. 

ARMY RESEARCH ~BORATORY 

On Propellant Surface Temperatures 

Derived From Calorimetry 

John A. Vanderhoff and Michael McQuaid 

ARL-TR-2434 March 2001 

Approved for public release; distribution is unlimited. 

20010403 087 
-_ 

. 

The findings in this report are not to be construed as an official 

Department of the Army position unless so designated by other 

authorized documents. 

Citation of manufacturer’s or trade names does not constitute an 

official endorsement or approval of the use thereof. 

Destioy this report when it is no longer needed. Do not return 

it to the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5067 

ARL-TR-2434 March 2001 

On Propellant Surface Temperatures 

Derived From Calorimetry 

John A. Vanderhoff and Michael McQuaid 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
Abstract 

Propellant surface temperatures for double base (JA2) and nitramine (XM39) propellant 

samples burning at pressures from 0.8 to 4 MPa have been measured using two different 

calorimetric techniques. The methods differ in the way combustion is extinguished; one involves 

depressurization, and the other involves burning into an inert base. For the experiments based on 

depressurization, a main source of uncertainty was in determining the area of the combusting 

surface. Moreover, this technique was prone to a large number of unproductive runs. Most of the 

data presented here was obtained from experiments in which combustion was extinguished by 

burning into a PolyEtherEtherKetone (PEEK) base. This robust material has thermophysical 

properties similar to the propellants studied. At higher pressures (and mass regression rates), 

radiative heating made nonnegligible contributions to total heat input to the inert base. Thus, a 

multivariate least squares model was developed to describe a time-dependent radiative and 

conductive heat input, and it was used to tit the experimental temperature histories. Propellant 

surface temperatures, radiative fluxes, and optical absorption coefficients are obtained from the 

tit to the data. For the regions of low mass regression rates (< 0.7 g/cm2-s), the propellant 

surface temperatures were in agreement with published values. At larger mass regression rates, 

the propellant surface temperatures were larger than published values. This was believed to be a 

consequence of the way contributions from radiative heating were treated. 

ii 
Acknowledgments 

The authors thank Peter Dehmer for hot pressing the PEEK material to create the 

inert base and Jeffrey Morris for measuring the FTIR optical absorption spectra 

from which the absorption coefficient for PEEK was determined. 

. . . 

ill 
. 

iv 
Contents 

Acknowledgments 

. . . 111 

List of Figures vii 

List of Tables ix 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

Introduction 1 

Analysis 2 

2.1 No Radiation, Time-Independent . . . . . . . . . . . . . . . . . . . . ..-......................................... 2 

2.2 No Radiation, Time-Dependent . . . . . . . . . . . . . . . . . . . . . . . . ..-........................................ 3 

2.3 Radiation, Time-Dependent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

Experimental 5 

3.1 Combustion Extinguishment by Depressurization . . . . . . . .._......................... 5 

3.2 Combustion Extinguishment by Inert Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

Results 9 

4.1 Surface Temperature From the Extinguishment by 

Depressurization Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

4.2 Surface Temperature From the Extinguishment by Inert Base 

Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

Discussion 21 

Conclusions 23 

References 25 

v 
Appendix A. Conductive and Radiative Contributions to the Thermal 

Combustion Wave 

Appendix B. Some Properties of Unfilled PolyEtherEtherKetone 29 

Distribution List 

Report Documentation Page 

27 

31 

33 

vi 
List of Figures 

Figure 1. Sketch of the mobile combustion diagnostic facility (MCDF) 

apparatus configured for propellant surface temperature 

measurements after extinguishment by depressurization. ._................................ 6 

Figure 2. Typical pressure history of the MCDF experiment recorded with a 

Kistler gauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..-............................................................................... 6 

Figure 3. (a) Sketch of windowed strand burner apparatus configured for 

propellant surface temperature measurements after extinguishment 

by an inert base, (b) diagram of the propellant sample, PEEK base and 

delrin stand, and (c) diagram of improved base arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

Figure 4. Temperature histories of XM39 and JA2 after extinguishment 

by depressurization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

Figure 5. Propellant surface temperatures for XM39 as a function of mass 

regression rate. The open squares are results from depressurization 

extinguishment. The open circles are results from inert base 

extinguishment. The black circle is inert extinguishment with the 

improved base. For reference, the solid line represents the surface 

temperature for pure RDX reported by Zenin [l]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

Figure 6. Propellant surface temperatures for JA2 as a function of mass 

regression rate. The open squares, open circles, and black circles have 

the same meaning as in Figure 5. The black triangle represents results 

with the improved base and Al foil barrier. The open triangle 

represents results with a JA2 base and a Mylar barrier. Upper and 

lower limits for double-base propellant surface temperatures reported 

by Zenin [1] are represented by dashed lines. . . . . . . . . . . . . . . . . . . . ..-............................... 12 

Figure 7. Temperature histories of the PEEK base (old) for JA2 burning in 

environments of 1 and 2 MPa nitrogen. . . . . . . . . . . . . .._............................................... 14 

Figure 8. Temperature history of the PEEK base (old) for XM39 burning 

in 2 MPa nitrogen . . . . . . . . . . . . . . . . .._.................................................................................. 14 

Figure 9. Temperature history data and fit for JA2 at 2 MPa.; old base 

configuration . . . . . . . . . . . . . . . . . . . . . . . . . . ..-.....................................................................-......... 17 

Figure 10. Temperature history data and fit for JA2 at 2 MPa; new base 

configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..-.............................................. 17 

Figure 11. Temperature history data and fit for JA2 at 4 MPa; new base 

configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

Figure 12. Temperature history data and fit for JA2 at 4 MPa; new base 

configuration with aluminum foil separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

Vii 
Figure 13. Temperature history data and fit for XM39 at 2 MPa; old base 

configuration. . . . . . . . . . . . . . . . . .._........................................................................................ 19 

Figure 14. Temperature history data and fit for XM39 at 4 MPa; old base 

configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

Figure 15. Temperature history data and fit for XM39 at 4 MPa; new base 

configuration. . . . . . . . . . . . . . . . . . .._....................................................................................... 20 

Figure 16. Temperature history data and fit for JA2 at 4 MPa; new base 

configuration, aged condition. . . . . . . . . . . . . . . . . . . . . . f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

Figure 17. Temperature history data and fit for JA2 at 2 MPa.; old base 

configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 

Figure A-l. Temperature vs. distance into the PEEK base for JA2 burning 

in an environment of 2 MPa nitrogen.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

Figure B-l. A semilog plot of optical transmittance vs. PEEK material 

thickness for three wavelengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 

. . . 

