CC BY
5
УДК 536.46+662.23
COMBUSTION OF HIGH ENERGY HETEROGENEOUS SYSTEM
. Yu.V.FROLOV, A.N.PIVKINA
117977 Moscow, Kosygin St.4, Institute of Chemical Physics RAS 7777 @ center, ch ph. n i
ABSTRACT. Combustion of HCS is a complex multistage process depending on many parameters and characterizing by some peculiarities. The order and completeness of deflagration and chemical reaction in the combustion wave depend on not only system energy, but on a composite structure.
Problem of the non-simultaneous bum -out of the components was investigated in different aspects , but there is no study of the combustion front shape with point of view the sample initial structure. Intuitive impression of the chaotic structure and non-uniformity of combustion front was used to plane combustion surface.
The paper is focused on the structure of HCS sample and its influence on the peculiarities of formation combustion front. Some phenomenological aspects are analysed on base of fractal and percolation theory. It is shown the fractal character of particle clusters occurring under certain concentration and the percolation phenomena prove the critical role of the structure in the combustion process. The continuous reaction surface formation is a necessary condition for combustion front propagation across HCS sample in common and for phenomena type agglomeration. Fractal dimension could be a one of key point of the non-simultaneous combustion process investigation.
Novel computer program is used to analyses of combustion front optical imaginations of the combustion propagation. It permit to receive the connection between the green structure of the sample and colour card of combustion front .The brightness of the image could be attributed to the certain temperature level. The information which is produced by fractal analysis give opportunity to reconstruct the temperature-time history of any point of combustion sample.
The deep knowledge of HCS combustion mechanism permits to develop a new processes and to receive new materials.
It is new effective Fair Extinguish Aerosol Generator (FEAG) and nitrogen gas generated composition, which are more effective than conventional systems. Fine non-toxic aerosol could be easily removed after fire put out.
A new technology of titanium powder production was developed on base of combustion synthesise (SHS). The process is ecologically clean, non-waste and needs small amount of additional energy. Titanium powder has a high specific surface (>20m2/g) and demonstrate nice chemical activity in reaction (for example with Nitrogen gas or oxidiser).
1. INTRODUCTION
Heterogeneous condensed systems (HCS) generally represent a wide range of energy release compositions, which includc powders, solid rocket propellants (SRP), pyrotechnics, SHS-compositions, and explosives.
The combustion process efficiency of HCS is a function of its composition and ingredient properties. Usually, HCS consisting of metals with high heat of combustion (boron, aluminum, magnesium, titanium, zirconium, and its alloys), oxidizers (traditionally, nitrates or perchlorates), and binder (rubber, polymers, other organic compounds). Some special additives could be intended in the mixture to meet technical requirements (catalysts, dyes, cake prevention materials, etc.).
All the observed phenomena are interconnected, and result in the combustion wave forming and moving with the certain burning rate. The classical combustion theory does not explain these phenomena.
The process of the combustion wave spreading through the sample has been investigated for many years. Problem of the non-simultaneous burnout of the heterogeneous condensed system (HCS) components was investigated in many aspects, recently reviewed [I], but still there is no study of the combustion front shape connection with the sample structure and combustion parameters. Intuitive impression of the "chaotic" structure and the non-uniformity of the combustion front line was used to approach the "plane" combustion surface (which is to be optimal for the combustion process stability) by means of different technological and chemical variations. The heterogeneity level is a function of physical, chemical and geometrical properties of the components, and of the sample forming technique.
We aim to construct the connection between the sample composition, the initial internal structure, the temperature statement of the sample, and the combustion front shape: b/urning rate dependence on a particle size, non-simultaneous bum-out of the components, concentration limit of combustion, agglomeration and dispergation of condense phase, destruction and phase transition on combustion wave, etc. There are several physical and chemical processes involved in the combustion front shape formation.
All these processes can influence the observed front morphology, which is the integrated characteristic of the process non-simultaneously. Fractal dimension measurement could be a key point of the non-simultaneous burnout investigation.
The fractal geometry introduced some parameters to distinguish the "chaotic" and "straight" lines - e.g. fractal dimension, the quantitative evaluation of the line ruggedness attained using this geometry appears to be the attractive feature. The first technique used to evaluate the fractal dimension of a rugged boundary is a Richardson technique for studying the structure of coastline [2]. The physical basis of this procedure is relatively easy but difficult to automate on a computer system. Computer-based analysis systems usually use the scan image inspection to transfer it to the computer memory. Firstly algorithm for calculating the fractal dimension of a profile interpreted by a set of parallel lines was suggested by Reid [3]. Next was the dilation algorithm, which was useful but relatively slow.
