兩相流數值方法及其對T型微管內液滴生成與分離之應用

吳榮昭

doi:10.6844/NCKU.2015.00933

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兩相流數值方法及其對T型微管內液滴生成與分離之應用

Numerical Method for Two Phase Flows and its Application to Droplet Formation and Breakup in T-junction Microchannels

吳榮昭 , Ph.D　　Advisor：林三益　　

英文 DOI： 10.6844/NCKU.2015.00933

鬼流體方法；四步分步算法；動量內插；壓力邊界法；清晰界面張力模型； ghost fluid method ； four-step fractional-step method ； momentum interpolation ； pressure boundary method ； sharp surface tension force model

Abstract │ Reference (90) │ Altmetrics

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A sharp interface method for simulating incompressible immiscible two-phase flows is presented in this thesis. Within the framework of volume of fluid (VOF), a flux-blending strategy based on the high resolution upwind and downwind schemes is utilized to determine the convective flux through each cell face and preserve both the interface sharpness and shape. A signed distance function is reconstructed from the VOF function to accurately obtain the interface curvature and normal vector. A mass recover technique, based on the distance information, is proposed to eliminate the overshoot/undershoot problem under the premise of mass conservation. The four-step fractional-step method, applied to a collocated structured grid system, is adopted to solve unsteady incompressible Navier-Stokes equations and coupling with a momentum interpolation technique to avoid the pressure checkerboard phenomenon.
    In the interfacial flow problem, the generation of spurious currents near the interface is a classical issue. In our knowledge, it is attributed to three reasons: (i) the finite thickness interface region introduced by the continuous surface tension force (CSF) model,(ii) the inaccurate estimation of geometrical information, (iii) a numerical imbalance between the surface tension force and the associated pressure gradient. In this study, the singular surface tension force is directly transformed into the form of a pressure jump without introducing a fictitious interface thickness while numerically smearing out the dynamic viscosity jump condition. A sharp discretization technique of the ghost fluid method (GFM) is employed to deal with the discontinuous jump of material properties while the pressure jump condition can be rewritten as a source term by a sharp surface tension force (SSF) model.
    A balanced-force technique is developed to ensure the numerical balance between the surface tension force and the associated pressure gradient. Similar to the pressure boundary method (PBM), a capillary pressure field within the dispersed phase is obtained from a Dirichlet problem to numerically balance the surface tension force while a dynamic pressure field is used to satisfy the continuity equation. After considering the discontinuity effect induced by the surface tension force, the numerical boundary condition for pressure becomes more complicated, especially in the outlet boundary, and can be well defined by these two pressure fields (capillary and dynamic). For numerical consistency, the surface tension force term and the pressure gradient are both discretized at the cell face and evaluated together at every time step.
    The efficiency and accuracy of our method are validated by various benchmark problems. The presented numerical algorithm successfully simulates the two dimensional, microfluidic channels at T-junction and is used to investigate the droplet formation and the droplet breakup problems.

Reference ( 90 ) 〈TOP〉

[1] Afkhami, S., Leshansky, A., Renardy, Y., 2011, "Numerical investigation of elongated drops in a microfluidic T-junction", Physics of Fluids (1994-present), Vol. 23, pp. 022002.
連結：
[2] Arias, S., Legendre, D., González-Cinca, R., 2012, "Numerical simulation of bubble generation in a T-junction", Computers & Fluids, Vol. 56, pp. 49-60.
連結：
[5] Brackbill, J., Kothe, D.B., Zemach, C., 1992, "A continuum method for modeling surface tension", Journal of computational physics, Vol. 100, pp. 335-354.
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[9] Cristini, V., Tan, Y.-C., 2004, "Theory and numerical simulation of droplet dynamics in complex flows—a review", Lab on a Chip, Vol. 4, pp. 257-264.
連結：
[11] Darwish, M., Moukalled, F., 2006, "Convective schemes for capturing interfaces of free-surface flows on unstructured grids", Numerical Heat Transfer, Part B: Fundamentals, Vol. 49, pp. 19-42.
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