Wake Characterisation of 3-Dimensional Multiscale Porous Obstacles

Abstract

In this research article we study the wake formation behind 3-Dimensional Multi-scale Porous Obstacles (3DMPOs). Particle Imaging Velocimetry (PIV) is used in a non-shallow ($B/h =1.5$) water flume, with measurements carried out across the $x$ - $y$ plane (at $z$ = 130 mm) and with $Re=70,000$ based on the free-stream velocity ($U_{\infty}$). To characterise the downstream wake characteristics of 3DMPOs the obstacles are split into 3 regimes; (1) non-porous, (2) porous with a single internal scale and (3) porous fractals (based on the Sierpinski carpet). The void fraction ($\phi=0.7$) and external dimensions ($D$) of the obstacles remained constant, whilst the internal geometrical parameters such as fractal dimension ($D_f$), lacunarity ($\Lambda$) and succolarity ($\sigma$) were varied. We are able to identify a relationship between these topological parameters characterising the 3DMPOs and the resultant wake characteristics. The fractal dimension ($D_f$) and lacunarity ($\Lambda$) are found to be responsible for the formation of the downstream steady wake region, whilst the succolarity ($\sigma$) affects the position of the detached low velocity recirculation region. The power spectral energy densities (PSDs) of the 3DMPOs are also seen to be affected by the succolarity ($\sigma$) in case (3), and indicate movement away from Kolomogorov's -5/3 power law.