Page 182 - Introduction to Computational Fluid Dynamics

P1: IWV
CB908/Date
0 521 85326 5
0521853265c06

6 2D Convection – Complex Domains May 25, 2005 11:10

6.1 Introduction

In practical applications of CFD, one often encounters complex domains. A domain
is called complex when it cannot be elegantly described (or mapped) by a Cartesian
grid. By way of illustration, we consider a few examples.
Figure 6.1 shows the smallest symmetry sector of a nuclear rod bundle placed
inside a circular channel of radius R. There are nineteen rods: one rod at the channel
center, six rods (equally spaced) in the inner rod ring of radius b 1 , and twelve rods in
the outer ring of radius b 2 . The rods are circumferentially equispaced. The radius of
each rod is r o . The fluid (coolant) flow is in the x 3 direction. The flow convects away
the heat generated by the rods and the channel wall is insulated. It is obvious that a
Cartesian grid will not fit the domain of interest because the lines of constant x 1 or x 2
will intersect the domain boundaries in an arbitrary manner. In such circumstances,
it proves advantageous to adopt alternative means for mapping a complex domain.
These alternatives are to use

1. curvilinear grids or
2. finite-element-like unstructured grids.

6.1.1 Curvilinear Grids
It is possible to map a complex domain by means of curvilinear grids (ξ 1 , ξ 2 )in
which directions of ξ 1 and ξ 2 may change from point to point. Also, curvilinear
lines of constant ξ 1 and constant ξ 2 need not intersect orthogonally either within the
domain or at the boundaries. Figure 6.2 shows the nineteen-rod domain of Figure 6.1
mapped by curvilinear grids. The figure shows that curvilinear lines generate clearly
identifiable quadrilateral control volumes. When the IOCV method is used, the task
is to integrate the transport equations over a typical control volume. To facilitate this,
it becomes necessary to first transform the transport equations written in Cartesian

161