Dynamic performance and control strategy of CO2-mixture transcritical power cycle for heavy-duty diesel engine waste-heat recovery

Energy Conversion and Management 205 (2020) 112389

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Dynamic performance and control strategy of CO2-mixture transcritical power cycle for heavy-duty diesel engine waste-heat recovery ⁎

T

⁎

Rui Wang, Gequn Shu , Xuan Wang , Hua Tian, Xiaoya Li, Mingtao Wang, Jinwen Cai State Key Laboratory of Engines, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Carbon dioxide mixture transcritical power cycle Heavy duty diesel engine Waste heat recovery Design parameter optimization Optimal control Constant control

Carbon dioxide mixture transcritical power cycle (CMTPC) is considered as a new promising technology for waste heat recovery (WHR), while there are still critical challenges arising from the transient fluctuations of heat sources when it comes to the heavy-duty diesel engines (HDDEs) applications. This paper presents a dynamic model of CMTPC systems, which is carefully validated against experimental data. Constant temperature, constant pressure and optimal control strategies are proposed to realize stable and optimal operation. The dynamic performance of the system with different control strategies is predicted under slow step change and transient change conditions. The results demonstrate that under slow step change conditions, the stability of optimal control system and constant pressure control system is better than that of constant temperature control system. In addition, the net power output keeps maximum under the optimal control because of the compromise between operating pressure and temperature. However, under transient conditions the control performance of optimal control is not as obvious as under slow step change conditions. Compared with open loop system, the improvement of system power by optimal control under slow step change is 2.31%, while that is only 0.07% under transient change condition. By contrast, it is found that the constant pressure control achieves the best power improvement of 0.58% under transient conditions because of the satisfactory control effect on operating pressure and relatively small fluctuations of expander inlet temperature. In a word, different control strategies behave obviously different performance under various conditions.

1. Introduction As the most primary mover for commercial road transportations, heavy duty-diesel engines (HDDEs) cause CO2 emission and oil consumption. The regulations on HDDEs adopted by the United States government in 2016 require a 25% decrease in fuel consumption and CO2 emissions in 2027 compared with 2018 baseline [1]. However, current HDDEs show no more than 50% thermal efficiency [2], releasing a large amount of energy to ambient in the form of exhaust and jacket water, which not only causes serious environmental pollution but also aggravates the energy crisis of fossil fuels. Therefore, effective utilization of waste heat is an effective way to improve thermal efficiency and reduce fuel consumption of engines. Some technologies such as thermoelectric generators [3,4], turbo-compounding [5], organic Rankine cycles (ORC) [6–8] are applied to recover the waste heat of engine. ORC technology is outstanding due to its low cost and good thermal efficiency. CO2 transcritical power cycles (CTPC) which is a kind of Rankine cycle with CO2 as working fluid [9,10] are applied to recover the waste heat of engine. The CTPC system has been widely

⁎

concerned as one of the most potential technologies for next generation of waste heat recovery (WHR) systems [11] due to the simultaneous utilization of the large gradient heat source and the advantage of miniaturization [12–14]. The CTPC system which contains the preheater and regenerator (PR-CTPC) is chosen as the research object in this paper because it has high thermal efficiency and can recover the energy of exhaust and jacket water at the same time [9,15]. However, owing to the critical temperature (31.1 °C) and pressure (7.38 MPa) of CO2, the CTPC systems often need to operate at low condensation temperatures and high operating pressure, which brings serious challenges in commercializing in real scenarios. CO2-mixtures have been proposed to replace pure CO2 in a CTPC system to deal with the challenges. The selection of refrigerant additives and thermodynamic properties of the system have been studied by many scholars [12,16,17]. Shu et al. [12] investigated eight CO2-based mixtures for CMTPC system and proved that the problems of the operating pressure and condensation temperature can be greatly improved compared with pure CO2. Wu et al. [13] used six different CO2-based binary zeotropic mixtures as the working fluid of transcritical power cycle to convert low

Corresponding authors. E-mail addresses: [email protected] (G. Shu), [email protected] (X. Wang).

https://doi.org/10.1016/j.enconman.2019.112389 Received 26 August 2019; Received in revised form 30 October 2019; Accepted 6 December 2019 0196-8904/ © 2019 Published by Elsevier Ltd.

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Nomenclature Cp ω Vcyl ρ h ηv ηsp Cv ηst T m

f1 f2

specific heat (kJ/kg·K) pump rotation (rpm/min) the cylinder volume (m3) the density of working fluid (kg/m3) enthalpy (kJ/kg·K) the volume efficiency isentropic efficiency of the pump nozzle coefficient isentropic efficiency of the expander temperature (K) mass flow rate (kg/s)

w i o

Abbreviations CTPC CO2 transcritical power cycle PR-CTPC CO2 transcritical Power cycle with preheater and regenerator CMTPC CO2 mixture transcritical power cycle PR-CMTPC CO2 mixture transcritical Power cycle with preheater and regenerator HDDEs heavy duty diesel engines WHR waste heat recovery ORC organic Rankine cycles

Subscripts P exp g j

working fluid heat source (exhaust or jacket water or working fluid after expander) tube wall inlet outlet

pump expander exhaust jacket water

fluid concentrations, pressure and temperature. Osorio et al. [29] analyzed the dynamic performance of concentrated solar supercritical CO2-based power generation closed-loop cycle. In general, the common control strategies can be classed into constant control strategies such as constant operating pressure, operating temperature and constant superheat degree, and the set-point optimal control. To the author’s knowledge, the dynamic performance and control strategy of the CO2 mixtures transcritical power cycle containing a preheater and a regenerator (PR-CMTPC) has not been reported so far. A dynamic model is required to investigate the system transient performance and control strategies under the engine actual operating profiles. Moreover, there are few articles combines experiment and simulation data resulting in the low credibility of model. Therefore, this paper establishes a dynamic model of PR-CMTPC system and carefully validates it against experimental data. Based on these, the dynamic performance of the system is researched and different control strategies are compared. The structure of the article is as follow: Section 2 represents the PR-CMTPC system. Section 3 describes the modeling process and the model is validated carefully against experimental date in order to eliminate the gap between actual test and simulation. The design point of PR-CMTPC and different system control strategies are proposed in Section 4. Section 5 analyses the design parameters optimization, the optimal point calibration, as well as the dynamic characteristics and control performance with different strategies under slow step change and transient change conditions respectively. The paper ends with the main conclusions in Section 6. It is believed that this work has the novelties and contributions below:

