Skip to main content
SpringerLink
Log in

Swirling turbulent flow through a curved pipe

Part I: Effect of swirl and bend curvature

Experiments in Fluids volume 14, pages 85–96 (1993)Cite this article

Abstract

An experimental study of a swirling turbulent flow through a curved pipe with a pipe-to-mean-bend radius ratio of 0.077 and a flow Reynolds number based on pipe diameter and mean bulk velocity of 50,000 has been carried out. A rotating section, six pipe diameters long, is set up at six diameters upstream of the curved bend entrance. The rotating section is designed to provide a solid-body rotation to the flow. At the entrance of the rotating section, a fully-developed turbulent pipe flow is established. This study reports on the flow characteristics for the case where the swirl number, defined as the ratio of the pipe circumferential velocity to mean bulk velocity, is one. Wall static pressures, mean velocities, Reynolds stresses and wall shear distribution around the pipe are measured using pressure transducers, rotating-wires and surface hot-film gauges. The measurements are used to analyze the competing effects of swirl and bend curvature on curved-pipe flows, particularly their influence on the secondary flow pattern in the crossstream plane of the curved pipe. At this swirl number, all measured data indicate that, besides the decaying combined free and forced vortex, there are no secondary cells present in the cross-stream plane of the curved pipe. Consequently, the flow displays characteristics of axial symmetry and the turbulent normal stress distributions are more uniform across the pipe compared to fully-developed pipe flows.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Abbreviations

B :

calibration constant

e :

bridge voltage

e 0 :

bridge voltage at zero flow

C f :

total skin friction coefficient, = 2 τ w/ρ W 20

D :

pipe diameter, = 7.62 cm

De :

Dean number, = α 1/2 Re

M :

angular momentum

n :

calibration constant

N s :

swirl number, = ΩD/2 W 0

r :

radial coordinate

R :

mean bend radius of curvature, = 49.5 cm

Re :

pipe Reynolds number, = DW 0/ν

S :

axial coordinate along the upstream (measured negative) and downstream (measured positive) tangent

U, V, W :

mean velocities along the radial, tangential and axial directions, respectively

u, v, w :

mean fluctuating velocities along the radial, tangential and axial directions, respectively

u′, v′, w′ :

root mean square normal stress along the radial, tangential and axial directions, respectively

v {ov2}, u{ov2} :

normal stress along the tangential and radial direction, respectively

W 0 :

mean bulk velocity, ∼ 10 m/s

W c W:

measured at pipe axis

W τ :

total wall friction velocity, \(\sqrt {\left( {\tau _w /\varrho } \right)} \)

\(\left( {w_\tau } \right)_s \) :

total wall friction velocity measured at S/D = -18

ū,v vw, w7#x016B;:

turbulent shear stresses

α :

pipe-to-mean-bend radius ratio, = D/2 R = 0.077

θ :

axial coordinate measured from bend entrance

θ :

fluid kinematic viscosity

ρ :

fluid density

τ w :

mean total wall shear stress

\(\tilde \tau _w \) :

instantaneous total wall shear

ψ :

azimuthal coordinate measured zero from pipe hori zontal diameter near outer bend

Ω :

angular speed of the rotating section

References

  • Agrawal, Y.; Talbot, L.; Gong, K. 1978: Laser anemometer study of flow development in curved circular pipes. J. Fluid Mech. 85, 497–578

    Google Scholar 

  • Akiyama, H.; Hanaoka, Y.; Cheng, K. C; Urai, I.; Suzuki, M. 1983: Visual measurements of laminar flow in the entry region of a curved pipe. Proc. 3rd Int. Symp. Flow visualization, Ann Arbor (ed. Yang, W. J.), 756–760

  • Anwer, M. 1989: Rotating turbulent flow through a 180° pipe bend. PhD thesis, Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USA

    Google Scholar 

  • Anwer, M.; So, R. M. C. 1989: Rotation effects on a fully-developed turbulent pipe flow. Exp. Fluids 8, 33–40

    Google Scholar 

  • Anwer, M.; So, R. M. C. 1990: Frequency of sublayer bursting in a curved bend. J. Fluid Mech. 210, 415–435

    Google Scholar 

  • Anwer, M.; So, R. M. C.; Lai, Y. G. 1989: Perturbation by and recovery from bend curvature of a fully developed turbulent pipe flow. Phys. Fluids A1, 1387–1397

    Google Scholar 

  • Azzola, J.; Humphrey, J. A. C.; lacovides, H.; Launder, B. E. 1986: Developing turbulent flow in a U-bend of circular cross-section: measurement and computation. J. Fluids Eng. 43, 771–783

    Google Scholar 

  • Berger, S. A.; Talbot, L.; Yao, L. S. 1983: Flow in curved pipes. Ann. Rev. Fluid Mech. 15, 471–512