We use the computer program to analyse optical images of the combustion front propagation process [4]. The focus has been done on the combustion front line chaotic structure characterisation.
The brightness of image could be attributed to certain temperature level; therefore investigations have been initiated to study temperature fields geometry in the burning sample. Furthermore, analysis of the information produced by fractal analysis will allow us to reconstruct the temperature-time history for the any point of the sample.
2. EXPERIMENTAL PHENOMENA
2.1. Burning Rate
Burning rate (U) is the integral energetic parameter of HCS combustion process and vary in a wide range - from 10'2 mm/s up to 105 mm/s.
MOGKNtOUS COMBUSTION
II
HETEROGENEOUS COMBUSTION
Fig.I. Different type of HCS combustion
This parameter is influenced by the energy release process, ambient pressure (P) and temperature (T), sample microstructure (porosity, particle size, heterogeneity level, etc.).
The burning rate dependence on the component particle size (Fig. 1) with the constancy of the rest parameters is a S-shaped curve, as shown on Figure 2a. There is a weak or no U dependence on the particle size for the very small (X/U>d, region III) and very large (%/U < d, region I) particles (yjU - is the preheated layer thickness). Region III could be described as "homogeneous" ones with the characteristics zones existence: dark zone, zone of the combustion product mixing, flame zone [5]. Combustion products succeed to mix in the dark zone, and "homogeneous" mixture of binder and oxidizer react in the flame zone.
U oc PY, where 1. On the other hand - the layer-ordered HCS type of "sandwich", where the combustion front propagates along the contact surface of oxidizer and binder layers [6, 7]. Both cases are examples of the ordered structure of HCS.
U,mm/s III |]
50 _
" ~ ^--
,0 -^ ---^^
' 1 J
JOO d.„ Jim
Fig.2. The burning rate dependence: a) 1-on oxidizer particle size, mixture AP+binder, P=const; 2-on the metal particle size, mixture AP+binder+20%AK. dox=const, b) on the ambient pressure: l-d=250 mkm, 2-d=12 mkm, 3-d<2 mkm
For the gas released system the burning rate is practically proportional to the pressure value (U °c P, where y * 1). Indicated regimes of HCS combustion and critical panicle size values depend on the ambient pressure, because of the pressure influence on the preheating and mixing zone thickness.
Note the ambient pressure growth leads to reduction of the particle size starting values for regions I, III, and to the spreading of intermediate region II Fig. 2b [5].
The intermediate zone (II, region of heterogeneous combustion) is the most difficult for theoretical and experimental studies because of non-linear U value dependence on the pressure and particle size:
U oc f (d, P*), y< 1
Analogously, the burning rate of the metal-containing SRP increases with the metal particle sizes reduction. The maximum U value corresponds to the oxidizer and metal particles equality (Fig. 2a):
The further dme reduction leads to the U stabilization, and even to decreasing (especially in the range of high metal content).
The same behavior demonstrate HCS on the base of complex oxidizer (AP + HMX). There is a maximum U value for the constant AP particle size but reducing the HMX d value.
For the gasless combustion process (type of termites) components react on the contact boundary through the intermediate layer of reaction products, and the burning rate doesn't depend on the ambient pressure and could be realized in different regimes (auto oscillating, pulse, spots, etc). The thicker products layer the higher it's diffusion resistance, and the lower the reaction rate. For such HCS (i.e. Ti + C. Ti + B) the initial disorder defines not the heat release only, but the different combustion regimes also.
2.2. Agglomeration
Agglomeration is the process of the component particle enlargement on the combustion surface or in preheated zone [8]. Generally, agglomeration process has a negative influence on system parameters (energy release, aerosol formation), but in some cases it could have a positive influence (synthesis of compact product, heating of object, etc.). Usually, an agglomeration phenomenon is observed during combustion of metal-containing HCS (Fig. 3).
This process could be divided to some steps [9, 10]: particles collecting, forming of the contacts between particles, coalescence of contacting particles in agglomerate, and it's separation from the combustion surface.
The collecting step is typical for HCS with the components melting on the combustion surface or in preheated zone.
The driving forces are surface tension and gravitation, for the "dry" deflagration case -
gravitation and the nonuniformity of the components burning-out. If the metal panicles are much
smaller than oxidizer ones, the initial structure is
favorable for the metal agglomeration due to the
metal particles collection inside the "pockets" of
oxidizer even in the initial mixture.
This process has some stages, and depends
on the particle size, contact spot surface, and
temperature (Fig. 4).
The first stage is the surface diffusion - the
mass transfer from the convex sections to the
concave surface of isthmus between particles.
