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Transition processes for junction vortex flow

Published online by Cambridge University Press:  07 August 2007

J. J. ALLEN  and
J. M. LOPEZ
J. J. ALLEN
Affiliation:
Department of Mechanical Engineering, New Mexico State University, Las Cruces, NM 88003, USA
J. M. LOPEZ
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
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Abstract

The details of the start-up transient vortex structure that forms near the junction of an impulsively started plate and a stationary plate where a step jump in velocity occurs at the plate surfaces are investigated. Numerical simulations have been conducted in a geometry representative of recent experiments of this flow. The experiments did not have access to data at very early times following the impulsive start, but they did suggest that the flow undergoes transitions from a viscous-dominated phase to an inertia-dominated phase. The numerical simulations presented here are designed to explore the early viscous-dominated transients. The simulations show that when the non-dimensional time, τ = tU2/ν (t is the time that the plate has been in motion and ν is the kinematic viscosity), is less than 100, the development process is dominated by viscous forces. In this regime similarity scaling is used to collapse the data, which scale as . The simulation results at low τ, when evaluated using entrainment diagrams, show an unsteady transition process consisting of the following stages. Initially, the flow consists of a non-rotating vorticity front with a single critical point for τ < 40. For 40 < τ < 50, the flow has three critical points, two nodes and a saddle. A rotational leading jet head develops for τ > 50 as the outermost node evolves into a spiral focus. The simulations span the viscous range to the inertial range. In the inertial range, for τ > 103, the flow structure scales as t5/6, as was observed in the experiments.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 457 - 467
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Allen, J. J. & Chong, M. S. 2000 Vortex formation in front of a piston moving through a cylinder. J. Fluid Mech. 416, 1–28.CrossRefGoogle Scholar
Allen, J. J. & Naitoh, T. 2007 Scaling and instability of a junction vortex. J. Fluid Mech. 574, 1–23.CrossRefGoogle Scholar
Cantwell, B. J. 1986 Viscous starting jets. J. Fluid Mech. 173, 159–189.CrossRefGoogle Scholar
Conlon, B. P. & Lichter, S. 1995 Dipole formation in the transient planar wall jet. Phys. Fluids 7, 999–1014.CrossRefGoogle Scholar
Guezet, J. & Kageyama, T. 1997 Aerodynamic study in a rapid compression machine. Revue Generale de Thermique 36, 17–25.CrossRefGoogle Scholar
Hughes, M. D. & Gerrard, J. H. 1971 The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 2. Experimental investigation and comparison with computation. J. Fluid Mech. 50, 645–655.CrossRefGoogle Scholar
Koseff, J. R. & Street, R. L. 1984 a The lid-driven cavity flow: A synthesis of qualitative and quantitative observations. J. Fluids Engng. 106, 390–398.CrossRefGoogle Scholar
Koseff, J. R. & Street, R. L. 1984 b Visualization studies of a shear driven 3-dimensional recirculating flow. J. Fluids Engng. 106, 21–29.CrossRefGoogle Scholar
Lopez, J. M. & Shen, J. 1998 An efficient spectral-projection method for the Navier–Stokes equations in cylindrical geometries. Part I. Axisymmetric cases. J. Comput. Phys. 139, 308–326.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.CrossRefGoogle Scholar
Tabaczynski, R. J., Hoult, D. P. & Keck, J. C. 1970 High Reynolds number flow in a moving corner. J. Fluid Mech. 42, 249–255.CrossRefGoogle Scholar
Taylor, G. I. 1960 Aeronautics and Aeromechanics. Pergamon.Google Scholar