[american institute of aeronautics and astronautics 45th aiaa aerospace sciences meeting and exhibit...

Coupling of Leading Edge Flames in the Combustion Zone of Composite Solid Propellants

N. Mansu,1 Vishal Srinivas,2 and S. R. Chakravarthy3

Indian Institute of Technology – Madras, Chennai 600 036, India

The burning rate trends of both pure binder sandwiches as well as those containing fine AP-filled binder (matrix) are investigated at different values of the middle lamina thickness over an appreciable range of pressure. The crucial aspect of this study is the variation of the ratio of fine AP/binder in the middle lamina of the matrix sandwiches. The surface profiles of matrix sandwiches quenched by rapid depressurization have also been mapped for different the different conditions. It is found that, as the fine AP is added to the pure binder, the AP particles tend to dilute the fuel and increase the lamina thickness for maximum interaction between the leading edge flames (LEFs). This causes a reversal in the trend of the variation of the optimum thickness for maximum burning rate with increase in pressure when compared to the case of pure binder sandwiches reported earlier. For addition of small quantities of fine AP in the middle lamina, the burning rates of these sandwiches decrease slightly as a consequence. As the fine AP content is increased further, there is greater interaction between the LEFs due to the inward shift of the stoichiometric surface and the extension of the fuel rich sides of the LEFs over the matrix lamina, ultimately resulting in the establishment of the canopy premixed flame between them. This restores the optimum thickness trends with pressure as in the case of pure binder sandwich. The surface profiles and the burning rates can be used to numerically obtain an estimate of the gas phase heat release rate distribution, as reported previously for an oxidizer/binder interface,1 with modifications to apply to matrix sandwiches. This is applied to the surface profiles of a family of the matrix sandwiches with different matrix lamina thicknesses, obtained experimentally in this study. The computations aid further with comparative locations of the LEFs and the consequent temperature distributions, among the cases considered.

I. Introduction HE combustion mechanism of composite solid propellants is known to be very complex due to the dependence of its burning rate on (a) coarse oxidizer particle size, (b) fine oxidizer particle size, (c) the loading of fine

oxidizer particle in the matrix and, finally, (d) the distance between the coarse oxidizer particles. The physical and chemical processes occurring during solid propellant combustion are yet to be fully understood. With reference to the previous studies on providing insight into the above combustion mechanism, the present work is aimed at further probing into the combustion mechanism of composite solid propellants. This is facilitated by investigating the microscopic features where the coarse oxidizer (ammonium perchlorate, AP) particles are replaced by thick oxidizer slabs separated by the fuel lamina. This representation is known as a pure binder sandwich. Sandwiches with the addition of fine AP particles to the binder are called matrix sandwiches. The sketches of the above sandwiches are shown in Figure 1. It is found in the past literature that the leading edge flame (LEF) is known to play a central role in the flame structure of composite solid propellant combustion and thereby control the burning rate of the composite solid propellants.2 The influence on the burning rate depends on the coupling or interaction of these LEFs, which in turn depends on different conditions such as pressure, the distance between them as dictated by the middle lamina thickness in a sandwich, and finally, the fine AP/binder ratio in the matrix.

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The phalanx flame model Fenn3 considered that the interface between the two solid phases receives the greatest heat flux from the reaction zone and vaporization occurs most rapidly near the interface. The central part of the 1M. S. Scholar, Department of Aerospace Engineering. Current address: Vikram Sarabhai Space Center, Indian Space Research Organization, Thiruvananthapuram 695022, India. 2Dual Degree M.Tech. Student, Department of Aerospace Engineering. 3Associate Professor, Department of Aerospace Engineering. Corresponding author (e-mail: [email protected]).

American Institute of Aeronautics and Astronautics

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45th AIAA Aerospace Sciences Meeting and Exhibit8 - 11 January 2007, Reno, Nevada

AIAA 2007-780

Copyright © 2007 by N. Mansu, V. Srinivas, and S. R. Chakravarthy. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

phalanx flame is responsible in regression of the unburnt surface. The need for the leading edge of the diffusion flame was first propounded in this work. Nadaud4 conducted experiments on samples where AP was sandwiched between fuel slabs. Tests were performed at several pressure ranges including at pressures less than atmospheric. The main attention was on the mixing rate and reaction rate. Beckstead et al.5 developed a model describing the combustion of AP composite propellants, in which the leading edge flame is identified by a separate chemical kinetic mechanism as the primary flame. Bakhmam and Librovich6 concentrated on flame propagation in thick slabs of oxidizer and fuel, and focused on the shape of the burning surface and the dependence of flame velocity on pressure and layer thickness. Manelis and Strunin7 have explained the mechanism of AP burning. AP is known to sublime at high temperatures, dissociating into perchloric acid and ammonia. The presence of ammonia results in the dilution of perchloric acid as an oxidizer. Nir8 has presented results concerning the low-pressure limit for self-sustained combustion of AP. In the above study, the physical properties of the pressed AP samples are related to its self-deflagration, especially density, initial temperature and size of the AP crystals.