Vlll 
List of Tables 

Table 1. Physical properties of studied propellants and the inert base.. .............. .11 

Table 2. Best fits for surface temperature and optical absorption 

coefficients for XM39 and JA2 ................................................................................ 15 

Table B-l. Optical Properties of unfilled PEEK, JA2, and XM39. .......................... .30 

ix 
. 

X 
1. Introduction 

. 

A wealth of information about the combustion characteristics of a propellant can 

be derived from accurately deter mining the spatial temperature profile for a 

steady-state burning process [l-3]. A key boundary condition in this profile is the 

temperature of the combusting surface. This boundary condition,-when given as 

a function of the mass regression rate, can be used to characterize condensed 

phase kinetics [l]. Over time, microthermocouples have emerged as the standard 

technique for dete rmining temperature profiles [l-4]. However, because the 

temperature gradients are large, the accuracy of obtaining the surface temperature 

with this technique can be dominated by uncertainties in surface position. 

Despite the current preeminence of the microthermocouple technique, one of the 

earliest measurements of propellant surface temperature was made by Aristova 

and Leipunskiy [5], who used a calorimeter to measure the heat content of an 

extinguished propellant sample. Based on this technique, these researchers 

obtained surface temperatures of 525 K and 603 K, respectively, for pyroxylin 

(double-base propellant) and nitroglycerin powders burning at 1 atm. 

Uncertainties were reported to be * 45K. For the pyroxylin case, the experiment 

consisted of dropping the combusting pyroxylin through a CO:! cloud 

(extinguishing the combustion in a l-atm environment) and into a small, liquidfilled dewar calorimeter. The temperature rise of the liquid in the calorimeter was 

one of the central measurements of the experiment. 

After reading about this work, several ideas surfaced about how to modify the 

experiment to measure the propellant surface temperature at elevated pressures. 

The motivation for proceeding with a calorimetric technique was to remove 

ambiguities of surface-microthermocouple distance and to relax the fast response 

time requirements and deconvolution associated with directly measuring steep 

thermal gradients. 

Proper extinguishment and thermal isolation are key factors in developing a 

calorimetric technique. The first series of experiments conducted in this effort 

involved employing depressurization to extinguish combustion. When this 

technique proved untenable, a second series of experiments based on burning 

samples down to a noncombustible base material was investigated. The reader 

who is only interested in an experimental technique of greater fidelity than 

microthermocouples will not find it in this report. However, the interplay 

between conduction and radiation is prominent in this work, and rough estimates 

of parameters such as burn rate, surface temperature, and optical absorption can 

be determined from the techniques and analyses described. 
2. Analysis 

2.1 No Radiation, Time-Independent 

Assuming constant coefficients and no source terms, the time-independent heat 

balance in any slice of the thermal wave associated with a steady-state burning 

process has the form 

k -- a*wG 

ax* file Wx) = 0 pax ’ (1) 

where T is the temperature, x is the direction which thq propellant regresses at a 

constant burning rate, k is the thermal conductivity, M is the mass regression 

rate, and c, is the specific heat at constant pressure. The first term represents the 

rate of change in heat content in the slice due to conduction; the second term is the 

rate of change of heat content due to mass flow. For the condensed phase, this 

equation can be integrated to obtain 

kc 

T(x) - TO = (T, - T,)exp(kx) , (2) 

where T, is the initial temperature of the propellant and T, is the surface 

temperature. Assuming that this is the temperature distribution in the propellant, 

then the total heat per unit area in the condensed phase is given by 

Q = )(T(x) - T,)pc,d~ = (T, - T,)pc, &p(+x)dx , (3) 

-m -ml 

where p is the propellant density. Performing the integration and rearranging 

yields 

(4) 

To recast the expression in terms of experimentally measured variables, the 

quantity of stored heat remaining in the quenched propellant specimen is 

rewritten as 

Q=(T,-To)?. 

S 

where TF is the final, equilibrated, adiabatic temperature of the sample, m is the 

mass of the unburned propellant, and As is the area of the propellant surface that 

2 
. 

underwent combustion. Substituting equation 5 into equation 4 and rearranging 

yields 

T, =To +(TF -To)z. (6) 

S 

If the therrnophysical properties and the burn rate (k = pr ) of the propellant are 

known, a measurement of TF from the calorimeter and As from the burnt surface 

will provide sufficient information to calculate Ts. Equation 6 is used to extract 

surface temperature results from experiments in which depressurization was the 

method of combustion extinguishment. 

2.2 No Radiation, Time-Dependent 

In another set of experiments, burning the propellant sample down to a 

noncombustible base was the method of combustion extinguishment. In these 

cases, the time-dependent temperature profile for a point in the base was desired. 

The one-dimensional heat transfer equation with steady-state conditions, constant 

coefficients, and no source term (as given in equation 1) yields the temperature 

distribution in the base f(x) = T, + (T, - T,) exp(y)x at t = 0. Assuming that 

the base of length L is perfectly insulated ( g(O,t) = E(L,t) = 0), the time 

evolution of the profile following extinguishment can be calculated via an 

analytical solution given in many differential equation texts [6] 

T(x,t) = A, + TA, cosy exp(- ;*;2k)t, 

II=1 P 

where A, =iif(x)dx, A, =$lf(x)cosydx,and n=1,2,... 

