Dynamic performance of the transcritical power cycle using CO2-based binary zeotropic mixtures for truck engine waste heat recovery

Journal Pre-proof Dynamic performance of the transcritical power cycle using CO2-based binary zeotropic mixtures for truck engine waste heat recovery Gequn Shu, Rui Wang, Hua Tian, Xuan Wang, Xiaoya Li, Jinwen Cai, Zhiqiang Xu PII:

S0360-5442(19)32520-4

DOI:

https://doi.org/10.1016/j.energy.2019.116825

Reference:

EGY 116825

To appear in:

Energy

Received Date: 27 March 2019 Revised Date:

25 August 2019

Accepted Date: 22 December 2019

Please cite this article as: Shu G, Wang R, Tian H, Wang X, Li X, Cai J, Xu Z, Dynamic performance of the transcritical power cycle using CO2-based binary zeotropic mixtures for truck engine waste heat recovery, Energy (2020), doi: https://doi.org/10.1016/j.energy.2019.116825. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2019 Published by Elsevier Ltd.

Dynamic performance of the transcritical power cycle using CO2-based binary zeotropic mixtures for truck engine waste heat recovery Gequn Shu, Rui Wang, Hua Tian*, Xuan Wang*, Xiaoya Li, Jinwen Cai, Zhiqiang Xu State Key Laboratory of Engines, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072, China * Corresponding author. Tel: +86 22-27409558 E-mail: [email protected] Dr. Xuan Wang: [email protected]

Abstract CO2 transcritical power cycle (CTPC) technology has received substantial interest and attention for use in waste heat recovery, but its high operating pressure and low condensing temperature restrict its wide application. CO2-based binary zeotropic mixtures are considered a promising solution. Therefore, a CTPC system dynamic model with different CO2 mixtures as the working fluids in the context of engine waste heat recovery is examined using Simulink simulation to understand the effects of different mixtures and composition ratios on system performance in various working conditions. A system dynamic model of the system is thoroughly validated against experimental data, and the results are reasonably consistent. Based on these foundations, the dynamic response of the CTPC system with CO2 mixtures of different proportions and components is compared and analysed. The results show that the system responds faster when the proportion of CO2 is greater. The proportion

of refrigerant also affects the optimal net power output and thermal efficiency. The preliminary results presented in this paper will be helpful for future design of CO2 transcritical power cycles and the development of control strategies for these systems. Key words: Waste heat recovery, CO2-based binary zeotropic mixtures, Finite volume method, CO2 transcritical power cycle, Dynamic performance 1. Introduction The total transportation market share of diesel fuel (including biodiesel) was 36% in 2012 [1], and heavy-duty vehicles contribute about 80% of total CO2 emissions from commercial vehicles [2]. Therefore, reducing engine emissions and improving energy efficiency have gained great attention from academia and industry [3]. Therein, waste heat recovery (WHR) technology is regarded as a promising solution in terms of energy savings and emission reduction. Some well-known institutions such as Argonne National Laboratory [4], Cummins [5], and BMW [6] pointed out that WHR has the maximum potential to increase engine efficiency, and is necessary in internal combustion engines. A CO2 transcritical power cycle (CTPC) system is considered one of the most promising WHR technologies [7, 8]. As the working fluid in CTPC, CO2 is natural, non-toxic, harmless, clean, and easy to produce. It was shown in earlier studies that CTPC can be used to recover energy from high temperature exhaust and low temperature jacket water simultaneously with maximum recovery rate of greater than 80%. This type of system has fast response speed and can be miniaturized [9-11]. Li et al. [11] compared the dynamic response of CTPC system with that of ORC system

with R123 as working fluid, and the experimental results show that the response speed of CTPC system was almost four times faster than the ORC system. A 10 MW CO2 turbine was studied by Echogen Power Systems Company [10], and their results show that the using heat exchangers with CO2 as working fluid provided 87.4% weight reduction. Simulations and experimental results on the use of CTPC for engine waste heat recovery have been performed. Chen at al. [8] compared different CO2 WHR systems for use with engines and found that the CTPC was more attractive than the CO2 Brayton cycle and the CO2 combined power and cooling cycle, because it can make full use of low-grade small-scale in the exhaust. A kW-scale CTPC for waste heat recovery in a 243 kW heavy-duty diesel engine was tested by Shi et al. [12]. Their results show that the CTPC can improve engine efficiency by 2%. These studies indicated the application potential of CTPC for HDDEs waste heat recovery. Thus, a CTPC system is an effective solution for waste heat recovery in a truck’s internal combustion engine. Nevertheless, the high operating pressure of CTPC, which is always above 15 MPa, brings safety problems during real operation [13]. The condensing temperature of CTPC must be lower than the CO2 critical temperature (31.1 °C). The high operating pressure and low condensing temperature limit the broader use of CTPC for waste heat recovery from truck engines. Moreover, the efficiency of CTPC with optimised operation parameters is no more than 6% [14]. To improve the performance of a CTPC system, CO2-based binary zeotropic mixtures were proposed as a replacement for pure CO2 as the working fluid. Shu et al. [15] focused on the use of

these CO2 mixtures in CTPC systems for engine waste heat recovery, and eight refrigerants were investigated. The results show that the condensing temperature of the CTPC system increased and the operating pressure decreased. Wu et al. [13] conducted a thermo-economic performance evaluation and optimisation of CTPC systems with CO2 mixtures as the working fluid. The results show that the thermodynamic and economic performance of the system with CO2 mixtures were deemed more attractive than the system with pure CO2. Prior research has mainly focused on the steady state performance of a CTPC system, with the goal of optimising power output, exergy efficiency, and thermal efficiency. However, the mass flow rate and temperature of engine are transient and variable [16]. For example, during actual operation, the exhaust temperature of heavy-duty engines ranges from 400 to 650 °C [17, 18]. The transiency and variability of the heat source brings great challenges to reliability, durability, and stability of a CTPC system because the dynamic performance of a WHR system influences the system’s characteristics and affects the control strategies. Therefore, dynamic modelling and dynamic performance appear as key areas of future research and development for WHRs. Models describing the dynamic of an organic Rankine cycle (ORC) and transcritical CO2 cycles can be found in the literature [19-22], which provides guidance for understanding the CO2 mixture model. Desideri et al. [19] developed a dynamic model of ORC using the ThermoCycle library and then validated the result against experimental data from a test rig. Their steady-state and dynamic simulation results are consistent with experimental. The dynamic model

