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National Advisory Committee for Aeronautics, Technical Notes - Driving Standing Waves by Heat Addition

Types of burner instability are enumerated and the role of standing
waves in burners is discussed. The status of the problem of flame-driven
standing waves is reviewed and a one-dimensional flow theory giving the
mechanism whereby a flame drives or damps a standing wave is presented.
In this theory, the reflection, transmission, and amplification of waves
passing through a flame region were determined from the continuity and
momentum equations. For the model considered, waves were found to pass
through the flame front with their velocity amplitudes unaltered so long
as the flame area remained unchanged. A change in flame area acted as a
source of waves propagating simultaneously into the hot and cold gases '
on either side of the flame zone.

Inlet Mach number and Tl/Tg the temperature ratio across the flame
zone), these waves are of equal magnitude and the driving criterion is
that proposed by Rayleigh, namely, that for heat to drive a standing
wave, the heat input should maximize with time at a place where the
pressure in the standing wave varies and at a time when the pressure is
near its local maximum value.

The role played by a flame in a standing-wave system was examined
experimentally by measuring the ability of a flame to damp a standing
wave. Factors investigated were: fuel—air ratio, inlet gas temperature,
sound amplitude, inlet velocity, flame- holder position, and flame area
as a function of time.

The percentage flame-area disturbance was found proportional to
percentage velocity disturbance entering the flame zone. The phase lag
of the area disturbance behind the velocity disturbance was found 3
dependent upon flame—holder geometry and flame speed; in general, this
lag increased as the flame speed decreased.

The flame shape was strongly influenced by a radial component of
the time—varying flow which appeared to follow a potential-flow velocity
distribution in the neighborhood of the flame holder. This radial com—
ponent of flow caused an initial growth of the disturbance in the flame
front until a position was reached such that normal flame propagation
caused these disturbances to undergo an apparent decay.