Page 337 - Design and Operation of Heat Exchangers and their Networks

Dynamic analysis of heat exchangers and their networks 323

distributed parameter model, the axial dispersion model takes the effect of
flow maldistributions on the dynamic behavior of heat exchangers into
account.
The cell method can be used for the heat exchangers with complex flow
patterns. In the cell method, the heat transfer surface is divided into several
subregions (cells), which are connected according to the real flow passages.
Each cell is considered as a single heat exchanger of which the type is most
closed to the real flow pattern. Thus, the performance and dynamic behavior
of the whole apparatus can be simulated by a system of interconnected
subunits (cells).
The numerical computation model is based on computational fluid
dynamics; therefore, it is often called CFD model. The fluid velocity distri-
butions in the flow passages of a heat exchanger and temperature distribu-
tions in the fluid and solid materials of the exchanger can be described in
detail with the Navier-Stokes equations and energy equations together with
a set of boundary conditions representing the complex structure of the
exchanger. For turbulent flow, additional relations and/or equations
describing the turbulent characteristics are needed. The resulting mathemat-
ical model is nonlinear and very complicated and can be solved only with a
numerical method, for example, finite-difference method or finite-element
method. Using a numerical method, one can obtain the whole time-
dependent velocity and temperature fields in the heat exchanger as well
as the local heat transfer coefficient and friction factor. Nowadays, the
CFD method has been well developed and can be found in numerous books.
The commercial CFD software such as FLUENT and ANSYS has been suc-
cessfully applied to the dynamic simulation of different kinds of heat
exchangers. A detailed introduction of the CFD method does not belong
to the task of this book. In this book, only the first four models will be
introduced.

7.1.1 Lumped parameter model

In the lumped parameter model, it is assumed that each fluid in the whole
heat exchanger has the same uniform temperature. The temperatures of the
fluids and the solid wall are only a function of time. In the early research of
heat exchanger dynamics, lumped parameter models were used to obtain the
transform functions of the outlet fluid temperatures to the disturbances in the
inlet fluid temperatures and mass flow rates. Hsu and Gilbert (1962) col-
lected a number of transfer functions for various types of heat exchangers.