Critical Energy for Direct Initiation of Spherical Detonation

9 Critical Energy for Direct Initiation of Spherical Detonation 

The Zeldovich model [31] for assessing the critical energy of detonation by direct initiation is based on an assumption that shock wave motion is determined by the total sum of the initiator energy and the chemical energy of gases reacted at the completion of the induction time. As this takes place, the wave intensity and velocity decrease to some minimum value, after that the velocity asymptotically approaches to the Dq- j value corresponding to the C-J point. 

According to the Zeldovich criteria, the duration of the initiating shock wave is approximately equal to the combustion mixture induction time T/, by the time the SW intensity falls to the C-J condition value. When the SW is rapidly attenuated, the chemical energy may have no time to be released. Therefore, there should be some minimum energy for spherical detonation initiation. 

models based on the relation below are used for assessing the energy of direct detonation initiation 

It was shown in [1-3] that there are correlations between some detonation parameters and the chemical induction time (ignition delay) calculated with the help of detailed chemical kinetic models. However, the detonation cell size a and the detonation wave width are in direct proportion when the induction zone length is significantly larger than the energy release area [12], Otherwise, the relation is more complicated. 

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