Influence of confinement and volumetric void fraction on the lift coefficient of a NACA0015 hydrofoil: Experimental analysis and semi-analytical modeling

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This work investigates how the volumetric void fraction (β) modifies the lift coefficient of a symmetric hydrofoil (NACA0015) operating in a confined, air–water two-phase flow. Experiments were carried out in two square test sections (L = 0.15 m and 0.25 m) with hydrofoil chords c = 0.15 m and 0.25 m, mounted either horizontally or vertically. Angles of attack α spanned, bulk liquid velocities ranged from 2m/s to 9m/s, and volumetricvoid fractions were set to β = 0, 0.01, 0.02, 0.03, yielding Re ∈ [3.0 × 105, 1.35 × 106].A semi-analytical confinement correction, derived from boundary-layer-driven internal velocity profiles, is applied to take account of the blockage effect according to CL = CL0/(1 − σ)2, with σ the confinement parameter. Based on this corrected lift coefficient, a correlation is proposed to quantify the influence of the volumetric void fraction: a˜(β)/a˜β=0 ≈ 1 − 4.5β, where ˜a is the linear coefficient in CL = aα˜ +˜bα3.The proposed correlation successfully collapses more than 80 experimental cases encompassing different test-section sizes and Reynolds numbers when combined with the confinement correction. The analysis also highlights the role of bubble distribution relative to the hydrofoil orientation within the duct.These findings provide a compact predictive framework for lift under realistic, confined multiphase conditions, and can inform early-stage design and control strategies where bubble injection is used to mitigate instabilities or environmental impacts.