Figure 1. Schematic sketch of sandwiches.

Price et al.9 have reported experimental results on sandwiches with PS, PBAN and HTPB as the binders with

its thickness in the range 10-150 μm. The main focus was on tapered sandwiches so as to determine the limiting binder thickness for which quenching occurs. Price et al.10 have studied the combustion of sandwiches over the pressure range from 13.9 MPa down to the low pressure combustion limit. The main emphasis was on the effect of variation of fuel lamina thickness and the pressure on the surface profiles. The protrusion of the binder lamina and the oxidizer lamina were understood from the features of the quenched surfaces. Price et al.11 have reported a series of experimental studies on sandwich combustion and also relevant details regarding the flame structure. The results so obtained were phenomenal in explaining the reason for the formation of the “smooth band”.

Further insight into sandwich combustion was obtained from Lee et al.,12 who reported experimental results on pure binder as well as matrix sandwiches. They have studied matrix sandwiches by varying the size of the AP particles in the matrix lamina and, thereby its effects on the combustion zone microstructure have been investigated. The work has provided a description of the interaction of the lamina-leading edge flames (LLEF) and the canopy premixed flame, when the matrix is capable is burning by itself. Based on this work, the flame structure for pure binder and matrix sandwich is as shown in Fig. 2.

The numerical study carried out by Prasad and Price13 has depicted the LEF as a flame-holding point for the rest of the diffusion flame. The reason for the flame stand-off distance as a function of surface temperature and concentration gradients of the reactants is explained. The theoretical work done by Buckmaster et al.14 is also useful in understanding the chemistry effects in composite solid propellant combustion. It is known from their work that


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the diffusion flame cannot extend all the way to the propellant surface, where the temperature is too low to sustain combustion.

Chakravarthy et al.15 have observed plateau burning trends in sandwich combustion for a specific range of pressures at specific matrix thicknesses. This work is noteworthy for comparable results on plateau burning of sandwiches and propellants with bimodal distribution of oxidizer. Panyam et al.1 have developed a numerical procedure to estimate the chemical heat release rate distribution in the gas phase with input of the burning rate and surface profile of an interface of a fuel and an oxidizer slab, without the knowledge of the chemical kinetic details of the flames. Brewster et al.16 have done experimental and computational studies on pure binder sandwiches as well as oxygenated fuel sandwiches. The influence of heat release was studied with the consideration of triple layer laminates.

The above works reveal the LEF-interaction at different conditions, such as pressure, fine AP/binder ratio in the matrix and middle lamina thickness. However, the influence of the fine AP/binder ratio on the interaction of the LEFs was not completely investigated. The effects of adding fine AP to the middle lamina are: (a) dilution of the fuel, (b) shifting of the stoichiometric surface towards the middle lamina, and (c) extension of the fuel rich side of the LEF towards the middle lamina.12 The first effect tends to increase the optimum thickness of the matrix lamina for maximum LEF interaction, while the other two effects result in the decrease of the above thickness by the enhancement of LEF interaction. The present study is aimed at a systematic variation of

the fine AP/binder ratio to resolve these competing effects on the optimum thickness for maximum LEF interaction at different pressures.

(a) Pure binder sandwich

(b) Matrix sandwich

Figure 2. Flame structure of sandwiches.

Based on the above motivation, the objectives of the present work are: (1) To determine the burning rate variation of matrix sandwiches for a wide range of matrix lamina thickness, at different pressures, with fine AP loading in the matrix lamina being systematically varied; (2) To examine the surface profiles of the quenched matrix sandwiches at the conditions mentioned above; (3) To demonstrate the use of the burning rate and surface profile information to numerically estimate the chemical heat release rate distribution in the gas phase combustion zone, following Panyam et al.1 and modifying their formulation to apply to matrix sandwiches with twin lamina-interfaces.