describing CTPC was built with an algebraic and moving boundary approach to analyse the design condition and operating strategy [20]. Moreover, the dynamic performance has also been researched in recent years. Shu et al. [23] created a dynamic model in MATLAB/Simulink and analysed the CTPC system performance under engine mapping conditions. Their results show that the net power output from the system varies significantly in different engine conditions. Li et al. [24] conducted experimental studies of a CTPC system with pure CO2 as the working fluid and examined the effect of external perturbations on dynamic performance. Zhao et al. [25] established an engine-WHR dynamic model and concluded that the net power output of a CTPC system varied visibly with operating conditions, and optimal parameters should be controlled to provide high dynamic engine conditions. Sylvain et al. [21] developed a dynamic model of a small-scale ORC and proposed three different control strategies to ensure the system operates effectively in different working conditions. What’s more, due to the different physical properties of different working fluids, in addition to operation model parameters, the dynamic response of an ORC system varies with the working fluid [26]. However, a review of related research reveals that limited information is available on the dynamic performance of a power cycle with CO2 mixtures in simulations and experiments. Essentially, the physical parameters of different working fluids significantly impact the dynamic performance of the system [26]. There are some difference between the process for modeling the dynamics of CTPC with CO2 mixture as working fluid and with pure CO2 due to a composition shift, which is

caused by the composition and velocity difference between gas and liquid [27], that occurs in the two-phase region [28, 29]. Therefore, this study focuses on the modelling process and dynamic performance of a CTPC system with CO2 mixtures as the working fluid when the components and proportions of CO2 mixtures are different. A dynamic mathematic model of a CTPC system is built based on the actual CTPC test bench and carefully validated against the experimental data. The simulation results are to be consistent with measurements. The real test bench was built by our group and was described in a previous publication [24]. Therein, the condenser is described using the moving boundary (MB) method, and a gas heater with 20 segments is built with the finite volume (FV) method. External disturbances such as pump rotation speed, and the temperature and mass flow rate of exhaust are considered with the goal of understanding the dynamic behaviour of systems with different proportions of CO2 mixtures. Moreover, the offset in the optimal net power output and thermal efficiency with different ratios of refrigerant is studied. In this work, the following contributions are made with respect to existing literature: 1) A dynamic CTPC system model with CO2 mixtures as the working fluid is developed and validated against experimental data. The model gives confidence to research the dynamic performance and control strategy for system with mixtures of different working fluid. 2) The influence of mixture components and proportions on the speed of the system’s dynamic response is assessed.

3) The influence of mixture proportions on the optimal points under the off-design condition is investigated, which can provide guidance for optimal system control. 2. System description The WHR system contains a topping system that provides a heat source and bottoming system that utilizes the heat source. The topping system is a heavy-duty diesel engine, and the bottoming system is a CTPC. The simulation model presented therein is based on an actual test bench that was built by our group. For more details on the actual system, please refer to the article published by our group [24]. 2.1 Topping system In this study, an inline 4-stroke 6-cylinder heavy-duty diesel engine is chosen as the topping system; its main parameters are listed in Table 1. The engine exhaust is used as the heat source for the bottoming CTPC system. The composition of the exhaust is: N2 = 73.4%, CO2 = 7.11%, H2O = 14.22%, and O2 = 5.27%. Table 1 Basic parameters of the diesel engine Parameter

Unit

Content

Engine type

——

Inline, 6 cylinders

Intake system type

——

Turbo-charge/Intercooler

Fuel type

——

Diesel

Bore

mm

113

Stroke

mm

140

Displacement

L

8.424

Maximum torque

N
m

1280

Compression ratio

——

17.5

Rate power

kW

243

Rate speed

rpm

2200

Speed at maximum torque

rpm

1200-1700

Valve per cylinder

——

4

2.2 Bottoming system Fig. 1 shows the basic cycle model of the CTPC, which consists of a gas heater, condenser coupled with a receiver, expander and a pump. The working fluid is pumped to supercritical pressure and then heated by the exhaust in the gas heater. Next, high-temperature, high-pressure working fluid expands through the expander to generate shaft power. Finally, the working fluid is cooled in the condenser and enters the receiver. Then the working fluid leaves the receiver in a saturated liquid state and enters the pump to finish a cycle. It is worth noting that the working fluid enters the pump as a supercooled liquid and thus pump cavitation is avoided.

Fig. 1. Schematic layout of the system.

3. Mathematic model A mathematic model of a CTPC system is built in MATLAB/Simulink (2014a) [30], and REFPROP (9.0) [31] software is used to calculate the thermodynamic properties of pure CO2 and CO2 mixtures. Four models for the main components are established using sequential S-function in MATLAB. The system model shown in Fig. 2. is built by combining the four component models based on their relationships.

Fig. 2. System model built in Simulink.

3.1 Heat exchanger model 3.1.1 Gas heater model The working fluid in the gas heater is in a supercritical state, thus there is no

phase change in the gas heater. The exhaust temperature changes violently, which causes a dramatic change in heat transfer along the length of the gas heater, so the dynamic mathematic model is established with the finite volume (FV) method. Fig. 3 shows a gas heater divided into n segments, where the length of each lumped volume is ∆x. For every control cell, the discrete nodes are at the centre. Along the radial direction, the subscript f (working fluid), w (pipe wall), and g (exhaust) are defined for every control cell, and their states are represented as an average state at the inlet and outlet. It is important to emphasise that the physical properties of CO2 in the supercritical state change violently, as shown in Fig. 4, so the number of control cells could affect the accuracy of heat transfer calculation. Details regarding the effects of the number of control cells will be described below. To simplify the FV model, the following assumptions are made. (1) The gas heater is a typical horizontal tube-in-tube heat exchanger. (2) The working fluid is compressible while the exhaust is incompressible, and the exhaust pressure is constant. (3) Axial heat conduction is negligible. (4) Heat transfer losses are negligible. (5) The organic working fluid is perfectly mixed with the CO2. (6) The lumped thermal capacitance and temperature of the tube wall are assumed. Based on these assumptions, the differential equations of mass and energy conservation for the working fluid are given in Eqs. (1) and (2), respectively. The energy conservation differential equation of the exhaust is listed in Eq. (3). The

energy conservation differential equation of the gas heater wall is given in Eq. (4).
 and
 are the heat transfer coefficient inside and outside the tube wall, respectively. 0.5  ∆

 , ,   , 



, 

   ∆



 ,   



 ! ",# $ ! ",

(1)

 ,  *, , , , 0.5  ∆ %&",'   (̅",'  +     ∆ %&", 

(̅",'

, * 

,

$ 1+

 

,








, -. ∆ /01, $ 0",' 2  ! ",# &",# $ ! ", &",  *

 

0.5 3 ∆ %&"3,' 4,  (̅"3,' 4, +  4,

4,

4, 



, 

 
, -5∆ /01, $

0"3,' 2  ! "3, &"3, $ ! "3,# &",#

1 ∆ (1 671

8, 

(2)

(3)


, -. ∆ /0"3,' $ 01, 2 
, -. ∆ 90",' $ 01, : (4)

Fig. 3. Finite Volume model of the gas heater.

