Dispersed Multi-phase Simulation in CMPS

Innovative Methods in CMPS Solver: Interfacial Area Transport

Based on Interfacial Area Transport, this method allows us to model the coalescence and breakup processes of droplets. Rooted in nuclear reactor applications, this approach offers the following distinct advantages: more accurate droplet size analysis, faster results, and reduced computational power requirements. Compared to the Lagrangian and population balance methods found in mainstream commercial software, this method can provide more accurate results in specific cases while requiring significantly less computational power.

• This method works with a fully Eulerian particle solver, enabling the physical tracking of particle size changes using a single additional equation. It ensures the continuous spatial distribution of particle sizes and densities, leading to more accurate, faster, and robust results.

• It is hundreds of times faster than Lagrangian (often referred to as "discrete phase") models. Memory usage is not a concern. In transient scenarios, particularly in combustion chambers and liquid fuel injection processes, the effects of billions of particles can be calculated quickly and efficiently. These scenarios include dynamic processes such as in-cylinder pressure oscillations and sudden combustion changes.

• Unlike population balance and Lagrangian models, particle sizes exhibit continuous variations as expected in reality, producing more physically accurate and realistic results. The assumption of particle size changes only between discrete ranges, as in population balance methods, is not required. This enables more physical, powerful, and faster simulations in many cases.

• The existing model allows for passive transitions to porous structures in cases of particle accumulation or granular flow blockage. However, for liquid droplets, a model for transitioning fully into the liquid phase due to accumulation has not yet been developed.

As an example application, consider solid-fuel rocket motors. Alumina droplets formed inside the motor generate acoustic and thermohydraulic effects that significantly impact motor performance, combustion efficiency, and stability. These effects directly influence the temperature distribution and flow resistance within the motor, playing a critical role in performance. Particles around 1 micron in size can coalesce under turbulent effects, especially in larger motors, growing to sizes of up to 100 microns. This size change emphasizes the role of particle coalescence in turbulent flows. Later, starting near the throat, these particles begin to break up again due to surface instabilities caused by flow imbalances. These instabilities result from vibrations induced by flow dynamics. Overall, these particles, which constitute approximately 40% of the mass, have effects that cannot be ignored. They significantly influence the combustion process and the flow and acoustic dynamics within the motor. Using the model we have integrated into the CMPS software, all these internal motor phenomena can be simulated. This aims to provide a detailed analysis of the critical processes affecting motor performance.

References

• T. Hibiki, M. Ishii, "Development of Interfacial Area Transport Equation," Nuclear Engineering and Design, Volume 202, Issues 2-3, 2000, Pages 183-200.

• Luo, H. (1993). Models for Turbulent Coalescence in Liquid–Liquid Dispersions. AIChE Journal, 39(9), 1438–1448.

• M. Ishii, T. Hibiki, "Thermal-Hydraulics of Two-Phase Flow," Springer, 2006.

• D. E. Clark, R. D. Williams, "Multiphase Flow Dynamics: Theory and Numerics," CRC Press, 2010.

• J. T. Jeong, M. Ishii, "Droplet Dynamics in Liquid-Liquid Systems," Chemical Engineering Science, Volume 55, Issue 21, 2000, Pages 4885-4895.

• M. Ishii, S. Kim, J. Uhle, "Interfacial Area Transport Equation: Model Development and Benchmark Experiments," International Journal of Heat and Mass Transfer, Volume 45, Issue 15, 2002, Pages 3111-3123.