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Metalized solid propellant combustion under high-speed blowing flow

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Abstract

This study presents a mathematical model and a calculation method of the nonstationary combustion rate of metalized solid propellant (nitroglycerin powder with aluminum particle additives) under blowing conditions. The combustion of metalized fuel flat surface under unlimited blowing flow is investigated. The mathematical model describes the erosion effects of solid fuel through boundary layer approximation. The blowing effect is considered in turbulent heat-mass transfer. Results of theoretical and numerical analyses show the influence of aluminum powder additives on the burning rate of solid propellant under blowing flow. This study provides data on the dependence of propellant burning rate on blowing flow speed and dispersion of metal particles in the solid propellant.

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Abbreviations

t :

Time

X :

Coordinate

Xs :

Coordinate of burning surface

ρ 1 :

Density of metalized solid fuel

ρ 2 :

Density of gas

ρ 3 :

Reduced density of particles

ρAl :

Density of aluminum

T 1 :

Temperature of solid fuel

T 2 :

Gas temperature

T 3 :

Particle temperature

T 0 :

Initial temperature of solid fuel

T ig :

Initial gas temperature

u :

Linear burning rate

U f :

Blowing flow speed

u 2,x :

Normal gas velocity

u 2,y :

Tangential gas velocity

w 3 :

Particle velocity

n 3 :

Number of particles per unit volume

r 3 :

Radius of particles

r Al :

Radius of unburnt part of Al particle

c 1 :

Specific heat of solid fuel

c 2 :

Specific heat of gas at constant pressure

c 3 :

Specific heat of particles

λ :

Thermal conductivity

λ t :

Eddy conduction coefficient

Q 1 :

Thermal effect of AP decomposition

Q 2 :

Thermal effect of reaction in the gas phase

Q Al :

Effective heat of aluminum combustion

k :

Pre-exponential factor in the Arrhenius law

E :

Activation energy

R u :

Universal gas constant

R :

Gas constant

α Al :

Aluminum mass fraction

a :

Excess oxidant ratio

p :

Gas pressure

Y :

Oxidant concentration in the gas phase

D :

Diffusion coefficient

k Al :

Aluminum particle burning constant

μ Al :

Molar mass of aluminum particles

μ o :

Molar mass of oxygen

G :

Particles mass-change rate during combustion

τ fr :

Friction force on particle surface

α :

Heat transfer coefficient

η :

Conversion level of N powder

μ m :

Dynamic viscosity

μ t :

Eddy viscosity

S m :

Midsection area

C R :

Friction coefficient

τ s :

Surface frictional drag

N :

Blowing parameter

L :

Characteristic linear dimension of burning surface

ν t :

Eddy kinematic viscosity

Re :

Reynolds number

Nu :

Nusselt number

Pr :

Prandtl number

c k, x*, B, K :

Constants of turbulent model

φ, δ, k, l :

Functions of turbulent model

Indexes :

1. Solid fuel, 2. Gas phase, 3. Particles

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Acknowledgments

This work was supported by The Tomsk State University Competitiveness Improvement Program under grant no 8.2.09.2018.

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Authors and Affiliations

  1. Department of Mathematical Physics, Tomsk State University, Tomsk, Russia

    Krainov Alexey, Poryazov Vasiliy, Moiseeva Ksenia & Krainov Dmitry

  2. School of Energy & Power Engineering, Tomsk Polytechnic University, Tomsk, Russia

    Krainov Dmitry

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  1. Krainov Alexey
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  2. Poryazov Vasiliy
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Correspondence to Krainov Alexey.

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Recommended by Editor Yong Tae Kang

Krainov Alexey is a Professor and doctor of Physical and Mathematical Sciences, specializing in Thermophysics and Theoretical Heat Engineering (2003, Russia, Tomsk). He works at the Department of Mathematical Physics of National Research Tomsk State University. His scientific interests include combustion theory, chemical gas dynamics, and heat and mass transfer. Krainov is a coauthor of the gas dynamic method for calculating explosion-proof distances in accidental explosions of methane in coal mines that is used by engineering and technical staff to construct plans for accident elimination.

Poryazov Vasiliy is an Associate Professor with a Ph.D. in Physical and Mathematical Sciences, specializing in Thermophysics and Theoretical Heat Engineering (2015, Russia, Tomsk). He works at the at the Department of Mathematical Physics of National Research Tomsk State University. His research interests include combustion theory, chemical gas dynamics, and heat and mass transfer.

Moiseeva Ksenia is an Associate Professor at the Department of Mathematical Physics of National Research Tomsk State University. She has a Ph.D. in Physical and Mathematical Sciences, specializing in Thermophysics and Theoretical Heat Engineering (2014, Russia, Tomsk). Her scientific interests include gas dynamics, numerical simulation, combustion, dynamics of two-phase reacting media, and combustion stability of reaction gas mixtures.

Krainov Dmitry works as an assistant at the National Research Tomsk Polytechnic University. He has a Ph.D. in Physical and Mathematical Sciences, specializing in Thermophysics and Theoretical Heat Engineering (2016, Russia, Tomsk). His scientific interests include gas dynamics, numerical simulation, combustion, and heat and mass transfer.

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Alexey, K., Vasiliy, P., Ksenia, M. et al. Metalized solid propellant combustion under high-speed blowing flow. J Mech Sci Technol 34, 2245–2253 (2020). https://doi.org/10.1007/s12206-020-0446-3

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  • DOI: https://doi.org/10.1007/s12206-020-0446-3

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