The next stage comes when the oxide film
disappeared at the contact points and the unit
"dumbbelF-like particle is formed. The last stage
is diffusion leveling of the agglomerate form.
The overall junction process could be
_ . , . c .. . . . . analytically expressed as: Fig.3. Agglomeration of Al particles during „
HCS combustion: particle's collecting and (X/Ro) =A(T)*t/R0 ,
contact at the combustion surface
l.g(X/R0)
-0 2
■0 4
0
II
at
D=200fini
TIME
-0 6
-4
n=0 5
-3 -2 Lg(t)
III
(X/Ro)n = A(T)*t/Ro'
m
Fig.4. Particles junction photos and the junction process plot
where n, in - constants of junction, A(T) - temperature function, t - time, R0 - panicle radius, X -contact spot radius.
As a result of some particles coalescence agglomerate could be formed with the size of much higher than initial metal one. Finally, agglomerate separates from the combustion surface and dispergates to the flame zone (Fig. 3, 4).
2.3. Dispergation
When the components melting occurs on the combustion surface, the large panicle Reparation is defined by the relationship of buoyant forces (gas flow of the component deflagration products) and keeping forces (surface tension, gravitation).
For the large oxidizer particle the combustion occurs alone the pocket boundary, and conglomerates of metal particles and binder destruction products can be dispergated to the flame zone simultaneously.
Note, that the large temperature and pressure gradients close to combustion surface, uncertain thermo-physical parameters in this zone significantly complicate the qualitative control of the dispergation process.
The dispergated objects could be metal agglomerates, conglomerates of metal and binder, and the large particles of the initial components type ofAP, HMX, RDX. Figure 5 shows the extinguished combustion surface of the HCS with the binary oxidizer (AP+HMX), and the HMX particles (initial size 500mcm), collectcd from the flame zone close to the combustion surface.
SOOmem
Fig.5a. Burning surface of the mixture with binary oxidizer (AP+HMX). HMX particles are surrounded by binder
Fig.5b. HMX particles dispergated from combustion surface
There are HMX and AP destruction processes along with the A1 particle combustion in the flame
zone.
The mechanism and completion of these processes influence on the level of chemical and two-phase Josses in the rocket chamber.
Being in the high temperature zone with the high heating rate, aluminum particles undergo sufficient thermal tension. The defense oxide film on the A1 particle surface cracks, because the thermal spreading coefficient for A1 is three times higher than for AI2O3 one's. As a result, the diffusion resistance of AI2O3 film dramatically decreases even before oxide melting, the A1 evaporation rate increases in the crack sections. At first along the crack and than around the
208
xumhheckafl oh3mka m me30ckc>nmfl. tom 1, № 2
particle, the high temperature zone of vapor-phase flame is formed where the Al vapor is oxidized. There is a heat feedback from the vapor-phase to the particle, which leads to Al and oxide film melting. Liquid A1203 forms spherical drops on the surface of melt aluminum. Metal vapor separates these drops to the flame zone. Generally, its size is proportional to the initial metal particle size (Figure 6a), and excecds the condensation A1203 product in the vapor-phase zone (and near it).
The time of the complete Al particle burning in the active ambient of HCS deflagration products (H20, C02, 02, CO) when T>2300K, can be defined as:
tai =-0.67*d7aK° 9 where n=1.5 (T>2300K), d - the initial metal particle size, mem, ait - relative active compound concentration [8].
fA1 ... Fig.6b. Al particle "re-oxidation" in Arson Fig.6a. Vapour-phase combustion of Al particle b 5
The HMX particles burned faster than A1 ones of equivalent size. The time of HMX particles combustion in analogous conditions can be defined as:
tHMX = 0.276*d17/P°J
The time of combustion of the HMX particle diameter 350-400mcm is equal to one of the A1 particle diameter 50mcm.
Thus, the agglomeration and dispergation processes have sufficient influence to the chemical incompleteness of the HCS combustion and to the two-phase losses level in the rocket chamber.
2.4. Combustion Limits
The combustion of HCS is characterized by concentration combustion limits, i.e. breaking of combustion or abrupt change in burning rate for the certain composition of the mixture [11].
When both of the binary HCS components are not combustion self-sustaining compounds, the "left" and "right" combustion limits are very sharp defined (Figure 7). The mass concentration values on the combustion limits could vary dramatically - from units up to tens pro cents - but the volume concentration critical values are very close to 16vol% (Table 1).
If even though one of the components self-sustains combustion, the indicated critical phenomenon are observed for its volume concentration close to 16vol.% also.