grade heat of geothermal water into power. Results indicated that the CO2-mixtures could decrease the high operating pressure and enlarge the condensation temperature range at the same time. Yang [18] implemented the Rankine cycle system with CO2-mixtures as working fluid, they demonstrated that not only the energy cost is reduced but the condensing temperature is also increased. Li et al. [19] pointed out that the system with CO2-mixture could tackle the challenges of high operating pressure. Moreover, the mass flow rate and temperature of the engine waste heat sources are highly transient and greatly variable due to the continuous fluctuations in actual operating profiles of engine [20]. The transient and variable heat sources bring great challenges for reliability, durability and stability of the CMTPC system. Both Zhao et al. [21] and Shu et al. [22] pointed out that the model of WHR systems is required to be shut down when engine operates under low-speed and low-torque conditions. Wang et al. [23] controlled the superheat degree of the WHR system and revealed that the system net power output varies significantly with different controlled superheat degree over the whole operation range. Therefore, appropriate control strategies must be adopted to ensure the continuous and effective operation of the system in the transcritical region. There are few published articles about CMTPC control, so the control about ORC system and CO2 power cycle can be referenced here. In recent years, some different control concepts about ORC have been presented [7,24–26]. Koppauer et al. [25] proposed a model predictive control strategy using a prediction model based on the gain scheduling of local models for an organic Rankine cycle, maximum energy recovery is achieved by tracing the optimal reference enthalpy of working fluid. Seitz et al. [7] proposed a PID feedback controller contained in a model-based nonlinear feedforward controller, the system performance was optimized by controlling the working fluid mass flow rate to trace the set point value. Stefano et al. [24] selected optimal set points for the controlled variables according to engine operating conditions. The simulation results showed that the control system successfully achieved the control targets under slow velocity ramps. The dynamic performance and control strategy of CTPC is also a research hotspot in recent years. Olumayegun et al. [27] established a supercritical CO2 power cycle model and researched the dynamic characteristics. PID controller was adopted to maintain a constant turbine inlet temperature by controlling the cooling water temperature and working fluid mass flow rate respectively. Li et al. [28] predicted the transient performance of four different CTPC systems over a heavy duty diesel engine and two PID controllers were adopted to realize stable and optimal operation by controlling the mass flow rate,

1) Develop a dynamic model of CO2 mixture transcritical power cycle with preheater and regenerator (PR-CTPC), and perform the validation against experimental data, which fills the gap of dynamic model with mixture working fluid. 2) Optimize the design parameters and propose a simplified optimal control strategy, which lay the foundation for system design and optimal control. 3) The effectiveness of three control strategies under slow step change and transient change conditions is pointed out. Furthermore, the applicability of different control methods to different situations is presented by comparing the system dynamic performance.

2

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2. System description

physical properties are considered stable during all working conditions.

An inline 4-stroke 6-cylinder heavy-duty diesel engine is chosen as the research object. The waste heat source of exhaust and jacket water are recovered by the PR-CMTPC system. The main parameters of the object engine are listed in Table 1. The main composition and mass fraction of the exhaust is as follow: N2 = 73.4%, CO2 = 7.11%, H2O = 14.22%, O2 = 5.27%. The jacket water is regarded as pure water without any impurity in the present work. The PR-CMTPC system (the CMTPC system with preheater and regenerator) model is mainly composed of preheater, gas heater, regenerator, condenser, pump and expander. Fig. 1 shows the schematic layout and T-s diagram of the PR-CTPC system, the high-pressure working fluid discharged from the pump outlet is heated by jacket water, then the working fluid transfers heat in regenerator and gas heater respectively. Then, the high-temperature and high-pressure working fluid is expanded through the expander to output power. Afterwards, the energy of working fluid is rejected through the regenerator and condenser. Last, the working fluid leaves the receiver and enters the pump to finish a cycle.

∂ρ f 1, ai dTf 1, i − 1 ∂ρf 1, ai dpf 1 dTf 1, i ⎞ ⎛ + + A1 Δx = ṁ f 1, i − 1 − ṁ f 1, i 0.5A1 Δx − ∂Pf 1 dt dt dt ∂Tf 1, ai ⎝ ⎠

3. Mathematic model

= αin πDi Δx (Tw, i − Tf 1, i ) + ṁ f 1, i − 1 hf 1, i − 1 − ṁ f 1, i hf 1, i

The PR-CMTPC system mathematic model is established in MATLAB/Simulink. Working fluid properties are firstly calculated from Refprop 9.0 software [30] and then made into several tables which are incorporated in the system models to look up to facilitate fast calculation. All the modular component models of PR-CMTPC are established by s-function in MATLAB considering the mass and energy conservation equations as well as other constitutive. After that, the system model is established by combining the component models according to their interrelationship. The Simulink PR-CMTPC system model is shown in Fig. 2. The heat exchanger model, the condenser model, the pump and expander model are described respectively. Then, the effect of grid number on the precision of heat exchanger models is also discussed. Moreover, the system model is validated carefully against experimental data, and the boundary conditions and heat source parameters refer to the actual test bench. The model which does not subject to the lack of controller installed on the laboratory bench can be used to study the system dynamic performance with different control strategies.

∂ρf 2, ai ⎛− dTf 1, i − 1 ⎞ ∂hf 2, ai ⎞ dT2, i − + ρf 2, ai − ⎟ ⎛ + = 0.5A2 Δx ⎜hf 2, ai − dt dt ⎠ ∂ ∂ ⎝ T T f 2, ai f 2, ai ⎠ ⎝

Based on above assumptions, the mass conservation of working fluid, the energy conservation of working fluid and heat sources (exhaust and jacket water), the energy conservation of tube walls are taken into consideration. The differential equations are listed in Eqs. (1)–(4). As for the regenerator, the mass conservation of high-temperature and low-temperature working fluid are not negligible. −

−

⎜

⎟

(1) − ∂ρf 1, ai ⎛− 0.5A1 Δx ⎜hf 1, ai −

∂Tf 1, ai

⎝

− −

+ ρf 1, ai

∂hf 1, ai ⎞ ⎛ dTf 1, i − 1 dTf 1, i ⎞ + + A1 − ⎟ dt dt ⎠ ∂Tf 1, ai ⎠ ⎝ ⎜

⎟

−

−

∂ρf 1, ai ⎞ dPf 1 ⎛− ∂hf 1, ai − + ρf 1, ai − 1⎟ Δx ⎜hf 1, ai ∂Pf 1 ∂Pf 1 dt ⎠ ⎝ −

