: This book has several purposes, including a broad historical summary of combustion instabilities in propulsion systems; a concise compilation of the main mechanisms for instabilities in liquid and solid fueled rockets, ramjets, thrust augmentors and gas turbines; development of a theoretical framework for investigating unsteady motions in combustion systems; and accessible surveys of the basic material required to understand the subject. Emphasis is placed throughout the book on observed behavior. For well-understood reasons, the best, and in many respects most useful quantitative data, have been obtained for solid propellant rockets. Hence that type of device occupies a special position in the subject. The book comprises nine chapters and eight annexes. Material in the annexes is not essential for reading and broadly understanding the main part of the book, but is likely interesting for those choosing to do research on the subject. The nine chapters divide into three parts.

Unsteady Motions in Combustion Chambers for Propulsion Systems

Experience with oscillatory combustion of solid rocket propellants is classified into three categories referred to as high-, intermediate-, and low-frequency instability. In the frequency range 1000 cps and up, instability (a) is usually encountered in transverse modes of the rocket motor; (b) results from interaction between acoustic pressure and the combustion process; and (c) is suppressed by metal fuel ingredients in the propellant (particularly aluminum), at least in part through acoustic damping by the metal oxide droplets in the gas. In the frequency range 100–1,000 cps, instability (a) is usually encountered in axial modes of the rocket motor; (b) is often initiated by large disturbances under linearly stable conditions; (c) results from interaction between both acoustic velocity and acoustic pressure with the combustion process; and (d) is not suppressed by metal fuel ingredients, but instead may be aggravated by the metal combustion. In the frequency range 1–100 cps, instability may occur in either acoustic or nonacoustic modes. Experience to date, at low frequency, pertains only to cases of interaction of acoustic pressure with combustion, but velocity-coupled contributions seem likely in rockets with dimensions large enough for axial acoustic modes in this frequency range. Low-frequency instability is more prevalent at low pressures, and is often confined to a narrow frequency range. The pattern of instability behavior has emerged as a consequence of extended experience with rocket motors and intensive investigations with burners designed specially for the purpose. The laboratory burners can be designed to control the type of acoustic behavior and the environmental conditions, permitting less equivocal interpretation of test results. The small propellant requirements in the laboratory burners have permitted greatly increased testing, including studies of propellant variables. While the gross aspects of instability behavior have fallen into a fairly orderly pattern, the inner microscopic behavior of the combustion zone under transient conditions is established only on a speculative basis, leaving the combustion scientist's job incomplete.

Experimental solid rocket combustion instability

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Propellant Combustion Instability as Measured by Combustion Recoil

An analysis is presented in which the instability, known as nonacoustic or L* instability, in the combustion of solid propellants is re-examined by means of an acoustic approach, i.e., by solving the wave equation for the cavity. It is found that nonacoustic instability is, in reality, a zeroth longitudinal acoustic mode for the motor, an observation not previously made. This conclusion allows the application of equations and data developed for acoustic instability to understand nonacoustic instability. The analysis was further developed by making use of the Denison-Baum combustion model to describe the combustion, after gaining assurance that this model could adequately describe existing acoustic and nonacoustic instability data. In this manner, it was possible to explain many experimental observations with considerable clarity. Finally, in the course of this analysis, a quantitative comparison has been made between the Denison-Baum combustion model and existing instability data in a rather complete manner for several propellants.

Combustion instability - The relationship between acoustic and nonacoustic instability.

Two systems were used for the study of low-frequency oscillatory combustion. The first was a small end-vented burner that employed end-burning grains and produced nonacoustic pressure oscillations. The second system was a side-vented, double-end burner of suitable lengths to produce low-frequency (5 to 320 cps) acoustic pressure oscillations. The propellant tested most extensively (a metallized double base) exhibited oscillations only over a very restricted pressure-frequency region. This region was similar for each type of burner. From these results it was inferred that the response function of the combustion zone showed a marked peak when plotted as a function of frequency at low pressures. Similar behavior was shown by a highly aluminized composite propellant; however, other propellants did not reveal the phenomenon.

J. L. Eisel

Papers

Preferred frequency oscillatory combustion of solid propellants

Low frequency acoustic oscillatory combustion