# Swirling turbulent flow through a curved pipe

## 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

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