air; it is assumed that natural convection has a negligible contribution to h0.

The pipe-wall conductivities kl and k: depend on the metal (or alloy) used in the construction of the pipes and their numerical values may be obtained from associated cryogenic literature.

SIMULATION OF A SPECIFIC LH2 PIPELINE

The principal parameters, employed in the simulation of LH2 flow and shown in Table 2, were selected on the basis of similar values proposed in the Lockheed study [2], with some small variations. The design pipe-flow Reynolds number, about 6.86 x 106 is about 40% larger than the Lockheed specification and about one-half of the Boeing specification [1]. The thermal properties of the system are summarized in Table 3; as expected, the cryogenic insulation is responsible for about 99.4% of the overall resistance to heat leakage from the surroundings and the overall heat transfer coefficient can be closely approximated as

LG3 U0 ~ - 0.0545 W/m2.K.

A0

In estimating q, the rate of heat leakage through pipe joints, supports and valves, it was assumed that 2 mm thick ring-shaped fiberglass sections [12] spaced at 2-m long separation distances would be adequate; their ultimate tensile strength (1720 MPa) and thermal conductivity (0.92 W/re.K) are favorable from a structural and thermal point of view. With an average overall thermal driving force of about 293 Kelvin, the leakage rate per support is about 30.63 W. The leakage rate through valves was estimated by assuming the use of 10-in. vacuum insulated valves [18] where the rate of leakage at 20 Kelvin is computed to be about 127 W.

It appears [9] that field-welded joints (where an outer casing is welded around the joint and the annular space

Table 2. Principal pipeline parameters employed in the simulation of LH2 flow

Numerical value Parameter and unit

Length of pipe 6 km Inner sheath, aluminum 2024-T4

Inner diameter Outer diameter Tensile strength Yield strength

Outer sheath, 347 stainless steel Inner diameter Outer diameter Tensile strength Yield strength

Cryogenic insulation: evacuated powder type (16) Thickness

LH2 mass flow rate Pipe-inlet LH2 temperature Pipe-inlet LH2 pressure

25.4 cm 27.4 cm

772.04 MPa 537.81 MPa

30.6 cm 32.7 cm

997.78 MPa 620.55 MPa

16 mm 16.27 kg/s

20.4 Kelvin 350 kPa


Table 3. Thermal properties of the simulated LH2 pipeflow

Property and symbol Numerical value and unit

LH2-to-inner pipe-wall heat transfer coefficient, h~ Inner sheath thermal conductivity, kl Cryogenic insulation: (fractional volume of solid particles: 0.5) apparent thermal conductivity, kc

Gas-space conductivity, k~ Solid conductivity, k, Radiation "conductivity", kR

Outer sheath thermal conductivity, k2 Outer sheath-to-ambient air heat transfer coefficient, h0

2460.16 W/m2.K 17 W/m.K

9.85 x 10 -4 W/m.K 5.65 x 10 4 1.73 x 10 4 2.46 x 10 -4 15 W/m.K

12.51 W/m2.K Thermal conductance, W/K.m (equation 17) per unit length of pipe

G~ = 1963.1 (40.85% of total conductance) G2 = 1409.3 (29.33) G3 = 0.056 (1.16 × 10 -3) G4 = 1419.9 (29.55) G5 = 1.285 (0.0267)

Overall average heat transfer coefficient, U0 Overall heat transfer area, A0 (based on outer sheath)

0.0543 W/m2.K

6163.8 m 2

627

is evacuated) would be a good choice for this system, although the rate of heat leakage cannot be easily estimated. One may assume cautiously, however, that this rate would not exceed the rate of leakage through a valve. If the pipeline is constructed of 20-ft (6.l-m) standard prefabricated sections and provided with two valves at each end, the rate of heat leakage per pipe

segment is estimated to be 318.3 W; 31.2% of this leakage is due to leak through the cryogenic insulation, 28.8% is due to leakage through the three supports per segment and 40% is due to leakage through the joint. The effect of q may be considered in the simulation as a component of the overall leakage rate Q (equation 4) or, alternatively, via an overall apparent heat transfer

FROM PREVIOUS SEGMENT

~ YES

_(n)

TO NEXT SEGMENT

Fig. 2. Simplified flow chart of the pipeline simulation.


coefficient with an average numerical value of 0.174 W/m2.K (including all individual thermal conductances).

