Numerical study of fractal-tree-generated non-equilibrium turbulence

Self-similar fractal tree models are numerically investigated to elucidate the drag coefficient, non-equilibrium dissipation behaviour and various turbulence statistics of fractal trees. For the simulation, a technique based on the lattice Boltzmann method with a cumulant collision term is used. Self-similar fractal tree models for aerodynamic computations are constructed using parametric L-system rules. Computations across a range of tree-height-based Reynolds numbers $Re_H$ , from 2500 to 120 000, are performed using multiple tree models. As per the findings, the drag coefficients ( $C_D$ ) of these models match closely with those of the previous literature at high Reynolds numbers ( $Re_H \geqslant 60\,000$ ). A normalization process that collapses the turbulence intensity across various tree models is formulated. For a single tree model, a consistent centreline turbulence intensity trend is maintained in the wake region beyond a Reynolds number of 60 000. The global and local isotropy analysis of the turbulence generated by fractal trees indicates that, at high Reynolds numbers ( $Re_H \geqslant 60\,000$ ), the distant wake can be considered nearly locally isotropic. The numerical results confirm the non-equilibrium dissipation behaviour demonstrated in previous studies involving space-filling fractal square grids. The non-dimensional dissipation rate $C_\epsilon$ does not remain constant; instead, it becomes approximately inversely proportional to the local Taylor-microscale-based Reynolds number, $C_\epsilon \propto 1/Re_\lambda$ . We find significant one-point inhomogeneity, production and transverse transport of turbulent kinetic energy within the non-equilibrium dissipation near wake region.