II. Experimental Details

A. Sample Preparation 1. Oxidizer Particles

The oxidizer particle used for the present work is ammonium perchlorate (AP), obtained from Tamil Nadu Chlorates Ltd, Madurai, India. The AP powders are of purity > 99%, containing chlorides, chlorates, sulphates, calcium, etc. in very small concentration levels (each < 0.01%). The oxidizer particles are subjected to grinding in a vibratory rod mill, where the oxidizer particles are crushed into different sizes. The ground oxidizer particles are segregated on the basis of their sizes using a sieving machine. The fine AP particles were collected using an apparatus called elutriator, which separates the particles by their size, based on Stoke’s law. Based on trial runs with different mass flow rates, the value of mass flow rate for yielding required size has been calibrated. The size distributions of the fine AP particles collected from the elutriator are determined by image processing. The elutriated fine oxidizer particles are mixed with HTPB and DOA in order to avoid the risk of the AP being affected by moisture and the above mixture was stored in a dessicator. A certain proportion is maintained for the mixture containing the above fine AP, HTPB and DOA. The oxidizer lamina is prepared by compacting AP powder of size distribution ~60 µm in a hydraulic press for 2 hours under a pressure of 12.5 tonnes. For pressing, ~1.8 grams of AP is weighed in an electronic balance with an accuracy of ±0.05% and transferred to a die which is kept in the hydraulic press for compaction. After the stipulated time, the oxidizer slab is taken out from the die and stored in an oven. Any evidence of cracks in the pellet does not permit its further use.


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Figure 3. Burning rates of pure binder sandwiches.

2. Fuel/Matrix Lamina

The binder or fuel used in the present study consists of three ingredients, namely, prepolymer, plasticizer and the curing agent. The prepolymer used is hydroxyl-terminated polybutadiene (HTPB), which functions as the hydrocarbon fuel. Di-octyl adipate (DOA) acts as plasticizer, and toluene di-isocyanate (TDI) plays the role of a curing agent. For the preparation of the binder the above ingredients were taken as follows: (1) HTPB—80%, (2) DOA—15%, and (3) TDI—5% by mass. In the case of pure binder sandwiches, the ingredients mentioned above are weighed in the electronic balance and thoroughly mixed. For matrix sandwiches, a certain amount of fine AP particles are added to the above ingredients to form a “matrix”. The AP/binder ratios in the matrix are varied as 70/30, 60/40and 50/50, 40/60 and 20/80. The mixing is followed by the removal of air bubbles trapped in the mixture with the help of an apparatus called vacuum degasser. 3. Sandwich Fabrication

Using the compacted AP quarter disks, the sandwiches are prepared with AP-filled/pure fuel for a thickness range of 25-500 µm. The fuel lamina thickness is controlled by a combination of shims of known thickness placed at the edges between the cut AP quarters. A small quantity of the fuel mixture was smeared between the spacer shims. Another AP quarter disk is placed in such a way that it is exactly above the first quarter disk, and it is pressed gently against the spacer shims at its edges to obtain uniform spreading of the binder/matrix in between the two disks. These samples are secured on an endplate and cured in an oven at 50 ºC. After curing, the spacer shims were then removed, and the cured samples are sanded down to obtain the desired dimensions. The thickness of the binder/matrix laminas is examined using an optical microscope. The samples are then stored in a dessicator until they are used for the experiments.

B. Experimental Procedure 1. Burning Rate Measurement

The burning rate of the samples is determined as a result of experiments performed in a set-up called “window bomb” The window bomb is a cylindrical pressure vessel which is designed up to a working pressure of 20 MPa. The measurement of burning rate is achieved through combustion photography, wherein the image of the burning sample is captured using a CCD video camera and recorded in a video cassette recorder. The cylindrical chamber has two windows made of toughened glass along its curved surface, one of whose diameter is ½" and the other 1". The purpose of the smaller window is to facilitate the imaging of the burning process and the other window is used to provide external illumination. The CCD camera is capable of imaging at a rate of 25 frames per second. Using the shuttle ring/dial control in the video cassette recorder, the recorded images can be viewed frame-by-frame for determining the burning rate of the samples. Before ignition, the chamber is flushed with nitrogen gas followed by maintaining the pressure required for combustion. The sample is then ignited and the images were acquired and recorded. The burning rate of the sample is determined by examining the images recorded in the video cassette. The time interval between successive frames is 40 milliseconds. The images are viewed frame-by-frame and the location of the flame front in each frame is noted. The actual position of the flame front is plotted against the time of


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each frame, after adjusting for the magnification of the images. The burning rate is obtained as the slope of the linear fit to the points. 2. Surface Profile Measurement

