Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface-Resolved Direct Numerical Simu
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Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface‑Resolved Direct Numerical Simulation Xu Chu1 · Wenkang Wang1 · Guang Yang2 · Alexandros Terzis3 · Rainer Helmig4 · Bernhard Weigand1 Received: 29 July 2020 / Accepted: 2 November 2020 © The Author(s) 2020
Abstract Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers ( Re ≈ 3000, 6000 ) and two porosities ( 𝜑 = 0.5, 0.8 ). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile. Keywords Porous media · Direct numerical simulation · Channel flow with porous wall List of symbols ⋅ Time average ⟨⋅⟩ Intrinsic area average ⟨⋅⟩s Superficial area average * Wenkang Wang [email protected]‑stuttgart.de 1
Institute of Aerospace Thermodynamics, University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
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Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, 200240 Shanghai, China
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Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, 3200003 Haifa, Israel
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Institute for Modelling Hydraulic and Environmental Systems, University of Stuttgart, Pfaffenwaldring 61, 70569 Stuttgart, Germany
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⟨⋅⟩ca Conditional average ⋅′ Instantaneous turbulent fluctuation ̃⋅ Form-induced fluctuation ̂⋅ Fourier transformation u, v, w Streamwise, wall-normal, and spanwise velocity x, y, z Streamwise, wall-normal, and spanwise direction P, C, T, Π, D𝜈 , 𝜀 Production, convection, turbulent diffusion, velocity-pressure diffusion, viscous diffusion, and dissipation Lx , Ly , Lz Dimension of the computation domain Δx, Δy, Δz Spatial resolution of the computation domain H Half height of the computation domain h Half height of the free flow channel D Distance between cylinders Dc Diameter of the cylinders p u𝜏,ut𝜏 Friction velocities at permeable wall and top wall + Normalized by friction velocity and kinematic vis
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