(2)

−

−

⎜

⎟

−

αout , i πoΔx (Tw, i − Tf 2, ai ) + ṁ f 2, i hf 2, i − ṁ f 2, i − 1 hf 1, i − 1

(3)

−

Aw Δxρw CPw

− − dTw, ai = αout , i πDo Δx (Tf 2, ai − Tw, i ) + αin, i πDi Δx (Tf 1, ai − Tw, i ) dt (4)

3.2. Condenser model There is phase transition of working fluid in the condenser and the physical properties change uniformly. Thus, the condenser model is established by move boundary (MB) method to represent the phase transition. The condenser which is coupled with a receiver [22] is shown in Fig. 4. The working fluid in the receiver is considered as saturated liquid, which can avoid deterioration of pump performance. The general mass balance for working fluid is given in Eq. (5), and the energy balance differential equations for cooling water and working fluid are given in Eq. (6). The general energy balance differential equation for condenser wall is given in Eq. (7). The Leibniz integration rule as shown in Eq. (8) is used to integrate the governing partial differential equations (PDEs).

3.1. Heat exchanger model The heat exchanger models include preheater, regenerator and gas heater in this paper. Considering the violent change of working fluid physical properties at supercritical state, the finite volume (FV) method is used to establish the heat exchanger model. The schematic layout of heat exchanger is shown in Fig. 3. Along the horizontal direction, the heat exchanger can be divided into n control cells, and each length of the section is Δx. The discrete nodes are at each control cell’s center, and their state is represented by the average state of inlet and outlet. The physical properties of supercritical working fluid change sharply, so, the control cell number of the heat exchanger may influence the calculation accuracy. This will be discussed below. Some necessary assumptions are needed to simplify the FV models.

∂ (Aρ) ∂ṁ + =0 ∂t ∂z

(5)

Table 1 Basic parameters of the object diesel engine.

(1) The preheater, regenerator and gas heater are all thought as horizontal tube-in- tube heat exchangers. (2) The axial heat conduction and the heat transfer loss are not taken into consideration. (3) The tube wall is assumed to be lumped thermal capacitance. (4) The pressure of heat sources is thought as constant while of working fluid is variable. (5) The heat source fluids are thought as incompressible while the working fluid is compressible. (6) The organic fluid and CO2 can be mixed homogeneously and the 3

Parameter

Unit

Content

Engine type Intake system type Fuel type Bore Stroke Displacement Maximum torque Compression ratio Rate power Rate speed Speed at maximum torque Valve per cylinder

—— —— —— mm mm L N·m —— kW rpm rpm ——

Inline, 6 cylinders Turbo-charge/Intercooler Diesel 113 140 8.424 1280 17.5 243 2200 1200–1700 4

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Fig. 1. Schematic layout and T-s diagram of the PR-CTPC system.

∂ (Aρh − AP ) ∂mḣ + = αi πDi (Tw − Tf ) ∂t ∂z Cpw ρw Aw

∫z

z2

1

ṁ pump = ηv ρp ωVcyl Wp = ṁ (hpout − hpin )

dTw = αi πDi (Tf − Tw ) + αo πDo (Tc − Tw ) dt

∂f (z , t ) d dz = dt ∂t

∫z

z2

1

f (z , t ) dz − f (z2, t )

(9)

(6)

(7)

dz2 dz + f (z1, t ) 1 dt dt

hpout = hpin +

(10)

hspout − hpin ηsp

(11)

(8) where, ω , Vcyl , ρp , and ηv are the pump rotation speed, the cylinder volume, the density of working fluid at the pump inlet, and the volumetric efficiency. hpin and hspout represent the working fluid enthalpy at the inlet of the pump and the ideal enthalpy of working fluid after isentropic pumping. ηsp is the isentropic efficiency of the pump. The expander model is replaced with a nozzle [31], the working fluid mass flow rate, the output power of the expander and the expander outlet enthalpy can be described as:

3.3. Pump and expander models The pump and expander always respond faster compared with the heat exchangers, so static models are used for pump and expander. The mass flow rate of working fluid, the consumed work and the pump outlet enthalpy of working fluid can be defined as:

Fig. 2. The PR-CTPC system model built in Simulink. 4

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Fig. 3. The finite volume model of heat exchangers.

(12)

3.5

Wt = ṁ (htin − htout )

(13)

3.0

htout = htin − (htin − hsout ) ηst

(14)

The relative error (%)

ṁ t = Cv ρexP P

where, Cv , ρexp , andP are nozzle coefficient, the density of working fluid at the inlet of the expander, and the operating pressure, respectively. hexpin and hsout represent the working fluid enthalpy at the inlet of the expander and the ideal enthalpy after isentropic expansion. ηst is the isentropic efficiency of the expander. 3.4. Determination of heat exchanger grid number

Gas heater Preheater Regenerator

2.5 2.0 1.5 1.0 0.5 0.0 0

Great emphasis should be placed on the accuracy of the heat exchangers due to the significant impact on system thermal inertia. The calculation accuracy of the finite volume method is related to the grid number of heat exchangers. Karellas et al. [32] pointed out that the finite volume calculation errors can be reduced by improving the grid number of gas heater. Therefore, as shown in Fig. 5, the relationship between the grid number and calculation accuracy for the gas heater, preheater and regenerator is discussed in present work. The prediction

20

40

60

80

100

The grid number (n) Fig. 5. Calculation error for heat exchanger models with different gird numbers.

Fig. 4. The move boundary model of condenser. 5

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adjusting the opening of the expansion valve. At 200 s, the valve opening is increased by 10.4%; at 400 s, the valve opening is increased by 12.3%. R134a is chosen as the ideal refrigerant fluid for waste heat recovery system by many scholars, due to its safety and environmental friendliness with a zero ODP and a relatively low GWP value [12,33–35]. The working fluid is the mixture of CO2 and R134a with the proportion of 0.7/0.3. The dynamic model is validated by comparing the operating pressure and mass flow rate of the working fluid when adjusting the expansion valve opening degree. Fig. 7 shows the simulation data and experimental data, which indicates the simulation results of our models are in good agreement with the experimental data, with the average relative errors of operating pressure and mass flow rate are 1.57% and 5.92%, respectively. It gives confidence to the validity of our models and the engineering-level prediction results reported in this work. The slight differences are caused by the uncertainties of the real operation and the neglection of the mechanical properties of the piston pump in our models.

errors are calculated for the different grid numbers against the reference 100 segments model. When the number of grids is 20 for the gas heater, the accuracy of calculation error is less than 0.5% and the accuracy will hardly improve with the increase of the grids number. Thus, the grid number of gas heater is set as 20 to make a prefer compromise between the calculation time and accuracy. Similarly, the grid number of preheater and regenerator is set as 20 and 10 respectively.

