Optimization and Computational Fluid Dynamics - Department of ...

228 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
∆T =(Tbi) h − (Tbo) c =(Tbo) h − (Tbi) c
(8.22)
U is the global heat transfer coefficient, and A is a reference heat transfer
surface, that has been taken as twice the projection of the interface wall on
the horizontal plane, A =2· Ah. This choice allows the comparison of heat
transfer coefficients for different surface geometries.
8.4 Numerical Methods
The numerical solution of the 2D and 3D wavy channel case was carried out by
means of the COMSOL software package [9]. Full details of the methodology
have been previously published elsewhere [30] and are summarized hereafter.
For the numerical simulation of the CC heat exchanger module, the ANSYS-
CFX CFD package has been employed. Hexahedral structured grids have
been generated by means of the ICEM-CFD grid generation package.
8.4.1 Fluid Dynamic Iterative Solution
For the wavy and CC channels the fluid dynamic equations are solved in a
similar way. As shown in Eq. (8.5), a forcing term β appears, due to the pressure
splitting introduced in Eq. (8.4). Since the Reynolds number is a given
constant of the problem, the non-dimensional mean velocity in the channel
must be unitary. It is, therefore, necessary to find the correct value of β that
ensures this condition. Other authors [31] have used proportional-integrative
iterative controls to reach the correct value of the pressure gradient, starting
from a trial value. At first, a similar approach has been attempted, but it
proved to be not very efficient in converging to the correct value of β, and
this can be a limiting factor for CPU-intensive optimization studies.
By the definition of the friction factor f as the non-dimensional surface
shear stress [49], it is easy to show by applying the second Newton’s law that:
f = β Dh
1
2 ρU2 av
. (8.23)
Recall that, for internal flows in laminar regime, the friction factor is proportional
to the inverse of the Reynolds number. From the definition of Re, it
follows that:
β ∝ Uav . (8.24)
This relation is not strictly valid in channels with varying cross section, but
nevertheless it is expected a proportionality law such as: