Pressure oscillation mode

When combustion instability occurs for an internal burning grain of a rocket motor, the burning rate of the grain varies with time and so does the pressure in the rocket motor. The pressure versus time curve shows oscillations of a certain frequency. When the propellant burning mode is not in harmony with the pressure oscillation mode, the combustion instabiUty tends to decay. However, when the burning mode is in harmony with the oscillation mode, the pressure oscillation is amplified. 

In this mode, acoustic-pressure oscillations are similar to those established in a closed organ pipe. The resulting pressure oscillations then couple with the pressure-sensitive combustion processes to further excite the oscillating pressure and thus produce the high-pressure amplitudes. 

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... 

Figure 4.22 Isothermal autoosclllations of the rate of heterogeneous catalytic reaction CO + 1/2 O2 CO2 over monocrystal Pt(lOO) accompanied by a monocrystal surface reconstruction and, as a result, by changing the oscillation mode. Temperature 450 K, CO pressure 4.5 10 Pa, the dioxygen pressure 1.7 10 Pa [8]. (Courtesy of V. I. Savchenko )...

Oscillations with only one frequency are monochromatic waves. Thus each normal mode of oscillation [each term in equation (8)] defines a monochromatic wave. There are special shapes of chambers for which more than one mode may have the same frequency this is called degeneracy and admits an infinite variety of monochromatic wave forms (for example, tangential modes in cylindrical chambers). Most of the normal modes describe standing waves, waves having nodal points for the velocity (points where the velocity is always zero) and for the amplitude of the pressure oscillations. Thus, according to equation (8), longitudinal modes have pressure nodes at nz/l = 1, I,..., and they have velocity nodes at nz/l = 0, 1, 2,..., as... 

The combustor is naturally unstable under certain operating conditions. Figure 16.7 shows combustor pressure oscillations and the Fast Fourier Transform (FFT) spectrum under atypical, unstable operating condition. The fundamental mode at 39 Hz and its higher harmonics were observed. The fundamental-mode frequency corresponds to the inlet quarter-wave mode of acoustic oscillations. During stable operation as shown in Fig. 16.8, the amplitude of pressure oscillations is much less. Also, no significant peak was observed in the pressure spectrum. 

Vortical structures are reported to cause flame/heat release oscillations in reacting flows or pressure oscillations in nonreacting flows [1-8]. In these cases, hydrodynamic instabilities leading to the formation of the vortical structures define the mode frequency, perturb the heat release, and feed energy into the acoustic held, which, under the circumstances, acts as an amplifier. During the past years, the authors have developed an approach to capture flame-acoustic shear-layer coupling. 

During the operation of some solid-propellant motors, several investigators have observed oscillations occurring at low frequences (0-500 cps), as shown in Fig. 23. These oscillations cannot be associated with any of the acoustic modes of the combustion chamber. Angelus (All) was one of the first to investigate these low-frequency oscillations later, Yount and Angelus (Yl) observed that the amplitude of the oscillations decreased and the frequency increased with increasing mean chamber pressure. They correlated... 

Pressure drop oscillations (Maulbetsch and Griffith, 1965) is the name given the instability mode in which Ledinegg-type stability and a compressible volume in the boiling system interact to produce a fairly low-frequency (0.1 Hz) oscillation. Although this instability is normally not a problem in modern BWRs, care frequently must be exercised to avoid its occurrence in natural-circulation loops or in downflow channels. 

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. - ...

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