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ASSIGNMENT AE 708: Aerospace Propulsion Indian Institute of Technology Bombay
Name of the Student KANDIMALLA CHACHA SRIHARI (183010034)
Software Used: NASA CEArun
Problem 1: EQUILIBRIUM FLOW
Oxidizer
- Ammonium Perchlorate
Fuel
- Hydroxyl Terminated Poly Butadiene (HTPB)
Chamber Pressure (Pc)
- 84bar
Initial Temperature (T1)
- 300K
Area Ratio (Ae/Ath)
- 10, 20, 50, 100, 500, 1000
Ambient Pressure (Pa)
- 0.1 bar
Case No.
Ammonium Perchlorate
HTPB
Aluminum
1
87
13
0
2
82
13
5
3
77
13
10
4
72
13
15
Plots: 1. Specific Impulse (Isp) Variation with Area ratio (Ae/Ath). 2. Characteristic Velocity (C*) Variation with Area ratio (Ae/Ath). 3. Exhaust Velocity (Ve) Variation with Area ratio (Ae/Ath). 4. Thrust Coefficient (CF) Variation with Area ratio (Ae/Ath). Calculation of Specific Impulse (Isp) at Ambient Pressure Pa = 0.1 bar: In the NASA CEArun, there is no option to give the ambient pressure as input. Hence the Specific Impulse is calculated for the ambient Pressure Pa = 0.1 bar as follows, The Specific Impulse at Vacuum condition is specified in the NASA CEArun and was taken from the CEArun Program. Using this Isp, vac , the specific impulse at given ambient pressure is calculated by the relation, 𝐴𝑒 𝑃𝑎 𝐼𝑠𝑝,𝑃𝑎 = 𝐼𝑠𝑝,𝑣𝑎𝑐 − 𝐶 ∗ ∗ ( ) ∗ ( ) 𝐴𝑡ℎ 𝑃𝑐,𝑡
Results: Case-1: Fuel/Oxidizer weight percentage AP HTPB AL 87 13 0
Area ratio (Ae/At) Chamber Pr. (Pc,t) Pr. Ratio (Pc,t/Pe) Mach No. (M) Sonic Speed (a) Thrust Coeff. (CF) C_star Isp_vac Isp_0.1bar Exit Velocity(Ve)
10 84 83.681 3.311 748.2 1.6153 1533.6 2660.5 2642.243 2477.29
20 84 211.93 3.833 685.7 1.7141 1533.6 2773.4 2736.886 2628.288
50 84 705.1 4.546 611.5 1.8126 1533.6 2888.5 2797.214 2779.879
100 84 1729.78 5.105 561.8 1.8702 1533.6 2956.7 2774.129 2867.989
500 84 12756.2 6.559 459.4 1.9646 1533.6 3073 2160.143 3013.205
1000 84 29039.6 7.07 432.7 1.9949 1533.6 3112.1 1286.386 3059.189
Case-2: Fuel/Oxidizer weight percentage AP HTPB AL 82 13 5
Area ratio (Ae/At)
10
20
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
84
84
Pr. Ratio (Pc,t/Pe)
78.194
196.8
648.26
1570.78
11672.5
26553.7
Mach No. (M)
3.228
3.732
4.416
4.952
6.309
6.863
Sonic Speed (a)
782.8
720.9
646.5
596.1
493.7
461.3
Thrust Coeff. (CF)
1.6251
1.7304
1.8361
1.8982
2.003
2.036
C_star
1555.1
1555.1
1555.1
1555.1
1555.1
1555.1
Isp_vac
2726
2848.9
2975.2
3050.7
3181.3
3224.6
Isp_0.1bar
2707.487
2811.874
2882.635
2865.569
2255.645
1373.29
Exit Velocity(Ve)
2526.878
2690.399
2854.944
2951.887
3114.753
3165.902
Case-3: Fuel/Oxidizer weight percentage AP HTPB AL 77 13 10
Area ratio (Ae/At)
10
20
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
84
84
Pr. Ratio (Pc,t/Pe)
72.947
182.85
599.99
1451.21
10764.2
24878.3
Mach No. (M)
3.139
3.625
4.283
4.801
6.064
6.67
Sonic Speed (a)
816.6
756
681.5
630
528.3
488.8
Thrust Coeff. (CF)
1.6293
1.7419
1.8555
1.9225
2.0361
2.0723
C_star
1573.3
1573.3
1573.3
1573.3
1573.3
1573.3
Isp_vac
2779.1
2912.7
3050.5
3133.2
3276.6
3323.6
Isp_0.1bar
2760.37
2875.24 2956.851 2945.902 2340.112 1450.624
Exit Velocity(Ve)
2563.307
2740.5
2918.865
3024.63
3203.611 3260.296
Case-4: Fuel/Oxidizer weight percentage AP HTPB AL 72 13 15
Area ratio (Ae/At)
10
20
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
84
84
Pr. Ratio (Pc,t/Pe)
67.754
168.92
552.06
1334.94
9988.5
23382.1
Mach No. (M)
3.046
3.509
4.139
4.636
5.872
6.435
Sonic Speed (a)
848.1
790.7
717.5
665.6
558.9
519.6
Thrust Coeff. (CF)
1.6279
1.7488
1.8716
1.9444
2.068
2.1074
C_star
1586.8
1586.8
1586.8
1586.8
1586.8
1586.8
Isp_vac
2817.3
2962.8
3113.5
3204.2
3360.9
3411.8
Isp_0.1bar
2798.41
Exit Velocity(Ve)
2925.019 3019.048 3015.295 2416.376 1522.752
2583.313 2774.566 2969.733 3085.722 3281.861 3343.626
Graphs: 1. Specific Impulse (Isp) Vs Area Ratio (Ae/Ath).
