Energy Conversion and Management xxx (xxxx) xxxx

Contents lists available at ScienceDirect

Energy Conversion and Management

journal homepage: www.elsevier.com/locate/enconman

Performance assessment and multi-objective optimization of a novel

transcritical CO2 trigeneration system for a low-grade heat resource
⁎
Qiang Zhang , Zewei Luo, Yongjie Zhao, Rui Cao
School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China

A R T I C LE I N FO A B S T R A C T

Keywords: This work focuses on designing a self-sufficient trigeneration system for low-grade heat resource applications.
Combined cooling For this purpose, a novel transcritical CO2 combined cooling, heating, and power (CCHP) system is proposed,
Heating and power which integrates a Rankine power cycle and an ejector refrigeration cycle (ERC). To evaluate the feasibility of
Low-grade heat resource the proposed system, the mathematical model of the combined cycle is built and validated. The effects of seven
Transcritical CO2 Rankine cycle
key parameters on system performance are investigated from the thermoeconomic viewpoint. Furthermore,
Transcritical CO2 ejector refrigeration cycle
Thermoeconomic analysis
multi-objective optimization is performed for the system when it generates both cooling and power or si-
multaneously produces heating and power. The results show that when using low-grade heat resource, the
proposed plant not only has desirable net power output under all considered conditions, but also achieves
adjustable output for cooling and heating in a broad range. The exergy efficiency of the proposed system and the
coefficient of performance (COP) of ERC under base case conditions are respectively improved by 13.3% and
167.7% compared to the reference cycle. Under optimal conditions, the total useful energy and exergy efficiency
of the system respectively are 127.3 kW and 22.7% for the combined cooling and power (CCP) mode, while
corresponding values are 126.2 kW and 43.6% for the combined heating and power (CHP) mode, respectively.
The cost per unit of exergy products for the system in the CCP mode is 3.4 times more than that in the CHP mode.

1. Introduction warming potential (GWP) and favorable thermo-physical properties

[10]. Moreover, the variable temperature of supercritical CO2 during
Over the past years, conventional fossil fuels shortages and en- heat addition process can generate a better thermal match with the heat
vironmental problems have enforced researchers to develop and use resource. Both experimental and theoretical studies have been per-
sustainable energy systems. Solar energy, geothermal energy, ocean formed to evaluate the CO2 Rankine cycles for low-grade heat resources
thermal energy, as well as industrial waste heat are considered as al- [11–13]. Meng et al. [14] explored the performances of four different
ternative energy sources to meet increasing energy demands and reduce transcritical CO2 (tCO2) cycles for a low temperature heat source and
the greenhouse gas emissions [1,2]. These energy sources are available compared them with the Kalina cycle and the ORC. Their results in-
in large quantity but usually possess a low energy flow density with dicated that transcritical CO2 power cycle had the largest net power
temperatures between ambient and 250 °C, which is the widely ac- output and its economic performance was also competent. An experi-
cepted temperature range for the low-grade heat [3,4]. Therefore, the mental study of tCO2 Rankine cycle for a small-scale power generation
further exploitation of these low-grade heat resources is meaningful but was performed by Ge et al. [15]. They found that parameters of heat
challengeable due to the inefficient energy conversion process. source and heat sink had significant effects on system performance. To
For more efficient use of the low quality heat, the Organic Rankine investigate performance improvements in tCO2 Rankine cycle, some
cycle (ORC) could be one of more appropriate solutions to generate researchers used different CO2-based mixtures as working fluids. Shu
useful power even at low temperatures [5,6]. However, to ensure effi- et al. [16] reported that CO2 mixtures could enlarge the condensation
cient energy conversion, it is vital to select appropriate working fluids temperature range and reduce the high operation pressure. Besides,
and have better temperature match during heat transfer processes in mixtures could obtain better thermoeconomic performance compared
designing ORCs [7–9]. More recently, the CO2 Rankine cycle has re- with the one using pure CO2 for both low and high temperature heat
ceived wide attention thanks to desirable eco-friendly characteristics of source conversions [17]. Much other research works have focused on
CO2 such as zero ozone depleting potential (ODP), very low global the system configuration and operating parameter optimization of the

⁎
Corresponding author.
E-mail address: zhangqiang@just.edu.cn (Q. Zhang).

https://doi.org/10.1016/j.enconman.2019.112281
Received 18 September 2019; Received in revised form 2 November 2019; Accepted 9 November 2019
0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Qiang Zhang, et al., Energy Conversion and Management, https://doi.org/10.1016/j.enconman.2019.112281
Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

Nomenclature 1c, 2c… state points

a air
A heat transfer area, m2 c cooling
c cost per unit of exergy product, $·GJ−1 C compressor
CRF capital recovery factor Cond condenser
E exergy flow rate, kW d diffuser
h specific enthalpy, kJ·kg−1 Eje ejector
m mass flow rate, kg·s−1 Eva evaporator
P pressure, MPa GC gas cooler
Q heat transfer rate, kW GH gas heater
s specific entropy, kJ·kg−1·K−1 h heating
T temperature, °C in inside
W power, kW m mixing
x vapor quality n nozzle
Z investment cost rate, $·h−1 out outside
P pump
Greek symbols r extraction ratio
Rec recuperator
ε recuperator effectiveness Sep separator
μ entrainment ratio tot total
η efficiency, % T turbine
V valve
Subscripts W water
WHX water heater
0 ambient state
1, 2, … state points

