Experimental study of operating load variation for organic Rankine cycle system based on radial inflow turbine

Journal Pre-proofs Experimental study of operating load variation for organic Rankine cycle system based on radial inflow turbine Tan Wu, Xinli Wei, Xiangrui Meng, Xinling Ma, Jiangtao Han PII: DOI: Reference:

S1359-4311(18)38006-2 https://doi.org/10.1016/j.applthermaleng.2019.114641 ATE 114641

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

29 December 2018 31 October 2019 3 November 2019

Please cite this article as: T. Wu, X. Wei, X. Meng, X. Ma, J. Han, Experimental study of operating load variation for organic Rankine cycle system based on radial inflow turbine, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114641

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Experimental study of operating load variation for organic Rankine cycle system based on radial inflow turbine Tan Wua,b, Xinli Weia,b, Xiangrui Meng a,b, Xinling Ma a,b,*, Jiangtao Hana,b a

School of chemical engineering and energy, Zhengzhou University, Zhengzhou, 450001, China

b

Engineering Research Center of Energy Saving Technologies and Equipments on Thermal System, Ministry of

Education (MOE), Zhengzhou 450001, China Corresponding author: E-mail address: [email protected] (Xinling Ma).

Abstract ： Based on the self-developed high-speed radial inflow turbine and R245fa as the working fluid, organic Rankine cycle (ORC) testing rig of low-temperature waste heat power generation was built. The effects of different operating load power on the ORC system performance were studied through the experiment. The results show that the isentropic efficiency of the turbine, output power, electric power, thermal efficiency, and exergy efficiency of system, all reach the maximum values at the optimal load power of 1.7 kW, and at this condition, electric power, thermal efficiency and exergy efficiency of system are 1.424 kW, 2.52% and 8.09%, respectively. Therefore, when the ORC system is designed, the turbine, generator and load power should be matched to the optimal performance of the system. By grey relational analysis (GRA), it is concluded that electric power has the closest correlation with load power, with its grey relational grade being 0.632. Compared with the exergy efficiency, the thermal efficiency maintains a higher relational grade. In addition, according to exergy analysis, the evaporator is the component with the highest exergy loss, followed by the condenser. Keywords：waste heat recovery, organic Rankine cycle, radial inflow turbine, load power, electric power output, energy and exergy analysis, grey relational analysis 1. Introduction A large amount of low-grade energy can be obtained from industrial waste heat [1], geothermal energy [2], solar thermal energy [3], biomass energy [4], ocean thermal energy [5], engine exhaust [6] and so on. In the industrial processes, fossil fuels, such as coal, oil and natural gas, are not fully utilized [7]. More than 50% of the energy used in the world is wasted in the form of thermal energy [8]. At present, the organic Rankine cycle (ORC) system is one of the most effective ways to recover low-temperature waste heat [9]. The advantages of ORC lie in high efficiency, environmental friendliness, simple structure and high reliability [10]. The main components of an ORC system are the evaporator, expander, generator, condenser, working fluid pump [11]. The expander, the core equipment of the ORC system, converts thermal energy into mechanical energy. The ORC system performance is mainly determined by the expander performance. In general, expanders can be categorized into two types: one is the velocity expander, such as radial inflow turbine [12] and axial turbine [13]; the other is the volume expander, such as screw expander [14], scroll expander [15], rotary vane expander [16] and piston expander [17]. Pethurajan et al. [18] found that the most widely-used expanders are radial turbines, screw and scroll expanders. Compared with the volume expander, the velocity expander is featured with many advantages, including better performance, greater compactness and less leakage. The application of turbines has been identified as a promising way of improving thermal efficiency because except for bearings, no sliding parts involve with each other in operation process. Pantano et al. [19] highlighted that no volume expander could outweigh

