The computation of turbulent natural convection flows - Turbulence ...

Inclined Cavity-2D simulations 192
The local Nusselt numbers are calculated as Nu = −L(∂Θ/∂xi) w /(Θh −Θc),
where L is distance between the hot and the cold walls.
x
y
Y=0.17
H
Hot Wall
Cold Wall
5 Degree
Figure 6.57 – Schematic of5◦ stable inclined tall cavity and its thermal boundary
condition.
6.6.2 Flow pattern
Adiabatic
Y=0.35
The flow pattern of air inside the 5 ◦ stable inclined tall cavity predicted by
the k-ε using LRN, AWF and SWF is shown in Figures 6.58-6.63. In this test
case,because of the temperature difference between the tall walls, 3 circulation
cells are created. One circulation cell covers most of the cavity apart from the
top right corner and the bottom left corner regions, in which the fluid is al-
most stagnant. Within this primary circulation cell, for some cases, there are
two smaller counter rotating circulation cells near the centre of the cavity. The
predicted distance between these two smaller circulation cells, from different
turbulence models varies. The temperature contours reveal that within the top
left corner and the bottom right corner heat is transfered almost in conduction
mode only, because of almost stagnant fluid and weak convection in those re-
gions. It is worth to note that the uniform temperature near the two ends of
the cavity is due to convection which moves the hot flow toward the top and
the cold flow toward the bottom. In the case of high turbulence flow, due to
high mixing, the temperature field tends to be uniform and equal to the aver-
age temperature. In this test case, low-turbulent flow exists near the hot and
the cold walls where circulation is present.
Y=0.5
Y=0.7
Y=0.87
Adiabatic
L