3.5. Model validation According to the author’s knowledge, there is no published literature data to validate the dynamic model of the PR-CMTPC system. The model validation is performed with experimental data gathered from the test bench designed by our group. More details about the hardware setup of the real test bench as shown in Fig. 6 can reference [9]. It’s worth to emphasize that the expansion valve is used to replace the expander in the test bench and the experimental data is obtained by

Fig. 6. (a) The experiment bench and (b) detailed structure of system. 6

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0.186

Exp. data Simulation

0.185

10200

Mass flow rate (kg/s)

Operating pressure (kPa)

Exp. data Simulation

10000

9800

0.184

0.183

0.182

9600 0

100

200

300

400

500

0.181

600

0

100

200

300

400

500

600

Time (s)

Time (s)

Fig. 7. Model validation results.

4. Design point description and control strategy

Table 2 Heat source parameters and necessary determined parameters at design point.

Studying of this part serves two major purposes: engine design point selection and control strategies description. The waste heat recovery system is designed under commonly used engine conditions. Two important control strategies – constant control strategy (including constant temperature and constant pressure control strategy) and optimal control strategy are proposed in this chapter. 4.1. Design point description The purpose of waste heat recovery (WHR) development is to improve the energy efficiency in actual operating profiles, so the engine operating point at which the PR-CMTPC is designed is worth to be considered carefully [2]. On the highway operating profile, most of the time the common HDDEs works constantly at medium to high speed and torque levels, being suitable for waste heat recovery thanks to its high waste energy density. The percentage pie chart of object heavy duty diesel engine’s speed and torque shown in Fig. 8 is based on EPA (United States Environmental Protection Agency) [36]. One can see that the engine works for more than 90% of the time at 60–100% speed, and more than 80% of the time at 60–100% torque. Therefore, the operating profile of 80% speed and 80% torque is chosen as the design point for PR-CMTPC system. The parameters of heat source and other determined parameters at design point are listed in Table 2.

Parameter

Unit

Values

Outlet temperature of exhaust/jacket water Mass flow rate of exhaust/jacket water Condensation temperature Pinch point in the gas heater Pinch point in the regenerator Pinch point in the preheater Pinch point in the condenser Turbine/pump isentropic efficiency

°C kg/s °C °C °C °C °C ——

389.7/85 0.32/3.23 22 30 20 10 5 0.7/0.6

strategies using PID controllers are put forward to observe the system dynamic performance, one is the constant pressure control by adjusting the opening degree of expander valve and the other is constant temperature control by adjusting the pump rotation speed. Thus, the operating pressure and operating temperature are set as control targets, the opening degree of expander valve and pump speed are set as control variables respectively. PID controllers are used to establish a feedback loop between control targets and control variables to keep the expander inlet temperature or pressure constant at the design values. The basic PID parameters are tuned at the optimal steady-state design point and listed in Table 3. Moreover, in order to obtain the maximum net power output of the system during the whole operation process, an optimal control strategy is proposed to track the optimal mass flow rate of the working fluid which can produce the largest power under off-design conditions. The optimal mass flow of working fluid is obtained by adjusting the pump rotation speed. The search for the optimal mass flow and the optimal control strategy are described in detail in the following section. The heat source parameters (the temperature and mass flow rate of exhaust

4.2. Control strategy One of the key aspects to predict the performance of the WHR system for a specified working condition is to determine parameters which is delivered to the expander [27], such as the temperature and pressure of the working fluid. Two kinds of constant value control

Fig. 8. Typical engine high way speed and torque time percentage distribution [36]. 7

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The aims of this part are as follows: first, the optimization of CMTPC design parameters under the steady engine working condition is done to obtain the best design performance. Then, the optimal mass flow under off-design conditions is searched to provide a basis for optimal control. Moreover, the open loop simulation under four different engine conditions is researched to observe the open loop dynamic performance without any controller action. Based on these, the dynamic performances with different control strategies are compared under slow step change conditions. Finally, the system performance with different control strategies under transient conditions is studied.

condition, and the heat source parameters of target HDDEs are listed in Table 2. The operating pressure, the expander inlet temperature and the proportion of R134a have significant impact on the system performance especially the net power output and total length of heat exchangers. Therefore, considering the thermodynamic and economic performance of the system, which are evaluated by the net power output and heat exchangers total length, the multi-objective optimization is necessary to get the optimal design parameters. Some scholars have explored multiobjective optimization aiming at obtaining better power and economic performance [37–39]. However, multi-objective optimization has never considered the proportion of CO2 and refrigerant. The operating pressure, the expander inlet temperature and the proportion of R134a are set as the optimization variables in the present work, with the purpose of obtaining the large net power output and small heat exchanger area simultaneously. The trade-off relationships between the optimal variables and targets are shown in Fig. 10. It’s worth noting that R134a is added to improve the performance of CO2, so the proportion of R134a is no more than 50% in this paper. It can be found that with the increase of refrigerant ratio, the net power output increases under the middle to high pressure, while it decreases under low pressure. The smaller length of heat exchangers appears in the high pressure and low to middle temperature range, and with the increase of refrigerant ratio, the total length of heat exchangers tends to increase. Based on the above analysis, the proportion of CO2 is defined as 0.7 to obtain great net power output without too large heat exchanger area to get preferable comprehensive performance. Under the proportion of 0.7/0.3 (CO2/R134a), the trade-off relationship between optimization variables and optimization targets is shown in Fig. 11. It is obvious that the optimization target can obtain prefer performance below 520 K, and the operating pressure should not exceed 12 MPa neither below 9.5 MPa to avoid low net power output and large heat exchangers area. Finally, the design parameters of 10 MPa and 473.15 K are selected to obtain the large net power output and small area of heat exchangers at the same time.

