Axisymmetric operator-splitting lattice Boltzmann modeling of coupled heat transfer and solidification during droplet freezing

Droplet freezing on cold solid surfaces involves the coupled evolution of multiphase flow, heat transfer, solid–liquid phase change, variable thermophysical properties, and freezing-induced volume change. An axisymmetric phase-field–hydrodynamic–thermal lattice Boltzmann framework is developed to describe these processes. Within this framework, an operator-splitting corrected energy-distribution formulation (OSCEDF) transports a radius-weighted sensible-energy variable, while latent-heat conversion and phase-state recovery are handled locally through total-enthalpy updating and piecewise enthalpy inversion. The corrected sensible-energy state is subsequently fed back to the thermal distributions, forming a closed coupling among energy transport, phase-state evolution, and thermophysical-property updating. A link-wise solid-fraction-dependent hydrodynamic feedback treatment is further employed to progressively reduce local momentum transport during solidification while retaining heat conduction in the solidified region. Benchmark freezing and melting problems assess freezing-induced volume variation, axisymmetric front propagation, and thermal phase-change coupling. The resulting front-propagation coefficients differ from the classical similarity solutions by less than 0.23%, while the condensed-phase and total-domain mass deviations remain below 0.3% during the coupled impact-freezing calculation. Application to an impact-freezing experiment reproduces the observed trends in contact-region evolution, bottom-up freezing-front propagation, and overall droplet morphology. The principal contribution of OSCEDF is its modular coupling of sensible-energy transport, local latent-heat conversion, phase-state recovery, and property updating. The present model focuses on continuum-scale freezing governed by the equilibrium phase-change temperature, while stochastic nucleation, supercooling, and recalescence remain outside its current scope.