tCO2 cycles. Cardemil et al [18] concluded that CO2-based power plants CCHP cycle by adding an extraction turbine. Parametric analysis re-
had the lower global conductance for certain operational conditions, vealed that exergy efficiency of the presented system was improved
revealing the potential compactness of these systems. Above mentioned compared to the case with no-extraction turbine. However, the turbine
studies justify the capability of tCO2 Rankine cycle to convert the low- power generation could only make up the compressor power con-
temperature heat into the useful power. sumption under certain conditions, resulting in a large amount of extra
In a typical transcritical CO2 Rankine cycle, the turbine exhaust energy input as well as low coefficient of performance (COP) of ERC.
contains considerable low-grade heat which could have been recovered Therefore, methods that can improve system net power output and COP
by using heat exchangers for heating purpose but is lost through the of the ejector refrigeration cycle are worth exploring. Recently, Ipakchi
condensation [19]. Meanwhile, various heat-driven refrigeration et al. [33] proposed an enhanced transcritical CO2 combined cooling
methods have demonstrated the feasibility of recovering the low-grade and power system for engine waste heat recovery. They pointed out
thermal energy [20]. Therefore, numerous combined cooling, heating that using an ejector to provide the required pressure of gas cooler
and power systems for more efficient utilization of low-grade heat have could result in a large decrease in power consumption of pump and
been proposed [21–23]. Wang et al. [24] investigated a novel CCHP compressors. However, an expansion valve was employed to keep the
system based on solar thermal biomass gasification. The thermo- CO2 stream exited from the gas cooler at subcritical state, which would
dynamic analysis indicated that the proposed hybrid system can im- cause expansion work losses.
prove the utilization efficiency of biomass energy. Ahmadi et al. [25] Above literature review shows that the transcritical CO2 Rankine
put forward a novel integrated multi-generation system with low-grade cycle is a promising alternative to low-grade heat utilization due to
heat resource and used R123 as working fluid. Their study covered both features of cycle itself and the working fluid. Additionally, the combi-
energy and exergy analyses and multi-objective optimization. Further- nation of a CO2-based power cycle and an ejector refrigeration cycle has
more, a closed form relationship between exergy efficiency and total been concerned widely in recent years because of higher energy utili-
cost rate was derived for practical applications. Boyaghchi et al. [26] zation efficiency. Though much research has been conducted on the
performed thermoeconomic analysis of a solar micro-CCHP system in- CO2-based CCHP system, most investigators have focused on the su-
tegrated with ORC. The extraction turbine was introduced to provide percritical CO2 power cycle coupled with a refrigeration cycle, and little
two split-streams for heating and cooling purposes, respectively. Par- effort has been devoted to the combined transcritical CO2 CCHP cycle.
ticularly, as one of heat-driven refrigeration techniques, the ejector Moreover, several improvements are still needed in low-grade heat
refrigeration cycle has gained considerable interest due to its several source applications. For instance, in certain existing CCHP system
advantages. Compared to the conventional vapor compression re- equipped with transcritical CO2 ejector, the available net power output
frigeration system, ERC has advantages of simple layout, low cost and can not cover the required power of compressors due to the low heat
easy maintenance [27–29]. Moreover, a large number of refrigerants resource temperatures or high operation pressures of CO2. As a result, a
can be chosen as working fluid in the ERC [30,31], which makes ERC considerable amount of additional electricity purchased from outside
even more attractive when it is coupled to other power generation has to be supplied to drive the system, resulting in high investment and
cycles for the employment of single working fluid (i.e. CO2). Some CO2- operating costs. Furthermore, considering the variable demand for
based CCHP systems with the ejector have been introduced and ana- cooling and heating in different seasons (i.e. winter or summer), the
lyzed. Wang et al. [32] proposed a new CCHP system driven by solar limited adjustable range of heating and cooling output in the conven-
energy, which integrated a supercritical CO2 Brayton cycle and a tional CO2-based CCHP systems is also a problem. Therefore, an effi-
transcritical CO2 ejector refrigeration cycle. The system performance cient and beneficial solution to relieve these limitations is urgently to be
was investigated thermodynamically. Then, Xu et al. [27] modified this proposed, and the obstacle is overcome in this paper. To authors’ best

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Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

knowledge, few relevant investigations have been reported.

Taking into account the aforementioned problems, this paper is
aimed to provide a self-sufficient transcritical CO2 CCHP system for the
low-grade heat utilization. The considered system integrates a Rankine
power cycle, an ejector refrigeration cycle and a heat exchanger to
produce electricity, cooling and heating, respectively. To assess the
feasibility and performance improvements of the presented CCHP
system, the mathematical model of the presented CCHP is built and
developed. A comprehensive parametric study is performed from the
thermoeconomic aspect. Furthermore, the influence of main operating
parameters on system performance is also investigated and discussed.
In addition, the multi-objective optimization for the system is per-
formed to find the favorable performance point in two different op-
eration modes.

