Theory of Solid-Propellant Nonsteady Combustion. Vasily B. Novozhilov

This method accounts only for the effects related to the time scale of oscillation amplitude variation. Numerical results are obtained for the simplest propellant combustion model in the absence of entropic waves in combustion products. Stable and unstable combustion regimes are identified. In the latter regime, nonlinear effects may trigger shock waves in the combustion chamber.

      The possibility of expanding the theory beyond the phenomenological framework is discussed in the final chapter. This development requires a more detailed combustion model that would adequately describe processes occurring in low‐inertia zones of a combustion wave. The influence of low‐inertia zones (the reacting layer of the condensed phase, preheat and reaction zones in the gas phase, the half‐space occupied by gaseous combustion products) on various nonsteady phenomena are investigated both analytically and numerically. The consideration is presented within the framework of the Belyaev model. It is demonstrated that under a weak dependence of surface temperature on initial temperature accounting for the above low‐inertia zones (even if their thermal inertia is small compared to the inertia of the preheat layer of the condensed phase) leads to significant corrections to the t_c approximation.

      Finally, it is our pleasure to acknowledge the significant contribution of the people who helped us in the preparation of this book.

      We are very grateful to Professor Vladimir Marshakov, who discussed various topics throughout the book with us at great length.

      Special thanks are given to Inga Novozhilov. It is certain that without her very careful and dedicated work the manuscript could not have been adequately prepared.

      We are also incredibly thankful to Professor Vladimir Posvyanskii, Ludmila Novozhilova, and Natalia Golubnichaya for their help in preparing the manuscript.

      The second author would like to thank his wife Natalia Golubnichaya again for her love and continuous support throughout the project.

      Moscow – Belfast – Melbourne

      2011–2019

       Boris V. Novozhilov Vasily B. Novozhilov

Important Notation and Abbreviations

      Abbreviations

ADN	Ammonium dinitramide
BVP	Boundary value problem
c.c.	Complex conjugate
ZN	Zeldovich–Novozhilov
FM	Flame model
HMX	Cyclotetramethylene tetranitramine
ODE	Ordinary differential equation
PDE	Partial differential equation
PETN	Pentaerythritol tetranitrate
QSHOD	Quasi‐steady, homogeneous, one‐dimensional
RDX	Cyclotrimethylene trinitramine
SHS	Self‐propagating high–temperature synthesis
SRM	Solid rocket motor

      Mathematical Functions

L n	Laguerre polynomials
lg	log10
erfc	Complimentary error function
He n	Hermite polynomials
W	Whittaker function

Notation

      Over‐bar complex conjugate; Laplace–Carson transform

prime	time derivative, case‐specific dimension; perturbed value, case‐specific dimension
Basic Physical Dimensions	M (mass), L (length), T (time), θ (temperature), N (amount of substance, e.g. mole)
a	speed of sound, LT^−1; amplitude, case‐specific dimension
a f	amplitude of forced oscillations, case‐specific dimension
A	nozzle discharge coefficient, L^−1T
b	combustion temperature, nondimensional; correction (Chapter 9)
c	specific heat at constant volume, L^2T^−2θ^−1
c p	specific heat at constant pressure, L^2T^−2θ^−1
D, Dg	gas diffusion coefficient, L^2T^−1; amplitude of perturbation (Chapter 3), L; integration constant, nondimensional (Chapter 9)
E	activation energy, ML^2T^−2N^−1
f	temperature gradient at the surface, condensed phase side, θL^−1
	Laplace–Carson transform of f(t), case‐specific dimension
J	Jacobian, L^2M^−1T
g	mass velocity of gas flow, ML^−2T^−1
G	response function of gas velocity to oscillating pressure, non‐dimensional; integration constant, nondimensional (Chapter 9)
h