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Published on: August 27, 2013
Stability of vortex flow in a modulated channel.
Ehab Abu-Ramadan1, Roger E Khayat
1Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9.
Summary
This study numerically analyzes fluid flow in a modulated channel. Increasing wall modulation decreases the critical Reynolds number, promoting instability and vortex formation.
Area of Science:
- Fluid dynamics
- Hydrodynamic stability
Background:
- Investigates linear stability of two-dimensional periodic steady flow.
- Focuses on spatially modulated symmetric channels with sinusoidal wall modulations.
Purpose of the Study:
- Numerically analyze flow stability in modulated channels.
- Examine the influence of geometric parameters on instability thresholds.
- Investigate vortex flow effects on stability.
Main Methods:
- Employs a regular perturbation expansion for base flow calculation.
- Utilizes Floquet theory and a two-point boundary value method for disturbance analysis.
- Validates a simple, direct, and efficient numerical procedure.
Main Results:
- Critical Reynolds number decreases with increasing wall modulation amplitude or wave number.
- Modulated channel flow exhibits recirculation regions or vortices above a critical threshold.
- Stable vortex flow parameter regime expands with modulation wave number, especially at low values.
Conclusions:
- Hydrodynamic instability is promoted by wall modulation.
- Vortex formation is linked to instability onset.
- Wall modulation wave number significantly impacts stable vortex flow regimes.
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