Page 61 - Design and Operation of Heat Exchangers and their Networks

48 Design and operation of heat exchangers and their networks

2.1.5 Axial dispersion models for design and rating of heat
exchangers

In heat exchangers having complex structure, there might exist severe mal-
distribution caused by bypassing, dead zones, recirculatings, and other non-
uniformities of fluid flow. In such cases, the axial dispersion model can be
used to take the influence of the nonuniform velocity distribution into
account.
The axial dispersion model was first proposed by Taylor (1954) for tur-
bulent mass transfer in tubes. It assumes that the fluid flow is fully mixed in
the lateral direction perpendicular to the flow direction and is also mixed to
some extent in the flow direction. Mecklenburgh and Hartland (1975)
introduced the axial dispersion term A c D(∂t/∂x) into the energy equation
of the fluid and suggested that the axial dispersion model can be used for the
thermal calculation of heat exchangers. The axial dispersion coefficient D
has the same dimension as the thermal conductivity λ, but it is not a fluid
property. The value of the axial dispersion coefficient depends on the flow
pattern in the heat exchanger and should be determined experimentally.
Diaz and Aguayo (1987) numerically investigated the effect of the axial dis-
persion on the steady-state thermal performance of heat exchangers. They
found that the fluid flow in a heat exchanger can be considered as a plug flow
if the axial dispersive Peclet number Pe¼uL/D>100. If Pe<20, the axial
dispersion should be taken into account. Roetzel and his coworkers (Spang,
1991; Xuan, 1991; Lee, 1994; Luo, 1998; Balzereit, 1999; Roetzel, 1996)
carried out a series of theoretical and experimental investigations on the axial
dispersion in heat exchangers.
The original parabolic dispersion model is applied in which the prop-
agation velocity of thermal disturbances is assumed to be infinitely
high, expressed by a zero dispersive Mach number, Ma¼0. Later, the
hyperbolic dispersion model has been investigated and further developed
in which finite propagation velocities are considered (Luo and Roetzel,
1995; Roetzel and Das, 1995; Roetzel et al., 1998; Roetzel and Na
Ranong, 1999; Sahoo and Roetzel, 2002; Das and Roetzel, 2004),
which are more realistic for maldistribution effects. The type and degree
of deviations from the plug flow are expressed with the dispersive Peclet
number 0 Pe ∞ and the dispersive Mach number 0 Ma ∞.Their
research shows that the axial dispersion model is suitable for the simulation
of the complicated flow and heat transfer in the heat exchangers, especially
for the dynamic simulation.