10

1200

15MPa 11MPa 8MPa

15MPa 13MPa 11MPa 9MPa 8MPa 7MPa Saturated liquid Saturated vapor

1000

800

D (kg/m3)

Cp (kJ/kg.K)

8

13MPa 9MPa 7MPa

6

4

400

200

2

200

600

300

400

Temperature (K)

500

600

0 200

300

400

500

600

Temperature (K)

Fig. 4. The physical properties of supercritical CO2. (a) The specific heat capacity

of supercritical CO2. (b)The density of supercritical CO2.

3.1.2

Condenser with receiver model

The condenser model is coupled to a receiver, as shown in Fig. 5. A phase transition occurs in the condenser, and different phase regions have different heat transfer characteristics. Thus, the dynamic model for the condenser is built using the moving boundary (MB) method. The condenser is divided into two regions: a superheated region and two-phase region. Component shift occurs in the condenser, and the component shift model is rather complicated. However, the model validation results presented below show that component shift has little effect on system performance. Therefore, component shift is ignored in this study. The lengths of superheated region and two-phase region are dynamically changing with time. Some assumptions are made in the MB method. (1) The condenser is a typical horizontal tube-in-tube heat exchanger. (2) The pressure of cooling water is considered to be constant, and the cooling water is considered incompressible. (3) Axial heat conductive is negligible in the working fluid, cooling water, and pipe wall. (4) The mean void fraction assumption is taken into account. (5) The value for the lumped thermal capacitance and temperature of the tube wall are assumed. The general mass balance differential equation for the working fluid in the

superheated region and two-phase region is: 9;: 




0

5

The general energy balance differential equation for the working fluid in the superheated region and two-phase region is: 9;*#;: 





 -. 901 $ 0" :

6

The general energy balance differential equation for the condenser wall of the superheated region and two-phase region is: 61 (1 1

8 


 -. /0" $ 01 2 
 -. 90> $ 01 :

7

where z is the direction along the tube, A and Aw are cross-sectional area of the tube interior and the tube wall, respectively; Tw, Tf and Tc are the temperature of the tube wall, working fluid, and cooling water. Di and Do are the inner and outer diameter of the tube, respectively. 61 and (1 are heat capacity and density of tube wall.
 is the heat transfer coefficient between the working fluid and tube wall, and
 is the heat transfer coefficient between the cooling water and tube wall. The Leibniz integration rule is used to integrate the governing partial differential equations (PDEs). Detailed modelling processes are shown in Appendix 1. =4 "9=,:

?=







=

@A   ?= 4 B9A, C:@A $ B9A3 , C: 

=4 

 B9A , C:

= 

(8)

Fig. 5. Condenser with receiver model.

3.1.3

Heat transfer coefficients

Because of the different properties of hot and cold fluids in the gas heater and condenser, the choice of different internal and external transfer correlations has a great influence on the simulation result. The heat transfer correlations especially of exhaust are carefully selected based on the heat transfer performance. Horst et al. [32] also proved that the exhaust side have the maximal influence on total heat transfer. The heat transfer coefficient of exhaust at the outside of the gas heater pipe is gained from [33], which is suitable for high temperature gas outside the tube heat exchangers. The Ptukhov-Krasnoshchekov-Protopopov correlation [34] is applied to CO2 and CO2 mixtures in tubes which are in supercritical phase. The working fluid outside the condenser tube is non-phase change cooling water, so the Petukhov-Kirillov correlation [35] is adopted. The working fluid inside the tube of condenser is CO2 or CO2 mixture where exists phase transition under the condensing pressure, and there are many heat transfer correlations can be applied to phase change heat exchanger. In current work, the heat transfer coefficients of two-phase region is thought as a function of the overheating and subcooled heat transfer coefficients, the saturated gas and liquid densities, the average team quality [36]. The Petukhov-Kirillov correlation [35] is implemented for overheating region in condenser and subcooled region in the receiver. All these heat transfer coefficients are listed in Table 2. where, the mean void fraction model is assumed and used [37] in the two-phase

region. The void fraction γ defined as the volume ratio of vapor to total flow has long be used to describe the properties of the working fluid in the two-phase region. The relationship between void fraction γ and liquid fraction η is described by Eq. 9 and it is the same with the average values F̅ and G̅ [37]. ηγ 1

(9)

The slip flow model proposed by Zivi [38] is used to calculate the liquid fraction. The average liquid fraction G̅ in the two-phase region can be expressed by Eq. 11, which is only the function of the density ratio, then the void fraction G̅ can be got according to it. S = IJ ⁄IK = ((J ⁄(K ) 

G̅ = ?O G(A)@A =

⁄M

= N ⁄M

P(⁄Q)4⁄R (3⁄M ST(⁄Q)#) 4⁄R ((⁄Q) #)4

(10) (11)

As for the average steam quality χ which can be elicited from the following equations. χ=

*VW #*X *W #*X

('YJ = (K (1 − F̅ ) + (J F̅ ℎ'YJ =

  )PX *X Z X *X (#Z VW *VW

(12) (13) (14)

Table 2 Heat transfer correlations Part

Fluid region

Gas heater Exhaust side Working fluid side Condenser Cooling water side

Heat transfer correlations ] @_ ` ( O.a 6 N  N O.^ ( ) ( )M ( ) N ] N1 @O.^  6 (B⁄8)
ef
7g ji Ni Nu = ( )O.Mh ( )#O.MM ( )O. O.h ⁄ j1 N1 12.7(B⁄8) (7g 3 M − 1) + 1.07 6i (B⁄8). ef. 7g kI> = 12.7(B⁄8)O.h (7g 3⁄M − 1) + 1.07
 = 1.72

NI" =

single phase

O.h

12.7(B⁄8)

(7g 3⁄M − 1) + 1.07 O.Mo

(K α =
K (((1 − ) + 1.2 O.^ (1 − ) m n )#3.3 + (J
J O.O (K ( (1 + 8(1 − )O.o ( )O.ao )#3 )#O.h
K (J

two-phase

3.2

(B⁄8)
ef
7g

Pump and expander models The model of the pump can be described as: ! < = GY ( ω q>rK