Analogously, experimental investigation of metal-containing HCS shows the same tendency. Thus, there is a sharp change of the burning rate of stoichiometric mixture AP/PMMA with the adding of metal powder (Al, Zr, Ni) when the metal concentration exceeds 16vol.%. There is no
combustion for these mixtures when the AP/PMMA concentration is less than 16vol.% [12].
Note the absence of correlation between experimental U(C) dependence and the calculated adiabatic temperature of combustion function on the active component concentration. Close to concentration limits the Tad for many of the HCS is higher 1500K (Figure 3 a), i.e. higher the combustion temperature of the active component more than 1.5 times.
Fig.7. Dependence on the metal content of (a) burning rate and adiabatic flame temperature; (b) heat effect of the reaction AL+NI
210
XMMMMECKAfl OM3MKA U ME30CKC>nMR Tom 1, № 2
Table 1. Concentration limits of combustion
Composition Concentr. Limits of the Second component, m% (Lowest/Highest) LITERATURE DATA Concentration Limits of the First component, v% the Second one, v% CALCULATIONS
Ta- Si 4.4/31.7 16.1 / 16.0
Hf- Si 7.3/38.6 19.9/ 14.3
Nb-Si 7.0/47.6 14.1 / 15.0
Zr-Si 12.1 /43.2 16.7/ 19.2
Ti-Si 14.9/57.0 15.2/ 16.8
Nb-Al 6.8/46.6 11.3/15.9
Nb-Ge 14.6/70.0 12.9/12.7
Ni-Al 13.3/58.0 20.0/ 10.8
Zr-Al 15.4/65.6 18.3/ 12.0
Ti -AI 15.8/62.8 14.3/15.7
Ti-Ni 28.5/87.6 10.1 / 13.6
Ti-Co 32.5/76.3 11.8/22.5
Hf-B 4.6/23.2 14.4/18.2
Nb-B 7.2/23.2 15.0/19.9
Zr-B 7.4/37.0 13.9/18.7
Ti-B 8.3/57.0 11.4/15.1
Mg-B 25.0/71.0 17.1 / 17.3
Zr-C 7.4/43.0 14.0/ 15.8
Ti-C 8.1/57.0 11.7/14.2
Pb02 - wo2 31.0/73.0 13.2/15.8
2.5. HCS Structure
Internal microstructure of HCS depends on the particle size and shape, the relationship of component particle size, composition, sample porosity and others factors. Figure 8 presents the initial internal microstructure of termite composition (Al-hFe^). Both cases have deal with the same composition, effective particle size, and compaction te6hnique (cold uniaxial pressing), the only difference is the A1 particle shape: spherical (8a) and scaly shape (8b). Comparison of these two structures shows that oxide particles (dclmcm) form a continuum matrix. However, in the first case spherical A1 particles form isolated clusters in this matrix, whereas scaly shape A1 particles form a percolation cluster (continuum chain) oriented relatively to the pressing direction. Experimental data show [1] that the mixture with spherical A1 particles are not combustible, but in the mixture with scaly shape A1 particles combustion wave could propagate along the pressing direction.
3. DISCUSSION
3.1 Analysis of Experimental Data
Presented above experimental data show that the importance of starting internal micro structure
Combustion
wave
direction
a)
No
combustion
b)
Fig.8. Initial structure (*420) of pressed samples of stoichiometric "termite" Mixture Fe203+AL: a) scaly-shape AL particles, b) spherical AL particles
implies a large role for the formation, propagation and structure of the combustion wave [15]. Generally, this fact complicated the direct application of theory of homogeneous powder combustion [13,14] to HCS systems. At the same time, analysis of experimental data allows to separate the regions of the theory applicability to the HCS combustion, depending on some internal (component particle size, ingredient properties, etc) and external parameters (ambient pressure and temperature).
There is so called "homogeneous" combustion (Figures 1, 2) of mixtures with the rather small particle size (x/U<d), and on the other pole - the layer-ordered HCS (x/U»d) type of "sandwich", where the combustion front propagate along the contact surface of oxidizer and binder layers with the recess forming.
The minimum particle diameter of the starting "homogeneous" or "layered" regimes shifts towards the less values with the pressure growth, because of reduction of preheated layer thickness with the pressure increasing:
x/u«py
Intermediate zone in the particle diameter demonstrates a strong dependence of combustion
parameters on the internal microstructure.
The difference in thermo-physical properties, particle size, destruction kinetics leads to the non-simultaneous bum-out of the components. Subsequently, the combustion surface is not a plane, even in the case of the volatile component destruction products, and the flame is not uniformed.
