On the Existence and Stability of Limit Cycles.for Longitudinal Acoustic Modes in a Combustion Chamber

REFERENCES

• Awad , E. ( 1983 ). Nonlinear acoustic instabilities in combustion chambers , Ph.D. Thesis , California Institute of Technology .
   Google Scholar
• Beckstead , M. W. , Bennion , D. U. , Butcher , A. G. , and Peterson , N. L. ( 1972 ). Variable area T-burner investigation . AFRPL-TR- 72 – 85 .
   Google Scholar
• Burstein , S. Z. , and Chintz , W. ( 1968 ). Unpublished work .
   Google Scholar
• Chu , B. T. , and Ying , S. J. ( 1963 ). Thermally driven nonlinear oscillations in a pipe with a traveling shock wave . Phys. Fluids 6 , 1636 .
   Google Scholar
• Culick, F. E. C. (Ed.) ( 1969 ). T-Burner Manual . CPIA pub . 191 .
   Google Scholar
• Culick , F. E. C. ( 1971 ). Nonlinear growth and limiting amplitude of acoustic oscillations in combustion chamber . Combustion Science and Technology 3 , 1 .
   Web of Science ®Google Scholar
• Culick, F. E. E. (Ed.) ( 1974 ). T-Burner Testing of Metallized Solid Propellants . Air Force Rocket Propulsion Laboratory Report AFRPL-TR- 74 – 28 .
   Google Scholar
• Culick , F. E. C. , and Levine , J. N. ( 1974 a). Comparison of approximate and numerical analysis of nonlinear combustion instabilities . AIAA paper 74 – 201 .
   Google Scholar
• Gantmacher , F. R. ( 1960 ). The Theory of Matrices . Chelsea Publishing Company , New York .
   Google Scholar
• Jensen , R. C. , and Beckstead , M. W. ( 1973 ). Nonlinear mechanisms of solid propellant instabilities . AIAA paper 73 – 1297 .
   Google Scholar
• Levine , J. N. , and Culick , F. E. C. ( 1974 b ). Nonlinear analysis of solid rocket combustion instability , Air Force Rocket Propulsion Laboratory , Report AFRPL-TR- 74 – 45 .
   Google Scholar
• Levine , J. N. , and Baum , J. D. ( 1981 ). A numerical study of nonlinear instabilities in solid rocket motors . AIAA Paper No . 81 – 1524 .
   Google Scholar
• Lores , M. E. ( 1973 ). Nonlinear longitudinal combustion instability in rocket motors . Combustion Science and Technology 7 , 245 .
   Web of Science ®Google Scholar
• Padmanabhan , M. S. , Zinn , B. T. , and Powell , E. A. ( 1979 ). On the applicability of the method of averaging in solid rocket stability analysis . Combustion Science and Technology 20 , 179 .
   Google Scholar
• Sirignano , W. A. , and Crocco , L. ( 1964 ). A shock wave model of unstable rocket combustors . A.l.A.A. Journal 2 ( 7 ), 1285 .
   Google Scholar
• Stoker , J. J. ( 1950 ). Nonlinear Vibration in Mechanical and Electrical Systems . Interscience Publishers Inc. , New York .
   Google Scholar
• Zinn , B. T. , and Powell , E. A. ( 1970 ). Application of the Galerkin method in the solution of combustion instability problems . Proceedings of the Nineteenth International Astronautical Congress on Propulsion, Re-Entry Physics 3 , pp. 59 – 73 .
   Google Scholar
• Zinn , B. T. , and Powell , E. A. ( 1971 ). Nonlinear combustion instability in liquid-propellant rocket engines . Thirteenth International Symposium on Combustion , pp. 491 – 503 .
   Google Scholar
• Zinn , B. T. , and Lores , M. E. ( 1972 ). Application of the Galerkin method in the solution of nonlinear axial combustion instability problems in liquid rockets . Combustion Science and Technology 4 , 296 .
   Google Scholar