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Multiphysics modelling of the coupled behaviour of precision-guided projectiles subjected to intense shock loads

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Abstract

Precision-guided projectiles (PGPs) typically deployed in smart munitions are operated and guided by highly sophisticated embedded electronic systems (EES). These PGPs are subjected to severe shock loads resulting from the ignition of the propellant during their launch. These shock loads, which are typically characterised by high intensity, short duration and wave reflections at varied frequencies, often lead to the failure of the EES. It is the objective of this work to conduct a comprehensive multiphysics analysis of the launch process of PGPs accounting for coupling and interaction effects between the different media (propellant, PGP, confined volume and free space). Specifically, we investigated the entire launch process that include the ignition of the propellant to observe local and global features of the setback, set forward pressure and acceleration histories using explicit axisymmetric Lagrangian–Eulerian finite element simulations. In this work, we also examine the severity and frequency of the reflected waves as well as the springback of the PGPs resulting from these local oscillations as they exit the muzzle. In addition, the flight state transition due to muzzle exit in terms of pressure and flow velocity is also discussed. Our results reveal the complex phenomena associated with the dynamic response of the PGPs and pressurization process resulting from the ignition of propellant during launch that are characterized by high oscillatory pressure profiles and projectile springback.

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Abbreviations

A:

Internal cross-sectional barrel area

B :

Hardening constant

b 0 :

Burn rate constant

\( \dot{b} \) :

Burn-rate

C:

Total propellant mass

C 0 :

Strain rate constant

c :

Growth reaction exponent

c p :

Propellant specific heat

D :

Reaction constant

Dw :

Propellant web size

Eproj :

Projectile kinetic energy

Eprop :

Propellant kinetic energy

e g :

Propellant specific energy

F:

Web fraction

G :

Reaction growth constant

G p :

Shear modulus for projectile

K g :

Bulk modulus for propellant

K p :

Bulk modulus for projectile

l:

Effective chamber length

m :

Thermal softening exponent

m s (t 0):

Initial solid propellant mass

m s (t):

Solid propellant mass

n :

Burn rate exponent

n 0 :

Hardening exponent

P:

Base pressure

P 1 :

Average pressure

P c :

Base pressure at burnout

P g :

Pressure of reaction product

T m :

Material melting temperature

U:

Effective chamber volume

V(t):

Projectile velocity at time t

W(t):

Work done on the system

x :

Projectile travel

x c :

Projectile location at burnout

β :

Burn rate constant

Γ:

Specific capacity ratio

θ :

Grain shape factor

λ :

Force constant of propellant

ρ g :

Gas density of reactive products

ρ p :

Projectile density

ρ s :

Solid density of propellant

σ y :

Yield strength

\( \dot{\phi } \) :

Reaction rate

ϕ(t):

Reaction ratio

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Acknowledgments

The authors would like to thank the Anonymous Sponsor for the financial support of this study. We also thank the Natural Sciences and Engineering Research Council of Canada and the Discovery Accelerated Supplement for their kind support. Finally, we wish to thank Drs. Missy Ji and Chris Quan of ANSYS Inc. for helpful discussions concerning the modelling of propellant combustion.

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Authors and Affiliations

  1. Mechanics and Aerospace Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Rd, Toronto, ON, M5S 3G8, Canada

    X. W. Yin, P. Verberne & S. A. Meguid

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  1. X. W. Yin
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  2. P. Verberne
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  3. S. A. Meguid
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Correspondence to S. A. Meguid.

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Yin, X.W., Verberne, P. & Meguid, S.A. Multiphysics modelling of the coupled behaviour of precision-guided projectiles subjected to intense shock loads. Int J Mech Mater Des 10, 439–450 (2014). https://doi.org/10.1007/s10999-014-9255-0

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