Question

Supersonic aircraft develop shock waves at the engine inlet when it flies supersonically. Consider the two types of engine inlets described as follows and calculate the total pressure recovery ratio for each engine inlet design when the aircraft flies at Mach 2.5. Take the specific heat ratio y to be 1.4. (a) A three-shock system (two oblique + one normal, external compression inlet) as shown in Fig. 1 Please note that the two blue arrows are not part of the calculations but are drawn in the diagram to show you the common flow diversion in inlet /diffuser such as the boundary layer porous bleed and the secondary airflow. The shock wave decelerates the flow to a subsonic value at station 4 and the diverging diffuser section after the station 4 is to further slow down the flow before it enters the compressor at station 5. Boundary layer porous bleed 80 23° 1 My = 2.5 2 3 5 4 This diagram is not to scale. Secondary airflow Figure 1: A three-shock external compression inlet configuration (b) A single-shock system (one normal shock, Pitot inlet) (c) What can you conclude when comparing your answers from part (a) with part (b)?

Answer 1

freestream mach number Mo 22.5 Specific heat ratio 8=1.4. 8" (a) | 23° 9 M, 22.5 Oblique Shock wave (osw) 8 x M, 22.5 2 Cot o z tan X & til mi 2 (mtsin x-1) - a 230.0052. 8/8-1 813-) Pt2 (8+1) m" sina Co ( (&+1) 28 m² sin²x -(87) Pto L68-1) masina+2 0.987 Pto 2 My sinh (ao) (8-1) m?, sinh +2 28 m2 sinta -(8-1) ima 2.1685

flow deflection angle. Q z 23 -3 7 15, 2 M22 2.1685 2 tano tan da 1 X = 41.829 z (8+1) Me 2 (masin 2-1) c 2 841 Pt3 18+1) må sina, Ptr arm sin 22 -(8-) (8-1) Må sin 2+2 Pt3 Pt2 0.9459 Mä sin (19-02) (8-1) M₂ sin²22 +2 28m² sinda 08-) IM 3 = 1.5975 Shock wave CNsw) # Normal 7-1 g f gt PtA X (18+) M3² [(8-1) M3 +2 28 m₂ -(81) Pr3 Ptu 6.8961 Pt3

Total Pressure Pressure recovery for condition a. Pot Poy Po 3 Poz > X Po Poz Poz Z 0-8961 x 0.9459 x 0-9870 Po4 Pol 0.8366 (b Shock. wave (now) Single Normal M 2.5 z da14 8/2-1 2- 2 (87) P44 sor) mi Pol (84)m, 2+2 luce zom, ²-(8-) Pty 0.4990

(0) Past (a) two oblique t Normal shock has Benune neu recovery ratio of Pry 0.8366 PA Pant (b) single Normal Shock has Pressure recovery natio of Pru -0.4990 - Total Pressure loss alross normal shock is preportional to shock much higher and Strength. part (as has Series of oblique Sholk which flow and shach number) decelerates before it enters Normal shock. It is always advisable for in lets natio desin for optimum Pressure recovery Series of oblique shocks t Normal Shock entr inlet .