ASHRAE Journal - April 2023 - 46

TECHNICAL FEATURE
FIGURE 2 The effect of the heat transfer rate on the coefficient of performance of the cycle: (a) the COP
(b) T-s diagram. Points A, B, C and D correspond to Q = 0 kJ/kg, Q = 300 kJ/kg, Q = 400 kJ/kg, and
Q = 500 kJ/kg, respectively.
A
4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
2.8
2.6
B
C
B
A
C
B
A
200
Q (kJ/kg)
where v is specific volume and ΔP is change in pressure.13
Both expander and compressor were considered individual
control volumes in the present analysis. The discretized
form of the governing equations (first law) was
solved by a marching numerical integration along the
pressure axis to simulate the expansion and compression
in the expander and compressor, using backward
differencing (implicit method). Saturated vapor at the
inlet of the compressor and saturated liquid at the inlet
of the expander were used as the initial conditions. The
enthalpy was calculated as a function of the pressure
and specific volume, and the two equations (Equation 6
and Equation 7) were solved iteratively before moving to
the next pressure step.
δQi = (hi - hi-1) - (vi + vi-1)(Pi - Pi-1)/2
hi = f(Pi, vi)
(7)
The heat transfer and pressure difference were a function
of the geometry of the compressor expander fusion
device. It was assumed for this analysis that there was a
constant heat transfer rate proportional to the pressure
ratio. A discrete pressure change step size was chosen,
and the heat transfer was divided equally according to
the assumption. The pressure step was reduced until the
solution converged to sufficient accuracy. The constant
heat transfer assumption provided a decent approximation
for an ideal scenario where constant heat transfer
occurred along the flow direction inside the device,
since volume ratio corresponds with pressure ratio. A
46
ASHRAE JOURNAL ashrae.o rg
A P R I L 2023
(6)
Refrigeration
Heat Pump
400
600
D
D
800
700
600
500
400
300
2
A
B
D
C
detailed fluid mechanics and heat
transfer simulation of an actual
design would be required during
design iterations to achieve a devicespecific
δQ/ΔP.
A BCD
4
s (kJ/kg)
6
8
A comparison of the COP in the
standard vapor compression refrigeration
cycle was performed for five
different fluids: two widely used
refrigerants, R-134a and R-410A; two
natural refrigerants, CO2 and ammonia;
and water. The vapor regions for
these refrigerants vary greatly in temperature,
making the use of the same
hot and cold reservoirs for all fluid
less likely to provide a fair comparison.
Therefore, hot and cold reservoirs were calculated,
respectively, 2/3 and 1/3 the difference between the critical
and triple temperatures (Equation 8 and Equation 9).
Hot reservoir: TH = 2/3 (Tcrit - Ttriple) + Ttriple
Cold reservoir: TC = 1/3 (Tcrit - Ttriple) + Ttriple
(8)
(9)
Results and Discussion
Heat transfer from the compressor into the expander
was beneficial in both the heat pump and refrigeration
cycles, as indicted by the improvement in the COP
(Figure 2a). The COP improvement was proportional
to the rate of heat transfer until a critical value was
reached, after which further heat transfer did not significantly
increase COP. When examining the cycle on a
T-s diagram (Figure 2b), it was found the point of diminishing
returns corresponded to the compression process
being tangential to the saturated vapor line, as shown by
the orange dotted line. The blue line on the same figure
represents an isentropic compression process. After the
critical point, further heat transfer from the compressor
resulted in a wet compressor exit, which is undesirable
theoretically and practically.
Heat transfer between the expander and compressor
was compared in Figure 3 for different fluids by normalizing
the COP with the COP of the isentropic cycle with
an expander and the heat transfer with the critical point
where the compressor exit was saturated vapor. The
increase in COP for refrigeration of the common HFC
refrigerants was small with 1% for R-134a and 3% for
COP
T (K)

http://ashrae.org

ASHRAE Journal - April 2023

Table of Contents for the Digital Edition of ASHRAE Journal - April 2023