Isp Vs Ae/Ath 3450 3200 2950
Isp (m/s)
2700 2450 2200 1950 1700
1450 1200
0
100
200
300
400
500
600
700
800
900
1000
1100
Ae/Ath [email protected]_1
[email protected]_2
[email protected]_3
[email protected]_4
Isp@Vacuum_1
Isp@Vacuum_2
Isp@Vacuum_3
Isp@Vacuum_4
2. Characteristic Velocity (C*) Vs Area Ratio (Ae/Ath).
C_Star Vs Ae/Ath 1590
C_Star (m/s)
1580 1570 1560 1550 1540 1530 0
200
400
600
800
1000
Ae/Ath C_Star_1
C_Star_2
C_Star_3
C_Star_4
1200
3. Exhaust Velocity (Ve) Vs Area Ratio (Ae/Ath).
Ve Vs Ae/Ath 3400 3300 3200
Ve (m/s)
3100
3000 2900 2800 2700 2600 2500 2400 0
100
200
300
400
500
600
700
800
900
1000
1100
800
900
1000
1100
Ae/Ath Ve_1
Ve_2
Ve_3
Ve_4
4. Thrust Coefficient (CF) Vs Area Ratio (Ae/Ath).
CF Vs Ae/Ath 2.15 2.1 2.05 2
CF
1.95 1.9 1.85 1.8 1.75 1.7 1.65 1.6 0
100
200
300
400
500
600
700
Ae/Ath CF_1
CF_2
CF_3
CF_4
Problem 2: EQUILIBRIUM FLOW LIQUID PROPELLANT
Oxidizer
- Liquid Oxygen
Fuel
- Liquid Hydrogen
Chamber Pressure (Pc)
- 84bar & 220bar
Initial Temperature (T1)
- LOX-90K, LH2-20K
Area Ratio (Ae/Ath)
- 50, 100, 500, 1000
Mixture Ratio (Ox/F)
- 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0
Mixture Ratio
Area Ratio
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Chamber Pressure (Pc) (bar)
Chamber Pressure (Pc) (bar)
84
220
50 100 500 1000
Plots: 1. Specific Impulse (Isp) Variation with Mixture ratio (Ox/F). 2. Characteristic Velocity (C*) Variation with Mixture ratio (Ox/F). 3. Exhaust Velocity (Ve) Variation with Mixture ratio (Ox/F). 4. Thrust Coefficient (CF) Variation with Mixture ratio (Ox/F). 5. Chamber Temperature (Tc) Variation with Mixture ratio (Ox/F). 6. Characteristic Velocity (C*) Variation with Area ratio (Ae/Ath). 7. Thrust Coefficient (CF) Variation with Area ratio (Ae/Ath).
Results: Case-1: Mixture ratio (Ox/F) 4
Area ratio (Ae/At) Chamber Pr. (Pc,t) Mixture Ratio (O/F) Pr. Ratio (Pc,t/Pe) Mach No. (M) Sonic Speed (a) Thrust Coeff. (CF) C_star Isp_vac Exit Velocity(Ve)
Mixture ratio (Ox/F) 4
Area ratio (Ae/At) Chamber Pr. (Pc,t) Mixture Ratio (O/F) Pr. Ratio (Pc,t/Pe) Mach No. (M) Sonic Speed (a) Thrust Coeff. (CF) C_star Isp_vac Exit Velocity(Ve)
Chamber Pressure Pc,t (bar) 84
50 84 4 847.64 4.791 905.8 1.7949 2417.9 4482.5 4339.688 Chamber Pressure Pc,t (bar) 220
50 220 4 850.65 4.798 904.8 1.7937 2420.3 4483.4 4341.23
Chamber Temp Tc (K) 2952.19
100 84 4 2214.51 5.522 807.7 1.8446 2417.9 4569.2 4460.119
500 84 4 20557.1 7.618 609.3 1.9196 2417.9 4700.2 4641.647
1000 84 4 53665.8 8.727 537.5 1.9401 2417.9 4736 4690.763
Chamber Temp Tc (K) 2976.77
100 220 4 2222.35 5.529 806.8 1.8432 2420.3 4569.9 4460.797
500 220 4 20629.7 7.628 608.6 1.9179 2420.3 4700.6 4642.401
1000 220 4 52916.5 9.717 482.7 1.938 2420.3 4736.3 4690.396
Case-2: Mixture ratio (Ox/F) 4.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3142.9
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
4.5
4.5
4.5
4.5
Pr. Ratio (Pc,t/Pe)
778.98
2012.95
18359.9
47650.7
Mach No. (M)
4.648
5.327
7.278
8.318
Sonic Speed (a)
934.5
839.7
641.8
568.2
Thrust Coeff. (CF)
1.8104
1.8642
1.9468
1.9696
C_star
2399.4
2399.4
2399.4
2399.4
Isp_vac
4498
4592.1
4736.4
4776.3
Exit Velocity(Ve)
4343.556
4473.082
4671.02
4726.288
Mixture ratio (Ox/F) 4.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3184.58
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
4.5
4.5
4.5
4.5
Pr. Ratio (Pc,t/Pe)
784.4
2027
18489.2
47986.9
Mach No. (M)
4.66
5.34
7.296
8.339
Sonic Speed (a)
932.7
838
640.3
566.9
Thrust Coeff. (CF)
1.8077
1.8611
1.9431
1.9658
C_star
2404.5
2404.5
2404.5
2404.5
Isp_vac
4500
4593.7
4737.3
4776.9
Exit Velocity(Ve)
4346.382
4474.92
4671.629
4727.379
Case-3: Mixture ratio (Ox/F) 5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3296.67
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
5
5
5
5
Pr. Ratio (Pc,t/Pe)
718.73
1834.76
16379.5
42245.1
Mach No. (M)
4.521
5.15
6.956
7.922
Sonic Speed (a)
958.8
868.4
674
599.4
Thrust Coeff. (CF)
1.8263
1.8842
1.9748
2.0004
C_star
2373.8
2373.8
2373.8
2373.8
Isp_vac
4500.4
4602
4760.3
4804.6
Exit Velocity(Ve)
4334.735
4472.26
4688.344
4748.447
Mixture ratio (Ox/F) 5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3357.82
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
5
5
5
5
Pr. Ratio (Pc,t/Pe)
726.86
1855.68
16570.3
42739.7
Mach No. (M)
4.54
5.171
6.984
7.955
Sonic Speed (a)
955.9
865.6
671.5
597.1
Thrust Coeff. (CF)
1.8217
1.879
1.9686
1.9938
C_star
2382.4
2382.4
2382.4
2382.4
Isp_vac
4504
4604.8
4761.8
4805.9
Exit Velocity(Ve)
4339.786
4476.018
4689.756
4749.931
Case-4: Mixture ratio (Ox/F) 5.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3416.44
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
5.5
5.5
5.5
5.5
Pr. Ratio (Pc,t/Pe)
665.82
1678.55
14618.1
37411.4
Mach No. (M)
4.406
4.992
6.656
7.548
Sonic Speed (a)
979.5
893.8
705.2
630.7
Thrust Coeff. (CF)
1.8423
1.9043
2.0034
2.0319
C_star
2342.9
2342.9
2342.9
2342.9
Isp_vac
4492.2
4601.1
4773.8
4823.1
Exit Velocity(Ve)
4315.677
4461.85
4693.811
4760.524
