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Ignition of double-base propellant in a hot stagnation-point flow
COMBUSTION A N D F L A M E 3 5: 81-87 (1979)
81
Ignition of Double-Base Propellant in a Hot Stagnation-Point Flow T. NIIOKA, M. TAKAHASHI, and M. IZUMIKAWA National Aerospace Laboratory, Kakuda Branch, P. O. Box 7, Ogawara, Miyagi 989.12, Japan
Ignition times of double-base propellant in a hot stagnation-point flow are measured experimentally. External flow temperatures are 568°K, 639°K, and 727°K, flow velocities 4-32 m/sec, and starting heat fluxes 0.5-3.5 cal/cm2 sec-1. Ignition times are detected by variation of surface temperature and infrared (IR) emission with time. Experimental results are compared with a theoretical formula for condensed-phase ignition, derived earlier by the asymptotic method in the limit of large activation energy. The resulting comparison shows excellent agreement; reasonable overall activation energy is found to be 30 kcal/mole for ignition.
INTRODUCTION In recent years a number of theoretical studies on ignition have been carried out using the asymptotic method in the limit of large activation energy. The results of such studies have been adopted for radiative ignitions of a condensed material with solidphase, heterogeneous, and gas-phase exothermicity. Equations derived for ignition times describe a parametric "thermal runaway" and show close agreement with numerical computations. The results are not only readily applicable to obtain ignition times, but are also useful in calculating overall kinetic parameters from experimental ignition times. Recently analytical treatment of radiant ignition has been extended to convective ignition of a hot stagnation-point flow system [1, 2]. For easy observation of ignition, a f'me control over the convective environment, and one-dimensionality to simplify theoretical treatment, we can say that the stagnation-point flow system is the most essential and convenient configuration in convective stimulus. Although a comparative study of experimental results with the asymptotic analysis mentioned above has been made for radiative ignition [3], there have not been enough studies on conCopyright © 1979 by The Combustion Institute Published by ElsevierNorth Holland, Inc.
vective heating despite the practical importance of ignition by a hot gas flow. In this paper we deal with convective ignition of a double-base propellant with solid-phase exothermicity. There have been a few experiments [4, 5] concerning a reactive solid in a stagnationpoint flow system, but a satisfactory comparison of experimental results with asymptotic analysis has not been made because of insufficient experimental data or different ignition mechanisms. Only one such comparison [1] has been reported, and that was for ignition of nitrocellulose within a small range of heat flux. The present experiments are made for a double-base propellant in a hot stagnation-point flow and are compared with the previous theoretical results, especially taking note of different flow temperatures. In these studies ignition mechanisms of a double-base propellant are reexamined; simultaneously, the validity of the analytical formula previously derived for ignition times is justified. EXPERIMENTAL APPARATUS AND PROCEDURE The double-base propellant used in this study contains the following components: 55.5% nitrocellu0010-2180/79/040081+7501.75
82 lose, 27.6% nitroglycerine~ 10.6% dinitrotoluene, 0.55% lead stearate, and others. It is known that even if a small amount of lead is present, changes in the overall energetics are not found in catalyzed double-base propellants [6]. The propellant specimen forms a hemisphere of 28 mm diameter, and its spherical surface is exposed to a hot flow as shown in Fig. 1. The initial temperature of the specimen is 293°K. A measured gas flow was first heated by being passed through an electric furnace and then issued from 15 mm-diameter nozzle. To avoid cooling, the nozzle was also heated by winding resistance wires. If the temperature and velocity distribution are flat within a circle of 10-mm diameter at the nozzle outlet, ignition times do not alter. The distance between the nozzle outlet and the specimen is 10-15 mm, in which an appreciable change of ignition time is not observed. The temperature at nozzle center is kept constant (568°K, 639°K, and 727°K) and the velocity is changed. Dry air, oxygen-augmented air, and helium are employed as a hot gas. If a propellant is inserted rapidly into a flow and is fixed instantaneously at the nozzle center, propellant vibration may not be eliminated. Therefore, a controlled hot flow is first impinged against a shutter. Then a specimen is set, the shutter pulled promptly, and the specimen exposed to a hot flow. Simultaneously, a single light beam that is detected by a phototransistor is blocked by the shutter as shown in Fig. 1, and the electro-motiveforce (emf) change is recorded on a photocorder as time zero. Since the time required for full opening of the nozzle is about 6 msec and characteristic time of flow is less than 2 msec in this experiment, the shutter speed can be considered to be infinite. On the other hand, an IR-sensitive resistance sighted for the stagnation point detects a distinct increase of IR emission, and the amplified gain of the detector is recorded on the same photocorder. The photoresistance is made of lead sulfide, the sensitive wavelength is 0.8-2.85/lm, and the response time is below 300/asec. As shown in Fig. 2, the rise of IR emission is distinctly detected. Ignition time is defined as the time from the rise of the phototransistor curve to the rise of IR emission. The middle curve in Fig. 2 shows the surface-
T. NIIOKA ET AL.
SAMPLE -
ft "~i = ;''1~'" ~SHUTTER rh /~ I\~ PHOTOTRANSI STOR [ / k - ~ 4 1 ~ I5R~DETECTOR " ~g2oO;RI
,O-,Smml
63 ~ I
I
] t HOT GAS FLOW Fig. 1. Schematicexplanationof experimentalapparatus. temperature history. A 25-#m-diameter platinum and platinum-13% rhodium thermocouple is imbedded exactly in the stagnation point so that the outer edge of thermocouple junction will coincide with the propellant surface. We can faintly see the junction from the outside. Wires are laid on the hemisphere surface. The rising point of the temperature-time profile always agrees precisely with the starting time of IR emission. RESULTS AND DISCUSSION All data obtained here are plotted in Fig. 3. The external flow temperature (ire) was kept constant and ignition times (te) were measured by allowing the flow velocity (ue) to change. Although the curve entered in Fig. 3 corresponds to the mean value of five tests, in order to save the samples, some data collection was suspended in a few experiments where the reproducibility was quite good. The scattering of ignition time was within 2% when the flow temperature was closely controlled at a certain constant value. The variation of ignition time in 18% oxygen-augmented air flow was the same as in air flow, but the ignition time in helium was reduced by a factor of 2 because the thermal conducitivity of helium is very large compared with air and oxygen. As described in the previous paper [1], such data should be rearranged on one line provided that the abscissa is the starting heat flux (~). Since heat flux at the surface varies with time in convective heating, ~ represents initial heat flux in a configuration when the heat-transfer coefficient is
83
DOUBLE-BASE PROPELLANT IGNITION
phototransistor
E.M.F. of
surface temperature 'star t of convective heating intensity of IR emission ~ / / ~ ,
ignition time
I sec
-
-
*
1 time
ignition
Fig. 2. Typical profiles of surface temperature and intensity of IR emission as a function of time (T e = 727°K, Ue = 5.25 m/sec, helium gas). 40
&
30
He
~j 20' .u
I0
i
I
i
I0
I
20
i
I
30
Ue (m/sec) Fig. 3. Variation of ignition time with hot gas flow velocity.
84
T. NIIOKA ET AL.
constant. The value ~ is given by [1] aT I
-
V~PeXe ce (1)
• v/~ ( T e - - T i ) .
where the notation employed here is identical to that of the previous paper [ 1] ; p, ~, and c represent density, thermal conductivity, and specific heat at constant pressure, respectively; and subscripts e denote the external flow and i, initial temperature. The values of properties can be referred to standard textbooks without distinct error for air, oxygen, and helium gas. The value 7* is a proportional constant of surface temperature and its gradient that is approximately equal to 2 [1]. The inverse value of characteristic flow time is calculated from 3ue/2R, where R equals the radius of hemispherical propellant. All data in Fig. 3 are rearranged in Fig. 4 by the use of ~. The theoretcal curves in Fig. 4 are calculated as follows. Nondimensional ignition time re* = (k + 1) at e ( 0 - 1)2/72 can be calculated by [I] I A* = e-°.a31x/~-*g¢
1 ~
gc I 1/2 Oe -- 1
• [1 + (0~-- 1)(1 _ g ~ ) ] - i
• exp 1 + (Oe - 1 ) 0 - g ¢ )
(2)
where
=
E*
r. ~* 1)zJ7erfclLO- ~x'~*] _1 ,
exp L(Oe-
= (E/t~Ti), A *
(3)
= [QB~2/(k + 1)apscsTd,
Oe = (Te/Ti), and 7 = 7*(Pshscs[P~AeCe)1/2. The values R, k, and Ti are the universal gas constant, unity for axisymetric flow, and the initial specimen temperature, respectively. Subscript s denotes the value of solid. Equation (2) is available for any system in which the heat-transfer coefficient (h) is