2. System description

The scheme of the proposed CCHP system is shown in Fig. 1. The

overall system is the combination of a Rankine power cycle and an
Fig. 2. T-S diagram of the presented cycle.
ejector refrigeration cycle with CO2 as working fluid. The low tem-
perature heat source, such as solar energy, or industrial waste heat, can
be considered here to power the system. Operation processes of the In the ejector refrigeration cycle, after rejecting heat in the re-
system are described as follows. cuperator (state 2c) and gas cooler sequently to a low temperature, the
As shown in Fig. 1, the liquid CO2 is cooled (state 1) in the con- CO2 stream (state 3c) then serves as the primary flow to entrain the
denser and compressed to a higher pressure (state 2) by the pump. The secondary flow (state 9c) from the evaporator. Both these CO2 streams
supercritical CO2 stream then is preheated in the recuperator and re- undergo mixing and diffusing processes in the ejector. Afterward, the
covers heat (state 3) by passing through gas heater. Afterward, the mixed stream (state 4c) is fed to the separator, where it separates into
stream (state 4) expands in the extraction turbine for power generation. saturated liquid (state 7c) and saturated vapor (state 5c). The saturated
The expanded CO2 stream is split into two parts at extraction turbine liquid passes through a throttle valve (state 8c) and then creates cooling
outlets. One with low supercritical pressure (state 5) rejects heat in the effect in the evaporator for air conditioning. Meanwhile, the saturated
water heater for producing heating as required, and the other with high vapor is directed back to the condenser by the compressor. Finally, this
supercritical pressure (state 1c) is used to drive the ejector refrigeration compressed CO2 stream (state 6c) joins the stream 6 prior to being
cycle for cooling purpose. cooled to saturated liquid in the condenser and the whole cycle is

Fig.1. Schematic diagram of the proposed CCHP.

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Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

completed. The corresponding thermodynamic state points associated where EQ̇ and Ẇ are exergy transfer through the heat and work inter-
with the proposed CCHP cycle are depicted in the T-S diagram (see actions at the system boundary, respectively. And EQ̇ is calculated by
Fig. 2). T0 ̇
Compared to the typical CO2-based CCHP cycle with an ejector, the EQ̇ = ∑ (1 − ) Qk
T (5)
considered cycle configuration characterizes that the power generation
where Q̇ k is the heat transfer rate at heat source temperature of T.
section of the system operates in the transcritical Rankine cycle instead
The definition of extraction ratio is given in Eq. (6) which is the
of the supercritical Brayton cycle. Hence, consumed work by pumping
ratio of the extracted flow mass flow rate to the total CO2 mass flow rate
liquid CO2 can be reduced because of the lower compressibility factor of
through the extraction turbine.
CO2 near the critical region, which has been proved to increase the net
power out of the system in authors’ previous study [34]. In addition, the r = ṁ 1c /ṁ 4 (6)
compressor in refrigeration cycle only needs to compress CO2 vapor
The recuperator effectiveness used to calculate the thermodynamic
leaving the separator to condenser pressure rather than the higher su-
states at each respective inlet and outlet is defined by
percritical pressure required in the typical cycle. Such a small pressure
ratio will further decrease compressor compression work and bring the εRec = (h1c − h2c )/(h1c − h2) (7)
high COP of the ERC. Moreover, by adjusting the extraction ratio, the The state value at the mixed point 7 is determined by
required amount of low grade energy (i.e. cooling and heating) can be
achieved to satisfy variable demands, revealing the potential flexibility ̇ 6c h6c
ṁ 7 h7 = ṁ 6 h6 +m (8)
of the proposed system. Additionally, the sharing of the condenser and
the pump for the Rankine power sub-cycle and the ejector refrigeration 3.1.2. The ejector refrigeration cycle
sub-cycle can lead to a more compact system. One-dimensional ejector model with constant-pressure mixing is
widely used by many researchers [36–38] and, hence considered for
3. Mathematical modeling ERC in this work. Additionally, other special assumptions are applied to
the ERC as follows:
In order to calculate the performance of the proposed system,
models of each component are built respectively and the simulation • The kinetic energy at ejector inlet and outlet is negligible.
code is written in FORTRAN environment. Thermodynamic properties
of carbon dioxide are calculated according to the fundamental equation
• The primary and secondary flows are not mixed until they reach the
mixing chamber.
of state developed by Span and Wagner [35]. • at evaporator and separator outlets is saturated.
CO 2

3.1. Thermodynamic model The entertainment ratio of the ejector is defined as the ratio of the
secondary to the primary mass flow rate.
In the analysis of both the tCO2 Rankine cycle and ERC, some ty- μ = ṁ 9c /ṁ 3c (9)
pical assumptions are considered as follows:
The primary flow expands and accelerates to very high velocity in
• The changes in kinetic and potential energies are neglected. the nozzle. Pressure and velocity of the primary flow at the nozzle
• Components are modeled under steady conditions. outlet are calculated as, respectively,
• The pump, compressor, turbine and ejector are adiabatic but non- P3c' = Pe − ΔP (10)
isentropic.
• The pressure drops in heat exchangers for both sides are neglected. u3c' = 2ηn (h3c − h3c') (11)
• Unless stated otherwise, pinch point temperature difference is 10 °C where △P is the pressure drop of the secondary flow in the nozzle, Pe is
between cold and hot fluids in the heat exchanger.
• The flow across the throttle valve is isenthalpic. the evaporation pressure, ηn is the efficiency of the nozzle.

