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Approaching the performance limit for economized cycles using simplified cycles
Accepted Manuscript Approaching the Performance Limit for Economized Cycles Using Simplified Cycles Margaret M. Mathison , James E. Braun , Eckhard A. Groll PII:
S0140-7007(14)00137-6
DOI:
10.1016/j.ijrefrig.2014.05.025
Reference:
JIJR 2801
To appear in:
International Journal of Refrigeration
Received Date: 2 November 2013 Revised Date:
27 May 2014
Accepted Date: 30 May 2014
Please cite this article as: Mathison, M.M., Braun, J.E., Groll, E.A., Approaching the Performance Limit for Economized Cycles Using Simplified Cycles, International Journal of Refrigeration (2014), doi: 10.1016/j.ijrefrig.2014.05.025. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights:
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A model of a vapor compression cycle with saturated vapor injection was developed. Saturated vapor injection through 3 ports is predicted to increase COP by 12%. It provides 67% of the improvement possible with continuous two-phase injection. Most of the benefits of economization are provided by saturated vapor injection. Most of the benefits of injection are provided with a small number of ports.
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Approaching the Performance Limit for Economized Cycles Using Simplified Cycles
a
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Margaret M. MATHISONa*, James E. BRAUNb, Eckhard A. GROLLb
Marquette University, Department of Mechanical Engineering,
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1637 W. Wisconsin Ave. Milwaukee, WI, 53233 USA
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Phone: 1-414-288-5650, Fax: 1-414-288-7790 [email protected]
b
Purdue University, School of Mechanical Engineering,
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140 S. Martin Jischke Drive
West Lafayette, IN, 47906 USA
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* Corresponding Author
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ABSTRACT Modifications such as economization aim to improve the efficiency of vapor compression
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equipment by cooling the refrigerant during the compression process. A previous study (Mathison et al., 2010) explored the theoretical limit to cycle performance with economizing, which was
defined as the performance when a saturated vapor state was maintained in the compressor by
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continuously injecting a two-phase mixture. However, achieving continuous injection and
controlling the quality of the injected refrigerant poses a substantial challenge. Therefore, the
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current paper investigates the ability of an economized cycle with saturated vapor injection through a finite number of ports to approach the limiting cycle performance. For an airconditioner using R-410A with an evaporation temperature of 5°C and a condensing temperature of 40°C, the model predicts that injecting saturated vapor through three ports will improve the
limiting case.
Multistage system, modeling, injection, energy saving, thermodynamic cycle
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Keywords:
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COP by 12%, which is approximately 69% of the maximum benefit provided by economizing in the
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NOMENCLATURE
COPnorm Normalized coefficient of performance [-]
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COPecon Coefficient of performance of the economized cycle [-]
Coefficient of performance of the single-stage cycle without economization [-]
h
Specific enthalpy [kJ·kg-1]
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Mass flow rate through the compressor [kg·s-1]
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COPss
Mass flow rate through the condenser [kg·s-1]
Mass flow rate through the injection line [kg·s-1]
N
Number of injection ports [-]
p
Pressure [kPa]
rcomp
Ratio of mass flow rate in the compressor to mass flow rate in the condenser [-]
rinj
Ratio of mass flow rate in the injection line to mass flow rate in the condenser [-]
x
Quality [-]
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1. INTRODUCTION 1.1 Background
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The ability of cycle modifications such as intercooling and economizing to improve the
performance of vapor compression equipment by reducing the compressor power consumption and, in some cases, improving the cooling capacity has been demonstrated both experimentally
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and theoretically (Bertsch and Groll, 2008; Cho et al., 2009; Torrella et al., 2009; Wang et al., 2009; Winandy and Lebrun, 2002). Even small improvements in energy efficiency provided by these
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modifications translate to significant overall energy savings due to the widespread use of vapor compression equipment. Therefore, these technologies prove increasingly important as concern over energy costs, energy security, and environmental sustainability continue to grow. Intercoolers and economizers are typically installed between compressor stages, but the
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cost of multi-stage compressors often prevents their implementation in smaller scale applications. The development of compressors with ports for refrigerant injection during the compression process presents a more cost-effective method for incorporating economization into vapor
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compression cycles, improving the viability of economizing for all applications. A scroll compressor with a single refrigerant injection port has been patented by Copeland Corporation
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(Perevozchikov, 2003) and marketed for air-conditioning applications, but other rotary compressor designs such as the rolling piston or screw could also be modified to incorporate injection ports. In addition, the number of injection ports can be increased at relatively low cost to essentially break the compression process into multiple stages within a single compression chamber. As the number of injection ports increases, providing more opportunities to inject cool, economized refrigerant, the performance of the compressor and the overall system should increase. This
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hypothesis is supported by the results of an experimentally validated model developed by Jung et al. (1999), which indicate that a cycle with three-stage compression and two economizers has a
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higher coefficient of performance (COP) than a cycle with two-stage compression and one economizer.
Therefore, Mathison et al. (2010) developed a thermodynamic model of the vapor
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compression cycle to study the effect of increasing the number of injection ports in an economized cycle and to predict the theoretical limit to cycle performance when refrigerant is injected
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continuously. The model assumes that the compressor operates with a constant isentropic efficiency that is unaffected by changing the number of injection ports. In addition, it is assumed that the injection process occurs instantaneously, at a constant pressure, and the injected refrigerant mixes instantaneously with the refrigerant in the compression chamber. The benefits of economizing will be maximized when the economized refrigerant provides as much cooling as
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possible; however, in most compressors the refrigerant in the compression chamber should remain in the vapor phase to avoid damage due to liquid droplets. While scroll compressors can tolerate the presence of liquid, supplying a two-phase refrigerant to the condenser will tend to
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decrease its effectiveness because the convective heat transfer coefficient decreases with quality.
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For these reasons, it is assumed that the limiting performance with economization is achieved when the refrigerant in the working chamber remains at the saturated vapor state throughout the compression process.
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In order to maintain a saturated vapor state in the compression chamber, it is necessary to inject a two-phase refrigerant mixture. Although this will introduce liquid into the compressor, it
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is assumed that the injected liquid is instantaneously vaporized as it absorbs the heat of compression and thus, will not cause any damage. The quality of the injected refrigerant is
determined such that the instantaneous injection and mixing process results in a saturated vapor state in the compression chamber. The economized refrigerant is supplied to the injection ports
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by phase separators, as Figure 1 illustrates for the case with three injection ports operating at
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three intermediate pressures. It is assumed that the phase separators operate by drawing off the saturated vapor generated during the expansion process, plus enough liquid to achieve the desired quality in the injection line. The result is that the refrigerant entering each expansion valve is a saturated liquid. Figure 2 plots the state of the refrigerant at each point in the cycle on a
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pressure-enthalpy diagram with labels corresponding to the cycle in Figure 1. The results are
Figure 1. Vapor compression cycle with injection and flash-tank economization.
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presented for a cycle using R-410A with an evaporating temperature of -20°C, a condensing temperature of 50°C, and a compressor efficiency of 70%; the superheat at the evaporator exit
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and the subcooling at the condenser exit are both specified as 0°C. As the number of injection ports increases infinitely, the compression process will follow the saturated vapor curve, as shown in Figure 3 for the same operating conditions used in Figure 2.
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Not only does this minimize the average temperature of the refrigerant as it undergoes the
compression process without entering the two-phase region, but also it maximizes the refrigerant
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density. Because less work is required to compress a denser working fluid, the power consumption of the compressor is minimized. An additional benefit of maintaining a saturated
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vapor state in the compressor is that the condensation process occurs isothermally, eliminating
Figure 2. Pressure-enthalpy diagram for an R-410A vapor compression cycle with three ports for injecting two-phase economized refrigerant in the compressor.
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the irreversibilities typically associated with supplying highly superheated vapor to the condenser. Similarly, the state of the refrigerant entering the expansion valves will follow the
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saturated liquid curve and saturated liquid will be supplied to the evaporator inlet. While this increases the cooling capacity of the cycle per unit of mass flow through the evaporator, the
cooling capacity of the cycle per unit of mass flow through the condenser actually decreases due
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to a reduction in mass flow rate through the evaporator. Nonetheless, the COP of the cycle
increases because the large reduction in power consumption compensates for the reduction in
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cooling capacity. The normalized cooling COP is defined as the ratio of the COP with economizing,
Figure 3. Pressure-enthalpy diagram for an R-410A vapor compression cycle with continuous injection of two-phase economized refrigerant in the compressor.
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COPecon, to the COP for the same cycle with a single-stage compressor and no economizing, COPss:
(1)
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=
Figure 4 plots the normalized cooling COP as a function of the number of injection ports assuming that equal pressure ratios exist between the injection ports. The horizontal line indicates the
maximum performance achieved with continuous injection. The operating conditions are the
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same as those used for Figures 2 and 3.
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While the theoretical benefits possible through economization are substantial, the obstacles to achieving the limiting performance are equally significant. Not only is there no
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mechanism for continuously injecting refrigerant into a compression chamber, but also there is no
Figure 4. Variation in normalized COP with number of injection ports for R-410A cycle operating at an evaporating temperature of -20°C and condensing temperature of 50°C with two-phase injection.
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mechanism for generating economized refrigerant at an infinite number of injection pressures. Even with a finite number of injection pressures, it proves very difficult to control the quality of
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the refrigerant supplied by the economizer. Therefore, one important simplification that improves the feasibility of this concept is the use of saturated vapor refrigerant in the injection process as opposed to two-phase refrigerant.
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While injecting saturated vapor will not provide as much cooling as injecting a two-phase mixture, the system will prove much easier to control. In addition, this reduces any concern about the
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effect of liquid droplets in the injected flow on compressor durability. The model developed in this paper compares the performance of an economized cycle with continuous injection of a saturated vapor to the optimum performance of an economized cycle with continuous injection of a two-phase mixture. In addition, the model is exercised with a finite number of injection ports to investigate the ability of a simplified cycle to approach the performance of a cycle with continuous
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injection. Although eliminating two-phase injection and reducing the number of injection ports considerably simplifies the cycle, actually designing a system to supply saturated vapor to multiple injection ports operating at different pressures remains very challenging. Beyond the practical
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issues associated with fitting additional ports in a compressor, the process of supplying saturated
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vapor to each port at a different pressure introduces significant complexity in the cycle. Therefore, this paper focuses on estimating the theoretical improvements possible with injection to determine whether further work is justified to implement these modifications.
