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Oscillating radial flow between parallel plates

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Abstract

An analysis is presented for laminar radial flow due to an oscillating source between parallel plates. The source strength varies according to Q=Q 0 cos ωt, and the solution is in the form of an infinite series in terms of a reduced Reynolds number, R *a =Q 0/4πνa/(r/a)2. (Q 0 = amplitude of source strength, ω = frequency, a = half distance between plates, r = radial coordinate, t = time, and ν = kinematic viscosity.) The results are valid for small values of R *a and all values of the frequency Reynolds number, α=ωa 2/ν. The effects of the parameters R *a and α are discussed.

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Abbreviations

a :

half distance between plates

r :

radial coordinate

r :

dimensionless radial coordinate, r/a

z :

axial coordinate

z :

dimensionless axial coordinate, z/a

t :

time

t :

dimensionless time, tv/a 2

R :

dimensionless radial coordinate of a cross-section in the flow

ū :

velocity component in radial direction

u :

dimensionless velocity component in radial direction, ūa/ν

v :

velocity component in axial direction

v :

dimensionless velocity component in axial direction, va/v

p :

pressure

p :

dimensionless pressure, pa 2/ρν 2

Q :

instantaneous source strength

Q 0 :

amplitude of source strength

ω :

frequency

R a :

amplitude of source Reynolds number, Q 0/4πνa

R *a :

amplitude of reduced Reynolds number, Q 0/r 2

α :

frequency Reynolds number, ωa 2/ν

ρ :

density

μ :

viscosity

ν :

kinematic viscosity, μ/ρ

τ 1 :

shear stress at the upper boundary

τ 1 :

dimensionless shear stress at the upper boundary, τ 1/(μQ 0/4πa 2r)

References

  1. Uchida, S., ZAMP 7 (1956) 403.

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  2. Na, T. Y., E. G. Nielsen and J. D. Grossman, ASME publication 67 - WA/FE - 20, Winter Annual Meeting, Nov. 1967.

  3. Elkouh, A. F., Appl. Sci. Res. 21 (1969) 284.

    Google Scholar 

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Authors and Affiliations

  1. Mech. Eng. Dept., Marquette Univ., Milwaukee, Wisconsin, USA

    A. F. Elkouh

Authors
  1. A. F. Elkouh
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Elkouh, A.F. Oscillating radial flow between parallel plates. Applied Scientific Research 30, 401–417 (1975). https://doi.org/10.1007/BF00455965

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  • DOI: https://doi.org/10.1007/BF00455965

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