Numerical Simulation of the Dynamics of Turbulent Swirling Flames

Turbulent Reacting Flows
Some of these drawbacks can be overcome using a dynamic formulation
of the constant C s at each point and at each time step [63, 65] (but it can
become computationally unstable [63,211]), or using a damping function
(as the Van Driest function [133, 205]) to recover the correct behavior at
the wall.
• The WALE Model:
The Wall-Adapting Local Eddy-viscosity (WALE) model from Nicoud and
Ducros [133] is based on the square of the velocity gradient tensor g i j
g i j
= ∂u i
∂x j
, (2.60)
and developed for wall bounded flows in an attempt to reproduce the
proper scaling at the wall (ν t =O(y 3 )).
The SGS turbulent viscosity is defined as:
ν t = ( C w ¯∆ e
) 2
(
S d i j Sd i j
) 3/2
) 5/2 ( ) 5/4
(2.61)
(S i j S i j + S d i j Sd i j
where,
S d i j = 1 ( )
g 2 i j
2
+ g 2 j i
− 1 3 δ i j g 2 kk , (2.62)
= S i k S k j + Ω i k Ω k j − 1 )
3 δ i j
(S mn S mn − Ω mn Ω mn , (2.63)
where Ω the anti-symmetric part of g :
Ω i j = 1 ( ∂ui
− ∂u )
j
. (2.64)
2 ∂x j ∂x i
The model constant C w = 0.4929 is set in AVBP. The WALE model is used
in the present study because [133]:
(a) the spatial operator consists of a mixing of the local strain and rotation
rates. All the turbulence structures relevant for the kinetic energy
dissipation are detected by the model.
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