DNS OF A FULLY DEVELOPED TURBULENT POROUS CHANNEL FLOW BY THE LATTICE BOLTZMANN METHOD

Abstract

To understand the turbulent flow physics over permeable porous surfaces, a direct numerical simulation (DNS) of a turbulent channel flow over a porous layer is performed by the D3Q27 multiple-relaxation time lattice Boltzmann method. The bulk mean Reynolds number is 3000 and the presently considered porous layer, whose porosity is 0.71, consists of staggered cube arrays. Using the DNS results, the phenomenological discussions through the twopoint autocorrelation, one-dimensional energy spectrum and proper orthogonal decomposition (POD) analyses are carried out. The reason why the streaky structure over the porous layer becomes shorter, wider and obscurer than that near the solid wall are discussed. It is found that the low wavenumber turbulence is enhanced over the porous layer. This low wavenumber large-scale motions are considered to stem from the Kelvin-Helmholtz instability due to the weakened wall-blocking effect and the strong shear over the porous layer. BACKGROUND Due to its high heat and mass transfer efficiency, porous structures commonly play important role in industrial fields and thus understanding and modelling the flows over porous media are industrially crucial issues. To understand the turbulent flow physics over permeable porous surfaces, partially direct numerical simulations (DNSs) of turbulent channel flows over porous layers were performed by Breugem et al.(2006). Although they solved the turbulent flows directly in the clear channel region, they applied the volume averaged momentum equation to the porous regions. Since their simulations did not take account of the influence of not only the porous structure but also the dispersion, the predicted turbulence phenomena around and inside the porous layers might not be exactly correct. Recently, Chandesris et al. (2013) performed a full DNS study for a low Prandtl number (Pr=0.1) heat transfer field with the same flow conditions as those of Breugem et al. (2006). Although they resolved the model porous structure, it was an unrealistically revitating structure. Since their focus was on heat transfer, they did not provide further information on the turbulent flow physics than that by Breugem et al. (2006). The turbulent porous channel flows were also investigated experimentally by Suga et al.(2010 and 2011), however, due to the difficulty of the measurements inside the porous media, the measurements were limited to the clear channel regions. Accordingly, as far as the authors know, there is no study on the precise turbulence structure in the interface region over the porous layer. Therefore in this study, a DNS study of a turbulent channel flow over a porous layer is performed. To directly treat the porous structure, the D3Q27 multiple relaxation time lattice Boltzmann method of Suga et al.(2015) is employed. NUMERICAL SCHEME The present DNS is performed by the D3Q27 multiple relaxation time lattice Boltzmann method (MRT-LBM) (Suga et al.,2015) whose time evolution equation is | f (x+ξ α δ t, t +δ t)⟩− | f (x, t)⟩ = −M−1Ŝ[| m(x, t)⟩− | meq(x, t)⟩] , (1) where the notations such as |f ⟩ is |f ⟩ = ( f0, f1, · · · , f26) , δ t is the time step andξ α is the discrete velocity. The transformation matrixM is a 27× 27 matrix which linearly transforms the distribution functions to the moments as|m⟩ = M |f ⟩. The collision matrixŜ is diagonal: Ŝ≡ diag(0,0,0,0,s4,s5,s5,s7,s7,s7,s10,s10,s10,s13, s13,s13,s16,s17,s18,s20,s20,s20,s23,s23,s23,s26). (2) The relaxation parameters presently applied are from Suga et al.(2015) as s4 = 1.54, s5 = s7, s10 = 1.5, s13 = 1.83, s16 = 1.4, s17 = 1.61, s18 = s20 = 1.98, s23 = s26 = 1.74. (3) The kinematic fluid viscosityν is related to the relaxation parameters5, ν = cs ( 1 s5 − 1 2 ) δ t, (4) wherecs/c = 1/ √ 3 andc = ∆/δ t where∆ is the lattice spacing. For the other details, see Suga et al.(2015). To reduce the computational costs, the multi-block method proposed by Dupuis et al. (2003) is modified and employed in this study. To take account of the continuity of 1 June 30 July 3, 2015 Melbourne, Australia 9 2B-4