The microscopic surface profile features of sandwiches are better explored with experiments performed in a quench bomb, a facility where a burning sample is quenched due to rapid depressurization that is triggered at a pre-set time after ignition. Depressurization occurs due to the bursting of a diaphragm. The time lag between the ignition and the bursting of the diaphragm can be controlled using a delay circuit. The time lag and the thickness of the diaphragm depends on the testing conditions especially the pressure. The quenched sandwiches are analyzed in a compound microscope; its image is obtained a CCD camera. The acquired images are viewed on the computer and the surface profile of the sample is identified by selecting different points along the surface. These points are plotted in a Cartesian co-ordinate system and a polynomial of suitably higher degree curve is fitted to them. The curve obtained is then analyzed for determining the surface profiles at different test conditions.

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Figure 4. Burning rates of matrix sandwiches.


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(a) Low pressure (b) High pressure

Figure 5. Flame structure at low fine AP loading in the matrix.

III. Experimental Results and Discussion

A. Burning Rates 1. Pure Binder Sandwiches

The pure binder sandwiches are tested to determine the burning rate variation with binder lamina thickness in the range of 25-150 µm as reported earlier.11 The results obtained in the present study correspond to the contemporary pre-polymer HTPB when compared to PBAN used in the previous works.11,12 Also, in the present work, the pressure is varied more closely than reported earlier. The graphs are plotted with the binder thickness on abscissa and the burning rate on the ordinate; the results are shown in Fig. 3. The curves are plotted for a pressure range of 1-7 MPa in steps of 1 MPa. The corresponding AP self-deflagration rate for each pressure is marked on the ordinate. As known earlier, AP does not self-deflagrate at pressures less than 2 MPa. For pressures greater than the AP self-deflagration limit, the AP burning rate is approached as the binder thickness goes to zero. So, the curve for each pressure above this limit is expected to meet the ordinate at a point corresponding to the burning rate of AP alone at the same pressure. It is evident from the plots that, for each curve, a peak occurs at an intermediate binder thickness, as reported in earlier works. The region around the LEF which controls the burning rate is called PVC (propagation velocity controlling) region.11 For a thick binder, the two LEFs burn independently, so that the merger of the PVCs is hindered. With the binder thickness decreased to an optimum value, the two LEFs now interact so that the PVCs get combined and the heat feedback to the surface is increased. At lower binder thickness, the burning rate falls due to reduced fuel supply. Again, as reported in earlier works, in the plot of burning rate vs. binder thickness, as the pressure is increased, there is an overall shift in the peak towards lower binder thickness as evident from previous works. As pressure is increased, the LEF stand-off distance decreases. So, in a situation of pressure rise, the LEFs move downward along the stoichiometric surface, so that, even though the binder thickness is small, the downward movement of LEF along the stoichiometric surface, in fact, positions them closer to each other, which eventually results in optimum interaction of the PVCs at a lower binder lamina thickness as compared to that at a lower pressure. 2. Matrix Sandwiches

An elaborate study on matrix sandwich combustion is carried out in the present work. For matrix sandwiches, the matrix lamina thickness is maintained in the range of 100-450 μm. The variation of the burning rate with matrix lamina thickness is determined at different pressure levels, namely, 2, 3.5, and 7 MPa. In this study, the focus is on the gradual increase of fine AP loading in the matrix lamina, with the size distribution of the fine AP in the matrix lamina kept as constant. This is aimed towards investigating the nature of the flame interaction as a function of the fine AP loading in the middle lamina. The results obtained are shown in Fig. 4, and they are discussed below for each fine AP/binder ratio in the matrix.


