Question

Quantitative: In the 1950s liquid hydrogen was considered as a fuel for a new type of aircraft being developed, the SR-71 Blackbird (shown in Figure 1). Figure 1: The SR-71 Blackbird Early research on the project focused on which fuel to use for the Blackbird. Pratt & Whitney had a J-57 engine that was designed for kerosene and being considered for implementation on the Blackbird. The J-57 only took 5 months to convert to running on liquid hydrogen, however tests with the modified J-57 could not determine a clear winner between the two fuels. Pratt & Whitney moved forward with optimizing engines to run on either fuel developing the J-58 kerosene fueled engine and the Model 304 liquid hydrogen fueled jet engine, shown in Figure 2 below.

Answer 1

Sol" Velocity of aire entering engin = 700 ma or - 312 2 mesec Mass flow rate of air entering = 154.1 kesen Inlet conditions P, = lookPa T=5°C - 278 K Density S, = P = 100x103 = 1.25 kg/m 2874278 . Sina m=s. AV A area of inlet 154.1 - 1.25 x A x 312.2 =) A=0.394 m² Since area is counlar Id = 0.394 di= 0.707m = 707.7mn.

b) Applying steady state condition in inlet Tt V.. Te + V 20 260 Since ₂=0 278 + 312.22 - Tz 2x(1005) -) T2 = 326.491 K Pressure ratio of compressor = 5.5. P2 = 5.5 Pa P₂= 2200kPa To - 177.5°C - 445.5 K

for Volumetrii flow rate we have to find density of flow exiting compressor S,- Ps 2200x10 2874 445.5 S₂ - 17.2 kg/m3 & Volumetri flow rate modo - 15+1 - 8.959 msee 17.2 o Work done by compressorriend Tz-T₂) = 154.1 1005 (445.5 -326.491) = 18429589.5 Joules/ su

d) Rate of heat transfer SCB. - inCp (Ta-T3) - 154.) x1005 (1120+273-445.5) - 146739798. 7 Joule see (e) Initial temperature of hydrogen full - 260k Tempratur after learning the heat tramafen - 1600°F 21144k Heat tearnsferred to hydrogen in heat exchanges= m+ CPH (1144-2607 + 1.814x14325 x(1144-26.) = 22971226.2 Joulse

f. Heat gained by hydrogen Heat loss by the air 22971226.2 - Main Spain (Ta - Ts) 148.32 - Tp-Ts Ts = T4-148.32 Ts a 1244.6k (f7 Power produced by trabine = Powere consumed by compressora apunp We - Wet We - 1842958.9.5 + 100x746 Wy= 18504 189.5 Jouly

19 Work done by turbin - imu Ts) 18504189.5 - 1.81 X 14325 (1144 - Ts) 716.66 = 1144-To To = 430.33K Now for after burner stady state equ Main (pair Ts & inng (H.() - C ain (pain To 154.1 xloo 5 x 1244.6 + la - Maint Cranx To T.=2647.06k NOTE) Assumption I am made here is Since materia MH + Marst man for R.4. Sof eah

Again using steady state egu for the nozzle To = Tp + v T2 =900°C = 1173k J2C (Ti-T) - To=2647.0kk V₂ = 1721.297 m/s Thrust equ of engine a Mantrin ( VW) Siramac. Main - Again man tino main T= 154.1 (1721.297-312.2) = 217.141 KN