5.1. Optimization of CTMPC design parameter

5.2. Searching for optimal points of net power output

This section aims at acquiring the optimal design parameters of the PR-CMTPC system. As mentioned above, the engine operating profile of 80% speed and 80% torque working condition is selected as the design

The HDDEs always work under off-design conditions and the heat sources are transient and changeable, which has great effects on the system performance. Thus, this paper aims to analyze the system

Table 3 The PID controller parameters for constant control strategy. Parameter Pump controller Expander controller

P −2.83e-3 −9.44

I −5.5e-2 −0.013

D 1.73e-4 0.361

and jacket water) varying with the fluctuation of engine working condition are considered as the input disturbance. The reference control scheme is illustrated in Fig. 9. At the same time, the control strategy should try to meet the following conditions: (1) Avoiding too low outlet temperature of jacket water and exhaust gas. The exhaust outlet temperature is limited to above 120 °C in this study to avoid corrosion and the jacket water outlet temperature is thought above 74 °C to avoid damage to the engine performance. (2) Keeping the operating pressure in supercritical state to avoid damage to the mechanical integrity of the system. (3) Achieving the maximum net power output under various engine working conditions. 5. Result and discussion

Fig. 9. The reference control scheme. 8

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Fig. 10. The trade-off relationship between the optimal variables and targets.

when the speed deviate from optimum value, thus engine operating conditions in the same region can correspond to the same optimal pump speed to simplify the optimal control strategy.

performance under different working conditions and illuminate the difference between the constant control strategy and optimal control strategy. The search for the optimal mass flow in this part is the foundation of the optimal control. Fig. 12 shows the optimal points of net power output under 20 engine conditions from medium to high engine speed and torque. The thermal balance experimental data of the target engine under the 20 conditions is listed in the Appendix. In each operating condition, the optimal point of net power output corresponds to a specific pump rotation speed. It can be observed that the optimal pump speeds of some working conditions are very close, while others are far apart as demonstrated in Fig. 12(a). If the engine condition is divided into four regions with the design point as the origin, the horizontal coordinate as the rotation speed, and the vertical coordinate as the torque, one can see that the optimal pump rotation speed of each region is very close as shown in Fig. 12(b). In the first region where the engine speed and torque are both higher than the design condition, the optimal pump speed is about 80 rpm. In the second region where the engine speed is below design condition and the engine torque is above design condition, the optimal pump rotation speed is slightly below 80 rpm. The optimal pump speed at the third and fourth regions is around 70 and 75 rpm, respectively. It is obvious that the net power output in region one and two is better than design condition, region four comes next, and region three is the worst. That means the system can achieve better power output under the conditions of large torque, and the system performance deteriorates obviously when both engine speed and torque are lower than design condition. The power output deteriorates slightly

5.3. Open loop response simulation In this part, four different engine working conditions at middle to high speed and torque shown in Table 4, are adopted as system step change to observe the open loop dynamic performance without any controller action. The engine condition step changes represented by the temperature and mass flow rate of heat sources are given at 500 s, 1000 s, 1500 s and 2000 s respectively and the total simulation time is 2500 s. The open loop simulation results are shown in Fig. 13 and Fig. 14. Fig. 13(a) presents the exhaust temperature at the outlet of gas heater and jacket water temperature at the outlet of preheater, Fig. 13(b) presents the utilization of heat source. It is clear that the exhaust outlet temperature demonstrated in Fig. 13, is consistent with the total energy of exhaust shown in Table 4. The total energy of exhaust is directly decided by engine working conditions. The jacket water outlet temperature of the PR-CMTPC system is consistent with the total energy and Tjout (jacket water temperature at the outlet of engine) as shown in Table 4. It can be found that the exhaust energy is positively correlated with engine operating conditions, while the jacket water is not. That means the exhaust outlet temperature can be directly adjusted according to engine operating conditions, while the jacket water outlet temperature needs to be adjusted according to Tjout . The exhaust outlet Total length of exchanger (m)

Net power output(W) 1.564E+04

191.5

600 1.474E+04

580 1.383E+04

560 1.293E+04

540 1.202E+04

520

1.112E+04

500

1.021E+04

480

9305

460 9

10

11

12

13

14

176.1

580 160.8

560 145.4

540 130.0

520

114.6

500

99.25

480

83.88

460

8400

8

Expander inlet temperature (K)

Expander inlet temperature (K)

600

15

68.50

8

High pressure (MPa)

9

10

11

12

13

14

High pressure (MPa)

Fig. 11. Net power output and total length of heat exchanger under 0.7/0.3 proportion. 9

15

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Design condition 1900r 80% 2200r 80% 2200r 90% 1700r 70% 1600r 60% 1500r 70% 2100r 70% 1900r 70% 2000r 60% 1600r 90% 1700r 90% 1600r 100%

17000

Net power output (W)

16000 15000 14000 13000 12000 11000 10000 9000 65

70

75

80

85

Pump rotation speed (r/min)

(a)

(b)

Fig. 12. The optimal points of net power output under off-design conditions.

sensitive to its temperature change. The higher jacket water outlet temperature of system is, the less water energy is absorbed and lower the utilization is. The jacket water entering the cylinder needs to maintain a certain temperature in the practical application of internal combustion engine. While the temperature change of jacket water at the outlet of preheater is complex, so it is necessary to take control measures. The net power output which is decided by the absorbed total heat source energy and thermal efficiency is consistent with the trend of operating pressure and working fluid outlet temperature as demonstrated in Fig. 14(a). That’s because the net power output is the function of operating pressure, turbine inlet temperature, condensing pressure, pump outlet pressure and working fluid mass flow rate. The pump rotation speed is fixed at 80 rpm in open loop simulation, so the working fluid mass flow rate is basically constant. The condensing pressure and pump outlet temperature depend on the condensation temperature, they change slightly due to the mildly fluctuation of condensation temperature shown in Fig. 14(a). Therefore, the net power output is positively correlated with operating pressure and turbine inlet temperature. As can be seen in Fig. 14(b), the total heat source energy absorbed by the system is composed of jacket water energy and exhaust energy. It’s obvious that the absorbed jacket water energy accounts for a large proportion compared with the absorbed exhaust energy. Therefore, the medium and low temperature heat sources should not be neglected. Thanks to the special density characteristic of CO2 mixtures that the low and high temperature heat sources can be recovered at the

Table 4 The parameters of target engine under design condition and step change conditions. Parameter

Design

Cond. 1

Cond. 2

Cond. 3

Cond. 4

Power output [kW] Engine speed (r/min) Engine load (%) Exhaust temperature/Tgout [°C]

