Engineering topics
Publications and source records attributed to Culick, F. E. C..
The chief purpose of this paper is to provide a brief review of some recent work on nonlinear acoustics applicable to combustion instabilities, largely in the framework of an approximate analysis. Some connections will be made with the modern theory of nonlinear dynamical systems, including very recent and incomplete attempts by others to assess the possible chaotic behavior observed in laboratory tests.
This is a summary of a progress report of the Los Angeles AIAA Section Wright Flyer Project. Begun in late 1978, the project is devoted chiefly to construction of two replicas of the 1903 Wright 'Flyer'. The first, now being covered, is an exact replica intended for full-scale wind tunnel tests. The second will be a flying replica, incorporating minimal modifications to produce a less unstable aircraft. Considerable attention has been given to the aerodynamics, stability, and control of the 1903 'Flyer'. Wind-tunnel tests have been conducted with a 1/6 flexible model, and a 1/8 scale steel model tested at full-scale Reynolds numbers. The data have provided the basis for analyzing both the closed-loop and open-loop performance of the aircraft. Consideration is also given to aeronautical history both before and after 1903, to provide a better appreciation for the Wrights' achievements and a clearer perspective of their work in the context of aeronautical progress.
An experimental investigation has been carried out for acoustic oscillations sustained by flow through a duct containing two baffles. Pure acoustic tones corresponding to longitudinal resonant modes of the duct are produced when certain flow and geometrical conditions are satisfied. The conditions are such as to ensure close coincidence between the frequency of vortex shedding from the forward baffle, and a natural frequency of the duct. Flow visualization has shown that under these conditions a stable vortex structure exists between the baffles, containing at all times an integral number of vortices.
Data were obtained for a resonance tube having a vent at the center in the lateral boundary, an average flow being introduced at the ends. Experiments were done for both circular and slot vents, over ranges of both frequency and Mach number. It was demonstrated that a subsonic exhaust vent in the lateral boundary of a cold flow resonance tube provides a gain of acoustic energy for the fundamental mode within the resonance tube. The gain of acoustic energy increases approximately linearly with the Mach number, as predicted by the one-dimensional analysis. The one-dimensional result gives the values for the slope representing the variation of the attenuation coefficient of the exhaust vent with respect to the average Mach number of the flow within roughly 30% of those measured. It has been verified that the subsonic vent produces a gain proportional to the average Mach number, proportional to the frequency, and independent of the shape. The results may be applicable to the study of vibration phenomena in solid propellant rocket engines.
Two problems crucial to the stability of longitudinal acoustic waves in solid rocket motors were examined experimentally. The first is the dissipation of energy associated with an average flow inward at the lateral boundary. Measurements reported here, though subject to considerable experimental error, show that the actual losses are much larger than predicted by the approximate one dimensional analysis. The second problem is the attenuation of waves accompanying reflection by the nonuniform flow in a choked exhaust nozzle. Emphasis on technique, to provide data relatively easily and inexpensively. It appears that good results can be obtained in a routine manner using small supersonic wind tunnel operated as an open cycle. At least for Mach numbers up to 0.04 at the nozzle entrance, difficulties with signal/noise are satisfactorily overcome with a tracking filter.
The treatment of unsteady flows in a combustion chamber is discussed. As an example a rocket motor is considered, where material enters through a lateral boundary with its stagnation enthalpy different from the average speed. The equations of motion for unsteady flow within a one-dimensional approximation are analyzed, and the production of entropy is deduced. In the equations, the term representing the dissipative processes are identified by constructing a representation for the production of entropy.
The response functions of composite propellants are theoretically derived, including explicitly the pressure-dependent degradation term in the condensed phase, hypothesizing that the overall rate-limiting reactions are in the relatively low temperature condensed phase. The method of 'inner' and 'outer' expansions with the reduced activation energy as the singular perturbation parameter has been employed. The results cover subsurface reactions with and without surface reactions, adiabatic and uniform-combustion models for the quasi-steady gas phase processes. The response functions display several experimentally observed features like dependence on mean pressure and the instability behavior of some 'zero-n' propellants.
The general problem of the nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber is treated in three parts: (1) the general conservation equations are expanded in two small parameters, and then combined to yield a nonlinear inhomogeneous wave equation, (2) the unsteady pressure and velocity fields are expressed as a synthesis of the normal modes of the chamber, but with unknown time-varying amplitudes, and (3) the system of nonlinear equations is treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. This approximate analysis is applied to the investigation of the unstable motions in a solid propellant rocket engine and in a T burner.
The nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber are considered. A formal framework is provided within which practical problems can be treated with a minimum of effort and expense. The general conservation equations were expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. The unsteady pressure and velocity fields were expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yielded a representation of a general unsteady field as a system of coupled nonlinear oscillators. The system of nonlinear equations was treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. The analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines.
At the present time, there are three general analytical techniques available to study problems of unsteady motions in rocket motors: linear stability analysis; approximate nonlinear analysis, founded on examining the behavior of coupled normal modes; and numerical calculations based on the conservation equations for one-dimensional flows. The last two yield the linear results as a limit. It is the main purpose of this paper to check the accuracy of the approximate analysis against the numerical analysis for some special cases. The results provide some justification for using the approximate analysis to study three-dimensional problems.
In the studies reported use was made of the T-burner to obtain a correlation between the average heat transfer coefficient along the burner and the amplitude of the flow oscillations. The T-burner used consists of a centrally-vented cylindrical chamber with disks of solid propellant bonded in each end. The obtained data provide a basis for predicting heat transfer rates in other combustion chambers containing oscillatory flows.
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Experimental study of the effects of minor compositional variables upon the combustion behavior of composite solid propellants. More specifically, it was attempted to determine the influence of ingredients that improve the mechanical properties upon the oscillatory combustion characteristics. Tests were carried out in the familiar Crawford bomb, a low-pressure L-star burner, and a high-pressure T-burner. Two families of propellants were investigated; each family consists of two propellants with a minor compositional variation between them. In the family that shows a decreasing (steady state) pressure index (n) with increasing pressures, all of the combustion characteristics are found to be very similar although the mechanical properties are widely different. In the other family, which shows an increasing n with increasing pressures, unmistakable differences are found between the two propellants in the low-pressure L-star instability behavior (along with the differences in the mechanical properties), while the other combustion characteristics are almost identical. The results are interpreted to be consistent with a theory that highlights the importance of condensed phase heat-transfer effects.
Review of the current state of analyses of combustion instability in solid-propellant rocket motors, citing appropriate measurements and observations. The work discussed has become increasingly important, both for the interpretation of laboratory data and for predicting the transient behavior of disturbances in full-scale motors. Two central questions are considered - namely, linear stability and nonlinear behavior. Several classes of problems are discussed as special cases of a general approach to the analysis of combustion instability. Application to motors, and particularly the limitations presently understood, are stressed.
Combustion instability with wave motion coupling in solid propellant rocket motors due to energy gain and loss mechanisms within chamber
Combustion instability data with same solid propellants by T-burner and L super asterisk burner, discussing theoretical models of transient combustion
Burning solid propellant behavior under pressure fluctuations expressed in response function terms defining small mass flux change ratio to small pressure change
Laboratory unsteady burning data applied to analysis of small amplitude combustion instability in solid propellant rockets