(15)

where, t , q>rK , ( , and GY is the pump rotation speed, the cylinder volume, the density of working fluid at the pump inlet and the volumetric efficiency, respectively. The consumed work and the working fluid enthalpy at the outlet of the pump can be defined as: u! = ! (ℎ − ℎ )

ℎ = ℎ +

*vwxyz #*w{ |vw

(16) (17)

where, ℎ and ℎ} represent the working fluid enthalpy at the inlet of the pump and the ideal enthalpy of working fluid after isentropic pumping. G} is the isentropic efficiency of the pump. The expander model can be replaced with a nozzle [37] and computed as follows: ! _~ = 6Y (_~ 7

(18)

where, 6Y , (_~ , and 7 are nozzle coefficient, working fluid density at the inlet of expander and the operating pressure, respectively. The power output of the expander and the working fluid enthalpy at the outlet of expander can be described as:

u! = ! (ℎ_~ − ℎ_~ )

(19)

ℎ_~ = ℎ_~ − (ℎ_~ − ℎ} )G}

(20)

where, ℎ_~ and ℎ} represent the working fluid enthalpy at the inlet of the expander and the ideal enthalpy of working fluid after isentropic expansion. G} is the isentropic efficiency of the expander. 4. Model validation Because the gas heater is modelled using the finite volume (FV) method, there is an inevitable trade-off between simulation accuracy and computation time. More segments or subsections of the gas heater will bring higher accuracy at the cost of greater additional calculation time. Therefore, the influence of the segments on the gas heater are fully examined in this part, and the results are presented in Section 4.1. The system model is validated against the experimental data in Section 4.2. The experiment bench shown in Fig. 6 was built by our group to validate the dynamic model for basic CTPC system. The major components of the system, installed sensors and their accuracy, and uncertainty analysis in the experiment are shown in Appendix 2. The experimental system primarily consists of a gas heater, condenser, receiver, pump, and expander (replaced by an expansion valve in this system). The system is a CO2 transcritical power cycle, and the working fluid can be pure CO2 or CO2 mixtures. The model with pure CO2 as the working fluid is validated against experimental data in a previous study [24], while the model with CO2 mixture as the working fluid is validated against experimental data gathered by the author using the test bench, these results have not been published yet.

(a)

(b) Fig. 6. (a)The experiment bench for CTPC dynamic model validation. (b)Detailed structure of the experiment bench.

4.1 The effect of segments on gas heater model The gas heater is one of the most important components as it influences the system’s thermal inertia. However, in the FV method, using more divided segments provides higher accuracy at the cost of additional computation time, thus the number of segments influences the computation time. Chowdhury [39] also presented that the errors in finite volume calculations were reduced when the number of segments used in a gas heater model increases. Therefore, the gas heater is modelled by dividing it into different segments (5, 10, 20, 50, and 100). The results are compared in Fig. 7, which shows the calculation errors and calculation time for the operating pressure and exhaust temperature at the gas heater outlet.

200

6

Temperature of exhaust gas Operating pressure

5

150

100

3

Time (s)

Error(%)

Caculation time 4

2 50 1 0

0 0

20

40

60

80

100

Number of segments

Fig. 7 Calculation error for the gas heater model with different number of segments.

The calculation errors in operating pressure and exhaust outlet temperature for different numbers of segments are compared against a reference model with 100 segments, as shown in Figure. 7. One can see that the accuracy of the gas heater model is quite significant. The operating pressure errors are less than 0.1% in all cases, while exhaust outlet temperature errors for 5, 10, 20, and 50 segments are 5.58%, 2.64%, 1.18%, and 0.29% respectively. Therefore, in order to find a compromise between the accuracy and iteration time, the number of segments in the gas heater is set as 20 in the following analysis. 4.2 Model validation In this section, the system model is validated against experimental data, using pure CO2 or CO2 mixture (CO2/R134a with the proportional of 0.7/0.3) as the working fluid. Validation is performed by comparing some critical parameters while changing the pump speed. Some parameters of the CTPC system, such as the expander nozzle coefficient and pump volumetric efficiency are calibrated against experimental data under the design condition and then determined as a constant value. This method is widely used in related researches [20, 40]. One should note that the same experimental processes are used for the system with pure CO2 and that with the CO2 mixture. The experimental data for pure CO2 were published by our team [24], while the result from the tests with CO2 mixture have not been published yet. During the experiment, the mass flow rate is changed by adjusting the pump speed after the system works safely and steadily. The experiment is repeated several times to check reproducibility. Table 3 shows the parameters of the heat source and

heat sink. The experimental pump speed and mass flow rate of working fluid are shown in Fig. 8. The working fluid mass flow varies with pump speed in real time, and data is collected using the experimental bench at 1 sample per second. The pump speed is set to 80 rpm initially, which then declined to 70 rpm. After regulating the pump speed back to 80 rpm, it is lowered to 65 rpm. The same regulation rules are used for 60 rpm and 55 rpm. Once should note that the cooling pressure of the CO2 mixture presents the tilted trend in Fig. 10(b) because the cooling water temperature is uncontrollable during the experiment. In order to ensure the boundary conditions in the simulation and experiment are consistent, the measured temperature of the cooling water is used in simulation. The measured temperature values and the values used in the simulation are shown in Fig. 9. Fig. 10 shows a comparison of the operating pressure, condensing pressure, mass flow rate of the working fluid, and temperature at the outlet of the gas heater in the experiment and simulation. One can see that most of the simulation results are consistent with the measurements. The average error in operating pressure, mass flow rate of pure CO2, condensing pressure, and working fluid temperature at the gas heater outlet are 1.04 %, 1.19 %, 7.62 %, and 2.32 %, respectively. For CO2 mixtures, the average errors are 4.76 %, 4.45 %, 6.55 % and 5.56 %, respectively. The average error of the system with CO2 mixture as the working fluid is greater than that of pure CO2. The pure CO2 system and the system with mixture share the same heat transfer correlations shown in Table 2, which are more suitable for pure CO2. In addition, the influence of component shift on the CO2 mixture is not considered. The results

indicate that the difference in heat transfer for pure CO2 and the CO2 mixture and the composition shift of the mixture can be ignored to simplify the modelling process. Meanwhile, these results show that the finite volume method and moving boundary method are suitable for describing the behavior of the gas heater and condenser with CO2 mixtures as the working fluid. Table 3

Parameter

Unit

Content

Engine speed

rpm

1100

Engine torque

N
m

603

Exhaust temperature

ºC

444.68—452.49

Exhaust mass flow rate

kg/s

0.10—0.11

Cooling water temperature

ºC

13.59—14.20

Cooling water mass flow rate

m3/h

1.86—1.92

Pump speed (rpm)

80

0.32

70

0.28 ωpof pure CO2 ωpof CO2 mixture mfof pure CO2 mfof CO2 mixture

60

50

0.24 0.20 0.16

40 0.12 30 0

1000

2000

3000

4000

Time (s) Fig. 8 Pump speed and working fluid mass flow rate.