192.9 1800 80 389.7

194.8 1900 80 381.7

144.5 1800 60 339.4

159.9 1700 70 367.3

193.3 2200 80 383.0

Exhaust mass flow rate [kg/s] Jacket water temperature/Tjout

0.320 85

0.339 87

0.284 86

0.280 84

0.385 81

3.23

3.36

3.21

3.05

3.86

91.6 149.0

94.0 183.5

65.8 161.7

73.5 132.9

107.6 113.2

temperature under condition (2) and (3) is below the acid dew temperature 393.15 K, which will lead to equipment corrosion. The utilization of exhaust under condition (2) and (3) in the shaded green is over 1 due to the exhaust temperature is lower than the design point 393.15 K. Thus, this phenomenon is worth noting and necessary control strategies should be taken into great consideration. It is also feasible to adopt special anti-corrosion treatment for heat exchanger. Moreover, the utilization rate of jacket water is contrary to its outlet temperature trend and not necessarily related to its available energy. That’s because the large specific heat capacity of water makes the jacket water energy

0.896

354

425

Jcaket water outlet temperature Exhaust outlet temperature

420

353

0.768 0.704

352 410 405

351

400

350

395

Temperature (K)

Temperature (K)

415

349

380

Utilization of jacket water

0.88 0.77 0.66 0.55 1.26

Utilization of exhaust aau ust

1.12

390

0.98

348

385

Utilization of total energy

0.832

Utilization

[°C] Jacket water mass flow rate [kg/s] Energy of exhaust [kW] Energy of jacket water [kW]

0.84

0

500

1000

1500

2000

347 2500

0

500

1000

Time (s)

1500

Time (s)

Fig. 13. Outlet temperature (a) and utilization (b) of heat source. 10

2000

2500

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16

10.0 480

14

9.8

460 13 12

9.6 9.4

440

9.2

11 420

9

186.0 179.8 173.6 110.0

99.0 93.5 102.3

500

1000

1500

2000

Exhaust

93.0 83.7

300 0

Jacket water

104.5

9.0

10

total energy

192.2

Temperature (K)

Power (kW)

15

10.2 500

Pressure (MPa)

Net power output Working fluid outlet temperature Operating pressure Cooling water temperature

Absorbed heat source energy (kW)

17

74.4

8.8

2500

0

500

1000

Time (s)

1500

2000

2500

Time (s)

Fig. 14. The main parameters of system (a) and absorbed heat source energy (b).

step change of working condition. Similar phenomena exist in the mass flow rate of working fluid as can be seen in Fig. 16(b). The energy supplied to the system varies with the change of engine operating conditions, so the energy absorbed by the system changes accordingly. The pump controller makes the turbine inlet temperature remain constant by adjusting the pump rotation speed. Thus, the working fluid mass flow rate changes with the engine working conditions and the amplitude change is the largest under constant temperature control. The amplitude change of mass flow rate under optimal control comes next, that’s because the change of pump speed is less drastic than that under constant temperature control. On the whole range, the working fluid mass flow rate without controller or with expander valve controller remains stable due to the pump speed remains unchanged, except for the slightly fluctuation near the step time points demonstrated in local magnification of Fig. 16(b). Fig. 17(b) is the comparison of the operating pressure among four kinds of systems. It is obvious that the operating pressure under the expander valve controller system remains constant and there is hardly any fluctuation. That means the controller works well. However, the operating pressure under the pump controller system changes most violently from 8.0 MPa up to 10.5 MPa due to the drastic change of working fluid mass flow rate. The variation of operating pressure under optimal control takes the second place and is more drastic than that of open-loop system. In summary, the variation range of mass flow rate and operating pressure under constant temperature control, the variation range of temperature under constant pressure control are large. The range of temperature, mass flow rate and operating pressure is eclectic under optimal control. All these factors will influence the

same time [14]. Generally speaking, the net power output decreases with the reduction of engine working conditions. 5.4. Dynamic simulation under slow step change conditions In this part, four kinds of simulation results including open loop, constant temperature control, constant pressure control, and optimal control are compared. In order to evidently observe the performance difference of different control systems, the step change of working condition is slow in this part, which varies every 500 s. Fig. 15(a) presents the input disturbance changing with the engine working condition. Fig. 15(b) presents the optimal pump rotation speed, and variation of the control variables under the action of PID controller. The pump controller acts to maintain the turbine inlet temperature at 473.15 K while the expander valve controller is regulated to keep the operating pressure at around 10 MPa. The pump rotation speed follows the optimal point under optimal control, while it keeps constant under open loop simulation. Results of the dynamic simulation are shown in Figs. 16–18. As illustrated in Fig. 16(a), the turbine inlet temperature is kept constant under pump controller while it varies in different magnitude in other three cases. The amplitude of temperature change is small under the optimal control strategy, because the pump speed changes according to the optimum value, which leads to the change of heat absorption with time. The amplitude changes of turbine inlet temperature under constant pressure control is even severer than open loop simulation. Although the turbine inlet temperature under pump controller is almost constant, there are overshoot or undershoot near the point of Mass flow rate of jacket water

3.77

79.2

3.19

75.9

361.1

Temperature of jacket water

358.8 356.5 354.2

Mass flow rate of exhaust

0.374

72.6

Control variables

2.90

Input disturbance

Optimal pump speed

82.5

3.48

Pump rotation speed(rpm)

87.0 78.3 69.6

0.340

60.9 19

0.306 0.272

Temperature of exhaust

-19

646

-38

629 0

500

1000

1500

2000

Valve opening degree(°)

0

663

612 2500

0

500

Time (s)

1000

1500

Time (s)

Fig. 15. The input disturbance (a) and control variables (b). 11

2000

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0.80 0.648

0.75

0.646

480

0.644

Mass flow rate (kg/s)

Working fluid outlet temperature (K)

500

460

440

Open loop Comstant pressure Constant temperature Optimal control

420

400

0

500

1000

0.70 0.642 1450

1500

1550

1600

0.65 0.60 0.55

open loop Comstant pressure Constant temperature Optimal control

0.50

1500

2000

0.45

2500

Time (s)

0

500

1000

1500

2000

2500

Time (s)

Fig. 16. Turbine inlet temperature (a) and mass flow rate (b) of working fluid.