• CO is supercritical at the pump outlet and saturated liquid at the

2
Velocity of outlet stream in the mixing chamber is determined by
condenser outlet. ηm
• Cooling water inlet temperature is 5 °C lower than condensation um = u3c'
1+μ (12)
temperature.
where ηm is the efficiency of the mixing chamber.
Specific enthalpy of the mixed stream at the mixing chamber outlet
3.1.1. The transcritical CO2 Rankine cycle
is obtained as
Based on above assumptions, mass and energy balance analysis in
all components are carried out. The general forms of conservation h3c + μ h9c u2
hm = − m
principles for each component are as follows 1+μ 2 (13)
∑ ṁ in = ∑ ṁ out (1) In the diffuser, kinetic energy of mixed stream converts to pressure.
And, specific enthalpy at the diffuser outlet can be calculated as
Q̇ − Ẇ = ∑ ṁ out hout − ∑ ṁ in hin (2) h4cs − h m
h4c = h m +
Exergy analysis is used to evaluate the quality of the available en- ηd (14)
ergy and to indicate the irreversibility of the system. The exergy of each where ηd is the efficiency of the diffuser, h4cs represents the isentropic
state point is expressed as enthalpy of the diffuser outlet flow.
Ei̇ = ṁ i [(h i − h 0 ) − T0 (si − s0 )] (3) Moreover, the mass conservation constraint of the ejector is ex-
pressed as
where subscripts 0 signifies the reference environmental state.
x = 1/(1 + μ) (15)
The exergy balance of each component used to obtain exergy de-
struction is defined as where x is the quality of CO2 at ejector outlet.
It is obvious that the iterative procedure is required for entrainment
∑ EQ̇ − Ẇ = ̇ −
∑ Eout ∑ Eiṅ + EḊ (4) ratio calculations in ejector. In other words, for the given operating

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Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

conditions, with an assumed entrainment ratio, the state parameters at Table 2

ejector outlet are obtained by using above mentioned equations until Cost functions for components of the system [42–44].
Eq. (15) gets satisfaction. Then, other performance parameters of the System component Equipment purchase cost
ERC can be determined.
A summary of the mathematical models for components of the Compressor ZC = 10167.5·Wċ 0.46
combined cycle is given in Table 1. Turbine ZT = 866.64·ẆT 0.82
Pump ZP = 1120·Ẇ p0.8
3.2. Thermodynamic performance criteria Gas heater/Recuperator ZGH/Rec = 2681·A0.59
Gas cooler/WHX ZGC/WHX = 2382.9·A0.68
The capacities of useful energies (i.e. heating, cooling and net Evaporator ZEva = 1397·A0.89
power) from the CCHP system can be calculated by the following Condenser ZCond = 2143·A0.514
equations Valve ZV = 114.5·ṁ
Ejector −0.75
ZEje = 13.5·(T3c/ P3c )0.05P4c
Qċ = μ·ṁ 3c (h9c − h8c ) (16)

Q̇ h = ṁ 1 (1 − r )(h5 − h6) (17) of Uk are 1.5, 2.0 and 1.6 kW·m−2·K−1 [39–41], respectively.
̇ = ẆT − WĊ − Wṗ The capital recovery factor (CRF) is used to convert a lump sum
Wnet (18)
value to an annual equivalent, which is defined as
Formulation for the exergetic efficiency of the CCHP system is given
below i·(i + 1)n
CRF =
(i + 1)n − 1 (24)
̇ + EQ,c
ηex = (Wnet ̇ + EQ,h
̇ )/ Ein
̇ (19)
̇ , EQ̇ , c and EQ̇ , h represent the heat exergy input the gas heater, cold where i is interest rate and set as 0.12, n is the economic life time with
Ein
the value of 20 years.
exergy and heat exergy of the system, respectively. They are expressed
Additionally, the component annual levelized capital investment
as
rate, Zk̇ ,is calculated by
̇ = Q̇in (1 − T0/ Thin )
Ein (20)
CRF + γk
Zk̇ = ⎛ ⎞·Zk
̇ = Qċ (T0/ Ta2 − 1)
EQ,c (21) ⎝ t ⎠ (25)

̇ = Q̇ h (1 − T0/ Tw2)
EQ,h (22) where Zk is the cost of kth component, t is annual plant operation hours
with the value of 8000, γk denotes the maintenance factor with the
where Thin is the heat resource temperature, Ta2 is the air temperature
value of 0.06.
at evaporator outlet and Tw2 is the domestic water outlet temperature.
The cost per unit of exergy products, i.e. cooling, heating and net
For the ejector refrigeration cycle, coefficient of performance is
power, is taken as the thermoeconomic index for the proposed CCHP
defined as the ratio of the refrigerating output to the compression
system, which is defined as
power required by the refrigeration as follows
n
COP = Qċ /(Ẇ c + r·ẆP ) (23) Cp,tot = ∑k=1 Żk /(Wnet
̇ + EQ,c
̇ + EQ,h
̇ )
(26)

3.3. Economic model

3.4. Simulation conditions
The system investment cost is an important economic factor for the
primary design of thermal system. The cost functions for each compo- In the present study, hot air with temperature of 230 °C is con-
nent in the system are given in Table 2. For the sake of simplicity as sidered as the low-grade heat resource to quantitatively simulate the
performed in literature, the constant value of overall average heat performance of the proposed CCHP system. This temperature level is
transfer coefficient (Uk) is considered to calculate the area of heat ex- close to that of solar heat or industrial waste heat reported elsewhere
changer. For gas cooler and water heater, the value of 1.0 kW m−2 K−1 [20,27]. Typical input parameters for the presented CCHP system are
[39] is used, while the value of 0.3 kW·m−2·K−1 is assigned for the specified according to the data reported in literature [27,32,34,41,45],
recuperator [33,40]. For evaporator, condenser and gas heater, values as is shown in Table 3.