Working fluid mass flow rate (kg/s)

Parameters of the heat source and heat sink used for model validation.

Cooling water temperature ( )

15 14 13 12 11 Experiment signal of CO2 mixture Experiment signal of CO2 Input signal of CO2 mixture Input signal of CO2

10 9 0

1000

2000

3000

4000

Time (s)

Fig. 9 Temperature of the cooling water in the simulation and experiment.

11000

experiment of CO2 simulation of CO2

10000

Operating pressure (kPa)

Operating pressure (kPa)

10500

9500

9000

8500

experiment of CO2 mixture simulation of CO2 mixture

10500

10000

9500

9000

8500 8000 8000 0

1000

2000

3000

4000

0

1000

Time (s)

2000

3000

4000

3000

4000

Time (s)

(a) Operating pressure of pure CO2 and CO2 mixture. 6300

experiment of CO2 mixture simulation of CO2 mixture

Condensing pressure (kPa)

Condensing pressure (kPa)

4900

6200

6100

6000

experiment of CO2 simulation of CO2

5900

4800

4700

4600

4500

4400

4300

5800 0

1000

2000

Time (s)

3000

4000

0

1000

2000

Time (s)

(a) Condensing pressure of pure CO2 and CO2 mixture.

0.20

0.16

0.19

Mass flow rate (kg/s)

Mass flow rate (kg/s)

0.17

0.15 0.14 0.13 0.12

0.18 0.17 0.16 0.15 0.14

experiment of CO2 simulation of CO2

0.11

experiment of CO2 mixture simulation of CO2 mixture

0.13

0.10

0.12 0

1000

2000

3000

4000

0

1000

Time (s)

2000

3000

4000

Time (s)

(b) Mass flow rate of pure CO2 and CO2 mixture. Evaporator outlet temperature (K)

Evaporator outlet temperature (K)

465

experiment of CO2 simulation of CO2

450 435 420 405 390 375

420

experiment of CO2 mixture simulation of CO2 mixture

410 400 390 380 370 360 350

360 0

1000

2000

3000

4000

0

Time (s)

1000

2000

3000

4000

Time (s)

(d) Temperature at the outlet of gas heater for pure CO2 and CO2 mixture Fig. 10 Model validation.

5. Results and discussion The dynamic behavior of the CTPC system with pure CO2 and CO2 mixtures as the working fluid based on the disturbance parameters are studied in Section 5.1. The dynamic speed of different CO2 mixtures is reflected by the rising time, settling time, and peak time which are compared in Section 5.2. Moreover, the offset of the optimal operation points corresponding to the largest net power output and thermal efficiency for pure CO2 and CO2 mixtures with different proportions are presented in Section 5.3.

The steady state parameters of the CTPC system are listed in Table 4. Table 4 Parameters at steady state. Component

Parameter

Gas heater

7_ =13 MPa

TJ =792.15 K

mg=0.2794 kg/s

. =0.025 m

. =0.02 m

0" =573.15 K

7> =5.09 MPa

0> =283.15 K

. =0.03 m

. =0.08 m

Expander

G_~ = 0.7

6Y = 2.5f − 7

Pump

G = 0.8

t = 80 rpm

condenser

> =3.256

kg/s

L=26.94 mm

> =12.92 m

0'
! " = 0.22 kg/s

‚Y =0.6

5.1 Dynamic behavior description As reported by Li et al. [20], the system exhibits different sensitivities with various disturbances. In this paper, the pump rotational speed, temperature, and mass flow rate of the exhaust gas are taken as disturbances when analysing the dynamic responses of CTPC systems with pure CO2 or CO2 mixtures as the working fluid. The low critical temperature (31.1°C) of pure CO2 brings difficulties for condensation in the CTPC system, and the operating pressure of the system is quite high. The CO2 mixture, including a certain refrigerant and can be used to overcome these challenges. The mixture working fluid, taking advantage of the temperature glide, can be used to increase the condensation temperature. The compounds in the mixture were investigated by many studies [41-43]. Refrigerant components selected

as potential candidates in the current work are reference to Shu [15]. Three kinds of non-corrosive, non-toxic refrigerants with low ODP and low GWP are analysed and compared with pure CO2. CO2/R32 (0.7/0.3) can decrease the optimal operation pressure by 1.4MPa and the net power output increases by 8.8%[15], so R32 is selected to analyze the effects of different proportions on the dynamic response of the CTPC system. The other two refrigerants used in the mixtures are R152a and R134a. The CO2/R32 working fluid is mixed in proportions of 1/0, 0.9/0.1, 0.7/0.3, and 0.5/0.5. The dynamic performances of the CTPC system with each fluid are compared. The refrigerant is added to improve the performance of CO2, so the proportion of refrigerant is no more than 50% in this paper. The same system design is used for all mixtures. The dynamic performance of the system is observed by the step change of disturbance parameters. At 300 s, the temperature of the exhaust decreased by 5%. At 600 s, the mass flow rate of exhaust increased by 10%. Finally, the pump rotation speed decreased by 10% at 900 s. Fig. 11 shows the dynamic response of the system under three different step changes. When exhaust temperature declines by 5%, all parameters decrease smoothly, except the mass flow rate of the working fluid, which shows obvious undershoot. Decreasing the exhaust temperature causes a sudden decrease in the heat absorbed by the working fluid. Thus, the operating pressure declines instantly, causing the mass flow rate decrease quickly. Then the density of working fluid increases as the working fluid temperature in the gas heater decreases, according to Eq. 18. The mass flow rate gradually rises to its original value. One can see that overshoot occurs in the operating

pressure and the working fluid mass flow rate when the exhaust mass flow rate increases by 10 %. This occurs due to a sudden increase in the exhaust mass flow rate before the flow rate of working fluid increase, resulting the heat imbalance in the gas heater. Several seconds later, the system returns to thermal equilibrium, then the pressure and flow rate stabilise to a constant value. When the pump speed decreases by 10%, the operating pressure and the working fluid mass flow rate both decrease, and the temperature of working fluid and exhaust at the gas heater outlet gradually increase. Figs. 11(c) and 11 (d) show that the difference between the outlet temperatures of the working fluid and exhaust with different proportions of CO2 and R32 under different steps are small. This means that the heat absorbed by the working fluids is nearly equal for all mixed working fluids. However, the mass flow rates of the CO2/ R32 mixtures change by different amounts with different steps, as shown in Fig. 11 (b). This is because the specific heat capacity of the working fluid increases as the refrigerant ratio increases. Fig. 11(a) shows that the operating pressure of CO2 mixture is nearly constant. A relative difference calculation is used to examine the dynamic response speed.

