R. Meyer J. Köhler A. Homburg Explosives

45 Burning Rate
Burning Rate
Abbrandgeschwindigkeit; velocity of combustion;
vitesse de combustion
The linear burning rate of a propellant is the velocity with which a
chemical reaction progresses as a result of thermal conduction and
radiation (at right angles to the current surface of the propellant). It
depends on the chemical composition, the pressure, temperature and
physical state of the propellant (porosity; particle size distribution of
the components; compression). The gas (fume) cloud that is formed
flows in a direction opposite to the direction of burning.
The burning rate describes the velocity with which the volume of the
burning propellant changes. It is proportional to the linear burning rate
and in addition it depends on the specific shape of the propellant (size
of the powder elements and conformation, e.g. flakes, spheres, tubes,
multi-perforated tubes etc. extending to the most complicated shapes
of rocket propellant charges).
In rocket engineering, “Burning rate” means specifically the stationary
progress of burning rate in the rocket chamber.
The following relationship exists between the burning rate dz/dt and
the linear burning
rate ˙e:
dz S(0)
= V f(z) V ˙e
dt V(0)
where ˙e is given by
˙e = ˙e(pref) V ( p(z)
pref ) a
z means the ratio of the volume burnt to that originally present
[V(0) – V] / V(0)
S(0)/V (0) means the ratio of the initial surface area to the initial
volume of the powder,
f(z) means the shape function of the powder, which takes into
account the geometrical conditions during burning rate
(sphere, flake, cylinder, n-hole powder)
(f(z) = current surface area/initial surface area)
˙e(pref) means the linear burning velocity at the reference gas
pressure pref
pref is the reference gas pressure and
a is the pressure exponent.
The equation for the burning rate rate dz/dt can also be written in the
form
dz
= A V f(z) V pa
dt