3 results
Direct numerical simulations of turbulent channel flow with a rib-roughened porous wall
- Kazuhiko Suga, Yusuke Kuwata
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- Journal:
- Journal of Fluid Mechanics / Volume 980 / 10 February 2024
- Published online by Cambridge University Press:
- 08 February 2024, A51
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To describe the effects of porous roughness on turbulence, we have carried out direct numerical simulations using the lattice Boltzmann method. The simulated flows are fully developed turbulent flows in channels consisting of a solid smooth top wall and a porous bottom wall with transverse porous ribs whose heights are 10 % of the channel height. The considered ratios of the rib spacing to the rib height are $w/k\simeq 1$ and 9. The Kelvin-cell structure is applied to construct faithfully the porous media whose porosities are $\varphi \ge 0.79$. Three kinds of porous media having different permeabilities are considered. The most permeable one has an approximately one order higher permeability than that of the least permeable one. The higher permeability case is designed to have a pore scale that is the same as the rib height so that it is the most permeable case for the rib roughness with the designed porosity. In the simulations, the bulk Reynolds number is set to $Re_b=5500$, and the corresponding permeability Reynolds numbers are $Re_K=2.2\unicode{x2013}7.5$. The simulated field data and the drag coefficient, which includes both the pressure drag by the ribs and the frictional drag over the porous wall, are analysed to understand the characteristics of the permeable roughness in terms of permeability. The decomposition of the drag coefficient into the integrated laminar, rib-drag, dispersion and turbulence parts elucidates the transition mechanism between the typical d-type to k-type roughness depending on $Re_K$. By the double (time and space) averaged budget equations for the dispersion and Reynolds stresses, we explain how the energy generated by the roughness transfers to turbulence through dispersion resulting in the k-type characteristics. The nominal roughness sublayer thickness and the characteristic roughness height are introduced with the parameters obtained by fitting the velocity data to Best's and Nikuradse's logarithmic velocity formulae. Along with data in the literature, it is suggested that the ratio of the characteristic roughness height to the nominal roughness sublayer thickness becomes constant irrespective of the rib spacing in the full permeable-wall turbulence at $Re_K> 7$.
Characteristics of turbulent square duct flows over porous media
- Kazuhiko Suga, Yuki Okazaki, Yusuke Kuwata
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- Journal:
- Journal of Fluid Mechanics / Volume 884 / 10 February 2020
- Published online by Cambridge University Press:
- 03 December 2019, A7
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Particle image velocimetry measurements have been carried out to assess the fully developed turbulence in square-sectioned porous duct flows. To the bottom duct wall, this study applies two types of porous media whose porosities are approximately 0.8 and ratios of wall-normal to streamwise permeabilities are 0.8 and 7.8. Both over- and under-surface turbulence of the porous layers are discussed at inlet flow Reynolds numbers of $Re\simeq 3500$ and 7500. Cross-sectional secondary flows are detected with an enhanced magnitude of approximately 6 % of the inlet bulk velocity. The secondary flow pattern consisting of four large vortices is observed to be insensitive to the porous structures. Over the porous wall, although turbulence is enhanced by the permeability, it is confirmed that turbulence over and under the porous surfaces is rather insensitive to the wall-normal permeability compared with the streamwise permeability as seen in porous-wall channel flows. In the present range of streamwise permeability Reynolds numbers of $Re_{K_{x}}=2.49{-}6.37$, the wall-normal fluctuations become dominant once underneath the porous surface while the streamwise ones become dominant again deep inside the porous layer. Applying streamwise–spanwise plane averaging, which covers a 52 % area in the middle of the duct, to the flow quantities, it is confirmed that the correlations between the pore-scale Reynolds number and the log-law parameters are similar to those seen in a wide range of porous-wall channels. The above characteristics are generally the same as those of porous-wall channels in the same range of porosities and permeability Reynolds numbers even with the enhanced secondary flows. However, from the spectral analysis of flows at the porous walls, it is found that, near the symmetry planes, the wavelengths of the Kelvin–Helmholtz waves become a little shorter than those in turbulent porous-wall channels possibly because of the sidewall boundary layers, particularly at low Reynolds numbers.
Anisotropic wall permeability effects on turbulent channel flows
- Kazuhiko Suga, Yuki Okazaki, Unde Ho, Yusuke Kuwata
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- Journal:
- Journal of Fluid Mechanics / Volume 855 / 25 November 2018
- Published online by Cambridge University Press:
- 21 September 2018, pp. 983-1016
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Streamwise–wall-normal ($x$–$y$) and streamwise–spanwise ($x$–$z$) plane measurements are carried out by planar particle image velocimetry for turbulent channel flows over anisotropic porous media at the bulk Reynolds number $Re_{b}=900{-}13\,600$. Three kinds of anisotropic porous media are constructed to form the bottom wall of the channel. Their wall permeability tensor is designed to have a larger wall-normal diagonal component (wall-normal permeability) than the other components. Those porous media are constructed to have three mutually orthogonal principal axes and those principal axes are aligned with the Cartesian coordinate axes of the flow geometry. Correspondingly, the permeability tensor of each porous medium is diagonal. With the $x$–$y$ plane data, it is found that the turbulence level well accords with the order of the streamwise diagonal component of the permeability tensor (streamwise permeability). This confirms that the turbulence strength depends on the streamwise permeability rather than the wall-normal permeability when the permeability tensor is diagonal and the wall-normal permeability is larger than the streamwise permeability. To generally characterize those phenomena including isotropic porous wall cases, modified permeability Reynolds numbers are discussed. From a quadrant analysis, it is found that the contribution from sweeps and ejections to the Reynolds shear stress near the porous media is influenced by the streamwise permeability. In the $x$–$z$ plane data, although low- and high-speed streaks are also observed near the anisotropic porous walls, large-scale spanwise patterns appear at a larger Reynolds number. It is confirmed that they are due to the transverse waves induced by the Kelvin–Helmholtz instability. By the two-point correlation analyses of the fluctuating velocities, the spacing of the streaks and the wavelengths of the Kelvin–Helmholtz (K–H) waves are discussed. It is then confirmed that the transition point from the quasi-streak structure to the roll-cell-like structure is characterized by the wall-normal distance including the zero-plane displacement of the log-law velocity which can be characterized by the streamwise permeability. It is also confirmed that the normalized wavelengths of the K–H waves over porous media are in a similar range to that of the turbulent mixing layers irrespective of the anisotropy of the porous media.