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

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8.7 Closing remarks
In this chapter the numerical simulation of annular horizontal penetration
byk-ε-AWF is presented at two different Rayleigh numbers (Ra = 4.5×10 8 and
Ra = 3.1 × 10 13 ). The simulations are carried out with both steady-state and
time-dependent methods to obtain greater understanding of the flow phenom-
ena. The steady-state simulation of the lower Ra case showed that within the
annular penetration there are irregular flow structures, which suggested exis-
tence of flow unsteadiness. The flow field is non-symmetric at the closed end
of the penetration and becomes more symmetric towards the open end. Turbu-
lence levels at this Rayleigh number are low and also that at some regions be-
come negligible. Time-dependent simulation of the lower Ra case showed that
the the flow inside the penetration changes with time. The time-dependency of
the flow near the closed end of the penetration is strong and it becomes weaker
in the cross-sections close to the open end of the penetration. An oscillatory
behaviour was observed in the downward flow inside the penetration which
separates from the cold tube. The time-averaged axial velocity is stronger than
the axial velocity resulting from the steady-state simulation. This is of course
an important characteristic of this flow and these comparisons suggest that,
for this Rayleigh number, it is necessary to employ a time-dependent RANS
approach to reproduce it reliably.
The steady-state simulation of the higher Ra case showed that the nor-
malisedk levels increased by an order of magnitude. Downward velocity near
the closed end of the penetration are more symmetric at the higher Rayleigh
number, which suggests that there is less large-scale unsteadiness. The axial
velocity at the higher Rayleigh number is stronger due to the stronger buoy-
ancy force at the higher Ra level. The time-dependent simulation of the higher
Ra case showed that the instantaneous vertical velocity, in common with those
at the lower Rayleigh number, has oscillatory pattern within the penetration,
but perhaps with smaller amplitude. The time-averaged predictions of ver-
tical velocity within the penetration are close to those of the steady RANS
computations. Distribution of time-averaged and steady-state axial velocity
are in close agreement over the entire length of the penetration but the steady
RANS predictions return a stronger axial flow within the penetration than the