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1.2 Objectives While the previous study investigated the limiting performance of the economized cycle
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when two-phase refrigerant is injected continuously to maintain a saturated vapor state in the compressor, the current study aims to develop a model of the economized vapor compression
cycle when saturated vapor is used as the injected refrigerant. The model will be used to study
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the effect of the number of injection ports on cycle performance and to predict the cycle
performance with continuous injection. The results with saturated vapor injection will be
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compared to the results with two-phase injection to determine how closely the limiting cycle performance can be approached using a simplified cycle. The effect of different operating conditions on the results will also be explored in order to identify applications that show the most
2. ANALYSIS 2.1 Model Development
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potential for improved performance through economizing.
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The vapor compression cycle was modeled both with and without economizing modifications using Engineering Equation Solver (EES; Klein, 2009). Mathison et al. (2010)
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describes the development of both the basic cycle model and the model of the economized cycle with multiple ports for injecting two-phase refrigerant during the compression process. Both models require the user to specify the evaporating and condensing temperatures, degree of superheat at the compressor inlet, compressor isentropic efficiency, and degree of subcooling at the condenser outlet. The model calculates the compressor power consumption, the cycle’s heating and cooling capacity, and the COP of the cycle assuming that pressure drops in the heat
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exchangers and heat transfer to the throttling device and compressor are negligible. Although economizing can be used to improve performance in both cooling and heating modes, the study
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focuses on the cycle performance in cooling mode because of the prevalence of vapor compression cycles in cooling equipment.
Figure 1 shows the configuration of the economized cycle considered in the previous
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study. In this cycle, a phase separator is used to supply two-phase refrigerant to each injection
port; the quality and mass flow rate of the refrigerant in the injection line is controlled such that
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mixing the injected refrigerant with the refrigerant in the compressor results in a saturated vapor state. Mathison et al. (2010) describes the process used to calculate the mass flow rate and quality in each injection line in more detail. The pressure in each injection line is determined such that the pressure ratios between the injection ports are equalized:
=
=
(2)
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where N represents the number of injection ports. In a multi-stage compressor, it can be shown that operating with equal pressure ratios across the compressor stages minimizes the compressor
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power consumption (Moran and Shapiro, 2000). However, this proof assumes that the working
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fluid can be modeled as an ideal gas with constant specific heats and that each stage operates isentropically with the same inlet temperature. While the same analysis applies to compressors with isentropic efficiencies less than 100% as long as each stage has the same efficiency, most compressors deviate from this behavior in practice. For example, the optimal injection pressure for minimizing power consumption will be slightly higher in the economized cycle due to the changing mass flow rate through the compressor, and therefore assuming equal pressure ratios will result in the model underestimating the cycle performance. Nonetheless, assuming equal
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pressure ratios will provide a reasonable estimate of the benefits available through economizing and the method for determining injection pressures becomes less significant as the number of
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injection ports increases. The model also assumes that each phase separator draws off all vapor generated during the previous expansion process, and thus a saturated liquid is supplied to the inlet of each
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expansion valve. Figure 2 shows the states of the refrigerant in the economized cycle with three injection ports when these assumptions are applied. The labeled states correspond to those
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identified on the cycle diagram in Figure 1. As described in Mathison et al. (2010), the specified evaporating temperature of -20°C and the evaporator superheat of 0°C fix the refrigerant properties at State 1, entering the compressor. The isentropic efficiency of the compressor, specified as 70%, is used to determine the properties at the end of each compression process (States 2[1..N] and State 4). States 3[1..N] are the saturated vapor states reached in the
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compressor after the instantaneous mixing processes at the respective injection pressures. Assuming that there is no subcooling at the condenser exit, the condensing temperature of 50ºC can be used to determine the saturated liquid properties at State 5. The refrigerant then expands
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in an isenthalpic process to the phase separator operating at the highest injection pressure;
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therefore, the enthalpy and pressure fix the state at the inlets to each of the phase separators, States 6[1..N]. States 9[1..N] represent the refrigerant states leaving the phase separators through the injection lines, and States 7[1..N] represent the saturated liquid states at the inlets to each of the expansion devices following the phase separators. In the current study, the same cycle is considered assuming that saturated vapor is supplied through the injection lines in place of two-phase refrigerant. The appearance of the cycle
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does not change, and therefore the same numbering system is used in the cycle analysis. The properties at the compressor inlet are still fixed by the evaporating temperature and superheat,
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and the isentropic efficiency of the compressor is still used to determine the properties at the end of each compression process (States 2[1..N] and State 4). However, it is no longer assumed that the refrigerant is saturated vapor at States 3[1..N], following the mixing process with the injected refrigerant. Instead, the injected refrigerant at States 9[1..N] is assumed to be at the saturated
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vapor state with properties fixed by the injection pressure. The properties at States 3[1..N] are
ℎ" # =
$% ∙'( )* ∙' $%
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determined by applying a mass and energy balance to the mixing process:
(3)
In this equation, rcomp and rinj represent the mass flow rates through the compressor and injection line, respectively, and are defined as a fraction of the total mass flow rate through the condenser.
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The index is used to indicate that rcomp[i] is the fraction of the total mass flow rate that enters the compressor at pressure pinj[i], and rinj[i] is the fraction of the total mass flow rate through the injection line at pressure pinj[i]:
,
)*
(4)
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+ # =
$%
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+ # =
(5)
,
The mass fractions must be known in order to solve for the enthalpy of the refrigerant at
States 3[1..N] and can be determined by applying mass and energy balances to the phase separators. Because each phase separator is assumed to be a well-insulated, steady-state device with one exit that is saturated liquid (States 7[1..N]) and one exit that is saturated vapor (States
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9[1..N]), it can be shown that the quality of the refrigerant entering the phase separator (States 6[1..N]) fixes the mass fractions: '0 1'2 3 ' 1'2
= + # + 1 ∙ 45 #
+ # = + # + 1 − + #
(6)
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+ # = + # + 1 /
(7)
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The term x6[i] represents the quality at the inlet to each phase separator, which is determined by assuming that the expansion valve that precedes each phase separator operates isenthalpically.
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The enthalpy of the refrigerant in each expansion valve can be determined based on the inlet pressure because it assumed that the refrigerant entering each expansion valve is saturated liquid. Equations (6) and (7) are solved by recognizing that the mass fraction entering the phase separator operating at the highest pressure is unity, rcomp[N+1] = 1, because it is defined relative to
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the mass flow rate through the condenser. Therefore, these equations can first be applied with i = N and the calculations can then be repeated for the phase separators at successively lower injection pressures until i = 1.
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2.2 Model Results
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Figure 5 shows the results obtained by solving these equations in EES for a cycle with three ports and the same operating conditions that were used to generate the previous figures. The compressor inlet state, State 1, and the injected refrigerant states, States 3[1..N], fall on the saturated vapor curve, while the inlet states to each of the expansion valves, State 5 and States 7[1..N], fall on the saturated liquid curve. Just as in the previous model, the results of which were plotted in Figure 2, the compression process follows a stair step pattern with the enthalpy of the refrigerant in the compressor decreasing instantaneously during each injection process. However,
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the decrease in enthalpy is much smaller when saturated vapor is used as the injected refrigerant instead of a two-phase mixture, and thus the overall increase in enthalpy from the inlet to the exit
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of the compressor is much greater. The refrigerant also exits the compressor at a much higher temperature when saturated vapor is injected instead of a two-phase mixture, as would be
expected; this corresponds to an increase in irreversibilities associated with desuperheating the
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refrigerant in the condenser.
The expansion processes appear identical regardless of whether the model considers
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saturated vapor or two-phase refrigerant injection. This results from specifying that the injection
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lines draw off all of the vapor generated during the expansion process in both cases; the cycle
Figure 5. Pressure-enthalpy diagram for a vapor compression cycle with three ports for injecting saturated vapor economized refrigerant in the compressor.
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using two-phase injection also draws off enough liquid to achieve the desired quality in the injection lines, but this does not change States 6[1..N], States 7[1..N], or State 8. This means that
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the mass flow rates through the injection lines are much lower when saturated vapor is used instead of two-phase refrigerant, which will significantly reduce the total mass flow rate of
refrigerant exiting the compressor when comparing two cycles designed to provide the same
cooling capacity. The reduction in mass flow rate through the condenser with saturated vapor
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injection is accompanied by an increase in refrigerant superheat entering the condenser.
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Therefore, a more detailed heat exchanger model would be required to fully understand the impact of saturated vapor versus two-phase injection on condenser performance. When the number of injection ports was increased to estimate the performance of the cycle with continuous injection of two-phase refrigerant, the state of the refrigerant in the compressor ultimately followed the saturated vapor curve. However, continuously injecting
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saturated vapor does not provide as much cooling to the compressor and thus, the state of the refrigerant in the compressor becomes more superheated during the compression process despite the continuous injection, as shown in Figure 6. As was the case with three injection ports, the
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state of the refrigerant entering the expansion valves is identical regardless of whether the
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continuous injection process uses saturated vapor or a two-phase mixture; in both cases the state of the refrigerant entering the expansion valves follows the saturated liquid curve.
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Figure 6. Pressure-enthalpy diagrams for a vapor compression cycle with continuous injection of
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saturated vapor economized refrigerant in the compressor.
Figure 7 compares the model results for the economized cycle with saturated vapor
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injected through an increasing number of ports to the results obtained previously considering injection of a two-phase mixture. The results are generated for a cycle using R-410A with an
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evaporating temperature of -20°C, a condensing temperature of 50°C, and a compressor efficiency of 70%; the superheat at the evaporator exit and the subcooling at the condenser exit are both specified as 0°C. The figure shows the normalized cooling COP, again defined as the ratio of the COP for the cycle with economizing to the COP for the same cycle with a single-stage compressor and no economizing, with varying numbers of injection ports.
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In both cases, the normalized COP of the cycle increases with the incorporation of additional injection ports and approaches a maximum value, as would be expected. In general,
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the performance improvements achieved with saturated vapor injection are less than those achieved with two-phase refrigerant injection and the difference between the performance
improvements increases as the number of injection ports increases. However, injecting saturated vapor actually improves the cycle COP by 21.5% over its baseline value with a single injection port,
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which is slightly better than the 21.1% improvement in COP seen with the injection of two-phase
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refrigerant through one port. With two injection ports, injecting two-phase refrigerant improves the COP by 29%, whereas injecting saturated vapor improves the COP by 28%. Similarly, injecting
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two-phase refrigerant through three ports improves the COP by 33%, whereas injecting saturated
Figure 7. Variation in normalized COP with number of injection ports for R-410A cycle operating at evaporating temperature of -20°C and condensing temperature of 50°C when economization is implemented with two-phase versus saturated vapor injection.