constant, provided that the substitution h 2 = [(k + 1)aPe?~eCe/7.2] is used in the results. Activation energy (E) and the frequency factor (B) in the present theoretical lines were determined in order to fit analytical ignition times given by (2) with experimental data of Te = 568°K. As a rule, activation energy and the frequency factor can be fixed by the slope of line and the actual value of ignition time in ~ - t e graph, respectively. The values E = 30 kcal/mole and QB = 8 × 10 la cal/cm a sec- 1 were obtained for the present propellant. The theoretical curves of T~ = 639°K and 727°K were drawn for the same values of E and QB. Agreement with the theory is excellent. As Te goes to infinity, the ignition time given by (2) corresponds to that for radiant ignition of a propellant whose absorption coefficient (~) is infinite. This line for ~ --- oo should lie further below the dotted line for/a = 150 cm - 1 , which is described in the following paragraphs. Price et al. [7] made experiments for radiant ignition of JPN double-base propellant. For large heat fluxes (~ > 10 cal/cm 2 sec-1), the solid-phase ignition is not available since the effect of pressure becomes significant [3]. For small heat-fluxes under 10 cal/cm 2 sec- 1 , however, the data fit the solid.phase ignition theory by Lifi~n and Williams [8]. The dotted line in Fig. 4 is drawn with the plausible combination of properties [3]: overall activation energy E = 30 kcal/mole, frequency factor multiplied by heat of reaction QB = 1.5 X 10 T M cal/cm a sec- 1 , and absorption coefficient tt = 150 cm - 1 . Although the composition of JPN propellant is a little different from the present double-base propellant, the same overall activation energy is selected. Lead contained in the propellant due to the casting technique may have an :%ct on the surface chemistry, but accompanying changes in the energetics do not appear [6]. The value of QB = 8 X 1013 cal/cm 3 sec- 1 given here was almost the same as QB = 1.5 × 10 T M cal/cm a sec- 1 obtained from the experiment by Price et al. and the theory by L i ~ n and Williams. The heat of reaction (Q) is lower than that of JPN propellant because about 10% of nitroglycerine is replaced by dinitrotoluene in this propellant. From the tabulated value for heat of reaction, 1230 cal/g for JPN
85
DOUBLE-BASE PROPELLANT IGNITION IOOr
, i68Ok
50
'\ \
\ "~ ,. \o,,,
/727°k
U U \\\\X ~ I0
X experiment 0
\\i
Air
\\
• 82%Air+18%Oz
5
\
Z~ H e
\\' \\
Niioka I. Williams' \\ t h e o r y (E=3Okcal/mole QB=8x I0 's cal/cm= sec)
\\
Lli~6n & Williams' radiative
"\\
I g n i t i o n t h e o r y f i t t e d to e x p e r i m e n t a l data by Price et a l ,
\\\ '
(E-30, OB-l.SxlO '4, kt=15Ocm") J
.3
.5
I
2 3 (cal/cm=sec)
4
5
Fig. 4. Theoretical and experimental ignition times vs starting heat fluxes. propellant and 753 cal/g for the present propellant, the frequency factors (B) are obtained to be 1.22 X 1011 g/cm a sec- 1 and 1.06 X 1011 g/cm 3 sec- 1 , respectively. It follows that reaction parameters of closely similar double-base propellants, which are derived from independent combinations of experiment and theory, will show a good agreement. Such an approach of theory and experiment makes certain that ignition occurs at solid phase in this range of experiments and the reliability of E = 30 kcal/mole and B = 10 al g/cm a see- 1 for solid-phase ignitions of double-base propellants is
high. As for experimental evidence of solid-phase
ignition, we have (1) a rapid rise of surface temperature history that always coincides with starting time of IR emission as shown in Fig. 2 (in gas-phase ignition a slower increase of surface temperature is expected at starting time of IR emission); (2) the surface temperature at ignition is equal to a constant value (-~--460°K) that is independent of gas composition and initial heat-flux as seen in Fig. 5; and (3) ignition times can be rearranged on one curve in Fig. 4, independent of external gas composition. The surface temperature at ignition was 460(+3)°K, although it is known that the temperature is around 600°K during steady combustion.
