Numerical Simulation of Heteorogeneous Pyrotechnic Compounds Combustion Processes
Drivotin O.I.(1), Drofa A.S.(2), Savchenko A.V.(2), Shilin A.G.(2), Shilin V.A.(1)
1 State University, 7, University naberezhnaya, Sanct-Peterburg, 199034, Russia
2 RPA “Typhoon”,4, Pobedy st., Obninsk, Kaluga Region, 249038, Russia
Knowledge of a yield of useful active aerosol particles in the products of pyrotechnic compounds combustion is needed for assessing the ice-forming efficiency of pyrotechnic
flares developed for super cooled cloud modification activities aimed at precipitation monitoring or hail protection (Zimin, 1992). As far as the majority of cloud modification
agents decompose to one or another degree during combustion of pyrotechnic compounds, the efficiency of the aerosol formed to a certain extent depends on the regimes of pyrotechnic
mixture combustion and agent evaporation. A theoretical estimate of active ice-forming particles yield is usually made on the basis of thermodynamic calculations of combustion of
a pyrotechnic mixture with a preset composition (Cruise, 1991). In this case it is assumed that during combustion the phase and chemical equilibrium states are conserved.
It is also assumed that a pyrotechnic mixture is homogeneous in structure and combustion proceeds in flat-parallel layers, that does not occur in real conditions.
Because of the nonhomogeneous structure of the substance the process of fragmented burning of separate granules of the mixture takes place.
Combustion fragmentation may be caused by granularity of the mixture or its components, local disturbances from the composition, the presence of defects or zones with
increased mechanical stress in the pyrotechnic compound. Because of these reasons a heterogeneous temperature field – maximum in the zone of intense burning of the granules
of the burning substance and a sharp decrease of temperature at a distance from them – is formed. A wide range of active substance evaporation at the destructive combustion
is realized depending on the existing actual temperature field and the geometry of the combustion front. The destructive combustion regime of pyrotechnic compounds in the
heterogeneous temperature field is likely to determine the dispersion properties and chemical composition of the aerosol formed. An extremal example of the pyrotechnic
compounds fragmentation combustion may be a blow-out of unburned particles of the active substance outside the combustion zone.
The data of experimental measurements of yields of aerosol particles generated by pyrotechnic substances with different dispersion properties performed at the SI RPA
“Typhoon” are shown in Figure 1. The same Figure gives the measurement results for the number of active
crystallization nuclei obtained at combustion of the ice-forming pyrotechnic compound AD-1 used in Russia in anti-hail activities. The components of this compound were
grounded in a ball mill. Depending on the time of grinding different dispersion properties of the pyrotechnic mixture was obtained – with increasing time of grinding the
sizes of pyrotechnic compound particles become smaller. The composition obtained is pressed into tablets and then burned in a closed aerosol chamber. The samples of aerosol
particles are taken and placed into the climatic chamber with supercooled fog at a temperature of – 10°C. Ice-forming activity of the compound was determined by counting the
number of crystals formed. As is seen from Figure 1, the activity of one and the same compound depends on the degree of grinding of the pyrotechnic mixture. There exists a
certain degree at which the activity of the compound is the highest.
A theoretical estimate of ice-forming particles for the given AD-1 composition made on the basis of thermodynamic calculations gives the value of 1.26·1013
of active AgI particles in combustion products of 1 g of pyrotechnic mixture. It is assumed that burning of AD-1 takes place in an equilibrium regime at a temperature of 14960K.
As is seen from Figure 1, the number of active particles measured is considerably less than the theoretical value. A high degree of grinding the pyrotechnic mixture components
is not optimal for obtaining the maximum activity of the aerosol formed. The results presented do not make it possible to interpret unambiguously depending on particle sizes of
the pyrotechnic mixture as the
grinding of different components of the mixture in the ball mill depends on mechanical properties of separate components. But the experimental data show that the heterogeneous
structure of distribution of separate components in the pyrotechnic compound influences significantly the yield of active particles generated. This effect should be considered
at choosing the combustion regime of pyrotechnic compounds.
At present, the theory of combustion of pyrotechnic compounds generation aerosol with preset characteristics is at the stage of formation. In the present paper, the combustion
processes of pyrotechnic compounds containing an active substance for aerosol particles generation were numerically simulated. The goal of the simulation is the investigation
of a dependence of active aerosol particle yield on the thermodynamic characteristics of the pyrotechnic compound components and on their disperse composition.