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vapor through three ports improves the COP by 32%. The horizontal line in Figure 7 represents the performance of the cycle with continuous injection; an improvement of approximately 46% is
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possible with two-phase refrigerant injection compared to an improvement of 40% with saturated vapor injection. Thus, the use of saturated vapor injection provides approximately 87% of the potential improvement possible with two-phase injection for this example.
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Although the difference between the cycle performance with saturated vapor and twophase injection becomes significant with large numbers of injection ports, these results suggest
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that much of the benefit of economizing can be achieved with only two or three injection ports. The incremental performance improvements gained by adding further ports, which require additional phase separators and expansion devices, are unlikely to justify the accompanying increase in cost and complexity. Similarly, the slightly better performance offered by two-phase injection compared to saturated vapor injection, especially when considering two or three
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injection ports, does not justify the substantial increase in complexity associated with controlling the quality of a two-phase refrigerant. Therefore, Figure 7 suggests that development of the
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economized cycle should focus on using saturated vapor injection with two to four ports. The small difference between the economized cycle performance with two-phase injection
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and saturated vapor injection can be explained by considering the trends in cooling capacity and power consumption, which are used to calculate COP. Both cycles should experience a decrease in power consumption relative to the unmodified cycle due to the cooling provided by economization. However, Figure 5 showed that the refrigerant exiting the compressor in a cycle with saturated vapor injected through three ports is still highly superheated, whereas using three injection ports with two-phase injection provides more cooling and substantially reduces the
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temperature at the compressor exit, as shown in Figure 2. Because decreasing the refrigerant temperature increases its density and less work is required to compress a higher density fluid, the
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cycle with two-phase injection consumes less power relative to the cycle with saturated vapor injection. Figure 8 confirms that the reduction in power consumption achieved by injecting twophase refrigerant is almost twice the reduction provided by injecting saturated vapor. The normalized power consumption is defined as the ratio of the power consumption of the
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of mass flow for the unmodified vapor compression cycle.
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economized cycle per unit of mass flow through the condenser to the power consumption per unit
Figure 8. Variation in normalized power consumption with number of injection ports for R-410A cycle operating at evaporating temperature of -20°C and condensing temperature of 50°C when economization is implemented with two-phase versus saturated vapor injection.
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While injecting two-phase refrigerant provides a greater cooling effect to the compressor than injecting saturated vapor, this benefit comes at the sacrifice of the cycle’s cooling capacity.
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Drawing off saturated vapor does not negatively impact the cooling capacity of the cycle because it has already evaporated and the model assumes that there is no superheat at the evaporator
exit. In fact, drawing off saturated vapor during the expansion process decreases the quality of
the refrigerant supplied to the evaporator, which increases its specific cooling capacity. Figure 9
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shows that, for the economized cycle with saturated vapor injection, the cooling capacity per unit
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mass flow through the condenser increases by almost 4% relative to the unmodified vapor
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compression cycle.
Figure 9. Variation in normalized cooling capacity with number of injection ports for R-410A cycle operating at evaporating temperature of -20°C and condensing temperature of 50°C when economization is implemented with two-phase versus saturated vapor injection.
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On the other hand, the cooling capacity per unit mass flow through the condenser decreases for the economized cycle with two-phase refrigerant injection because liquid is drawn
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off in the injection lines along with the saturated vapor. Similar to the cycle with saturated vapor injection, the quality of the refrigerant supplied to the evaporator will decrease relative to the
unmodified cycle, but any benefit that this might provide to the cooling capacity of the cycle is
negated by the substantial decrease in mass flow rate through the evaporator. With the increase
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in mass flow through the injection lines, part of the evaporator’s cooling capacity is essentially
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diverted to provide cooling to the compressor.
The previous study (Mathison et al., 2010) focused on estimating the limit to the economized cycle performance that can be achieved by continuously injecting two-phase refrigerant. However, the current study demonstrates that many of the benefits of economizing can be achieved by injecting saturated vapor through a finite number of injection ports. For the
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conditions discussed previously, an R-410A cycle with an evaporating temperature of -20°C and a condensing temperature of 50°C, the maximum improvement in COP with continuous injection of two-phase refrigerant was found to be approximately 46%. Under the same conditions, an
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economized cycle with three ports for injecting saturated vapor will experience a 32%
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improvement in COP over the baseline cycle, achieving approximately 70% of the maximum benefit of economizing.
The benefits of economizing, and the impact of using a finite number of injection ports or
saturated vapor in lieu of two-phase refrigerant, depend upon the operating conditions and working fluid used in the cycle. For example, supermarket refrigeration systems using R-404A have been identified as an application with significant potential because the benefits of
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economizing are most pronounced in applications with large temperature lifts. Figure 10 illustrates the effect of operating conditions on the economized cycle performance for an R-410A
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system, plotting the improvement in COP provided by economizing as a function of the evaporating and condensing temperatures. The results are plotted for both the optimum case, when two-phase refrigerant is injected continuously to maintain a saturated vapor state in the
compressor, and the more practical case which considers the injection of saturated vapor through
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three ports. As was seen previously, the performance improvements afforded by economizing
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become less significant as the temperature lift across the cycle decreases, whether due to an increase in evaporating temperature or a decrease in condensing temperature. The graph also shows that using three injection ports with saturated vapor provides a substantial portion of the maximum benefit of economizing over the entire range of operating conditions. In the high temperature lift application discussed previously, with an evaporating temperature of -20°C and a
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condensing temperature of 50°C, the model predicted that injecting saturated vapor through three ports would provide 69% of the maximum benefit of economizing. The model predicts similar results when the cycle operates with a lower temperature lift; with an evaporating
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temperature of 15°C and a condensing temperature of 30°C, injecting saturated vapor through
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three ports provides 65% of the maximum benefit of economizing.
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Figure 10. Improvement in COP as a function of operating conditions for an R-410A cycle with continuous
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injection of two-phase refrigerant versus three port injection of saturated vapor refrigerant.
Figure 11 plots the same results for a cycle that uses propane as the working fluid and
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Figure 12 shows the results with R-1234yf as the working fluid. While the cycle performance exhibits the same dependence on evaporating temperature and condensing temperature that was
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observed with R-410A, the percent improvement in COP achieved with continuous two-phase injection changes with the working fluid, as would be expected. Whereas the R-410A cycle experiences a 46% improvement in COP at an evaporating temperature of -20°C and a condensing temperature of 50°C, the COP of the propane cycle increases by 40% and the COP of the R-1234yf cycle increases by 55% under the same conditions. With R-410A, the model predicts that using three ports for saturated vapor injection under these conditions will provide 69% of the maximum improvement in COP possible with continuous injection of two-phase refrigerant. However, the
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difference between saturated vapor injection and two-phase refrigerant injection is even smaller with propane or R-1234yf as the working fluid; injecting saturated vapor through three ports will
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provide 78% of the maximum improvement possible with propane as the working fluid, or 79% of the maximum improvement possible with R-1234yf as the working fluid. Based on these results, it is concluded that R-1234yf in particular shows significant potential to benefit from the
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incorporation of economization.
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Figure 11. Improvement in COP as a function of operating conditions for a propane cycle with continuous injection of two-phase refrigerant versus three port injection of saturated vapor refrigerant.
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Figure 12. Improvement in COP as a function of operating conditions for an R-1234yf cycle with
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continuous injection of two-phase refrigerant versus three port injection of saturated vapor refrigerant.
3. CONCLUSIONS and RECOMMENDATIONS
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Previous theoretical and experimental work has shown that economizing holds significant potential to improve the performance of vapor compression equipment. Mathison et al. (2010)
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predicted that the maximum performance improvement with economizing can be achieved by continuously injecting two-phase refrigerant to maintain a saturated vapor state in the compressor. The work showed that the performance improvements provided by this modification depend upon both the cycle operating conditions and the working fluid. For an R-410A cycle evaporating at 5°C and condensing at 40°C, the cycle model predicted that economizing would improve the COP by approximately 18% in the limiting case. The predicted benefits were even
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greater for a larger temperature lift application, such as a supermarket refrigeration system; with an evaporation temperature of -30°C and a condensing temperature of 40°C, the prior results
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showed that economizing can provide up to a 39% improvement in COP for a cycle using R-410A or a 51% improvement for a cycle using R-404A. Under the same operating conditions, continuous two-phase injection provides a 49% improvement in the COP of an R-1234yf cycle. Therefore, economizing shows great potential for improving the performance of equipment using both
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current refrigerants and alternative refrigerants that are under development for future
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applications. However, continuously injecting refrigerant is not only beyond the capabilities of current compressors, but also requires the development of equipment to continuously supply refrigerant to the compressor at the desired pressure and quality. In addition, injecting a twophase mixture introduces the possibility for damage to the compressor if the evaporation process is not well-understood.
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The current study demonstrates that using a finite number of injection ports and saturated vapor in place of a two-phase mixture provides a practical means for approaching the limiting cycle performance. For the R-410A cycle evaporating at 5°C and condensing at 40°C, the
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model predicts that injecting saturated vapor through three ports will provide a 12% improvement
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in COP, which is approximately 68% of the maximum benefit provided by economizing with continuous injection of two-phase refrigerant. For a cycle operating with R-1234yf under the same conditions, the model predicts that saturated vapor injection through three ports will provide 78% of the benefit of continuous two-phase injection. Therefore, future development of the economized cycle should focus on using saturated vapor injection with two to four ports. Equipment that uses R-1234yf appears to be particularly well-suited to these modifications.
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Although implementing economization with saturated vapor injection in lieu of two-phase refrigerant injection simplifies the cycle, developing the mechanisms and controls required to use
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multiple injection ports still poses a substantial challenge. One of the greatest challenges will be the design of low-cost phase separators that are robust enough to operate over a wide range of conditions and in applications where the equipment experiences on/off cycling. Additional
modeling and experimental efforts are also required to gain a better understanding of the effect of
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economizing on compressor performance. The current model assumes that adding injection ports
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does not change the isentropic efficiency of the compressor, but in addition to lowering the temperature of the working fluid, adding injection ports will introduce new leakage paths in the compressor. Despite these challenges, implementing economizing with multiple injection ports
4. REFERENCES
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shows great potential for improving the energy efficiency of vapor compression equipment.
