William,
1. You may kindly go through a few topics discussed in this forum regarding solar radiation. Mr. Ankur has provided several useful links to understand the subject better.
2. During flowing condition, solar radiation heat into the liquid through insulation and foil is very very less (not enough heat to raise the liquid temperature to Tsat). However, when one starts the pump after a shut down (as the pipe and pump temperatures would be high), one can expect vaporization of a part of liquid, causing pump cavitation.
3. If the liquid flow rate drops below a value, where heat in from solar radiation matches sensible heat of liquid causing it to reach Tsat, one can expect vaporization in such line.
4. Solar radiation subjected on Al sheet shall absorb a part and reflect the rest. Assuming all the heat absorbed by Al sheet is available for LPG to get heated up;
alpha_s = 0.15
Emmissivity = 0.05
G_solar = 1000 W/m2
Sigma = 5.67 e-8
T_s = 62 + 273 = 335 K
T_sky = 280 K
Qnet_radiation = alpha_s * G_solar - Emissivity * Sigma * (T_s^4 - T_sky^4) ............. Equation 1
Qnet_radiation = 132 W/m2
A. 50 kW suction pipe:
10 m length
219.1 mm od + 25.4 mm insulation = 244.2 mm is net diameter
Total surface area = 3.142 * 0.2442 * 10 = 7.7 m2
Q_absorbed_1 = 132 * 7.7 = 1016 W
Now let's check if this heat is high enough to raise LPG temperature to its Tsat.
Tsat at 10.5 kg/cm2g = 48.1 oC.
LPG temperature = 35.5 oC
m = 61948 kg/h (120 m3/h)
Q_1 = m*Cp_1 * (Tsat - T) = 61948 / 3600 * 2710 * (48.1 - 35.5) = 5.9 e5 W
As Q_absorbed_1 << Q_1, therefore no vapor formation in liquid.
B. 400 kW suction pipe:
1500 m length
219.1 mm od + 25.4 mm insulation = 244.2 mm is net diameter
Total surface area = 3.142 * 0.2442 * 1500 = 1146 m2
Q_absorbed_2 = 132 * 1500 = 151272 W
Now let's check if this heat is high enough to raise LPG temperature to its Tsat.
Tsat at 14.2 kg/cm2g = 60.93 oC.
LPG temperature = 35.87 oC
m = 61948 kg/h (120 m3/h)
Q_2 = m*Cp_2 * (Tsat - T) = 61948 / 3600 * 2702 * (60.93 - 35.87) = 1.2 e6 W
As Q_absorbed_2 << Q_2, therefore no vapor formation in liquid.
C. For flow rate 8043 kg/h (15.6 m3/h), Q_absorbed shall equal Q.
Regards.
Ajay S. Satpute