Table 1
Energy and exergy relations for each component.
Component Energy Exergy

Pump Ẇ P = ṁ 2 (h2 − h1) EṖ = Ẇ P + E1̇ − E2̇

Compressor WĊ = ṁ 5c (h6c − h5c ) EĊ = WC ̇ + E5ċ − E6̇ c
Turbine Ẇ T = ṁ 4 (1 − r )(h4 − h5) + r·ṁ 4 (h4 − h1c ) EṪ = Ẇ T + E4̇ − E5̇ − E1c
̇
Gas heater Q̇in = ṁ h (hhin − hhout ) = ṁ 3 (h4 − h3) EGḢ = E3̇ + Ehin
̇ − E4̇ − Ehouṫ
Recuperator Q̇Rec = ṁ 2 (h3 − h2) = ṁ 1c (h1c − h2c ) EReċ = E2̇ + E1ċ − E3̇ − E2c
̇
WHX Q̇ WHX = ṁ 5 (h5 − h6) = ṁ w (hw2 − hw1) ̇
EWHX = E5̇ + E ̇w1 − E6̇ − E ̇w2
Gas cooler ̇ = ṁ 2c (h2c − h3c) = ṁ 03 (h 04 − h 03)
QGC EGĊ = E2c
̇ + E03
̇ − E3c ̇ − E04̇
Ejector ṁ 3c h3c + ṁ 9c h9c = ṁ 4c h4c ̇ = E3c
EEje ̇ + E9c
̇ − E4c
̇
Evaporator Q̇Eva = ṁ 8c (h9c − h8c) =ṁ a (ha1 − ha2) ̇ = E8c
EEva ̇ + Ea1
̇ − E9ċ − Ea2
̇
Separator ṁ 4c h4c = ṁ 5c h5c + ṁ 7c h7c ̇ = E4c
ESep ̇ − E5c
̇ − E7c
̇
Condenser ̇
QCond = ṁ 1 (h7 − h1) = ṁ w (h 02 − h 01) ̇
ECond = E7̇ + E01 ̇ − E1̇ − E02
̇
Valve h7c = h8c EV̇ = E7̇ c − E8̇ c

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Table 3 Table 5
Simulation conditions for the proposed CCHP system. Thermodynamic data at different state points for the proposed cycle.
Parameters Value State point Fluid P (MPa) T (°C) h (kJ·kg−1) s (kJ·kg−1·K−1) ṁ (kg·s−1)

Ambient pressure (MPa) 0.1013 1 CO2 5.73 20.0 255.87 1.1877 0.782
Ambient temperature (°C) 15 2 CO2 12.0 30.1 265.72 1.1942 0.782
Heat resource capacity (kW) 218.2 3 CO2 12.0 56.9 370.41 1.5235 0.782
Temperature of heat resource (°C) 230 4 CO2 12.0 220.0 649.36 2.2397 0.782
Turbine inlet temperature (°C) 220 5 CO2 5.73 156.0 599.71 2.2603 0.352
Turbine inlet pressure (MPa) 12 6 CO2 5.73 45.0 464.44 1.8926 0.352
Turbine extraction rate 0.55 7 CO2 5.73 34.5 446.17 1.8343 0.782
Condensation temperature (°C) 20 1c CO2 8.40 188.0 624.40 2.2493 0.430
Ejector primary flow pressure (MPa) 8.4 2c CO2 8.40 52.2 434.06 1.7506 0.430
Ejector primary flow temperature (°C) 36 3c CO2 8.40 36.0 325.30 1.4044 0.430
Ejector back pressure (MPa) 4.6 4c CO2 4.60 10.9 358.66 1.5560 0.639
Evaporation temperature (°C) 5 5c CO2 4.60 10.9 421.93 1.7788 0.430
Heating water outlet temperature (°C) 90 6c CO2 5.73 27.5 431.21 1.7850 0.430
Cooling air outlet temperature (°C) 10 7c CO2 4.60 10.9 228.13 1.0965 0.209
Compressor isentropic efficiency (%) 80 8c CO2 3.97 5.0 228.13 1.0996 0.209
Turbine isentropic efficiency (%) 85 9c CO2 3.97 5.0 427.48 1.8163 0.209
Pump isentropic efficiency (%) 80 a1 Air 0.122 25.0 298.47 6.8063 2.753
Recuperator effectiveness (%) 86 a2 Air 0.122 10.0 283.37 6.7543 2.753
Pinch point temperature difference of condenser (°C) 3 w1 Water 0.101 25.0 104.92 0.3672 0.175
w2 Water 0.101 90.0 377.06 1.1928 0.175
01 Water 0.101 15.0 63.077 0.2244 14.197
02 Water 0.101 17.7 73.562 0.2607 14.197
Table 4
03 Water 0.101 15.0 63.077 0.2244 2.236
Results for model validation of tCO2 power cycle.
04 Water 0.101 20.0 84.077 0.2965 2.236
Parameters Ref. [46] Present

̇ −1 19.4 19.4
Wpump (kJ·kg ) Table 6
̇
Wturbine (kJ·kg−1) 169.9 169.8 Performance comparison between presented cycle and reference cycle.
Q̇ heater (kJ·kg−1) 373.1 373.0
Performance Parameters Ref. [27] This study
̇
Qcondenser (kJ·kg−1) 222.7 222.6
Q̇recuperator (kJ·kg−1) 449.0 449.0 Turbine power (kW) 58.88 28.22
The overall exergy loss (kJ·kg−1) 99.5 99.5 Pump power (kW) – 7.71
The overall exergy efficiency (%) 61.4 60.2 Compressor power (kW) 71.82 3.99
Net power output (kW) −12.94 16.52
Refrigeration output (kW) 74.51 41.57
Heating output (kW) 166.0 47.60
Exergy efficiency (%) 25.67 29.08
COP 1.886 5.048

Fig. 3. Comparison of calculated results to experimental data form Ref. [47].