86
T. NIIOKA ET AL. 1200
"E O~
I100 u
0 O~
K~ I000
c~ ~ 800
~1 = ,0"
-0"
1"--
•
d
0
-0"
.0"
O~ (10 tO to m
.¢__
600 0
1"
v,-t_ (/)
400
0
I0
i
i
i
r
20
30
40
50
time
(sec)
Fig. 5. Surface-temperature histories.
Radiant loss of thermocouple was not estimated herein, but there should be no distinct loss because the thermocouple is laid along the hemisphere surface. The value of Ts = 460°K seems to correspond to the preignition temperature described by Dauerman and Tajima [9]. Since the mechanisms of ignition are different from the steady burning process, there may be a clear explanation for this low surface temperature at ignition. However, a detailed discussion at this point must wait for another opportunity. The most interesting point of the present study is that the "thermal runaway" times are completely consistent with IR emission times. CONCLUDING REMARKS Ignition mechanisms of double-base propellant were examined by means of a convective heating system; simultaneously, the practical use of rigorous and convenient formulas derived by asymptotic analysis was demonstrated for condensed-phase ignition. The activation energy E = 30 kcal/mole was derived from experimental results for the starting heat fluxes c~ = 0.5 ~ 5 cal/cm 2 sec- 1 , and this value agreed with that obtained from the radiant ignition test. For larger heat fluxes, ignition times may not exist on the extension of lines in Fig. 4, and the
ignition mechanism may transfer from condensedphase to gas-phase ignition. It is suggested that the region of condensed-phase ignition by convection would be wider than that by radiation since convection decreases the concentration of gasified products. At any rate, no single ignition mode dominates all ranges of external heat flux, and perhaps two regions exist. Considering the results in other studies [3, 4] and the present data, we can conclude that solid-phase ignition is available for low heat fluxes (ca. ~ < 10 cal/cm 2 sec- 1 ) and gas-phase ignition for higher heat fluxes. In the earlier papers [10, 11] there are some data for double-base propellant ignition given by "go/no-go" tests. We have not discussed them here because these tests have more complex and different aspects than the "thermal runaway" criterion in asymptotic analysis. Significant temperature rise or IR emission would best express "thermal runaway." The in-depth absorption coefficient is a complicated factor in the problem of radiant ignition, especially for solid-phase ignition. Since this is eliminated in convective heating, it can be expected that analytical procedures may be developed and reaction parameters selected through a wellcontrolled convective configuration such as stagnation-point flow described above. Furthermore, it would be of interest to study the region
DOUBLE-BASE PROPELLANT IGNITION transient ignition.
from
condensed-phase
to
gas-phase
ICe are indebted to Professor F. A. ICilliams f o r encouraging us to produce this experiment and f o r helpfully reviewing the manuscript. ICe are also indebted to Dr. N. Kubota f o r discussions o f his w o r k on double-base propellant combustion and f o r useful advice about much o f the experimental technique.
REFERENCES 1. Niioka, T., and Williams, F. A., Combust. Flame 29:43(1977). 2. Niioka, T., Heterogeneous Ignition o f a Solid Fuel in a Hot Stagnation-Point Flow (in preparation). 3. Niioka, T., and Williams, F. A., Seventeenth Symposium (International} on Combustion The Combustion Institute, Pittsburgh (in preparation).
87 4. Churchill, S. W., Kruggel, R. W., and Brier, J. C., AIChEJ 2:568(1956). 5. Sutton, D., and Welling, P. C., The Ignition Delay Times of Solid Propellants Heated by Forced Convection, Rocket Propulsion Establishment, Wescott, Bucks, England, report No. 45, 1964. 6. Kubota, N., Olilemiller, T. J., Caveny, L. H., and Summerfield, M., AIAAJ 12:1709(19741). 7. Price, E. W., Bradley, H. H., Jr., Hightower, J. D., and Fleming, R. O., Jr., AIAA preprint No. 64-120, 1964. 8. Li'fidn, A., and Williams, F. A., Combust. Flame 18:85(1972). 9. Dauerman, L., and Tajima, Y. A., AIAAJ 6: 678(1968). 10. DeLuca, L., Caveny, L. H., OhlemiUer, T. J., and Summerfield, M., AIAAJ 14:940(1976). 11. DeLuca, L., OhlemiUer, T. J., Caveny, L. H., and Summerfield, M., AIAAJ 14:1111 (1976).
