A Singularity Handling Approach To The Rayleigh Plesset Equation

Open Access
Author:
Balu, Asish T
Area of Honors:
Engineering Science
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Michael P Kinzel, Thesis Supervisor
  • Judith A Todd, Honors Advisor
Keywords:
  • eulerian
  • bubble
  • dynamics
  • singularity
  • rayleigh
  • plesset
  • differential
  • equation
  • lagrangian
  • handling
  • approach
  • balu
  • kinzel
Abstract:
Cavitation dynamics of nuclei are largely governed by the Rayleigh-Plesset Equation. This research analyzes various approaches to solving the RPE that decrease computing time and power with a minimal loss of accuracy. These approaches are conducted in both the numerical integration of the RPE as well as in the implementation of the RPE into CFD models. First, a number of singularity-handling algorithms that traverse the Rayleigh-Plesset Equation are explored. In order to maintain a constant time step size while maintaining solution quality, the RPE is put through a momentum conservation test to ensure the solution recovers symmetry across collapse events. This increase in efficiency and accuracy allows the program to provide useful solutions in the field of fluids engineering, particularly in the study underwater explosions, optimization methods, and other such applications. Next, the RPE is implemented in a computational fluid dynamics solver. This requires an extension of the equation from a Lagrangian framework into an Eulerian framework through the use of a material derivative. In addition, formulas are developed to impose upper and lower bounds for the bubble parameters, thereby allowing the use of larger time steps. Cavitation growth and collapse are analyzed in three different flow situations: a simple square model, bubble formation in a shaken bottle, and flow over a cylinder. Data from the models is extracted and validated against numerical solutions, thus showing that the RPE can be implemented efficiently in CFD within an Eulerian framework. This is especially useful when considering simulations with high bubble density because Eulerian methods are better suited than Lagrangian methods to handle large numbers of particles.