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Rotation effects on a fully-developed turbulent pipe flow

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Abstract

A fully-developed turbulent pipe flow is allowed to pass through a rotating pipe section, whose axis of rotation coincides with the pipe axis. At the exit end of the rotating section, the flow passes into a stationary pipe. As a result of the relaxation of surface rotation, the turbulent flow near the pipe wall is affected by extra turbulence production created by the large circumferential shear strain set up by the rapid decrease of the rotational velocity to zero at the wall. However, the flow in the most part of the pipe is absent of this extra turbulence production because the circumferential strain is zero as a result of the solid-body rotation imparted to the flow by the rotating pipe section. The combined effect of these two phenomena on the flow is investigated in detail using hot-wire anemometry techniques. Both mean and turbulence fields are measured, together with the wall shear and the turbulent burst behavior at the wall. A number of experiments at different rotational speeds are carried out. Therefore, the effects of rotation on the behavior of wall shear, turbulent burst at the wall, turbulence production and the near-wall flow can be documented and analysed in detail.

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Abbreviations

a :

radius of the pipe

C f1 :

friction coefficient, \(\tau _w /\frac{1}{2}\rho W_0^2 \)

C f2 :

friction coefficient, \(\tau _w /[\frac{1}{2}\rho (W_0^2 + (a\Omega )^2 )]\)

D :

diameter of the pipe

E τw (f) :

energy spectrum of shear stress

f b :

dimensional burst frequency

\(\bar f_b \) :

normalized burst frequency, \(\frac{{f_b }}{{\left( {f_b } \right)_0 }}\)

F :

normalized kurtosis, \(\frac{{(\overline {\tau _w^{'4} } )/(\overline {\tau _w^{'2} } )^2 }}{{[(\overline {\tau _w^{'4} } )/(\overline {\tau _w^{'2} } )^2 ]_0 }}\)

k :

threshold level (used in VITA)

N s :

swirl number, aΩ/W 0

P(T) :

probability of inter-burst time, T

r :

radial coordinate

S :

normalized skewness, \(\frac{{(\overline {\tau _w^{'3} } )/(\overline {\tau _w^{'2} } )^{3/2} }}{{[(\overline {\tau _w^{'3} } )/(\overline {\tau _w^{'2} } )^{3/2} ]_0 }}\)

t :

integration time (used in VITA)

T B :

mean inter-burst time, 1/f b

\(\bar T_B \) :

normalized scaled burst frequency, \(\frac{{w_\tau ^2 T_B /v}}{{\left( {w_\tau ^2 T_B /v} \right)_0 }}\)

U, V, W :

mean velocity components in radial, circumferential and axial directions, respectively

u′, v′, w′ :

fluctuating components of velocity in radial, circumferential and axial directions, respectively

W 0 :

axial bulk mean velocity

w τ :

friction velocity, \(\left( {\frac{{\tau _w }}{\rho }} \right)^{1/2} \)

X :

distance measured from the entrance of the bend

δ :

thickness of the viscous layer

ν :

kinematic viscosity

ρ :

density of fluid

σ :

normalized standard deviation, \(\frac{{(\overline {\tau _w^{'2} } )^{1/2} }}{{(\overline {\tau _w^{'2} } )_0^{1/2} }}\)

Ω :

rotational speed of pipe in RPM

0:

condition at X/D=-18

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Authors and Affiliations

  1. Mechanical and Aerospace Engineering, Arizona State University, 85287-6106, Tempe, AZ, USA

    M. Anwer & R. M. C. So

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  1. M. Anwer
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  2. R. M. C. So
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Anwer, M., So, R.M.C. Rotation effects on a fully-developed turbulent pipe flow. Experiments in Fluids 8, 33–40 (1989). https://doi.org/10.1007/BF00203062

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