2.3 Radiatio:, Time-Dependkt 

During the course of experimental work, it was soon apparent that radiation was 

contributing to the measured temperature profiles. Thus, a radiative source term 

was added, viz. 

k 3*T --$c, z=-d, aexp(ax), 

ax* 

where an optical absorption coefficient a (cm-r) has been introduced and G, is a 

radiant heat flux. This heat source term is exponentially attenuated as a function 

of x. The solution for equation 8 is of the same form as equation 2, but is now the 

sum of two exponentials. It is written as 

3 
T(x)-TO =(T, -TO - pcpf~aD)bM;)+ pcp~~aD)exPw~ (9) 

k where D =- is the diffusivity of the propellant. Equation 9 is still of the 

PC, 

form f (x) , and may thus be used in equation 7 to obtain temperature histories for 

the case where there is a radiant heat source. This was facilitated by employing 

equation 7 as a governing equation in a multivariate least squares fitting routine 

to determine parameter values that yield the “best fit” to experimental data. For 

the particular case at hand, the fit is to the temperature at one position (the bottom 

center of an inert PEEK base) as a function of time. At flame extinguishment, the 

radiant heat source is switched off. This time can be obtained from the video 

record, and it manifests itself as a knee in the temperature-time history. 

Measured values are available for most of the parameters in equation 9, and are 

given later in Table 1. The condition, r = aD did not arise in this study with r 

being always greater than crD. However, as shown in Appendix A, even with 

r = aD, there is a real, positive contribution from radiation. The radiative and 

conductive contributions (equation 9) that give rise to the increase in PEEK base 

temperature are also plotted as a function of distance in Appendix A. 

There are several difficulties in quantifying the radiation flux, and 

approximations are made. First, the radiation flux and optical absorption 

coefficient can be wavelength dependent, but this functional dependence will not 

be considered here. Probably of more significance is the position or positions of 

the radiant heat source. There are several forms for the flame structure of solid 

propellants. At the lowest pressures that a propellant can bum, it may do so 

without establishing a visible flame. As the pressure is increased, a visible flame 

appears at a distance from the propellant surface. As the pressure increases more, 

the visible flame approaches the combusting propellant surface. Different 

propellants have different rates at which they approach the combusting surface as 

a function of pressure, as well as different final flame temperatures. These 

radiation flux phenomena are approximated here by a surface-positioned radiant 

heat source attenuated according to Beer’s Law. Two adjustable parameters are 

employed to fit the data-the radiation flux, & , and an .optical absorption 

coefficient, cx. From equation 9, increasing values of the bum rate (r) cause the 

first term on the right to decrease exponentially (x is negative). Since r and 

& increase with pressure, this technique will be in trouble with increasing 

pressure, unless the radiation contribution can be well approximated. 

4 
3. Experimental 

3.1 Combustion Extinguishment by Depressurization 

An existing apparatus, the mobile combustion diagnostic fixture (MCDF) [7J, was 

used to conduct propellant surface temperature experiments where combustion 

was extinguished by depressurization. A sketch of the pertinent details of MCDF 

is shown in Figure 1. The small chamber volume is 100 cc, and the large chamber 

is 35,000 cc. The small chamber contains the cylindrical propellant sample, which 

is held in place by nylon screws. The sample is ignited when electric current is 

applied to a wire slightly buried at the top center of the sample. A temperature 

history is recorded by an Omega-manufactured, 0.075~mm wire Chromel-Alumel 

thermocouple. The thermocouple is placed at the bottom center of the propellant 

sample and a thin (- 1 mm) propellant disk is solvent-welded to the bottom of the 

propellant sample to shield it from the influence of circulating gases. 

A description of the experiment is given by relating the sequence of events 

necessary to perform an experimental run. A burst disk (for construction details, 

see [7J) is installed between the small and large chambers. The propellant sample 

is also installed and electrically connected to the ignition power supply and 

thermocouple readout. The large chamber is evacuated with a mechanical 

roughing pump and then valved off. Just prior to the igniting propellant, the 

small chamber is prepressurized to a value > 0.3 MPa. This pressurization insures 

reliable ignition and provides a baseline pressure so that the additional pressure 

provided by the propellant combustion gases will break the burst disk prior to 

completely consuming the propellant sample. The prepressurization line is 

valved off, and the ignition circuit is activated. Energizing the ignition circuit 

provides a trigger input for the dual time base Nicolet digital oscilloscope. The 

scope records the pressure history from a Kistler gauge and a temperature history 

from the thermocouple. 

A typical pressure history is shown in Figure 2. Here, the small chamber was 

prepressurized to 0.3 MPa, and propellant combustion increases the pressure to 

about 2.8 MPa, at which time the burst disk functions. The gases in the small 

chamber rapidly vent into the large chamber. The final system pressure is close to 

vacuum conditions, a factor of two pressure drop occurs in a time frame of less 

than 0.4 ms (the time between data points is 0.2 ms). This depressurization 

extinguishes combustion, and the thermocouple provides a measure of the heat 

content of the remaining propellant sample. A representative example will be 

discussed in Section 4. To obtain the necessary parameters to solve equation 6 for 

the surface temperature, the extinguished propellant sample is weighed, and 

5 
-----.---- __.. “. __ __ ---.-- -- 

; 

I 

1 Y 

r 

4 

Burst Disk .L. 

1 Readout 1 

Figure 1. Sketch of the mobile combustion diagnostic facility (MCDF) apparatus 

configured for propellant surface temperature measurements 

extinguishment by depressurization. 

after 

2.6 

1.8 

0.6 

300 400 500 600 

Time (ms) 

Figure 2. Typical pressure history of the MCDF experiment recorded with a 

Kistler gauge. 

6 
the surface area that has undergone combustion is measured. These values, 

together with the propellant bum rate (at the burst pressure value), specific heat, 

thermophysical properties, ambient temperature, and Tr (assumed to be the 

maximum temperature obtained from thermocouple history) were employed in 

equation 6 to determine the propellant surface temperature. 

3.2 Combustion Extinguishment by Inert Base 

The other set of experiments to measure propellant surface temperature were 

performed in a windowed strand burner. Briefly, this strand burner has four 

opposed windows through which cornbusting propellant samples can be 

illuminated, and the dynamic burning process is recorded with a video camera. 

The apparatus was originally developed to obtain propellant bum rate as a 

function of pressure for pressures up to 10 MPa. A simple sketch of the major 

functions of the apparatus is shown in Figure 3(a). A new feature of this 

experiment is the thermocouple added to record the temperature history of the 

inert base. Details of the first propellant sample and inert base configuration 

employed in the experiment are given in Figure 3(b). The inert base is made from 

PolyEtherEtherKetone (PEEK). This material was chosen for its ability to 

continuously withstand temperatures of 250 “C (and higher temperatures for a 

short time) and for its thermophysical properties similar to those of the solid 

propellants under study. Optical properties of this material are described in 

Appendix B. The base is a disk with the same diameter as that of the propellant 

sample (0.635 cm) and a nominal thickness of 0.3 cm. A 75-p wire 

Chromel-Alumel thermocouple is glued to the center of the base’s bottom face, 

and the propellant sample is solvent-welded to the top face with acetone. Times 

on the order of 48 hr were given for the acetone to diffuse and evaporate away 

before an experimental run. 

