Innovative methods applied to the acoustic paradigm of the motion of hot gases inside a solid rocket motor, with special emphasis on combustion instability



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The acoustic model (or “paradigm”) developed by F. E. C. Culick at the California Institute of Technology in the 1960s assumes that pressure oscillations (often described as combustion instability) inside a rocket motor are primarily governed by acoustical waves superimposed on the mean flow of combustion gases. The fluctuations affect the motor operating behavior often in unexpected ways. Nonlinear mechanisms may lead to elevated mean pressure that threatens the structural integrity of the motor case itself, sometimes catastrophically. Despite these nonlinear effects, the acoustic field remains an important part of any description of moving gases inside a choked combustion chamber. The basic features of this unsteady flow phenomenon can be readily demonstrated using a Rijke Tube,or even an organ pipe. The phase angle of the fluctuations relative to the principal pressure wave for each mode represents an important part of the mathematical description of the amplitude of each mode (m is the mode integer) as a function of time. Additionally, modal amplitudes (and their derivatives) are needed to compute the pressure and the flow velocity inside the motor. It has proved difficult to provide closure on the phase angle issue, and acceptable solutions have not yet emerged. A direct solution for the phase angle is described in this thesis. Several methods of solution are presented which include not only Taylor Series approximations but an elegant double-solve technique—which yields an implicit algebraic equation in. Other issues are dealt with also, such as deriving a condition for motor stability and attempting to address the concern that the accepted theoretical model for combustion instability may not even be valid.



Rocket combustion instability, Culick's acoustical model, Solid rocket interior ballistics