Mixture ratio (Ox/F) 5.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3497.57
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
5.5
5.5
5.5
5.5
Pr. Ratio (Pc,t/Pe)
676.67
1706.16
14866.6
38054.1
Mach No. (M)
4.433
5.021
6.695
7.593
Sonic Speed (a)
975.4
889.8
701.6
627.3
Thrust Coeff. (CF)
1.8359
1.8969
1.9945
2.0225
C_star
2355.2
2355.2
2355.2
2355.2
Isp_vac
4497.9
4605.6
4776.5
4825.1
Exit Velocity(Ve)
4323.948
4467.686
4697.212
4763.089
Case-5: Mixture ratio (Ox/F) 6
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3504.98
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
6
6
6
6
Pr. Ratio (Pc,t/Pe)
618.81
1541.64
13069.3
33134.6
Mach No. (M)
4.299
4.847
6.38
7.198
Sonic Speed (a)
997.6
916.3
735.2
661.8
Thrust Coeff. (CF)
1.858
1.9243
2.0322
2.0639
C_star
2307.9
2307.9
2307.9
2307.9
Isp_vac
4474.7
4590.7
4778.4
4832.9
Exit Velocity(Ve)
4288.682
4441.306
4690.576
4763.636
Mixture ratio (Ox/F) 6
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3604.83
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
6
6
6
6
Pr. Ratio (Pc,t/Pe)
632.22
1575.3
13366.5
33900.5
Mach No. (M)
4.334
4.885
6.431
7.256
Sonic Speed (a)
992.1
910.9
730.2
657
Thrust Coeff. (CF)
1.8502
1.9151
2.0207
2.0517
C_star
2323.7
2323.7
2323.7
2323.7
Isp_vac
4483.2
4597.6
4782.5
4836.1
Exit Velocity(Ve)
4299.761
4449.747
4695.916
4767.192
Case-6: Mixture ratio (Ox/F) 6.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3565.33
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
6.5
6.5
6.5
6.5
Pr. Ratio (Pc,t/Pe)
576.12
1419.96
11711.6
29374.9
Mach No. (M)
4.193
4.71
6.125
6.873
Sonic Speed (a)
1013.9
936.6
763.7
692.2
Thrust Coeff. (CF)
1.8729
1.9435
2.0607
2.0958
C_star
2270
2270
2270
2270
Isp_vac
4448.5
4571.7
4774.7
4834.8
Exit Velocity(Ve)
4251.283
4411.386
4677.663
4757.491
Mixture ratio (Ox/F) 6.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3680.73
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
6.5
6.5
6.5
6.5
Pr. Ratio (Pc,t/Pe)
591.76
1458.71
12045.6
30231.1
Mach No. (M)
4.237
4.758
6.188
6.945
Sonic Speed (a)
1007
929.8
757.2
686
Thrust Coeff. (CF)
1.8644
1.9332
2.0472
2.0814
C_star
2288.7
2288.7
2288.7
2288.7
Isp_vac
4460.5
4581.5
4780.6
4839.5
Exit Velocity(Ve)
4266.659
4423.988
4685.554
4764.27
Case-7: Mixture ratio (Ox/F) 7
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3601.19
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
7
7
7
7
Pr. Ratio (Pc,t/Pe)
536.2
1309.21
10515.4
26068.7
Mach No. (M)
4.086
4.575
5.888
6.569
Sonic Speed (a)
1029.2
955.9
790.9
722.1
Thrust Coeff. (CF)
1.8855
1.9609
2.0879
2.1268
C_star
2230.3
2230.3
2230.3
2230.3
Isp_vac
4413.2
4543.8
4762.7
4828.9
Exit Velocity(Ve)
4205.311
4373.243
4656.819
4743.475
Mixture ratio (Ox/F) 7
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3727.37
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
7
7
7
7
Pr. Ratio (Pc,t/Pe)
553.57
1351.85
10872.7
26977.6
Mach No. (M)
4.139
4.633
5.961
6.653
Sonic Speed (a)
1021.1
947.6
783
714.3
Thrust Coeff. (CF)
1.8776
1.9507
2.0736
2.1112
C_star
2250.9
2250.9
2250.9
2250.9
Isp_vac
4429.5
4557.2
4771
4835.6
Exit Velocity(Ve)
4226.333
4390.231
4667.463
4752.238
Case-8: Mixture ratio (Ox/F) 7.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3617.09
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
7.5
7.5
7.5
7.5
Pr. Ratio (Pc,t/Pe)
497.84
1204.04
9436.4
23112.1
Mach No. (M)
3.976
4.432
5.654
6.275
Sonic Speed (a)
1042.8
975.4
818
752.1
Thrust Coeff. (CF)
1.8934
1.9742
2.1121
2.1551
C_star
2189.9
2189.9
2189.9
2189.9
Isp_vac
4366.3
4505.1
4741.3
4814.1
Exit Velocity(Ve)
4146.173
4322.973
4624.972
4719.428
Mixture ratio (Ox/F) 7.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3748.64
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
7.5
7.5
7.5
7.5
Pr. Ratio (Pc,t/Pe)
515.89
1249.06
9802.92
24035.4
Mach No. (M)
4.032
4.5
5.738
6.37
Sonic Speed (a)
1035
965.8
808.6
742.7
Thrust Coeff. (CF)
1.8874
1.9654
2.0984
2.1398
C_star
2211.1
2211.1
2211.1
2211.1
Isp_vac
4387.6
4522.8
4752.6
4823.3
Exit Velocity(Ve)
4173.12
4346.1
4639.747
4730.999
Case-9: Chamber Pressure Pc,t (bar) 84
Mixture ratio (Ox/F) 8
Chamber Temp Tc (K) 3617.76
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
8
8
8
8
Pr. Ratio (Pc,t/Pe)
474.49
1121.32
8549.12
20727.2
Mach No. (M)
3.943
4.333
5.436
6.009
Sonic Speed (a)
1032.6
981.2
840.7
777.4
Thrust Coeff. (CF)
1.8941
1.9776
2.1258
2.1729
C_star
2149.8
2149.8
2149.8
2149.8
Isp_vac
4298.5
4443.3
4695.8
4775.2
Exit Velocity(Ve)
4071.542
4251.54
4570.045
4671.397
Mixture ratio (Ox/F) 8
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3750
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
8
8
8
8
Pr. Ratio (Pc,t/Pe)
488.55
1162.13
8909.71
21626.6
Mach No. (M)
3.978
4.386
5.527
6.111
Sonic Speed (a)
1031.1
975.4
830.1
766.9
Thrust Coeff. (CF)
1.8892
1.9707
2.1136
2.1588
C_star
2170.9
2170.9
2170.9
2170.9
Isp_vac
4323.4
4464.9
4710.1
4787
Exit Velocity(Ve)
4101.716
4278.104
4587.963
4686.526
Graphs: 1. Specific Impulse (Isp) Vs Mixture Ratio (Ox/F).