The PEEK base is mounted on a Delrin stand in a way that minimizes thermal 

conduction. The top of the Delrin stand was machined such that three 

equally-spaced edge points would make contact. The bottom of the PEEK disk 

was edge glued to these Delrin contact points. A series of experiments were run 

with this configuration, but after looking at the data in detail, the effects of 

radiation and possibly convection were noticeable. A configuration directed at 

minimizing these unwanted contributions was employed. In this configuration, 

Figure 3(c), the Delrin stand was modified. No longer were the three points used 

to support the PEEK base. Instead, the top of the Delrin solid cylinder was drilled 

out so that a thin lip of about 0.025 cm remained, and the PEEK base was edge 

glued to this Delrin lip. This seal eliminated radiative contributions by reflection 

and convection currents around the thermocouple region. The thermocouple lead 

wires were covered with insulation tubing and routed down the inside of the 

Delrin stand. Just prior to the bottom, the leads exited a small hole that was 

subsequently sealed with glue. The propellant sample was hot-wire ignited by 

impressing a small Chrome1 wire into the center of its upper surface. 
0 a 

(b) “old”’ 

~ 

rFigure 3. 

0 c “new” 

. FIamc - 

A Propellant - 

- PEEK ’ 

-y TC lcads. insulated 

(a) Sketch of windowed strand burner apparatus configured for propellant 

surface temperature measurements after extinguishment by an inert base, (b) 

diagram of the propellant sample, PEEK base and delrin stand, and (c) 

diagram of improved base arrangement. 

8 
The sequence of events occurring in an experimental run with this apparatus is as 

follows. A prepared propellant sample is placed in the windowed chamber and / 

electrically connected to the ignition power supply and thermocouple recording 

circuitry. Next, the chamber is closed and pressurized with nitrogen. The video 

camera is placed in the recording mode, and the Nicolet digital scope employed 

for recording the thermocouple output is triggered. Several seconds after 

triggering the scope, the ignition wire current supply is turned on. Combustion 

commences, and the regression of the combusting surface is recorded by video. 

The temperature history of the PEEK base is also recorded. Video records give 

bum rate, and the thermocouple histories provide data for heat content 

determinations. 

4. Results 

4.1 Surface Temperature From the Extinguishment by Depressurization 

Technique 

To minimize the number of nonproductive runs when using the depressurization 

technique, proper initial conditions are necessary. Maximum pressure is 

controlled to within about HO% by a burst disk. This pressure is provided by two 

sources-prepressurization with nitrogen gas and pressurization from the 

combustion gas. Establishing of a planar propellant bum is desired before burst 

disk functioning, but the disk should function prior to the thermal combustion 

wave reaching the embedded thermocouple. By knowing the free volume of the 

small chamber and propellant ingredient information, the maximum pressure can 

be calculated for a given mass of propellant using the NASA-Lewis code. This 

thermochemical equilibrium calculation [8] assumes adiabatic conditions, a poor 

assumption for this experiment where the combustion gas pressurization is 

relatively slow. In fact, for the experimental geometry and initial conditions used, 

the maximum pressure is about a factor of two lower than that predicted by the 

code. Nonetheless, the code provides a useful estimate of maximum pressure for 

choosing the amount of energetic material. Once a proper mass of propellant is 

selected, care must be taken in properly positioning and mounting the propellant 

sample because robust gas flow occurs after the disk bursts. Thus, designs that 

have minimum gas volume behind the propellant sample are necessary. Also, 

mounts must be made with low thermal conductivity materials, and mounting 

contact with the sample must be minimal to prevent substantial heat loss. On 

several occasions, with 0.5-m diameter propellant samples, the gas exit flow was 

sufficient to launch the sample from the mount, stopping only when the 

thermocouple leads became taut. 

9 
Representative temperature histories for experiments with XM39 and JA2 

propellant samples are shown in Figure 4. For XM39, the burst disk functioned 

8 s after the ignition current was applied. The maximum pressure reached was 

2.4 MPa, and the temperature of the sample increased from 296.6 to 300.3 K. For 

JA2, the burst disk functioned 2 s after the ignition current was applied. The 

maximum pressure reached was 2.6 MPa, and the sample temperature increased 

from 296.7 to 299.3 K. Postmortem analyses of the samples determined remaining 

mass and combustion surface area. These values, together with thermophysical 

property parameters given in Table 1, are sufficient to calculate propellant surface 

temperatures from equation 6. Propellant surface temperature values obtained 

via this experiment are plotted as a function of the propellant mass regression rate 

in Figures 5 and 6. 

301 

300 

5 299 

5 

G 

Q 298 

E 

c 

297 

296 

: 

XM39 

0 20 40 60 80 100 120 140 

Time (set) 

Figure 4. Temperature histories of XM39 and JA2 after extinguishment by 

depressurization. 

10 
Table 1. Physical properties of studied propellants and the inert base. 

‘ 

Parameter Magnitude 

JA2a ] XM39b ] PEEK 

Units Reference 

4 

Length (1) - 0.3 cm 

Thermal conductivity (k) 0.000694 0.000587 0.00060 Cal/cm-s-K [9,W 

Specific heat (CP) 0.321 0.269 0.38 c/g-K [9,101 

Density (p) 1.57 1.64 1.286~ g/cm3 [lo-121 

Thermal diffusivity (D) 0.00138 0.00133 0.00123 cm2/s k/w 

Pressure (P) I- - - 1 MPa 1 

I I I 

Bum rate (r) 1 0.274P.83 0.05P.98 - cm/s I [13,141 1 

a Ingredients for JA2 are 58.2% nitrocellulose (13.04% N), 25.2% diethyleneglycoldinitrate, 15.8% 

nitroglycerin, and 0.05% AKARDIT II. 

b XM39 ingredients in weight percent are 76% RDX, 12% cellulose acetate butyrate, 7.6% acetyl 

triethyl citrate, 4% nitrocellulose (12.6% N) and 0.4% ethyl Centralite. 

c Measurement of weight and volume of PEEK sample. 

