Question

You already learned about the performance calculations of a jet engine. It is expected to draw performance curves (i.e. "specific thrust" and "TSFC" plots) for an ideal jet engine with different compressor pressure ratios, say 5, 10, 15, 20, 25, and 30, and the turbine inlet temperature of 750, 1000, 1250, and 1500 K, at three different Mach numbers, say M=0.0, 0.8, and 2.0. Ambient condition is 25°C and 0.1 MPa. Assume that yair and Rair are constant and equal to 1.4 and 0.287 j/kg.K, respectively and the fuel heating value is 45,000 kJ/kg. assume that there is no change in mass flow rate prior and after burning. Do all the calculations and plots in excel or another programming language (whatever fits you). Hint: Follow the calculation algorithm for a jet engine. Using known variables (six pressure ratio and four temperatures) you have to do the calculations for "6x4=24" times at each Mach number. Plot graphs of thrust - Prcomp) and (TSFC – Pr comp). Typical example of these graphs are provided below. tha T-1700K To-1600 Specific Thrust TSFC T-1700K T-1500 Compressor Pressure Ratio

Answer 1

T2 3.5 put r= 1.4 P2 1000 (298759.567? 298 1000 4 It 59.56 m² KREON/m² 292 be the compressor pressure ratio Р. ХР. -100or (it 59.56 M2 292 0.285 P3 22 Tg = 7260)" 2 2984.59.80m2] (301225 We hy-hy-hy-hs - Tz - T2 - Ty - Tsi Tr Ty - Iz + Tz let T be the turbine inter temperature Ту: Т-

To T (298+59.56 M² [gaars 1). Ts (298+59.56 m2 160 Ty y Ts 13.5 7 Py = P₂ - 1000X (1+59.5571? 298 59.569 298 ... Ps 1000Y P6 P1000 pa. TT/ Ps Tr 3.5 114 59.56M may fi- 6971596841318095 TE you 444 52 ny (T=698 457.53 m2) *** (rgres 1+ 59.56 M2

To a 298T 2984 57.56 m² 0 225 [2Cp (Ts I.) x 1000] - fextoostis Textovo) Thoust = m Thrust V6 - V. im put tv in or above and blot for the specific values of r.

G17 X ✓ fic G H. J K N P 1200 1000 Plot Area 300 B с D E F 1 FORMULA USED 2 3 Nozzle inlet Temp. 15= T-1208+50.56*M^2 UP^0.285-1) 4 Nozzle exit Temp, T6=1298*TY/Up^0.285 (298+59.56 M2) Velocity at exit, V6=12CP115-T6A11/2 6 velocity at entry V1-346M 7 8 Mach number, M O 9 Turbine inlet Temp. TE 750 10 11 Compress Nozzle Nozzle thrust/ 12 or inlet exit Temp. Velocity at velocity at mass flow 13 pressure Temp. TS TE exit, V6 entry. V1 rate 14 5 576.564 474.0935 463.8567 ol 463.8567 15 10 473.5076 399.1 412.1166 412.1166 16 15| 403.2039 346.6373 337.2818 0 337.2819) 17 20 348.1422 319.2506 240.5642 0 240.5642 18 25 302.1993 209.6735 71.09717| 0 71.007171 19 30 262.4102 204.4906 #NUM! 600 100 C 200 D D 5 10 15 20 25 30 35 750k 1000 K 1250 1500 21 Turbine inlet Temp. T+ 1000K 22 23 Compress Nozzle Nozzle thrust/ 24 or inlet exit Temp. Velocity at velocity at mass flow pressure Temp. Ts TE exit, V6 entry, V1 rate 26 5 826.564 632.1113 625.181 0 625.181 27 101 723.5076 518.8 641.5041 0 641.5041 28 15 663.2339 462.183 619,697 0 619.697 20 588.1422 425.9000 590.5629 0 598.56291 20 25 562.1893 390.5647 563.8714 0563.8714 31 30 512.4102 379.3328 517.191 0 517.191

