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

Introduction 42
1.2 Turbulent flow
1.2.1 Characteristics
Most flows found in industrial applications are turbulent flows. Among
these industrial applications, we can identify boundary layers growing on air-
craft wings, combustion processes, natural gas and oil flow in pipelines and
the wakes of ships, cars, submarines and aircraft.
It is difficult to state a definition for turbulent flow. The best way is to
explain different characteristics of the turbulence. The first feature of turbu-
lent flow is irregularity. That is why analytical methods are not suitable for
turbulent flow and statistical and numerical methods are employed to resolve
the turbulent flow. Another characteristic of turbulence is its diffusivity. The
turbulence diffusivity is used to denote the mixing of momentum, mass and
thermal energy by the turbulent eddies. The diffusivity of turbulence is the
most important effect of turbulence in industrial applications. For example it
will delay separation in flows over airfoils at high angles of attack, or will in-
crease heat transfer rates etc.
Two major dimensionless numbers in forced and mixed convection are the
Rayleigh and Reynolds numbers. They are defined as:
Ra = βg∆ΘL3
να
Re = UL
ν
where the symbols are defined as: β: volumetric expansion coefficient,g: grav-
ity acceleration, ∆Θ: temperature difference, L: length scale, ν: kinetic viscos-
ity, α: thermal diffusivity and U: velocity scale.
Turbulent flows occur at high Reynolds numbers in the case of forced con-
vection and at high Rayleigh numbers in the case of natural convection. Be-
cause of the inherent apparent randomness and the nonlinearity of turbulent
flows, the phenomenon is almost intractable. Both mathematical models and