Oxygen is used as a propellant on a missile. You are investigating a cryogenic technique for storing oxygen on the missile and providing that oxygen at high pressure to the combustor. A V_tank = 25 liter cryogenic tank (called a Dewar) is filled with oxygen at atmospheric pressure, P_fill = 1 atm. The filling is stopped when the tank holds V_f, 1 = 15 liter of liquid oxygen; the remainder of the tank contains saturated vapor (Figure 1). a.) What is the mass of liquid in the tank (kg) after it is filled, m_f, 1? b.) What is the quality of the oxygen in the tank after it is filled, x_1? c.) What is the temperature and specific volume of the oxygen in the tank after it is filled? Rather than pump the liquid in the tank to the high pressure required by the combustor (P_comb = 30 atm), you are designing a system that will self-pressurize; this avoids the need for an expensive and potentially unreliable cryogenic pump. The tank is closed after it is filled. A pressure relief valve opens once the pressure in the tank reaches P_comb. The tank is cold, and therefore it experiences a heat transfer rate (sometimes referred to as a parasitic heat leak) of Q_parasitic = 20 W from the surrounding missile components. You have also installed an electrical heater (a resistor which converts electrical work transfer to heat transfer) that provides W_heater = 500 W to the tank. The heater is activated until the pressure relief valve opens (state 2). d.) What is the temperature in the tank when the relief valve opens, T_2? e.) What is the mass of liquid in the tank at the time that the relief valve opens? f.) What is the total amount of energy (heater power and parasitic heat transfer) required to self-pressurize the tank (i.e., to go from state 1 to state 2)? How long does this process take (min)?
a) Liquid Oxygen mass = 1.141 kg/L
there fore 15 liter liquid Oxygen weighs = 1.141 x 15 = 17.115 kg
b) The quality of Oxygen in the tank is 15 liter of Liquid oxygen and 10 liters of gaseos oxygen.
c) The specific volume of oxygen = 1/ density
= 1/1.141 = 0.876 l/kg
Temperature of liquid oxygen is = -183 degree C
d) Liquid Oxygen expansion ratio is 1: 861 at 20 degree C
To find the volume of oxygen required to pressurise the 10 liter space to 30 bar =
P1 V1 / T1 = P2V2/ T2; T1 and T2 can be assumed to be same and hence ve can find V2 = 0.333L
the liquid oxygen that has to convert into gas and fill is 10-0.333 = 0.96L
0.96 L of gas needs 0.111 L of liquid Oxygen since the expansion ratio is 1:861
therfore the liquid oxygen in the tank at the time of pressure relief opening is = 15- 0.01111 = 14.9889 L
e)
Latent heat of liquid oxygen = 214 kJ/Kg , to evaporate 0.0111 kg , energy required is = 214 X 0.1111= 2.375 kJ
Total heat available is 520 watts.ie 520 joules /sec.
therfore time required = 2375/520 = 4.56 sec
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