Isp@Vacuum (m/s)
Isp Vs Mixture Ratio 4850 4800 4750 4700 4650 4600 4550 4500 4450 4400 4350 4300 4250 3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
8
8.5
Mixture Ratio (Ox/F) Isp@Ae/At=50_84
Isp@Ae/At=50_220
Isp@Ae/At=100_84
Isp@Ae/At=100_220
Isp@Ae/At=500_84
Isp@Ae/At=500_220
Isp@Ae/At=1000_84
Isp@Ae/At=1000_220
2. Characteristic Velocity (C*) Vs Mixture Ratio (Ox/F).
C_Star Vs Mixture Ratio 2450 2400
C_Star (m/s)
2350 2300 2250 2200 2150 2100 3.5
4
4.5
5
5.5
6
6.5
Mixture Ratio (Ox/F) C_star_Pe=220
C_star_Pe=84
7
7.5
3. Exhaust Velocity (Ve) Vs Mixture Ratio (Ox/F).
Ve (m/s)
Ve Vs Mixture Ratio 4800 4750 4700 4650 4600 4550 4500 4450 4400 4350 4300 4250 4200 4150 4100 4050 3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
Mixture Ratio (Ox/F) Ve_Ae/At=50_Pe=84
Ve_Ae/At=50_Pe=220
Ve_Ae/At=100_Pe=84
Ve_Ae/At=100_Pe=220
Ve_Ae/At=500_Pe=84
Ve_Ae/At=500_Pe=220
Ve_Ae/At=1000_Pe=84
Ve_Ae/At=1000_Pe=220
4. Thrust Coefficient (CF) Vs Mixture Ratio (Ox/F).
CF Vs Mixture Ratio 2.15 2.1 2.05
CF
2 1.95 1.9 1.85 1.8 1.75 3.5
4
4.5
5
5.5
6
6.5
7
7.5
Mixture Ratio (Ox/F) CF_Ae/At=50_Pe=84
CF_Ae/At=50_Pe=220
CF_Ae/At=100_Pe=84
CF_Ae/At=100_Pe=220
CF_Ae/At=500_Pe=84
CF_Ae/At=500_Pe=220
CF_Ae/At=1000_Pe=84
CF_Ae/At=1000_Pe=220
8
8.5
5. Chamber Temperature (TC) Vs Mixture Ratio (Ox/F).
Tc Vs Mixture Ratio 3800 3700 3600
Tc (K)
3500 3400 3300 3200 3100 3000 2900 3.5
4
4.5
5
5.5
6
6.5
7
7.5
800
900
8
8.5
Mixture Ratio (Ox/F) Tc_Pe=84
Tc_Pe=220
6. Characteristic Velocity (C*) Vs Area Ratio (Ae/Ath).
C_Star (m/s)
C_Star Vs Area Ratio 2450 2425 2400 2375 2350 2325 2300 2275 2250 2225 2200 2175 2150 2125 0
100
200
300
400
500
600
700
1000
Area Ratio (Ae/At) C_Star_Pe=84_O/F=4
C_Star_Pe=220_O/F=4
C_Star_Pe=84_O/F=4.5
C_Star_Pe=220_O/F=4.5
C_Star_Pe=84_O/F=5
C_Star_Pe=220_O/F=5
C_Star_Pe=84_O/F=5.5
C_Star_Pe=220_O/F=5.5
C_Star_Pe=84_O/F=6
C_Star_Pe=220_O/F=6
C_Star_Pe=84_O/F=6.5
C_Star_Pe=220_O/F=6.5
C_Star_Pe=84_O/F=7
C_Star_Pe=220_O/F=7
C_Star_Pe=84_O/F=7.5
C_Star_Pe=220_O/F=7.5
C_Star_Pe=84_O/F=8
C_Star_Pe=220_O/F=8
1100
7. Thrust Coefficient (CF) Vs Area Ratio (Ae/Ath).
CF Vs Area Ratio 2.2
2.15
2.1
2.05
CF
2
1.95
1.9
1.85
1.8
1.75 0
100
200
300
400
500
600
700
800
900
1000
Area Ratio (Ae/At) CF_Pe=84_O/F=4
CF_Pe=220_O/F=4
CF_Pe=84_O/F=4.5
CF_Pe=220_O/F=4.5
CF_Pe=84_O/F=5
CF_Pe=220_O/F=5
CF_Pe=84_O/F=5.5
CF_Pe=220_O/F=5.5
CF_Pe=84_O/F=6
CF_Pe=220_O/F=6
CF_Pe=84_O/F=6.5
CF_Pe=220_O/F=6.5
CF_Pe=84_O/F=7
CF_Pe=220_O/F=7
CF_Pe=84_O/F=7.5
CF_Pe=220_O/F=7.5
CF_Pe=84_O/F=8
CF_Pe=220_O/F=8
1100
Name of the Student KANDIMALLA CHACHA SRIHARI (183010034)
Software Used: NASA CEArun
Problem 1: EQUILIBRIUM FLOW
Oxidizer
- Ammonium Perchlorate
Fuel
- Hydroxyl Terminated Poly Butadiene (HTPB)
Chamber Pressure (Pc)
- 84bar
Initial Temperature (T1)
- 300K
Area Ratio (Ae/Ath)
- 10, 20, 50, 100, 500, 1000
Ambient Pressure (Pa)
- 0.1 bar
Case No.
