Sound speed frozen

Detonation, Sound Speed Frozen in. Under the heading "Chapman-Jouguet Detonation with Varying Product Composition Frozen Sound Speed , Evans 8t Ablow (Ref 4, pp 150-51) stated the following ... 

These subjects are discussed by Evans Ablow in Ref 66, pp 150-52 and in this Volume under Detonation, Sound Speed Frozen in, p D547... 

Now the assumption is dropped that the chemical reaction is a rate-controlled conversion to an invariant product composition, and the composition is permitted to vary with local thermodynamic state. Zel dovich, Brinkley Si Richardson, and Kirkwood Wood pointed out that since in a chemically reactive wave, pressure is a function not only of density and entropy but also of chemical composition, the sound speed for a reacting material should be defined as the frozen sound speed... 

Chapman- Jouguet Detonation with Varying Product Composition Frozen Sound Speed... 

A frozen (constant-composition) sound speed may be defined as... 

The quantity t is clearly a representative reaction time, and 3 will now be shown to be simply related to the difference between the frozen and equilibrium sound speeds. 

In order to relate 3 to the equilibrium sound speed and the frozen sound speed Uy, let us compute l/a = (dpjdp) y=y for the present gas. In view of equation (51),... 

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... 

Amplification expressions in general are not as simple as equation (51) for two-phase flows in rocket motors [128]. Equilibrium and frozen sound speeds with respect to droplet behavior may be identified (compare Sections 9.1.4.6 and 4.2.6), and a mass-source term may arise in equation (51) in the development of a conservation equation for the acoustic energy in the gas. From the viewpoint of equation (14), the quantity O must include amplification effects that arise from both energy sources and mass sources. Acoustic theories may be derived from the conservation equations of Chapter 11 for the purpose of analyzing acoustic amplification in spray combustion. 

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