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

Introduction 44
3 1/4
ν
ν
1/2 η ≡ ,τ ≡ ,υ ≡ (νε)
ε ε
1/4
(1.1)
These scales are called the Kolmogorov microscales of length, time and
velocity[9].
1.2.3 Turbulent buoyancy-driven flow
Turbulent flows can be greatly influenced by body forces. One of the most
common examples is the effect of gravity on flows with density fluctuations.
This can occur in flows in which there are variations of mean density. One ex-
ample of such a case is flow over heated or cooled horizontal plates. Another
case is a flow which is driven by mean density difference, such as buoyant cav-
ity flows, or buoyant plumes in still air. In a situation that a unstable thermal
stratification ,which means the hot surface is located below the cold surface, is
imposed to a volume of fluid, mean density fluctuates due to mean tempera-
ture fluctuations. In turn, the mean density fluctuation gives rise to buoyancy
force and velocity fluctuations which increases the amount of turbulence in the
flow.
In situations where density increases in the vertical direction, the flow is
unstable and consequently the potential energy is converted into turbulent ki-
netic energy. In this case, the buoyancy force leads to an increase in the level of
turbulence. On the other hand, when the density decreases vertically in a way
that its gradient is steeper than would be the case for hydrostatic equilibrium,
the turbulent kinetic energy is converted into potential energy[10]. In this case,
the buoyancy force leads to a decrease in the level of turbulence in the flow.
1.3 Turbulence modelling
The main priority in many studies of turbulence is to contribute to the de-
velopment of mathematical models that can reliably and efficiently compute
relevant quantities in practical applications. Past decades of research on tur-
bulent flows have proved that it is impossible to obtain a simple analytical
solution[9]. Instead the application of computers is increasingly growing as