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Figure 4(a) shows the burning rate variation with the matrix lamina thickness for the matrix with a fine AP/binder ratio of 20/80, at the three pressure levels mentioned above. For each curve obtained, a peak occurs at a matrix thickness in the range of 175-200 µm, unlike the range of 45-75 µm in pure binder sandwiches for the same pressure range in Fig. 3. This increase in the peak for matrix sandwiches occurs mainly due to the effect of adding fine AP in the middle lamina. As oxidizer is added to the binder in the middle lamina, the fuel is diluted, i.e., the fuel concentration is reduced. Consequently, the LEFs face a situation of low heat release. In this situation, sufficient heat release from the LEF is possible only if an adequate fuel supply is provided; which implies that the thickness of the middle lamina should be increased. It was discussed from earlier studies that the peak occurs due to maximum LEF interaction.11,12 It is found in Fig. 4(a) that the optimum matrix lamina thickness for peak burning rates increases with increase in pressure, a trend contrary to that observed with pure binder sandwiches in Fig. 3. Note that the 20/80 matrix does not burn by itself, so at large thicknesses as in the above range, the matrix lamina protrudes, as will be seen from the surface profiles later. In this case, the competing effects are fuel deficiency in the low-thickness range and lateral heat loss to the protruding matrix lamina in the large-thickness range, which results in a peak in the burning rate variation with the matrix lamina thickness, and not due to maximum interaction between the LEFs, as they are spaced too far apart. This scenario is depicted in Fig. 5. At low pressures, the standoff distance of the LEFs is probably greater than height of the protrusion of the matrix lamina, so the LEF interaction is somewhat facilitated, leading to peak burning rates even at a low lamina thickness, further aided by the inward shift of the stoichiometric surface and the extension of the fuel-rich branches of the LEFs. On the contrary, at high pressures, the LEF standoff distance is comparable to the height of protrusion of the matrix lamina, which precludes any interaction, and causes a continuous decrease in the burning rate with further increase the matrix lamina thickness beyond the optimum value, as can be seen in Fig. 4(a).

Figure 6. Optimum interaction thickness vs. fine AP loading in the matrix.

In the case of the fine AP/binder ratio = 40/60 in the matrix, the burning rates of whose sandwiches are shown in

Fig. 4(b), the trends are similar to that observed in the case of the ratio being 20/80 in Fig. 4(a), in that the optimum matrix lamina thickness for peak burning rates increases with increase in pressure, albeit to a milder extent. This is because of the increasing contribution of the inward shift of the stoichiometric surface and the extension of the fuel-rich branches of the LEFs promoting their mutual interaction, particularly at lower pressures. It must be noted that the 40/60 matrix also does not burn by itself, causing a protrusion of its lamina in the sandwiches, particularly for large thicknesses.


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When the fine AP/binder ratio in the matrix lamina is increased to the 50/50 level (Fig. 4(c)), the trends in the burning rates are restored to those observed for pure binder sandwiches in Fig. 3, i.e., that the peak-thicknesses decrease with increase in pressure, as reported by Lee et al.11 Note that the 50/50 matrix too does not burn by itself, which causes its protrusion, but not as much with those with lower AP content, in the middle laminas of the sandwiches. Further, note that the peak-thickness for this fine AP/binder ratio is quite larger than that for pure binder sandwiches at any given pressure. Considering these, the restoration of the trend in the variation of the peak-thickness with pressure for this fine AP/binder ratio as in the pure binder sandwiches is mainly due to the contribution of the inward shift of the stoichiometric surface and the extension of the fuel-rich branches of the LEFs promoting their mutual interaction.

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Figure 7. Maximum burning rate vs. fine AP loading.

The matrix with the fine AP/binder ratio of 60/40 burns by itself at the three test pressures; its burning rates are

marked along the right ordinate in Fig. 4(d). This causes a connection to prevail between the extended fuel-rich branches of the LEFs in the form of a canopy premixed flame (for the given fine AP size, in the test pressure range). Therefore, a full-scale interaction of the LEFs is possible, and is further enhanced by the presence of the canopy flame itself and an absence of the protrusion of the matrix lamina, which is in turn due to the presence of the canopy flame. As a result, the burning rate trends are as expected,11 similar to those of the pure binder sandwiches, but over a larger thickness range, understandably.

The case of the matrix with a 70/30 ratio of fine AP/binder (Fig. 4(e)) is similar to the previous case. The large increase in the peak burning rate at high pressure is noteworthy. This is clearly due to the enhancement of the interaction by the LEFs due to the presence of the canopy premixed flame connecting them.

The variation of the optimum lamina thickness with the fine AP/binder ratio (including 0% corresponding to the pure binder sandwiches) at the three test pressure levels is consolidated in Fig. 6. It can be seen that the curves taper off and begin to decrease at the high end of the matrix AP loading for the lower pressures, but the high pressure curve decisively peaks at a slightly lower matrix AP loading level than the maximum tested, indicating that the different competing effects do indeed point to an optimum fine AP loading in the matrix at a given pressure, beyond which the factors impeding the increase in burning rate are mitigated.

Figure 7 shows the peak burning rates obtained at the optimum thicknesses as a function of the fine AP loading in the matrix lamina, at the test three pressures. The figure shows that the burning rate does not increase substantial with modest increases in fine AP content, until a reasonably high value, since the low levels, the dilution effect of the AP predominates and precludes the interaction of the LEFs, further aggravated by the protrusion of the matrix lamina.


