Abstract
Based on fractal theory, a regular fractal is used to construct symmetrical reef models (e.g., cube and triangle reef models) with different fractal levels (n = 1, 2, 3). Using the concept of fractal dimension, we can better understand the spatial effectiveness of artificial reefs. The void space complexity index is defined to quantify the complexity of the internal spatial distribution of artificial reefs models under different levels. The computational fluid dynamics (CFD) flow simulation approach was used to investigate the effects of void space complexity on the flow field performances of the symmetrical artificial reef models. The upwelling convection index (Hupwelling/HAR, Vupwelling/VAR), wake recirculating index (Lwake/LAR, Vwake/VAR) and non-dimensionalized velocity ratio range were used to evaluate the efficiency of the flow field effect inside or around artificial reefs. The surface area and spatial complexity index of artificial reefs increase with increasing fractal level. The numerical simulation data shows that the Menger-type artificial reef models with a higher spatial complexity index have better flow field performances in the upwelling and wake regions. Compared to the traditional artificial reef models, the upwelling convection index (Vupwelling/VAR) and recirculating index (Vwake/VAR) of n = 3 fractal cube artificial reef increase by 37.5% and 46.8%, respectively. The efficiency indices of the upwelling region and wake region around the fractal triangle artificial reef model are 2–3 times those of the fractal cube artificial reef model when the fractal level is 3.
Highlights
Fractal cube and triangle artificial reefs (ARs) models were constructed based on the fractal theory, which is expected to improve the space complexity and expand the surface area of ARs
We can conclude that the application of the fractal theory to construct ARs effectively improves the space complexity and expands the surface area
AR models have greater void space complexity index (VSCI) values than the traditional AR model with a simple large hollow, and the surface area and VSCI of AR models increase with increasing fractal levels
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In the 1960s the term “fractal” was first used by Benoit B. Mandelbrot [1] to describe complex geometry objects, which cannot be characterized by an integral dimension. Fractal geometry has been extensively applied in various fields (one-dimensional, 1D; two-dimensional, 2D; or three-dimensional, 3D), such as geophysics, biology, and fluid dynamics [2]. Application of the fractal in different ways leads to different results [3,4,5]
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