0.23

13000

0.22

Mass flow rate (kg/s)

Operating pressure (kPa)

13200

12800

12600

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

12400

12200

0.21

0.20

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

0.19

12000

0.18 0

200

400

600

Time (s)

800

1000

1200

0

200

400

600

Time (s)

800

1000

1200

(a) Operating pressure. (b)Mass flow rate. 445

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

590

580

Temperature of exhaust (K)

Temperature of working fluid (K)

600

570

560

550

540

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

440

435

430

425

420 0

200

400

600

800

Time (s)

1000

1200

0

200

400

600

800

1000

1200

Time (s)

(c) Outlet temperature of working fluid. (d)Outlet temperature of exhaust. Fig. 11. Dynamic response of the CTPC system under different step changes

5.2 Dynamic response speed Figs. 12-14 show that the dynamic performance of the system under three different steps presents different trend. Meanwhile, the trend is similar for working fluids with different proportion under the same step change, but the transient responses are visibly different. Overall, the average transient slope for pure CO2 is the steepest among all the four proportions, meaning it provides the fastest dynamic response speed. The setting time, time constant, and the peak time are used to qualify the transient response. The setting time (C} ) is the time required for the response curve to reach and stay within a range of certain variation (usually 5% or 2%; 5% is used here) of the final value [44]. The time constant (τ) is the time required for the step response to reach 1-1⁄f 63.2% of its final value. The peak

time (C ) describes the time that the system’s unit step response reaches the first peak during overshoot. Fig. 12 illustrates the dynamic response under a step change in the exhaust

temperature. The response speed decreases as the proportion of refrigerant increases. The dynamic response under a step change in exhaust mass flow rate and pump speed (Fig. 13 and 14, respectively) exhibit the same dependence on the proportion of refrigerant. Based on Fig. 12, Table 5 presents calculated data of the system due to the step change in gas temperature. The response time in the mass flow rate and temperature of the working fluid, and the waste heat gas temperature, increase as the refrigerant proportion increases. Meanwhile, the trend in the operating pressure is not obvious. Tables 6 and 7 show the calculated values of the system due to a step change in the gas mass flow rate and pump speed, respectively. It is clear that the response times for the four parameters increase as the proportion of R32 increases. As mentioned above, the different outlet temperature of the working fluid and exhaust under different step changes is small, which means that the different working fluids absorb nearly the same amount of heat, although the mixtures contain different proportions of refrigerant. In other words, the mass flow rate of the working fluid is determined by the working fluid’s heat capacity and density. The heat capacity and density of working fluid increase as the refrigerant proportion increases, resulting in the decreased mass flow rate. One can see that the working fluid with larger mass flow rate always responds more quickly. This can be explained as follows: the working fluid stored in the gas heater and condenser is stable after the gas heater stabilises. The thermal inertia of the working fluid increases as more the working fluid is stored in the gas heater. Large mass flow rates accelerate the update of the working fluid in the heat exchanger, which enables

the system operate quickly and stably. The influence of mass flow rate on the dynamic response speed was also examined by Gao.et [45]. The mass flow rate of the working fluid with large heat capacity is always small. Therefore, the working fluid with slower dynamic response speed tends to have greater heat capacity in general.

0.0000

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

-100

-200

-0.0006

Mass flow rate (kg/s)

Operating pressure (kPa)

0

-300

-400

-500 200

-0.0012

-0.0018

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

-0.0024

-0.0030

250

300

350

400

450

500

-0.0036 200

250

300

350

400

450

500

Time (s)

Time (s)

(a) Operating pressure. (b) Mass flow rate. 0

-5

-10

-15

Temperature of exhaust (K)

Temperature of working fluid (K)

0

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

-20

-4

-6

-8

-10

-25

-30 200

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

-2

250

300

350

400

450

500

-12 200

Time (s)

250

300

350

400

450

Time (s)

(c) Outlet temperature of working fluid. (d) Outlet temperature of exhaust. Fig. 12. Dynamic response of the CTPC system under the changes in exhaust temperature

Table 5

500

Dynamic characteristics due to a step change in gas temperature CO2 C}

P_

T"

TJ

CO2/R32(9/1)

τ

C

C}

τ

CO2/R32(7/3)

C

C}

τ

CO2/R32(5/5)

C

C}

22.6

8.7

/

20.4

8.8

/

18.8

8.96

/

18.6

8.74

/

73.2

26.

/

76.9

27.

/

79.6

27.9

/

81.9

28.9

/

60.9

13.

/

63.2

14.

/

64.8

14.7

/

66.9

15.1

/

/

/

16.6

/

/

17.7

/

/

18.6

/

/

19.6

m"

500

0.007

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

0.006 400

Mass flow rate (kg/s)

Operating pressure (kPa)

C

τ

300

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

200

100

0 500

550

600

650

700

750

0.005 0.004 0.003 0.002 0.001 0.000

800

-0.001 500

550

600

Time (s)

650

700

750

800

Time (s)

(a) Operating pressure. (b) Mass flow rate. 16

20

Temperature of exhaust (K)

Temperature of working fluid (K)

25

15

10

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

5

0 500

550

600

650

700

750

12

8

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

4

0

800

Time (s)

500

550

600

650

700

750

800

Time (s)

(c) Outlet temperature of working fluid. (d) Outlet temperature of exhaust. Fig. 13. Dynamic response of the CTPC system under the changes in exhaust mass flow rate Table 6

Dynamic characteristics due to a step change in gas mass flow rate CO2

TJ

CO2/R32(7/3)

