One way to liquefy a gas is to flash it through a valve. However, this requires that the inlet…

One way to liquefy a gas is to flash it through a valve.
However, this requires that the inlet conditions to the valve be at a state
where an expansion will cause the gas to flash into a saturated mixture of
liquid and vapor. Consider a situation where helium gas is at 10 bar and the
desired pressure of the liquid is 1 bar. In order to produce liquid helium, the
inlet state to the throttling process must lie between the two states
identified as a and b on the P-h diagram shown in Figure P6.15A. For an inlet
pressure of 10 bar, this temperature range is 2.53 K _ T _ 7.60 K
for helium. One

One way to liquefy a gas is to flash it through a valve.
However, this requires that the inlet conditions to the valve be at a state
where an expansion will cause the gas to flash into a saturated mixture of
liquid and vapor. Consider a situation where helium gas is at 10 bar and the
desired pressure of the liquid is 1 bar. In order to produce liquid helium, the
inlet state to the throttling process must lie between the two states
identified as a and b on the P-h diagram shown in Figure P6.15A. For an inlet
pressure of 10 bar, this temperature range is 2.53 K _ T _ 7.60 K
for helium. One possible way to achieve this low temperature at the entrance to
the valve is shown in Figure P6.15B. This system is known as a liquefaction
system.

In this system, the helium gas is supplied at 10 bar, 18
K at a flow rate of 4.6 g/s. This gas is cooled further using two heat
exchangers. The cooling of the gas is accomplished by mixing the cold saturated
vapor leaving the separator and the cold gas at the exhaust of a small turbine
operating between the high and low pressures of the system. The UA product of
each heat exchanger is 70 W/K. The separator operates at a pressure of 1 bar.
Manufacturer’s performance data for the turbine relate the turbine temperatures
and mass flow rate with two empirical equations,

In these turbine performance equations a1 = 4.6 K, a2
= 0.1, b1 = 3.75 g/s, and b2 = _0.125 g/s-K. Write and solve a
simulation for this helium liquefaction system and determine the,

a. Unknown temperatures in the cycle (K)

b. Heat transfer rate in each heat exchanger (W)

c. Liquid helium mass flow rate leaving the separator
(g/s)

d. Power delivered by the turbine (W)Evaluate the system
to determine how the inlet helium flow rate at State 2 influences the liquid
helium production rate and the turbine output power. Plot the following
parameters as a function of the inlet helium mass flow rate for the range 3.4
_ &m1
_ 5.0 g/s,

e. Liquid helium mass flow rate leaving the separator
(g/s)

f. Quality of the helium leaving the valve at State
7g.Turbine output power (W)