Aerothermodynamics classroom exercises

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1 Aerothermodynamics classroom exercises – Prof. Vigevano 1) The nozzle of a rocket expands supersonically the combustion gases, which molecular mass is W = 0 .012 kg/mol and specific heat C p = 4157 J/kg K. The stagnation conditions at the no zzle inlet are: pressure P 0 = 15 atm and temperature T0 = 2500 K, while the gas temperature at the nozzle exit is Te = 1350 K. Compute the values of pressure, Mach number and gas velocity at the exit section of the nozzle. Repeat the exercise using air as working gas. 2) The section area of a convergent-divergent nozz le is given by the equation: dcx bx ax xA +++= 23) ( [dm 2] where 25 827 49 83 : 31 2 0 3 2 : 10 =−==−=<≤ ==−==<< dcbax dcbax ,,, ,,, For the following values of stagnation pressu re and temperature: P = 3 bar , T = 150 ºC, determi ne the distribution of Mach number, pressure and temperature along the nozzle axis, assuming an isentropic flow of air wit hin the nozzle and supersonic conditions at the nozzle outlet. In addition, compute the value of the mass flow rate. 3) Air at temperature T = 300 ºC is discharged f rom a reservoir into the atmosphere through a conic al duct with length L=5 cm, inlet radius r i = 100 mm and outlet radius r o = 50 mm. Plot the value of the resulting mass fl ow rate as function of the reservoir pressure, assuming the la tter varying from P 0,MIN = 1.5 bar to P 0,MAX = 2.5 bar. Determine the distribution of velocity, pressure and temperat ure along the duct axis for the two values of reser voir pressure P0,MIN and P0,MAX . 4) A constant section duct with friction is employ ed as diffuser to decelerate a supersonic air flow. For a duct of diameter D = 12 cm and length L = 2 m, compute the minimum value of Mach number which can exist at th e duct inlet and determine the distribution of…