    Google Scholar 

  • Bissonnette, L. R.; Mellor, G. L. 1974: Experiments on the behavior of an axisymmetric turbulent boundary layer with a sudden circumferential strain. J. Fluid Mech. 63, 369–413

    Google Scholar 

  • Bradshaw, P. 1987: Turbulent secondary flows. Ann. Rev. Fluid Mech. 19, 53–74

    Google Scholar 

  • Cheng, K. C.; Yuen, F. P. 1987: Flow visualization studies on secondary flow patterns in straight tubes downstream of a 180 degree bend and in isothermally heated horizontal tubes. J. Heat Transfer 109, 49–54

    Google Scholar 

  • Cheng, K. C.; Inaba, T.; Akiyama, M. 1983: Flow visualization studies of secondary flow patterns and centrifugal instability in curved circular and semicircular pipes. Proc. 3rd Int. Symp. Flow Visualization, Ann Arbor (ed. Yang, W. J.), 531–536

  • Choi, U. S.; Talbot, L.; Cornet, I. 1979: Experimental study of wall shear rates in the entry region of a curved tube. J. Fluid Mech. 93, 465–489

    Google Scholar 

  • Daskopoulos, P.; Lenhoff, A. M. 1989: Flow in curved ducts: bifurcation structure for stationary ducts. J. Fluid Mech. 203, 125–148

    Google Scholar 

  • Dean, W. R. 1928: Fluid motion in a curved channel. Proc. R. Soc. 121 A, 402 -420

    Google Scholar 

  • Enayet, M. M.; Gibson, M. M.; Taylor, A. M. K. P.; Yianneskis, M. 1982: Laser-Doppler measurements of laminar and turbulent flow in a pipe bend. Int. J. Heat Fluid Flow 3, 213–219

    Google Scholar 

  • Kikuyama, K.; Murakami, M.; Nishibori, K. 1983: Development of three-dimensional turbulent boundary layer in axially rotating pipe. J. Fluids Eng. 105, 154–160

    Google Scholar 

  • Kitoh, O. 1987: Swirling flow through a bend. J. Fluid Mech. 175, 429–446

    Google Scholar 

  • Lai, Y. G.; So, R. M. C.; Anwer, M.; Hwang, B. C. 1991a: Calculations of a curved-pipe flow using Reynolds-stress closures. J. Mech. Eng. Sci. 205, 231–244

    Google Scholar 

  • Lai, Y. G.; So, R. M. C.; Zhang, H. S. 1991b: Turbulence-driven secondary flows in a curved pipe. Theor. Comput. Fluid Dyn. 3, 163–180

    Google Scholar 

  • Laufer, J. 1954: The structure of turbulence in fully developed pipe flow. NACA Rep. No. 1174

  • Launder, B. E. 1989: Second-moment closure: present... and future? Int. J. Heat Fluid Flow 10, 282–300

    Google Scholar 

  • Nandakumar, K.; Masliyah, J. H. 1982: Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 150, 139–158

    Google Scholar 

  • Olson, D. E.; Snyder, B. 1985: The upstream scale of flow development in curved circular pipes. J. Fluid Mech. 150, 139–158

    Google Scholar 

  • Rowe, M. 1970: Measurements and computations of flow in pipe bends. J. Fluid Mech. 43, 771–783

    Google Scholar 

  • Shimizu, Y.; Sugino, K. 1980: Hydraulic losses and flow patterns of a swirling flow in U-bends. Bull. JSME 23, 1443–1450

    Google Scholar 

  • So, R. M. C.; Anwer, M. 1992: Swirling turbulent flow through a curved pipe. Part II: Recovery from swirl and bend curvature. Exp. Fluids, accepted for publication

  • So, R. M. C.; Mellor, G. L. 1973: Experiment on convex curvature effects in turbulent boundary layer. J. Fluid Mech. 60, 43–62

    Google Scholar 

  • So, R. M. C.; Mellor, G. L. 1975: Experiments on turbulent boundary layer on a concave wall. Aero. Quart. 26, 25–40

    Google Scholar 

  • So, R. M. C.; Zhang, H. S.; Lai, Y. G. 1991: Secondary cells and separation in developing laminar curved-pipe flows. Theor. Comput. Fluid Dyn. 3, 141–162

    Google Scholar 

Download references

Author information

Author notes

  1. M. Anwer

    Present address: , 4/2 Zikatola, 1209, Dhaka, Bangladesh

Authors and Affiliations

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

    M. Anwer & R. M. C. So

Authors
  1. M. Anwer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. M. C. So
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Anwer, M., So, R.M.C. Swirling turbulent flow through a curved pipe. Experiments in Fluids 14, 85–96 (1993). https://doi.org/10.1007/BF00196992

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00196992

Keywords

search

Navigation