0 

0 

RDX-Zenin 

0 

L 0.1 0.2 0.3 0.4 0.5 

Mass Regression Rate (g/m*-see) 

Figure 5. Propellant surface temperatures for XM39 as a function of mass regression rate. 

The open squares are results from depressurization extinguishment. The open 

circles are results from inert base extinguishment. The black circle is inert 

extinguishment with the improved base. For reference, the solid line represents 

the surface temperature for pure RDX reported by Zenin [l]. 
0.2 0.4 0.6 0.8 1.0 1.2 1.4 

Mass Regression Rate (g/cm*-set) 

Figure 6. Propellant surface temperatures for JA2 as a function of mass regression rate. 

The open squares, open circles, and black circles have the same meaning as in 

Figure 5. The black triangle represents results with the improved base and Al 

foil barrier. The open triangle represents results with a JA2 base and a Mylar 

barrier. Upper and lower limits for double-base propellant surface 

temperatures reported by Zenin [l] are represented by dashed lines. 

In all depressurization cases, the propellant surface was not planar at burn 

extinguishment. In the best cases, a hemispherical combustion surface was 

established. Thus, significant uncertainties in the surface area were present for 

many of the experimental runs. Another concern in reducing the data was the 

dynamics of depressurization. While depressurization was fast, whether it was 

fast enough that the influence on combustion kinetics was minimal prior to 

extinguishment is unknown. For these reasons, as well as the frequent occurrence 

of nonproductive runs, combustion extinguishment by burning into an inert base 

was pursued. 

4.2 Surface Temperature From the Extinguishment by Inert Base 

Technique 

The idea of combustion extinguishment by burning into an inert base had been 

thought about at the beginning of this work; however, it was assumed that heat 

transfer to the base via the pressurizing and combustion gases would be a large 

influence that could not be well quantified. Early results with the MCDF 

experiment demonstrated that heat loss from a propellant sampie as a function of 

chamber pressure was not as large as assumed. With this knowledge, and the 

advantage of being able to simultaneously measure the bum rate with this 

technique, a series of inert base extinguishment experiments were conducted. 

12 
Two temperature histories of the PEEK base observed in experiments where JA2 

was burned at 1 MPa and 2 MPa are shown in Figure 7. Arrows marking 

temperature breaks in the 2 MPa data are also included in this figure. The 

temperature break at 9 s marks the ignition (flame establishment) of the 

propellant sample, and the temperature break at about 13 s marks flame 

extinguishment at the inert base. What was not expected was the temperature 

rise in the inert base before flame extinguishment. Nonetheless, the data shows 

that the thermocouple temperature starts to increase as soon as the propellant 

flame is established and “hesitates” at flame extinguishment. Moreover, identical 

effects are also seen for the 1 MPa case at about 10 and 17 s, but the breaks are not 

as pronounced. 

These observations are consistent with radiation, providing nonnegligible heating 

to the inert base and thermocouple. A further demonstration of this type of 

heating is shown in Figure 8, which is obtained from an experiment with XM39 

burned at 2 MPa. Again, the thermocouple temperature starts to increase at 

around 9 s (flame establishment) and takes off at 29 s. Here it is not obvious 

where flame extinguishment takes place, but it is slightly earlier than 29 s. A 

closer comparison of the 2 MPa results shown in Figures 7 and 8 reveals that the 

early temperature rise is faster for JA2. This is because the JA2 flame is hotter and 

therefore brighter. For the 2 MPa case, the calculated adiabatic flame temperature 

for JA2 is 2800 K, whereas for XM39 it is 2355 K [8]. Another observation, 

consistent with radiative heating, is that when the length of the propellant sample 

is divided by the amount of time taken for the early temperature rise, a burn rate 

consistent with the video record rate is obtained. Realizing that radiation could 

be a substantial fraction of the total heat input into the PEEK base, it became clear 

that its contribution had to be included. 

The simplest way to account for a radiative contribution is to use the flame 

extinguishment temperature value for T,. This is a lower limit since the 

thermocouple indicates temperatures at the bottom of the PEEK base (see the 

radiation contribution plot in Appendix A). In an attempt to obtain a better 

account of the radiative contribution, a source term was included in the 

one-dimensional heat conduction equation, allowing a time-dependent solution 

for the temperature at any centerline depth in the PEEK base to-be obtained. A 

multivariate least squares fitting program is used to find the best set of solution 

parameters for equation 7, including the propellant surface temperature. 

The remainder of the temperature history data will also include a fit to the data 

with a reported best value for surface temperature. Initially, three experiments 

were conducted with JA2 at 1 MPa pressure (mass regression rate of .43 g/cm%). 

These data are shown as open circles on Figure 6, and the parameters obtained for 

all fits are given in Table 2. Only the optical absorption coefficient and density 

were actually measured for the in-house, hot-pressed PEEK base 

13 
4‘ 

z 3oo ,f 299 

F 

g 298 

294t..““““‘.“‘...““““““.“““.“.“. 

5 10 15 20 25 30 35 40 45 

Time (set) 

Figure 7. Temperature histories of the PEEK base (old) for JA2 burning in environments 

of 1 and 2 MPa nitrogen. 

311 

309 

g 307 

g 305 0” 

5 0” 

tij 303 

i 301 0 

I- 299 

297 

295 J 

5 IO 15 20 25 30 35 40 45 50 

Time (set) 

Figure 8. Temperature history of the PEEK base (old) for XM39 burning in 2 MPa 

nitrogen. 

14 
Table 2. Best fits for surface temperature and optical absorption coefficients for XM39 

and JA2. 

15 
used; the other two parameters used to calculate the diffusivity, cP and k, are 

nominal literature values. Initially, the diffusivity value of 0.00123 cm*/s was 

used for PEEK, but this led to very poor fits to the data. By allowing the 

diffusivity to vary, a value of 0.00206 cm*/s was obtained as a best overall fit to 

the data and thus was used for obtaining the values given in Table 2. Data from 

Figure 7, JA2 at 2 MPa, are repeated on Figure 9, and the fit to the data is shown 

as a solid line. Here, and in all other fits, the time history over which the data is 

fit has been shortened to minimize temperature-gradient-driven heat loss effects. 

