Flow around a fractal tree : dynamics and implications to urban environment in microscale

Abstract

Greening and vegetation, though widely adopted in urban areas to optimize built environment, have uncertainty in mitigating pollutants or heat in breathing zone, in favor of multiscale tree geometries. The simplification of urban trees into single characteristic parameter neglects the real turbulence interaction with sub-scale geometries. Thus, this study investigates the influence of multi-scale tree geometries on wake dynamics and scalar transport. Preserving multi-scale characteristics and simplifying computational complications, fractal method is applied for three-dimensional tree models with different crown porosities (Po). Large-eddy simulation (LES) is adopted for numerical calculation, examined by particle image velocimetry (PIV). The statistical analysis of high-order moments of flow fields are compared, revealing that trees with lower 〖Po〗_ave (averaged) and higher 〖Po〗_bottom (crown bottom) are recommended to block guts and suppress near-ground vortices. The locations susceptible to rare, extreme events are addressed. The transport potential, scalar distribution, and their mechanism are visualized, suggesting that involving multi-scale tree geometries can optimize urban environmental studies. Extracting disturbance from different sub-scale geometries, several decomposition methods are employed and compared. Wavelet transform determines relationships between quadrant events and instantaneous frequency, suggesting a procedure that decomposes scales first, then evaluates transport efficiency. Empirical mode decomposition (EMD) decomposes the local turbulence into intrinsic modes (IMFs), mapping to corresponding geometries. The contributions of IMFs to vertical momentum flux ¯(u'w') indicate the dominance of tree height (h) and branches in soil erosion and canopy ventilation, respectively. Exuberance supplements optimal spacing distances within 1-2h, suppressing ground entrainment. The spanwise momentum flux ¯(u'v') emphasizes IMF2 (1st generation branch) on pedestrian-traffic transport. The pollutant fluxes driven by diversified motions further verify the subscale contribution. The dominant vegetation geometries in various urban issues are revealed. Deepening investigation of EMD results, Hilbert-Huang Transform (HHT) compares the statistically dominant scale with Fast-Fourier transform (FFT), exhibiting similar peak scales but different energetic locations. HHT innovatively divides the 3D wake into characteristic regions following instantaneous frequency-amplitude distribution, validating the assumption of relationships between sub-scale turbulence and geometries. Meanwhile, the proper orthogonal decomposition (POD) is adopted for dominant spatial-temporal patterns. The dominant time coefficients are analyzed through wavelet transform, low-pass filter, and coherence analysis for wake instability. The extended POD (EPOD) connects scalar fluxes to major aerodynamics, indicating that larger motion scale drives more scalar. Tree species with low 〖Po〗_ave and high 〖Po〗_edge (crown edge) are recommended to mitigate pollutant concentration in breathing zone. Connecting the wake mechanism to urban implications, the coupling effects of building-fractal-tree in different distance arrangements are investigated by PIV technology. The results are decomposed by spectral proper orthogonal decomposition (SPOD). The reconstructed dominant vertical momentum reveals a higher capability to drive larger mass of sparser crown. The in-depth wake dynamics and scalar transport affected by subscale tree geometries are investigated in this research, by statistical and scale decomposition analysis. It improves the understanding of various decomposition techniques’ performance and the mechanism behind urban greening design to optimize the microscale environment. Further detailed research on specific tree structures is required in the future.