3.5. Model validation

The accuracy of present mathematical model for the tCO2 Rankine

Fig. 4. Percentage of each component in total exergy destruction of the present
cycle and the ejector refrigeration cycle has been individually verified system.
on the basis of theoretical or experimental results available in litera-
ture. As is shown in Table 4, for the same input parameters of tran-
scritical CO2 Rankine cycle, the calculated results from the present while the pressure drop in the nozzle is set to 310 kPa, which are
model are closely matching with theoretical data in Ref. [46]. For the decided by using a trial-and-error method to approach the experimental
validation of the ejector model, efficiencies of the nozzle, mixing results in Ref. [47]. It should be noted that these values are also em-
chamber and diffuser respectively are taken as 0.90, 0.82 and 0.80 ployed to the following simulation. As is observed in Fig. 3, the

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Fig. 5. Effects of turbine inlet temperature on the performance of the CCHP system.

Fig. 6. Effects of turbine inlet pressure on the performance of the CCHP system.

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Fig. 7. Effects of condensation temperature on the performance of the CCHP system.

calculated entrainment ratios by the present model are in good agree- the total. The exergy destruction of above three components approxi-
ment with experiment results in Ref. [47], where the relative errors are mately accounts for 75.9% of the total exergy loss in the system. Ad-
within 4.73%. Furthermore, the calculated COP values of the ERC from ditionally, it is observed that ejector and turbine share 4.7% and 4.5%
the present model are also in good agreement with the data in experi- of system exergy destructions rate, respectively. Since the exergy de-
ments [47], where the relative errors are within ± 4.67% as shown in struction mainly occurs in heat exchangers of the system, the further
Fig. 3. improvement in heat transfer process should be emphasized, i.e. re-
ducing heat transfer temperature differences between cold and hot
4. Results and discussion flows. Also, enhancing components efficiencies by means of optimiza-
tion design would be one of good solutions to reduce the internal ir-
4.1. Comparison of the presented cycle and the typical cycle reversibility of the system.

Table 5 presents the thermodynamic properties at each state point 4.3. Parametric study
of the system under base case conditions. In order to demonstrate the
performance improvement of the proposed CCHP cycle, the thermo- In this section, parametric study is conducted to evaluate effects of
dynamic performance is compared with that presented in Ref. [27] and key parameters on the performance of the proposed system based on
the results are shown in Table 6. Regardless of the system layout, under thermodynamics and economics in details. The considered operation
the same heat source conditions and turbine inlet parameters, the parameters are turbine inlet pressure (P4), turbine inlet temperature
proposed system can provide more net power output compared to the (T4), condensation temperature (T1), ejector primary flow temperature
reference cycle at the cost of reducing cooling and heating. It will be (T3c), ejector primary flow pressure (P3c), ejector back pressure (P4c)
beneficial to obtain a better balance between various energy outputs of and extraction ratio (r). It should be stated that when on specific
the CCHP system. Furthermore, the exergy efficiency of the proposed parameter is evaluated, the other parameters are kept constant as
system and COP of the ejector refrigeration cycle is 29.08% and 5.048, shown in Table 3.
which indicates 13.3% and 167.7% improvement compared with the Fig. 5 shows the effects of turbine inlet temperature on the perfor-
reference cycle, respectively. mance of the CCHP system. It is well known that the turbine inlet
temperature is limited by available inlet temperature of heat resource
4.2. Component exergy analysis medium. In this case study, the considered turbine inlet temperature is
within the range of 170–220 °C, which is made possible to assess the
To improve the system performance in terms of the exergy utiliza- potential of the CCHP system for low-grade heat resources. As Fig. 5
tion, the percentage of exergy destruction for each component in the indicates, an increase of turbine inlet temperature results in the in-
proposed system is plotted in Fig. 4. As can be seen, the gas heater alone crease of the net power output and the heating output, while the de-
contributes to about 52.2% of system exergy destruction, and the re- crease of the cooling capacity. This is due to the fact that as turbine
cuperator and the water heater have respectively 17.7% and 6.0% of inlet temperature increases, the CO2 mass flow rate at the gas heater

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Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

Fig. 8. Effects of turbine extraction ratio on the performance of the CCHP system.

