: 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

This paper reviews the problem of unstable combustion in solid-propellant rockets, with special emphasis on the status of theory and, where possible, the comparison between theory and experiment. The manifestation of the problem in terms of the appearance of periodic pressure waves, and the consequences which ensue when these reach sufficient amplitude are first outlined. A rocket motor is then viewed as an acoustic cavity. The possible sources and sinks of acoustic energy are enumerated, and the gain-loss balance is discussed with respect to self-excited oscillation, and also with respect to influences of outside perturbations on a stable cavity which has a high Q . The quantitative approach to the representation of, the various gain-loss mechanisms in the domain of linear stability theory is then reviewed. Particular emphasis is put on the modifications to ordinary acoustic stability theory which are required because of the existence of a mean flow field. The contributions to linear instability of the response of the burning propellant, both to the pressure and velocity components of the acoustic field, are then discussed. Attention is then turned to the fundamental theory of the interaction of the burning surface with a pressure oscillation. The linear (small perturbation) theory of the acoustic response of this region is reviewed in terms of the analytic models, and postulates that have been made, and their theoretical results. Some qualitative comparison with experiment is made. The remaining part of the paper is then devoted to nonlinear effects. The theory of nonlinear instability in such systems is first reviewed to the extent that it exists. Then, the consequences of oscillation of finite amplitude arising from nonlinear effects are discussed. Under this heading, amplitude limitation in unstable cavities, wave distortion, and changes in the mean properties of the system are considered. In the alst category, changes in the mean burning rate due to nonlinear pressure response and due to the erosion associated with the velocity component of the acoustic field are noted. The induction of vortex flow by acoustic streaming, as described by Swithenbank and Sotter and by Flandro, is discussed with particular reference to its consequences in producing increased erosion, decreased nozzle flow, and angular torques. Brief mention is also made of the effects of the amplitude oscillations on combustion, efficiency and the composition of the product gases.

Theory of acoustic instability in solid-propellant rocket combustion

Combustion instabilities in motors and furnaces are contrasted under three separate headings: System instabilities involve, in an essential way, interactions between processes occuring in the combustion chamber and processes occurring in at least one other component of the system. Combustion chamber instabilities consist of unsteady phenomena that are localized within the combustion chamber. Intrinsic instabilities are inherent in the reactants themselves and would be observed if combustion were to occur in the absence of any external influences. The second category, combustion-chamber instabilities, is again divided into three subcategories: Acoustic instabilities involve, in an essential way, the propagation of acoustic waves in the combustion chamber. Shock instabilities are characterized by the presence of steep-fronted finite-amplitude shock or detonation waves in the combustion chamber. Fluid-dynamic instabilities are associated with the establisment of special kinds of flow patterns, such as vortices, in the chamber. Experimental and theoretical aspects of each of these types of instabilities are discussed separately. Characteristics of each type of instability are described, and the kinds of chambers in which each has been observed are indicated. Attention is given to surface-burning systems, such as solid-propellant rockets and hybrid rocket motors, and also to volume-burning systems, such as liquid-propellant rocket engines and both gas-fired and oil-fired industrial burners. Experimental procedures for investigating each type of instability are reviewed along with selected experimental results, and the character and state of development of the theoretical methods that have been used for describing each type of instability are compared. The review is an attempt to bring about discussions between specialists who study combustion instabilities in different systems. Classification according to the type of instability rather than the type of system can emphasize the similarities and differences that exist among combustion instability problems encountered in different systems. One resulting observation is that examples of system instabilities and of acoustic instabilities are common to all kinds of combustion systems.

Comparison of combustion instabilities found in various types of combustion chambers

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

Vortices are generated by acoustic oscillations as a second-order viscous effect. Traveling tangential modes in an axially perforated solid propellant rocket give a single vortex swirling about the axis. Tangential velocity at the periphery, typically a few hundred feet per second, can be predicted approximately using acoustic streaming theory modified by heat addition and radial flow effects. Serious consequences of the vortex are 1) torque, which gives undesired roll, especially in large vehicles as torque varies as (radius), and 2) pressure rise caused largely by reduction in the effective area of the nozzle throat. Standing tangential modes produce a pair of vortices rotating in opposite directions for each pressure antinode. These give no net torque and are much less destructive. Experimental data include 3200 frames/ sec cine-films of the vortices, torque measurements, and radial pressure gradient determinations in the head end of a motor. The traveling tangential modes can be initiated readily by tangential injection of nitrogen into the motor.

G. Sotter

Papers

Vortex generation in solid propellant rockets

Vortices in Solid Propellant Rocket Motors