Analysis of

tion Inside a
Hot Gun Tube

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 SAND 2003-8230
Unlimited Release
Printed May 2003

Finite Element Thermal Analysis of

155-mm Projectile Exudation Inside
a Hot Gun Tube
T. R. Shelton and Y.R. Kan
Engineering Mechanics Modeling & Simulation Department
Sandia National Laboratories
Livermore. California 94551-0969

Abstract

The high firing rates of new and developing cannons create higher operating temperatures
that projectiles experience. Higher temperatures in-bore bring the possibility of high
explosive exudation from chambered shells during misfire, hang-fire, or hold-fire. The
development of a finite element thermal model to predict high explosive exudation inside
a hot gun tube brings an improved level of insight to existing physical test results. The
MI98 towed howitzer and M107 155-mm shell are modeled to compare to physical test
results from Morales 1997 and Zimmerman 1980. During creation of the model special
focus is taken to simulate the heat flow between the contact of the rotating band and
cannon wall. A strong correlation between test results and model is seen with both
reports and validates the model setup. Model results suggest that time to exudation
predicted by Morales and Zimmerman may be too conservative.
 ACKNOWLEDGEMENT
Special thanks goes to Tim Dacier and Kok Chung of ARDEC for technical guidance,
Yuki Ohashi (8727 Engineering Mechanics Modeling & Simulation Department) for
thermal analysis support and Carmella Orham (8727 Engineering Mechanics Modeling &
Simulation Department) for help on formatting and presentation of results.
 CONTENTS

1.o Introduction...... ...............I

2.0 Related Studies.. ...... ..............7
3.0 Building a FE Model.. ....................... ~~~~~~ .8

.O Validating Model Setup and Simulation

by Comparison to Physical Testing........ .......................... 12

5.0 Insight ftom Model Visualization.......... .................... 18

6.0 Conclusion............................... .......21

7.0 References........ .......22
Oistribution.......... ............................ .......23

! .
LIST OF FIGURES

1. Material interfaces............................................................................................... 8
2. Mesh detail at material interfaces......................................................................... 8
3. Material properties............................................................................................... 9
4. Surface for interface conductance approximation ............................................... 10
5. Table and figure from Handbook of Heat Transfer
used in determining the interface conductance ................................................... 11
6. Rifling of cannon determines contact percentage with rotating band ..................11
7. Model setup compared to 1997 Morales test setup ............................................. 12
8. Thermocouple to Node data comparison for 1997 Morales Testing.. ...............13
9. Time. to. exudation results of 1997 Morales testing compared to analytical
predictions.. .................................................................................. 14
IO. Model setup compared to 1981 Zimmermann and Geany test setup.. ............... 15
11. Thermocouple temperature versus time from 1981 testing compared with
analytical prediction. Initial tube temperature of 250 "F and initial round
temperature of 145 "F ........................................................................................ 16
12. Thermocouple temperature versus time from 1981 testing compared with
analytical prediction. Initial tube temperature of 350 OF and initial round
temperature of 100 "F ........................................................................................ 16
13. Thermocouple temperature versus time from 1981 testing compared with
analytical prediction. Initial tube temperature of 350 O F and initial round
temperature of 125 O F ........................................................................................ 17
14. Infrared image of MI07 projectile
from testing done by Benet Laboratories....................... ............... 18
15. Finite element model thermal contours illustrate
comparable heat bands to the infrared image........................ ........ 19
16. Finite element model thermal contours illustrate heat flow
from gun tube to round through rotating band .............................. ........20
17. Thin layer of melt temperatures in high explosives
seen in model at time predicted for exudation .............................. ........ 20
18. Zoomed in picture of thin layer of melt temperatures
in high explosives seen in model at time predicted for exudation ........ ........ 21

LIST OF EQUATIONS

-
No.

1. Approximation of the effective interface conductivity... 10

 Finite Element Thermal Analysis of
155-mm Projectile Exudation Inside
a Hot Gun Tube

1.0 introduction
As the army demands artillery guns with higher fuing rates, increasing from two to three
rounds per minute up to ten rounds per minute, operating temperatures of the bores on
tanks and howitzers increase comparatively. In the course of normal operation, a
chambered shell does not remain chambered long enough to be affected by the raise in
operating temperature. However, if a misfire, hang-fire, or hold-fire occurs then the
chambered shell begins to rise in temperature approaching the melting temperature of its
incased explosive. If the explosive melts it has the potential to escape through the fuze
and into the bore. The escaping of melted explosives is termed “exudation”. Exudation
generates an in-bore detonation hazard. Predicting when exudation occurs is a vital part
to setting a standard for safe-time-to-fire. The safetime-to-fire tells the operator how
long they have to un-chamber/fire the loaded round before they need to evacuate the
mount/tank. Earlier tests have been performed to establish the existing safe-time-to-fire
and it is the objective of this study to expand and improve on these tests through the use
of a finite element thermal model.

