Hello All!
Thanks for this opportunity. This is my first post at iMechanica. So, I'm wondering if some of you can help me with this:
I work with underwater explosion (UNDEX) modeling and I'm trying to simulate in a FEM code an experiment of UNDEX. According to the Principle of Similarity develped by Hilliar, if the actual dimensions of a prototype is reduced by a linear scale and the time as well, important characteristics of the impulse loading keep the same such as maximum pressure. Other characteristics as time decay or maximum radius of the bubble are reduced by the same scale than before. So, the principle of similarity works very well for the impulse loading although it has some limitations as gravity and internal energy of the explosive. They cannot be reduced. However, for gravity, it is expected that the pressure of the explosion should be extremelly high in comparison with the hydrostatic pressure. Then, the influence of gravity can be neglectable.
But, let's the question: the explosion can be modeled in two different ways. One of them is the modeling of explosion by a real detonation of an explosive. This model seems more complicated and it searches to capture the characteristics of the dynamic of detonation. This model is known as real explosion. The second model is a simplification of the explosion as a sphere of gas. It works as the explosion becomes a sphere of gas instataneously. It can be modeled as the gamma-law of ideal gas and it is known as virtual explosion. My model is based on this last one. It seems simpler, however I have a hard doubt that is related to the principle of similarity and this gamma-law of ideal gas.
I described the principle of similarity above focused on the relation of hydrodynamic after the detonation through the fluid. But, now, I have no idea how can I apply this relation for the gamma-law. According to Cole, it is not an easy task and I don't see it very well explained. But this reference is old and maybe there is more recent and clear reference about that.
So, could someone help me with this?
Thanks you very much,
Odilon.