Unsteady Laminar Duct Flow With a Given Volume Flow Rate Variation

[+] Author and Article Information
D. Das, J. H. Arakeri

Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India

J. Appl. Mech 67(2), 274-281 (Sep 15, 1999) (8 pages) doi:10.1115/1.1304843 History: Received July 17, 1998; Revised September 15, 1999
Copyright © 2000 by ASME
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Szymanski,  P., 1932, “Some Exact Solutions of the Hydrodynamic Equations of a Viscous Fluid in the Case of a Cylindrical Tube,” J. Math. Pures Appl., 11, pp. 67–107.
Uchida,  S., 1956, “The Pulsating Viscous Flow Superposed on the Steady Laminar Motion of Incompressible Fluids in a Circular Pipe,” Z. Angew. Math. Phys., 7, pp. 403–422.
Weinbaum,  S., and Parker,  K., 1975, “The Laminar Decay of Suddenly Blocked Channel and Pipe Flows,” J. Fluid Mech., 69, pp. 729–752.
Das, D., 1998, Ph.D. thesis, Department of Mechanical Engineering, I.I.Sc., Bangalore, India.
Das,  D., and Arakeri,  J. H., 1998, “Transition of Inflectional Velocity Profiles With Reverse Flow,” J. Fluid Mech., 374, pp. 251–283.
Lefebvre,  P. J., and White,  F. M., 1989, “Experiments on Transition to Turbulence in a Constant-Acceleration Pipe Flow,” ASME J. Fluids Eng., 111, pp. 428–432.
Wemersley,  J. R., 1955, “Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient is Known,” J. Physiol., 127, pp. 553–563.
Akhavan,  R., Kamm,  R. D., and Shapiro,  A. H., 1991, “An Investigation of Transition to Turbulence in Bounded Oscillatory Stokes Flows, Part 1—Experiments,” J. Fluid Mech., 225, pp. 395–422.


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The variation of pressure gradient with time for trapezoidal piston motion
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Velocity profiles at different times (a) during the acceleration of the piston motion (profiles are shown at time intervals of to*/6), (b) when the piston velocity is constant (profiles are at time intervals of (t1*−to*)/6), (c) during the deceleration of the piston velocity (profiles are at time intervals of (t2*−t1*)/4), and (d) after the piston motion has stopped (profiles are at time intervals of (0.0427−t2*)/6)
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Velocity profiles at different nondimensional times for constant acceleration of the piston motion
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Velocity profiles (a) and pressure gradient (b) for impulsively started motion
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Comparison of the present solution (solid line) for the unidirectional oscillatory flow starting from rest with the experimental data of Akhavan et al. 8 (symbols)
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Velocity profiles at different phases for two cycles, for oscillating pipe flow starting from rest at t=0(R/2ν/ω=10)




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