Combustion instabilities: mating dance of chemical, combustion, and combustor dynamics

Combustion instabilities exist as consequences of interactions among three classes of phenomena: chemistry and chemical dynamics; combustion dynamics; and combustor dynamics. These dynamical processes take place simultaneously in widely different spatial scales characterized by lengths roughly in the ratios (10^(-3) - 10^(-6)):1:(10^3-10^6). However, due to the wide differences in the associated characteristic velocities, the corresponding time scales are all close. The instabilities in question are observed as oscillations having a time scale in the range of natural acoustic oscillations. The apparent dominance of that single macroscopic time scale must not be permitted to obscure the fact that the relevant physical processes occur on three disparate length scales. Hence, understanding combustion instabilities at the practical level of design and successful operation is ultimately based on understanding three distinct sorts of dynamics

Oscillatory and unsteady processes in liquid rocket engines

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Rotational axisymmetric mean flow and damping of acoustic waves in a solid propellant rocket

.!LTHOUGH for many purposes the one-dimensional ap-ft proximation to the steady flow in a rocket chamber is adequate, there are occasions when more precise information is required. For example, analysis of the stability of pressure oscillations involves knowledge of the streamlines. It has been common practice to use the solution for potential flow subject to the boundary conditions of no flow through the head end and uniform speed normal to the burning surface. Since the Mach number generally is very small, one may as-sume the density to be constant; the result for the Mach number in a cylindrical chamber i

Comments on a Ruptured Soap Film

Subsequent to puncturing at a point, a horizontal soap film develops a hole whose edge, owing to surface tension, propagates outward from the point of puncture at apparently constant velocity. Measurements by Ranz [1] yielded results roughly 10% lower than those calculated on the basis of a simple energy conservation suggested by Rayleigh [2]. The discrepancy was attributed to an additional retarding viscous stress not included in the analysis. It appears, however, that the energy balance quoted [1] neglects an important contribution, indeed related to th viscous effect noted by Ranz, but which reduces the calculated values to 20% below those measured. A more detailed analysis of the motion of the edge gives this result; the neglected contribution arises from inelastic acceleration of the undisturbed fluid up to the velocity of the edge. The concomitant loss in mechanical energy may be identified with viscous dissipation which is estimated to be confined to a relatively thin region. Lack of agreement between calculated and measured values of the edge velocity seems to be causes by a second-order effect in the method used [1] to determine the thickness of the film

Nonlinear behavior of acoustic waves in combustion chambers—II

The approximate analysis developed in Part I of Ihis work is apllied to severa1 specific problems. One purpose is to illustrate the use of the formalism, and second is to demostrate the validity of the method by comparing results with numerical solutions, obtained elsewhere, for the "exact" equations. A simple problem is treated first, the decay of a standing wave in a box containing a mixture of gas and suspended particles; one example of the steepening of an initially sinusoidal wave in pure gas is included. Viscous losses on an inert surface are treated essentially according to classical linear theory; recent experimental results are used as the basis for incorporating approximately the influence of nonlinear heat transfer in unsteady flow. All of the preceding results are combined in calculations of two examples of unstable motions in a solid propellant rocket motor and in a T-burner

The Wright Brothers: First Aeronautical Engineers and Test Pilots

Sir George Cayley invented the conventional configuration of the airplane at the turn of the 19th century. Otto Lilienthal realized that building a successful aircraft meant learning how to fly; he became the first hang glider pilot and also the first flight fatality in 1896. Beginning in the late 1890s, the Wright Brothers absorbed all that was known in aeronautics before them, then added their own discoveries and developed the first successful airplane. Technically, their greatest fundamental achievement was their invention of three-axis aerodynamic control. Less obviously, their success was a consequence of style, their manner of working out their ideas and of progressing systematically to their stunning achievements. They were indeed the first aeronautical engineers, understanding as best they could all aspects of their aircraft and flying. They were thinkers, designers, constructors, analysts, and especially flight-testpilots. Their powers of observation and interpretation of the behavior of their aircraft in flight were remarkable and essential to their development of the airplane. Their work in the period 1899–1905 constitutes the first true research and development program carried out in the style of the 20th century. As the centenary of their first powered flights approaches, the Wright Brothers’ magnificent achievements excite growing admiration and respect for their achievements. The broad features of their accomplishments have long been well known. Only in the past two decades has serious attention been directed to the scientific and technical content of their work, to explain the nature of the problems they faced and how they solved them. After a century’s progress in aeronautics, the principles, understanding,and methods not available to the Wrights provide the basis for interpreting in modern terms the experiences that the Wrights themselves documented so meticulously in their diaries, papers, and correspondence. It is a unique opportunity in the history of technology

Calculation of the Admittance Function for a Burning Surface

Calculation of the Admittance Function for a Burning Surface. A thorough analysis of pressure oscillations in a solid propellant rocket requires specification of the response of the burning solid. Indeed, for the case of small amplitude waves, this is the most crucial aspect of the problem; unfortunately, it is also poorly understood. The admittance function is merely a convenient expression of the response which contains the primary mechanism for driving waves. In the work reported here, the usual one-dimensional approximation is made, and three main regions are distinguished: the solid phase being heated, the solid phase involving decomposition (a thin region near the surface), and the gas phase. The problem reduces simply to the solution of appropriate ordinary differential equations and satisfaction of boundary conditions, which include matching at interfaces. The most significant differences from previous work are incorporation of a decomposition region and the treatment of the gas phase. A greatly simplified analysis of the latter leads essentially to the same results found elsewhere, but with substantially less labor. Only a quasistatic analysis, valid for frequencies less than a few thousand cycles per second, is covered, but it can be extended to higher frequencies. Laboratory measurements have shown that the response consists generally of a single peak in the range of frequency for which the quasi static approximation appears to be accurate. The qualitative aspects of such peaks, and their connection with 'self-excited' oscillations, are discussed. In particular, the influence of decomposition and pressure sensitivity of the various chemical reactions is examined. Limited numerical results are included. Eventually, the aim of calculations is principally to gain some understanding of the unsteady combustion process and to aid in classifying propellants. The regions involved in the burning are separately characterized by a small number of dimensionless groups. It appears that the effects represented by these parameters may be distinguished in the response function; one may therefore be able, by use of experimental results, to determine at least qualitative connections between the response to pressure oscillations and changes of composition. In this regard, observations made in both T -burners and L * burners should prove useful