At the inlet to the combustor of a supersonic combustion ramjet (or scramjet), the flow Mach number is supersonic. For a fuel-ai
r mass ratio of .03 and a combustor exit temperature of 4800 degr, calculate the inlet Mach number above which the flow will be unchoked. Assume one- dimensional frictionless flow with y = 1.4, with heat release per slug of fuel equal to 4.5 x 108 ft-lbf. (Anderson 3.11) The temperatures for the above combustion problems are pretty high. A more representative value of the heat capacity ratio for products of combustion at these temperatures is y = 1.28 The value of the specific gas constant R may still be approximated as equal to that of air. b) For problem #2, calculate the inlet Mach number above which the flow will be unchoked, based on y = 1.28
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Answer:
You need a 120V to 24V commercial transformer (transformer 1:5), a 100 ohms resistance, a 1.5 K ohms resistance and a diode with a minimum forward current of 20 mA (could be 1N4148)
Step by step design:
- Because you have a 120V AC voltage supply you need an efficient way to reduce that voltage as much as possible before passing to the rectifier, for that I recommend a standard 120V to 24V transformer. 120 Vrms = 85 V and 24 Vrms = 17V = Vin
- Because 17V is not 15V you still need a voltage divider to step down that voltage, for that we use R1 = 100Ω and R2 = 1.3KΩ. You need to remember that more than 1 V is going to be in the diode, so for our calculation we need to consider it. Vf = (V*R2)/(R1+R2), V = Vin - 1 = 17-1 = 16V and Vf = 15, Choosing a fix resistance R1 = 100Ω and solving the equation we find R2 = 1.5KΩ
- Finally to select the diode you need to calculate two times the maximum current and that would be the forward current (If) of your diode. Imax = Vf/R2 = 10mA and If = 2*Imax = 20mA
Our circuit meet the average voltage (Va) specification:
Va = (15)/(pi) = 4.77V considering the diode voltage or 3.77V without considering it
