Instabilities, bifurcations, and multiple solutions in expanding channel flows.

Area of Science:

• Fluid Dynamics
• Experimental Physics
• Nonlinear Dynamics

Background:

• Classical Jeffery-Hamel flows describe fluid motion in channels with non-parallel walls.
• Understanding these flows is crucial for applications involving complex geometries.
• Previous studies relied on numerical and analytical methods, lacking extensive experimental validation.

Purpose of the Study:

• To experimentally realize and investigate Jeffery-Hamel flows in a wedge-shaped channel.
• To compare experimental velocity fields with Jeffery-Hamel theory predictions.
• To analyze the stability and bifurcation properties of the observed flow regimes.

Main Methods:

• Experimental setup utilizing a wedge-shaped channel.
• Particle Image Velocimetry (PIV) for measuring velocity fields.
• Systematic variation of flow parameters to study bifurcation diagrams.

Main Results:

• Experimental velocity fields closely matched Jeffery-Hamel theory predictions.
• Demonstrated the absolute stability of the pure outflow solution.
• Observed a hysteretic structure in flow bifurcations.
• Confirmed the existence of a multiple-vortex flow regime.

Conclusions:

• The experimental study validates classical Jeffery-Hamel theory in wedge channels.
• The research highlights complex nonlinear behaviors, including hysteresis and multiple vortices.
• Findings provide a foundation for further investigations into non-Newtonian and complex fluid flows.