Numerical modeling of supercooled droplet freezing on cold surfaces: gravity correction and parameter sensitivity analysis

Accurate prediction of droplet freezing behavior on cold surfaces is fundamental to anti-icing system design and cryogenic heat transfer optimization. This study establishes a three-dimensional numerical framework coupling the Volume of Fluid (VOF) model with an enthalpy–porosity approach to simulate freezing dynamics. Unlike conventional models that assume an idealized spherical cap, this framework incorporates a gravity-corrected Young–Laplace equation to reconstruct the realistic initial droplet profile. The model is validated against representative experimental cases from the literature, showing good agreement in freezing-time prediction within the fixed-contour modeling framework, with a mean absolute deviation of 3.35% under the validated conditions. Based on this validated framework, extensive systematic parametric simulations were conducted across a broad range of operating conditions (droplet volumes: 5–40 μL, contact angles: 30°–150°, and surface temperatures: −10 °C to −30 °C). These systematic parametric analyses reveal that: (1) a mushy-zone constant of A _mush = 10⁶ kg·m⁻³·s⁻¹ provides good agreement with experimental observations under the present validation conditions; (2) increasing droplet volume prolongs freezing time due to the increased thermal mass, while gravitational flattening partially offsets this effect by enhancing the basal heat-transfer area; (3) contact angle is the dominant factor controlling freezing time, as hydrophobic conditions significantly retard freezing by reducing the solid–liquid contact area; and (4) the extracted solid–liquid interface profiles exhibit approximate normalized-time similarity under wall-temperature and droplet-volume variations, although this similarity should be interpreted within fixed or similar wettability conditions. These findings quantitatively clarify the competing mechanisms in freezing kinetics and provide a theoretical basis for optimizing anti-frosting surfaces.