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Instability and transition in an elementary porous medium

Xu Chu1,*, Yongxiang Wu2, Ulrich Rist2, and Bernhard Weigand1

  • 1Institute of Aerospace Thermodynamics, University of Stuttgart, Pfaffenwaldring 31, D-70569 Stuttgart, Germany
  • 2Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, D-70569 Stuttgart, Germany

  • *xu.chu@itlr.uni-stuttgart.de
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Phys. Rev. Fluids 5, 044304 – Published 22 April, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.044304

Abstract

Instability and transition in an elementary porous medium are investigated via global linear stability analysis and numerical simulation. The porous medium is presented by a representative elementary volume which consists of a staggered array of square cylinders. The stability analysis indicates the first critical Reynolds number at Recr≈84. Two unstable modes are captured from the linear stability analysis: a two-dimensional oscillatory mode and a three-dimensional stationary mode. A series of analyses based on direct and adjoint methods is conducted on both the unstable modes. The energy analysis shows that lift-up and converging-flow effects are both responsible for the unstable modes. In the numerical simulation, the averaged fluctuation profiles exhibit spatial distributions similar to those of the perturbation kinetic energy from the three-dimensional mode, which confirms the prediction from the stability analysis. In addition, we observe stationary counterrotating streamwise vortices beginning at the subcritical Reynolds number, which is a consequence of lift-up instability.

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Information

Phys. Rev. Fluids 5, 044304– Published 22 April, 2020
  • Received 18 December 2019
  • Accepted 31 March 2020
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