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B. Surface Profiles The surface profiles are obtained for selected matrix sandwiches, especially for cases where, in one case, the

matrix does not burn by itself, and in the other, the matrix undergoes self-burning at all the test pressures. So, the experiments are mainly focused on sandwiches with the matrix lamina ratios of 70/30 and 40/60. The profiles are obtained by selecting the points along the surface. The results are discussed below.

(a)Profiles for fine AP/binder ratio = 40/60

Matrix lamina

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(b) Profiles for fine AP/binder ratio = 70/30

Figure 8. Profiles for two fine AP/binder ratios at pressure = 35 bar at different thicknesses.

1. Variation of Matrix Lamina Thickness First, the variation in the matrix lamina thickness is considered, with the pressure kept constant at 3.5 MPa, for

two fine AP/binder ratios mentioned above. The surface profiles are shown for three matrix lamina thickness in each case, in Fig. 8. At a lamina thickness for 110.5 μm of the 40/60 matrix sandwich (Fig. 8(a)), the matrix lamina is recessed, even though the 40/60 matrix does not burn by itself at all the test pressures. This is because, for a lower thickness, the LEFs are very close to each other, even if fuel-deficient. For an intermediate thickness of 221 μm and the large thickness of 374 μm, the matrix lamina protrudes, which indicates the non-burning nature of the 40/60 matrix. It is seen that the point of maximum regression moves away from the interface as the matrix lamina thickness is increased. As the lamina thickness is increased, there is a slight increase in the flame stand-off distance which results in lateral displacement of the LEF from the interface based on the flame geometry, which accounts for this observation.

When the fine AP content in the lamina is increased to the 70/30 level, the matrix burns by itself, which is reflected in its lamina being recessed for all thicknesses in the sandwiches (Fig. 8(b)). The depth of recession was decreases with increase in the matrix lamina thickness, however. For the thin lamina at 93.5 μm, the heat feedback from the LEF is localized due to the close spacing between them. As the thickness is increased, the LEF stand-off distance increases slightly, and the LEFs also move apart from each other, thereby resulting in a larger heat feedback to the interface rather than the middle portion of the matrix lamina unlike the case with thin matrix lamina. 2. Variation of Pressure

Sandwiches with matrix lamina thickness approximately in the optimum range have been quenched at the three test pressures, for the two fine AP/binder ratios mentioned above. The surface profiles are shown in Fig. 9. In the case with the 40/60 matrix (Fig. 9(a)), the point of maximum regression shifts away from the interface into the AP lamina, indicating the control of the LEFs as they move closer to the burning surface with increase in pressure, in


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the absence of the matrix flame, as shown by the matrix protrusion noted earlier. In the case of the 70/30 matrix (Fig. 9(b)), the increase in pressure is observed to cause the slopes of the AP lamina surfaces to decrease as they approach the matrix lamina interfaces, again suggesting the decrease in the flame standoff distance. However, the effect is not as drastic as in the previous case due to the additional contribution of the matrix flame, which is manifested in the recessed appearance of the matrix lamina surface at all the pressures.

(a) Profiles for fine AP/binder ratio = 40/60

files for two fine AP/binder different pressures.

IV. Numerical Estimation of the Gas Phase Heat Release Rate Distribution This paper further demonstrates the application of the information on the burning rates and the quenched surface

profiles to obtain an estimation of the distribution of the chemical heat release rate in the gas phase, without recourse to informa se reaction mechanism ical kinetics, whi vailable in reliable manner. This approach follows that eluc am et al.,1 but with modifications to consider thesimultaneous presence of two adjac aining fine AP particles. The first aspect requires the adoption of Neumann boundary conditions at the far-field boundaries of the gas phase domain as opposed to a Dirichl e between fuel and oxidizer slabs below the self-deflagration limit of the latte The second aspect is addressed by treating the presence of the fine AP in the matrix in a homogenized manner, following the recent work of Chen et al.17

(b) Profiles for fine AP/binder ratio = 70/30

35 bar

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Matrix lamina Matrix lamina Matrix lamina

20 bar 212 µm

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Matrix lamina Matrix lamina Matrix lamina

re 9. Pro ratios atFigu

tion on the gas pha s and their chemidated by Pany

ch is scarcely a a

ent interfaces separating a matrix lamina cont

et boundary condition to vertical surfaces on either side of a single interfacr.

(a) 93 μm (b) 229 μm (c) 357μm

Figure 10. Surface profiles of sandwiches with different matrix lamina thickness of fine AP/binder = 70/30 matrix, obtained experimentally at 3.5 MPa, and adapted for the computational study.


