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The energy transfer mechanism of a perturbed solid-body rotation flow in a rotating pipe

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Abstract

Three-dimensional direct numerical simulations of a solid-body rotation superposed on a uniform axial flow entering a rotating constant-area pipe of finite length are presented. Steady in time profiles of the radial, axial, and circumferential velocities are imposed at the pipe inlet. Convective boundary conditions are imposed at the pipe outlet. The Wang and Rusak (Phys. Fluids 8:1007–1016, 1996. doi:10.1063/1.86882) axisymmetric instability mechanism is retrieved at certain operational conditions in terms of incoming flow swirl levels and the Reynolds number. However, at other operational conditions there exists a dominant, three-dimensional spiral type of instability mode that is consistent with the linear stability theory of Wang et al. (J. Fluid Mech. 797: 284–321, 2016). The growth of this mode leads to a spiral type of flow roll-up that subsequently nonlinearly saturates on a large amplitude rotating spiral wave. The energy transfer mechanism between the bulk of the flow and the perturbations is studied by the Reynolds-Orr equation. The production or loss of the perturbation kinetic energy is combined of three components: the viscous loss, the convective loss at the pipe outlet, and the gain of energy at the outlet through the work done by the pressure perturbation. The energy transfer in the nonlinear stage is shown to be a natural extension of the linear stage with a nonlinear saturated process.

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Acknowledgements

The project was supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant 11601411) and the Scientific Research Program Funded by Shannxi Provincial Education Department (Grant 15JK1313).

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Authors and Affiliations

  1. School of Aeronautics, Northwestern Polytecrhnical University, Xi’an, 710072, China

    Chunjuan Feng

  2. Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, 92697, USA

    Feng Liu

  3. Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Zvi Rusak

  4. Department of Mathematics, University of Auckland, Auckland, 1142, New Zealand

    Shixiao Wang

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  1. Chunjuan Feng
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  2. Feng Liu
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  3. Zvi Rusak
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  4. Shixiao Wang
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Correspondence to Chunjuan Feng.

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Feng, C., Liu, F., Rusak, Z. et al. The energy transfer mechanism of a perturbed solid-body rotation flow in a rotating pipe. Acta Mech. Sin. 33, 274–283 (2017). https://doi.org/10.1007/s10409-017-0642-2

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