Generally, the combustion process propagation requires the continues net of the reaction surface formation. Experimentally shown, that in the opposite case the process could be stopped even for the systems with a high energy content.
The concentration combustion limits, and the U(c) function behavior prove this circumstance. According to the fractal theory approach [2], the clusters of the component particles are formed during sample fabrication. Those clusters are fractals under the percolation threshold (16vol.% for chaotically packed system of equivalent sized spheres). The concentration growth leads to the threshold overcoming - isolated clusters form a percolation cluster, which mean the formation of the continuous net of the component particle.
In the case of heterogeneous combustion regime, components react at the contact surface, so the percolation cluster formation means the formation of continuous reaction surface inside the sample. Experiments show that this condition is critical for the combustion process propagation (Fig. 8a).
There is a significant increase in agglomeration over the percolation threshold for the A1 concentration (16vol.%). Initial sample structure is favorable for the particle contact formation before the combustion process. Thus, there is no contact formation stage, just particle fusion.
Note that the larger agglomerate size formed during multi-component HCS combustion, the more complex it's structure. Agglomerates can consist of the metal particles, the binder destruction products, and oxidizer. When we consider HCS with the bimodal oxidizer particle size distribution (or with two oxidizers having different particle size), the real components concentration doesn't coincide with the "receipt" one. According to the "pocket" theory combustion process goes along the large particle boundary, and the large oxidizer fraction form substructures inside the sample with a new ratio between fine oxidizer and metal particles.
Table 2 presents calculated values of the "real" component concentration inside "pockets" of large oxidizer fraction (or large sized HMX particles for the systems with complex oxidizer).
The size of the large AP particles is 250mcm, fine one's - 5mcm, HMX particles are 500mcm, and A1 metal particles are 7mcm. Table 2 presents the experimental results of the agglomerate particle size measurements from the combustion surface (Do43), at the 30mm distance from it (D3043), and the size of A1203 particles selected at the nozzle exit d43 (data of N M.Pivkin and A.A.Kohno).
Generally, the larger the ratio of coarse and fine oxidizer fractions, the faster the agglomerate "bum-out", process (D0'3< D3043). The big agglomerates are less mechanically strength, therefore its disintegrate to the smaller parts in the high temperature flame zone. It leads to the Final A1203 size decreasing (d43).
Thus, the control of the internal HCS structure allows to regulate not only the agglomeration process, but the burning rate value, and the final size of condensed combustion products, subsequently, the level of the two-phase losses in a rocket engine. Presented above experimental data show the importance of the condition of the continuous reaction surface formation, the per-
Table 2. "Real" component concentrations inside the "pockets" formed by the large AP (or large HMX) particles, Agglomerate size D43, A203 size d43
Average mass, content,0/«» Inside the "Pockets" Aggl. D3043, A1203
AI, AP AP AP Do", d4\
c, cf cvcf Al binder cf mem mem mem
24 21 45 0.47 30.4 12.6 57.0 202 185 2.8
24 33 33 1.0 35.8 16 49.2 374 2.4
24 58 8 1.25 57.2 23.8 19.0 609 115 1.8
20 20* 50 0.4 25 12.5 62.5 206 3.2
20 40* 30 1.33 33.3 16.67 50 479 1.8
* - complex oxidizer: fine AP + coarse HMX
colated cluster provides the combustion front propagation throughout the sample. In the region over the percolation threshold the outer surface of percolated cluster defines the burning rate. Figure 9
presents experimental data of the burning rate for the HCS with boron (amorphous and crystal) and different oxidizers (AP and NN). There is no correlation between the U value and the boron particle size (or it's specific surface), but the U function linearly correlates with the contact surface of boron and oxidizer particles (Sij):
U=a+b*Sy, where a, b - constants.
Special analysis [12] allows defining the components of mixture reaction between those controls the burning rate (Fig. 10).
30 so
Boron Concentration, mus %
70
U.
m m/s
75
$0
2$
10 3 0 5 0
Coiiud Surfice Bofon/Oxidizer. mm'/cra'
b)
0.2
0.4
0.6
s/s„
Fig.9. burning rate dependence (P=40 ATM) on Fig.10. Burning rate (experiment) Vs outer (a) born mass concentration; and contact surface fractal surface (calculations) for compositions between boron and oxidizer Al/AP/PMMA and Zr/AP/PMMA
Computer modeling of the HCS combustion process proves the percolation phenomena existents, and describes some peculiarities of the combustion wave propagation, depending on the sample structure and composition. Thus, observed in direct experiments three regimes of combustion front propagation (channel, whistle, and layer-by-layer) could be modeled by the cell automata technique [15].