2.0 Related Studies

The concern about weapon exudation is not a new topic. Since the Navy started firing at
high rates sooner, they have been examining exudation and gun barrel temperature
related problems since as early as 1953 111. Zimmermann and Geanny performed one of
the earliest tests in 1980 that relates to safe-time-to-fire for the army [2]. The MI98
towed howitzer had recently been developed with a TWD (Thermal Warning Device) and
Zimmennann and Geanny were attempting to use readings from the TWD to more
accurately predict exudation of M107 and M549 155-mm rounds. Zimmermann and
Geanny concluded the safe-time-to-fire should be reduced from the accepted 10 min.
when the TWD temperature reads 350 OF. Following the Zimmerman study, thermal
testing was again performed on the MI98 towed howitzer. Testing in 1997 by Morales
concluded the safe-time-to-fire should be reduced even further than Zimmerman’s
suggested time [3]. To better understand exudation and the reasons for different findings
in the two tests, a thermal finite element model can be very useful.
3.0 Building A FE Model

The expected primary heat transfer we are trying to capture flows from the hot cannon
wall into the round by means of conduction. The magnitude of convection and radiation
heating the round are small enough relative to the expected conduction that they can be
ignored in creating the model. For this model, the most complicated aspect is all the
material interfaces (Figure I). To aid in capturing the heat flow between these materials,
the mesh size is kept relatively small around the interfaces (Figure 2).

Fuze

~~

- CunTube

Figure 1: Material interfaces. Figure 2: Mesh detail at material interfaces.

Looking at the material properties, it is important to note the differences in the

conductivities (Figure 3). Comparing the different conductivities of all the materials
further emphasizes the need to capture interface interactions because the rotating band
has four times the conductivity of steel and steel has one hundred and fifty times the
conductivity of the explosives.
 Aluminum 7075-Tj
Density: 0.102 I b h
conductivity: 902 Btu-in/hr-#-”F
Specific Heat: 0.229 Btu/lb-’F

ExDlosive
E i t y : 0.0596 Ib/in3
Conductivity: 1.804 Btu-in/hr-#-”F
Specific Heat: 0,3308 Btu/lb-’F

praSs/ CODOW Alloy

Density: 0.318 lb/in’
Conductivity: 1308 Btu-in/hr-#-”F
Specific Heat: 0.1 14 Btuilb-OF

4340 Steel
Density: 0.284 l b h 3
Conductivity: 308 Btu-in/hr-#-”F

I Specific Heat: 0.1 14 Btuilb-”F

I
Figure 3: Material properties.

An approximation is needed to model the conductance between the rotating band and the
cannon wall. All the other interfaces in the round are easily approximated as welds or
perfect conductance between materials.
A small surface in the model was made so its conductivity could be adjusted to simulate
the contact interface of the rotating band and cannon wall seen in Figure 4.

I
Jhite Area Made to
[odel Interface by
djusting Conductivity

Width
I

Figure 4: Surface for interface conductance approximation.

Using the formula [l] below from a report generated by Yuki Ohashi, a linear
approximation of the effective interface conductivity was determined for the white area.

( k -hi .L )
Kc = (hi.L+ k )

L in the formula stands for the width of the adjusted material, k stands for the current
conductivity of the material which is going to be adjusted. In this caseL = 0.0714 in and k
is that of steel, k 308 . Btu , in
hr. f?:F
. The variable hi,interface conductance, is determined
by referring to the Handbook of Heat Transfer. Figure 5 shows a table and plot taken
from the Handbook of Heat Transfer. Assuming an initial contact pressure of 50 psi and
using curve 15, because it corresponds to a copper interface, gets a value for
hi - 1400
Btu
hr d . ° F
. The interface conductance can be assumed to remain constant even
though the contact pressure will increase due to thermal expansion. The assumption of a
constant interface conductance is valid because of the horizontal nature of curve 15 for
copper, which implies changes in pressure. bring about very little change in the interface
conductance.

