Combustion Instability

There seem to be two types of combustion instability: a set of acoustic resonances or pressure oscillations, which can occur with any rocket motor, and a vortex shedding phenomenon, which occurs only with particular types of grains.

Acoustic Instabilities

When a solid propellant rocket motor experiences unstable combustion, the pressure in the interior gaseous cavities (made up by the volume of the port or perforations, fins, slots, conical or radial groves) oscillates by at least 5% and often by more than 30% of the chamber pressure. When instability occurs, the heat transfer to the burning surfaces, the nozzle, and the insulated case walls is greatly increased; the burning rate, chamber pressure, and thrust usually increase; but the burning duration is thereby decreased. The change in the thrust-time profile causes significant changes in the flight path, and at times this can lead to failure of the mission. If prolonged and if the vibration energy level is high, the instability can cause damage to the hardware, such as overheating the case and causing a nozzle or case failure. Instability is a condition that should be avoided and must be carefully investigated and remedied if it occurs during a motor development program. Final designs of motors must be free of such instability.

There are fundamental differences with liquid propellant combustion behavior. In liquid propellants there is a fixed chamber geometry with a rigid wall; liquids in feed systems and in injectors that are not part of the oscillating gas in the combustion chamber can interact strongly with the pressure fluctuations. In solid propellant motors the geometry of the oscillating cavity increases in size as burning proceeds and there are stronger damping factors, such as solid particles and energy-absorbing viscoelastic materials. In general, combustion instability problems do not occur frequently or in every motor development, and, when they do occur, it is rarely the cause for a drastic sudden motor failure or disintegration. Nevertheless, drastic failures have occurred.

Undesirable oscillations in the combustion cavity propellant rocket motors is a continuing problem in the design, development, production, and even long-term (10 yr) retention of solid rocket missiles. While acoustically "softer" than a liquid rocket combustion chamber, the combustion cavity of a solid propellant rocket is still a low-loss acoustical cavity containing a very large acoustical energy source, the combustion process itself. A small fraction of the energy released by combustion is more than sufficient to drive pressure vibrations to an unacceptable level.

Combustion instability can occur spontaneously, often at some particular time during the motor burn period, and the phenomenon is usually repeatable in identical motors. Both longitudinal and transverse waves (radial and tangential) can occur. Figure 13-5 shows a pressure-time profile with typical instability. The pressure oscillations increase in magnitude, and the thrust and burning rate also increase. The frequency seems to be a function of the cavity geometry, propellant composition, pressure, and internal flame field. As

FIGURE 13-5. Simplified diagram showing two periods of combustion instability in the pressure-time history, with enlargements of two sections of this curve. The dashed lines show the upper and lower boundaries of the high-frequency pressure oscillations, and the dot-dash curve is the behavior without instability after a slight change in propellant formulation. The vibration period shows a rise in the mean pressure. With vibration, the effective burning time is reduced and the average thrust is higher. The total impulse is essentially unchanged.

FIGURE 13-5. Simplified diagram showing two periods of combustion instability in the pressure-time history, with enlargements of two sections of this curve. The dashed lines show the upper and lower boundaries of the high-frequency pressure oscillations, and the dot-dash curve is the behavior without instability after a slight change in propellant formulation. The vibration period shows a rise in the mean pressure. With vibration, the effective burning time is reduced and the average thrust is higher. The total impulse is essentially unchanged.

Burning time

Burning time the internal grain cavity is enlarged and local velocities change, the oscillation often abates and disappears. The time and severity of the combustion vibration tend to change with the ambient grain temperature prior to motor operation.

For a simple grain with a cylindrical port area, the resonant transverse mode oscillations (tangential and radial) correspond roughly to those shown in Fig. SM for liquid propellant thrust chambers. The longitudinal or axial modes, usually at a lower frequency, are an acoustic wave traveling parallel to the motor axis between the forward end of the perforation and the convergent nozzle section. Harmonic frequencies of these basic vibration modes can also be excited. The internal cavities can become very complex and can include igniter cases, movable as well as submerged nozzles, fins, cones, slots, star-shaped perforations, or other shapes, as described in the section on grain geometry in Chapter 11; determination of the resonant frequencies of complex cavities is not always easy. Furthermore, the geometry of the internal resonating cavity changes continually as the burning propellant surfaces recede; as the cavity volume becomes larger, the transverse oscillation frequencies are reduced.

The bulk mode, also known as the Helmholtz mode, L* mode, or chuffing mode, is not a wave mode as described above. It occurs at relatively low frequencies (typically below 150 Hz and sometimes below 1 Hz), and the pressure is essentially uniform throughout the volume. The unsteady velocity is close to zero, but the pressure rises and falls. It is the gas motion (in and out of the nozzle) that corresponds to the classical Helmholtz resonator mode, similar to exciting a tone when blowing across the open mouth of a bottle (see Fig. 9-7). It occurs at low values of L* (see Eq. 8-9), sometimes during the ignition period, and disappears when the motor internal volume becomes larger or the chamber pressure becomes higher. Chuffing is the periodic low-frequency discharge of a bushy, unsteady flame of short duration (typically less than 1 sec) followed by periods of no visible flame, during which slow out-gassing and vaporization of the solid propellant accumulates hot gas in the chamber. The motor experiences spurts of combustion and consequent pressure buildup followed by periods of nearly ambient pressure. This dormant period can extend for a fraction of a second to a few seconds (Ref. 13-13 and Chapter 13 by Price in Ref. 13-1).

A useful method of visualizing unstable pressure waves is shown in Figs. 9-5 and 13-6 and Ref. 13-14. It consists of a series of Fourier analyses of the measured pressure vibration spectrum, each taken at a different time in the burning duration and displayed at successive vertical positions on a time scale, providing a map of amplitude versus frequency versus burning time. This figure shows a low-frequency axial mode and two tangential modes, whose frequency is reduced in time by the enlargement of the cavity; it also shows the timing of different vibrations, and their onset and demise.

The initiation or triggering of a particular vibration mode is still not well understood but has to do with energetic combustion at the propellant surface. A sudden change in pressure is known to be a trigger, such as when a piece of t

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