maximum under the optimal control system because of the compromise between pressure and temperature. Sometimes it is not obvious because of our simplification of optimal control strategy. On the other hand, the calculation results show that the optimal control and constant temperature are particularly prominent when the engine operating conditions are lower than design condition; when the engine operating conditions are higher, the advantage is not obvious. On the whole, high turbine inlet temperature is more advantageous to obtain larger net power output than high operating pressure. As presented in Fig. 18, the dynamic variation of exhaust and jacket water outlet temperature reveals that the system can avoid acid dew point only under the constant temperature control and optimal control strategy in all engine work conditions. Under constant temperature and optimal control strategies, the amplitude change of exhaust outlet temperature is small after stabilization. That is caused by the slight change of energy absorbed by the gas heater. The trend of exhaust temperature at the outlet of gas heater is consistent with the turbine inlet temperature of working fluid. The high turbine inlet temperature of working fluid means small heat transfer temperature difference. Thus, the total heat transfer rate is small, leading to the high exhaust outlet temperature. For the same reason, the large total heat transfer rate leads to the low exhaust outlet temperature. The heat transfer temperature under constant pressure control system and open loop system is larger, so the exhaust temperature is lower. The trends of jacket water outlet temperature have remained largely the same and consistent with Tjout as mentioned above, and the difference of different control strategies is less than 1 K under all working conditions. That’s because the specific heat capacity of water is large, although the energy

system net power output to a certain extent. Fig. 17(a) presents the system net power output under different control strategies. The neglectable difference in working fluid mass flow, operating pressure and turbine inlet temperature under condition (1) result in smaller difference of net power output. The mass flow rate under constant pressure control system and open loop system are almost the same, lower turbine inlet temperature resulting in the less energy converted into useful work. Although the high pressure is conductive to obtain greater net power output, the effect of temperature is greater than that of pressure. Thus, the net power output under constant pressure control is less than open-loop system in condition (2) and (3). For the same reason, high turbine inlet temperature of working fluid under constant temperature control and optimal control system makes the larger net power output compare with constant pressure control and open-loop system, even though the working fluid mass flow rate is less. Under condition (4), no obvious increasement in mass flow rate and lower turbine inlet temperature under control systems lead to no significant improvement in net power output compared with openloop system. On the whole simulation, the enhancement of net power output under optimal control strategy and constant temperature control system is almost the same and better than constant pressure control system. However, the stability of optimal system is better than that of constant temperature control system which shows that there is no overshoot phenomenon. High temperature is beneficial to net power output, but at the same time it will reduce pressure, thereby reduce net power output. High pressure is beneficial to net power output, but lowers the temperature, which is not conducive. The net power output keeps the basic

Fig. 17. Net power output (a) and operating pressure (b) of the system. 12

Energy Conversion and Management 205 (2020) 112389

Jcaket water outlet temperature (K)

R. Wang, et al.

Exhaust outlet temperature (K)

420

410

400

390

open loop constant pressure constant temperature Optimal control

380

370

0

500

open loop constant pressure constant temperature Optimal control

353

352

351

350

349

348

1000

1500

2000

2500

0

500

Time (s)

1000

1500

2000

2500

Time (s)

Fig. 18. Exhaust outlet temperature (a) and jacket water outlet temperature (b).

with the open loop simulation. Because the inertia of the system hinders its timely response, the controller cannot control the system to the steady state in time, and the system basically in an unsteady state. Thus, the control effect under transient conditions is not as obvious as slow step change conditions. The exhaust and jacket water outlet temperature dynamic variation are presented in Fig. 22. Exhaust responds faster than jacket water because it has less viscous resistance. The exhaust temperature is higher than acid dew temperature only under the optimal control strategy. Moreover, the nearly uniform response of jacket water outlet temperature once again indicates that the influence of control strategy on it is little. The average improvement of net power output by different control strategies compared with open-loop simulation under slow step change and transient change conditions are shown in Fig. 23. It can be found that under slow step change conditions, the system with constant pressure control strategy has negative power improvement of −0.912% compared with open loop condition. That’s because the expander inlet temperature which are conducive to net power output is especially low compared with open loop situation. The system net power output under the constant temperature control and optimal control strategy is increased by 2.39% and 2.31%, respectively. The large fluctuation around the step point makes the power improvement by the constant temperature control slightly higher than the optimal control as can be seen in Fig. 17. Under transient change conditions, the power improvement of the system with constant temperature control is −1.82% which exhibits poor performance compared with under sloop step change conditions. That is caused by the sharp fluctuations in temperature, pressure and mass flow. Under the constant pressure control, owing to the satisfactory control effect of operating pressure and relatively small fluctuations of expander inlet temperature compared with open-loop,

absorbed from jacket water under different control systems is different, the jacket water outlet temperature difference is very small. This means both PID controllers and optimal control strategy have little influence on the jacket water temperature. 5.5. System performance under transient conditions The previous part compares the performance of the different control strategy under slow step change conditions. However, the step change of engine is always transient and changeable in real-operating conditions. In this part, under transient operating conditions, the dynamic responses of constant control strategy and optimal control strategy are analyzed and compared with the open loop simulation. The transient temperature and mass flow rate signals of the heat sources are illustrated in Fig. 19. The dynamic response characteristic of the system with the transient heat source is shown in Figs. 20–22. As shown in Fig. 20(a), the working fluid temperature cannot be well maintained constant or tracked optimal value under constant temperature control and optimal control strategy respectively because of the violent change of heat source. Fig. 20(b) demonstrates the dynamic response of working fluid mass flow rate. The working fluid mass flow rate fluctuates over a small range under constant pressure control and open loop simulation due to the constant of pump speed, while it changes violently in another two systems and the amplitude at constant temperature changes more dramatically, which is not conducive to the stability of the system. Fig. 21(b) illustrates that the operating pressure can be kept constant under the action of expander valve controller, while it fluctuates violently under pump controller. As for the net power output, one can see in Fig. 21(a), the advantage under constant temperature control and optimal control strategy is not obvious compared

4.2

Exhaust Jacket water

760

3.6

680

Mass flow rate (kg/s)

Temperature (K)

720

640 600 360

3.3 3.0 2.7 0.4

355

0.3

350

0.2

345

Exhaust Jacket water

3.9

0

200

400

600

800

0.1

1000

Time (s)

0

200

400

600

Time (s)

Fig. 19. Transient temperature and mass flow rate signals of heat sources. 13

800

1000

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Open loop Optimal control Constant pressure Constant temperature

0.80 500

Mass flow rate (kg/s)

Expander inlet temperature (K)