The simulation procedure is illustrated in the simplified flow diagram of Fig. 2. The outlet pressure and temperature from the previous pipe segment is set as the inlet pressure and temperature, respectively, for an arbitrary segment. The LH2 bulk temperature is first set equal to the inlet temperature and the first estimates of the overall heat transfer coefficient and the segment outlet temperature are obtained. The LH2 bulk temperature is modified by averaging and both U2 and T2 are recomputed. If the difference between the new and the old value of T2 is less than a predetermined error criterion e, the pressure drop over the segment and the segment outlet pressure are calculated. Then, the thermodynamic equilibrium temperature T~', corresponding to saturated vapor pressure P2 is computed (see sequel) and if it is smaller than the computed segment outlet temperature, a warning is issued about the danger of two-phase hydrogen flow past this segment. If the computed segment outlet temperature is lower than the equilibrium temperature, the outlet temperature and pressure are set as inlet properties of the next segment and the entire procedure is repeated until the appear- ance of two-phase flow, or the attainment of the pipeline exit.

The saturated vapor pressure/temperature relationship for hydrogen

Since extensive tabulations of thermodynamic properties of hydrogen are readily available, eg. [10, 14], it would be inviting to enter empirical (P, T *) data into the simulation programme and interpolate linearly within the range of interest. However, given

the rather tight restrictions on the increase in temperature of hydrogen flowing in the pipeline and on the operating pressure level, the thereby computed values of T* in each pipe segment would not be accurate enough as demonstrated in the next section. The linear least squares regression model on T* in the 100-400 kPa range

lb?~ = 18.7865 + 0.018728(P) (17)

has SSE = 0.4875 and r z = 0.9808, whereas the nonlinear model

^

T~ = 8.7971(P) °18°19 (18)

has SSE = 0.0122 and r z = 0.9946 (in equations 17 and 18 P is in kPa and 7 ~* in Kelvin).

Numerical results of simulation; parameter sensitivity

Table 4 contains the summary of the base simulation run where the parameters in Tables 1-3 and an arbitrary segment length of 100 m have been employed. The linear (P, T*) model predicts two-phase flow past 5400 m of flow whereas the nonlinear model predicts no partial evaporation of LH2 in the pipeline, indicating an essentially safe design (provided that an ~2.5 Kelvin increase in the LH2 temperature is a priori acceptable). The effect of varying certain system parameters is illustrated in Table 5. The nonlinear (P, T*) model predicts single-phase LH2 flow in every case shown in Tables 4 and 5, whereas the less-accurate linear model predicts a number of danger points on account of its "under- estimation" of the saturated vapor temperature in the pressure-temperature range of interest. As shown in Table 4, discrepancies between the two model predic- tions are only fractions of a degree Kelvin, but so are design temperature changes along the pipeline. The

Table 4. Summary of the base simulation run*

Distance from pipe entrance, X Pressure, P Temperature, T

(km) (kPa) (K)

Temperature at saturation vapor pressure P = P*

(K) Linear model, Nonlinear model, equation 17 equation 18

0 350 20.40 25.34 2 5 . 2 8 0.5 337 20.64 25.10 25.11 1.0 325 20.88 24.87 24.94 1.5 312 21.11 24.63 24.76 2.0 300 21.34 24.42 24.59 2.5 287 21.56 24.16 24.39 3.0 275 21.79 23.94 24.20 3.5 263 22.01 23.71 24.01 4.0 250 22.23 23.47 23.79 4.5 238 22.44 23.24 23.58 5.0 226 22.66 23.01 23.36 5.3 218 22.78 22.87 23.21 5.4 216 22.83 22.83 23.17 5.5 214 22.87 22.79 23.13

* No elevation in the pipeline (Z1 = Z2),


Table 5. Summary of sensitivity analysis

629

Parameter and its Temperature Pressure numerical value (K) (kPa)

Danger of two-phase flow occurring at distance from

pipeline entrance (km) Linear model, Nonlinear model,

equation 17 equation 18

Segment length, No danger* L, = 60 m 22.85 215 5.46 (ND) LH2 mass flow rate,

rn = 13.49 kg/s 23.63 255 5.60 ND m 3.6 kg/s 25.35 347 2.30 ND

Insulation: multilayer 22.82 214 5.40 ND Insulation thickness (r4 - r3) = 10.5 mm 22.91 219 5.30 ND Heat leakage rate through supports, 100 W/support 22.60 203 5.90 ND 75 W/support 22.22 200 ND ND Pipeline elevation with coordinates X1 = 1 km; Z I = 5 m ; X 2 =2km; Z2 = 25 m 21.75 148 2.90 ND Fractional volume of solid particles in insulation, f = 0.99 22.78 211 5.50 ND Boeing-study (1) r~ = 20.3 cm; rn = 63.0 kg/s 21.18 133 ND ND

* No danger of two-phase flow predicted at the distance designated dangerous by the linear model.

simulation examples shown here do not represent final design values but they serve as a guide for the proper selection of operating variables (most importantly, pressure drop and pressure level), which is the prime goal of simulation.