τ

C

C}

τ

C

C}

τ

C

C}

τ

C

/

4.56

15.03

/

4.79

15.79

/

5.00

17.29

/

5.30

19.29

83.27

36.88

/

86.54

38.54

/

89.64

40.19

/

92.79

41.89

/

62.28

13.27

/

64.69

13.81

/

66.59

14.14

/

68.39

14.54

/

/

/

13.02

/

/

13.79

/

/

15.04

/

/

16.29

m"

0

0.000

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

-200

-400

Mass flow rate (kg/s)

Operating pressure (kPa)

CO2/R32(5/5)

C}

P_

T"

CO2/R32(9/1)

-600

-800

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

-0.005

-0.010

-0.015

-0.020

-1000 800

900

1000

1100

1200

-0.025 800

900

Time (s)

1000

1100

1200

Time (s)

(a) Operating pressure. (b) Mass flow rate. 10

30

Temperature of exhaust (K)

Temperature of working fluid (K)

35

25 20 15

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

10 5 0

8

6

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

4

2

0

-5 800

900

1000

Time (s)

1100

1200

800

900

1000

1100

1200

Time (s)

(c) Outlet temperature of working fluid. (d) Outlet temperature of exhaust. Fig. 14. Dynamic response of the CTPC system under the changes in pump speed

Table 7

Dynamic characteristics due to a step change in pump speed CO2 C}

τ

CO2/R32(9/1) C

C}

τ

CO2/R32(7/3)

C

C}

τ

CO2/R32(5/5)

C

C}

τ

C

Pe

26.25

11.65

/

28.75

12.3

/

34.15

13.35

/

41.65

14.25

/

T"

86.15

33.3

/

89.75

34.95

/

93.25

36.35

/

96.5

38.00

/

91.75

36.65

/

94.75

37.6

/

97.5

38.28

/

100.00

38.85

/

48.75

16

/

53

16.85

/

58.5

18.5

/

64.00

20.00

/

TJ

m"

The dynamic speed of the system with CO2/R152a and CO2/R134a as the working fluid are also calculated and show the same regular as CO2/R32, so there is no detailed description on CO2/R152a and CO2/R134a. The dynamic response of the system with different mixture working fluids due to a step change of exhaust mass flow rate is shown in Fig. 15. The response of system with pure CO2 and three different kinds of CO2 mixtures in proportions of 7:3 is shown in the figure. Obviously, the four working fluids exhibit consistent response. The response time is slightly different for various CO2 mixtures due to the difference in their physical properties. From another perspective, the response time is slower when there is more refrigerant. That is because the heat capacity and density of the working fluid increase as the proportion of the refrigerant increases.

500

CO2 CO2/R134a(7/3) CO2/R32(7/3) CO2/R152a(7/3)

400

300

200

CO2 CO2/R134a(7/3) CO2/R32(7/3) CO2/R152a(7/3)

100

0 500

550

600

650

700

750

Mass flow rate (kg/s)

Operating pressure (kPa)

0.0060

0.0045

0.0030

0.0015

0.0000

500

800

550

600

700

750

800

25

12 10 8 6

CO2 CO2/R134a(7/3) CO2/R32(7/3) CO2/R152a(7/3)

4 2 0 500

550

600

650

700

750

Temperature of working fluid (K)

14

Temperature of exhaust (K)

650

Time (s)

Time (s)

20

15

10

CO2 CO2/R134a(7/3) CO2/R32(7/3) CO2/R152a(7/3)

5

0

800

Time (s)

500

550

600

650

700

750

800

Time (s)

Fig. 15. Response with different kinds of CO2 mixtures.

5.3 The offset of the optimal operation point Most of the WHR systems were designed to operate in special working conditions to maxim energy savings, but these systems often work in different conditions, and the operating parameters vary greatly. Therefore, it is of great significance to explore the optimal operation points that provide the greatest power and efficiency under off-design condition for control. The mass flow rate of the working fluid increase as the pump rotation speed increases, which increases the amount of absorbed heat. Therefore, the net power output and thermal efficiency increase. The continuous increase in the working fluid mass flow rate causes the temperature of the working fluid at the gas heater outlet decrease, and the net power

output and thermal efficiency decrease. Thus, the net power output and thermal efficiency first increase and then decrease as the pump speed increase. As shown in Fig. 16(a) and (b), CO2 mixtures with different proportion have the same trend as pure CO2. The system has higher net power output and thermal efficiency when the proportion of refrigerant is larger. Of particular note is that the optimal net power output and thermal efficiency offset to the direction of the lower pump speed with the increase of refrigerant proportion. The optimal net power output and thermal efficiency do not correspond to the same pump speed. This means the CTPC system with CO2 mixture as the working fluid should use a lower pump speed compared to the system with pure CO2 in order to maximise net power output or thermal efficiency. Fig. 16(c) and (d) show the operating pressure and temperature of the working fluid at the gas heater outlet, where the black dots correspond to the system’s maximum net power output. One can see that the operating pressure decreases as the refrigerant proportion increases, which reduces the operation pressure in the CTPC system. The working fluid temperature at the gas heater outlet increases because of the mass flow rate decreases.

14000

12000

10000

8000

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

6000

Netpower output (W)

Netpower output (W)

14000

12000

10000

8000

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

6000

4000

4000 40

60

80

100

120

140

160

40

60

Pump speed (rpm)

80

120

140

160

750

20

520

16.0

700

18

510

15.5

500 15.0

490

14.5

16

95

100

105

110

115

14

12

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

10

8

Temperature (K)

Operating pressure (MPa)

100

Pump speed (rpm)

650

480 470

600

96

100

104

108

112

550 500

CO2 CO2/R134a(9/1) CO2/R134a(7/3) CO2/R134a(5/5)

450 400

40

60

80

100

120

Pump speed (rpm)

140

160

40

60

80

100

120

140

160

Pump speed (rpm)

Fig. 16. (a) Net power output (b) Thermal efficiency (c) Operating pressure (d) Outlet temperature of the working fluid

6. Conclusion In this study, a dynamic model of the CO2 mixture transcritical power cycle for waste heat recovery in an engine is created in Simulink and carefully validated against experimental data. The dynamic performance of the system with mixture working fluid in different components and proportions are examined. It is found that: (1) The finite volume method and moving boundary method are suitable for modelling a gas heater and condenser with CO2 mixtures as the working fluid, respectively. It gives confidence in the CTPC system modelling especially with mixture working fluid, which can provide reference value for future simulation

work. (2) The CTPC system with pure or mixture working fluid exhibits the same variation tendency under the same step change of external disturbance. The dynamic response time of the system increases as the proportion of refrigerant increases, while the magnitude of the system parameters changes slightly. (3) The optimal net power output and thermal efficiency offset to the direction of the lower pump speed as the proportion of refrigerant increases. The operating pressure decreases and the temperature of working fluid at the gas heater outlet increases. These studies will be helpful for future design, optimization, and control of CTPC system. Control of over the CO2 mixture transcritical power cycle will be examined in future studies.

