Optimization and Computational Fluid Dynamics - Department of ...

224 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto
(a)
Fig. 8.3 Computational domain for the CC heat exchanger: a undulated plates to be
stacked; b final geometry of CC channel; c periodic module
Before describing the boundary conditions, it is useful to focus on the
meaning of the pressure term along with the mean flow direction, x, ofthe
channel. Omitting any discussion about the entrance and exit regions of the
channel, in the fully developed regime zone the velocity profiles can be considered
periodic (of the same period as the channel). On the other hand,
the effect of the pressure field is to allow the fluid flow, acting against friction
forces due to the viscous behavior of the mean. The dissipative work is
negligible and its contribution is not included in the energy equation, yet a
pressure drop is present along the streamwise direction. The pressure field
can be split into two contributions [49]:
1. a linear decaying, which counteracts friction forces;
2. a periodic term related to the detailed local motion.
It follows that the pressure assumes the following expression:
(b)
(c)
p(x, y, z)=−β · x +˜p(x, y, z) (8.4)
where ˜p(x, y, z) is the periodic part of the pressure. Therefore, the momentum
equation in the x direction can be rewritten as:
∇·(ρuu)=∇·(μ∇u) − ∂˜p
+ β (8.5)
∂x
where β becomes a volume force term whose value, influencing the Reynolds
number obtained, will be adjusted in the solution procedure.
8.3.2 Fluid Dynamic Boundary Conditions
The condition of periodic velocity profiles can be expressed in the inlet and
outlet boundaries, as illustrated in Fig. 8.1 for the 2D wavy-channel, as fol-