A Successful Case on Numerical Simulation of Interfacial Instabilities Using MATFOR

As most scientific data is in large-scale format these days, the bottleneck of a simulation usually occurs when performance and visual effect both require attention. Although new supplemental tools are being developed constantly, most existing applications cannot effectively satisfy these requirements; hence resulting in either process delay or unsatisfactory visual presentations. In view of that, a sound simulation toolkit is not only practical but essential for conducting simulations. Available only from AnCAD, MATFOR brings an unprecedented availability for creating a dynamic interpretation of the simulation. It embraces a full-range of functionalities, including 3-D visualization, real-time animation, runtime data manipulation, interactive movie presentation and recording. In the near future, MATFOR will be an indispensable tool for every scientist and engineer in the scientific computing field.

The Importance of Choosing the Right Toolkit

Prof. Ching-Yao Chen and Mr. Cheng-Hua Chen have been researchers in the field of computational fluid dynamics for several years. One of their joint researches focuses on the interfacial instabilities of a rotating Hele-Shaw flow. Matlab has been their choice of tool due to its generality. However, despite its simplicity, MATLAB does not allow manipulation of the data displayed during runtime, and creating a standalone executable was relatively complicated. In the process of exploring new tools, they came to learn about MATFOR. With a few lines of code, they were able to plot simulation results, analyze data during runtime and further record the simulations. For that reason, they have been able to utilize movie presentation during the exams.

Numerical Simulations of Interfacial Instabilities

The fingering instabilities in a rotating Hele-Shaw flow have been a subject of intensive studies due to their potential applications to the spin-coating technology, i.e. precious metals for electronic wafers or organic solvents for cleaning purposes. In these studies, the effects of significant Coriolis forces have yet been explored thoroughly. On the other hand, a time-dependent gap Hele-Shaw flow, where the upper plate is lifted or pressed uniformly and the plates remain parallel to each other during the process, is also studied. In this type of problems, a simple radial geometry flow in lifting cell has been investigated theoretically and experimentally. From the report, the lifting puts the fluid under a lateral straining flow which induces an unstable inward driving force and forms visually striking fingering patterns. However, these studies are only the results of a stationary droplet. For further investigation in this numerical study, the focus is on a rotating miscible droplet in a time-dependent gap Hele-Shaw cell with significant Coriolis effects.
Theoretical background

The study on the interfacial instability of a heavier and more viscous droplet is conducted with a miscible fluid in a rotating Hele-Shaw cell with the temp-dependent gap. In the diagram below, Do is the initial diameter surrounded by the miscible fluid with less density and viscosity. With such confined environment, the flow takes place in narrow space between two flat plates, where the upper plate is lifted up or pressed down at a specified rate. The initial plate spacing is represented by bo. An exponentially increasing gap width is assumed in the present study.


Fig.1: Schematic representation of the miscible fluids in a rotating Hele-Shaw cell with the time-dependent gap.

Simulation Results

Figure 2. Using MATFOR procedure msColormap with argument type ¡§hot¡¨ presents the colors vary smoothly from black, red, orange and yellow, to white. The beautiful interfacial patterns show the fingers rotating counter-clockwise with drops emission in the tangential direction.

Figure 3. From above, all fingers demonstrating the absence of finger competition as well as the nonlinear activities. Towards the end of the presentation, extremely slim fingers turn counter-clockwise due to the effects of the strong centrifugal force and Coriolis force.

MATFOR, Making Computational Programming Completes

Using MATFOR shortens the length of code needed for simulations, and more to the point, a higher performance can be obtained. Both researchers were pleased by the high performance visualization and the way MATFOR manages hundred of sets of data with ease. The interfacial instabilities have been analyzed systematically, and the simulation results indicate explicitly the relation between relevant control forces of the system influence the morphology of the interfacial patterns.
Acknowledgments

Field data provided by

  1. Associate Prof. Chen, Ching-Yao
    Department of Mechanical Engineering
    National Yunlin University of Science & Technology, Taiwan
  2. Lecturer Chen, Cheng-Hua
    Department of Automation Engineering
    Nan Kai Institute of Technology, Taiwan

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