Ammonium Perchlorate
HTPB
Aluminum
1
87
13
0
2
82
13
5
3
77
13
10
4
72
13
15
Plots: 1. Specific Impulse (Isp) Variation with Area ratio (Ae/Ath). 2. Characteristic Velocity (C*) Variation with Area ratio (Ae/Ath). 3. Exhaust Velocity (Ve) Variation with Area ratio (Ae/Ath). 4. Thrust Coefficient (CF) Variation with Area ratio (Ae/Ath). Calculation of Specific Impulse (Isp) at Ambient Pressure Pa = 0.1 bar: In the NASA CEArun, there is no option to give the ambient pressure as input. Hence the Specific Impulse is calculated for the ambient Pressure Pa = 0.1 bar as follows, The Specific Impulse at Vacuum condition is specified in the NASA CEArun and was taken from the CEArun Program. Using this Isp, vac , the specific impulse at given ambient pressure is calculated by the relation, 𝐴𝑒 𝑃𝑎 𝐼𝑠𝑝,𝑃𝑎 = 𝐼𝑠𝑝,𝑣𝑎𝑐 − 𝐶 ∗ ∗ ( ) ∗ ( ) 𝐴𝑡ℎ 𝑃𝑐,𝑡
Results: Case-1: Fuel/Oxidizer weight percentage AP HTPB AL 87 13 0
Area ratio (Ae/At) Chamber Pr. (Pc,t) Pr. Ratio (Pc,t/Pe) Mach No. (M) Sonic Speed (a) Thrust Coeff. (CF) C_star Isp_vac Isp_0.1bar Exit Velocity(Ve)
10 84 83.681 3.311 748.2 1.6153 1533.6 2660.5 2642.243 2477.29
20 84 211.93 3.833 685.7 1.7141 1533.6 2773.4 2736.886 2628.288
50 84 705.1 4.546 611.5 1.8126 1533.6 2888.5 2797.214 2779.879
100 84 1729.78 5.105 561.8 1.8702 1533.6 2956.7 2774.129 2867.989
500 84 12756.2 6.559 459.4 1.9646 1533.6 3073 2160.143 3013.205
1000 84 29039.6 7.07 432.7 1.9949 1533.6 3112.1 1286.386 3059.189
Case-2: Fuel/Oxidizer weight percentage AP HTPB AL 82 13 5
Area ratio (Ae/At)
10
20
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
84
84
Pr. Ratio (Pc,t/Pe)
78.194
196.8
648.26
1570.78
11672.5
26553.7
Mach No. (M)
3.228
3.732
4.416
4.952
6.309
6.863
Sonic Speed (a)
782.8
720.9
646.5
596.1
493.7
461.3
Thrust Coeff. (CF)
1.6251
1.7304
1.8361
1.8982
2.003
2.036
C_star
1555.1
1555.1
1555.1
1555.1
1555.1
1555.1
Isp_vac
2726
2848.9
2975.2
3050.7
3181.3
3224.6
Isp_0.1bar
2707.487
2811.874
2882.635
2865.569
2255.645
1373.29
Exit Velocity(Ve)
2526.878
2690.399
2854.944
2951.887
3114.753
3165.902
Case-3: Fuel/Oxidizer weight percentage AP HTPB AL 77 13 10
Area ratio (Ae/At)
10
20
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
84
84
Pr. Ratio (Pc,t/Pe)
72.947
182.85
599.99
1451.21
10764.2
24878.3
Mach No. (M)
3.139
3.625
4.283
4.801
6.064
6.67
Sonic Speed (a)
816.6
756
681.5
630
528.3
488.8
Thrust Coeff. (CF)
1.6293
1.7419
1.8555
1.9225
2.0361
2.0723
C_star
1573.3
1573.3
1573.3
1573.3
1573.3
1573.3
Isp_vac
2779.1
2912.7
3050.5
3133.2
3276.6
3323.6
Isp_0.1bar
2760.37
2875.24 2956.851 2945.902 2340.112 1450.624
Exit Velocity(Ve)
2563.307
2740.5
2918.865
3024.63
3203.611 3260.296
Case-4: Fuel/Oxidizer weight percentage AP HTPB AL 72 13 15
Area ratio (Ae/At)
10
20
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
84
84
Pr. Ratio (Pc,t/Pe)
67.754
168.92
552.06
1334.94
9988.5
23382.1
Mach No. (M)
3.046
3.509
4.139
4.636
5.872
6.435
Sonic Speed (a)
848.1
790.7
717.5
665.6
558.9
519.6
Thrust Coeff. (CF)
1.6279
1.7488
1.8716
1.9444
2.068
2.1074
C_star
1586.8
1586.8
1586.8
1586.8
1586.8
1586.8
Isp_vac
2817.3
2962.8
3113.5
3204.2
3360.9
3411.8
Isp_0.1bar
2798.41
Exit Velocity(Ve)
2925.019 3019.048 3015.295 2416.376 1522.752
2583.313 2774.566 2969.733 3085.722 3281.861 3343.626
Graphs: 1. Specific Impulse (Isp) Vs Area Ratio (Ae/Ath).