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(a) 93 μm (b) 229 μm (c) 357 μm

Figure 11. Condensed phase isotherms of sandwiches of different matrix lamina thickness. Results are obtained for a family of the surface profiles obtained experimentally in the present study. The

experimental profiles are fitted separately over the each of the AP and matrix laminas, but only over a limited region on the quenched surface in the vicinity of the interfaces, for the sake of retaining accuracy. The fitted profiles on the

0 full surface profiles with these extensions, as considered for the computations, is shown in Fig. 10.

a Ref. 1. No

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outer AP laminas are extended further on either side to occupy a reasonably large computational domain of 100μm. The

Note that the information on the burning rate and the full surface profile is sufficient to evaluate the surface temperature along the entire burning surface via the Arrhenius surface-pyrolysis laws.1 This completely decouples the condensed phase heat transfer problem, supplying a Dirichlet boundary condition at the burning surface, and Neumann boundary conditions in the far-field upstream and on the sides. The isotherms in the condensed phase are s shown in Fig. 11, for the considered surface profiles, with the non-dimensionalized quantities as defined in

te the slightly lower surface temperatures for the case of the sandwich with the thin matrix lamina, indicating the fuel deficiency for that thickness (Fig. 11(a)).

The gas phase flow problem is solved by assuming a constant density, as the difference between the results with that assumption and by relaxing it are insignificant.1 The streamlines obtained in the gas phase are shown in Fig. 12. As expected, mostly the streamlines are vertical, except near the surface.

(b) 229 μm (c) 357 μm

To solve the gas phase thermal problem, given the flow field obtained as above, it is necessary to assume asuitable spatial distribution of the chemical volumetric heat release rate. The suitability is governed by thsatisfaction of the energy balance at the solid-gas interface within a specified tolerance, within a number of constraints.1 This is iteratively obtained until the near-surface gas phase temperature is within an acceptable tolerance of that expected one, based on a full satisfaction of the interface energy balance.

(a) 93 μm Figure 12. Gas phase streamlines for sandwiches with different matrix lamina thickness.

(b) 229 μm (c) 357 μm(a) 93 μm Figure 13. Gas phase heat release distribution for sandwiches with different matrix lamina thickness.


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(b) 229 μm (c) 357 μm(a) 93

The gas phase heat release rate distributions obtained after iterative convergence satisfying the interface energy he

eratures associated with the two interfaces can be

derive me

sion The leading edge flame interaction in matr gradual increase of fine AP loading is studied.

The coupling is enhanced at high fine AP conte at high pressures. The LEF interaction is found to

the fine AP size in the middle lamina and the inclusion of IPDI as the curing agent that are

entally, to esti

References 1Panyam. R. R., Price, E. W., and Chakravarthy, S. R., “ the Interface of a Laminate System of Solid Oxidizer and

Solid Fuel,” Combustion and Flame, Vol. 136, 2004, pp.

balance within the acceptable tolerance are shown in Fig. 13 for the chosen experimental surface profiles. For tmatrix lamina thicknesses of 93 and 229 μm, the satisfaction is within 12%, and for 357 μm, it is within 7%. By contrast, the interface energy balance was satisfied only to 30% in the previous study.1 Typically, the heat release distribution is approximate, as it is a coarse distribution manually considered and refined with subsequent iterations to satisfy the interface energy balance with the acceptable tolerance.

The temperature distributions in the gas phase corresponding to the three cases considered are shown in Fig. 14. The two regions of maximum heat release rates and maximum temp

clearly seen in these two figures for each of the surface profiles. Note the need to include a significant amount of heat release rate near the surface of the fine AP/binder matrix for the ratio considered here, in all the cases of Fig. 13. It is seen that the regions of heat release in the gas phase associated with the adjacent interfaces stay connected, albeit not at maximum magnitudes, across the matrix lamina, signifying the presence of the matrix flame for all matrix lamina thicknesses (Fig. 13). However, the regions of maximum temperatures are closely connected for the thin lamina case, but progressively move farther apart as the matrix lamina thickness is increased, in Fig. 14.

From the foregoing, it is thus possible to obtain insight into the gas phase heat release region, i.e., approximate flame structure, and compare the different cases for which the surface profiles are obtained experimentally, to

aningful conclusions about their combustion mechanism.

V. Concluix sandwiches withnt in the matrix and

increase the value of the burning rate, which is essential for solid propellants. The circumstances leading to the above has been studied with emphasis on the effect of fine AP content in the matrix lamina. The surface profile study is carried out to examine the effect of leading edge flames on the burning surface, especially on the oxidizer laminas near the interface.

