lect. notes #3.pdf - Normal Shock Waves Recall P P0 P P0...

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30 Normal Shock Waves Recall Distance along nozzle Complete isentropic solution is impossiblefor some boundary conditions ( ???), i.e; for some Pbvalues ???. If Solutions are to be found, a newPHENOMENONmust be introduced; Discontinuity??Shock Wave??It has been observed and seen that at SUPERSONIC speeds, very rapid changes in the properties of the flow may occur, mainly: Pressure Velocity Shock Wave 0PP0*PP?????
31 Schlieren Photo of "Supersonic Flow Past X15 flight, M=3.5" Schlieren Photo of "Supersonic Flow Past Blunt Body"
32 Normal shock waves Oblique shock waves ? Curved shock waves ? ?
m
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33 Governing Relations of NSW Energy Equation: (1) "Adiabatic, No work & Steady" Continuity Equation: (2) Momentum Equation: (3) State Equations: (4) (5),pss,shhxyN. S. W.xVyVo2yy2xxh2Vh2Vh2yyy2xxxxyyxVpVpVVmAppAmVVyyxx
34 Fanno Line ? If conditions at xare fixed, and we are to calculate conditions at y, equations (1), (2), and (4) define a locus of states passing through x. This locus is called Fanno Linei.e.; Choose VyCalculate yfrom (2) Calculate hyfrom (1) Calculate syfrom (4) Repeat for other values of VyNotes: Fanno Line is a line of constant

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