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International Journal of Energetic Materials and Chemical Propulsion
ESCI SJR: 0.142 SNIP: 0.16 CiteScore™: 0.29

ISSN Print: 2150-766X
ISSN Online: 2150-7678

International Journal of Energetic Materials and Chemical Propulsion

DOI: 10.1615/IntJEnergeticMaterialsChemProp.v5.i1-6.860
pages 825-836

LIMIT CYCLES FOR SOLID PROPELLANT BURNING RATE AT CONSTANT PRESSURE

B. V. Novozhilov
Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia
Fabio Cozzi
Dipartimento di Energetica Politecnico di Milano Via La Masa 34 Milan, Italy

ABSTRACT

In the framework of the Zel'dovich-Novozhilov theory, limit cycles for solid propellant burning rate at constant pressure are investigated. The zeroth and the first two oscillation modes are involved in the analytical study. The equations for the mode amplitudes and frequency of the limit cycle occurring near the intrinsic stability boundary are derived in the third order nonlinear approximation. They are valid for any propellant model and contain the first, second, and third derivatives of the surface temperature and temperature gradient at the propellant surface with respect to the burning rate. Close to the stability boundary two branches of the limit cycles are obtained. The limit cycle frequency at the α -branch is close to the natural frequency of the propellant. At the β -branch, it approximately equals one half of that. The zero mode (DC shift) in both cases is negative and proportional to the square of the first mode amplitude. Numerical results are given for three particular propellant models with different steady-state burning laws.


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