10
 -
I
1
3
4
5
6
7
8
9
LO
I1
I1
13
I4
-7'5
16
17
- 18

-8. Tm- mwf%emdwwm ditr.

rigure 5: Table and figure from Handbook of Heat Transfer used in determining the
interface conductance.

Before combining all the variables to calculate the effective conductivity, it is also
necessary to adjust the effective conductivity for the percentage of contact it actually
makes with the barrel. The rotating band sits in the rifling shown in Figure 6.

3.68 in (Contact L-mW I,

IO. 13 in (Overall Length)
36,33% Contact
I x..
*-.==- -
Figure 6: Rifling of cannon determines contact percentage with rotating band.
'40

Taking the contact percentage, 36.33%, and the other variables into consideration yield
-
an effective conductivity, K e f 27.43
Bhl.in
hr .f i 2 .' F
. This new conductivity for the white area
in Figure 4 comes out to be about 9% of its original conductivity. Having materials,
geometry, mesh, and interface conditions defined the model is ready to start simulating
varying initial conditions.
4.0 Validating Model Setup and Simulation by Comparison to Physical Testing

To compare with the testing performed by Morales in 1997, temperature data collected by
thermocouples was compared to nodal data in the simulation model. Figure 7 shows a
diagram of the instrumented round along side the model to point out the comparison of
thermocouple 17 to node 5950.

crl
L.

E!.
ii:

c3
W
W
Node/Thermocouple 4

Node 5950/T17

-M
Figure 7: Model setup compared to 1997 Morales test setup.

12
 The thermocouple 17 was chosen to compare to since it obtains the maximum
temperature during the testing. The comparison between the thermocouple and node can
be seen in Figure 8.

Exparimenhi and Analytical Exudation Testlng Result. of Thennocouple 17 In M107,

Initial Round=70 O F , inithi Tub.p9MoF
220
210
200
190
180
170

130
120
110
100
90
80
70

Figure 8: Thermocouple to Node data comparison for 1997 Morales Testing.

The data remains very close all the way through the melt temperature of the high
explosives.

'i

13
 Analytical and Experimental Projectile Exudation

+Initial Pmjoctile Temp

0 1 2 3 4 5 6 7 8 9 10
Time to Exudation (min)
Figure 9: Time to exudation results of 1997 Morales testing compared to
analytical predictions.

The most comprehensive plot that collects data from multiple tests was chosen for
comparison. Experimental data plotted in Figure 9 was gained by placing a round at
70 OF or 145 O F into a cannon at an initial temperature ranging from 550 "F to 250 O F
and waiting for any of the thermocouples to reach 176 "F and recording this time. 176 "F
is the melt temperature of HE. The time it takes a thermocouple to reach 176 OF is
considered the time to exudation. The analytical data plotted was obtained by letting a
simulation with similar initial temperatures run until node 5950 reached the melt
temperature of 176 "F. The analytical data compares very well with the experimental
data closely predicting the same time to exudation.

A comparison to testing performed by Zimmermann and Geany in 1981 is done in a

similar manner as was done with the 1997 testing by Morales. Again, a thermocouple to
node reading was used. The test setup compared to model setup for the 1981 test can be
seen in Figure 10.

14
 Figure 10: Model setup compared to 1981 Zimmermann and G a y test setup.

The data from the 1981 tests was not compiled in the same manner as the 1997 tests.
Instead, individual thermocouple temperature readings versus time plots were made for
shells loaded at varying initial temperatures and into a cannon at varying temperature.
Thermocouple data from several of the tests are plotted with the node temperature data
with the same conditions in the following figures. The analytical results follow the same
trend as the experimental results while slightly over predicting the temperature. The over
predicting of the temperature can be explained by the test setup for the experiment. Since
thermocouples were placed by drilling into the shell, removing of the material in front of
the thermocouple would block heat flow to the thermocouple. Good correlation to both
the 1981 and 1997 testing helps validate the model setup and output.
 Analytical and Experimental Data
Tube Temp. 250 "F, Round Temp: 145 "F

n 4 A 17 1R 70
Time (min)

Figure 11: Thermocouple temperature versus time from 1981 testing compared with analytical
prediction. Initial tube temperature of 250 "F and initial round temperature of 145 "F

Analytical and Experimental Data

Tube Temp: 350 "F, Round Temp: 100 "F

....
n 4 A 12 16 20
Time (min)
Figure 12: Thermocouple temperature versus time from 1981 testing compared with analytical
prediction. Initial tube temperature of 350 "F and initial round temperature of 100 OF.

