Fractal grid-induced turbulence strength characterization via piezoelectric thin-film flapping velocimetry

The centerline streamwise and cross-sectional (x/D_h = 0.425) turbulence characteristics of a 2D planar space-filling square-fractal-grid (SFG) composed of self-similar patterns superimposed at multiple length-scales is experimentally unveiled via piezoelectric thin-film flapping velocimetry (PTFV). The fluid-structure-interaction between a flexible piezoelectric thin-film and SFG-generated turbulent flow at Re_Dh = 4.1 × 10⁴ is investigated by analysis of the thin-film's mechanical response. Measurements of the thin-film-tip deflection δ and induced voltage V demonstrate increasing flow fluctuation strength in the turbulence generation region, followed by rapid decay further downstream of the SFG. Interestingly, SFG-induced turbulence enables the generation of maximum centerline thin-film's response (V_rms, δ_rms) and millinewton turbulence-forcing (turbulence-induced excitation force acting on the thin-film) F_rms which are respectively, 7× and 2× larger than the classical square-regular-grid of similar blockage ratio. The low frequency, large-scale energy-containing eddies at SFG's central opening plays a critical role in driving the thin-film vibration. Most importantly, the SFG-generated turbulence at (y/T = 0.106, z/T = 0.125) away from the centerline allows equivalent mechanical characteristics of turbulence generation and decay, with peak of 1.9× nearer from grid. In short, PTFV provides a unique expression of the SFG-generated turbulence, of which, the equivalent turbulence length-scale and induced-forcing deduced could aid in deciphering the flow dynamics for effective turbulence management.