The mathematics of fractal geometry could be successfully applied to investigation of the combustion wave structure anisotropy.
3.2. Fractal Analysis
Non-traditional geometry is used to analyze experimental optical images of the combustion front spreading process. New computer technique allows to distinguish areas having different temperature and to calculate the fractal dimension of the "fractal clouds".
The algorithm was realized to analyze the preliminary scanned optical images. The program treats the Grey scale images by transformation them into black-and-white images according to the brightness level (Z). Different levels of brightness could be attributed to the different temperature values of the object. The area of the image with brightness higher, than the chosen value of Z became white and the area with brightness below Z became black. The program allows to convert one Grey scale image to the set of images with the fixed Z value which is equivalent to some "cross-sections" of the image by-horizontal plane on the different temperature levels. Fractal dimension of the every cross-section could be calculated.
To evaluate the adiabatic combustion temperature the standard thermodynamics calculations were performed (Table 3).
Si02 powder was chosen as inert component, and specially fabricated granules of termite mixture (27.3%Fe + 36.4%KMn04+ 36.3% Mn02) - as an active component.
Granules were dry mixed and pressed into blocks 14.4*15.6*76.2mm. Termite concentration varied from 67.3mass.% to 90.0mass.%. The total porosity of samples was in the range of 51.5 to 56.6%, all the samples had so-called "open" porosity. To initiate a plane combustion wave the termite pellet (height 1mm) was placed on the top of the mixture to be compacted by cold uniaxial
Table 3. Sample composition and results of thermodynamics calculation
№ T,K Combustion products,
sample ' Composition, mass% molar fraction
. Si02 Fe KMnO< Mn02 K2Su09 Fe203
1 32.7 18.37 24.50 24.43 1179.6 0.1Ç4 y¿. 0.166
2 26.8 19.98 26.64 26.57 1101.1 0.173 0.175
3 20.9 21.59 28.79 28.71 1143.3 0.165 0.184
4 18.7 22.19 29.59 29.51 1165.8 0.122 0.187
5 9.1 24.82 33.09 33 1177.6 0.155 0.196
pressing under the constant pressure 2000atm.
Optical fixation of the combustion front spreading process was performed using zoom photo-camera. The time interval between images is about 5s. Fig. 11 presents one of the images of the combustion front for the mixture 3 in Table 3.
For visualization of temperature fields of the burning sample we consider a number of images obtained by scanning at the different levels of brightness. Figs. 12 (a-e) show color images with 16 values of color transferred from the 256 gray-scale images of the sample 3. The temperature-color scale (Fig. 12) was constructed on the basis of assumption of the linear brightness dependence on the temperature. Points with the maximum brightness level were attributed to the adiabatic temperature of combustion (Table 1), black points -to the room temperature (300K). The non-uniformity of both the combustion front lines and of temperature fields of the sample over the combustion front is good appeared. Boundaries of the temperature fields (isotherms) have a chaotic character; moreover, some temperature "spots" are chaotically introduced inside temperature fields. It means the non-simultaneous burnout of the components and the substantial process anisotropy.
To describe the chaotic geometry of the combustion front line and the temperature fields the fractal geometry approach seems to be best suited.
Thus we can clear distinguish the temperature fields boundary, the combustion front line, and estimate its fractal dimension. Table 4 present the calculation results; temperature fields could be attributed as a "fractal clouds"8 with the Df varied from 1.29 to 1.43. The average tendency is the Df increasing with the temperature growth.
Visualized temperature fields could be transformed into a number of Temperature versus Coordinate dependencies. Figs. 13, 14 show temperature profiles T(X) and T(Y) as cross-sections of the burning and cooling regions in horizontal and vertical directions. Temperature profiles follow the geometry of combustion front line and temperature fields. Thus, T(X) curve (Fig. 13a) crosses the combustion front line at X= 5mm, than after smooth growth up to 420K the T value increases dramatically up to the maximum temperature value. In the present case the T profile crosses two regions with the high temperature, subsequently the T(X) dependence has an asymmetrical bimo-
dal character. Fig. 6b presents the cross-section of the cooling region (without crossing the combustion front line), which is also considerably asymmetrical.
