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Propagation of blast waves with exponential heat release and internal heat conduction and thermal radiation

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Abstract

The problem of reactive blast waves in a combustible gas mixture, where the heat release at the detonation front decays exponentially with the distance from the center, is analyzed. The central theme of the paper is on the propagation of reactive blast into a uniform, quiescent, counterpressure atmosphere of a perfect gas with constant specific heats. The limiting cases of Chapman-Jouguet detonation waves are considered in the phenomenon of point explosion. In order to deal with this problem, the governing equations including thermal radiation and heat conduction were solved by the method of characteristics using a problem-specific grid and a series expansion as start solution. Numerical results for the distribution of the gas-dynamic parameters inside the flow field are shown and discussed.

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Abbreviations

a :

speed of sound

e :

specific internal energy

E i :

explosion energy

E j :

blast wave energy

f :

nondimensional particle velocity

g :

nondimensional pressure

h :

nondimensional density

I :

mass integral

j :

factor of symmetry

J :

energy integral

K :

thermal conductivity

K a :

constant

M j :

blast wave mass

M s :

shock Mach number

n j :

geometrical factor

p :

pressure

q :

total heat flux

qc :

heat flux by conduction

q R :

heat flux by radiation

Q :

chemical heat release

Q 0 :

constant

r :

space coordinate

r 0 :

characteristic length of flow field

t :

time coordinate

T :

absolute temperature

u :

particle velocity

W n :

front propagation velocity

x :

similarity variable

y :

front variable

α R :

Rosseland mean absorption coefficient

αR a :

constant

β C :

temperature exponent of thermal conductivity

β R :

temperature exponent of absorption coefficient

Γ :

nondimensional heat flux parameter

Γ C :

conduction parameter

Γ R :

radiation parameter

Δ :

finite difference

κ :

specific heat ratio

λ :

decay parameter

ξ :

nondimensional shock radius

π :

ratio between perimeter and diameter of a circle

ρ :

density

σ :

Stefan-Boltzmann constant

0, 1:

zeroth, first order

a:

undisturbed gas

CJ:

Chapman-Jouguet

i :

condition at the center

n :

conditions immediately behind the shock front

T:

particle path

η :

along characteristicη=const.

ξ :

along characteristicξ=const.

*, ∼:

nondimensional variable

...:

differentiation with respect to time

;:

differentiation with respect

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Authors and Affiliations

  1. Institute of Fluid Mechanics and Gas Dynamics, Technical University of Graz, 8010, Inffeldgasse 25, Graz, Austria

    W. Gretler & P. Wehle

Authors
  1. W. Gretler
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  2. P. Wehle
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This article was processed using Springer-Verlag TEX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.

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Gretler, W., Wehle, P. Propagation of blast waves with exponential heat release and internal heat conduction and thermal radiation. Shock Waves 3, 95–104 (1993). https://doi.org/10.1007/BF02115889

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  • DOI: https://doi.org/10.1007/BF02115889

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