Shock tube theory

One may calculate the rate of vapor generation on the basis of Fig. 5. The pressure at the contact surface is Pv = Pi + Ap2. If the saturated vapor is assumed to obey the ideal gas law, one has p = Pv/Rv vt where Ry is the gas constant of the vapor and Ty is the temperature of the saturated vapor at pressure Py. According to the shock tube theory, the flow velocity of a vapor/air mixture is given by the following expression ... 

CA 49, 10625 (1955) (Structure of detonation wave front of gases was studied by method of shock tube) (See its abstract under Detonation Wave Structure) 38a) R.E. Duff E. Houston, 2nd ONRSympDeton (1955), p 225 (See under Detonation Wave Structure Measurements in Condensed Explosives) 39) S. Minshall, JApplPhys 26, 463- 69 (1955) (Properties of elastic and plastic waves determined by pin contactors and crystals) 40) C.G. Dunkle, "Introduction to Theory of Detonation of Explosives, Syllabus of 21 Nov 1955 and Lecture Delivered at Picatinny Arsenal on 13 Dec, 1955 (Structure of the deton wave)... 

The shock wave theory is easier to understand, if we consider a planar shock wave, such as the one shown in Fig. 11, on the assumption that the tube is indestructible (such shock wave tubes are utilized as research instruments in gas dynamics and in solid state physics the shock sources are explosions or membranes bursting under pressure). 

White [215] has reported shock-tube data for N2 + 02 mixtures over the range 1000-3000°K. He has concluded that the V-V exchange probability leading to N2 deactivation increases from 1 x 10 to 2.3 x 10 s over this range. As seen from Figure 3.4, the near-resonant theory of Rapp gives a probability which is higher by a factor of 12 at 3000°K. 

Chen and Moore s investigation [220] of room-temperature relaxation in HC1 and in DC1 shows that the high-temperature shock-tube results [222,225] do not extrapolate smoothly according to a 7 1/s law. Figure 3.29, taken from their paper, shows that while log P versus r 1/s appears to be fairly linear above 1000°K, the room-temperature deactivation probability is 15 times larger than the value expected by linear extrapolation of the shock-tube data. The upper dashed curve represents a probable interpolation between the shock-tube data and the fluorescence data the lower dashed line is an interpolation based on SSH theory for V-T transfer. The datum represented by the square is for vibrational deactivation of DC1 by HC1. 

Earlier investigations on N20 have been summarized by Herzfeld and Litovitz [8] and by Calvert [252]. Simpson, Bridgman, and Chandler [253] have more recently examined vibrational relaxation in pure N20 over the range 320-820°K using shock-tube interferometry. As in the case of C02, single relaxation is observed. Experimental relaxation times are depicted in Figure 3.31, and are compared with SSH theory. 

Aat °(SF4)/4. Bott ( ) has reported the results of shock-tube experiments on the dissociation of SF over the temperature range 1650-1950 K. Rate constants based on spectroscopic measurements were correlated with the Rice-Ramsperger-Kassel (RRK) theory. This study strongly suggests that D (SFg-F) = 79.0+3.0 kcal mol . ... 

Different experimental techniques, including static pyrolysis, carrier (flow) techniques, shock tube methods, and very-low-pressure-pyrolysis, have been used to measure hunt as a function of temperature and pressure. One of the most significant achievements of RRKM theory is its ability to match measurements of kum with pressure. 

The interpretation of the shock tube results is that during the induction period the branching chain reaction predominates until significant amounts of H2 and O2 have reacted and back reactions have become important. After the induction period, the concentration of free radical propagators go through a maximum and then slowly approach equilibrium values until the higher-order termination steps limit chain propagation, and the back reactions become important. All of the individual rate constants in the mechanism could be evaluated and are consistent with simple collision theory. 

An introduction to the general theory of shock tubes is given in Appendix C and in many general references [17-19]. For our purposes, we note that measurement of the velocity of the shock front U permits calculation of the properties of the shocked gas. The Mach number of the unshocked gas, which is the ratio of the shock velocity to the velocity of sound in the unshocked gas, can be written as... 

Measurements of dissociation rates in shock-heated gases have enabled the determination of atom recombination rates to be made at elevated temperatures. Overlap of the ranges of temperatures and third bodies in shock tube experiments and in discharge-flow studies would enable dependences of kg on these parameters to be well established, thus providing raw material for the testing and further development of theories of third-order atom recombination reactions. Such data, with overlapping ranges of T and M, would also provide... 

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