16
 Analytical and Experimental Data
Tube Temp:350 OF, Round Temp: 125 "F
27

24

21

18

15

12
0 4 0 12 16 20
Tim (mln)
- Figure 13: Thermocouple temperature versus time from 1981 testing compared with analytical
prediction. Initial tube temperature. of 350 "F and initial round temperature of 125 O F .

17
5.0 Insight from Model Visualization

One of the strengths of finite element models is the their ability to aide in visualizing
results. In thermal analysis an infrared picture is one of the best ways to see heat bands.

Figure 1 4 Infrared image of M107 projectile from testing done by

Benet Laboratories.

Evidence that all the heat flow from the cannon comes through the rotating band was
demonstrated by a thermal image captured in testing by Benet Laboratories (Figure 14).
A M107 projectile was loaded and then unloaded and photographed when the rotating
band reached 176 "F. The picture clearly indicates all the heat is absorbed in through the
rotating band. A thermal contour plot of the shell and rotating band from the finite
element model shows comparable heat bands (Figure 15).

18
 I, NTll
- +1.810et02
-t1.754et02
. +1.699e+02
- +1.643e+02
- +l. 588e+02
- +l. 532et02
- +l. 477e+02
- +l. 421e+02
+1.366e+02
t1.310et02
+l. 255e+02
t1.199e+02
+l. 144e+02
t1.088et02
t1.033e+02
t9.775et01
t9.220et01
t8.665e+01
t8. llOetOl
+7.555e+01
+7,00Oe+01

Figure 15: Finite element model thermal contours illustrate comparable

heat bands to the infiared image.

Also, an overall contour plot of the model correctly shows the model pulling heat from
the gun tube into the shell (Figure 16). Using the finite element model to focus on the
high explosives at the time predicted as melt shows a very thin layer, which is at or above
the melt temperature (Figure 17 & Figure 18). This thin layer of melt may not be enough
to actually cause exudation.

19
 t3.440et02
t3.303et02
t3.166et02
t3.029et.02
t2.892et02
t2.755et02
t2.618et02
t2.481et02
t2.344et02 Tube Through
t2.207et02 Rotating Bind
t2.070e+02
t1.933et02
t1.796et02
t1.659et02
t1.522et02
t1.385et02
t1.248et02
tl. llle+02
t9.740et01
t8.370et01
t7.000et01

Figure 16: Finite element model thermal contours illustrate heat flow from
gun tube to round through rotating band.

t2.142et02
t2.070et02
t1.998et02
t1.926et02
+1.854et02
t1.182e+02
t1.709etO2
t1.637et02
t1.493et02
t1.421et02
+1.349et02
+1.277et02
t1.205et02 icrMa from
t1.133et02
~~~~~~ .. Rohtl~tg
t1.061etOZ
t9.884et01
+9.163e+01
t8.442et01
t7.721etOl
t7.000eS01
1

Figure 17: Thin layer of melt temperatures in high explosives seen in

model at time predicted for exudation.
20
 142

70 I
Figure 18: Zoomed in picture of thin layer of melt temperatures in high explosives
seen in model at time predicted for exudation.

6.0 Conclusions
An accurate finite-element thermal analysis model has been developed to predict the
heating of a seated projectile. The model correlates to results produced by experiments in
1997 by Morales and 1981 by Zimmerman and Geany. Also, the model brings insight to
the depth of melt, which may prove the safe-time-to-fire predicted by Morales and
Zimmerman to be too conservative. A thin layer melt may not be a concern for
exudation, but when the melting propagates to the entire backend then it poses an in-bore
safety risk from torsional impulse loading. This model can be used for further study into
the thickness of the melting zone. Finally, this approach can be extended to model
various munitions and gun systems.

21
/I
7.0 References
1. Macatician and Nanigian. “A Thermocouple to Record Transient Temperatures at
the Bore Surface of Guns.” 1953, NPG Report 1130, Dahgren, Virginia

2. Geany, Ronald G. and John R. Zimmerman. “Temperature Corerelation for

Heated M198 Towed Howitzer Gun Tube and Chambered 155-MM Projectile.”
1981, ARTSD-TR-80004, Dover, New Jersey

3. Ciro A. Morales 111. “Thermal Effects of a Hot Weapon on High Explosive

Projectiles.” 1997, ARCCB-TR-97024, Watervliet, New York

22
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