Page 225 - Introduction to Computational Fluid Dynamics

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10 0 521 85326 5 2D CONVECTION – COMPLEX DOMAINS
OUTER (COLD) Ra = 4.8 × 10 4
8 ∈/L = 0.652

6
K eq INNER (HOT)

4

2

0
0 50 100 150
Θ
Figure 6.24. K eq versus θ for natural convection in an eccentric annulus.

in this region. It must be mentioned, however, that the results with quadrilateral
meshes compare extremely favourably with previous curvilinear grid predictions
[32, 58]. It is for this reason that many CFD analysts prefer to use quadrilateral
elements near curved surfaces while still employing triangular elements away
from such surfaces. Thus, they prefer to use mixed elements for the domain as
a whole.
Figure 6.25 shows the vector plots on the two meshes. It is seen that there is
a strong upward flow near the hot inner cylinder where density is lower. Mass
conservation, however, requires that circulation be set up with a downwards flow
neartheoutercylinder.Thereis,however,aregionofweakcontrarotatingcirculation

TRIANGULAR QUADRILATERAL

Figure 6.25. Vector plots for natural
convection in an eccentric annulus.