Bertsch, S.S., Groll, E.A., 2008. Two-stage air-source heat pump for residential heating and cooling
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applications in northern U.S. climates. Int. J. Refrig. 31, 1282-1292. Cho, H., Baek, C., Park, C., Kim, Y., 2009. Performance evaluation of a two-stage CO2 cycle with gas
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injection in the cooling mode operation. Int. J. Refrig. 32, 40-46. Klein, S.A., 2009. Engineering Equation Solver [Computer Software]. F-Chart Software. Jung, D., Kim, H., Kim, O., 1999. A study on the performance of multi-stage heat pumps using mixtures. Int. J. Refrig. 22, 402-413.
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Mathison, M.M., Braun, J.E., Groll, E.A., 2010. Performance limit for economized cycles with continuous refrigerant injection. Int. J. Refrig. 34, 234-242.
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Moran, M.J., Shapiro, H.N., 2000. Fundamentals of Engineering Thermodynamics, fourth ed. Wiley, New York.
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Perevozchikov, M., 2003. Scroll compressor with vapor injection. U.S. Patent 6,619,936.
Torella, E., Llopis, R., Cabello, R., 2009. Experimental evaluation of the inter-stage conditions of a
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two-stage refrigeration cycle using a compound compressor. Int. J. Refrig. 32, 307-315. Wang, X., Hwang, Y., Radermacher, R., 2009. Two-stage heat pump system with vapor-injected scroll compressor using R-410A as a refrigerant. Int. J. Refrig. 32, 1442-1451. Winandy, E.L., Lebrun, J., 2002. Scroll compressors using gas and liquid injection: experimental
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analysis and modeling. Int. J. Refrig. 25, 1143-1156.
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Electronic Annex: EES Code for Saturated Vapor Injection "Note that P_inj[1] represents the lowest injection pressure in the system (equivalent to p9[1]) while P_inj[N] represents the highest injection pressure in the system (equivalent to p9[N])."
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PROCEDURE Pressures(P_evap,P_cond,N:P_inj[1..600]) "Calculates injection pressures assuming equal pressure ratios between injection lines." P_inj[N] := P_cond^(N/(N+1))*P_evap^(1/(N+1)) IF (N > 1) THEN i := N -1 P_inj[i] := P_inj[i+1]^2/P_cond IF (N > 2) THEN Repeat i := i - 1 P_inj[i] := P_inj[i+1]^2/P_inj[i+2] Until (i = 1) ENDIF ENDIF END
PROCEDURE Cycle(R$,P_evap,P_cond,N,N_1,N_tot,eta_s,P_inj[1..600]:h_f[1..600],h_g[1..600], v_g[1..600],m_inj[1..600],m_dot[1..600],h_1[1],h_2[1..600],h_3[1..600],h_4[1],h_5[1],x[1..600], s_2s[1..600],h_2s[1..600]) “Calculates properties at each state point in the system.”
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“First calculate saturated liquid and vapor properties at injection pressures:” i := 0 Repeat i := i+1 h_f[i] := Enthalpy(R$,P=P_inj[i],x=0) h_g[i] := Enthalpy(R$,P=P_inj[i],x=1) v_g[i] := Volume(R$,P=P_inj[i],x=1) Until (i = N)
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h_4[1] = Enthalpy(R$,P=P_cond,x=0) h_5[1] = h_f[1]
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“Next calculate the flowrate through each line based on the quality at the end of each expansion process:” i := N Repeat IF (i = N) THEN h_in = Enthalpy(R$,P=P_cond,x=0) x[i] := Quality(R$,P=P_inj[i],h=h_in) m_dot[i] := (1 - x[i])*1 m_inj[i] := x[i] ELSE x[i] := Quality(R$,P=P_inj[i],h=h_f[i+1]) m_dot[i] := (1 - x[i])*m_dot[i+1] m_inj[i] := x[i] * m_dot[i+1] ENDIF i := i-1 Until (i = 0)
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“Finally, calculate the properties in the compressor based on the isentropic efficiency and a mass and energy balance on each mixing process;” h_1[1] = enthalpy(R$,P=P_evap,x=1) s_2s[1] := entropy(R$,P=P_evap,x=1) h_2s[1] := enthalpy(R$,P=P_inj[1],s=s_2s[1]) h_2[1] := h_1[1] + (h_2s[1] - h_1[1]) / eta_s i := 1 IF (N >1) THEN Repeat h_3[i] := (m_dot[i] * h_2[i] + m_inj[i] * h_g[i])/m_dot[i+1] s_2s[i+1] := entropy(R$,P=P_inj[i],h=h_3[i]) h_2s[i+1] := enthalpy(R$,P=P_inj[i+1],s=s_2s[i+1]) h_2[i+1] := h_3[i] + (h_2s[i+1] - h_3[i])/ eta_s i := i + 1 Until (i > (N-1)) ENDIF h_3[N] := (m_dot[N] * h_2[N] + m_inj[N] * h_g[N])/1 s_2s[N_1] := entropy(R$,P=P_inj[N],h=h_3[N]) h_2s[N_1] := enthalpy(R$,P=P_cond,s=s_2s[N_1]) h_2[N_1] := h_3[N] + (h_2s[N_1] - h_3[N])/ eta_s END
PROCEDURE Work(R$,N,N_1,N_tot,h_1[1],h_2[1..600],h_3[1..600],m_dot[1..600]:w_dot_i[1..600], w_dot,DELTAh[1..600],w_dot_tot[1..600]) “Calculates the compressor power consumption per unit mass flow rate.”
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i := 1 DELTAh[1] := h_2[1] - h_1[1] w_dot_i[1] := m_dot[1]*(h_2[1] - h_1[1]) w_dot := w_dot_i[1] w_dot_tot[1] := w_dot i := i+1 IF (N > 1) THEN Repeat DELTAh[i] := h_2[i] - h_3[i - 1] w_dot_i[i] := m_dot[i]*(h_2[i] - h_3[i - 1]) w_dot := w_dot + w_dot_i[i] w_dot_tot[i] : = w_dot i := i+1 Until (i > N) ENDIF DELTAh[N_1] := h_2[N_1] - h_3[N] w_dot_i[N_1] := 1*(h_2[N_1] - h_3[N]) w_dot := w_dot + w_dot_i[N_1] w_dot_tot[N_1] := w_dot END
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"Cycle Inputs:" R$ = 'R410A’ eta_s = 0.7
N=3 N_1 = N + 1
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T_evap = -20 [C] T_cond = 50 [C] P_evap = Pressure(R$,T=T_evap,x=1) P_cond = Pressure(R$,T=T_cond,x=0)
"Number of injection ports" "Number of compression segments (e.g. one injection port will result in two compression segments)" "Number of pressures in the system (e.g. one injection port will result in three pressures)"
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N_tot = N + 2 temp = 4*N_1 + 1
DELTAT_sup_1 = 0.00001 DELTAT_sub = 0.00001
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q_evap = m_dot[1]*(h_1[1] - h_5[1]) q_cond = (h_2[N + 1] - h_4[1]) q_evap_2 = q_evap / m_dot[1] q_cond_2 = q_cond / m_dot[1] w_dot_2 = w_dot / m_dot[1] COP_CC = q_evap / w_dot COP_HP = q_cond / w_dot
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CALL Pressures(P_evap,P_cond,N:P_inj[1..N]) CALL Cycle(R$,P_evap,P_cond,N,N_1,N_tot,eta_s,P_inj[1..N]:h_f[1..N],h_g[1..N],v_g[1..N], m_inj[1..N],m_dot[1..N],h_1[1],h_2[1..N_1],h_3[1..N],h_4[1],h_5[1],x[1..N],s_2s[1..N_1], h_2s[1..N_1]) CALL Work(R$,N,N_1,N_tot,h_1[1],h_2[1..N_1],h_3[1..N],m_dot[1..N]:w_dot_i[1..N_1], w_dot,DELTAh[1..N_1],w_dot_tot[1..N_1])
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"Compare the economized cycle results to the traditional vapor-compression cycle with single stage compression:"
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"Compressor inlet is specified by superheat and evaporating pressure:" P_ss[1] = P_evap T_ss[1] = T_evap + DELTAT_sup_1 h_ss[1] = enthalpy(R$,T=T_ss[1],P=P_ss[1]) s_ss[1] = entropy(R$,T=T_ss[1],P=P_ss[1]) "Compressor exit is specified by condensing pressure and compressor efficiency:" P_ss[2] = P_cond h_2s_ss = enthalpy(R$,P=P_ss[2],s=s_ss[1]) eta_s = (h_2s_ss - h_ss[1])/(h_ss[2] - h_ss[1]) T_ss[2] = temperature(R$,P=P_ss[2],h=h_ss[2]) s_ss[2] = entropy(R$,P=P_ss[2],h=h_ss[2])
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"Condenser exit is specified by subcooling and condensing pressure:" P_ss[3] = P_cond T_ss[3] = T_cond - DELTAT_sub h_ss[3] = enthalpy(R$,P=P_ss[3],T=T_ss[3]) s_ss[3] = entropy(R$,P=P_ss[3],T=T_ss[3])
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"Evaporator inlet is specified by isenthalpic expansion process from state 3:" P_ss[4] = P_evap h_ss[4] = h_ss[3] T_ss[4] = temperature(R$,P=P_ss[4],h=h_ss[4]) s_ss[4] = entropy(R$,P=P_ss[4],h=h_ss[4]) x_ss = quality(R$,P=P_ss[4],h=h_ss[4])
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q_evap_rel = q_evap / q_evap_ss q_cond_rel = q_cond / q_cond_ss w_dot_rel = w_dot / w_dot_ss COP_CC_rel = COP_CC/COP_CC_ss COP_HP_rel = COP_HP/COP_HP_ss
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“Compare performance metrics:” q_evap_ss = (h_ss[1] - h_ss[4]) q_cond_ss = (h_ss[2] - h_ss[3]) w_dot_ss = (h_ss[2] - h_ss[1]) COP_CC_ss = q_evap_ss/w_dot_ss COP_HP_ss = q_cond_ss / w_dot_ss
S0140-7007(14)00137-6
DOI:
10.1016/j.ijrefrig.2014.05.025
Reference:
JIJR 2801
To appear in:
International Journal of Refrigeration
Received Date: 2 November 2013 Revised Date:
27 May 2014
Accepted Date: 30 May 2014
Please cite this article as: Mathison, M.M., Braun, J.E., Groll, E.A., Approaching the Performance Limit for Economized Cycles Using Simplified Cycles, International Journal of Refrigeration (2014), doi: 10.1016/j.ijrefrig.2014.05.025. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights:
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A model of a vapor compression cycle with saturated vapor injection was developed. Saturated vapor injection through 3 ports is predicted to increase COP by 12%. It provides 67% of the improvement possible with continuous two-phase injection. Most of the benefits of economization are provided by saturated vapor injection. Most of the benefits of injection are provided with a small number of ports.
