ON THE OPTIMUM INTER-STAGE PARAMETERS

FOR CO2 TRANSCRITICAL SYSTEMS

Dr. Dan Manole

Tecumseh Products Company
100 E. Patterson St.
Tecumseh, MI 49286 USA
517-423-8426 fax, dmanole@tecumseh.com

ABSTRACT
The search for environmentally friendly refrigerants in systems with low LCCP calls for the use of
natural refrigerants like CO2, ammonia, and hydrocarbons. In order to match the efficiency of R134a or
R22 refrigeration systems, the natural refrigerants require more complex system configurations.
Part of the solution to designing refrigeration systems using transcritical refrigerants is the use of two
stage compression compressors. The increased system complexity adds at least two more variables to
the thermodynamic optimization of the refrigeration cycle: the inter-stage pressure and temperature.
The present study does a review of the current practices in selecting the inter-stage pressure and
temperature values and then points out the potential to further increase the system efficiency.
Experimental data are used to further tune the analytical results used to make recommendations on
selecting the intermediate pressure in two stage compression refrigeration systems.

1. INTRODUCTION

1.1. Engineering System Optimization Goals

One can list a large variety of refrigeration systems configurations using transcritical refrigerants.
Then, for each system configuration there is multitude of options in selecting components. The analysis
can be theoretical, experimental, or numerical. Next, components must be optimized in the system. In
conclusion, there are many studies that can be made on possible combinations of analysis method,
configuration, choice of components, and operating control scheme.
The refrigerant performances nowadays are compared by using the Life Cycle Climate Performance
that includes, besides the immediate cost of energy, the side effects of producing the various materials
or components used in the system. The lower the LCCP value of a system, the lower the impact is upon
the global warming. From an Engineering point of view, global warming is also consequence of the
entropy generation. Similar to LCCP, entropy generation encompasses irreversible changes to
environment caused by heat transfer, substance mixing, fluid flow, friction, combustion, etc.
Bejan (1995) makes an elemental analysis of entropy generation during various processes happening in
Engineering systems. Bejan underlines that it is essential to keep track of whether the optimization of
one system component, or process, causes thermal degradation of other components to which it may be
connected if a larger thermodynamic system is considered. A great example of the importance of this
fact is the paradox of the ‘vanishing’ heat exchanger. By plainly removing a component out of a system
one would create as little thermodynamic loss as by using a perfect component. For practical systems to
work one still needs physical components; thus, a system with optimum performance is expected to be
assembled out of less-than-optimum components.
At this time in the introduction one must recall another object function that must be included in a
system optimization study, although it is not included in the LCCP. It has to do with optimizing a
refrigeration system having in mind the purpose of refrigeration. I would refer to the inaugural speech

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006
held by Mr. Vallort (2004) on his plans as ASHRAE 2004-2005 president to emphasize the widespread
benefits of refrigeration as the technology for survival and ASHRAE as the strongest link in the cold
chain. "We need to advance the technology of refrigeration to enable all the people of the world to
enjoy its benefits. …We now can distribute life saving food and nutrition around the world to others
who are less fortunate," Mr. Vallort said in a statement.

