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Numerical studies on erosive burning in cylindrical solid propellant grain

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Abstract

This paper addresses erosive burning of a cylindrical composite propellant grain. Equations governing the steady axisymmetric, chemically reacting boundary layer are solved numerically. The turbulence is described by the two equation (k-ɛ) model and Spalding’s eddy break up model is employed for the gas phase reaction rate. The governing equations are transformed and solved in the normalized stream function coordinate system. The results indicate that the dominant reaction zone lies within 20% of the boundary layer thickness close to the wall. The sharp gradient of the temperature profile near the wall is found responsible for bringing the maximum heat release zone near the surface and hence enhancement in the burning rate. The model reproduces the experimental observation that erosive burning commences only above a threshold value of axial velocity.

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Abbreviations

a :

pre exponent in strand-burning rate law, (0.245 ×  10−2 (m/s)/(Mpa)n)

A :

cross-sectional flow area

A s :

Arrhenius frequency factor in propellant surface decomposition, (5.65 m/s)

A + :

damping constant in van Driest’s hypothesis (26)

C 1 → C 4,C μ, C ω :

constants in turbulence models (C 1 =  1,  C 2 =  1.3,  C 3 =  1.57, C 4 =  2,  C ω =  0.18,  C μ =  0.09)

C p :

\({\sum\limits_k {Y_{k}}}{C_{pk}}\) average heat capacity of reacting gases, (1.254 kJ/kg K)

C pk :

heat capacity of kth species (kJ/kg K)

C s :

heat capacity of solid propellant, (1.59 kJ/kg-K)

d Ap :

average diameter of ammonium per-chlorate particles

D :

port diameter of rocket motor (m)

D f :

diffusion coefficient in Fick’s law (m2/s)

E as :

activation energy in propellant surface decomposition, (62.7 kJ/kmole)

Δh o f,k :

heat of formation of kth species, (233.662 kJ/kg for fuel, −3937.56 kJ/kg for oxidizer, −4753.914 kJ/kg for products)

k :

von Karman’s constant (0.41)

K :

\(\overline{{u_{i}^{\prime} u_{i}^{\prime}}}/2,\) turbulent kinetic energy (m2/s2)

ℓ:

mixing length (m)

n :

exponent in strand-burning rate law (0.41)

P :

pressure (Pa)

Pr:

C p  μ/λ, Prandtl number based upon molecular properties of fluid

Pr t :

Prandtl number for turbulent flow (0.9)

r :

coordinate in radial direction (m)

r b :

total burning rate of a solid propellant (m/s)

r bo :

ap n strand burning rate of a solid propellant (mm/s)

R:

port radius of rocket motor (m)

R h :

roughness height (m)

R u :

universal gas constant (J/kmol k)

Sc :

\(\mu /\bar{\rho}D_{i},\) Schmidt number based upon molecular properties of fluid

Sc t :

Schmidt number for turbulent flow

T :

temperature (K)

T ci :

initial centerline temperature (K)

T o :

reference temperature, 298.14 K

Q s,ref :

surface heat release due to pyrolysis at reference temperature (J/kg)

T p :

propellant temperature (K)

T pi :

propellant initial temperature, (298 K)

T ps :

propellant surface temperature, (800 K)

T oi :

initial stagnation temperature (K)

\(\bar{T}_{ps}\) :

reference surface temperature of propellant (K)

u :

gas velocity in x-direction (m/s)

U :

axial velocity outside boundary layer (m/s)

U ci :

initial centerline velocity (m/s)

u * :

\({\sqrt \frac{\tau_{w}}{{\rho_{\infty}}}},\) friction velocity (m/s)

v :

gas velocity in y-direction (m/s)

W :

\({\left({{\sum\limits_k {Y_{k}}}/W} \right)}^{{- 1}} \) average molecular weight of gases (kg/kmol)

W k :

molecular weight of kth species, kg/kmol (30 kg/kmol for fuel, 27.9 kg/kmol for oxidizer, 20.4 kg/kmol for products)

x :

coordinate in axial direction (m)

y :

coordinate normal to propellant surface (m)

Y k :

mass fraction of k-th species

Y FS :

mass fraction of fuel in a composite solid propellant (0.25)

Y OS :

mass fraction of oxidizer in a composite solid propellant (0.75)

\(\overline{{{\left({} \right)}}}\) :

time-averaged quantity

\((^{\tilde{}})\) :

Favre averaged quantity

\({\left({} \right)}^{\prime}\) :

fluctuating quantity

δ:

boundary-layer thickness (m)