Received 12 July 1978; revised 30 October 1978
81
Ignition of Double-Base Propellant in a Hot Stagnation-Point Flow T. NIIOKA, M. TAKAHASHI, and M. IZUMIKAWA National Aerospace Laboratory, Kakuda Branch, P. O. Box 7, Ogawara, Miyagi 989.12, Japan
Ignition times of double-base propellant in a hot stagnation-point flow are measured experimentally. External flow temperatures are 568°K, 639°K, and 727°K, flow velocities 4-32 m/sec, and starting heat fluxes 0.5-3.5 cal/cm2 sec-1. Ignition times are detected by variation of surface temperature and infrared (IR) emission with time. Experimental results are compared with a theoretical formula for condensed-phase ignition, derived earlier by the asymptotic method in the limit of large activation energy. The resulting comparison shows excellent agreement; reasonable overall activation energy is found to be 30 kcal/mole for ignition.
INTRODUCTION In recent years a number of theoretical studies on ignition have been carried out using the asymptotic method in the limit of large activation energy. The results of such studies have been adopted for radiative ignitions of a condensed material with solidphase, heterogeneous, and gas-phase exothermicity. Equations derived for ignition times describe a parametric "thermal runaway" and show close agreement with numerical computations. The results are not only readily applicable to obtain ignition times, but are also useful in calculating overall kinetic parameters from experimental ignition times. Recently analytical treatment of radiant ignition has been extended to convective ignition of a hot stagnation-point flow system [1, 2]. For easy observation of ignition, a f'me control over the convective environment, and one-dimensionality to simplify theoretical treatment, we can say that the stagnation-point flow system is the most essential and convenient configuration in convective stimulus. Although a comparative study of experimental results with the asymptotic analysis mentioned above has been made for radiative ignition [3], there have not been enough studies on conCopyright © 1979 by The Combustion Institute Published by ElsevierNorth Holland, Inc.
vective heating despite the practical importance of ignition by a hot gas flow. In this paper we deal with convective ignition of a double-base propellant with solid-phase exothermicity. There have been a few experiments [4, 5] concerning a reactive solid in a stagnationpoint flow system, but a satisfactory comparison of experimental results with asymptotic analysis has not been made because of insufficient experimental data or different ignition mechanisms. Only one such comparison [1] has been reported, and that was for ignition of nitrocellulose within a small range of heat flux. The present experiments are made for a double-base propellant in a hot stagnation-point flow and are compared with the previous theoretical results, especially taking note of different flow temperatures. In these studies ignition mechanisms of a double-base propellant are reexamined; simultaneously, the validity of the analytical formula previously derived for ignition times is justified. EXPERIMENTAL APPARATUS AND PROCEDURE The double-base propellant used in this study contains the following components: 55.5% nitrocellu0010-2180/79/040081+7501.75
82 lose, 27.6% nitroglycerine~ 10.6% dinitrotoluene, 0.55% lead stearate, and others. It is known that even if a small amount of lead is present, changes in the overall energetics are not found in catalyzed double-base propellants [6]. The propellant specimen forms a hemisphere of 28 mm diameter, and its spherical surface is exposed to a hot flow as shown in Fig. 1. The initial temperature of the specimen is 293°K. A measured gas flow was first heated by being passed through an electric furnace and then issued from 15 mm-diameter nozzle. To avoid cooling, the nozzle was also heated by winding resistance wires. If the temperature and velocity distribution are flat within a circle of 10-mm diameter at the nozzle outlet, ignition times do not alter. The distance between the nozzle outlet and the specimen is 10-15 mm, in which an appreciable change of ignition time is not observed. The temperature at nozzle center is kept constant (568°K, 639°K, and 727°K) and the velocity is changed. Dry air, oxygen-augmented air, and helium are employed as a hot gas. If a propellant is inserted rapidly into a flow and is fixed instantaneously at the nozzle center, propellant vibration may not be eliminated. Therefore, a controlled hot flow is first impinged against a shutter. Then a specimen is set, the shutter pulled promptly, and the specimen exposed to a hot flow. Simultaneously, a single light beam that is detected by a phototransistor is blocked by the shutter as shown in Fig. 1, and the electro-motiveforce (emf) change is recorded on a photocorder as time zero. Since the time required for full opening of the nozzle is about 6 msec and characteristic time of flow is less than 2 msec in this experiment, the shutter speed can be considered to be infinite. On the other hand, an IR-sensitive resistance sighted for the stagnation point detects a distinct increase of IR emission, and the amplified gain of the detector is recorded on the same photocorder. The photoresistance is made of lead sulfide, the sensitive wavelength is 0.8-2.85/lm, and the response time is below 300/asec. As shown in Fig. 2, the rise of IR emission is distinctly detected. Ignition time is defined as the time from the rise of the phototransistor curve to the rise of IR emission. The middle curve in Fig. 2 shows the surface-
