2. Space vehicles use a special type of insulation called Multi-Layer Insulation (MLI). As

the name implies, MLI consists of multiple layers of thin sheet aluminum (approx. 6

micron thick), with an aluminized kapton outer layer. Since the multiple layers act

as radiation shields, the heat leak through the MLI is not calculated by conduction,

but instead by Leak = 0A(TULI - Tinner), where e* is the effective emissivity of the

blanket, TULI is the temperature of the outer layer, and Tinner is the surface tempera-

ture of whatever object is being insulated.

Consider a 3 m² (0.5 m³) liquid oxygen tank with a 10% initial ullage in outer space.

The tank is filled with saturated oxygen at 90 K and left in orbit for 30 days during

the winter solstice. Assuming the MLI has an e* value of 0.01, and an outer layer with

an emissivity of 0.75 and absorptivity of 0.14.

(a) Using an energy balance on just the MLI, determine the heat leak (in Watts) into

the tank through the MLI if the solar flux, G, is 1414 W/m² during the winter

solstice and Tapace = 4 K, assuming the tank temperature is 90 K, and the MLI

surface area equals the tank surface area.

(b) Calculate the pressure and temperature in the tank after 30 days using the heat

leak calculated in part a. Draw a P-v diagram of this process.

1

Hint: Use REFPROP to obtain the thermodynamic properties. The final pressure

should be approximately 45 times higher than the initial pressure.

Qrad=50A(TLI-pace)

Qolar = QGA

GOX

•Q Look

LOX

Ullage

space

Figure 1: LOX tank with MLI for problem 2.

Vallage

= 0.1 Votal

€ = 0.75

MLI a = 0.14

€* = 0.01

-Tank (T-90 K)