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Unsteady flow in rotating drums using laser Doppler velocimetry

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Abstract

Non-destructive measurements by laser Doppler velocimetry is employed to study unsteady flow in a hollow drum filled with liquid. The drum is suddenly accelerated from rest or is suddenly decelerated from a steady rotation to rest. Pure water and glycerin-water mixtures are used as the test liquid in which polyethylenelatex particles are mixed as the light scattering tracer. The boundary layer formation, the time history of velocity, momentum and kinetic energy of the liquid, the wall-to-fluid force transfer, and the transient response time are determined. Also determined are the effects of side walls and fluid viscosity on the transient flow response. Of importance is the disclosure of Ekman layer instability near the inner radial wall of the test drum. It is actuated by the centripetal acceleration-induced buoyancy force.

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Abbreviations

A :

wetted surface area of test drum, cm2

a :

reciprocal of characteristic velocity, = t sH, s/cm

B :

width of test drum, cm

b :

axial coordinate of test drum, cm

D :

diameter of test drum, cm; D 1, inner diameter; D 2, outer diameter

d :

diameter of laser beam, mm

d p :

particle diameter, mm

E :

kinetic energy of liquid, kg · cm2/s2; E s, steady value

F :

force transferred from drum walls to liquid, N

f :

focal length of lens, mm

G :

one-half of spacing between two parallel split beams, Fig. 1

H :

characteristic length of test drum, cm; = V/A

M :

momentum of liquid, kg·cm/s; M s, steady value

m :

mass of control volume, kg

r :

radial coordinate of test drum, cm

S :

fringe spacing, mm

t :

time, s

t p :

time for particle to travel through fringe spacing, s

t s :

transient time, s

u :

liquid velocity, cm/s

V :

liquid volume in test drum, cm3

V s :

effective volume of sample volume, mm3

v :

velocity of tracer particle, cm/s; = S/t

W :

waist diameter of parabola in Fig. 2, mm

(x, y, z):

coordinates for paraboloid in Fig. 2, mm

θ :

crossing angle of splitting beams, degrees

λ :

wavelength of laser length, cm

v :

kinematic viscosity, cm2/s

ϱ :

liquid density, kg/cm3

φ :

Doppler frequency, l/s

s:

at steady state

1:

outer

2:

inner

References

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  2. Drain, L. E. 1980: The laser Doppler technique, p. 241. New York: Wiley

  3. Greenspan, H. P. 1968: The theory of rotating fluids. Cambridge: Cambridge Univ. Press

  4. Kohashi, Y. 1974: Flow measurements by lasers. J. Jpn. Soc. Mech. Eng. 77, 297–303 (in Japanese)

  5. Nakaya, N.; Yamada, A. 1976: Measurements of flow by lasers. Res. Mach. 28, 377–383 (in Japanese)

  6. Nakayama, Y. 1980: Techniques of flow measurements and visualization. Res. Mach. 32, 1447–1451 (in Japanese)

  7. Owen, J. M. 1984: Fluid flow and heat transfer in rotating disc. systems. In: Heat and mass transfer in rotating machinery (eds. Metzger, D. E.; Afgan, N. H.), pp. 81–103. Washington/DC: Hemisphere

  8. Schlichting, H. 1968: Boundary layer theory. New York: McGraw-Hill

  9. Takahei, T. (ed.) 1983: The application of laser Doppler velocimetry. Tokyo: Power Comp

  10. Yih, C.-S. 1977: Fluid mechanics. Ann Arbor: West River Press

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On leave from the Dept. of Mechanical Engineering, Musashi Institute of Technology, Tokyo, Japan

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Kawashima, G., Yang, W. Unsteady flow in rotating drums using laser Doppler velocimetry. Experiments in Fluids 6, 165–171 (1988). https://doi.org/10.1007/BF00230728

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Keywords

  • Boundary Layer
  • Velocimetry
  • Transient Response
  • Buoyancy Force
  • Unsteady Flow