A SINGLE-SEGMENT LUMPED PARAMETER MODEL

Although a long pipeline is intrinsically a distributed-parameter system, its single-segment lumped parameter model is useful in checking out the computation algorithms and the soundness of the physical parameters employed in numerical simulation. In this simple model all heat transfer characteristics are evaluated at the pipeline inlet temperature and using a single value of U0, the outlet temperature is obtained by a "single-pass" use of equation 15. In a more sophis- ticated approach the outlet temperature is assumed and the heat transfer characteristics are computed at the average temperature in the pipeline. Then, a second estimate of the outlet temperature is obtained and this iteration is continued until the estimated outlet temperature remains essentially constant. However, this iterative version is not warranted for an a pr ior i crude model. Thus, in the instance of base-run conditions, using m=16 .27kg /s , T0=313K, T1=20.4K, q = 217.024KW, C v = 9.712kJ/kg.K, a single value of

U0 = 0.055 W/mE.K is computed and equation 15 yields T: = 21.03 K. The lumped parameter model obviously underestimates the rise in LH2 temperature along the pipeline but the numerical closeness of this figure to the values shown in Table 4 indicates that there is no sig- nificant error in the syntax of the distributed-parameter model.

MODULAR VARIATIONS OF THE COMPUTER SIMULATION PROGRAM

An important feature of the simulation program is the modular structure of its building blocks. While the main program computes via balances the segment temperatures and pressure, the parameter and data filing and the computation of individual thermal eonductanees is carried out by individual computer subroutines. These subroutines may be removed or modified and further subroutines and initialization routines may be added, if necessary. If the designer wants, for instance, to study the effect of various cryogenic insulations on pipeline performance, only the subroutine which computes kc has to be changed from one simulation run to another. The WATFIV program used for this project contained 227 statements, including documentation comments; in a typical simulation run corresponding to Fig. 2, about 9400 statements are executed and one pipeline simulation would typically require about 1.4 s compilation


time and about 1.6 s execution time on an IBM 4341 computer. Typical execution time for the computer simulation of the single segment lumped parameter model is about 0.25 s.

CONCLUSIONS

It has been shown that the pressure/temperature vari- ation in liquid hydrogen flow in a cryogenic pipeline can be modelled at relative ease and computer-based simu- lations can be performed rapidly and efficiently. The use of such simulation programs is recommended prior to the design of large-scale pipelines for servicing hydrogen-fuelled aircraft at special airports.

REFERENCES

1. Boeing Commercial Airplane Co., Study to determine integrated technology on air transportation system ground requirements of subsonic longhaul, NASA CR-2699 (May 1976).

2. C. D. Brewer, LH2 airport requirements study, Lockheed Co., California NASA CR-2700 (October 1976).

3. J. G. Hoyt, Design concept for LH2 airport facilities, The Ralph M. Parsons Co., Pasadena, California.

4. G. D. Brewer, A proposed liquid hydrogen development program for aircraft, Lockheed Co., California.

5. Anon., Financial Post (19 September, 1981). 6. D. S. Scott (University of Toronto), private communica-

tion (1981). 7. John Mitchell (Transport Canada), private communication

(1981). 8. L. Jones and C. Wuschke, Cryogenic LH2 pipeline simu-

lation for airport ground distribution system, Report SD461/462, Department of System Design, University of Waterloo (1982). R. Barron, Cryogenic Systems. McGraw-Hill, New York (1966). R. C. McCarty, Hydrogen: Its Technology and Implica- tions, Vol. III. CRC Press Inc., Florida (1975). J. J. Tuma, Handbook of Physical Calculations. McGraw-Hill, New York, Florida (1976). G. G. Haselden, Cryogenic Fundamentals. Academic Press, New York (1971). Aerojet-General Corp., Heat transfer to cryogenic hydrogen flowing turbulently in straight and curved tubes at high heat fluxes, NASA CR-678 (February 1967). W. Frost (ed.), Heat Transfer at Low Temperatures. Plenum Press, New York (1975). R. B. Scott, Cryogenic Engineering. Van Nostrand Rein- hold, Wokingham (1959). R. F. Barron, Principles of Evacuated Cryogenic Insula- tions, AIChE Symp. Series No. 125, p. 40 (1968). F. Kreith and W. Z. Black, Basic Heat Transfer. Harper and Row, London (1980). G. H. Bell, Cryogenic Engineering. Prentice Hall, New York (1963).

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Model of a cryogenic liquid-hydrogen pipeline for an airport ground distribution system