# Swirling turbulent flow through a curved pipe

- Received:

- 16 Citations
- 446 Downloads

## 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.

### List of symbols

*B*calibration constant

*e*bridge voltage

*e*_{0}bridge voltage at zero flow

*C*_{f}total skin friction coefficient, = 2

*τ*_{w}/ρ W_{0}^{2}*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}Wmeasured 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

## Preview

Unable to display preview. Download preview PDF.

### References

- Agrawal, Y.; Talbot, L.; Gong, K. 1978: Laser anemometer study of flow development in curved circular pipes. J. Fluid Mech. 85, 497–578Google 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.), 756–760Google Scholar
- Anwer, M. 1989: Rotating turbulent flow through a 180° pipe bend. PhD thesis, Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ, USAGoogle Scholar
- Anwer, M.; So, R. M. C. 1989: Rotation effects on a fully-developed turbulent pipe flow. Exp. Fluids 8, 33–40Google Scholar
- Anwer, M.; So, R. M. C. 1990: Frequency of sublayer bursting in a curved bend. J. Fluid Mech. 210, 415–435Google 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, 1387–1397Google 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, 771–783Google Scholar
- Berger, S. A.; Talbot, L.; Yao, L. S. 1983: Flow in curved pipes. Ann. Rev. Fluid Mech. 15, 471–512Google 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, 369–413Google Scholar
- Bradshaw, P. 1987: Turbulent secondary flows. Ann. Rev. Fluid Mech.
**19**, 53–74Google 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, 49–54Google 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.), 531–536Google Scholar
- 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, 465–489Google Scholar
- Daskopoulos, P.; Lenhoff, A. M. 1989: Flow in curved ducts: bifurcation structure for stationary ducts. J. Fluid Mech. 203, 125–148Google Scholar
- Dean, W. R. 1928: Fluid motion in a curved channel. Proc. R. Soc. 121 A, 402 -420Google 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, 213–219Google Scholar
- Kikuyama, K.; Murakami, M.; Nishibori, K. 1983: Development of three-dimensional turbulent boundary layer in axially rotating pipe. J. Fluids Eng. 105, 154–160Google Scholar
- Kitoh, O. 1987: Swirling flow through a bend. J. Fluid Mech. 175, 429–446Google 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, 231–244Google 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, 163–180Google Scholar
- Laufer, J. 1954: The structure of turbulence in fully developed pipe flow. NACA Rep. No. 1174Google Scholar
- Launder, B. E. 1989: Second-moment closure: present... and future? Int. J. Heat Fluid Flow 10, 282–300Google Scholar
- Nandakumar, K.; Masliyah, J. H. 1982: Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 150, 139–158Google Scholar
- Olson, D. E.; Snyder, B. 1985: The upstream scale of flow development in curved circular pipes. J. Fluid Mech. 150, 139–158Google Scholar
- Rowe, M. 1970: Measurements and computations of flow in pipe bends. J. Fluid Mech. 43, 771–783Google Scholar
- Shimizu, Y.; Sugino, K. 1980: Hydraulic losses and flow patterns of a swirling flow in U-bends. Bull. JSME 23, 1443–1450Google 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 publicationGoogle Scholar
- So, R. M. C.; Mellor, G. L. 1973: Experiment on convex curvature effects in turbulent boundary layer. J. Fluid Mech. 60, 43–62Google Scholar
- So, R. M. C.; Mellor, G. L. 1975: Experiments on turbulent boundary layer on a concave wall. Aero. Quart. 26, 25–40Google 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, 141–162Google Scholar