The vertical T profile intersects regions with a quite a constant temperature increase up to the maximum value. The temperature curve decrease dramatically when crossing the combustion front line. Note that there is a certain distance between the combustion front line and the region with the maximum temperature level. According to image analysis this distance is about 2mm. Before crossing the combustion front line the temperature gradient oscillates
f Temperature sc»Je. К
Fig.12. Temperature field visualization and temperature-color scale
Table 4. Fractal dimension of temperature fields (sample 3)
Temperature level, К Dr
400 1.3
500 1.29
600 1.32
700 1.38
800 1.32
900 1.43
around value 40K/mm, subsequently the T values increase with a constant rate practically. But after combustion front line crossing the temperature gradient achieves a maximum value. Thus the combustion front line coordinate could be attributed as a set of points with the maximum temperature gradient.
b
Fig.13 Temperature profile T(X) of sample 3.
The combustion front line spreading process could be presented as a set of profiles with the maximum temperature gradient value (Fig. 15). Combustion front lines are considerably non-uniformed. The intuitive impression about lines "similarity" could be proved by the fractal analysis. Note that all the calculated Df values are quite close (average value is 1.11) proving the assumption about the fractal dimension constancy during combustion process of the certain sample under certain experimental condition.
ISUC
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2D 00
IP , . ,
, 400
1S0C-
J JiflM -
HfV^i l.'iL,
______II !| i fh v
1200- 1 v y ' ¡¡y
-400
T,K„ A T/-dx 0___10___
4000
X,u
£>000
4. CONCLUSIONS
Analysis of the experimental data shows the importance of the HCS microstructure for the combustion process propagation. The particle clusters occurring under certain concentration and the percolation phenomena existence prove the critical role of the structure parameters in the combustion process. The continuous reaction surface formation is a necessary condition for the combustion front spreading through the mixture.
dT/dy
1UDO
-2COO
-3000
—tooo
Fig 14. Temperature profile T(Y) of the sample 3.
lMfl
iznq
Fig.15. Dynamics of the combustion front propagation through sample 3.0
The fractal approach to the combustion study is a fruitful way of heterogeneous condensed system investigations.
Optical image analysis shows that both the temperature fields and combustion front have a fractal morphology and could be adequate characterized in terms of fractal geometry (e.g. fractal dimension).
The combustion front line fractal dimension could be used to show how the geometrical shape of the combustion surface departs from a plane shape, which is important for the components non-simultaneous burnout investigation.
The proposed approach allows analyzing the temperature - time history of the any point 011 the base of the optical image, to find the critical geometrical size of the process non-uniformity, and to
1
construct the combustion front line propagation process.
Finally, the fractal concept may be used either as an introduction to the study of the system and the process heterogeneity or to a qualitative analysis of combustion front surfaces and temperature fields structure.
APPENDIX - Some Applications of HCS A. SYNTHESIS OF TITANIUM POWDER
The method for making the high surface area titanium powders is based on high-temperature reduction ofTi02 using magnesium as a reducer (Fig. 1).
Commercial grade Ti02 paint pigment powders (99.8%) were mixed with a slight excess of fine Mg powder (99.7%, 44^im), and pressed into cylindrical tablets (5 cm diameter, height 20 cm, porosity 10%). They were put into a reactor under argon (1 bar), and locally heated for ignition. The heat of the SHS reaction
Ti02+2Mg=>Ti+2MgO (AH=-330kJ/mole) is sufficient to sustain the conversion reaction once ignited. In the reaction front of the combustion wave the measured maximum temperatures were above 2000°C. The solid product which consists of a mixture of Ti, unreacted Mg, MgO and unreacted Ti02 was leached with hydrochloric acid, washed with destilled water, dried, milled, and sieved in air. Analysis revealed the following impurities (weight percent): Mg: 0.8 %; MgO: 0.5 %; Ti02: 2 %; CI: 0.01 %.
The specific surface area of the powders was measured by BET using krypton. It varied with particle (cluster) size as Figure A. 2 shows. The particle size fractions were 1,15 and 200 |irn.
Assuming self-similarity, one obtains a surface fractal dimension of 2.67. It is of some interest to compare the morphologies of the titanium powders obtained by different methods. The industrial Kroll method of producing sponge titanium by reducing TiCl4 in molten magnesium yields metal powders having a specific surface area of the order of 0.1 m2/g after milling.
Since the adiabatic reaction temperature is well over the melting points of magnesium and titanium dioxide, and the reaction times are short, the SHS process for the novel titanium powders consists of a complicated set of local reactions between solid, liquid, and vapour phases leading to coral-like morphologies and high specific surface areas (up to 20 m2/g). The combustion wave method for making high surface area powders of metals, which are stable enough for use as
220
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precursors of rcaclion-bonded nitride ceramics, is a convenient process which can be scaled up for bulk production.
The combustion-wave-gencrated titanium was used for titanium nitride synthesis by reaction with pure nitrogen [17] and as a component of pyrotechnics mixtures for the different use.