1.2 Inter-Stage Pressure

Pressure in a refrigeration system is a very important parameter and a multi-stage compression system
adds variables to system design. It is interesting to note that ASHRAE Handbooks do not have the
‘inter-stage pressure’ as a keyword in the search index.
The intermediate pressure selection in two stage subcritical systems is very often made by setting it to
the geometric mean of the maximum and minimum pressures in the system. The formula is so simple to
use in parametric studies that often the underlying assumptions are neglected. The geometric mean
pressure assumes the compression of an ideal gas with identical suction temperature for each stage.
Raha (2002) is using the geometric ratio for an ammonia two stage system. Numerous other studies
(MEBS6006, 2004, IIR, 2003, Jia et al., 2004, and Mitchell and Braun, 1998) use the geometric mean
as the optimum inter-stage pressure value.
Zubair (1996) concludes the COP corresponding to the arithmetic mean of the condensation and
evaporation temperatures is the closest to the maximum COP. Zubair considered the real compressor
performance in his studies and compares his findings to other previous studies that indicate values
different than the geometric mean. Gupta (1984) makes an analytical study of optimum intermediate
pressure and it comes to different values than the geometrical mean but uses saturated conditions for
each stage suction as a constraint. Gupta (1986) continues then the study for azeotrope multi-stage
systems. Ouadha et al. (2005) concludes that the most efficient cycles are those operating with a
saturation intermediate temperature very close to an arithmetic mean of condensation and evaporation
temperatures. The study was made on propane and ammonia assuming a fixed compressor isentropic
efficiency of 80%.
There are multi-stage system studies that focus rather on heat exchangers than compressor. Chen
(1999) makes an optimization for n-stages systems but the study focuses at the heat exchanger
performances and not on the compressor effect upon the system efficiency. Sahin et al. (2001) and
Chen and Wu (1996) optimize a second stage system with regards to the heat loads at different
temperatures by using the analysis methods detailed in Bejan (1995).
Radcenco et al. (1983) recommends a refrigerant specific correction coefficient for the geometric mean
value. Mitchell and Braun (1998) indicate similar differences but it is difficult to determine the
assumptions included in the analysis. The inter-stage pressure is 1.125 the value of the geometric mean
for a screw compressor and 0.875 for a reciprocating compressor. Tiedeman and Sherif (2003) and
Manole (2002) challenge the applicability of the geometric mean indicating the order of magnitude of
the possible errors. The limitation of the geometric mean formula applicability is more evident when
using transcritical refrigerants, due to the increased curvature of the isotherms near the critical point.
Lorentzen and Pettersen (1996) and Pettersen (1997) elaborate on the importance of the gas cooler
pressure upon refrigeration cycle cooling capacity and efficiency. Lorentzen and Pettersen show also a
method to control the gas cooler pressure by adding or removing mass out of the system by mechanical
means or by thermal means (Lorentzen et al., 1993). Manole (2005a) is using thermal means and
Manole (2005b) combined thermal and mechanical means to accomplish the same task.
Furuya and Kanai (2001), Lord et al. (1997), and Lorentzen (1993) use a two stage compressor to get
vapors from economizer but no comments are made on the optimum compressor efficiency. Manole
(2002, 2005a), Teknologisk Institute Vesttherm (2001), Muehlbauer (2004), and Liao et al. (2000)

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006
show various methods to calculate the optimum gas cooler pressure. The gas cooler pressure is very
important to provide most of liquid to the evaporator with minimum work.

1.3. System Optimization

An expert compressor design must start with understanding how the system works. The extended
literature review made in this study quickly revealed that the pieces of information needed for
optimizing compressor operating parameters in multi-stage systems are available but not easily
interlocking. Same observation was made in a recent review on the challenges of lubricating CO2
compressors (Manole, 2006.)
A compressor is a system component that has mechanical, electrical, and thermal losses. There are
system thermodynamics studies that present results itemizing the losses introduced in the system by
compressor (Liang and Huehn, 1991 and ARTI, 2003). Bejan (1996), Mironova and Tsirlin (1994),
Chen and Huang (1988), and Stone (1996) apply Second Law of Thermodynamics analysis to system
components by using flow, volume, surface, and time constraints that reflect the system operating
conditions. Ait-Ali (1995) and Velasco et al. (1997) review the extensive work done by Chen and
Bejan (1996) on heat exchanger optimization and work further on a finite-time optimization of a heat
exchanger integrated in a system. Mohamed (2006) and Bejan (1995) studied unbalanced heat
exchangers that experience variable intensity heat transfer along the heat transfer surface. Krakow
(1994) makes an itemized analysis of a heat pump entropy generation and proves that the compressor,
followed by the condenser, are the main entropy generators

2. Inter-Stage Pressure and Temperature

2.1. Compressor Discharge Temperature

Figure 1 shows a generic temperature profile for the refrigerant supercritical vapors in the gas cooler of
a counter flow water heater. The isotherm curvature by the critical point leads to more complicated
thermodynamic optimization of the gas cooler (Neksa et al., 1998) and the attention is again focused on
the heat exchanger while still using the geometric mean assumption for the two-stage compressors. The
temperature of the gas cooler cold end is significant in controlling the system efficiency and cooling
capacity (Manole, 2002 and Manole, 2005a). The curvature of the temperature profile above the critical
point is due to the higher specific heat value of the supercritical CO2 in that region. The pinch towards
the hot end of the gas cooler is encountered also in condensers. The approach temperature and the

Figure 1 Temperature profile in a gas cooler Figure 2 Thermodynamic losses in a gas cooler

