Acoustic oscillations in solid propellant rocket chambers

Acoustic Oscillations in Solid Propellant Rocket Chambers. Among the various kinds of periodic motions observed in rocket combustion chambers, the most common and simplest to analyze are those related to classical acoustic modes. If the amplitudes are small, the main perturbations of the familiar standing or travelling waves in a closed chamber are proportional to the Mach number of the mean flow. The correct equations describing the problem are here obtained from the general equations of motion by a limit process which will also provide equations for studying waves of finite amplitude. Subsequently, a single non-homogeneous wave equation is deduced, and solved by an iteration· perturbation procedure. The principal result is a simple formula for the complex frequency showing explicitly the effects of burning, suspended particles in the gases, the exhaust nozzle, and viscous wall forces as well as the mean flow itself. The last is particularly interesting since, owing primarily to the flow inward from the burning surface, the mean flow, if it is irrotational, never acts to damp modes which do not involve axial oscillations. As a particular application, the extensive data taken by BROWNLEE and MARBLE are interpreted to the extent that the linear analysis permits. A stability boundary was obtained from 250 firings of small cylindrical rockets, the principal variables being initial port diameter and length. The propellant did not contain metal particles, and it appears that the observations cannot be explained by the supposition that viscous damping associated with particles in the product gases was the main source of energy loss. Apparently dissipation at the head end, such as that associated with tangential wall shear forces, was an important loss. On the other hand, there is little doubt that if the combustion produces particles, the consequent dissipation is adequate to damp small amplitude waves

Nonlinear analysis of pressure oscillations in ramjet engines

Pressure oscillations in ramjet engines have been studied using an approximate method which treats the flow fields in the inlet and the combustor separately. The acoustic fields in the combustor are expressed as syntheses of coupled nonlinear oscillators corresponding to the acoustic modes of the chamber. The influences of the inlet flow appear in the admittance function at the inlet /combustor interface, providing the necessary boundary condition for calculation of the combustor flow. A general framework dealing with nonlinear multi-degree-of-freedom system has also been constructed to study the time evolution of each mode. Both linear and nonlinear stabilities are treated. The results obtained serve as a basis for investigating the existence and stabilities of limit cycles for acoustic modes. As a specific example, the analysis is applied to a problem of nonlinear transverse oscillations in ramjet engines

Application of dynamical systems theory to the high angle of attack dynamics of the F-14

Dynamical systems theory has been used to study the nonlinear dynamics of the F-14. An eight degree of freedom model that does not include the control system present in operational F-14's has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearities as functions of the angles of attack and sideslip, the rotation rate, and the elevator deflection. A continuation method has been used to calculate the steady states of the F-14 as continuous functions of the control surface deflections. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena which cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations

Overview of Combustion Instabilities in Liquid-Propellant Rocket Engines

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Aerodynamics, Stability and Control of the 1903 Wright Flyer

The Los Angeles Chapter of the American Institute of Aero and Astronautics is building two replicas of the 1903 Wright Flyer airplane; one to wind-tunnel test and display, and a modified one to fly. As part of this project the aerodynamic characteristics of the Flyer are being analyzed by modern wind-tunnel and analytical techniques. Tnis paper describes the Wright Flyer Project, and compares key results from small-scale wind-tunnel tests and from vortex-lattice computations for this multi-biplane canard configuration. Analyses of the stability and control properties are summarized and their implications for closed-loop control by a pilot are derived using quasilinear pilot-vehicle analysis and illustrated by simulation time histories. It is concluded that, although the Wrights were very knowledgeable and ingenious with respect to aircraft controls and their interactions (e.g., the good effects of their wing-warp-to-rudder linkage are validated), they were largely ignorant of dynamic stability considerations. The paper shows that the 1903 Flyer was readily controllable about all axes but was intrinsically unstable in pitch and roll, and it could barely be stabilized by a skilled pilot

The role of non-uniqueness in the development of vortex breakdown in tubes

Numerical solutions of viscous, swirling flows through circular pipes of constant radius and circular pipes with throats have been obtained. Solutions were computed for several values of vortex circulation, Reynolds number and throat/inlet area ratio, under the assumptions of steady flow, rotational symmetry and frictionless flow at the pipe wall. When the Reynolds number is sufficiently large, vortex breakdown occurs abruptly with increased circulation as a result of the existence of non-unique solutions. Solution paths for Reynolds numbers exceeding approximately 1000 are characterized by an ensemble of three inviscid flow types: columnar (for pipes of constant radius), soliton and wavetrain. Flows that are quasi-cylindrical and which do not exhibit vortex breakdown exist below a critical circulation, dependent on the Reynolds number and the throat/inlet area ratio. Wavetrain solutions are observed over a small range of circulation below the critical circulation, while above the critical value, wave solutions with large regions of reversed flow are found that are primarily solitary in nature. The quasi-cylindrical (QC) equations first fail near the critical value, in support of Hall's theory of vortex breakdown (1967). However, the QC equations are not found to be effective in predicting the spatial position of the breakdown structure

Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber

For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary differential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics is accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the modal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our analysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character is shown here also to produce triggered limit cycle behavior

Feasibility and Performance of the Microwave Thermal Rocket Launcher

Beamed-energy launch concepts employing a microwave thermal thruster are feasible in principle, and microwave sources of sufficient power to launch tons into LEO already exist. Microwave thermal thrusters operate on an analogous principle to nuclear thermal thrusters, which have experimentally demonstrated specific impulses exceeding 850 seconds. Assuming such performance, simple application of the rocket equation suggests that payload fractions of 10% are possible for a single stage to orbit (SSTO) microwave thermal rocket. We present an SSTO concept employing a scaled X-33 aeroshell. The flat aeroshell underside is covered by a thin-layer microwave absorbent heat-exchanger that forms part of the thruster. During ascent, the heat-exchanger faces the microwave beam. A simple ascent trajectory analysis incorporating X-33 aerodynamic data predicts a 10% payload fraction for a 1 ton craft of this type. In contrast, the Saturn V had 3 non-reusable stages and achieved a payload fraction of 4%

Application of dynamical systems theory to nonlinear aircraft dynamics

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamical model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was use to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations