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

Annular horizontal penetration 392
8.6 Time-dependent simulation (Ra = 3.1×10 13 )
Figures 8.42-8.56 show the solution of 3D time dependent simulation of
the horizontal penetration test case at the higher Ra using the k-ε-AWF. In the
steady-state simulation, it has been observed that results are not completely
symmetrical, specially inside the tube away from the open end of the tube.
That is why time dependent calculations have been carried out for this case, to
reach a better understanding how flow develops in the horizontal penetration.
In the time dependent calculations, the normalized time step is set equal
to 0.19,normalized by D2
V0 (where D2 is the diameter of the tube and V0 =
√ gβ∆ΘD2) and the implicit scheme is employed for time descritisation. In
each time step, it is set to iterate 20 times unless it gets to convergence criteria
(all residuals below 10 −3 ).
Figures 8.42-8.45 show the velocity contours within the central, X=0, longi-
tudinal (y-z) plane. For the vertical, V, velocity component, Figure 8.43, as was
also the case at the lower Ra number, Figure 8.18, the non-uniformity of the
contours suggests the presence of large-scale flow structures, which change
with time, both within and outside the penetration. It is difficult to detect a
Rayleigh number effect from these comparisons. By contrast, the correspond-
ing comparisons for the axial velocity, Figures 8.44 and 8.19, show that at the
higher Ra the axial velocity field shows no signs of unsteadiness whereas at
the lower Ra, the effects of large-scale unstable structures are clearly evident.
This leads to the conclusion that at the higher Ra, the unstable flow structures
are less influential.
Figures 8.46-8.51 show contours of the vertical and axial velocities and of
the turbulent kinetic energy within a number of cross-sections inside the pene-
tration, at Z=0.23, 0.46, 0.69 and 0.87 and at different times. The contours of the
instantaneous vertical velocity, in common with those at the lower Rayleigh
number of Figures 8.21 to 8.24, show flow oscillations within the penetration,
but perhaps with smaller amplitude. While, also in common with the lower
Ra behaviour, these oscillations considerably weaken at the exit, Z=0.87, they
can still be detected, but confined to the region below the inner pipe.