Oscillatory combustion

Kilham, J. K., E. G. Jackson, and T. B. Smith. 1965. Oscillatory combustion in tunnel burners. 10th Symposium (International) on Combustion Proceedings. Pittsburgh, PA The Combustion Institute. 1231-40. 

When an energetic material burns in a combustion chamber fitted with an exhaust nozzle for the combustion gas, oscillatory combustion occurs. The observed frequency of this oscillation varies widely from low frequencies below 10 Hz to high frequencies above 10 kHz. The frequency is dependent not only on the physical and chemical properties of the energetic material, but also on its size and shape. There have been numerous theoretical and experimental studies on the combustion instability of rocket motors. Experimental methods for measuring the nature of combustion instability have been developed and verified. However, the nature of combustion instability has not yet been fully understood because of the complex interactions between the combustion wave of propellant burning and the mode of acoustic waves. 

Combustion of a propellant in a rocket motor accompanied by high-frequency pressure oscillation is one of the most harmful phenomena in rocket motor operation. There have been numerous theoretical and experimental studies on the acoustic mode of oscillation, concerning both the medium-frequency range of 100 Hz-1 kHz and the high-frequency range of 1 kHz-30 kHz. The nature of oscillatory combustion instability is dependent on various physicochemical parameters, such... 

Fig. 13.21 shows another example of oscillatory burning of an RDX-AP composite propellant containing 0.40% A1 particles. The combustion pressure chosen for the burning was 4.5 MPa. The DC component trace indicates that the onset of the instability is 0.31 s after ignition, and that the instability lasts for 0.67 s. The pressure instability then suddenly ceases and the pressure returns to the designed pressure of 4.5 MPa. Close examination of the anomalous bandpass-filtered pressure traces reveals that the excited frequencies in the circular port are between 10 kHz and 30 kHz. The AC components below 10 kHz and above 30 kHz are not excited, as shown in Fig. 13.21. The frequency spectrum of the observed combustion instability is shown in Fig. 13.22. Here, the calculated frequency of the standing waves in the rocket motor is shown as a function of the inner diameter of the port and frequency. The sonic speed is assumed to be 1000 m s and I = 0.25 m. The most excited frequency is 25 kHz, followed by 18 kHz and 32 kHz. When the observed frequencies are compared with the calculated acoustic frequencies shown in Fig. 13.23, the dominant frequency is seen to be that of the first radial mode, with possible inclusion of the second and third tangential modes. The increased DC pressure between 0.31 s and 0.67 s is considered to be caused by a velocity-coupled oscillatory combustion. Such a velocity-coupled oscillation tends to induce erosive burning along the port surface. The maximum amplitude of the AC component pressure is 3.67 MPa between 20 kHz and 30 kHz. - ...

D.W. Rice, CombstnFlame 8(1), 21-8 (1964) CA 60, 14325 (1964) (Effect of compositional variables upon oscillatory combustion of solid rocket propellants) N ) R.W. Hart F.T. McClure, "Theory of Acoustic Instability in Solid Propellant Rocket Combustion , lOthSympCombstn (1965), pp 1047-65 N2) E.W. Price, "Experimental Solid Rocket Combustion Instability , Ibid, pp 1067-82 Qi) R.S. Levine, "Experimental Status of High Frequency Liquid Rocket Combustion Instability , Ibid, pp 1083-99 O2) L. Crocco,... 

Pugh, S. A., Schell, M. Ross, J. 1986 Effects of periodic perturbations on the oscillatory combustion of acetaldehyde. J. Chem. Phys. 58(2), 868-878. 

Accdg to Mr. R. Baumann of PicArsn, these compds are not catalysts, but rather "modifiers , or additives . They are incorporated into solid proplnts in order to modify or affect their combustion characteristics The compds which affect burning rate include Prussian blues, Aram dichromate, trichromate or tetrachromate, etc). Some compds may be employed to reduce the variability of burning rate with combustion pressure and temperature (Eg Pb stearate or salicylate). Other compds may be used to reduce the tendency toward oscillatory combustion(Eg A1 powder in small quantity), or to affect flash characteristics of exhaust gases [Eg KaS04, Ba(N03)2,... 

Results for oscillatory combustion assuming quasi-steady gas and condensed phase reaction zone (surface reaction approximation) are presented in two groups. First, general characteristics of oscillatory combustion are discussed in the context of the non-dimensional formulation, similar to the steady-state benehmark problem of Table 1. Second, specific results for the common materials NC/NG and HMX are presented. 

As a companion to the steady-state results presented above, oscillatory combustion results and model comparisons are also presented for NC/NG and HMX. The model parameters are those given in Table 2. Thus a unified, coherent steady and unsteady theory is considered. 

M. M. Ibiricu, "Experimental Studies on the Oscillatory Combustion of Solid Propellants," Naval Weapons Center, China Lake, CA, NWC TP 4393, (1969). 

Numerical simulations were performed on the planar problem in [83], which showed that the transition to the self-oscillatory combustion occurs when a parameter related to the Zeldovich number is increased. Numerical studies [5, 6, 79] of the one-dimensional problem found transitions to relaxation oscillations and period doublings, and these studies demonstrated two routes to chaotic dynamics as the bifurcation parameter related to the Zeldovich number was increased. Numerical studies [36 1,1,7,4] of the two- and three-dimensional model found spinning modes of propagation as well as standing modes, which describe multiple point propagation, and quasi-periodic modes of propagation. 

The operation of a pulse combustor is controlled by a complex interaction between an oscillatory combustion process and acoustic waves that are excited inside the combustor (Ligure 21.13). Ignition of the fuel-air mixture by a spark plug... 

These experimentally detected combustion modes were analytically predicted follo-v fing a nonlinear stability analysis of the set of equations governing the combustion process (essentially the energy conservation in the condensed phase with appropriate initial and boundary conditions). This nonlinear analysis accounts for the influence of the properties of the burning material and the ambient conditions (included pressure and diabaticity), allowing to predict PDL and the values of pressure and radiant flux intensity originating oscillatory combustion. Moreover, several numerical checks of the analytical predictions were performed by numerical integration of the basic set of equations under the appropriate ambient conditions. Both the numerical checks and experimental results fully confirm the validity of the analytical predictions. 

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