Numerical study of fractal-tree-generated turbulence

Abstract

We study the aerodynamics of fractal trees by using a simulation based on the Lattice Boltzmann Method with a cumulant collision term. We have applied L-system rules to construct self-similar fractal tree models in aerodynamic computations. We found that the drag coefficient closely matches that of previous literature at high tree-height-based Reynolds numbers (ReH ≥ 60 000). A normalization process capable of collapsing turbulence intensity for various tree models is made. This process reveals that, at the same Reynolds number, different tree models exhibit the same behaviour in the turbulence intensity of their wake region. Our assessment of global and local isotropy in the turbulence generated by fractal trees reveals that the distant wake can be considered nearly locally isotropic at a high Reynolds number (ReH ≥ 60 000). Finally, the present numerical results confirm the non-equilibrium dissipation behaviour previously observed in the case of space-filling fractal square grids[2]. In the wake region, the non-dimensional dissipation rate Cϵ = constant is not valid. Instead, it is inversely proportional to the local Taylor-microscale-based Reynolds number, Cϵ ∝ 1/Reλ.

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