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006
pinch temperature values are so important to the gas cooler optimization that often the region between
the pinch zone and the hot end is not studied much further.
Figure 2 shows how important is the region between the pinch point and the hot gas of the gas cooler
(Kim et al., 2005, Sienel, 2002, and Bullard and Rajan, 2004). In that region thermodynamic losses
occur at a high rate. Since the hot gas temperature is set by the compressor discharge temperature, the
gas cooler thermodynamic efficiency is strongly dependent on the compressor discharge temperature.
The compressor can be optimized using the discharge function as an object function.
There is another reason why there is less interest in studying the compressor discharge temperature.
Compressor’s performance is often evaluated by comparing to the isentropic work. The isentropic
compression is regarded as requiring the minimum work, as indicated by the Carnot diagram (see
reference USU, 2005). The discharge temperature of an isentropic compression appears to be the best
that can be achieved. Riffe (1994) and Wu (1994) point out towards the great effect that the internal
cooling in a compressor can have upon the overall cycle efficiency and even suggest the use of a cycle
different than the reverse Carnot cycle as the perfect refrigeration cycle. Riffe shows that an isothermal
compression is termodynamically feasible and leads to a better efficiency than the reverse Carnot cycle.
Prasad (1981) realizes the significance of the discharge gas temperature and chooses to remove the
‘superheat horn’ during the analysis of a two-stage system. His analysis concludes that optimum inter-
stage pressure is about 14% larger than the geometrical mean value. Alefeld (1987) makes a detailed
analysis of compressor heat pumps and refrigerators. He points out that there is no such thing like First
Law analysis since the experimentally determined charts are already embedding the Second Law.
Cooling compressors is common for air or ammonia compressors thus the concept of a isothermal
compression is not a novelty. Süß and Kruse (1998) studied the heat transfer during compression in a
CO2 reciprocating compressor cylinder and indicate that the residence time of the gas in the cylinder is
top short for a significant heat exchange between gas and compression. It happens though that the
compression duration in a scroll compressor can be five times longer.

2.2. The cost of the last cooling Watt

For example, let us consider a heat pump that has a COP of 2.5. That means that for each W of
additional power delivered to the compressor, 2.5 W of heat will be delivered at the discharge
temperature. That means that the extra 2.5 W have a high available work content. Comparing to the
thermodynamic potential at 20°C, the temperature of the incoming water, 0.61 available work is wasted
for each watt of additional power input. If it is to compare to the temperature of the heat source, -4°C,
then each additional watt of power input leads to 0.87 W available work loss.
Table l. The cost of last cooling watt (water outlet: 60°C, compressor discharge: 140°C)
Reference temperature, °C -4 20 60 80
Available work loss, W/K 0.87 0.73 0.48 0.36
Table 1 suggests that 0.36 W available work will be saved for each last added compressor power watt if
the compressor could deliver a larger flow rate at a lower discharge temperature value of 80°C. A
similar analysis would show the approach temperature causing much less available work loss in the gas
cooler.
There are a few studies considering the effect of the suction or discharge temperature upon the
compressor and system efficiency. The ARTI (2003) report offers experimental data and empirical
equations to calculate the effect of superheating upon the efficiency for single and two stage
compressors. Kim et al. (2004) show a high-pressure ‘pump’ in the second stage that can be used as a
method of reducing the thermodynamic losses at the hot end of the gas cooler. However, the isentropic
efficiency of single and two-stages is calculated for a constant 10°K superheating. The beneficial effect

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006
of cooling during compression is detected experimentally by Cutler et al. ( 2000) but is rather attributed
in the results interpretation to experimental error than to lower polytropic coefficient. Manole (2002)
indicates that the polytropic coefficient during compression is a major factor in optimizing the inter-
stage pressure. The optimum design of in-series heat exchangers is studied by Nafey (2000). By
treating the hot end of the gas cooler as a heat exchanger in-series with the rest of the gas cooler, one
can use different optimization criteria for the two in-series gas cooler components.
Liao et al. (2000) use empirically obtained compressor efficiency to optimize gas cooler pressure. The
gas cooler pressure control is made with the goal of controlling the thermodynamic state at the cold end
of the gas cooler. The present study makes a step further and investigates how system efficiency can be
enhanced by making the compressor reduce or eliminate the less efficient gas cooler hot end.