When constructing the 3-D numerical model it is assumed that the pyrotechnic compound consists of two components – a burning substance realizing the process of combustion and
an active substance evaporating in the temperature field formed within the substance. These substances are in the form of spherical granules of different diameters. The
distribution of the granules is taken to be normal with preset modal diameters and dispersion of distributions. The granules of both types are located in the cylindrical
part of the space randomly at the condition of minimizing a free space among the granules. Modeling of granules allocation in the cylinder is made with the help of a genetic
algorithm (Lakhmi, 1998). The space among the granules is filled with a binder, the heat of combustion of which is neglected as compared to the heat of combustion of a burning
substance. Purposeful numerical simulations are made for a pyrotechnic compound in which the ballistite is used as a burning agent. AgI is an active substance. The physical,
chemical and thermodynamic characteristics of these substances are known.
Modeling of the processes of combustion, heat transfer in the medium and evaporation of the components of the compound is made on the basis of a numerical solution of the
equation of changing heat within the pyrotechnic compound space:
t – actual time;
T – temperature of the medium at the point with coordinates x,y,z;
Q1(x,y,z,t,T) – amount of heat released in the region of burning substance combustion;
Q2(x,y,z,t,T) – amount of heat absorbed in the region of burning substance evaporation;
α i – heat conductivity coefficient of the medium in corresponding regions.
The ignition of the burning substance is simulated by a contact of a granule with the hot surface. A heat outflow induced by the chemical combustion reaction from the surface
of the granule takes place with the intensity calculated with the use of the heat conductivity equation for non-stationary exothermic reaction. Combustion of burning granules is
calculated under the assumption that at the temperatures of the granule surface lower than the critical Tc heat absorption occurs, and when the temperature of the granule becomes
higher than this, the process of combustion takes place with heat emission at a constant mass velocity.
To calculate the sublimation of the active substance in a heterogeneous temperature field the calculated dependence of the degree of destruction of the active substance on
temperature was used. It was found with the use of programs for the calculations of the thermodynamic equilibrium. The calculations were made for the pyrotechnic compound AD-1
containing 8% of active AgI. Changes of the temperature of the compound combustion were modeled by the addition of the Mg-MgO substance (up to 20% in mass). As the calculations
have shown, the composition of combustion products changed insignificantly, and the combustion temperature changed by more than 5000K. The calculation results for the yield of
non-destructed AgI are shown in Figure 2. The dashed line shows the calculation data approximated by the polynomial of degree:
Formula 2 was used in numerical simulation at calculations of AgI sublimation from the surface of the granule of the pyrotechnic compound active substance. It is assumed that
after sublimation the
vapor phase of AgI leaves the combustion zone and does not destruct under high temperatures.
For numerical solution of the boundary-value problem (1) with corresponding initial and boundary conditions a non-uniform three-dimensional grid of space decomposition is
applied. At calculations in the regions inside the granules a 1/10 of a granule diameter step was used. In the range between the granules the step equal to 1/10 of minimal
diameter of the granules of the pyrotechnic compound was used. At transition from one integration range to another the decomposition step changes and the recalculation of the
nodal values is made by the linear interpolation method.
The results of numerical simulation of a yield of non-destructed AgI in the vapor phase at the combustion of pyrotechnic compounds with different dispersion properties are
given in the Table. The calculations are carried out for pyrotechnic compounds containing 8% of the active substance (AgI) at granules different sizes of the burning and active
substances. As is seen from the Table, a non-monotonous dependence of non-destructed AgI is observed at varying initial sizes of pyrotechnic compound particles. When determining
the grinding degree of the pyrotechnic compound components, maximum yield of AgI into the vapor phase without destruction is observed. The same character of changing active
particles yield is also observed in the experimental data on the activity of ice-forming aerosol in the AD-1 pyrotechnic compound presented above.
Table. Results of modeling AgI transition into the vapor phase at different diameters of burning and active substances.
Thus, the results of numerical simulation show that the processes of fragmentary combustion of pyrotechnic compounds can significantly affect the efficiency of pyrotechnic
generators operation. This effect must be taken into consideration at the development of such generators.
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