Instabilities of Decaying Flow in a Rectangular Channel
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ORIGINAL CONTRIBUTION
Instabilities of Decaying Flow in a Rectangular Channel N. Ramalingam1 • S. P. Das1
Received: 13 December 2019 / Accepted: 30 May 2020 Ó The Institution of Engineers (India) 2020
Abstract Instabilities near the wall of a rectangular water channel in decaying freestream flow is investigated experimentally. A sliding piston imparts trapezoidal velocity variation (constant acceleration from rest, constant velocity, and constant deceleration to rest) onto the freestream in the channel. With the onset of deceleration, a space invariant unsteady wall jet like velocity profiles develop opposite to the flow direction as evident from particle image velocimetry (PIV) measurements. Strong shear and decaying velocity profiles with reverse flow are observed in the deceleration phase and after piston stops. Velocity profiles at this stage are found to be highly inflectional. Dye visualization shows that the outer layer becomes unstable resulting in the formation of array of vortices similar to Kelvin–Helmholtz vortices in shear layer instability. Secondary vortices of opposite sign evolve in the inner layer close to the wall due to the adverse pressure gradient induced by the primary vortices. Vortex formation is not observed below a critical value of Reynolds number. Due to decaying nature of the base flow, i.e., decreasing Reynolds number, the instability vortices do not break down to turbulent flow. The wavelength of instability vortices (k) scales with the average boundary the average being taken from start of layer thickness d, reverse flow to appearance of a vortex. The ratio k=d is 2:6. The vortex formation time scales with the average convective time scale and is 16=ðDu=dÞ, where Du ¼ umax umin and umax ; umin , d are maximum velocity, minimum velocity, and boundary-layer thickness respectively & S. P. Das [email protected] 1
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
of the base flow at any instant. Visualization in the transverse plane reveals vortical structures appear at later times after vortex formation in stream-wise direction indicating three dimensional flow. Keywords Boundary layer Inflectional velocity profile Instability Flow separation Wavelength of vortices
Introduction Time varying fluid flows are present in variety of natural situations as in flapping wings of a bird [1] and respiratory flow in trachea. It also has wide range of technological applications as in rotor blade aerodynamics, reciprocating piston-driven flows, etc. The unsteady flows can be classified into two types, namely, oscillatory flow (zero mean over a cycle) and pulsatile flow (non-zero mean over a cycle). The cyclic nature of the heart pump creates pulsatile conditions in all arteries. Flow in water supply and natural gas pipe lines are pulsatile at start up, shut down, and during change of valve settings. In dynamic stall, sudden change in orientation of the airfoil leads to unsteadiness. A common feature of above flows is the existence
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