The parameters can be adjusted so that equation 7 represents the data well, 

including reproducing the observed knee at flame extinguishment. Moreover, 

there is a significant temperature rise prior to extinguishment at the inert base. 

Since this temperature rise begins with flame establishment, it is apparent that 

radiation is affecting the thermocouple, possibly directly impinging on the 

thermocouple via multiple reflections. 

To minimize this effect, modifications to the inert base and thermocouple wire 

routing were made, and these modifications are described in the experimental 

section. Data taken before the modification of the base are referred to as “old” 

and data taken after base modification are termed “new” in Table 2. Figure 10 

represents the temperature history of JA2, again at 2 MPa nitrogen pressure, 

obtained using the new base configuration. Here, the temperature rise before 

flame extinguishment is about a factor of three less than that depicted in 

Figure 9. Hence, radiation shielding is definitely improved. On the other hand, 

a best fit for surface temperature is 837 K, about 200” higher than the value found 

using the old base configuration. This value is much higher than literature 

values [l] for the surface temperature of this class of propellants. 

A variety of experiments were conducted at 4 MPa, two experiments using the 

old base configuration and three experiments with the new base configuration. 

Flame extinguishment is represented by a more pronounced knee at 4 MPa, and 

in Figure 11 it looks more like a cusp. The best fit to surface temperature results 

in a very high value, 1,112 K. In an attempt to explore the radiative contribution, 

a 25.4 l.~ thick piece of aluminum foil was placed between the PEEK base and the 

JA2 propellant sample. The temperature history for this configuration is shown 

in Figure 12. The radiation component was reduced by about a- factor of two, 

and the cusp was removed. A best fit for surface temperature is about 200 K less, 

but still higher than literature values. It is conjectured that m-depth absorption 

leads to propellant heating, which is being conducted through the Al foil barrier. 

As discussed earlier, XM39 has a lower flame temperature than JA2, and the 

radiation contributions are expected to be less. This supposition is supported by 

the temperature histories shown on Figures 13-15. Figure ‘13 represents a 

temperature history for burning at 2 MPa, where the best fit for surface 

temperature is 559 K. Figures 15 and 16 show temperature histories for burning 

16 
302 

- s- 300 

i?? 3 5 iii 296 

P 8) 296 

294 

5 10 15 20 

Time (set) 

Figure 9. Temperature history data and fit for JA2 at 2 MPa.; old base configuration. 

Time (set) 

17 

Figure 10. Temperature history data and fit for JA2 at 2 MPa; new base 

configuration. 
296 ' I I 

5 10 

Figure 11. 

296 

Time (set) 

Temperature history data and fit for JA2 at 4 MPa; new base 

configuration. 

5 10 15 

Time (set) . 

Figure 12. Temperature history data and fit for JA2 at 4 MPa; new base configuration 

with aluminum foil separation. 

18 
306 

302 

298 

296 

20 25 

Time (set) 

Figure 13. Temperature history data and fit for XM39 at 2 MPa; old base configuration. 

Q 302 

- 

10 15 20 25 

Time (set) 

Figure 14. Temperature history data and fit for XM39 at 4 MPa; old base configuration. 

19 
296 I I I 

IO 15 

Time (set) 

20 

Figure 15. Temperature history data and fit for XM39 at 4 MPa; new base 

configuration. 

sz 

298 

22 

2 296 

Et 

292 

I 

10 

Time (set) . 

Figure 16. Temperature history data and fit for JA2 at 4 MPa; new base configuration, 

aged condition. 

20 
at 4 MPa, where old and new base configurations were used, respectively. The 

temperature histories up until flame extinguishment were almost identical in 

both cases, but the surface temperature determined from the new base 

configuration is about 100 K lower. The surface temperature with the new base 

is consistent with literature values for similar propellants. The implication of 

these results will be discussed in the next section. 

A potential problem with the sample PEEK interface was uncovered by accident. 

Several JA2 propellant samples were not run until several months after ‘they 

were prepared. A temperature history for one of these runs is displayed in 

Figure 16. A best fit for surface temperature results in the extraordinarily high 

value of 1,684 K; Furthermore, exa minktg the top surface of the PEEK inert base 

showed a definite discoloration and a slight charring not seen previously. This 

burning presumably arises from propellant diffusion into the PEEK. 

I . 

5. Discussion 

Examining Figures 5 and 6, where the present results are compared to literature 

values of Zenin [l], reveals significant scatter and deviation. The 

depressurization method, abandoned for a presumably better inert base 

extinguishment method, displays better agreement with literature values. The 

scatter is distributed, more or less, uniformly about the limit lines (Figure 6). On 

the other hand, data obtained by inert base extinguishment, in addition to having 

scatter, gives larger Ts values for mass regression rates above about 0.7 g/cm%. 

Part of the scatter can be due to a change in the base geometry. But for both 

cases, large Ts values were determined at the higher mass regression rates, where 

the radiation source is closer to the surface of the propellant. 

Perhaps more problematic is that the propellants and PEEK have different 

optical absorption. Efforts were made to select an inert material with 

thermophysical properties similar to the propellants under study. This was done 

so that the conduction-driven thermal profile would be unperturbed, but 

differences in optical properties were initially considered much less important. 

During the course of this research, the optical absorption of PEEK was briefly 

investigated, and the details are given in Appendix B. The optical absorption of 

PEEK was substantially larger than that of JA2 or XM39. Thus, radiation can be 

partly absorbed by the propellant, and the remainder passing through the 

unburned propellant is absorbed in the PEEK base. With these considerations, it 

is not surprising that the simple radiation source term employed is inadequate to 

quantitatively account for the radiation contribution as a function of mass 

regression rate. Moreover, as the mass regression rate increases, both the 

21 
conductive and radiation contributions decrease, leading to a smaller 

experimental temperature signal. 