ɛ:

\(\mu \overline{{u^{\prime}_{{ij}} u^{\prime}_{{ij}}}}/\overline{\rho},\) turbulent dissipation (m2/s3)

γ:

constant-pressure to constant-volume specific heat ratio (1.26)

λ:

thermal conductivity of gas (kJ/m s K)

λ s :

thermal conductivity of solid propellant (kJ/m s K)

μ:

gas viscosity (kg/m s)

μ eff :

μ + μ t , effective viscosity (kg/m s)

μ t :

turbulent viscosity (kg/m s)

(μ/Pr ) eff :

μ/Pr + μ t /Pr t (kg/m s)

(μ/Sc ) eff :

μ/Sc + μ t /Sc t (kg/m s)

ν k :

number of moles of kth species (1 kmol for fuel, 3.23 kmol for oxidizer, 5.9 kmol for products)

ρ:

gas density (kg/m3)

ρ s :

solid propellant density (1600 kg/m3)

τ:

\(\mu_{{eff}} \partial \overline{u}/\partial y,\) local shear stress (N/m2)

ω k :

rate of production of species k due to chemical reactions (kg/m3 s)

b :

bulk or averaged variable

c :

centerline condition

k :

species index representing fuel gas [F], oxidizer gas [O], and product gas [P].

∞:

free stream condition

w :

wall (propellant surface) condition

References

  1. Corner J (1947) The effect of turbulence on heterogeneous reaction rates. Trans Faraday Soc 43:635

    Article  Google Scholar 

  2. Green L Jr (1954) Erosive burning of some composite solid propellants. Jet Propulsion 24:9

    Google Scholar 

  3. Lenoir JM, Robillard G (1957) A mathematical method to predict the effects of erosive burning in solid propellant rocket, sixth international symposium on combustion, pp 667–683

  4. Klimov AM (1975) Erosive burning of propellants. Combust Explosion Shock Waves 11(5):678–681

    Article  Google Scholar 

  5. Lengelle G (1975) Model describing the erosive combustion and velocity response of composite propellants. AIAA J 13:315

    Google Scholar 

  6. Yamada K, Goto M (1976) Simulative study on the erosive burning of solid rocket motors. AIAA J 14:1170

    Google Scholar 

  7. Beddini RA (1978) Reacting turbulent boundary layer approach to solid propellant erosive burning. AIAA J 16:898

    Google Scholar 

  8. Beddini RA (1980) Aerothermochemical analysis of erosive burning in a laboratory solid rocket motor. AIAA J 18:1346

    Google Scholar 

  9. Vilyunov VN, Isaev Yu M, Revyagin LN (1981) Erosive burning of condensed materials in an acoustic field. Combust Explosion Shock Waves 17(4):383–386

    Article  Google Scholar 

  10. Razdan MK and Kuo KK (1982) Turbulent flow analysis of erosive burning of cylindrical composite solid propellants. AIAA J 20:122–128

    MATH  Google Scholar 

  11. Mukunda HS and Paul PJ (1997) Universal behavior in erosive burning of solid propellants. Combust Flame 109(1–2):224–236

    Article  Google Scholar 

  12. Godon JC, Duterque J, Lengelle G (1993) Erosive burning in solid propellant motors. J Propulsion Power 9(6):806–811

    Article  Google Scholar 

  13. Kuo KK (1986) Principles of combustion. Wiley, New York

    Google Scholar 

  14. Lockwood FC (1977) The modeling of turbulent premixed and diffusion combustion in the computation of engineering flows. Combust Flame 29:111

    Article  Google Scholar 

  15. Spalding DB (1977) GENMIX: a general computer program for two—dimensional parabolic phenomena. Pergamon Press, New York

    Google Scholar 

  16. Chambers TL and Wilcox WC (1977) Critical examination of two-equation turbulence closure models for boundary layers. AIAA J 15:821

    Google Scholar 

  17. Vilyunov VN, Dvoryashin AA (1971) An experimental investigation of the erosive burning effect. Combust Explosion Shock Waves 7(1):38–42

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    K. Srinivasan & S. Narayanan

  2. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    O. P. Sharma

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  1. K. Srinivasan
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  2. S. Narayanan
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  3. O. P. Sharma
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Correspondence to K. Srinivasan.

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Srinivasan, K., Narayanan, S. & Sharma, O.P. Numerical studies on erosive burning in cylindrical solid propellant grain. Heat Mass Transfer 44, 579–585 (2008). https://doi.org/10.1007/s00231-007-0280-5

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