Space Grant Consortium - University of Wisconsin - Green Bay

The enthalpy (h3) of the 2 nd stage fluid entering the precooling evaporator is calculated using:
( amb, nd , nd
high )
h = enthalpy T P y
(7)
3 ,2 2
The ratio of the mass flow rate in the 1 st to the mass flow rate in the 2 nd stage (MR) is defined as:
MR = m� m�
(8)
st nd
1 2
and is computed using an energy balance on the precooling evaporator:
MR = h −h h − h
(9)
( ) ( )
3 4 8 11
The rate of precooling heat transfer as well as all subsequent energy transfer rates are computed
on a per unit of 2 nd stage mass flow rate basis.
Q� m� = MR h −h
(10)
pc
2 nd
( )
8 11
The precooling heat exchanger is divided into a number ( N pc ) of small heat exchangers, as
shown in FIGURE 2(a), where each section transfers an equal fraction (1/Npc) of the total
precooling load. Dividing the heat exchanger into equal heat transfer segments rather than equal
physical sizes facilitates direct computation of the enthalpy distribution in the heat exchangers
and significantly improves computation speed and convergence. The first heat exchanger section
is located at the hot end of the precooling evaporator and is shown in FIGURE 2(b). The
enthalpy of the 1 st stage working fluid leaving the precooling evaporator is equal to the enthalpy
of the 1 st stage fluid at the first node of the heat exchanger.
h = h
(11)
st
1 , pc,0
The enthalpy of the mixture entering the precooling evaporator is equal to the enthalpy for the
mixture at the first node of the heat exchanger.
h2 nd, pc,0
= h3
(12)
The enthalpies of the hot and cold exit streams at the interface of each segment are computed
using an energy balance.
heat exchanger
section index - i
1
2
3
N pc -1
N pc
h h
st
1 , pc,0
h h
= 8 nd
2 , pc,0
3
.
.
h = h
heat exchanger
node index - i
0
1
2
3
h = h
N pc -2
N pc -1
N pc
st =
1 , pc, N 11 nd
4
pc 2 , pc, N pc
8
1st of N differential segments of HX
h st = h
1 , pc,0
8
Q�
pc
m�nd 2
1
Npc
h nd = h
2 , pc,0
3
Q�
1
h st = h st −
1 , pc,1 1 , pc,0
m N MR
Q�
pc 1
= −
m� N
pc
h nd h nd
� 2 , pc,1 2 , pc,0
nd
2 pc
(a) (b)
FIGURE 2. a) Precooling heat exchanger divided into Npc sections and (Npc + 1) nodes. b) First differential heat
exchanger element.
( )
h = h −Q m N MR
� � i = 1…Npc (13)
st st nd
1 , pc, i 1 , pc, i−1
pc 2 pc
32
nd
2
pc