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Particle image velocimetry measurements of flow field behind a circular square-edged orifice in a round pipe

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Abstract

In this paper, we use a planar particle image velocimetry system to measure the flow field downstream of a circular square-edged orifice plate in a round pipe. The flow field is a fully developed pipe flow well upstream of the orifice plate. The Reynolds number based on pipe diameter and cross-sectional mean velocity is in the range of 25,000–55,000. We present detailed mean and turbulent fields and investigate similarities and differences with other separated flows. A noteworthy difference is the formation of a vena contracta behind the orifice at a distance of approximately one pipe radius. Upstream of the vena contracta, the properties of the shear layers in the orifice flow are quite similar to those of other separated flows. However, because the shear layer in the orifice flow begins to merge at a distance of approximately one pipe diameter, it is significantly different from the shear layers in other separated flows. Finally, we assess the reliability of the Reynolds stress model to represent orifice flows by comparing numerical results with experimental results.

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Abbreviations

d :

Orifice throat diameter

h :

Orifice step height

L :

Measurement area length

l :

Orifice thickness, l = 5 mm

D :

Pipe inner diameter, D = 46 mm

R :

Pipe radius, R = D/2

\(\beta\) :

Orifice ratio, \(\beta \equiv d/D\)

v :

Kinematic viscosity of the working fluid

U 0 :

Pipe cross-sectional mean streamwise velocity

U d :

Cross-sectional mean streamwise velocity at the orifice throat

U max :

Maximum mean streamwise velocity

U cl :

Centerline mean streamwise velocity

u, v :

Streamwise and vertical components of the instantaneous velocity

U, V :

Streamwise and vertical components of the mean velocity

u′, v′:

Streamwise and vertical components of the fluctuating velocity

u rms, v rms :

Root mean square of the fluctuating velocity

\(u_{\text{rms}}^{\text{p}}\), \(v_{\text{rms}}^{\text{p}}\) :

Peak values of u rms and v rms at each streamwise location

\(\kappa\) :

Turbulent kinetic energy, \(\kappa = \frac{1}{2}( < u^{\prime } u^{\prime } > + < v^{\prime } v^{\prime } > + < w^{\prime } w^{\prime } > )\)

Re :

Pipe Reynolds number, Re ≡ U 0 D/v

Re h :

Reynolds number based on orifice height and cross-sectional mean streamwise velocity at orifice throat, Re ≡ U d h/v

x :

Downstream distance from the orifice plate

y :

Vertical distance from the pipe center

y w :

Vertical distance from the pipe wall

x r :

Shear-layer reattachment length

\(x_{r2}\) :

Length of the secondary recirculation region

\(\lambda\) :

Filter cutoff wavelength

\((\nabla \varvec{u})_{{2{\text{D}}}}\) :

Two-dimensional velocity gradient

\(\Upomega_{{2{\text{D}}}}\) :

Swirling strength

\(\omega_{z}\) :

Out-of-plane vorticity

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Acknowledgments

We gratefully acknowledge the reviewers for their valuable comments and for identifying mistakes in the draft version of this paper. In addition, the first author wants to acknowledge the China Scholarship Council (CSC) and the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT). His Ph.D. study is supported by a cooperative agreement between CSC and MEXT.

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Authors and Affiliations

  1. Department of Energy Engineering and Science, Nagoya University, Nagoya, 464-8603, Japan

    Feng Shan, Atsushi Fujishiro, Tatsuya Tsuneyoshi & Yoshiyuki Tsuji

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  1. Feng Shan
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  2. Atsushi Fujishiro
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  3. Tatsuya Tsuneyoshi
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  4. Yoshiyuki Tsuji
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Correspondence to Feng Shan.

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Shan, F., Fujishiro, A., Tsuneyoshi, T. et al. Particle image velocimetry measurements of flow field behind a circular square-edged orifice in a round pipe. Exp Fluids 54, 1553 (2013). https://doi.org/10.1007/s00348-013-1553-z

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