B. CHEMICAL GENERATORS OF PURE GASES
The Institute of Chemical Physics of Russian Academy of Science has great scientific experience in the development of chemical gas generating compositions. Last years much attention is spared to seeking new chemical systems having the ability to store and liberate great amounts of high purity gases. Basic fields of investigations are pyrotechnics gas generators, dissolved solid gas generating systems and gas accumulators.
There are next scientific products:
The pyrotechnical source of pure nitrogen.
Gas carrier sodium aside
Block density 1.5-2.0 g/cm'
Ignition technique local heating impulse Burning rate 0.8-8.0 mm/c
Burning temperature 400 - 800 °C
Gas rate 2-30 litters per 1 cm" of burning surface in 1 minute
Gas yield up to 400 litters per 1 kg of solid composition
Nitrogen admixtures hydrogen - traces ammonia - up to 0,2 mg/liter
hydrocarbons - none dust-0,1 - 10 mg/liter
Dust and ammonia may be eliminated by chemical filters.
The pyrotechnical source of pure nitrous oxide.
Gas carrier potassium sulfohyponitrite
Block density 1.2 g/cm3
Ignition technique local heating impulse
Burning rate 0.1 - 0.4 mm/c
Burning temperature 90-120 °C
Gas rate ' 0.2-3.0 liters per 1 cm2 of burning surface in 1 minute
Gas yield up to 100 liters per 1 kg of solid composition
USSR PATENT №698917
The pure carbon dioxide source [ 18]
Gas carrier sodium bicarbonate
Block density 1.4 g/cm3
Ignition technique water addition
Gas rate 0.1 - 0,3 liters per 1 cm2 of reacting surface in 1 minute
Gas yield up to 100 liters per 1 kg of solid composition
Nitrogen admixtures water vapour and sprays
C. FIRE EXTINGUISH GENERATOR
The small-size Fire extinguish aerosol generator is designed to suppress the indoor Fire (book store, museums, computer store, transport, special technology rooms).
Technical parameters:
Total working time, sec 20-100
Initiation time delay, sec 1-3
Burning rate, mm/s 0.5-8.0
Rate of aerosol generation. I/kg* sec up to 150
Gas generation, I/kg up to 500
Aerosol temperature (nozzle), C 75-200 Aerosol temperature (0.5m from the nozzle), C less 75
Fire-Extinguish parameter, g/qm 20-60
Valid time of generator, years 5
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2. Mandelbrot B. B. '"Fractal Geometry of Nature". Freeman, 1982.
3. Avnir D. Fractal Approach to Heterogeneous Chemistry. Wiley, 1989.
4. Pivkina A., Yablokov M., Frolov Yu. "Fractal Analysis of Heterogeneous Condensed System Combustion". Proceedings of Second International High Energy Materials Conference and Exhibit (2nd IHEMCE), December 8-10, 1998.
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Condensed Systems" (in Russian). Fizika Goreniya I Vzryva, 1997. Vol. 33, № 5. Pp.3-19.
13. Zci'dovich Ya.B. "Theory of Powder and Explosives Combustion" (in Russian), Zumal Electro-Techcheskoi Physiki, 1942. Vol. 1 1-12. №4. Pp.498-525.
14. Belyaev A.F. "About Explosives Combustion" (in Russian). Zumal Phxsicheskoi Khimii, 1939. Vol. 12, № I. Pp. 93-99.
15. Pivkina A., Frolov Yu... Aleshin A. and Vinokurov A. "Combustion Front Geometry of HCS: Experiment and Computer Modelling," Proceedings of the 23rd Int. Pyrotechnics Seminar. Tsukuba, Japan, 1997. Pp. 706-719.
16. Frolov Yu.V., Pivkina A.N. "Structure and Combustion of Heterogeneous Condensed Systems", Proceedings of56 Congres International de Pyrotechnic (EUROPYRO 1993), Strasbourg, France, 6-11 June 1993.
17. Pivkina A.. P.J. van der Put, Frolov Yu., J. Schoonman Reaction-Bonded Titanium Nitride Ceramics, J. European Ceramic Society, 16, 1996. P. 35-42.
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SUMMARY. The paper is focused on the structure of HCS sample and its influence on the peculiarities of formation combustion front. Some phenomenological aspects are analysed on base of fractal and percolation theory. It is shown the fractal character of particle clusters occurring under certain concentration and the percolation phenomena prove the critical role of the structure in the combustion process. The continuous reaction surface formation is a necessary condition for combustion front propagation across HCS sample in common and for phenomena type agglomeration. Fractal dimension could be a one of key point of the non-simultaneous combustion process investigation.