Isp Vs Ae/Ath 3450 3200 2950
Isp (m/s)
2700 2450 2200 1950 1700
1450 1200
0
100
200
300
400
500
600
700
800
900
1000
1100
Ae/Ath [email protected]_1
[email protected]_2
[email protected]_3
[email protected]_4
Isp@Vacuum_1
Isp@Vacuum_2
Isp@Vacuum_3
Isp@Vacuum_4
2. Characteristic Velocity (C*) Vs Area Ratio (Ae/Ath).
C_Star Vs Ae/Ath 1590
C_Star (m/s)
1580 1570 1560 1550 1540 1530 0
200
400
600
800
1000
Ae/Ath C_Star_1
C_Star_2
C_Star_3
C_Star_4
1200
3. Exhaust Velocity (Ve) Vs Area Ratio (Ae/Ath).
Ve Vs Ae/Ath 3400 3300 3200
Ve (m/s)
3100
3000 2900 2800 2700 2600 2500 2400 0
100
200
300
400
500
600
700
800
900
1000
1100
800
900
1000
1100
Ae/Ath Ve_1
Ve_2
Ve_3
Ve_4
4. Thrust Coefficient (CF) Vs Area Ratio (Ae/Ath).
CF Vs Ae/Ath 2.15 2.1 2.05 2
CF
1.95 1.9 1.85 1.8 1.75 1.7 1.65 1.6 0
100
200
300
400
500
600
700
Ae/Ath CF_1
CF_2
CF_3
CF_4
Problem 2: EQUILIBRIUM FLOW LIQUID PROPELLANT
Oxidizer
- Liquid Oxygen
Fuel
- Liquid Hydrogen
Chamber Pressure (Pc)
- 84bar & 220bar
Initial Temperature (T1)
- LOX-90K, LH2-20K
Area Ratio (Ae/Ath)
- 50, 100, 500, 1000
Mixture Ratio (Ox/F)
- 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0
Mixture Ratio
Area Ratio
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Chamber Pressure (Pc) (bar)
Chamber Pressure (Pc) (bar)
84
220
50 100 500 1000
Plots: 1. Specific Impulse (Isp) Variation with Mixture ratio (Ox/F). 2. Characteristic Velocity (C*) Variation with Mixture ratio (Ox/F). 3. Exhaust Velocity (Ve) Variation with Mixture ratio (Ox/F). 4. Thrust Coefficient (CF) Variation with Mixture ratio (Ox/F). 5. Chamber Temperature (Tc) Variation with Mixture ratio (Ox/F). 6. Characteristic Velocity (C*) Variation with Area ratio (Ae/Ath). 7. Thrust Coefficient (CF) Variation with Area ratio (Ae/Ath).
Results: Case-1: Mixture ratio (Ox/F) 4
Area ratio (Ae/At) Chamber Pr. (Pc,t) Mixture Ratio (O/F) Pr. Ratio (Pc,t/Pe) Mach No. (M) Sonic Speed (a) Thrust Coeff. (CF) C_star Isp_vac Exit Velocity(Ve)
Mixture ratio (Ox/F) 4
Area ratio (Ae/At) Chamber Pr. (Pc,t) Mixture Ratio (O/F) Pr. Ratio (Pc,t/Pe) Mach No. (M) Sonic Speed (a) Thrust Coeff. (CF) C_star Isp_vac Exit Velocity(Ve)
Chamber Pressure Pc,t (bar) 84
50 84 4 847.64 4.791 905.8 1.7949 2417.9 4482.5 4339.688 Chamber Pressure Pc,t (bar) 220
50 220 4 850.65 4.798 904.8 1.7937 2420.3 4483.4 4341.23
Chamber Temp Tc (K) 2952.19
100 84 4 2214.51 5.522 807.7 1.8446 2417.9 4569.2 4460.119
500 84 4 20557.1 7.618 609.3 1.9196 2417.9 4700.2 4641.647
1000 84 4 53665.8 8.727 537.5 1.9401 2417.9 4736 4690.763
Chamber Temp Tc (K) 2976.77
100 220 4 2222.35 5.529 806.8 1.8432 2420.3 4569.9 4460.797
500 220 4 20629.7 7.628 608.6 1.9179 2420.3 4700.6 4642.401
1000 220 4 52916.5 9.717 482.7 1.938 2420.3 4736.3 4690.396
Case-2: Mixture ratio (Ox/F) 4.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3142.9
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
4.5
4.5
4.5
4.5
Pr. Ratio (Pc,t/Pe)
778.98
2012.95
18359.9
47650.7
Mach No. (M)
4.648
5.327
7.278
8.318
Sonic Speed (a)
934.5
839.7
641.8
568.2
Thrust Coeff. (CF)
1.8104
1.8642
1.9468
1.9696
C_star
2399.4
2399.4
2399.4
2399.4
Isp_vac
4498
4592.1
4736.4
4776.3
Exit Velocity(Ve)
4343.556
4473.082
4671.02
4726.288
Mixture ratio (Ox/F) 4.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3184.58
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
4.5
4.5
4.5
4.5
Pr. Ratio (Pc,t/Pe)
784.4
2027
18489.2
47986.9
Mach No. (M)
4.66
5.34
7.296
8.339
Sonic Speed (a)
932.7
838
640.3
566.9
Thrust Coeff. (CF)
1.8077
1.8611
1.9431
1.9658
C_star
2404.5
2404.5
2404.5
2404.5
Isp_vac
4500
4593.7
4737.3
4776.9
Exit Velocity(Ve)
4346.382
4474.92
4671.629
4727.379
Case-3: Mixture ratio (Ox/F) 5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3296.67
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
5
5
5
5
Pr. Ratio (Pc,t/Pe)
718.73
1834.76
16379.5
42245.1
Mach No. (M)
4.521
5.15
6.956
7.922
Sonic Speed (a)
958.8
868.4
674
599.4
Thrust Coeff. (CF)
1.8263
1.8842
1.9748
2.0004
C_star
2373.8
2373.8
2373.8
2373.8
Isp_vac
4500.4
4602
4760.3
4804.6
Exit Velocity(Ve)
4334.735
4472.26
4688.344
4748.447
Mixture ratio (Ox/F) 5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3357.82
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
5
5
5
5
Pr. Ratio (Pc,t/Pe)
726.86
1855.68
16570.3
42739.7
Mach No. (M)
4.54
5.171
6.984
7.955
Sonic Speed (a)
955.9
865.6
671.5
597.1
Thrust Coeff. (CF)
1.8217
1.879
1.9686
1.9938
C_star
2382.4
2382.4
2382.4
2382.4
Isp_vac
4504
4604.8
4761.8
4805.9
Exit Velocity(Ve)
4339.786
4476.018
4689.756
4749.931
Case-4: Mixture ratio (Ox/F) 5.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3416.44
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
5.5
5.5
5.5
5.5
Pr. Ratio (Pc,t/Pe)
665.82
1678.55
14618.1
37411.4
Mach No. (M)
4.406
4.992
6.656
7.548
Sonic Speed (a)
979.5
893.8
705.2
630.7
Thrust Coeff. (CF)
1.8423
1.9043
2.0034
2.0319
C_star
2342.9
2342.9
2342.9
2342.9
Isp_vac
4492.2
4601.1
4773.8
4823.1
Exit Velocity(Ve)
4315.677
4461.85
4693.811
4760.524
Mixture ratio (Ox/F) 5.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3497.57
