

Artikel
The planar Xjunction flow: stability analysis and control
Författare: 
Lashgari, I., Tammisola, O., Citro, V., Giannetti, F., Brandt, L.B. 
Dokumenttyp: 
Artikel 
Tillstånd: 
Publicerad 
Tidskrift: 
Journal of Fluid Mechanics 
Volym: 
753
128 
År: 
2014 
AbstractThe bifurcations and control of the flow in a planar Xjunction are studied via linear stability analysis and direct numerical simulations. This study reveals the instability mechanisms in a symmetric channel junction and shows how these can be stabilized or destabilized by boundary modification. We observe two bifurcations as the Reynolds number increases. They both scale with the inlet speed of the two side channels and are almost independent of the inlet speed of the main channel. Equivalently, both bifurcations appear when the recirculation zones reach a critical length. A twodimensional stationary global mode becomes unstable first, changing the flow from a steady symmetric state to a steady asymmetric state via a pitchfork bifurcation. The core of this instability, whether defined by the structural sensitivity or by the disturbance energy production, is at the edges of the recirculation bubbles, which are located symmetrically along the walls of the downstream channel. The energy analysis shows that the first bifurcation is due to a liftup mechanism. We develop an adjustable control strategy for the first bifurcation with distributed suction or blowing at the walls. The linearly optimal wallnormal velocity distribution is computed through a sensitivity analysis and is shown to delay the first bifurcation from Re = 82.5 to Re = 150. This stabilizing effect arises because blowing at the walls weakens the wallnormal gradient of the streamwise velocity around the recirculation zone and hinders the liftup. At the second bifurcation, a threedimensional stationary global mode with a spanwise wavenumber of order unity becomes unstable around the asymmetric steady state. Nonlinear threedimensional simulations at the second bifurcation display transition to a nonlinear cycle involving growth of a threedimensional steady structure, timeperiodic secondary instability and nonlinear breakdown restoring a twodimensional flow. Finally, we show that the sensitivity to wall suction at the second bifurcation is as large as it is at the first bifurcation, providing a possible mechanism for destabilization.

