Page 497 - Mechanical Engineers' Handbook (Volume 4)

486 Cryogenic Systems

corrugated sheets of aluminum coated with brazing flux. This assembly is then immersed in
molten salt where the aluminum brazes together at points of contact. After removal from the
bath the salt and flux are washed from the exchanger paths, and the assembly is enclosed
in end plates and nozzles designed to give the desired flow arrangement. Usually the ex-
changer is roughly cubic, and is limited in size by the size of the available salt bath and the
ability to make good braze seals in the center of the core. The core can be arranged for
countercurrent flow or for cross flow. Figure 21 shows the construction of a typical plate-fin
exchanger.
Procedures for calculating heat-transfer and pressure loss characteristics for plate-fin
exchangers have been developed and published by the exchanger manufacturers. Table 4 and
Fig. 22 present one set of these.

3.3 Regenerators
A regenerator is essentially a storage vessel filled with particulate solids through which hot
and cold fluid flow alternately in opposite directions. The solids absorb energy as the hot
fluid flows through, and then transfer this energy to the cold fluid. Thus this solid acts as a
short-term energy-storage medium. It should have high heat capacity and a large surface
area, but should be designed as to avoid excessive flow pressure drop.
In cryogenic service regenerators have been used in two very different applications. In
engine liquefiers very small regenerators packed with, for example, fine copper wire have
been used. In these situations the alternating flow direction has been produced by the intake
and exhaust strokes of the engine. In air separation plants very large regenerators in the form
of tanks filled with pebbles have been used. In this application the regenerators have been
used in pairs with one regenerator receiving hot fluid as cold fluid enters the other. Switch
valves and check valves are used to alternate flow to the regenerator bodies, as shown in
Fig. 23.
The regenerator operates in cyclical, unsteady-state conditions. Partial differential equa-
tions can be written to express temperatures of gas and of solid phase as a function of time
and bed position under given conditions of flow rates, properties of gaseous and solid phases,
and switch time. Usually these equations are solved assuming constant heat capacities, ther-
mal conductivities, heat-transfer coefficients, and flow rates. It is generally assumed that flow
is uniform throughout the bed cross section, that the bed has infinite conductivity in the
radial direction but zero in the longitudinal direction, and that there is no condensation or
vaporization occurring. Thermal gradients through the solid particles are usually ignored.
These equations can then be solved by computer approximation. The results are often ex-
pressed graphically. 26
An alternative approach compares the regenerator with a steady-state heat exchanger
and uses exchanger design methods for calculating regenerator size. 27 Figure 24 shows the
temperature–time relationship at several points in a regenerator body. In the central part of
the regenerator Ts are nearly constant throughout the cycle. Folding the figure at the switch
points superimposes the temperature data for this central section as shown in Fig. 25. It is
clear that the solid plays only a time-delaying function as energy flows from the hot stream
to the cold one. Temperature levels are set by the thermodynamics of the cooling curve such
as Fig. 15 presents. Thus, the q UA T equation can be used for small sections of the
regenerator if a proper U can be determined.
During any half cycle the resistance to heat transfer from the gas to the solid packing
will be just the gas-phase film coefficient. It can be calculated from empirical correlations
for the packing material in use. For pebbles, the correlations for heat transfer to spheres in