Lattice Boltzmann Method for Convection with Phase Change in Nanofluids
From June 2012 to May 2013, I worked for Dr. Luis Cueva-Parra as a paid research assistant funded by the U.S. Department of Energy. Our efforts were part of a larger group under the name NePCM (Nano-enhanced Phase Change Materials). The purpose of my team was to explore the physics of nanofluids undergoing phase change and to model it using computer simulations and advanced modeling techniques.
My task was twofold. Firstly, I was to model convection with phase change in nanofluids using an adapted Lattice Boltzmann Method. Secondly, I was to explore techniques to visualize the resultant data.
I began by building a program in C++ from scratch which took various fluid parameters as input and then performed a melting simulation using a Lattice Boltzmann method adapted for phase change as given in . The data was output both numerically and visually. The visual output was achieved by using the simple grayscale image PGM format. After a range of values was established, each value could be mapped to a certain gray level and then to a corresponding pixel. We tested the accuracy of our program by comparing the one-dimensional melting experiment (1-d Stefan problem) with the well-known analytical solution (see figure 1).
Having a strong base for the program, I moved on to write a program to simulate convection. Referencing the wiki and , I was able to obtain a working convection model. Some example output can be seen in the following two videos of an experiment which involved a liquid in a closed box with the left side of the box suddenly heated at time t=0.
Next, I used Maxwell's equations to incorporate nanofluid properties given certain input properties of the nanoparticles as well as their concentration in the base fluid. Then, I combined our convection model and phase change model into one program which performed the convection operations on any liquid portion and the phase change operations on any solid portion. This worked well to provide a reasonable model which simulated both phase change and convection within a nanofluid. I also used system calls to ImageMagick within the program to output the final images as color images as well as automatically converting them to animations as can be seen in the figure to the right of a solid nanofluid melting from a sine-shaped (half period) heat source along the bottom (orange/red boundary is the solid-liquid interface).
Download the final program here.
 W. Jiaung, J. Ho, and C. Kuo, "Lattice Boltzmann Method for the Heat Conduction Problem with Phase Change". Numerical Heat Transfer, Part B, 39: 167-187, 2001.
 Y. Xuan and Z. Yao, “Lattice Boltzmann Model for Nanofluids”. Heat Mass Transfer 41: 199–205, 2005.