T. NIIOKA ET AL.
SAMPLE -
ft "~i = ;''1~'" ~SHUTTER rh /~ I\~ PHOTOTRANSI STOR [ / k - ~ 4 1 ~ I5R~DETECTOR " ~g2oO;RI
,O-,Smml
63 ~ I
I
] t HOT GAS FLOW Fig. 1. Schematicexplanationof experimentalapparatus. temperature history. A 25-#m-diameter platinum and platinum-13% rhodium thermocouple is imbedded exactly in the stagnation point so that the outer edge of thermocouple junction will coincide with the propellant surface. We can faintly see the junction from the outside. Wires are laid on the hemisphere surface. The rising point of the temperature-time profile always agrees precisely with the starting time of IR emission. RESULTS AND DISCUSSION All data obtained here are plotted in Fig. 3. The external flow temperature (ire) was kept constant and ignition times (te) were measured by allowing the flow velocity (ue) to change. Although the curve entered in Fig. 3 corresponds to the mean value of five tests, in order to save the samples, some data collection was suspended in a few experiments where the reproducibility was quite good. The scattering of ignition time was within 2% when the flow temperature was closely controlled at a certain constant value. The variation of ignition time in 18% oxygen-augmented air flow was the same as in air flow, but the ignition time in helium was reduced by a factor of 2 because the thermal conducitivity of helium is very large compared with air and oxygen. As described in the previous paper [1], such data should be rearranged on one line provided that the abscissa is the starting heat flux (~). Since heat flux at the surface varies with time in convective heating, ~ represents initial heat flux in a configuration when the heat-transfer coefficient is
83
DOUBLE-BASE PROPELLANT IGNITION
phototransistor
E.M.F. of
surface temperature 'star t of convective heating intensity of IR emission ~ / / ~ ,
ignition time
I sec
-
-
*
1 time
ignition
Fig. 2. Typical profiles of surface temperature and intensity of IR emission as a function of time (T e = 727°K, Ue = 5.25 m/sec, helium gas). 40
&
30
He
~j 20' .u
I0
i
I
i
I0
I
20
i
I
30
Ue (m/sec) Fig. 3. Variation of ignition time with hot gas flow velocity.
84
T. NIIOKA ET AL.
constant. The value ~ is given by [1] aT I
-
V~PeXe ce (1)
• v/~ ( T e - - T i ) .
where the notation employed here is identical to that of the previous paper [ 1] ; p, ~, and c represent density, thermal conductivity, and specific heat at constant pressure, respectively; and subscripts e denote the external flow and i, initial temperature. The values of properties can be referred to standard textbooks without distinct error for air, oxygen, and helium gas. The value 7* is a proportional constant of surface temperature and its gradient that is approximately equal to 2 [1]. The inverse value of characteristic flow time is calculated from 3ue/2R, where R equals the radius of hemispherical propellant. All data in Fig. 3 are rearranged in Fig. 4 by the use of ~. The theoretcal curves in Fig. 4 are calculated as follows. Nondimensional ignition time re* = (k + 1) at e ( 0 - 1)2/72 can be calculated by [I] I A* = e-°.a31x/~-*g¢
1 ~
gc I 1/2 Oe -- 1
• [1 + (0~-- 1)(1 _ g ~ ) ] - i
• exp 1 + (Oe - 1 ) 0 - g ¢ )
(2)
where
=
E*
r. ~* 1)zJ7erfclLO- ~x'~*] _1 ,
exp L(Oe-
= (E/t~Ti), A *
(3)
= [QB~2/(k + 1)apscsTd,
Oe = (Te/Ti), and 7 = 7*(Pshscs[P~AeCe)1/2. The values R, k, and Ti are the universal gas constant, unity for axisymetric flow, and the initial specimen temperature, respectively. Subscript s denotes the value of solid. Equation (2) is available for any system in which the heat-transfer coefficient (h) is