Concern about optical property differences between the propellant and the PEEK 

base led to another experiment where the base material was the propellant. The 

problem here is stopping combustion. First, a 12.7-p disk of Mylar was used to 

separate the propellant cylinders, but it did not stop the combustion wave. A 

thicker (38-4 disk worked, and the temperature history data and fit are shown in 

Figure 17. The fit to the data provided support for the model. As opposed to 

fitting the experiments with a PEEK base, where the thermal diffusivity value 

had to be set higher than its nominal value, the Table 1 value for the thermal 

diffusivity of JA2 was required for a proper fit. Secondly, the obtained surface 

temperature of 621 K agrees with literature values. The fitted value for the 

optical absorption coefficient is one of the largest measured values, but it is about 

a factor of two lower than values reported by Cohen et al. [X5]. 

10 15 

Time (set) 

20 

Figure 17. Temperature history data and fit for JA2 at 2 ,MPa.; old base configuration. 

In this case, the base material was JA2, and combustion was stopped by a 

Mylar film. 

In addition to surface temperature values coming from the least squares fit of the 

temperature history, radiation fluxes and optical absorption coefficients are also 

obtained and are given in the fourth and fifth columns of Table 2. These data are 

somewhat scattered, but they indicate that the radiation flux is increasing with 

pressure, and the optical absorption coefficient of JA2 is larger than that of XM39. 

The larger optical absorption of JA2 is also suggested in Table B-2. In reality, the 

22 
optical absorption coefficients reported are for the combination of propellant and 

the PEEK base; the only exception is the experiment where JA2 was used as the 

base. For JA2, it also appears that the “new” base configuration has resulted in a 

lower radiation flux seen by the thermocouple. 

Part of these results include data that can be used simply and efficiently to obtain 

bum rate without needing a window. An estimate of the propellant bum rate can 

be determined by taking the time interval from where the thermocouple 

temperature starts to rise until the knee in the profile, and dividing into the 

propellant length. For example, take the 2 MPa JA2 case shown in Figure 7. The 

propellant length is 2 cm, and when divided by 4.5 s, it results in a value of 

0.44 cm/s. This value is close to the exponential form given in Table 1. The same 

result holds for the 2-cm-long XM39 sample of Figure 8. 

6. Conclusions 

The temperature of a propellant surface burning at atmospheric pressure can be 

obtained by a calorimetric technique [5]. Furthermore, the test of time has 

indicated that these measurements are reliable [l, 41. Present measurements are 

also reliable, although somewhat scattered, near the pressure deflagration limit 

where the propellant burns with a wispy extended flame or no flame at all. In 

this region, the burn rate is low, and the heat from conduction is much larger 

than the radiative heat. As the pressure increases, radiative heat flux increases, 

and the conductive heat contribution decreases, causing the radiative component 

to become important. While a radiative source term has been incorporated into 

the heat balance, it is inadequate to handle the many variables involved with the 

radiative contribution, and probably necessitates matching the optical properties 

of the burning sample and base. Revisiting Figure 6, where the pressure variable 

is contained within the mass regression rate, an upper limit of about 0.7 g/cm% 

is placed on the reliability of these techniques for obtaining the propellant 

surface temperature. 

23 
24 
I i 

7. References 

1. Zenin, A. A. “Thermophysics of Stable Combustion Waves of Solid 

PropeIIants.” Nonsteady Burning and Combustion Stability of Solid Propellants, 

edited by L. DeLuca, E. W. Price, and M. Summerfield, vol. 143, pp. 197-231, 

1992. 

2. Huggett, C. “Combustion of Solid Propellants.” Combustion Processes, edited 

by B. Lewis, R. N. Pease, and H. S. Taylor, vol. II, pp. 514-574,1956. 

3. Kubota, N. “Combustion Mechanisms of Nitramine Composite Propellants.” 

7he Eighteenth Symposium (Int.) on Combustion, The Combustion Institute, 

pp. 187-194,1981. 

4. KIein, R., M. Mentser, G. vonElbe, and B. Lewis. “Determination of the 

Thermal Structure of a Combustion Wave by Fine Wire Thermocouples.” 

J. Phys. Chem., vol. 54, pp. 877-884,195O. 

5. Aristova, Z. I., and 0. I. Leipunskiy. “Surface Heating of Burning Powder.” 

J. Phys. Chem., vol. 20, pp. 1391-1397,1946. 

6. Kreyszig, E. Advanced Engineering Mathematics, New York: John Wiley and 

Sons, 1962. 

7. Devynck, D. “Design of a Mobile Combustion Diagnostic Fixture.” 

BRL-MR-3412, U.S. Army Ballistic Research Laboratory, Aberdeen Proving 

Ground, MD, 1984. 

8. SvehIa, R. A., and B. J. McBride. “Fortran IV Computer Program for 

Calculation of Thermodynamic and Transport Properties of Complex 

Chemical Systems.” TND-7056, National Aeronautics and Space 

Administration, 1973. 

9. Miller, M. “Thermophysical Properties of Six Solid Gun Propellants.” 

ARL-TR-1322, U.S. Army Research Laboratory, Aberdeen Proving Ground, 

MD, 1997. 

10. Boedeker Plastics Incorporated. MateriaZs Guide, www.boedeker.com. 

11. Radford Arsenal Propellant Description Sheet. DA lot number 

RAD-PE-792-68,199O. 

12. Indian Head Arsenal Propellant Description Sheet. 

XM39-098%100,199O. 

Lot number 

13. Miller, M. Updated data, 1993. 

25 
14. Teague, M. W., G. Singh, and J. A. Vanderhoff. “Spectral Studies of Solid 

Propellant Combustion TV: Absorption and Burn Rate Results for M43, XM39, 

and Ml0 Propellants.” ARL-TR-180, U.S. Army Research Laboratory, 

Aberdeen Proving Ground, MD, 1993. 

15. Cohen, A., J. E. Newberry, R. Kranze, K. L. McNesby, and R. A. Beyer. 

“Derivation of Optical Parameters From Integrating Sphere Measurements 

for NC Propellants.” 34th JANNAF Combustion Subcommittee Joint 

Meeting, 27-31 October 1997. 

