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Simulation of Condensed Products Formation at the Surface of a Metalized Solid Propellant

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Innovative Energetic Materials: Properties, Combustion Performance and Application

Abstract

This article considers mathematical simulation of a process of condensed products formation near the surface of a burning solid propellant. These products include agglomerates and smoke oxide particles (SOP). The idea of predicting properties of these products is based on classification of propellants with various combustion regularities depending on formulation factors. For these types of propellants, the developed models are used to determine (estimate) the relations between the two main fractions, size of the agglomerates and SOP, parameters of the chemical composition and structure of the agglomerates. Validity of the used approaches is confirmed by comparing the calculation results and experimental data.

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Abbreviations

fm (D):

Mass function of size-distribution density of agglomerates

fm (d):

Mass function of size-distribution density of smoke oxide particles

Z a m :

Fraction of initial metal in propellant used to form agglomerates

η :

Mass fraction of oxide in agglomerate

D 43 :

Mass-average diameter of agglomerates

T Al ig :

Al ignition temperature

T C d :

Carbon elements decomposition

λV, λ :

Average quantity of oxidizer particles in fixed and unit volume of the propellant

N ox :

Number of oxidizer particles

P ( N ox ) :

Probability of Nox oxidizer particles location in a fixed volume of the propellant

\(\upsilon\) :

Propellant volume

nAl, nAl2O3, ng:

Molar content of Al, Al 2 O 3 , gaseous products

p :

Pressure

t :

Time, characteristic time

W 1 :

Spreading velocity of particles material

W 2 :

Velocity of inhomogeneity appearance

L :

Work that can be performed by the separation forces

ΔE :

System energy change due to the particle separation

k1, k2, k3, ca, cd, Kp, K0:

Matching coefficients

Ω 1 , Ω 2 :

Areas of contact spots at non-equilibrium (in case of heterogeneity) and equilibrium states correspondently

T p :

Particle temperature

mAl, mAl2O3:

Aluminum and oxide masses in a particle

χ :

Fraction of the particle surface which is opened for oxidation after the fracture

S Al :

Area of the aluminum core surface

ρAl2O3, ρgas:

Oxide and gas density

M ox :

Oxidizer molar mass

h :

Oxide film thickness

j μ :

Molar oxidizer flow through a liquid film

cAl, cAl2O3:

Specific heat capacities of aluminum and oxide

Q chem :

Heat flux due to chemical reaction

Q conv :

Convective heat flux

Q rad :

Radiation heat flux

up, ugas:

Particle and gas velocities

C D :

Aerodynamic drag coefficient of the particle

S mid :

Area of the particle mid-section

K D :

The ratio of increasing of activated flaws number per unit time to increasing of activated flaws per unit time in hypothetical situation without material relaxation

λc, λh:

Critical flaws density and critical flaws per unit area

S ( t ) :

Surface area as a function of time

σ :

Stress

N 1 :

Activated flaws number without relaxation

N 2 :

Activated flaws number

C :

Wave speed in the solid

a :

Characteristic size of the relaxed area around the growing crack

mw, σ0:

Weibull distribution parameters

p s :

Saturated vapor pressure inside the bubble

r nucl :

Nuclei radius

R1, R2:

Internal and external radii of oxide film, respectively

\(\sigma_{{{\text{AlO}}_{3} - gas}}^{s} ,\), \(\sigma_{{{\text{Al}} - {\text{Al}}_{2} O_{3} }}^{s} ,\), \(\sigma_{{\text{Al}} - gas}^{s}\):

Surface tension: lower indexes Al2O3, gas and Al denote oxide, gas and aluminum, respectively

a* :

Maximal acceleration

a* eff :

“Effective” acceleration

λ * :

Most dangerous wavelength which corresponds to Rayleigh–Taylor instability

d mean :

Mean droplet size

Da:

Damköhler number

t diff :

Characteristic diffusion time in gas phase

t gas :

Characteristic time of gas-phase reaction

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Authors and Affiliations

  1. Baltic State Technical University «VOENMEH», 1st Krasnoarmeyskaya Str, St. Petersburg, 190005, Russia

    Valery A. Babuk, Nikita L. Budnyi & Alexander A. Nizyaev

Authors
  1. Valery A. Babuk
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  2. Nikita L. Budnyi
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  3. Alexander A. Nizyaev
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Corresponding author

Correspondence to Valery A. Babuk .

Editor information

Editors and Affiliations

  1. Science and Technology on Combustion and Explosion Laboratory, Xi’an Modern Chemistry Research Institute, Xi’an, China

    WeiQiang Pang

  2. Space Propulsion Laboratory (RET), Politecnico di Milano, Milan, Italy

    Luigi T. DeLuca

  3. Department of Non-Ferrous Metal and Gold, National University of Science and Technology “MISiS”, Moscow, Russia

    Alexander A. Gromov

  4. School of Chemistry, University of Edinburgh, Edinburgh, UK

    Adam S. Cumming

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Babuk, V.A., Budnyi, N.L., Nizyaev, A.A. (2020). Simulation of Condensed Products Formation at the Surface of a Metalized Solid Propellant. In: Pang, W., DeLuca, L., Gromov, A., Cumming, A. (eds) Innovative Energetic Materials: Properties, Combustion Performance and Application. Springer, Singapore. https://doi.org/10.1007/978-981-15-4831-4_17

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