Characteristic energy factors for energy sink problem of the ideal fluid cavity annihilation

In physics, a “source” denotes the origin of matter or energy, while a “sink” refers to the terminal point of matter or energy. By analogizing with the energy source problem in underground explosions, this study proposes an energy sink problem for ideal fluid cavity annihilation. A detailed analysis is conducted on the energy balance and adjustment mechanisms in the ideal fluid cavity annihilation problem, establishing the relationships among fluid pressure work, energy convergence, transmission and transformation. A characteristic energy factor is introduced to describe the “centripetal convergence” behavior of energy sinks. The characteristic energy factor for energy sinks incorporates the information on converged energy, geometric dimensions of cavities and physical properties of fluids, effectively characterizing the “convergence” behavior of energy sink problems and laying a theoretical foundation for the subsequent research on “energy sink” problems in solids. The physical mechanisms and mathematical foundations of the characteristic energy factor are analyzed, and its characteristics and advantages are expounded. Specifically, the introduction of the characteristic energy factor circumvents the need for complex stress-strain relationships, boundary conditions, and unknown internal material structures in traditional continuum mechanics, significantly simplifying the complexity of the problem. The characteristic energy factor is primarily applicable to the predictions of engineering disasters with large scales or well-defined failure zones (e.g., underground explosions, large-scale surrounding rock deformation, zonal disintegration or pendulum waves, and shear-slip rock bursts in ore pillars), whereas its applicability to highly localized engineering disasters with unknown failure zones (e.g., strain-type rock bursts) requires further investigation.