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• • • • •
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Approaching the Performance Limit for Economized Cycles Using Simplified Cycles
a
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Margaret M. MATHISONa*, James E. BRAUNb, Eckhard A. GROLLb
Marquette University, Department of Mechanical Engineering,
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1637 W. Wisconsin Ave. Milwaukee, WI, 53233 USA
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Phone: 1-414-288-5650, Fax: 1-414-288-7790 [email protected]
b
Purdue University, School of Mechanical Engineering,
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140 S. Martin Jischke Drive
West Lafayette, IN, 47906 USA
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* Corresponding Author
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ABSTRACT Modifications such as economization aim to improve the efficiency of vapor compression
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equipment by cooling the refrigerant during the compression process. A previous study (Mathison et al., 2010) explored the theoretical limit to cycle performance with economizing, which was
defined as the performance when a saturated vapor state was maintained in the compressor by
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continuously injecting a two-phase mixture. However, achieving continuous injection and
controlling the quality of the injected refrigerant poses a substantial challenge. Therefore, the
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current paper investigates the ability of an economized cycle with saturated vapor injection through a finite number of ports to approach the limiting cycle performance. For an airconditioner using R-410A with an evaporation temperature of 5°C and a condensing temperature of 40°C, the model predicts that injecting saturated vapor through three ports will improve the
limiting case.
Multistage system, modeling, injection, energy saving, thermodynamic cycle
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Keywords:
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COP by 12%, which is approximately 69% of the maximum benefit provided by economizing in the
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NOMENCLATURE
COPnorm Normalized coefficient of performance [-]
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COPecon Coefficient of performance of the economized cycle [-]
Coefficient of performance of the single-stage cycle without economization [-]
h
Specific enthalpy [kJ·kg-1]
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Mass flow rate through the compressor [kg·s-1]
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COPss
Mass flow rate through the condenser [kg·s-1]
Mass flow rate through the injection line [kg·s-1]
N
Number of injection ports [-]
p
Pressure [kPa]
rcomp
Ratio of mass flow rate in the compressor to mass flow rate in the condenser [-]
rinj
Ratio of mass flow rate in the injection line to mass flow rate in the condenser [-]
x
Quality [-]
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1. INTRODUCTION 1.1 Background
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The ability of cycle modifications such as intercooling and economizing to improve the
performance of vapor compression equipment by reducing the compressor power consumption and, in some cases, improving the cooling capacity has been demonstrated both experimentally
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and theoretically (Bertsch and Groll, 2008; Cho et al., 2009; Torrella et al., 2009; Wang et al., 2009; Winandy and Lebrun, 2002). Even small improvements in energy efficiency provided by these
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modifications translate to significant overall energy savings due to the widespread use of vapor compression equipment. Therefore, these technologies prove increasingly important as concern over energy costs, energy security, and environmental sustainability continue to grow. Intercoolers and economizers are typically installed between compressor stages, but the
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cost of multi-stage compressors often prevents their implementation in smaller scale applications. The development of compressors with ports for refrigerant injection during the compression process presents a more cost-effective method for incorporating economization into vapor
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compression cycles, improving the viability of economizing for all applications. A scroll compressor with a single refrigerant injection port has been patented by Copeland Corporation
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(Perevozchikov, 2003) and marketed for air-conditioning applications, but other rotary compressor designs such as the rolling piston or screw could also be modified to incorporate injection ports. In addition, the number of injection ports can be increased at relatively low cost to essentially break the compression process into multiple stages within a single compression chamber. As the number of injection ports increases, providing more opportunities to inject cool, economized refrigerant, the performance of the compressor and the overall system should increase. This
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hypothesis is supported by the results of an experimentally validated model developed by Jung et al. (1999), which indicate that a cycle with three-stage compression and two economizers has a
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higher coefficient of performance (COP) than a cycle with two-stage compression and one economizer.
Therefore, Mathison et al. (2010) developed a thermodynamic model of the vapor
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compression cycle to study the effect of increasing the number of injection ports in an economized cycle and to predict the theoretical limit to cycle performance when refrigerant is injected
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continuously. The model assumes that the compressor operates with a constant isentropic efficiency that is unaffected by changing the number of injection ports. In addition, it is assumed that the injection process occurs instantaneously, at a constant pressure, and the injected refrigerant mixes instantaneously with the refrigerant in the compression chamber. The benefits of economizing will be maximized when the economized refrigerant provides as much cooling as
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possible; however, in most compressors the refrigerant in the compression chamber should remain in the vapor phase to avoid damage due to liquid droplets. While scroll compressors can tolerate the presence of liquid, supplying a two-phase refrigerant to the condenser will tend to
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decrease its effectiveness because the convective heat transfer coefficient decreases with quality.
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For these reasons, it is assumed that the limiting performance with economization is achieved when the refrigerant in the working chamber remains at the saturated vapor state throughout the compression process.
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In order to maintain a saturated vapor state in the compression chamber, it is necessary to inject a two-phase refrigerant mixture. Although this will introduce liquid into the compressor, it
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is assumed that the injected liquid is instantaneously vaporized as it absorbs the heat of compression and thus, will not cause any damage. The quality of the injected refrigerant is
determined such that the instantaneous injection and mixing process results in a saturated vapor state in the compression chamber. The economized refrigerant is supplied to the injection ports
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by phase separators, as Figure 1 illustrates for the case with three injection ports operating at
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three intermediate pressures. It is assumed that the phase separators operate by drawing off the saturated vapor generated during the expansion process, plus enough liquid to achieve the desired quality in the injection line. The result is that the refrigerant entering each expansion valve is a saturated liquid. Figure 2 plots the state of the refrigerant at each point in the cycle on a
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pressure-enthalpy diagram with labels corresponding to the cycle in Figure 1. The results are
Figure 1. Vapor compression cycle with injection and flash-tank economization.
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presented for a cycle using R-410A with an evaporating temperature of -20°C, a condensing temperature of 50°C, and a compressor efficiency of 70%; the superheat at the evaporator exit
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and the subcooling at the condenser exit are both specified as 0°C. As the number of injection ports increases infinitely, the compression process will follow the saturated vapor curve, as shown in Figure 3 for the same operating conditions used in Figure 2.
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Not only does this minimize the average temperature of the refrigerant as it undergoes the
compression process without entering the two-phase region, but also it maximizes the refrigerant
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density. Because less work is required to compress a denser working fluid, the power consumption of the compressor is minimized. An additional benefit of maintaining a saturated
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vapor state in the compressor is that the condensation process occurs isothermally, eliminating
Figure 2. Pressure-enthalpy diagram for an R-410A vapor compression cycle with three ports for injecting two-phase economized refrigerant in the compressor.
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the irreversibilities typically associated with supplying highly superheated vapor to the condenser. Similarly, the state of the refrigerant entering the expansion valves will follow the
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saturated liquid curve and saturated liquid will be supplied to the evaporator inlet. While this increases the cooling capacity of the cycle per unit of mass flow through the evaporator, the
cooling capacity of the cycle per unit of mass flow through the condenser actually decreases due
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to a reduction in mass flow rate through the evaporator. Nonetheless, the COP of the cycle
increases because the large reduction in power consumption compensates for the reduction in
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cooling capacity. The normalized cooling COP is defined as the ratio of the COP with economizing,
Figure 3. Pressure-enthalpy diagram for an R-410A vapor compression cycle with continuous injection of two-phase economized refrigerant in the compressor.
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COPecon, to the COP for the same cycle with a single-stage compressor and no economizing, COPss:
(1)
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=
Figure 4 plots the normalized cooling COP as a function of the number of injection ports assuming that equal pressure ratios exist between the injection ports. The horizontal line indicates the
maximum performance achieved with continuous injection. The operating conditions are the
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same as those used for Figures 2 and 3.
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While the theoretical benefits possible through economization are substantial, the obstacles to achieving the limiting performance are equally significant. Not only is there no
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mechanism for continuously injecting refrigerant into a compression chamber, but also there is no
Figure 4. Variation in normalized COP with number of injection ports for R-410A cycle operating at an evaporating temperature of -20°C and condensing temperature of 50°C with two-phase injection.
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mechanism for generating economized refrigerant at an infinite number of injection pressures. Even with a finite number of injection pressures, it proves very difficult to control the quality of
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the refrigerant supplied by the economizer. Therefore, one important simplification that improves the feasibility of this concept is the use of saturated vapor refrigerant in the injection process as opposed to two-phase refrigerant.
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While injecting saturated vapor will not provide as much cooling as injecting a two-phase mixture, the system will prove much easier to control. In addition, this reduces any concern about the
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effect of liquid droplets in the injected flow on compressor durability. The model developed in this paper compares the performance of an economized cycle with continuous injection of a saturated vapor to the optimum performance of an economized cycle with continuous injection of a two-phase mixture. In addition, the model is exercised with a finite number of injection ports to investigate the ability of a simplified cycle to approach the performance of a cycle with continuous
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injection. Although eliminating two-phase injection and reducing the number of injection ports considerably simplifies the cycle, actually designing a system to supply saturated vapor to multiple injection ports operating at different pressures remains very challenging. Beyond the practical
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issues associated with fitting additional ports in a compressor, the process of supplying saturated
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vapor to each port at a different pressure introduces significant complexity in the cycle. Therefore, this paper focuses on estimating the theoretical improvements possible with injection to determine whether further work is justified to implement these modifications.
