Localized front structures

Essential to the discussion of the previous Section was the existence of a linearly unstable state. The growth of perturbations on top of it pull the rest of the front structure. We now consider front solutions connecting linearly stable states. This happens in situations of multistability, as the ones mentioned in Sect. 3.1.5. If the initial condition is such that initially different parts of the system approach locally one of the possible stable states, competition between them makes the interfaces between the states to move. In this case any front motion should be pushed by the nonlinearities since the linear approximation predicts that any perturbation is damped and does not propagate. The situation is illustrated in Fig. 4.5. 

In Figure 3.8a, a plane shock wave is moving toward a rigid structure. As the incident wave encounters the front wall, the portion striking the wall is reflected and builds up a local, reflected overpressure. For weak waves, the reflected overpressure is slightly greater than twice the incident (side-on) overpressure. As the incident (side-on) overpressure increases, the reflected pressure multiplier increases. See Appendix C, Eq. (C-1.4). 

Once the explosion occurs it creates a blast wave that has a very steep pressure rise at the wave front and a blast wind that is a transient flow behind the blast wave. The impact of the blast wave on structures near the explosion is known as blast loading. The two important aspects of the blast loading concern is the prediction of the magnitude of the blast and of the pressure loading onto the local structures. Pressure loading predications as a result of a blast, resemble a pulse of trapezoidal or triangular shape. They normally have a duration of between approximately 40 msec and 400 msec. The time to maximum pressure is typically 20 msec. 

They also establish the interesting fact that the dimensionless quantity (c—u)/D is much more sensitive to small changes in the gas state than D, u, P, or p. Here c is the local sound velocity. Their results are summarized in Fig 8, whose abcissa (d/a) is diameter/cell size. The cell size refers to inhomogeneities (cells) in the structure of the detonation front. These become smaller as initial pressure increases, ie, d/a is generally large at ambient pressures of 1 atm or greater... 

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