520

480

460

440

Open loop Optimal control Constant pressure Constant temperature

420 0

200

0.75 0.70 0.65 0.60 0.55 0.50

400

600

800

1000

0

200

400

Time (s)

600

800

1000

Time (s)

Fig. 20. Expander inlet temperature (a) and mass flow rate (b) of working fluid.

control strategy. (2) The exhaust energy is positively correlated with engine operating conditions, while the jacket water is not. That’s means the exhaust temperature at the outlet of gas heater can be directly adjusted according to the engine operating conditions, while the jacket water temperature at the outlet of preheater needs to be adjusted according to the actual engine water outlet temperature. Moreover, the absorbed jacket water energy occupies a large proportion compared with the exhaust energy. Therefore, the medium and low temperature heat sources should not be neglected. (3) Under slow step change, when the engine operating conditions are lower than design condition, the net power output keeps maximum with the optimal control strategy because of the compromise between pressure and temperature. The net power output under the optimal control and constant temperature control strategy is increased by 2.31% and 2.39%, while the increasement is −0.91% under constant pressure control. That means high turbine inlet temperature is more advantageous to obtain large net power output than high operating pressure. Moreover, the exhaust temperature is higher than acid dew point under constant temperature and optimal control strategy. (4) The control effect under transient conditions is different from under slow step change conditions. The improvement of system power with the optimal control and constant temperature control is 0.07% and −1.81% respectively under transient conditions, which is less than those under the slow step conditions. That’s because the inertia of the system prevents timely response. The slow response results the system basically works in unsteady state, so the controller cannot make the system track the optimal steady state at any time. By contrast, the constant pressure control achieves the best

the system net power output is increased by 0.58%, which is contrary to the trend under slow step change condition. The improvement of system power by optimal control is only 0.07% as shown in Fig. 23, the effect is not as obvious as that under slow step condition. Therefore, the effectiveness of different control strategies under different step change conditions has something difference. The effect of optimal control and constant temperature control under transient conditions is not as obvious as that under slow step change condition, while the constant pressure control achieves the best performance under transient conditions. 6. Conclusion In current work, the dynamic model of CO2 mixture transcritical power cycle with preheater and regenerator for heavy duty diesel engine waste heat recovery is established by Simulink and carefully validated against experimental data. The design parameters at steadystate are optimized to get better system performance. The optimal mass flow of the working fluid which can produce the most power under offdesign condition is searched to prepare for the optimal control. Under the condition of slow step change and transient change, the system dynamic characteristics with constant and optimal control strategies are compared with open-loop simulation. The results indicate that: (1) The effect of pump rotation speed on net power output is smaller under high torque conditions than that under lower conditions, so the net power output deteriorates quite obviously when the speed deviates from optimum value under low engine torque conditions. The optimal pump speed of the four regions divided in this work is close to each other, which can be used to simplify the optimal

Operating pressure (MPa)

Net power output (kW)

13

Open loop Optimal control Constant pressure Constant temperature

25

20

15

10

Open loop Optimal control Constant pressure Constant temperature

12

11

10

9

8

5 0

200

400

600

800

7

1000

Time (s)

200

400

600

Time (s)

Fig. 21. Net power output (a) and operating pressure (b) of the system. 14

800

1000

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Jacket water outlet temperature (K)

Exhaust outlet temperature (K)

430

420

410

400

390

Open loop Optimal control Constant pressure Constant temperature

380

370

0

200

400

600

800

1000

352 350 348 346 344

Open loop Optimal control Constant pressure Constant temperature

342 340

0

200

Time (s)

400

600

800

1000

Time (s)

Fig. 22. Exhaust outlet temperature (a) and jacket water outlet temperature (b).

Improvement of net power output (%)

3

Slow step Transient

2

2.39102

performance under various conditions. Present work indicates that simple control strategies are not effective enough to cope with the transient performance of engine heat sources. The traditional optimal control cannot give full play to its advantages when the heat source is transient, even worse than constant pressure control. Therefore, there is an urgent need to develop a controller suitable for transient conditions which present the direction of future research. Another option is to speed up the dynamic response of system components such as heat exchanger, this can be achieved by reducing the components volume and strengthening the heat transfer performance, while keeping the system performance and costs. This requires a comprehensive multiobjective optimization for system design which is another interesting subject of further research.

2.30603

1 0.57969 0.07229

0

-1

-0.91158

-1.81274

-2 Constant pressure

Constant temperature

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Optimal control

Fig. 23. The improvement of net power output by control strategies.

performance of 0.58% improvement under transient conditions because of the satisfactory control effect on operating pressure and relatively small fluctuations of expander inlet temperature.

Acknowledgement This work was supported by National Natural Science Foundation of China (51906173).

In a word, different control strategies behave obviously different

the

Appendix Engine speed r/min

Torque N·m

Power kW

Fuel consumption g/kWh

Tg °C

mg kg/h

1800 2000 1900 1800 1700 2200 1600 2200 2000 2100 1500 1600 1700 1500 1900 2000 1600 2100 1600 1900

80% 90% 80% 60% 70% 80% 60% 90% 80% 70% 90% 90% 90% 70% 70% 60% 100% 100% 80% 100%

192.96 218 194.8 144.5 144.5 193.38 128.66 217.8 194.42 169.4 180.76 192.52 205.2 140.66 170.4 145.5 213.83 241.6 171.42 243.2

197.2336 206.1835 199.4951 202.6167 207.2688 216.06 198.3621 213.9059 204.527 212.1085 192.8292 195.1208 197.7245 194.8213 200.8019 209.9094 196.3174 211.3994 194.4901 206.3905

389.7 426.06 381.7 339.4 367.32 383.04 358.46 415.94 386.1 341.62 422.32 418.52 431.24 384.18 349.6 316 456.55 464.62 390.8 486.24

1152.584 1249.52 1219.7 1021.69 1009 1386.668 821.26 1368.7 1233.04 1266.5 921.7 1010.84 1084 799.64 1131.96 1144.34 1044.14 1334.52 954.3 1227.62

15

Tj °C 85.2 74 87 86 84.4 81 87 72.4 76 81.6 87 87.6 84 85 82.6 85.8 84.5 75.8 85.6 74

mj m3/h 11.62 12.76297 12.11 11.56 10.96435 13.88618 10.36898 14.06129 12.75297 13.42089 9.95122 10.38899 10.95935 9.906191 12.12258 12.7054 10.41484 13.35085 10.4015 12.12758

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