Analytical methods and four computer programs have been developed for calculating wave motion in closed, baffled chambers with rigid and non-rigid boundaries. Application of these methods to design of injector-face baffles in liquid propellant engines will provide significant insight into effects of baffles on combustion stability

Oberg, C. L.

Schmeltzer, R. A.

Wong, T. L.

English

NASA Technical Reports Server

September 1972
	 B72-10577 
NASA TECH BRIEF 
Lewis Research Center 
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Analysis and Computer Programs to Calculate 
Acoustic Wave Properties of Baffled Chambers 
Analytical methods and four computer programs have 
been developed for calculating the wave motion in 
closed, baffled chambers with rigid and nonrigid bound-
aries. Application of these methods to the design of 
injector-face baffles in liquid-propellant engines will 
provide significant insight into the effects of baffles on 
combustion stability. 
Approximate solutions to the wave equation, with 
essentially continuous pressure distributions, were ob-
tained for closed, two-dimensional chambers containing 
an unrestricted number of equal length and equally 
spaced baffles. Solutions were obtained by converting 
the wave equation and boundary conditions to an 
integral equation; this integral equation was solved with 
a combination of variation and iteration methods. The 
mathematical techniques used to obtain these solutions 
apply equally well to cylindrical or annular chambers, 
and to unequal baffle lengths or spacing, although with 
some increase in complexity. 
These methods encompass solving the wave equation 
for the baffled chamber by converting the differential 
equation and boundary conditions to an integral equa-
tion which, in turn, is solved by approximate means. 
A variational technique in combination with an iterated 
approximation was used to solve the integral equation. 
Numerical results were obtained for two-dimensional 
chambers containing one or several equal length and 
equally spaced baffles. The results show an essentially 
continuous pressure distribution along the baffle tips. 
Requirements for continuity of velocity and energy 
flux are automatically met with this method. Further-
more, the effects of a single baffle on the stability of 
a chamber with non-rigid walls, i.e., gain/loss type 
boundary conditions, have been successfully analyzed 
for one particular two-dimensional geometry. Thus, the 
ability to generalize the method for nonzero boundary 
conditions has also been demonstrated.
The first computer program was written to solve the 
iterative characteristic equation for the rigid boundary 
case. The method used to solve this equation was to 
calculate the value of the function while incrementally 
changing the wave characteristic and frequency until the 
value of the function changed signs. The usual practice 
was to calculate the characteristic equation over a large 
interval by taking large increments for the wave charac-
teristic. After noting the interval in which the value of 
the function changed signs, that interval was subdivided 
into small increments. The procedure was repeated until 
an accurate value of the wave characteristic was obtained. 
The second program calculates the pressure across 
the baffle tips on the main chamber side of the interface 
across the baffle tips. With the wave characteristic fixed 
for a given set of parameters, it is possible to determine 
the relationship between pressure and the position 
coordinate. Pressure at the baffle tips was calculated 
across the width of the chamber. 
The third program was used to calculate the pressure 
at the baffle tips on the compartment side of the inter-
face. Considering the pressure as a function of the posi-
tion coordinate, it is possible to determine the pressure 
for a given wave characteristic. 
The fourth program was written to determine the 
stability limit of a combustion chamber with active 
boundaries located at both ends. The characteristic 
equation is in complex notation, and the root of the 
characteristic equation is a complex eigenvalue (the real 
part is the nondimensional frequency and the imaginary 
part is the nondimensional damping coefficient). Thus, 
for a given set of parameters, nozzle admittance, and 
injector admittance, the complex root which satisfies 
the characteristic equation specifies the frequency and 
the damping coefficient of the system. The acoustic 
admittance obtained defines the maximum amount of 
acoustic energy (related to the admittance) that can 
(continued overleaf) 
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be pumped into the system and still have the system 
stable. This avenue was taken to evaluate the stability 
limit.
Source: C. L. Oberg, T. L. Wong, 
Note: and R. A. Schmeltzer of 
1. These programs were written in FORTRAN IV for North American Rockwell Corp. 
use on a GE 420 time sharing computer system. under contract to 
2. Inquiries concerning this program should be directed Lewis Research Center 
to: (LEW-11529) 
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: LEW-1 1529 
B72-10577 Category 09


Analysis and computer programs to calculate acoustic wave properties of baffled chambers

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