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1.2 Objectives While the previous study investigated the limiting performance of the economized cycle
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when two-phase refrigerant is injected continuously to maintain a saturated vapor state in the compressor, the current study aims to develop a model of the economized vapor compression
cycle when saturated vapor is used as the injected refrigerant. The model will be used to study
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the effect of the number of injection ports on cycle performance and to predict the cycle
performance with continuous injection. The results with saturated vapor injection will be
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compared to the results with two-phase injection to determine how closely the limiting cycle performance can be approached using a simplified cycle. The effect of different operating conditions on the results will also be explored in order to identify applications that show the most
2. ANALYSIS 2.1 Model Development
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potential for improved performance through economizing.
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The vapor compression cycle was modeled both with and without economizing modifications using Engineering Equation Solver (EES; Klein, 2009). Mathison et al. (2010)
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describes the development of both the basic cycle model and the model of the economized cycle with multiple ports for injecting two-phase refrigerant during the compression process. Both models require the user to specify the evaporating and condensing temperatures, degree of superheat at the compressor inlet, compressor isentropic efficiency, and degree of subcooling at the condenser outlet. The model calculates the compressor power consumption, the cycle’s heating and cooling capacity, and the COP of the cycle assuming that pressure drops in the heat
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exchangers and heat transfer to the throttling device and compressor are negligible. Although economizing can be used to improve performance in both cooling and heating modes, the study
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focuses on the cycle performance in cooling mode because of the prevalence of vapor compression cycles in cooling equipment.
Figure 1 shows the configuration of the economized cycle considered in the previous
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study. In this cycle, a phase separator is used to supply two-phase refrigerant to each injection
port; the quality and mass flow rate of the refrigerant in the injection line is controlled such that
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mixing the injected refrigerant with the refrigerant in the compressor results in a saturated vapor state. Mathison et al. (2010) describes the process used to calculate the mass flow rate and quality in each injection line in more detail. The pressure in each injection line is determined such that the pressure ratios between the injection ports are equalized:
=
=
(2)
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where N represents the number of injection ports. In a multi-stage compressor, it can be shown that operating with equal pressure ratios across the compressor stages minimizes the compressor
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power consumption (Moran and Shapiro, 2000). However, this proof assumes that the working
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fluid can be modeled as an ideal gas with constant specific heats and that each stage operates isentropically with the same inlet temperature. While the same analysis applies to compressors with isentropic efficiencies less than 100% as long as each stage has the same efficiency, most compressors deviate from this behavior in practice. For example, the optimal injection pressure for minimizing power consumption will be slightly higher in the economized cycle due to the changing mass flow rate through the compressor, and therefore assuming equal pressure ratios will result in the model underestimating the cycle performance. Nonetheless, assuming equal
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pressure ratios will provide a reasonable estimate of the benefits available through economizing and the method for determining injection pressures becomes less significant as the number of
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injection ports increases. The model also assumes that each phase separator draws off all vapor generated during the previous expansion process, and thus a saturated liquid is supplied to the inlet of each
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expansion valve. Figure 2 shows the states of the refrigerant in the economized cycle with three injection ports when these assumptions are applied. The labeled states correspond to those
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identified on the cycle diagram in Figure 1. As described in Mathison et al. (2010), the specified evaporating temperature of -20°C and the evaporator superheat of 0°C fix the refrigerant properties at State 1, entering the compressor. The isentropic efficiency of the compressor, specified as 70%, is used to determine the properties at the end of each compression process (States 2[1..N] and State 4). States 3[1..N] are the saturated vapor states reached in the
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compressor after the instantaneous mixing processes at the respective injection pressures. Assuming that there is no subcooling at the condenser exit, the condensing temperature of 50ºC can be used to determine the saturated liquid properties at State 5. The refrigerant then expands
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in an isenthalpic process to the phase separator operating at the highest injection pressure;
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therefore, the enthalpy and pressure fix the state at the inlets to each of the phase separators, States 6[1..N]. States 9[1..N] represent the refrigerant states leaving the phase separators through the injection lines, and States 7[1..N] represent the saturated liquid states at the inlets to each of the expansion devices following the phase separators. In the current study, the same cycle is considered assuming that saturated vapor is supplied through the injection lines in place of two-phase refrigerant. The appearance of the cycle
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does not change, and therefore the same numbering system is used in the cycle analysis. The properties at the compressor inlet are still fixed by the evaporating temperature and superheat,
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and the isentropic efficiency of the compressor is still used to determine the properties at the end of each compression process (States 2[1..N] and State 4). However, it is no longer assumed that the refrigerant is saturated vapor at States 3[1..N], following the mixing process with the injected refrigerant. Instead, the injected refrigerant at States 9[1..N] is assumed to be at the saturated
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vapor state with properties fixed by the injection pressure. The properties at States 3[1..N] are
ℎ" # =
$% ∙'( )* ∙' $%
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determined by applying a mass and energy balance to the mixing process:
(3)
In this equation, rcomp and rinj represent the mass flow rates through the compressor and injection line, respectively, and are defined as a fraction of the total mass flow rate through the condenser.
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The index is used to indicate that rcomp[i] is the fraction of the total mass flow rate that enters the compressor at pressure pinj[i], and rinj[i] is the fraction of the total mass flow rate through the injection line at pressure pinj[i]:
,
)*
(4)
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+ # =
$%
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+ # =
(5)
,
The mass fractions must be known in order to solve for the enthalpy of the refrigerant at
States 3[1..N] and can be determined by applying mass and energy balances to the phase separators. Because each phase separator is assumed to be a well-insulated, steady-state device with one exit that is saturated liquid (States 7[1..N]) and one exit that is saturated vapor (States
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9[1..N]), it can be shown that the quality of the refrigerant entering the phase separator (States 6[1..N]) fixes the mass fractions: '0 1'2 3 ' 1'2
= + # + 1 ∙ 45 #
+ # = + # + 1 − + #
(6)
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+ # = + # + 1 /
(7)
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The term x6[i] represents the quality at the inlet to each phase separator, which is determined by assuming that the expansion valve that precedes each phase separator operates isenthalpically.
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The enthalpy of the refrigerant in each expansion valve can be determined based on the inlet pressure because it assumed that the refrigerant entering each expansion valve is saturated liquid. Equations (6) and (7) are solved by recognizing that the mass fraction entering the phase separator operating at the highest pressure is unity, rcomp[N+1] = 1, because it is defined relative to
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the mass flow rate through the condenser. Therefore, these equations can first be applied with i = N and the calculations can then be repeated for the phase separators at successively lower injection pressures until i = 1.
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2.2 Model Results
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Figure 5 shows the results obtained by solving these equations in EES for a cycle with three ports and the same operating conditions that were used to generate the previous figures. The compressor inlet state, State 1, and the injected refrigerant states, States 3[1..N], fall on the saturated vapor curve, while the inlet states to each of the expansion valves, State 5 and States 7[1..N], fall on the saturated liquid curve. Just as in the previous model, the results of which were plotted in Figure 2, the compression process follows a stair step pattern with the enthalpy of the refrigerant in the compressor decreasing instantaneously during each injection process. However,
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the decrease in enthalpy is much smaller when saturated vapor is used as the injected refrigerant instead of a two-phase mixture, and thus the overall increase in enthalpy from the inlet to the exit
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of the compressor is much greater. The refrigerant also exits the compressor at a much higher temperature when saturated vapor is injected instead of a two-phase mixture, as would be
expected; this corresponds to an increase in irreversibilities associated with desuperheating the
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refrigerant in the condenser.
The expansion processes appear identical regardless of whether the model considers
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saturated vapor or two-phase refrigerant injection. This results from specifying that the injection
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lines draw off all of the vapor generated during the expansion process in both cases; the cycle
Figure 5. Pressure-enthalpy diagram for a vapor compression cycle with three ports for injecting saturated vapor economized refrigerant in the compressor.
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using two-phase injection also draws off enough liquid to achieve the desired quality in the injection lines, but this does not change States 6[1..N], States 7[1..N], or State 8. This means that
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the mass flow rates through the injection lines are much lower when saturated vapor is used instead of two-phase refrigerant, which will significantly reduce the total mass flow rate of
refrigerant exiting the compressor when comparing two cycles designed to provide the same
cooling capacity. The reduction in mass flow rate through the condenser with saturated vapor
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injection is accompanied by an increase in refrigerant superheat entering the condenser.
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Therefore, a more detailed heat exchanger model would be required to fully understand the impact of saturated vapor versus two-phase injection on condenser performance. When the number of injection ports was increased to estimate the performance of the cycle with continuous injection of two-phase refrigerant, the state of the refrigerant in the compressor ultimately followed the saturated vapor curve. However, continuously injecting
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saturated vapor does not provide as much cooling to the compressor and thus, the state of the refrigerant in the compressor becomes more superheated during the compression process despite the continuous injection, as shown in Figure 6. As was the case with three injection ports, the
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state of the refrigerant entering the expansion valves is identical regardless of whether the
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continuous injection process uses saturated vapor or a two-phase mixture; in both cases the state of the refrigerant entering the expansion valves follows the saturated liquid curve.
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Figure 6. Pressure-enthalpy diagrams for a vapor compression cycle with continuous injection of
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saturated vapor economized refrigerant in the compressor.
Figure 7 compares the model results for the economized cycle with saturated vapor
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injected through an increasing number of ports to the results obtained previously considering injection of a two-phase mixture. The results are generated for a cycle using R-410A with an
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evaporating temperature of -20°C, a condensing temperature of 50°C, and a compressor efficiency of 70%; the superheat at the evaporator exit and the subcooling at the condenser exit are both specified as 0°C. The figure shows the normalized cooling COP, again defined as the ratio of the COP for the cycle with economizing to the COP for the same cycle with a single-stage compressor and no economizing, with varying numbers of injection ports.
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In both cases, the normalized COP of the cycle increases with the incorporation of additional injection ports and approaches a maximum value, as would be expected. In general,
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the performance improvements achieved with saturated vapor injection are less than those achieved with two-phase refrigerant injection and the difference between the performance
improvements increases as the number of injection ports increases. However, injecting saturated vapor actually improves the cycle COP by 21.5% over its baseline value with a single injection port,
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which is slightly better than the 21.1% improvement in COP seen with the injection of two-phase
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refrigerant through one port. With two injection ports, injecting two-phase refrigerant improves the COP by 29%, whereas injecting saturated vapor improves the COP by 28%. Similarly, injecting
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two-phase refrigerant through three ports improves the COP by 33%, whereas injecting saturated
Figure 7. Variation in normalized COP with number of injection ports for R-410A cycle operating at evaporating temperature of -20°C and condensing temperature of 50°C when economization is implemented with two-phase versus saturated vapor injection.
