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Transition, turbulence and oscillating flow in a pipe a visual study

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Abstract

Transitional and turbulent oscillatory flow in a rigid pipe with long entry sections was investigated using flow visualization to establish the existence of coherent structures. Flow tracer and high speed motion pictures were used. The simple harmonic motion of a scotch yoke and flywheel linked to a piston and cylinder provided the flow driving force. The camera was convected with the flow by attaching it through a gearing system to the scotch yoke.

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Abbreviations

A :

cross sectional area of flow

C, K :

constants

D :

pipe diameter

N Re,ave :

Reynolds number based on average velocity (DU ave /v)

N Re,p :

Reynolds number based on maximum oscillatory velocity (DU max /v)

\(N_{Re,\delta } \) :

Reynolds number based on maximum oscillatory velocity and Stokes (boundary) layer thickness (δU max /v)

R :

pipe radius

U :

instantaneous velocity in the flow direction

Ū:

short-term average instantaneous velocity \(\left( {\frac{1}{T}\int\limits_T {U dt} } \right)\)

U * :

friction velocity (U ave (f/2)1/2)

U amp :

amplitude parameter (U max /U ave )

U ave :

average velocity \(\left( {\frac{1}{{AT}}\int\limits_T {\int\limits_A U {\text{ dA dt}}} } \right)\)

U s :

steady velocity

U t :

instantaneous oscillatory velocity

U max :

maximum oscillatory velocity (π X max /T)

u r , u z :

deviations from Ūr, and Ūz

y :

radial coordinate from wall (R−r)

y + :

dimensionless radial coordinate from wall (y U*/v)

α :

frequency parameter [R (ω/v) 1/2]

δ :

Stokes (boundary) layer thickness [C (2 v/ω)1/2]

θ :

normalized time into cycle

μ :

fluid viscosity

v :

fluid kinematic viscosity (μ/ϱ)

ϱ :

density

ω :

angular frequency (2π/T)

-:

overbar, average

sub-c :

critical value

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Authors and Affiliations

  1. 606 Solano Circle, 92670, Placentia, CA

    L. S. Fishler

  2. Dept. of Chemical Engineering, The Ohio State University, 140 W. 19th Ave., 43210-1180, Columbus, OH

    R. S. Brodkey

Authors
  1. L. S. Fishler
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  2. R. S. Brodkey
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Fishler, L.S., Brodkey, R.S. Transition, turbulence and oscillating flow in a pipe a visual study. Experiments in Fluids 11, 388–398 (1991). https://doi.org/10.1007/BF00211793

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