This study has been carried out at ICMCB (Bordeaux, France) under the supervision of Jalil Ouazzani and Yves Garrabos.
The instabilities appeared in two-dimensional single-phase conunterflowing jets.
Figure 1: Instability schematics of some property X (measured at a fixed position) in function of time.
The jets evolve until a stabilization is reached. After a certain amount of time, the solution destabilizes with growing amplitude periodic oscillations, finally leading to chaotic behavior.
In this study, the balance equations for the laminar two-dimensional case without external forces can be written as
where a cartesian coordinate system have been used in a 100x100 non-uniform grid.
Deflecting jets instability:
Jet nozzles are separated a distance h and have a diameter d. Reynolds number ranges between Re=1000 and Re=2000.
Antisymmetric case:
Figure 2: Velocity contours of the deflecting jets instability. Blue: v=0, red: v=1. Re=1000, h/d=10.
Symmetric case:
Figure 3: Velocity contours of the deflecting jets instability. Blue: v=0, red: v=1. Re=1000, h/d=100.
Capillary waves instability:
Superimposed to the deflecting jets instability, a new type of instability appears at Re>1000 (for h/d=10) in form of capillary waves:
Figure 4: Velocity contours of the capillary waves instability. Blue: v=0, red: v=1. Re=2000, h/d=10.
The capillary waves instability is inhibited by turbulent mechanisms. Within the Chen and Kim turbulence model, the equation for the turbulent kinetic energy is
where S is the rate-of-strain tensor
The equation for the turbulent dissipation can be written as
The equations have been solved using the SIMPLE algorithm in conjunction with the CHARM differencing scheme.
Figure 5: Inhibition of capillary waves instability by turbulent mechanisms. Top: Laminar case. Bottom: Turbulent case (Chen and Kim variant of the k-epsilon model).