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
5.5
5.5
5.5
5.5
Pr. Ratio (Pc,t/Pe)
676.67
1706.16
14866.6
38054.1
Mach No. (M)
4.433
5.021
6.695
7.593
Sonic Speed (a)
975.4
889.8
701.6
627.3
Thrust Coeff. (CF)
1.8359
1.8969
1.9945
2.0225
C_star
2355.2
2355.2
2355.2
2355.2
Isp_vac
4497.9
4605.6
4776.5
4825.1
Exit Velocity(Ve)
4323.948
4467.686
4697.212
4763.089
Case-5: Mixture ratio (Ox/F) 6
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3504.98
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
6
6
6
6
Pr. Ratio (Pc,t/Pe)
618.81
1541.64
13069.3
33134.6
Mach No. (M)
4.299
4.847
6.38
7.198
Sonic Speed (a)
997.6
916.3
735.2
661.8
Thrust Coeff. (CF)
1.858
1.9243
2.0322
2.0639
C_star
2307.9
2307.9
2307.9
2307.9
Isp_vac
4474.7
4590.7
4778.4
4832.9
Exit Velocity(Ve)
4288.682
4441.306
4690.576
4763.636
Mixture ratio (Ox/F) 6
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3604.83
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
6
6
6
6
Pr. Ratio (Pc,t/Pe)
632.22
1575.3
13366.5
33900.5
Mach No. (M)
4.334
4.885
6.431
7.256
Sonic Speed (a)
992.1
910.9
730.2
657
Thrust Coeff. (CF)
1.8502
1.9151
2.0207
2.0517
C_star
2323.7
2323.7
2323.7
2323.7
Isp_vac
4483.2
4597.6
4782.5
4836.1
Exit Velocity(Ve)
4299.761
4449.747
4695.916
4767.192
Case-6: Mixture ratio (Ox/F) 6.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3565.33
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
6.5
6.5
6.5
6.5
Pr. Ratio (Pc,t/Pe)
576.12
1419.96
11711.6
29374.9
Mach No. (M)
4.193
4.71
6.125
6.873
Sonic Speed (a)
1013.9
936.6
763.7
692.2
Thrust Coeff. (CF)
1.8729
1.9435
2.0607
2.0958
C_star
2270
2270
2270
2270
Isp_vac
4448.5
4571.7
4774.7
4834.8
Exit Velocity(Ve)
4251.283
4411.386
4677.663
4757.491
Mixture ratio (Ox/F) 6.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3680.73
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
6.5
6.5
6.5
6.5
Pr. Ratio (Pc,t/Pe)
591.76
1458.71
12045.6
30231.1
Mach No. (M)
4.237
4.758
6.188
6.945
Sonic Speed (a)
1007
929.8
757.2
686
Thrust Coeff. (CF)
1.8644
1.9332
2.0472
2.0814
C_star
2288.7
2288.7
2288.7
2288.7
Isp_vac
4460.5
4581.5
4780.6
4839.5
Exit Velocity(Ve)
4266.659
4423.988
4685.554
4764.27
Case-7: Mixture ratio (Ox/F) 7
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3601.19
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
7
7
7
7
Pr. Ratio (Pc,t/Pe)
536.2
1309.21
10515.4
26068.7
Mach No. (M)
4.086
4.575
5.888
6.569
Sonic Speed (a)
1029.2
955.9
790.9
722.1
Thrust Coeff. (CF)
1.8855
1.9609
2.0879
2.1268
C_star
2230.3
2230.3
2230.3
2230.3
Isp_vac
4413.2
4543.8
4762.7
4828.9
Exit Velocity(Ve)
4205.311
4373.243
4656.819
4743.475
Mixture ratio (Ox/F) 7
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3727.37
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
7
7
7
7
Pr. Ratio (Pc,t/Pe)
553.57
1351.85
10872.7
26977.6
Mach No. (M)
4.139
4.633
5.961
6.653
Sonic Speed (a)
1021.1
947.6
783
714.3
Thrust Coeff. (CF)
1.8776
1.9507
2.0736
2.1112
C_star
2250.9
2250.9
2250.9
2250.9
Isp_vac
4429.5
4557.2
4771
4835.6
Exit Velocity(Ve)
4226.333
4390.231
4667.463
4752.238
Case-8: Mixture ratio (Ox/F) 7.5
Chamber Pressure Pc,t (bar) 84
Chamber Temp Tc (K) 3617.09
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
7.5
7.5
7.5
7.5
Pr. Ratio (Pc,t/Pe)
497.84
1204.04
9436.4
23112.1
Mach No. (M)
3.976
4.432
5.654
6.275
Sonic Speed (a)
1042.8
975.4
818
752.1
Thrust Coeff. (CF)
1.8934
1.9742
2.1121
2.1551
C_star
2189.9
2189.9
2189.9
2189.9
Isp_vac
4366.3
4505.1
4741.3
4814.1
Exit Velocity(Ve)
4146.173
4322.973
4624.972
4719.428
Mixture ratio (Ox/F) 7.5
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3748.64
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
7.5
7.5
7.5
7.5
Pr. Ratio (Pc,t/Pe)
515.89
1249.06
9802.92
24035.4
Mach No. (M)
4.032
4.5
5.738
6.37
Sonic Speed (a)
1035
965.8
808.6
742.7
Thrust Coeff. (CF)
1.8874
1.9654
2.0984
2.1398
C_star
2211.1
2211.1
2211.1
2211.1
Isp_vac
4387.6
4522.8
4752.6
4823.3
Exit Velocity(Ve)
4173.12
4346.1
4639.747
4730.999
Case-9: Chamber Pressure Pc,t (bar) 84
Mixture ratio (Ox/F) 8
Chamber Temp Tc (K) 3617.76
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
84
84
84
84
Mixture Ratio (O/F)
8
8
8
8
Pr. Ratio (Pc,t/Pe)
474.49
1121.32
8549.12
20727.2
Mach No. (M)
3.943
4.333
5.436
6.009
Sonic Speed (a)
1032.6
981.2
840.7
777.4
Thrust Coeff. (CF)
1.8941
1.9776
2.1258
2.1729
C_star
2149.8
2149.8
2149.8
2149.8
Isp_vac
4298.5
4443.3
4695.8
4775.2
Exit Velocity(Ve)
4071.542
4251.54
4570.045
4671.397
Mixture ratio (Ox/F) 8
Chamber Pressure Pc,t (bar) 220
Chamber Temp Tc (K) 3750
Area ratio (Ae/At)
50
100
500
1000
Chamber Pr. (Pc,t)
220
220
220
220
Mixture Ratio (O/F)
8
8
8
8
Pr. Ratio (Pc,t/Pe)
488.55
1162.13
8909.71
21626.6
Mach No. (M)
3.978
4.386
5.527
6.111
Sonic Speed (a)
1031.1
975.4
830.1
766.9
Thrust Coeff. (CF)
1.8892
1.9707
2.1136
2.1588
C_star
2170.9
2170.9
2170.9
2170.9
Isp_vac
4323.4
4464.9
4710.1
4787
Exit Velocity(Ve)
4101.716
4278.104
4587.963
4686.526
Graphs: 1. Specific Impulse (Isp) Vs Mixture Ratio (Ox/F).
