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

87
c1 c2 c3 c1w c2w
1.8 0.6 0.5 0.5 0.3
Table 3.4 – The coefficients required in the basic Reynolds-stress closure.
It has been reported [51] thatφ w ij
in the form shown above does not perform
well in all situations. It gives satisfactory results for flows parallel to single
walls, but in an impinging jet flow, for example, it does not work well. Its un-
satisfactory behavior can be explained as follows. In a near wall shear flow,
φij2 tends to decrease a component of production of the stress dependent on
anisotropy ofPij and to redistribute it between the other components of stress.
Theφ w ij2
acts against this process and tends to reduce stress normal to the wall.
In an impinging flow, the production term of the stress equation tends to in-
crease the component of stress normal to the wall andφij2 is designed to redis-
tribute energy, so tends to reduce the stress normal to the wall. As mentioned
before, φ w ij2
acts against this process but this time tends to increase stress nor-
mal to the wall which is against the concept of the wall reflection terms.
Another form ofφ w ij2
in impinging flow as well as simple shear:
was suggested by Craft and Launder[52] to work well
φ w ij2 = −0.08 ∂Ul
l
ulum(δij −3ninj)
∂xm 2.5y
∂Uk
−0.1kalm nlnkδij −
∂xm
3 ∂Ui
nlnj −
2∂xm
3 ∂Uj
2∂xm
+0.4k ∂Ul
nlnm ninj −
∂xm
1
3 δij
l
2.5y
nlni
then this form of wall reflection term is used in the present study.
l
2.5y
(3.56)
The other term which needs modelling is εij. In high Reynolds number
flows, because of local isotropy, εij can be modelled as follows:
εij = −2ν ∂ui ∂uj
∂xk ∂xk
≈ 2
3 εδij
(3.57)