Ambiguities associated with frozen and equilibrium sound speeds

Ambiguities associated with frozen and equilibrium sound speeds 

If a detonation is viewed as a plane Chapman-Jouguet wave traveling steadily in a tube in a direction away from its closed end, then we may question whether the result that v o = e,oo obtained in Section 2.3.3, is consistent with the end-wall condition. From the standpoint of the method of characteristics for reacting gas mixtures (Section 4.3), the fact that the characteristics propagate at the frozen sound speed implies [59] that the upstream end of the rarefaction wave that follows the detonation (Section 

TABLE 6.1. Comparison of calculated and observed fractional velocity deficit at 1-atm pressure in I-cm radius tubes [58] 

1) can smoothly join the downstream end of the detonation wave only at a point where the flow velocity relative to the detonation wave is the frozen sound speed Uf, From the characteristic analysis (specifically, from the requirement that the pressure and velocity gradients must remain finite where rarefaction joins the detonation), it is found that the condition which must be applied at this point is [compare equations (4-54), (4-55), and (4-91)] 

Family of frozen Hugoniot curves (fixed composition corresponds to point of intersection with equilibrium Hugoniot) 

If a detonation is viewed as a plane Chapman-Jouguet wave traveling steadily in a tube in a direction away from its closed end, then we may question whether the result that o. obtained in Section 2.3.3, is 

---