Acknowledgements This work was supported by the National Key R&D Program of China (2017YFE0102800), and the authors gratefully acknowledge it for support of this work. Nomenclature C

D A ρ h d T P α

specific heat (kJ/kg
K) density (kg/m3) area (m2) density (kg/m3) specific enthalpy (J/kg) diameter (m) temperature (K) pressure (Pa) heat transfer coefficient (W/m2
K)

e_ N 7† γ η x µ η} η} ω V>rK CY ts tp τ W ! t L

Reynolds number Nusselt number Prandtl number void fraction (m2/s) liquid fraction (m2/s) average steam quality density ratio isentropic efficiency of the pump isentropic efficiency of the expander pump rotation (rpm/min) the cylinder volume (m3) nozzle cofficient settling time (s) peak time (s) time constant (s) output power (w) mass flow rate (kg/s) time (s) length (m)

Subscripts i o f1 f2 c l g p exp in out w avg rec amb

inside outside working fluid exhaust gas cooling water liquid gas pump expander inlet outlet wall average receiver ambiance

Abbreviations CTPC WHR WHRs FV MB ORC

CO2 transcritical power cycle waste heat recovery waste heat recovery system finite volume moving boundary organic Rankine cycle

Appendix 1 Mass conservation for superheated region of working fluid: 

  + ˆ

  *W

3 * ‰

    7>! + *  ℎ! + ((K − (J ) ! = !  − !  3

(1a)



Mass conservation for two-phase region of working fluid: W  /(J − (K 2(1 − F̅ ) ! + ŠX (1 − F̅ ) +  F̅ ‹ 3 7>! + /(J − (K 2 3 F! = !  − ˆ

! 3

ˆ

(2a)

Energy conservation for superheated region of working fluid: 

Š  + ˆ

  *W 3 * ˆ

 ℎ +

 *W 3 ˆ

( − 1‹  7> + 

  3 *

 ℎ + (   ℎ! + /( ℎ − 3

Œ (J ℎJ 2 ! = !  ℎ − !  ℎJ +
  Œ (01 − 0† )

(3a)

Energy conservation for two-phase region of working fluid: /(J ℎJ − (K ℎK 2(1 − F̅ ) ! + Š

(X *X ) ˆ

(1 − F̅ ) +

(K ℎK 2 3 F! = !  ℎJ − ! 3 ℎ3 +
3 

Œ4 Œ

(W *W ) ˆ

F̅ − 1‹ 3 7>! + /(J ℎJ −

(013 − 0†3 )

(4a)

Energy conservation for superheated region of tube wall: 61 (1 1  0!1 + (01 − 013 )! Ž =
   (0† − 01 ) +
O O  (0> − 01 ) (5a) Energy conservation for two-phase region of tube wall: 61 (1 1 3 0!13 =
3  3 (0†3 − 013 ) +
O O 3 (0>3 − 013 )

(6a)

Energy conservation for superheated region of cooling water:

> /(̅> 1ℎ> − (>3 ℎ>3 2! + 3 >  (̅> 

ˆ * 

! > (ℎ>3 − ℎ> ) =
 -.  (01 − 0> )

+ ℎ>

ˆ  



ˆxyz 

+

ˆ4 

− (7a)

Energy conservation for two-phase region of cooling water:    *   

> /(>3 ℎ>3 − (̅>3 ℎ>3 2!3 + 3 > 3 (̅>3 ˆ4 + ℎ>3 ˆ4   { + ˆ4  + ! > (ℎ>3 −

ℎ> ) =
3 -. 3 (013 − 0>3 )

(8a)

Mass conservation for receiver model of working fluid: ! †_> = ! 3 − ! 

(9a)

Energy conservation for receiver model of working fluid: 

W

qI ˆ J J

+

W W #X X

%

W #X

X qI ˆ K K

+

W J  ˆ

+

X K  ˆ

−(

W W #X X W #X

W

)(

q ˆ J

+

X q ) 7>! ˆ K

+

+ ! †_> = ! 3 ℎ3 − !  ℎK − ‘ †_> (0†_> − 0'
(10a)

Appendix 2 Table 1 Main components of test bench. Component Gas heater Condenser Pump Expansion valve Receiver

Type S-shaped tube-in-tube Brazed-plate Reciprocating plunger Needle valve Cylinder-shaped

Details Self-designed SWEP B18x40 3RC50A-1.7/13 Self-designed Self-designed

Specification 3.09 m2 1.56 m2 1.7 m3/h 0-100% 10 L

Table 2 Measuring instruments and accuracy of main parameters. Parameter

Sensor type

Scale

Exhaust side temperature

sheathed thermocouple sensors with first-class precision

-60-650

Other

sheathed Pt100 thermo-resistive type

-200-500

place’s

with A-class

Accuracy

ºC ºC

±1% ±0.15%

temperature

precision

High pressure of CO2

pressure transmitters

0-14 MPa

±0.065%

Low pressure of CO2

pressure transmitters

0-12 MPa

±0.065%

Exhaust pressure

pressure transmitters

0-0.5 MPa

±0.065%

Cooling water pressure

pressure transmitters

0-0.5 MPa

±0.065%

CO2 mass flow rate

Coriolis mass flowmeter

0-1080 kg/h

Cooling water flow rate

turbine flowmeter

0-12 m3/h

Fuel flow rate of engine

fuel consumption meter

5-2000 kg/h

±0.8%

Air intake flow of engine

air flow meter

0-1350 kg/h

±0.5%

±0.2% ±1%

Table 3 Uncertainty analysis of the heat transfer rate. Parameters Heat transfer rate of working fluid in the heating process Heat transfer rate of exhaust in the heating process Heat transfer rate of working fluid in the cooling process Heat transfer rate of water in the cooling process

(Ir )max 0.89 kW 2.41 kW 1.17 kW 4.53 kW

(gr )max 1.73 % 4.51 % 2.28 % 9.17 %

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Highlights 1. Methods of modeling the CTPC system with CO2 mixtures are validated. 2. Dynamic response speed decreases with the increase refrigerant proportion. 3. The optimal power output is offset to the direction of lower pump speed. 4. The operation pressure reduction can be achieved over refrigerant addition.