Untitled - Aerobib - Universidad Politécnica de Madrid

270 CHAPTER 11. SIMILARITY IN COMBUSTION. APPLICATIONS
11.4 Scaling of rockets for non-steady conditions
The motion on gases through the combustion chamber of a rocket is always strongly
turbulent with oscillations of pressure, velocities, etc., distributed at random in time
and space, which does not cause important disturbances in the normal operation of the
rocket. Under these circumstances the combustion is called steady.
However, there is also the case, frequently observed, where combustion is unstable
with strong self-excited periodic oscillations of pressure which in some case
destroy the rocket in a few seconds. This phenomenon is at present one of the main
difficulties for the development of rockets, specially large ones. It was observed for
the first time in the United States in 1941 by the research staff of the Jet Propulsion
Laboratory of the California Institute of Technology under the guidance of Professor
von Kármán. Thereafter the great effort applied to the study of this problem has
consderably increased the technical literature on the subject.
Ross-Datner [11] and Crocco-Gray-Grey [12] have written two excellent reviews
on this problem describing the kinds of instabilities observed, their causes, experimental
techniques and the results of the measurements performed, in addition to
the fundamentals of the theories available. These reviews include as well an extensive
bibliography. The most up to date and complete work on the subject is the one
performed by Crocco and Cheng [13] which was recently published by AGARD, including
an abundant bibliography.
Initially, due to limitations of the instruments available for observation, it was
only possible to isolate one type of low-frequency oscillations of the order of about
100 cycles per second, which is normally known as chugging. Later on, as the instrumentation
was improved, it became feasible to isolate other high-frequency oscillations,
over 1000 c.p.s., generally called screaming.
Soon, the origine of the low-frequency oscillations was known and it was possible
to derive practical rules to prevent them which resulted efficient when applied to
practice. Summerfield [14] stated the fundamentals of the theory and the preventive
rules born from it. In low-frequency oscillations, the combustion chamber behaves
like a resonating cavity whose oscillations of pressure act on the feeding system,
changing the rate of fuel injected. The influence of this variation reflects on the chamber
with a certain delay which is due partially to the relaxation times of the chamber
and of the feeding system, and partially to the physico-chemical time lag described
in the preceding paragraph. If this delay is the adequate one, the oscillations result
self-excited. Consequently, the unit combustion chamber-feeding system behaves as a
dynamic system with a characteristic time lag, able of producing unstable oscillations.