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Petersen, Kasper Juel

University of British Columbia

Boiling and cavitation—the phenomena which describe thermally- and pressure-driven, first-order phase transitions of liquids to their gaseous states—are central to many industrial, natural, and medical flows. By example, “rapid phase transitions” can cause vapour explosions in paper and metal processing, nuclear reactors, and cryogenics technologies when superheated volatile liquids become perturbed out of their equilibrium condensed state. In particular, phase-transitions are (i.) metastable, instigated by (ii.) thermal fluctuations, and are (iii.) multiscale, (iv.) heterogeneous processes; vapour bubbles O(< 10−⁶ m) form preferentially at microscopic nucleation sites, and are fully grown on the macroscale O(10−² m). From two literature reviews of phase-change modelling and simulation, it was found that (i.–iv.) are rarely considered in engineering numerical simulations except for (i.,ii.) in fluctuating hydrodynamics theories solved with the finite-volume method. Rather, the physics are frequently modelled by empirical models, leaving little opportunity for peering into realistic phase change dynamics. The fluctuating lattice-Boltzmann method (FLBM) has become a popular choice for studying thermal fluctuations. However, similar to fluctuating hydrodynamics, the FLBM relies on sampling techniques of probability distributions for imposing thermal noise in to the simulation variables. In an alternative effort, this research revolves around modelling thermal fluctuations by the Fokker-Planck equation (FPE) where LBM-techniques are repurposed to solve the FPE on the lattice. To introduce metastability and accommodate a high level of thermo-hydrodynamic nonideality into the model, its kinetics are recast with Particles-on-Demand—a recently proposed semi-Lagrangian realization of the LBM. The primary contribution is the mathematical derivation of the resulting latticeFokker-Planck-Boltzmann model. Asymptotic analysis shows that the limit of the model is the stochastic Navier-Stokes-Fourier equations with a stochastic stress tensor analogous to the deterministic equivalent derived on the basis of the Boltzmann equation. An initial fluctuation-dissipation theorem was formulated indicating equivalent behaviour to the FLBM. Numerical tests of the model are reported and show promise in computing thermal fluctuations evolved from the initial conditions in simulations. The research opens the door to intriguing numerical, theoretical, and computational research with the FPE, which has not yet been employed to investigate phase-transitioning liquids.

Text

2024-08-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/88994

Mechanical Engineering

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/