The understanding of the combustion mechanism of composite solid propellants developed in this study should prove helpful for variation of

needed to understand the plateau-burning mechanism. For a given pressure as well as for a given fine AP content in the matrix, the amount and the size of the coarse AP to be used can be modeled so that the average distance between the coarse AP particles in some sense is the same as the optimum interaction thickness.

The results obtained in this present study are also expected to aid in computational modeling of the solid propellant combustion. This has been demonstrated on a family of surface profiles obtained experim

mate the spatial distribution of the volumetric chemical heat release rate in the gas phase combustion zone, including the near-surface heat release. This throws some light on the interaction of LEFs qualitatively alluded to in discussing the experimental burning rate and surface profile results in the present study, to a limited extent. Further work on other surface profiles would further illuminate the LEF dynamics with regard to the role of the AP loading in the matrix.

Combustion at1-15.

2Price, E. W., “Effect of Multi-Dimensional Flamelets in Composite Propellant Combustion,” Journal of Propulsion and Power, Vol. 11, No. 4, 1995.

μm Figure 14. Gas phase isotherms for sandwiches with different matrix lamina thickness.


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3Fenn, J. B., “A Phalanx Flame Model for the Combustion of Composite Solid Propellants,” Combustion and Flame, Vol. 12, 1968, pp. 201–216.

4Naudaud, L., “Models Used at ONERA to Interpret Combustion Phenomenon in Heterogeneous Solid Propellants,” Combustion and Flame, Vol. 12, 1968, pp. 177-195

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levated Pressures,” Journal of Propulsion and Power, Vol. 19, No. 1, 2003, pp. 56-64.

onium Perchlorate,” Combustion and Flame, Vol. 136, 2004, pp. 313-326.

5Beckstead, M. W., Derr, R. L., and Price, C. F., “A Model of Composite Solid-Propellant Combustion Based on Multiple Flames,” AIAA Journal, Vol. 8, No. 12, 1970, pp. 22

6Bakhman, N. N. and Librovich, V. B., “Flame Propagation Along Solid Fuel-Solid Oxidizer Interface,” Combustion and Flame, Vol. 15, No. 2, 1970, pp. 143-153.

7Manelis, G.B. and Strunin, V.A., “The Mechanism of Ammonium Perchlorate Burning,” Combustion and Flame, Vol. 17, 1971, pp. 69-77.

8E. C Nir, “An Experimental Study of the Low Pressure Limit for Steady Deflagration of Ammonium Perchlorate,” Combustion and F

9Price E. W., Panyam, R. R., and Sigman, R. K., “Microstructure of the Combustion Zone: Thin-binder AP-Polymer Sandwiches,” Proceedings of the 17th JANNAF

10Price, E. W., Handley, J. C., Panyam, R. R., Sigman, R. K., and Ghosh, A., “Combustion of Ammonium Perchlorate – Polymer Sandwiches,” AIAA Journal, Vol. 19, No. 3, 1981, pp. 380-386.

11Price, E. W., Sambamurthi, J. K., Sigman, R. K., and Panyam, R. R., “Combustion of Ammonium Perchlorate – Polymer Sandwiches,” Combustion and Flame, Vol. 63, 1986, pp. 381 – 413.

12Lee, S. T., Price, E. W., and Sigman, R. K., “Effect of Multi-Dimensional Flamelets in Composite Propellant Combustion,” Journal of Propulsion and Power, Vol. 10, No. 6, 1994, pp. 761 – 768

13Prasad, K. and Price, E. W., “A Numerical Study of the Leading Edge of Laminar Diffusion Flames,” Combustion and Flame, Vol. 90, 1992, pp. 155-173.

14Buckmaster, J., Jackson, T. L., and Yao, J., “An Elementary Discussion of Propellant Flame Geometry,” Combustion and Flame, Vol. 117, No. 3, 1999, pp. 54

15Chakravarthy . S. R., Price . E. W., Sigman, R. K., and Seitzman. J. M., “Plateau Burning Behavior of Ammonium Perchlorate Sandwiches and Propellants at E

16Brewster. M. Q., et al., “Flame and Surface Structure of Laminate Propellants with Coarse and Fine Amm

17Chen, M., Buckmaster, J. D., Jackson, T. L., and Massa, L., “Homogenization Issues in the Combustion of Heterogeneous Solid Propellants,” Proceedings of the Combustion Institute, Vol. 29, 2002.


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