Optimization and Computational Fluid Dynamics - Department of ...

28 Gábor Janiga
be shown later, the POF is clearly visible as soon as enough non-dominated
configurations have been identified and plotted.
All parameters of the EA procedure used in this work are listed later in
corresponding sections (Table 2.2, 2.4 and 2.6). Parameters usually chosen in
the literature as well as further parameter sets have been tested extensively in
previous works [6], showing that the values retained in these tables are wellsuited
for the problems considered here. The applied mutation probability
may seem quite high. It should be pointed out, that the mutation magnitude
is continuously decreasing at each generation to stabilize the population. A
high initial mutation probability is needed to obtain a fine-grain resolution
of the POF.
2.3 The Optimal Position of the Tubes in a Heat
Exchanger (Case A)
2.3.1 Tube Bank Heat Exchanger
A two-dimensional model of a cross-flow tube bank heat exchanger is considered
first. One possible configuration can be seen in Fig. 2.1. Air enters the
domain at Tinlet = 293 K and is warmed up by passing between the tubes in
which warm fluid flows in the corresponding practical application. The tubes
are supposed to have a constant outer wall temperature, Twall = 353 K. The
outlet is at atmospheric pressure.
The optimization problem consists of finding the best locations of the tubes
to increase heat exchange while at the same time to limit the pressure loss.
The two corresponding numerical parameters to optimize are the average
temperature difference ∆T and pressure difference ∆P between inflow and
outflow.
The domain bounded by a black line in Fig. 2.1 is simulated in this
study. The Reynolds number is equal to 41 defined using the tube diameter
D = 2 cm and the uniform velocity at the inlet, vinlet =0.03 m/s. The
length of the domain has been chosen to prevent any influence of the inflow
or outflow boundary conditions on the inter-blade flow. Corresponding tests
have, in particular, demonstrated the importance of extending the computational
domain well beyond the last tube in order to avoid the influence of the
outflow boundary conditions. The full extent of the numerical domain and a
typical numerical grid can be seen in Fig. 2.5.
The stability analysis in Barkley and Henderson [5] proved that threedimensional
effects first appear at a Reynolds number around 188 in the
flow around a cylinder. Furthermore, the flow around a single cylinder is
steady up to a Reynolds number of 46 [4]. In the present investigation, several
cylinders are simulated and will interact with each other, but due to the low