26 
l 

Appendix A. Conductive and Radiative Contributions to the 

Thermal Combustion Wave 

* 

This appendix is provided to give the reader a feel for the implications of the 

model employed to reduce the experimental data and the length scales 

associated with typical parameters used. The main equation is equation 9 in the 

main body of the report, which can be rewritten as 

T(x)-To = (Ts -T&x@)+ d, 

D pc,(r-aD) 

exp(ax) - exp(E) . 1 

Applying L’Hopital’s rule at r = aD , define f(a) = exp(ax) - exp(F) and 

f(a) 

g(a)=r-aD, where -= 

f’ (a = fD) 

g’(a = fD) 

in 

ida) 

the limit of cx+fD. 

Differentiation gives the result E exp(F), which is a real, positive contribution 

due to radiation. 

The spatial profile of the thermal combustion wave in the PEEK base, following 

the bum of a JA2 sample, is plotted in Figure A-l. Both the conductive and 

radiative contributions are displayed. PEEK base thermophysical values 

(Table l), as well as values appropriate for JA2 burning at 2 MPa (i.e., T, = 600 K, 

To = 300 K, and r = 0.49 cm/s are used in equation 9 in the main body of the 

report. The two radiation parameters, 6, and CI, are assigned the values 0.4 

cal/crr+s and 30 cm-*, respectively. To show the radiative contribution clearly, 

the temperature and distance values have been truncated. At x = 0, the value of 

the temperature would be 600 K, and the thickness of the PEEK base is 0.3 cm; 

however, at this instant in time, the profiles do not extend that far into the base. 

27 
I 

300 

-0.15 -0.10 -0.05 

Distance in PEEK Base (cm) 

Figure A-l. Temperature vs. distance into the PEEK base for JA2 burning in an 

environment of 2 MPa nitrogen. Two contributions are plotted: the 

dashed line represents the radiative contribution, and the dotted line is 

the conductive contribution. The solid line is the sum of these 

contributions. 

28 
Appendix B. Some Properties of Unfilled 

PolyEtherEtherKetone 

I - 

PolyEtherEtherKetone (PEEK) is a high-performance engineering thermoplastic 

that can be used continuously at 250 “C without permanent loss in physical 

properties. Some of the thermophysical properties used for calculations in the 

text are provided in Table 1 in the main body of the report. Values for the 

optical absorption coefficient for PEEK could not be found. Thus, they were 

measured using infrared absorption spectroscopy. A one-flux model equation of 

the form 

+-=(1-R)exp(-aL), 

0 

has been used to reduce the data, where + is the transmittance, R is the 

0 

reflectivity, and a is the absorptivity. Possible scattering effects are not included 

in this analysis. Figure B-l shows PEEK transmittance as a function of length 

(L) for three different wavelengths, and Table B-l gives values for the 

reflectivity and absorptivity obtained from a regression fit to the data. These 

PEEK values are for bulk absorption, as they are taken in spectral regions of no 

apparent specific molecular absorption. 

1 

0.01 

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 O.OE 

Distance (cm) 

Figure B-l. A semilog plot of optical transmittance vs. PEEK material thickness for three 

wavelengths. 

29 
Table B-l. Optical properties of unfilled PEEK, JA2, and XM39. 

PEEK 1.5 .51 48 

PEEK 2.0 .36 29 

L , 

JA2* 1.06 0.04 9 

JA2’ 1.71 0.03 13 

XM392 0.53 0.99 8 

h I I 

1 Cohen, A., J. E. Newberry, R. Kranze, K. L. McNesby, and R. A. Beyer. “Derivation 

of Optical Parameters From Integrating Sphere Measurements for NC Propellants.” 

34th JANNAF Combustion Subcommittee Joint Meeting, 27-31 October 1997. 

2 Stufflebeam, J. H. “Surface and Gas-Phase Diagnostics for Solid Propellant 

Combustion.” U.S. Army Research Office Progress Report, Contract: 

DAAI-W-94-C-0076,28 November 1997. (These values are for RDX. XM39 contains 

76% RDX by weight.) 

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1n Propellant Surface Temperatures Derived From Calorimetry 622618.HSO 

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fohn A. Vanderhoff and Michael McQuaid 

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13. ABSTRACT(Maximum 200 words) 

Propellant surface temperatures for double base (JA2) and n&amine (XM39) propellant samples burning at 

pressures from 0.8 to 4 MPa have been measured using two different calorimetric techniques. The methods differ in 

the way combustion is extinguished; one involves depressurization, and the other involves burning into an inert 

base. For the experiments based on depressurization, a main source of uncertainty was in determining the area of the 

cornbusting surface. Moreover, this technique was prone to a large number of unproductive runs. Most of the data 

presented here was obtained from experiments in which combustion was extinguished by burning into a 

PolyEtherEtherKetone (PEEK) base. This robust material has thermophysical properties similar to the propellants 

studied. At higher pressures (and mass regression rates), radiative heating made nonnegligible contributions to total 

heat input to the inert base. Thus, a multivariate least squares model was developed to describe a time-dependent 

radiative and conductive heat input, and it was used to fit the experimental temperature histories. Propellant surface 

temperatures, radiative fluxes, and optical absorption coefficients are obtained from the fit to the data. For the 

regions of low mass regression rates (< 0.7 g/cm*-s), the propellant surface temperatures were in agreement with 

published values. At larger mass regression rates, the propellant surface temperatures were larger than published 

values. This was believed to be a consequence of the way contributions from radiative heating were treated. 

14. SUBJECT TERMS 

propellant surface temperature, radiative heating, heat conduction, propellant burning 

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This Laboratory undertakes a continuing effort to improve the quality of the reports it publishes. Your comments/answers to 

the items/questions below will aid us in our efforts. 

1. ARL Report Number/Author ARL-TR-2434 Wanderhoff) Date of Report March 2001 

+ 2. Date Report Received 

3. Does this report satisfy a need? (Comment on purpose, related project, or other area of interest for which the report will be 

t used.) 

4. Specifically, how is the report being used? (Information source, design data, procedure, source of ideas, etc.) 

5. Has the information in this report led to any quantitative savings as far as man-hours or dollars saved, operating costs 

avoided, or efficiencies achieved, etc? If so, please elaborate. 

6. General Comments. What do you think should be changed to improve future reports? (Indicate changes to organization, 

technical content, format, etc.) 

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City, State, Zip Code 

7. If indicating a Change of Address or Address Correction, please provide the Current or Correct address above and the Old or 

Incorrect address below. 

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OLD 

l ADDRESS 

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