Page 76 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 63

In this case, the acceleration pressure drop is usually negligible compared
with the total pressure drop, except in the case of flow boiling or flow
condensation.
For two-phase in a straight channel, the acceleration pressure drop is
often expressed as
" # " #
G 2 G 2 G 2 G 2
g l g l
Δp a,1 2 ¼ + + (2.170)
aρ 1 aÞρ aρ 1 aÞρ
g ð l g ð l
2 1
For variable cross-sectional area, Eq. (2.171) can be used for the calcu-
lation of the acceleration pressure drop:
" 2 !#
1 G G 2
1 g l
dp a ¼ d _m g u g + _m l u l ¼ d A c + (2.171)
A c A c aρ ð 1 aÞρ
g l
2.3 Heat exchanger dynamics

Heat exchanger dynamics is very important for the design of automatic con-
trol systems dealing with heat exchangers and their networks. The task of the
dynamic analysis of a heat exchanger is to obtain the dynamic response of the
outlet fluid temperatures to the variations of various operating conditions.
The linearization method and Laplace transform are the useful tools for
the dynamic analysis of heat exchangers.

2.3.1 Linearization of nonlinear problems with small
disturbances

If the properties of fluids and wall materials depend on temperature, or ther-
mal flow rates of fluids and heat transfer coefficients between the fluids and
heat transfer surfaces vary with time, the dynamic thermal analysis of heat
exchangers is a nonlinear problem. To simplify the problem, one can use
average values of properties, thermal flow rates, and heat transfer coefficients
in the real operation region of the heat exchanger to get a linear mathemat-
ical model. With this method, the transient temperature responses of heat
exchangers to the disturbances in inlet fluid temperatures can be obtained
analytically. However, if the disturbances to be investigated are thermal flow
rates or heat transfer coefficients or the properties strongly depend on the
temperatures, this method cannot be used.
Another linearization method is the method for small disturbances.
Assume that the properties of the fluids and wall materials in the heat