2.3. Inter-Stage Pressure and Temperature – Parametric Study

The ARTI (2003) analysis shows how complex the job is, that is to include both the pressure ratio, and
the superheat in optimizing a refrigeration system. The reason is that different to other refrigerants, the
curvature of the isotherms change dramatically near the critical point
A temperature profile along a heat pump gas cooler was selected out of data available in literature
(Hwang et al., 2005, Kim et al., 2005, Liao et al., 2000.) The length of the gas cooler is normalized in
this study. The first investigated detail is the fast temperature decrease at the hot end of the gas cooler.
The refrigerant side heat transfer coefficient and specific heat were calculated to determine the cause of
the rapid temperature variation at the beginning of the cooling process in the gas cooler. It is interesting
to observe that despite the intense cooling experienced by the gas, the local heat transfer coefficient has
actually the least values at the end of the cooler (Manole, 2002.) That indicates that the main cause of
the intense heat transfer at the hot end of the gas cooler is the larger temperature difference between gas
and cooling medium, as indicated in Figure 1.
Let us assume that the increase in superheat is directly translated into an increase of cooling capacity.
Figure 3 shows the effect of one degree of additional superheating upon the isentropic work and
cooling increase. Both parameters have a fast decrease with increasing the superheat at low values of
superheat. Figure 4 shows the ratio between the increase in cooling capacity and isentropic
compression work for various suction pressures. At low suction pressure, the larger the superheating
the more cooling can be obtained for each additional superheating. At a suction pressures of 6.2 MPa

Figure 3 Rate of work and cooling increase Figure 4 Last Cooling Watt COP
(suction: 6.9 MPa, discharge: 9.6 MPa) (discharge: 9.6 MPa)
and higher, at first the efficiency of the additional superheating decreases and for superheating of more
than 25K an increase in superheating leads to more efficient compression. The values of the COP in

7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006
Figure 4 are high because it represents the cooling efficiency accomplished only by the last additional
Watt of cooling obtained by the additional superheating. The study continues with the effect of suction
superheating in a refrigeration system with a COP value of 2. Figure 5 shows the positive effect of
superheating upon the COP of the system. Same analysis can be made considering now the effect of
irreversibility introduced to the system by using real compressor. Figure 6 shows a series of compressor
isentropic efficiency as reported by various references. In Figure 5 are plotted data obtained under
various assumptions with regards to superheating and illustrate the large variance that one should
expect in a system efficiency analysis when using one compressor or another or when designing for
various operating conditions.
The calculation of the combined effect of the inter-stage pressure and temperature does not take much
time but leads to a large number of charts. Figure 8 shows a chart of the results obtained for the inter-
stage and discharge conditions of a CO2 two stage compressor. The chart in Figure 8 is representative
for various compressor isentropic efficiency empirical formulae and for various refrigerants as CO2,
R290, R404a, and R410a.

Figure 5 System COP variation with suction Figure 6 Compressor isentropic efficiency
superheating and isentropic compression

Figure 7 COP variation with suction superheating Figure 8 Optimum inter-stage pressure
The curves illustrate the compression work for suction pressures from 2.9 to 6.9 MPa, a discharge
pressure of 9.6 MPa, and an ambient temperature of 15.5°C. The dashed line connecting the dots on the
left side of the chart illustrates the loci when the two stage system efficiency is equal to the efficiency
of a single stage system (the horizontal lines). The dashed line connecting the dots on the left side of
the chart illustrates the loci when the compression work curve has the minimum values. The full line
that connects the dots between the dashed lines shows the loci of the points representing the
compressor performances when the inter-stage pressure has the geometric mean value of the evaporator
7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006
and gas cooler pressures. The vertical dashed line indicates the saturation pressure at the ambient
temperature. The minimum compression work is always achieved at higher values of the inter-stage
pressure than the geometric mean. For the case depicted in Figure 8, the minimum compression work is
accomplished with no superheating at low pressures (upper two curves) and at values near the critical
point for suction pressures higher than 3.6 MPa. At suction pressures around 4 MPa the difference
between the optimum inter-stage pressure and the geometric mean value is the largest.

3. CONCLUSIONS
• The isentropic compression of the reverse Carnot does not have the lowest compression work
that can be obtained in a multi-stage transcritical cycle;
• The isotherms experience strong curvatures in the neighborhood of the critical point and the
effect of the superheating upon the compression work of a transcritical compressor can be either
positive or negative depending on the inter-stage pressure and temperature values;
• Empirically determined compressor efficiency values ought to be used in system optimization;
• The geometric mean does not provide the optimum inter-stage pressure of a transcritical
system;
• A lower discharge temperature in the second stage of compression is recommended. The lower
discharge temperature will set off less entropy generation, thus less available work will be
wasted and lower LCCP value for the thermal system can be achieved.

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7th IIR Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, May 28-31, 2006