constant, provided that the substitution h 2 = [(k + 1)aPe?~eCe/7.2] is used in the results. Activation energy (E) and the frequency factor (B) in the present theoretical lines were determined in order to fit analytical ignition times given by (2) with experimental data of Te = 568°K. As a rule, activation energy and the frequency factor can be fixed by the slope of line and the actual value of ignition time in ~ - t e graph, respectively. The values E = 30 kcal/mole and QB = 8 × 10 la cal/cm a sec- 1 were obtained for the present propellant. The theoretical curves of T~ = 639°K and 727°K were drawn for the same values of E and QB. Agreement with the theory is excellent. As Te goes to infinity, the ignition time given by (2) corresponds to that for radiant ignition of a propellant whose absorption coefficient (~) is infinite. This line for ~ --- oo should lie further below the dotted line for/a = 150 cm - 1 , which is described in the following paragraphs. Price et al. [7] made experiments for radiant ignition of JPN double-base propellant. For large heat fluxes (~ > 10 cal/cm 2 sec-1), the solid-phase ignition is not available since the effect of pressure becomes significant [3]. For small heat-fluxes under 10 cal/cm 2 sec- 1 , however, the data fit the solid.phase ignition theory by Lifi~n and Williams [8]. The dotted line in Fig. 4 is drawn with the plausible combination of properties [3]: overall activation energy E = 30 kcal/mole, frequency factor multiplied by heat of reaction QB = 1.5 X 10 T M cal/cm a sec- 1 , and absorption coefficient tt = 150 cm - 1 . Although the composition of JPN propellant is a little different from the present double-base propellant, the same overall activation energy is selected. Lead contained in the propellant due to the casting technique may have an :%ct on the surface chemistry, but accompanying changes in the energetics do not appear [6]. The value of QB = 8 X 1013 cal/cm 3 sec- 1 given here was almost the same as QB = 1.5 × 10 T M cal/cm a sec- 1 obtained from the experiment by Price et al. and the theory by L i ~ n and Williams. The heat of reaction (Q) is lower than that of JPN propellant because about 10% of nitroglycerine is replaced by dinitrotoluene in this propellant. From the tabulated value for heat of reaction, 1230 cal/g for JPN
85
DOUBLE-BASE PROPELLANT IGNITION IOOr
, i68Ok
50
'\ \
\ "~ ,. \o,,,
/727°k
U U \\\\X ~ I0
X experiment 0
\\i
Air
\\
• 82%Air+18%Oz
5
\
Z~ H e
\\' \\
Niioka I. Williams' \\ t h e o r y (E=3Okcal/mole QB=8x I0 's cal/cm= sec)
\\
Lli~6n & Williams' radiative
"\\
I g n i t i o n t h e o r y f i t t e d to e x p e r i m e n t a l data by Price et a l ,
\\\ '
(E-30, OB-l.SxlO '4, kt=15Ocm") J
.3
.5
I
2 3 (cal/cm=sec)
4
5
Fig. 4. Theoretical and experimental ignition times vs starting heat fluxes. propellant and 753 cal/g for the present propellant, the frequency factors (B) are obtained to be 1.22 X 1011 g/cm a sec- 1 and 1.06 X 1011 g/cm 3 sec- 1 , respectively. It follows that reaction parameters of closely similar double-base propellants, which are derived from independent combinations of experiment and theory, will show a good agreement. Such an approach of theory and experiment makes certain that ignition occurs at solid phase in this range of experiments and the reliability of E = 30 kcal/mole and B = 10 al g/cm a see- 1 for solid-phase ignitions of double-base propellants is
high. As for experimental evidence of solid-phase
ignition, we have (1) a rapid rise of surface temperature history that always coincides with starting time of IR emission as shown in Fig. 2 (in gas-phase ignition a slower increase of surface temperature is expected at starting time of IR emission); (2) the surface temperature at ignition is equal to a constant value (-~--460°K) that is independent of gas composition and initial heat-flux as seen in Fig. 5; and (3) ignition times can be rearranged on one curve in Fig. 4, independent of external gas composition. The surface temperature at ignition was 460(+3)°K, although it is known that the temperature is around 600°K during steady combustion.