outlet is decreased and it causes a decrease in the consumed power by the system increases. On the other hand, the heating output of the
the pump and compressor. However, the turbine power output is in- system is decreased as turbine inlet pressure increases. This is mainly
creased due to the significant increment in enthalpy drop of the CO2 due to the fact that a higher turbine inlet pressure decreases the turbine
through the turbine. As a result, the net power output increases with the exhaust temperature. Since the variations of turbine inlet pressure have
rising of turbine inlet temperature. Meanwhile, the decreased CO2 mass no effect on operation parameters of the ERC, the cooling capacity re-
flow rate also brings the reduction in secondary flow mass flow rate in mains unchanged. Moreover, by increasing turbine inlet pressure, the
ERC, leading to a lower cooling capacity of the system. On the other net power output improves about 136.4% while the heating output
hand, when turbine inlet temperature increases, the temperature at decreases 25.8%, which increases the exergy efficiency of the system
water heater inlet is increased, and hence, the heating output increases. under the constant rate of total exergy input. Due to the higher increase
It is observed that heating output improves 41.1%, which means that in specific consumption work of the pump when turbine inlet pressure
turbine inlet temperature has more significant effect on the heating increases, the values of COP for the ECR drop. Additionally, the cost per
output than other useful outputs. Moreover, the increase in net power unit of the exergy product decreases gradually with the increasing
output as well as heating output results in the increasing exergy effi- turbine inlet pressure because of more significant increment in net
ciency of the system. Since the ratios of the specific cooling effect to the power output although the total investment cost rises simultaneously.
specific consumption work in ERC do not change with the increase of Fig. 7 reveals the effects of condensation temperature on the per-
turbine inlet temperature, the COP remains unchanged. Furthermore, as formance of the CCHP system. As is shown in the figure, the increasing
turbine inlet temperature increases, the required heat-exchanger areas condensation temperature will decrease the net power output while
of the system will decrease, causing total investment cost of the system increase the heating and cooling outputs. The reduction in net power
to reduce. Therefore, the cost per unit of exergy product for the overall output can be explained as follows. When the condensation tempera-
system shows a decreasing trend with the increase of the turbine inlet ture is rising, overall mass flow rate of CO2 in the system increases.
temperature. Therefore, the power consumed by the pump and compressor is in-
It is worth emphasizing that at lower turbine inlet temperatures (i.e. creased, so are the investment costs of these two components. In con-
between 120 and 170 °C) the proposed CCHP system can still provide trast, the enthalpy difference through the turbine decreases sig-
desirable net power and cooling effect, but the heating water terminal nificantly, which leads the turbine power output to decrease through
temperature would decrease within the range of 50–85 °C because of this variation. As a result, the net power output of the considered CCHP
the decreased water heater inlet temperature. system declines by 50.3%. Additionally, this increased mass flow rate of
The influences of turbine inlet pressure on system performance are CO2 brings more available heat in water heater, which increases the
illustrated in Fig. 6. As can be seen, the increasing turbine inlet pressure heating output of the CCHP system. Similarly, the ejector secondary
improves the net power output of the system. The reason is that both flow also increases due to above stated increase of overall mass flow
turbine generation power and pump consumption power grow with the rate. So, cooling capacity of the system gets increased too. Moreover,
increase of turbine inlet pressure. However, the increase rate of the the growth rate of heating capacity reaches to 46.3% compared with
former is higher than the later, and resultantly, the net power output of 13.4% for the cooling capacity, implying that condensation

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Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

Fig. 9. Effects of ejector primary flow pressure on the performance of the CCHP system.

temperature has more influence on the heating output. The exergy ef- sharp increase in cooling effect of the system by increasing ejector
ficiency and the cost per unit of exergy product show opposite trends primary flow pressure. This is because of the dramatic increase of the
with the increase of condensation temperature, mainly due to dominant ejector entrainment ratio when ejector primary flow pressure rises,
effect of the decreasing net power output of the system. It is found that which gives the desirable increase in mass flow rate of secondary flow
COP of the ECR declines with the increase of condensation temperature, entering the evaporator for more cooling output. In addition, the in-
because the increment of refrigerant consumption power outpaces that creasing ejector primary flow pressure also increases the temperature at
of cooling capacity. gas heater inlet, which results in a higher CO2 mass flow rate when the
Fig. 8 shows effects of turbine extraction ratio on the system per- temperature at the gas heater outlet is fixed. With this increased CO2
formance. As expected, increasing turbine extraction ratio enhances the mass flow rate, the power required by the pump and compressor in-
CO2 mass flow rate for refrigeration while decreases that for heating. creases. On the other hand, it is inevitable that the turbine power
Thus, the growth of the cooling capacity and the reverse trend of the output is decreased due to the decrease of turbine expansion ratio as the
heating capacity can be seen in Fig. 8. Moreover, it can be found that ejector primary flow pressure rises. Therefore, the net power generation
the heating capacity decreases from 72.9 kW to 13.9 kW, and the of the CCHP system decreases with the increase of ejector primary flow
cooling capacity varies in the range of 5.8–89.4 kW when the extraction pressure. The increase in heating output of the system can also be ex-
ratio increases. In other words, both heating output and cooling output plained in terms of the increased mass flow rate of CO2 through water
can be adjusted in a wide range to satisfy variable demands of energy heater. Since effect of net power generation is much more prevailing
loads. In addition, as extraction ration increases, the net power output than that of heating and cooling outputs, the exergy efficiency keeps
of the system decreases. The main reason for this is that a higher tur- decreasing as the ejector primary flow pressure increases. Similarly, the
bine extraction ratio will cause the total consumption power of the considerable increase in investment costs of compressor, gas cooler and
system to increase due to the increase of CO2 mass flow rates through evaporator leads the cost per unit of the exergy product for the system
the pump and compressor. Likewise, because of more dominant effect to grow. As shown in Fig. 9, the COP of ERC increases with the ejector
caused by the reduction in net power output and heating capacity, the primary flow pressure due to higher amount of cooling output through
exergy efficiency of the system decreases too. On the other hand, the this variation.
COP of the ERC keeps constant because of the same order of variations Fig. 10 presents variations in the system performance with the
in refrigerant consumption power and cooling effect. Furthermore, a ejector primary flow temperature. It is obvious that ejector primary
higher turbine extraction ratio will bring considerable increase of in- flow temperature has important impact on the cooling capacity of the
vestment costs for compressor, gas cooler evaporator and recuperator. CCHP system. With the increase of ejector primary flow temperature,
As a result, the cost per unit of the exergy product of the system is the cooling capacity of the system decreases significantly. This can be
increased with the increase of extraction ratio. explained by the fact that the deteriorated entrainment ratio of the
Fig. 9 gives the result about the impacts of ejector primary flow ejector reduces the mass flow rate of the secondary flow. Also, the
pressure on the system performance. It can be observed that there is a compressor consumption power reduces with this decreased mass flow

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Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

Fig. 10. Effects of ejector primary flow temperature on the performance of the CCHP system.

