A statistical criterion for image-based spray angle determination from ensemble-averaged axial intensity profiles

Image-derived spray angles depend strongly on how the spray boundary and the axial fitting extent are defined, yet no physically motivated rule exists for selecting the downstream limit of the fitting window. This study introduces a statistical criterion that defines this limit directly from the image data, removing operator dependence from the measurement. High-speed shadowgraphy images of a hollow-cone pressure swirl nozzle were acquired at injection pressures from 0.5 to 4.0 MPa using a shallow depth-of-field optical arrangement that resolves the focal plane spray envelope while relegating out-of-plane liquid structures to a defocused background. From the ensemble averaged images (2000 frames), the axial profile of the row-wise intensity standard deviation σ(Z) and its spatial derivative dσ/dZ were computed. The dσ/dZ minimum (Z σ',min ) identifies the axial location where resolved morphological heterogeneity decays most rapidly, indicating the transition from sheet breakup to a dispersed droplet field. As injection pressure increases, Z σ',min shifts upstream from 11.2 to 6.9 mm. The spray angle is then obtained by fitting the detected boundaries between the nozzle exit and Z σ',min . Because this downstream limit is derived from the image statistics itself, it adapts inherently to each operating condition without the need for manual tuning. The resulting angles ranged from 50° at 0.5 MPa to 72° at 4.0 MPa.