Pressure oscillation tangential mode

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. - ...

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... 

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