rate. Since the turbine output power and pump consumption power are exergy output. Since the compressor consumption power is decreased
independent of the ejector inlet temperature, the net power output of upon the increasing ejector back pressure, it can be seen that COP of the
the system tends to rise when the ejector primary flow temperature ERC increases through this variation.
increases. Additionally, when ejector primary flow temperature varies,
thermodynamic parameters of water heater do not change, and thus
heating output of the system experiences no change. The net effect of 4.4. Multi-objective optimization study
the above variations in useful energy outputs is to improve the system
exergy efficiency when the ejector primary flow temperature increases. The findings from parametric study show that energy outputs (i.e.
Because the increase of primary flow temperature reduces the heat cooling, heating and power) of the CCHP system are varied in a wide
transfer areas of heat exchangers in ERC, overall investment cost of the range as system parameters change. Moreover, there is a conflict in
system declines, resulting in the decreased cost per unit of exergy obtaining the maximal output of certain useful energy simultaneously.
product for the overall system. Moreover, the decreased cooling capa- Therefore, the multi-objective optimization to find optimal operation
city together with the increased compressor power results in the de- parameters is performed in the present work. The enhanced Artificial
crease of COP of ECR as shown in Fig. 10. Bee Colony optimization method developed by authors [48] together
Fig. 11 depicts the effects of ejector back pressure on the system with the fast-non-dominated sorting approach in NSGA-II [49] was
performance. On increasing the ejector back pressure, the pressure ratio employed. The details about the genetic algorithm (GA) can be found in
of compressor decreases, which reduces the required power of the literature [50,51]. The control parameters of the optimization are
compressor. Meanwhile, the turbine generation power and the pump specified according to the following values: colony size 100, maximum
consumption power remain unchanged since a higher ejector back cycle number 100 and trial limit value 24 [34]. Since net power gen-
pressure has no effect on them. As a result, the increase in net power eration is required by users all the time while the demand for cooling or
output of the system can be clearly observed in Fig. 11. In addition, the heating load is variable in different seasons (i.e. summer or winter),
heating capacity also remains constant resulting from the unchanged there are two common operation modes for the CCHP system, namely
thermodynamics proprieties through the water heater. Moreover, due combined cooling and power mode and combined heating and power
to the increasing ejector back pressure and unchanged condensation mode. Therefore, the target objectives for the present optimization are
pressure, the enthalpy difference of the refrigerant CO2 through the supposed to have the maximum useful energy outputs in the given
evaporator decreases, causing a decrease in cooling capacity of the operation mode, i.e. maximum net power output and cooling capacity
CCHP system. It is understandable that system exergy efficiency in- simultaneously in CCP mode or maximum net power output and
creases with a higher ejector back pressure because of the increment in heating capacity simultaneously in CHP mode. The decision variables
net power output of the system. In addition, the cost per unit of exergy and their ranges are the same to those in the previous parametric study.
product for the overall system shows a decreasing trend due to the During the optimization process, all these decision variables vary to-
decrease in investment cost of compressor while the increase of overall gether within their ranges.
Fig. 12 shows the Pareto frontier solution for the presented system

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Q. Zhang, et al. Energy Conversion and Management xxx (xxxx) xxxx

Fig. 11. Effects of ejector back pressure on the performance of CCHP the system.

Fig. 12. Pareto frontier of multi-objective optimization in CCP mode.

Fig. 13. Pareto frontier of multi-objective optimization in CHP mode.

in CCP mode with consideration of cooling output and net power output
output of 17.1 kW and the cooling output of 98.9 kW. Fig. 13 presents
as objective functions. As observed, there is a conflicting relation be-
the Pareto frontier solution for optimizing the cycle heating output and
tween the net power output and the cooling output for the CCHP
the net power output in CHP mode. It can also be found that both these
system. The cycle net power output decreases with the increasing
optimized parameters cannot reach the individual optimal objective at
cooling output as expected, and vice versa. It is worth noting that all the
the same time. In other words, to determine an optimum solution with
points on the Pareto frontier can be chosen as optimum operation
higher heating output, the net power output is decreased. In the similar
parameters. The point A, which is the closest Pareto frontier point to the
manner, the final optimal point B is selected on the Pareto optimal
ideal point, is decided as the final optimum solution with the net power
curve. At the optimal point B, the net power output and heating output

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Table 7 system and exergy efficiency of the system are 127.3 kW and 22.7%
Optimal results for the CCHP system in different operation modes. for the CCP mode, while corresponding values are 126.2 kW and
Design parameter CCP mode CHP mode 43.6% for the CHP mode, respectively. And the cost per unit of
exergy product for the overall system in the CCP mode is 3.4 times
̇ (kW)
Wnet 17.1 19.7 more than that in the CHP mode.
Qė (kW) 98.9 5.9
Q̇ h (kW) 11.3 100.6 In summary, this novel transcritical CO2 CCHP system is feasible
ηex (%) 22.7 43.6
and efficient in the low-grade heat resource application. The outcomes
Cp,tot ($/GJ) 34.1 10.0
are helpful to provide a better understanding of the similar low-grade
COP 4.49 2.71
T4 (°C) 220 220 heat-driven system, which then can instruct further system design and
P4 (MPa) 14.99 14.01 performance enhancement in future.
T1 (°C) 20.1 30.0
P3c (MPa) 8.41 8.81
Declaration of Competing Interest
T3c (°C) 35.0 38.5
P4c(MPa) 4.57 4.74
r 0.898 0.101 The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
are found to be 19.7 kW and 100.6 kW, respectively.
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