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Turbulence-driven secondary flows in a curved pipe

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Abstract

If the torque exerted on a fluid element and the source of streamwise vorticity generation are analyzed, a turbulence-driven secondary flow is found to be possible in a curved pipe. Based on this analysis, it is found that the secondary flow is primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend (furthest from the center of curvature of the bend). This secondary flow appears as a counterrotating vortex pair embedded in a Dean-type secondary motion. Recent hot-wire measurements provide some evidence for the existence of this vortex pair. To verify the formation and extent of this turbulence-driven vortex pair further, a near-wall Reynolds-stress model is used to carry out a detailed numerical investigation of a curved-pipe flow. The computation is performed specifically for a U-bend with a full developed turbulent flow at the bend entrance and a long straight pipe attached to the exit. Numerical results reveal that there are three vortex pairs in a curved pipe. The primary one is the Dean-type vortex pair. Another pair exists near the pipe core and is a consequence of local pressure imbalance. A third pair is found near the outer bend and is the turbulence-driven secondary flow. It starts to appear around 60° from the bend entrance, grows to a maximum strength at the bend exit, and disappears altogether at about seven pipe diameters downstream of the bend. On the other hand, calculations of developing laminar curved-pipe flows covering a range of pipe-to-bend curvature ratios, Reynolds number, and different inlet conditions fail to give rise to a third cell near the outer bend. Therefore, experimental and numerical evidence together lend support to the formation of a pair of turbulence-driven secondary cells in curved-pipe flows.

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Author notes

  1. Y. G. Lai

    Present address: CFD Research Corporation, Huntsville, Alabama, U.S.A.

Authors and Affiliations

  1. Mechanical and Aerospace Engineering, Arizona State University, 85287, Tempe, AZ, U.S.A.

    Y. G. Lai, R. M. C. So & H. S. Zhang

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  1. Y. G. Lai
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  2. R. M. C. So
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  3. H. S. Zhang
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Additional information

Communicated by M.Y. Hussaini

Research supported by the Office of Naval Research under Grant No. N0014-81-K-0428 and by the David Taylor Research Center, Annapolis, Maryland, under Contract No. N00167-86-K0075.

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Lai, Y.G., So, R.M.C. & Zhang, H.S. Turbulence-driven secondary flows in a curved pipe. Theoret. Comput. Fluid Dynamics 3, 163–180 (1991). https://doi.org/10.1007/BF00271800

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