Isp@Vacuum (m/s)
Isp Vs Mixture Ratio 4850 4800 4750 4700 4650 4600 4550 4500 4450 4400 4350 4300 4250 3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
8
8.5
Mixture Ratio (Ox/F) Isp@Ae/At=50_84
Isp@Ae/At=50_220
Isp@Ae/At=100_84
Isp@Ae/At=100_220
Isp@Ae/At=500_84
Isp@Ae/At=500_220
Isp@Ae/At=1000_84
Isp@Ae/At=1000_220
2. Characteristic Velocity (C*) Vs Mixture Ratio (Ox/F).
C_Star Vs Mixture Ratio 2450 2400
C_Star (m/s)
2350 2300 2250 2200 2150 2100 3.5
4
4.5
5
5.5
6
6.5
Mixture Ratio (Ox/F) C_star_Pe=220
C_star_Pe=84
7
7.5
3. Exhaust Velocity (Ve) Vs Mixture Ratio (Ox/F).
Ve (m/s)
Ve Vs Mixture Ratio 4800 4750 4700 4650 4600 4550 4500 4450 4400 4350 4300 4250 4200 4150 4100 4050 3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
Mixture Ratio (Ox/F) Ve_Ae/At=50_Pe=84
Ve_Ae/At=50_Pe=220
Ve_Ae/At=100_Pe=84
Ve_Ae/At=100_Pe=220
Ve_Ae/At=500_Pe=84
Ve_Ae/At=500_Pe=220
Ve_Ae/At=1000_Pe=84
Ve_Ae/At=1000_Pe=220
4. Thrust Coefficient (CF) Vs Mixture Ratio (Ox/F).
CF Vs Mixture Ratio 2.15 2.1 2.05
CF
2 1.95 1.9 1.85 1.8 1.75 3.5
4
4.5
5
5.5
6
6.5
7
7.5
Mixture Ratio (Ox/F) CF_Ae/At=50_Pe=84
CF_Ae/At=50_Pe=220
CF_Ae/At=100_Pe=84
CF_Ae/At=100_Pe=220
CF_Ae/At=500_Pe=84
CF_Ae/At=500_Pe=220
CF_Ae/At=1000_Pe=84
CF_Ae/At=1000_Pe=220
8
8.5
5. Chamber Temperature (TC) Vs Mixture Ratio (Ox/F).
Tc Vs Mixture Ratio 3800 3700 3600
Tc (K)
3500 3400 3300 3200 3100 3000 2900 3.5
4
4.5
5
5.5
6
6.5
7
7.5
800
900
8
8.5
Mixture Ratio (Ox/F) Tc_Pe=84
Tc_Pe=220
6. Characteristic Velocity (C*) Vs Area Ratio (Ae/Ath).
C_Star (m/s)
C_Star Vs Area Ratio 2450 2425 2400 2375 2350 2325 2300 2275 2250 2225 2200 2175 2150 2125 0
100
200
300
400
500
600
700
1000
Area Ratio (Ae/At) C_Star_Pe=84_O/F=4
C_Star_Pe=220_O/F=4
C_Star_Pe=84_O/F=4.5
C_Star_Pe=220_O/F=4.5
C_Star_Pe=84_O/F=5
C_Star_Pe=220_O/F=5
C_Star_Pe=84_O/F=5.5
C_Star_Pe=220_O/F=5.5
C_Star_Pe=84_O/F=6
C_Star_Pe=220_O/F=6
C_Star_Pe=84_O/F=6.5
C_Star_Pe=220_O/F=6.5
C_Star_Pe=84_O/F=7
C_Star_Pe=220_O/F=7
C_Star_Pe=84_O/F=7.5
C_Star_Pe=220_O/F=7.5
C_Star_Pe=84_O/F=8
C_Star_Pe=220_O/F=8
1100
7. Thrust Coefficient (CF) Vs Area Ratio (Ae/Ath).
CF Vs Area Ratio 2.2
2.15
2.1
2.05
CF
2
1.95
1.9
1.85
1.8
1.75 0
100
200
300
400
500
600
700
800
900
1000
Area Ratio (Ae/At) CF_Pe=84_O/F=4
CF_Pe=220_O/F=4
CF_Pe=84_O/F=4.5
CF_Pe=220_O/F=4.5
CF_Pe=84_O/F=5
CF_Pe=220_O/F=5
CF_Pe=84_O/F=5.5
CF_Pe=220_O/F=5.5
CF_Pe=84_O/F=6
CF_Pe=220_O/F=6
CF_Pe=84_O/F=6.5
CF_Pe=220_O/F=6.5
CF_Pe=84_O/F=7
CF_Pe=220_O/F=7
CF_Pe=84_O/F=7.5
CF_Pe=220_O/F=7.5
CF_Pe=84_O/F=8
CF_Pe=220_O/F=8
1100
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