dc.contributor.author Cheng, Zekang dc.date.accessioned 2019-02-01T09:16:46Z dc.date.available 2019-02-01T09:16:46Z dc.date.issued 2019-03-30 dc.date.submitted 2019-01-30 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/288661 dc.description.abstract In this thesis, a numerical method is developed for simulating non-isothermal multiphase flows, which are important in many technical applications such as crystal growth and welding. The method is based on the arbitrary Lagrangian Eulerian method of Li (2013). The interface is represented explicitly by mesh lines, and is tracked by an adaptive moving unstructured mesh. The $P2-P1d$ finite element method (FEM) is used for discretisation and the incompressible Navier-Stokes equations are solved by the uzawa method. Firstly, a thorough study is presented on the method’s capability in numerically representing the force balance condition on the interface. An inaccurate representation of this condition induces the non-physical spurious currents, which degrade the simulation accuracy especially when the viscous damping is weak (small Ohnesorge number, $Oh$). For the example of a circular/spherical droplet, the interfacial tension and the associated pressure jump are exactly balanced numerically and thus the static Laplace solution exists in our method. The stability of this solution is examined numerically. The amplitude of the dimensionless spurious currents is found to be around $10^{−15}$ for $Oh \geq 10^{−3}$. Another benchmark test is the axisymmetric oscillation of a freesurface droplet/bubble. The simulation results are in good agreement with the analytical solution for $Oh = 10^{−3}$. This is by far the first successful simulation of droplet/bubble oscillation with such weak viscous damping and it demonstrates the ability of our method in simulating flows with strong capillary forces. Secondly, a numerical treatment of interface topology changes is incorporated into our method for studying problems with interface breakup. Thanks to the adaptive mesh generator, the thin region between the interface boundary and another boundary consists of one layer of elements. The interface topology change is performed once the minimum distance between the two boundaries falls below a pre-set scale $l_{breakup}$ . The numerical implementation is verified through two different examples: dripping faucet and droplet coalescence. Remarkably good agreement has been obtained with the experimental results. The simulation of the low Oh dripping problem shows both the accuracy and robustness of our method. The simulation of droplet coalescence demonstrates the great advantage of our method in solving problems with a large disparity in length scales. Finally, an FEM solver for temperature is developed and the non-isothermal effects are included in our method for the purpose of simulating non-isothermal multiphase flows. The modified method is validated to be accurate through three benchmark examples: natural convection in a cavity, thermocapillary convection of two layers, and droplet migration subject to a temperature gradient. Our method is then applied to investigate the liquid bridge breakup with thermocapillary effect. The non-isothermal liquid bridge breakup in the viscous and inertial regimes are studied. It has been found that the inertial regime breakup exhibits different pinchoff shapes as the Capillary number increases, and that the viscous regime breakup is accelerated by the thermocapillary motion. dc.description.sponsorship Cambridge Trust and the China Scholarship Council dc.language.iso en dc.rights All rights reserved dc.rights All Rights Reserved en dc.rights.uri https://www.rioxx.net/licenses/all-rights-reserved/ en dc.subject moving mesh dc.subject FEM dc.subject multiphase flows dc.subject droplet dc.subject bubble dc.subject thermocapillarity dc.subject fluid dynamics dc.subject computational fluid dynamics dc.title A moving mesh method for non-isothermal multiphase flows dc.type Thesis dc.type.qualificationlevel Doctoral dc.type.qualificationname Doctor of Philosophy (PhD) dc.publisher.institution University of Cambridge dc.publisher.department Engineering dc.date.updated 2019-01-30T22:40:56Z dc.identifier.doi 10.17863/CAM.35929 dc.publisher.college Queens' College dc.type.qualificationtitle PhD in engineering cam.supervisor Li, Jie cam.thesis.funding false rioxxterms.freetoread.startdate 2020-02-01
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