Numerical Simulation of the Dynamics of Turbulent Swirling Flames

Turbulent Reacting Flows
Figure 2.1: Measurement of axial velocity on the center line of a turbulent jet.
In [164] from the experiment of Tong and Warhaft [203].
the characteristic length scale of the flow (which depends of the geometry),
respectively. When the Reynolds number exceeds a certain value (called critical
Reynolds number), the flow starts a transition process and the fluctuations
produced by the instability would grow in a chaotic manner leading to the development
of a fully turbulent flow. The inertial forces from convection have a
“destabilization” effect, while the viscous forces try to “stabilize” the flow from
the instability [214]. As illustration, a typical measurement velocity in a turbulent
flow is shown in Fig. 2.1.
The turbulent flow field can be characterized by the Reynolds decomposition
in its steady mean velocity 〈u〉 obtained from a statistical average, and a fluctuating
contribution u ′ superimposed on it [208]:
〈u〉 = 1 T
u(t) = 〈u〉 + u ′ (t), (2.2)
∫ t+T
t
u(t)d t, (2.3)
〈
u ′ (t) 〉 = 0. (2.4)
where T is a time interval much longer than all the time scales of the turbulent
flow [145].
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