Transient surface temperature inside the combustion chamber of an interior liquid propellant gun.

1.
Julio C. Banks, MSME, PE Page 1 of 20
Combustion ChamberTransient Temperature Response Simulation
of a
Regenerative Liquid Propellant Gun
by
Julio C. Banks, MSME, PE
Thermo-structural Simulations Consultant
e-mail: Sell-A-Vision@Outlook.com

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN
THE EXACT SOLUTION

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN
Interior Ballistics Simulation

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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TRANSIENT THERMAL RESPONSE
OF A
REGENERATIVE LIQUID PROPELLANT GUN

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18. C = 0.00676
Time Temp∙ Pressure Velocity h
ms o
C Psi m/s W/m2
‐o
C
0 20 14.7 0.000 5.0
1 1842 775.1 3.175 76.0
2 2015 1679 6.350 225.0
3 2024 1783 9.525 323.7
4 2027 1834 12.70 415.0
5 2035 1950 15.63 512.5
6 2056 2242 27.35 888.6
7 2091 2956 53.73 1882.0
8 2130 4603 101.6 4419.8
9 2151 8407 161.2 10298.5
10 2122 17510 185.0 20806.6
11 2011 27320 181.7 30018.8
12 1876 28740 164.1 29759.5
13 1775 26170 39.08 8990.9
14 1714 23100 20.00 4840.4
15 1682 20580 12.29 3017.0
16 1666 18590 11.88 2719.1
17 1660 17010 11.47 2466.9
18 1649 15360 11.06 2215.5
19 1606 12730 10.65 1872.8
20 1464 8489 9.832 1325.9
21 1361 6229 9.422 1034.4
22 1275 4745 9.012 827.3
23 1202 3716 8.602 673.4
24 1120 2787 8.193 531.4
25 1084 2127 7.783 417.7
26 964 1519 7.373 322.1
27 863 983 6.964 228.8
28 761 606 6.554 157.1
29 675 385 6.144 110.2
30 603 252 5.735 79.0
31 542 170 5.325 57.9
32 490 118 4.915 43.2
33 447 83.3 4.505 32.9
34 411 60.4 4.096 25.6
35 380 44.7 3.686 20.2
36 355 33.7 3.276 16.3
37 333 25.8 2.867 13.3
38 316 20.1 2.457 11.1
39 301 15.8 2.047 9.4
40 289 14.7 1.638 8.5
41 235 14.7 1.638 8.7
42 181 14.7 1.228 8.1
43 127 14.7 0.818 7.4
44 74 14.7 0.408 6.5
45 20 14.7 0.204 5.9
Maxima 2151 28740 185 30018.8
Work updated to Excel Sotware by on JCB 07/22/93
Julio C. Banks, MSME, PE Page 18 of 20

19. RLPG Heat Transfer Coefficient - 01.mcdx
RLPG (Regenerative Liquid Propellant Gun) Heat Transfer Coefficient
by Julio C. Banks, MSME, PE
＝h((t)) ⋅C ―――――
(( ⋅V((t)) P((t))))
0.8
(( +T((t)) 273))
0.53 Where the scaling factor, ≡C ⋅0.00676 ―――
WWWW
⋅mmmm
2
∆°C∆°C∆°C∆°C
Check the heat transfer coefficient at its maximum value occuring at t = 11 ms
≔P ⋅27.32 ksiksiksiksi ≔T ⋅2011.0 ∆°C∆°C∆°C∆°C ≔V ⋅181.7 ―
mmmm
ssss
Let ≡KW ⋅10
3
wattwattwattwatt
=
⎛
⎜
⎜
⎝
――
V
―
mmmm
ssss
⎞
⎟
⎟
⎠
181.7
≔h =⋅C ――――――
⎛
⎜
⎜
⎝
⋅
⎛
⎜
⎜
⎝
――
V
―
mmmm
ssss
⎞
⎟
⎟
⎠
⎛
⎜⎝
――
P
PaPaPaPa
⎞
⎟⎠
⎞
⎟
⎟
⎠
0.80
⎛
⎜⎝
――――
+T ⋅273 KKKK
KKKK
⎞
⎟⎠
0.53
30.01 ―――
KW
⋅m
2
∆°C∆°C∆°C∆°C
=
⎛
⎜⎝
――
P
PaPaPaPa
⎞
⎟⎠
⋅1.8836 10
8
=
⎛
⎜⎝
――――
+T ⋅273 KKKK
KKKK
⎞
⎟⎠
⋅2.284 10
3
=psipsipsipsi 6894.757 PaPaPaPa=atmatmatmatm 14.70 psipsipsipsi
Julio C. Banks, MSME, PE Page 1 of 2
Julio C. Banks, MSME, PE Page 19 of 20

20. RLPG Heat Transfer Coefficient - 01.mcdx
Heat transfer coefficient conversion factor
SI Units: =h 30.01 ―――
KW
⋅m
2
∆°C∆°C∆°C∆°C
US Units: =h ⎛⎝ ⋅5.286 10
3 ⎞⎠ ―――――
BTUBTUBTUBTU
⋅⋅hrhrhrhr ftftftft
2
∆°F∆°F∆°F∆°F
≔ϕ =―――――
―――
KW
⋅mmmm
2
∆°C∆°C∆°C∆°C
―――――
BTUBTUBTUBTU
⋅⋅hrhrhrhr ftftftft
2
∆°F∆°F∆°F∆°F
176.11
≔Φ ⋅ϕ ―――――
⎛
⎜
⎝
―――――
BTUBTUBTUBTU
⋅⋅hrhrhrhr ftftftft
2
∆°F∆°F∆°F∆°F
⎞
⎟
⎠
⎛
⎜
⎝
―――
KW
⋅mmmm
2
∆°C∆°C∆°C∆°C
⎞
⎟
⎠
=⋅h Φ ⎛⎝ ⋅5.286 10
3 ⎞⎠ ―――――
BTUBTUBTUBTU
⋅⋅hrhrhrhr ftftftft
2
∆°F∆°F∆°F∆°F
Therefore, the conversion factor is ≔Φ ⋅176.11 ―――――
⎛
⎜
⎝
―――――
BTUBTUBTUBTU
⋅⋅hrhrhrhr ftftftft
2
∆°F∆°F∆°F∆°F
⎞
⎟
⎠
⎛
⎜
⎝
―――
KW
⋅mmmm
2
∆°C∆°C∆°C∆°C
⎞
⎟
⎠
Julio C. Banks, MSME, PE Page 2 of 2
Julio C. Banks, MSME, PE Page 20 of 20