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vapor through three ports improves the COP by 32%. The horizontal line in Figure 7 represents the performance of the cycle with continuous injection; an improvement of approximately 46% is
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possible with two-phase refrigerant injection compared to an improvement of 40% with saturated vapor injection. Thus, the use of saturated vapor injection provides approximately 87% of the potential improvement possible with two-phase injection for this example.
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Although the difference between the cycle performance with saturated vapor and twophase injection becomes significant with large numbers of injection ports, these results suggest
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that much of the benefit of economizing can be achieved with only two or three injection ports. The incremental performance improvements gained by adding further ports, which require additional phase separators and expansion devices, are unlikely to justify the accompanying increase in cost and complexity. Similarly, the slightly better performance offered by two-phase injection compared to saturated vapor injection, especially when considering two or three
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injection ports, does not justify the substantial increase in complexity associated with controlling the quality of a two-phase refrigerant. Therefore, Figure 7 suggests that development of the
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economized cycle should focus on using saturated vapor injection with two to four ports. The small difference between the economized cycle performance with two-phase injection
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and saturated vapor injection can be explained by considering the trends in cooling capacity and power consumption, which are used to calculate COP. Both cycles should experience a decrease in power consumption relative to the unmodified cycle due to the cooling provided by economization. However, Figure 5 showed that the refrigerant exiting the compressor in a cycle with saturated vapor injected through three ports is still highly superheated, whereas using three injection ports with two-phase injection provides more cooling and substantially reduces the
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temperature at the compressor exit, as shown in Figure 2. Because decreasing the refrigerant temperature increases its density and less work is required to compress a higher density fluid, the
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cycle with two-phase injection consumes less power relative to the cycle with saturated vapor injection. Figure 8 confirms that the reduction in power consumption achieved by injecting twophase refrigerant is almost twice the reduction provided by injecting saturated vapor. The normalized power consumption is defined as the ratio of the power consumption of the
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of mass flow for the unmodified vapor compression cycle.
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economized cycle per unit of mass flow through the condenser to the power consumption per unit
Figure 8. Variation in normalized power consumption with number of injection ports for R-410A cycle operating at evaporating temperature of -20°C and condensing temperature of 50°C when economization is implemented with two-phase versus saturated vapor injection.
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While injecting two-phase refrigerant provides a greater cooling effect to the compressor than injecting saturated vapor, this benefit comes at the sacrifice of the cycle’s cooling capacity.
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Drawing off saturated vapor does not negatively impact the cooling capacity of the cycle because it has already evaporated and the model assumes that there is no superheat at the evaporator
exit. In fact, drawing off saturated vapor during the expansion process decreases the quality of
the refrigerant supplied to the evaporator, which increases its specific cooling capacity. Figure 9
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shows that, for the economized cycle with saturated vapor injection, the cooling capacity per unit
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mass flow through the condenser increases by almost 4% relative to the unmodified vapor
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compression cycle.
Figure 9. Variation in normalized cooling capacity with number of injection ports for R-410A cycle operating at evaporating temperature of -20°C and condensing temperature of 50°C when economization is implemented with two-phase versus saturated vapor injection.
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On the other hand, the cooling capacity per unit mass flow through the condenser decreases for the economized cycle with two-phase refrigerant injection because liquid is drawn
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off in the injection lines along with the saturated vapor. Similar to the cycle with saturated vapor injection, the quality of the refrigerant supplied to the evaporator will decrease relative to the
unmodified cycle, but any benefit that this might provide to the cooling capacity of the cycle is
negated by the substantial decrease in mass flow rate through the evaporator. With the increase
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in mass flow through the injection lines, part of the evaporator’s cooling capacity is essentially
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diverted to provide cooling to the compressor.
The previous study (Mathison et al., 2010) focused on estimating the limit to the economized cycle performance that can be achieved by continuously injecting two-phase refrigerant. However, the current study demonstrates that many of the benefits of economizing can be achieved by injecting saturated vapor through a finite number of injection ports. For the
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conditions discussed previously, an R-410A cycle with an evaporating temperature of -20°C and a condensing temperature of 50°C, the maximum improvement in COP with continuous injection of two-phase refrigerant was found to be approximately 46%. Under the same conditions, an
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economized cycle with three ports for injecting saturated vapor will experience a 32%
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improvement in COP over the baseline cycle, achieving approximately 70% of the maximum benefit of economizing.
The benefits of economizing, and the impact of using a finite number of injection ports or
saturated vapor in lieu of two-phase refrigerant, depend upon the operating conditions and working fluid used in the cycle. For example, supermarket refrigeration systems using R-404A have been identified as an application with significant potential because the benefits of
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economizing are most pronounced in applications with large temperature lifts. Figure 10 illustrates the effect of operating conditions on the economized cycle performance for an R-410A
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system, plotting the improvement in COP provided by economizing as a function of the evaporating and condensing temperatures. The results are plotted for both the optimum case, when two-phase refrigerant is injected continuously to maintain a saturated vapor state in the
compressor, and the more practical case which considers the injection of saturated vapor through
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three ports. As was seen previously, the performance improvements afforded by economizing
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become less significant as the temperature lift across the cycle decreases, whether due to an increase in evaporating temperature or a decrease in condensing temperature. The graph also shows that using three injection ports with saturated vapor provides a substantial portion of the maximum benefit of economizing over the entire range of operating conditions. In the high temperature lift application discussed previously, with an evaporating temperature of -20°C and a
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condensing temperature of 50°C, the model predicted that injecting saturated vapor through three ports would provide 69% of the maximum benefit of economizing. The model predicts similar results when the cycle operates with a lower temperature lift; with an evaporating
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temperature of 15°C and a condensing temperature of 30°C, injecting saturated vapor through
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three ports provides 65% of the maximum benefit of economizing.
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Figure 10. Improvement in COP as a function of operating conditions for an R-410A cycle with continuous
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injection of two-phase refrigerant versus three port injection of saturated vapor refrigerant.
Figure 11 plots the same results for a cycle that uses propane as the working fluid and
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Figure 12 shows the results with R-1234yf as the working fluid. While the cycle performance exhibits the same dependence on evaporating temperature and condensing temperature that was
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observed with R-410A, the percent improvement in COP achieved with continuous two-phase injection changes with the working fluid, as would be expected. Whereas the R-410A cycle experiences a 46% improvement in COP at an evaporating temperature of -20°C and a condensing temperature of 50°C, the COP of the propane cycle increases by 40% and the COP of the R-1234yf cycle increases by 55% under the same conditions. With R-410A, the model predicts that using three ports for saturated vapor injection under these conditions will provide 69% of the maximum improvement in COP possible with continuous injection of two-phase refrigerant. However, the
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difference between saturated vapor injection and two-phase refrigerant injection is even smaller with propane or R-1234yf as the working fluid; injecting saturated vapor through three ports will
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provide 78% of the maximum improvement possible with propane as the working fluid, or 79% of the maximum improvement possible with R-1234yf as the working fluid. Based on these results, it is concluded that R-1234yf in particular shows significant potential to benefit from the
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incorporation of economization.
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Figure 11. Improvement in COP as a function of operating conditions for a propane cycle with continuous injection of two-phase refrigerant versus three port injection of saturated vapor refrigerant.
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Figure 12. Improvement in COP as a function of operating conditions for an R-1234yf cycle with
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continuous injection of two-phase refrigerant versus three port injection of saturated vapor refrigerant.
3. CONCLUSIONS and RECOMMENDATIONS
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Previous theoretical and experimental work has shown that economizing holds significant potential to improve the performance of vapor compression equipment. Mathison et al. (2010)
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predicted that the maximum performance improvement with economizing can be achieved by continuously injecting two-phase refrigerant to maintain a saturated vapor state in the compressor. The work showed that the performance improvements provided by this modification depend upon both the cycle operating conditions and the working fluid. For an R-410A cycle evaporating at 5°C and condensing at 40°C, the cycle model predicted that economizing would improve the COP by approximately 18% in the limiting case. The predicted benefits were even
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greater for a larger temperature lift application, such as a supermarket refrigeration system; with an evaporation temperature of -30°C and a condensing temperature of 40°C, the prior results
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showed that economizing can provide up to a 39% improvement in COP for a cycle using R-410A or a 51% improvement for a cycle using R-404A. Under the same operating conditions, continuous two-phase injection provides a 49% improvement in the COP of an R-1234yf cycle. Therefore, economizing shows great potential for improving the performance of equipment using both
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current refrigerants and alternative refrigerants that are under development for future
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applications. However, continuously injecting refrigerant is not only beyond the capabilities of current compressors, but also requires the development of equipment to continuously supply refrigerant to the compressor at the desired pressure and quality. In addition, injecting a twophase mixture introduces the possibility for damage to the compressor if the evaporation process is not well-understood.
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The current study demonstrates that using a finite number of injection ports and saturated vapor in place of a two-phase mixture provides a practical means for approaching the limiting cycle performance. For the R-410A cycle evaporating at 5°C and condensing at 40°C, the
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model predicts that injecting saturated vapor through three ports will provide a 12% improvement
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in COP, which is approximately 68% of the maximum benefit provided by economizing with continuous injection of two-phase refrigerant. For a cycle operating with R-1234yf under the same conditions, the model predicts that saturated vapor injection through three ports will provide 78% of the benefit of continuous two-phase injection. Therefore, future development of the economized cycle should focus on using saturated vapor injection with two to four ports. Equipment that uses R-1234yf appears to be particularly well-suited to these modifications.
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Although implementing economization with saturated vapor injection in lieu of two-phase refrigerant injection simplifies the cycle, developing the mechanisms and controls required to use
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multiple injection ports still poses a substantial challenge. One of the greatest challenges will be the design of low-cost phase separators that are robust enough to operate over a wide range of conditions and in applications where the equipment experiences on/off cycling. Additional
modeling and experimental efforts are also required to gain a better understanding of the effect of
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economizing on compressor performance. The current model assumes that adding injection ports
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does not change the isentropic efficiency of the compressor, but in addition to lowering the temperature of the working fluid, adding injection ports will introduce new leakage paths in the compressor. Despite these challenges, implementing economizing with multiple injection ports
4. REFERENCES
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shows great potential for improving the energy efficiency of vapor compression equipment.