B3 Turbine inlet Temp, T1= 1250 84 25 Compress Nozzle Nozzle thrust/ 86 or inlet exit Temp. Velocity at velocity at mass flow 7 pressure Temp. T5 T6 exit, V6 entry, V1 rate 88 5 1076.564 790.1391 758.7582 0 758.7582 29 10 973.5976 648.5 808.3601 0 808.3601 10 15903.2338 577.7289808.8665 0 808.8665 11 20 848.1422 532.251 796.8321 0| 796.8321 12 25 802.1883 499.4559 780.0592 0 780.0592 13 30 762.4102| 474.166 761.1641 0 761.1641 14 15 Turbine inlet Temp. T1= 1500 16 17 Compress Nozzle Nozzle thrust/ or inlet exit Temp. Velocity at velocity at mass flow 19 pressure Temp, T5 T6 exit, V6 entry. V1 rate 50 5 1326.564 948.1669 872.1113 0 872.1113 51 10 1223.598 778.2001 946.176 0 946.176 52 15| 1153.234 693.2745 961.5186 0 961.5186 53 20 1098.142 638.7012 960.9768 0 960.9769 54 25 1052.188 599.347 954.0498 0 954.0498 55 30 1012.41 568.9993 944.0636 0 944.0636 56 FOR M=0 FOR M=0.8 Sheet1 FOR M=2.0

Chart 1 А EX fic B CD FORMULA USED F G Н - j K L M N P 800 700 HH+ LO 600 500 400 3 Nozzle inlet Temp. T5 = T-298+59.56 (M)^2 40.285-1) 4. Nozzle exit Temp, T6=(298*T)/Up)^0.285* (298+59.56*M^2)) Velocity at exit, V6=(2CpxT5-T6))(1/2) 6 velocity at entry.V1=346M 7 8 Mach number, M= 0.8 9 Turbine inlet Temp. T1= 750 10 11 Compress Nozzle Nozzle thrust/ 12 or inlet exit Temp. Velocity at velocity at mass flow 13 pressure Temp. T5 T6 exit, V6 entry. V1 rate 14 5 554.3791 420.3188 519.0966 276.8 242.2966 15 10 438.2418 344.9731 432.9782 276.8 156.1782 16 15 358.8775| 307.3259 321.8985 276.8 45.09845 17 20 296.7389 283.1338 165.3672 276.8 111.433 18 25] 244.9069| 265.6882 #NUM! 276.8 #NUM! 19 30 200.0406 252.2352 #NUM! 276.8 #NUM! 300 200 100 Series "750" Point "10" (10, 156.1781679) 0 0 10 15 20 25 30 35 750 1000 K 1250 -1500

CO V1 34 20 21 Turbine inlet Temp. Tu 1000 K 22 23 Compres Nozzle Nozzle velocity thrusti 24 sor inlet exit Velocity at entry. mass 25 pressure Temp. T. Temp. To at exit, V6 flow rate 26 5 804.379 560.425 700.248 276.8 423.448 27 10 688.242 459.964 677.376 276.8 400.576 28 15 608.877 409.768 632.622 276.8 355.822 29 20 546.739 377.512 583.221 276.8 306.421 30 25 494.907 354.251 531.7131 276.8 254.913 31 30 450.041 336.314 478.112 276.8 201312 32 33 Turbine inlet Temp. Tu 1250 35 Compres Nozzle Nozzle velocity thrusti 36 sor inlet exit Velocity at entry. mass 37 pressure. Temp. Ts Temp. To at exit, V6 V1 flow rate 5 105438 700.531 843.347 276.8 566.547) 39 10 938 42 574.955 854.521 276.8 577.721 40 15 858.877 512.21 834.747 276.8557.947 41 20 796.739 471.89 808.051 276.8 531.251 42 25 744.907 442.814 779.235 276.8 502.435 43 30 700.041 420.392 749.729 276.81 472.929 44 45 Turbine inlet Temp. Ti 1500 46 47 Compres Nozzle Nozzle velocity thrusti 48 sor inlet exit Velocity at entry. mass 49 pressure. Temp. Ts Temp. To at exit, V6 V1 flow rate 50 5 1304.38 840.638 965.464 276.8 688.664 51 10 1188.24 689.946 1000.79 276.8 723.987 52 15 1108.88 614.652 996.691 276.8 719.891 53 20 1046.74 566.268 982.724 276.8 705.924 54 25 994.907 531.376 965.244 276.8 688.444 30 950.041 504.47 946.359 276.8669559 56 57 55 58

FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW * Cut Le Copy HelveticaNeueLT - 12 Α Α΄ Paste BIU - 2-1 HII Format Painter Clipboard Font Alignment K54 1 X ✓ fx E H н C FORHULA USED 1500 H...lill Teen TS-TJET...SH.205-11 H...le rail Tror TC-I'TUUL215201-59.5FH211 Vrlo.ill railYC-12CHTS.TIP1/2 urlu il alla LEH Hasbunar, H- Torbieriscono Corruser Haciale! H... Veleill.ill Irsal? PFFRET ralis al rail Trap. To flow al Tro. To YE roles rals s 137.1975 269.1503 532.1526 10 252.624141 216.2312 271.4615 632 -421.53111 15 126.116596 182.6917 THUH! THUH: 20 26.1717169 177.1693 HUH! THIHI 25 -55.1215452 166.575 THUH! THUHE 11 .127.9120 151.1125 HUH! 632 THUH! T-E-F II T TI- H... Veleill.ill Iruel? Prrrr rall. Trop To al Tro. TS YE roles rals s 517.11975 351.2722 122.5791 632 111.121122 10 512.624141 211.9112 ESC.333 692 -35.FESEZ 15 176.11696 256.15-19.00 532 203.5145 21 276.171716 296.626 214.4165 632 17.5155 25 19.12955 232.EE THUH! 632 THUH: 11 122.6112 211.11 HUH! 632 THUH: Turbirill Tror. TI- 1251 Havel Vrlouilloall Irsal? PFFE EFF rali. Tror. To al rail, Tror. To VE 5337.311375_133.1973 11.10 522 312.121 0752.62.41 361.3153 117.310 632 195.31114 15 GEE.UIESC 321.15.2 712.5113 612 1.914536 20 325.171715 225.7122 611.5925 532 -11.45551 25 444.17455 R22.50.2125 52.111.2171 30 972.ELIZE6.SLEEPLES 532 .224.2210 Torbieriell Trop, T- 1511 Havel Vrlouilloall Ibrsel! Tror. To al rail, TEC VE 51107.31137 526.3166 1152.66 532 TEL.13 101112.62414192.46241070.SRC 5:20121.525SE 15 17.115996224539.1699 592 31161.13 21 276.171716 550.933 21.913 592 321.31139 25 694.173455993.051 OSATZ 512 151.35662 622.6112 316.215 PM 11 592 33.769050 FOR M=0 FOR M=0.8 Sheet1 FOR M=2.0 +

Mach number- M. V, Crinkt) My Velocity of air at 9 card 0.1 MPa. -346 M. thrustma (Vexist - Vinlet). os con 3 76 2 - Const. T25C = 290k. 'Pi: 0.impan 105 N/m? 100DN For sentropic flow of air in the diffusor 0,.2 - kling= hach, f g ² - ? 2 VO hy: Ta hi:CI 072-30W-30 (12-1)-V,? D 2 2 Tea Titu 29 T2 = 298+ (344) 2X105 : 298+59.56 m²,

all graph drawn in excel has been attached with the file. calculation of foprmula has been attached and is in handwritten format. hope you will get your queries solved.