Abstract
A dependence of the burning rate of solid energetic materials on the burning surface curvature is investigated. The model predicts an existence of a limiting value of curvature above which self-sustained combustion is impossible. This result is used for explaining the critical conditions of combustion of homogeneous condensed energetic materials. The critical combustion diameters of several homogeneous energetic materials are calculated and compared with experimental data. A combustion model for mixtures of energetic binders with inert and active fillers which takes into account the curvature of the burning surface of the binder layers and ignition delay of the filler is developed. A parametric study of the proposed model was performed over a wide range of particle sizes of the filler, its concentration in the mixture, and burning rates of the binder. The results of the model were compared with experimental data for mixtures of energetic binders with SiO2, HMX, AP, and CL-20. A unified dependence of the ignition delay of HMX, AP, and CL-20 particles on their size, the burning rate of the mixture, and the thickness of the binder layers is proposed. The model is used for calculation of temperature sensitivity of the burning rate of propellants based on energetic binders.
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Abbreviations
- b :
-
coefficient that takes into account the spatial geometry of the burning surface of the binder layer
- D :
-
particle diameter
- D′:
-
difference between burning surface of the binder and particle
- d cr :
-
critical grain diameter
- h :
-
thickness of the binder layer between the particles of the filler
- K :
-
burning surface curvature, dimensionless mean curvature of the burning surface
- \( k=\beta \left({T}_s-{T}_0\right) \) :
-
nondimensional parameter
- \( {k}_0=16bk \) :
-
nondimensional parameter
- K 0 :
-
dimensionless mean curvature of the burning surface at the burning rate u 0 N (p)
- Mi:
-
Michelson–Markstein criterion
- p :
-
pressure
- R :
-
curvature radius
- R 1 and R 2 :
-
principal radii of curvature of the burning surface
- T 0 :
-
initial grain temperature
- T ′0 :
-
effective initial temperature connected with a curvature of burning surface
- T s :
-
burning surface temperature
- ΔT 0 :
-
effective change of the initial temperature connected with a curvature of burning surface
- t ign :
-
ignition delay of the particles in propellant
- \( {t}_{ign}^{\infty } \) :
-
ignition delay of the single particle in binder
- u :
-
burning rate
- u b :
-
burning rate of the binder with planar burning surface
- u p :
-
burning rate of the particle
- u 0 :
-
steady-state burning rate
- u 0 N (p):
-
dependence of the burning rate on pressure at a certain nominal initial temperature
- \( Z=\frac{u}{u_N^0} \) :
-
nondimensional burning rate
- α :
-
volume concentration of the filler particles in the mixture
- α max, δ, τ ign , η :
-
nondimensional parameters
- β :
-
temperature sensitivity of the burning rate or \( \beta ={u}_b/{u}_p \)
- β ign :
-
temperature sensitivity of ignition delay
- β T :
-
temperature sensitivity of the propellant burning rate
- κ :
-
thermal diffusivity of the condensed phase
- \( \xi =\frac{uR}{\kappa } \), \( {\xi}_i=\frac{u{R}_i}{\kappa } \) :
-
nondimensional radii of curvature of the burning surface
- \( {\tau}_{ign}^{\infty } \) :
-
nondimensional ignition delay of the single particle binder
- \( {\tau}_0^{\infty } \), γ 0 and n :
-
constants
- ν :
-
pressure exponent
- σ and χ :
-
factors of order unity which depends on the shape of the particles
- Ï• :
-
temperature gradient in the c-phase near the burning surface
- AFB:
-
nitroglycerine urethane binders
- AGS:
-
polyurethane rubber and a plasticizer which is a mixture of nitrate esters
- CEM:
-
condensed energetic material
- c-phase:
-
condensed phase
- cr :
-
critical parameter
- b :
-
binder
- p :
-
filler particle
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Rashkovskiy, S.A., Milyokhin, Y.M., Fedorychev, A.V. (2017). Combustion of Solid Propellants with Energetic Binders. In: De Luca, L., Shimada, T., Sinditskii, V., Calabro, M. (eds) Chemical Rocket Propulsion. Springer Aerospace Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-27748-6_16
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DOI: https://doi.org/10.1007/978-3-319-27748-6_16
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