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Unsteady 1-D Thrust Modeling with EOS Effects for Ram Accelerator Experiments at Different Bores

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Abstract

Advances made to the unsteady, one-dimensional (1-D) modeling of the thermally choked ram accelerator thrust-Mach number characteristics include the use of real-gas equations of state to account for the compressibility effects of the combustion products. Equations of state based on generalized empirical and theoretical considerations are incorporated into a 1-D computer code to predict the combustion end state equilibrium conditions when the propellant starts out a relatively high fill pressure (>2.5 MPa) and the projectile acceleration exceeds 100 km/s2. The objective of this work is to improve the unsteady 1-D model as a useful tool to predict the thrust of the thermally choked ram accelerator propulsive mode by utilizing key results from the more computationally intensive 2-D or 3-D simulations. New thrust-Mach number calculations compared with experimental data from 25-mm, 30-mm, 38-mm, 90-mm, and 120-mm-bore experiments are generally in good agreement until the point where enhanced accelerations are observed, presumably due to projectile material combustion. The results of this investigation indicate the need for more research on ram accelerator flow fields and the role projectile material may play in the combustion process.

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Abbreviations

A:

cross sectional of the tube

ap:

acceleration of the projectile

Bi:

co-volume of species i

cp:

specific heat capacity at constant pressure

CJ:

Chapman-Jouguet state

CV:

control volume

DCJ:

CJ detonation speed

e:

specific internal energy

F:

thrust

h:

specific enthalpy

Lp:

length of projectile

LCV:

length of control volume

M:

Mach number

mp:

mass of projectile

p:

static pressure

Δq:

heat of reaction

Q:

non-dimensional heat release, Δq/cp1T1

R:

gas constant

T:

temperature

V:

projectile velocity

v:

specific volume

Xi:

molar fraction

1, 2:

inlet, outlet reference of control volume

α:

acceleration parameter, (Lcvap)

β:

adjustable parameter in BKW EoS

Γ:

adiabatic heat capacity rate,(dh/de)s

γ:

specific heat ratio

ζ:

adjustable parameter in BKW EoS

η:

non-dimensional enthalpy, h/cp1T1

θ:

adjustable parameter in BKW EoS

σ:

compressibility factor

χ:

adjustable parameter in BKW EoS

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Author information

Authors and Affiliations

  1. University of Washington, Seattle, WA, 98195, USA

    C. Knowlen & A. P. Bruckner

  2. Laboratory PPRIME, ENSMA, Futuroscope, 86960, France

    P. Bauer & T. Bengherbia

  3. University of the West of England, Bristol, BS16 1QY, UK

    Y. F. Yao

  4. Exobal Consulting, Saint-Louis la Chaussée, 68300, France

    M. Giraud

Authors
  1. C. Knowlen
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  2. P. Bauer
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  3. T. Bengherbia
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  4. Y. F. Yao
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  5. A. P. Bruckner
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  6. M. Giraud
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Knowlen, C., Bauer, P., Bengherbia, T. et al. Unsteady 1-D Thrust Modeling with EOS Effects for Ram Accelerator Experiments at Different Bores. Aerotec. Missili Spaz. 97, 19–26 (2018). https://doi.org/10.1007/BF03404761

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