晶格波茲曼法在高密度比下之多相流模型

A lattice Boltzmann multiphase fluid model with large density ratio

藍偉華

指導教授 ： 林昭安

國立清華大學/工學院/動力機械工程學系/碩士(2008年)

https://doi.org/10.6843/NTHU.2008.00207

摘要

In this thesis, a lattice Boltzmann multiphase fluid model capable to deal with large density ratio is proposed. Multiphase fluid can be computed using the the Navier--Stokes equations in conjunction with a convective Cahn-Hilliard equation [22], where the latter equation is used to capture the interface of multiphase fluid with large density difference. The free energy is incorporated
into the Cahn-Hilliard equation to model the effects of the surface tension and the interface width and the formulation adopted is that proposed by Zheng et al [36]
For the multiphase model of Zheng et al.[36], two different lattice Boltzmann equations are used to model the Naiver--Stokes equation and the Cahn-Hilliard equation, and the corresponding lattice models are D2Q9 and D2Q5,respectively. Also, the adopted equilibrium distribution functions are also different. To unify the
formulation, we propose a multiphase model using D2Q9 lattice model, where the adopted equilibrium distribution functions are the same for both the Navier-Stokes and the Cahn-Hilliard equations, except that the leading quantities are density and scalar, respectively. The Cahn-Hilliard equation consists of two processes. One is the convective transport for scalar and the other one is the diffusive
transport for chemical potential, which is related to the free energy. The convective part is modeled through the convective and diffusive equation for scalar without chemical potential term. Therefore, a source term is added to recover the chemical potential term in the Cahn-Hilliard equation.

The capability of the present model to compute two phase flows with high density ratio (>1000) is validated by simulating one bubble in the stationary fluid and two merging bubbles. Predicted surface tension coefficient obtained from the Laplace's law and the interface profile agree very well with the respective analytical
solutions. Factors affecting the evolutions of the bubble dynamic are also discussed, i.e., the mobility coefficient, surface tension coefficietn, interface width, and the gap between two bubbles.

關鍵字

兩相流 ； 高密度比 ； 氣泡

參考文獻

University, Taiwan, (2007)

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