BAIL 2006 Book of Abstracts - Institut für Numerische und ...

M. HÖLLING, H. HERWIG: Computation of turbulent natural convection at vertical
walls using new wall functions
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T in K
380
370
360
350
340
330
8×200
4×200
DNS
320
0 0.05
y in m
0.1
u in m/s
0.25
0.2
0.15
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
8×200
4×200
DNS
−0.25
0 0.05
y in m
0.1
Figure 1: Temperature and velocity profile of Versteegh and Nieuwstadt [3] for Ra = 5.0 · 10 6
compared to results of the modified CAFFA code using two grid sizes.
that it is inadequate for natural convection. Instead of trying to find another modification of
an existing turbulence model, the deficiences could be compensated by modifying the boundary
conditions for k and ω.
The results are again compared to the DNS data of Versteegh and Nieuwstadt [3] and good
agreement is found. Figure 1 shows the temperature and velocity profile for Ra = 5.0 · 10 6
together with the results of the modified CAFFA code. Two different grid sizes were used and
despite the very few control volumes (8 and 4 CVs) across the channel width the profiles are
matched very well. Also the wall gradients, i.e. the Nusselt number and the shear stress, are
correct within 4 %.
References
[1] T. Tsuji and Y. Nagano, “Characteristics of a turbulent natural convection boundary layer
along a vertical flat plate”, Int. J. Heat Mass Transfer 31, 1723–1734 (1989).
[2] W.K. George and S.P. Capp, “A theory for natural convection turbulent boundary layers
next to heated vertical surfaces”, Int. J. Heat Mass Transfer 22, 813–826 (1979).
[3] T.A.M. Versteegh and F.T.M. Nieuwstadt, “A direct numerical simulation of natural convection
between two infinite vertical differentially heated walls: scaling laws and wall functions”,
Int. J. Heat Mass Transfer 42, 3673–3693 (1999).
[4] R.A.W.M. Henkes and C.J. Hoogendoorn, “Numerical determination of wall functions for
the turbulent natural convection boundary layer”, Int. J. Heat Mass Transfer 33, 1087–
1097 (1990).
[5] M. Hölling and H. Herwig, “Asymptotic analysis of the near wall region of turbulent natural
convection flows”, J. Fluid Mech. 541, 383–397 (2005).
[6] J.H. Ferziger and M. Peric, “Computational methods for fluid dynamics”, 2nd ed., Springer,
Berlin (1999).
Speaker: HÖLLING, M. 92 BAIL 2006
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