86
T. NIIOKA ET AL. 1200
"E O~
I100 u
0 O~
K~ I000
c~ ~ 800
~1 = ,0"
-0"
1"--
•
d
0
-0"
.0"
O~ (10 tO to m
.¢__
600 0
1"
v,-t_ (/)
400
0
I0
i
i
i
r
20
30
40
50
time
(sec)
Fig. 5. Surface-temperature histories.
Radiant loss of thermocouple was not estimated herein, but there should be no distinct loss because the thermocouple is laid along the hemisphere surface. The value of Ts = 460°K seems to correspond to the preignition temperature described by Dauerman and Tajima [9]. Since the mechanisms of ignition are different from the steady burning process, there may be a clear explanation for this low surface temperature at ignition. However, a detailed discussion at this point must wait for another opportunity. The most interesting point of the present study is that the "thermal runaway" times are completely consistent with IR emission times. CONCLUDING REMARKS Ignition mechanisms of double-base propellant were examined by means of a convective heating system; simultaneously, the practical use of rigorous and convenient formulas derived by asymptotic analysis was demonstrated for condensed-phase ignition. The activation energy E = 30 kcal/mole was derived from experimental results for the starting heat fluxes c~ = 0.5 ~ 5 cal/cm 2 sec- 1 , and this value agreed with that obtained from the radiant ignition test. For larger heat fluxes, ignition times may not exist on the extension of lines in Fig. 4, and the
ignition mechanism may transfer from condensedphase to gas-phase ignition. It is suggested that the region of condensed-phase ignition by convection would be wider than that by radiation since convection decreases the concentration of gasified products. At any rate, no single ignition mode dominates all ranges of external heat flux, and perhaps two regions exist. Considering the results in other studies [3, 4] and the present data, we can conclude that solid-phase ignition is available for low heat fluxes (ca. ~ < 10 cal/cm 2 sec- 1 ) and gas-phase ignition for higher heat fluxes. In the earlier papers [10, 11] there are some data for double-base propellant ignition given by "go/no-go" tests. We have not discussed them here because these tests have more complex and different aspects than the "thermal runaway" criterion in asymptotic analysis. Significant temperature rise or IR emission would best express "thermal runaway." The in-depth absorption coefficient is a complicated factor in the problem of radiant ignition, especially for solid-phase ignition. Since this is eliminated in convective heating, it can be expected that analytical procedures may be developed and reaction parameters selected through a wellcontrolled convective configuration such as stagnation-point flow described above. Furthermore, it would be of interest to study the region
DOUBLE-BASE PROPELLANT IGNITION transient ignition.
from
condensed-phase
to
gas-phase
ICe are indebted to Professor F. A. ICilliams f o r encouraging us to produce this experiment and f o r helpfully reviewing the manuscript. ICe are also indebted to Dr. N. Kubota f o r discussions o f his w o r k on double-base propellant combustion and f o r useful advice about much o f the experimental technique.
REFERENCES 1. Niioka, T., and Williams, F. A., Combust. Flame 29:43(1977). 2. Niioka, T., Heterogeneous Ignition o f a Solid Fuel in a Hot Stagnation-Point Flow (in preparation). 3. Niioka, T., and Williams, F. A., Seventeenth Symposium (International} on Combustion The Combustion Institute, Pittsburgh (in preparation).
87 4. Churchill, S. W., Kruggel, R. W., and Brier, J. C., AIChEJ 2:568(1956). 5. Sutton, D., and Welling, P. C., The Ignition Delay Times of Solid Propellants Heated by Forced Convection, Rocket Propulsion Establishment, Wescott, Bucks, England, report No. 45, 1964. 6. Kubota, N., Olilemiller, T. J., Caveny, L. H., and Summerfield, M., AIAAJ 12:1709(19741). 7. Price, E. W., Bradley, H. H., Jr., Hightower, J. D., and Fleming, R. O., Jr., AIAA preprint No. 64-120, 1964. 8. Li'fidn, A., and Williams, F. A., Combust. Flame 18:85(1972). 9. Dauerman, L., and Tajima, Y. A., AIAAJ 6: 678(1968). 10. DeLuca, L., Caveny, L. H., OhlemiUer, T. J., and Summerfield, M., AIAAJ 14:940(1976). 11. DeLuca, L., OhlemiUer, T. J., Caveny, L. H., and Summerfield, M., AIAAJ 14:1111 (1976).
Received 12 July 1978; revised 30 October 1978