tailieunhanh - Aeronautical Engineer Data Book Episode 6

Tham khảo tài liệu 'aeronautical engineer data book episode 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Basic fluid mechanics 91 Normal shock waves 1D flow A shock wave is a pressure front which travels at speed through a gas. Shock waves cause an increase in pressure temperature density and entropy and a decrease in normal velocity. Equations of state and equations of conservation applied to a unit area of shock wave give see Figure State P1 P1T1 P2 P2T2 Mass flow m p1u1 p2u2 Shock wave travels into area of stationary gas 7 Pi Pi u1 P2 u p2 Shock wave becomes a stationary discontinuity 7 Pi Pi u1 P2P2 u Fig. b Aircraft shock waves 92 Aeronautical Engineer s Data Book Momentum p1 p1u2 p2 P2u2 p- P1 u1 u2 Energy Cp T1 Cp T2 -y Cp To Pressure and density relationships across the shock are given by the Rankine-Hugoniot equations 2 1 a - 1 7 -1 P1 7 1 - Pl 7 - 1 P1 Ờ 1 P2 . _ y -1 A 1 iti ĨÍ 7 -1 p1 pressure ratio across the shock is given ft P1 2y m2 - y - 1 Static by P1 _ P2 7 1 Temperature ratio across the shock is given by T1 21 pj P1 T2 2y m2 - y 1 V2 y - 1 M __ I -L ll 1 -t I 7 7 Ĩ i y 1 M2 Velocity ratio across the shock is given by From continuity u2 u1 p-Ịp-2 u2 _ 2 y - 1 M1 W1 y 1 M2 In axisymmetric flow the variables are independent of 0 so the continuity equation can be expressed as 1 d R2 gR R2 dR R sin ọ dọ Similarly in terms of stream function ực so 1_ d sin er 0 dR R sin Basic fluid mechanics 93 - 1 dỳ qR R2 sin p 3 p 1 30- q R sin ỳ dR Additional shock wave data is given in Appendix 5. Figure b shows the practical effect of shock waves as they form around a supersonic aircraft. The pitot tube equation An important criterion is the Rayleigh supersonic pitot tube equation see Figure . y 1 2 M2 7 7 - 1 02 Pressure ratio P1 Fig. Pitot tube relations 2M - y - 1 y 1 Axisymmetric flows Axisymmetric potential flows occur when bodies such as cones and spheres are .