Bertsch, S.S., Groll, E.A., 2008. Two-stage air-source heat pump for residential heating and cooling
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applications in northern U.S. climates. Int. J. Refrig. 31, 1282-1292. Cho, H., Baek, C., Park, C., Kim, Y., 2009. Performance evaluation of a two-stage CO2 cycle with gas
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injection in the cooling mode operation. Int. J. Refrig. 32, 40-46. Klein, S.A., 2009. Engineering Equation Solver [Computer Software]. F-Chart Software. Jung, D., Kim, H., Kim, O., 1999. A study on the performance of multi-stage heat pumps using mixtures. Int. J. Refrig. 22, 402-413.
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Mathison, M.M., Braun, J.E., Groll, E.A., 2010. Performance limit for economized cycles with continuous refrigerant injection. Int. J. Refrig. 34, 234-242.
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Moran, M.J., Shapiro, H.N., 2000. Fundamentals of Engineering Thermodynamics, fourth ed. Wiley, New York.
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Perevozchikov, M., 2003. Scroll compressor with vapor injection. U.S. Patent 6,619,936.
Torella, E., Llopis, R., Cabello, R., 2009. Experimental evaluation of the inter-stage conditions of a
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two-stage refrigeration cycle using a compound compressor. Int. J. Refrig. 32, 307-315. Wang, X., Hwang, Y., Radermacher, R., 2009. Two-stage heat pump system with vapor-injected scroll compressor using R-410A as a refrigerant. Int. J. Refrig. 32, 1442-1451. Winandy, E.L., Lebrun, J., 2002. Scroll compressors using gas and liquid injection: experimental
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analysis and modeling. Int. J. Refrig. 25, 1143-1156.
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Electronic Annex: EES Code for Saturated Vapor Injection "Note that P_inj[1] represents the lowest injection pressure in the system (equivalent to p9[1]) while P_inj[N] represents the highest injection pressure in the system (equivalent to p9[N])."
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PROCEDURE Pressures(P_evap,P_cond,N:P_inj[1..600]) "Calculates injection pressures assuming equal pressure ratios between injection lines." P_inj[N] := P_cond^(N/(N+1))*P_evap^(1/(N+1)) IF (N > 1) THEN i := N -1 P_inj[i] := P_inj[i+1]^2/P_cond IF (N > 2) THEN Repeat i := i - 1 P_inj[i] := P_inj[i+1]^2/P_inj[i+2] Until (i = 1) ENDIF ENDIF END
PROCEDURE Cycle(R$,P_evap,P_cond,N,N_1,N_tot,eta_s,P_inj[1..600]:h_f[1..600],h_g[1..600], v_g[1..600],m_inj[1..600],m_dot[1..600],h_1[1],h_2[1..600],h_3[1..600],h_4[1],h_5[1],x[1..600], s_2s[1..600],h_2s[1..600]) “Calculates properties at each state point in the system.”
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“First calculate saturated liquid and vapor properties at injection pressures:” i := 0 Repeat i := i+1 h_f[i] := Enthalpy(R$,P=P_inj[i],x=0) h_g[i] := Enthalpy(R$,P=P_inj[i],x=1) v_g[i] := Volume(R$,P=P_inj[i],x=1) Until (i = N)
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h_4[1] = Enthalpy(R$,P=P_cond,x=0) h_5[1] = h_f[1]
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“Next calculate the flowrate through each line based on the quality at the end of each expansion process:” i := N Repeat IF (i = N) THEN h_in = Enthalpy(R$,P=P_cond,x=0) x[i] := Quality(R$,P=P_inj[i],h=h_in) m_dot[i] := (1 - x[i])*1 m_inj[i] := x[i] ELSE x[i] := Quality(R$,P=P_inj[i],h=h_f[i+1]) m_dot[i] := (1 - x[i])*m_dot[i+1] m_inj[i] := x[i] * m_dot[i+1] ENDIF i := i-1 Until (i = 0)
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“Finally, calculate the properties in the compressor based on the isentropic efficiency and a mass and energy balance on each mixing process;” h_1[1] = enthalpy(R$,P=P_evap,x=1) s_2s[1] := entropy(R$,P=P_evap,x=1) h_2s[1] := enthalpy(R$,P=P_inj[1],s=s_2s[1]) h_2[1] := h_1[1] + (h_2s[1] - h_1[1]) / eta_s i := 1 IF (N >1) THEN Repeat h_3[i] := (m_dot[i] * h_2[i] + m_inj[i] * h_g[i])/m_dot[i+1] s_2s[i+1] := entropy(R$,P=P_inj[i],h=h_3[i]) h_2s[i+1] := enthalpy(R$,P=P_inj[i+1],s=s_2s[i+1]) h_2[i+1] := h_3[i] + (h_2s[i+1] - h_3[i])/ eta_s i := i + 1 Until (i > (N-1)) ENDIF h_3[N] := (m_dot[N] * h_2[N] + m_inj[N] * h_g[N])/1 s_2s[N_1] := entropy(R$,P=P_inj[N],h=h_3[N]) h_2s[N_1] := enthalpy(R$,P=P_cond,s=s_2s[N_1]) h_2[N_1] := h_3[N] + (h_2s[N_1] - h_3[N])/ eta_s END
PROCEDURE Work(R$,N,N_1,N_tot,h_1[1],h_2[1..600],h_3[1..600],m_dot[1..600]:w_dot_i[1..600], w_dot,DELTAh[1..600],w_dot_tot[1..600]) “Calculates the compressor power consumption per unit mass flow rate.”
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i := 1 DELTAh[1] := h_2[1] - h_1[1] w_dot_i[1] := m_dot[1]*(h_2[1] - h_1[1]) w_dot := w_dot_i[1] w_dot_tot[1] := w_dot i := i+1 IF (N > 1) THEN Repeat DELTAh[i] := h_2[i] - h_3[i - 1] w_dot_i[i] := m_dot[i]*(h_2[i] - h_3[i - 1]) w_dot := w_dot + w_dot_i[i] w_dot_tot[i] : = w_dot i := i+1 Until (i > N) ENDIF DELTAh[N_1] := h_2[N_1] - h_3[N] w_dot_i[N_1] := 1*(h_2[N_1] - h_3[N]) w_dot := w_dot + w_dot_i[N_1] w_dot_tot[N_1] := w_dot END
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"Cycle Inputs:" R$ = 'R410A’ eta_s = 0.7
N=3 N_1 = N + 1
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T_evap = -20 [C] T_cond = 50 [C] P_evap = Pressure(R$,T=T_evap,x=1) P_cond = Pressure(R$,T=T_cond,x=0)
"Number of injection ports" "Number of compression segments (e.g. one injection port will result in two compression segments)" "Number of pressures in the system (e.g. one injection port will result in three pressures)"
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N_tot = N + 2 temp = 4*N_1 + 1
DELTAT_sup_1 = 0.00001 DELTAT_sub = 0.00001
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q_evap = m_dot[1]*(h_1[1] - h_5[1]) q_cond = (h_2[N + 1] - h_4[1]) q_evap_2 = q_evap / m_dot[1] q_cond_2 = q_cond / m_dot[1] w_dot_2 = w_dot / m_dot[1] COP_CC = q_evap / w_dot COP_HP = q_cond / w_dot
M AN U
CALL Pressures(P_evap,P_cond,N:P_inj[1..N]) CALL Cycle(R$,P_evap,P_cond,N,N_1,N_tot,eta_s,P_inj[1..N]:h_f[1..N],h_g[1..N],v_g[1..N], m_inj[1..N],m_dot[1..N],h_1[1],h_2[1..N_1],h_3[1..N],h_4[1],h_5[1],x[1..N],s_2s[1..N_1], h_2s[1..N_1]) CALL Work(R$,N,N_1,N_tot,h_1[1],h_2[1..N_1],h_3[1..N],m_dot[1..N]:w_dot_i[1..N_1], w_dot,DELTAh[1..N_1],w_dot_tot[1..N_1])
EP
"Compare the economized cycle results to the traditional vapor-compression cycle with single stage compression:"
AC C
"Compressor inlet is specified by superheat and evaporating pressure:" P_ss[1] = P_evap T_ss[1] = T_evap + DELTAT_sup_1 h_ss[1] = enthalpy(R$,T=T_ss[1],P=P_ss[1]) s_ss[1] = entropy(R$,T=T_ss[1],P=P_ss[1]) "Compressor exit is specified by condensing pressure and compressor efficiency:" P_ss[2] = P_cond h_2s_ss = enthalpy(R$,P=P_ss[2],s=s_ss[1]) eta_s = (h_2s_ss - h_ss[1])/(h_ss[2] - h_ss[1]) T_ss[2] = temperature(R$,P=P_ss[2],h=h_ss[2]) s_ss[2] = entropy(R$,P=P_ss[2],h=h_ss[2])
ACCEPTED MANUSCRIPT
"Condenser exit is specified by subcooling and condensing pressure:" P_ss[3] = P_cond T_ss[3] = T_cond - DELTAT_sub h_ss[3] = enthalpy(R$,P=P_ss[3],T=T_ss[3]) s_ss[3] = entropy(R$,P=P_ss[3],T=T_ss[3])
RI PT
"Evaporator inlet is specified by isenthalpic expansion process from state 3:" P_ss[4] = P_evap h_ss[4] = h_ss[3] T_ss[4] = temperature(R$,P=P_ss[4],h=h_ss[4]) s_ss[4] = entropy(R$,P=P_ss[4],h=h_ss[4]) x_ss = quality(R$,P=P_ss[4],h=h_ss[4])
AC C
EP
M AN U
TE D
q_evap_rel = q_evap / q_evap_ss q_cond_rel = q_cond / q_cond_ss w_dot_rel = w_dot / w_dot_ss COP_CC_rel = COP_CC/COP_CC_ss COP_HP_rel = COP_HP/COP_HP_ss
SC
“Compare performance metrics:” q_evap_ss = (h_ss[1] - h_ss[4]) q_cond_ss = (h_ss[2] - h_ss[3]) w_dot_ss = (h_ss[2] - h_ss[1]) COP_CC_ss = q_evap_ss/w_dot_ss COP_HP_ss = q_cond_ss / w_dot_ss