velocity expander in terms of turbine efficiency, compactness and power-to-weight ratio. In particular, compared with the axial turbine, radial inflow turbine maintains better performance and is suitable for low-powerful units, so it is widely applied to various devices, such as microcombustion engines, turbochargers, refrigeration units and ORC system, etc. The studies on ORC remain the research stage so far for the limitations of laboratory conditions. Therefore, the size of the turbine can only be a kW class or even lower. The efficiency of radial inflow turbine could reach 85%, which is the highest in the ORC system [17]. Park et al. [20] concluded that turbomachines could be operated in a wide range power from just under a kW class with the maximum reaching 250 kW. As for designing the small-scale radial inflow turbine, on the basis of experimentally validated 1D models, Mounier et al. [21] updated the non-dimensional maps for the turbine, and in the design, the downscaling effects were taken into account. Fiaschi et al. [22] introduced a design procedure for small scale radial turbines for ORC system, adopting a 0D tool for the basic size and using a 3D approach to refine the design, which identified the dependability of the 0D design. Costall et al. [23] designed three different scale turbines with maximum isentropic efficiency being 56.1%, and the results showed that isentropic efficiency decreases with the decrease of the power level. Kang [24] constructed an ORC system with a radial turbine and R245fa as working fluid, and then conducted the test. The maximum average cycle efficiency, turbine efficiency, and electric power were found to be 5.22%, 78.7% and 32.7 kW, respectively. Li et al. [25] studied the turboexpander performance of a small-scale ORC system under different operating conditions, and drew a conclusion that the turboexpander was considered appropriate for a small-scale ORC system application. Pei et al. [26] set up a kW class ORC system with a radial inflow turbine, and the experimental results showed the turbine isentropic efficiency and ORC system efficiency were 65%, 6.8%, respectively. Liu et al. [27] presented the off-design performance analysis of ORC system for the internal combustion engine under various engine loads. The results showed the exhaust utilization rate ascended from 89.4% to 99.5%, and the engine load dropped from 100% to 40%. The current studies for the ORC system mainly focus on the expander selection, parameter optimization and operational condition analysis [28]. However, only a few researches were carried out about performance analysis of ORC system with radial inflow turbine under various load power conditions [29]. Rahbar et al. [30] proposed an unprecedented approach for the optimization of ORC with radial inflow turbine, and it was found that the overall size of turbine and the electric power output were closely related to the variation of load. Zhu et al.[31] discovered that the resistive load which was coupled to the scroll expander-generator unit affected the expander performance and power output characteristics, and concluded that an optimal pressure ratio was obtained with the maximum power output. Tang et al. [32] investigated the small ORC system performance under different heat resource temperature and different load resistance, and found there was an optimum load resistance value which made output power, and power generation efficiency maximum. In practical application, the electrical energy generated by small ORC system usually cannot be transmitted to the grid system, and it can only be directly utilized by users. Therefore, the load will have a great impact on ORC system. A 3 kW ORC system with self-developed high-speed radial inflow turbine, R245fa as working fluid and resistance as load was designed and built. The effects of ten different load power on the performance of ORC system and radial inflow turbine were carried out experimentally under the same inlet condition in this paper. It investigated the best matching relation among radial inflow turbine, generator and load. In addition, grey relational analysis (GRA)

was used to calculate the grey relational grade between parameters and load power, and hereby the level of correlation was clarified. It will provide some reference for the selection of the main components, the design of radial inflow turbine and performance optimization of ORC system. 2. Mathematical model 2.1 Thermodynamic analysis The thermodynamic model of the system assumes the following: (1) steady state conditions, (2) no pressure drop in the evaporator, condenser, and pipes, (3) isentropic efficiencies for the turbine and pump. The dry fluid has a positive slope, and T-s diagram of ORC system is shown in Fig.1. The ORC cycle consists of four different processes: adiabatic expansion process (1-2), isobaric heat rejection process (2-5), adiabatic compression process (5-6), isobaric heat addition process (6-8) [33].

Fig. 1. Temperature-entropy diagram of the ORC system Process 1 - 2: Organic vapor from the evaporator at Point 1, expands through the turbine to produce mechanical work and then passes to the condenser at Point 2. Under ideal condition, the organic working fluid in the turbine is an isentropic expansion process 1 to 2s. However, the energy conversion efficiency in the turbine cannot reach 100%, and the state point of the working fluid at the turbine outlet is point 2. The turbine output power Wt is calculated by, Wt = qm(h1 - h2) = Wt,sηt,s = qm(h1 - h2s)ηt,s (1) Where Wt,s is the ideal power of the turbine, t,s is the turbine isentropic efficiency, qm is the mass flow rate of the working fluid, h1 is the enthalpy of the working fluid at the turbine inlet, h2 is the enthalpy of the working fluid at the outlet of the turbine for the actual case, and h2s is the enthalpy for the ideal case. The exergy loss of the expander It can be determined as, It = (E1 - E2) - Wt = T0qm(s2 - s1) (2) Where E1 is the exergy of the working fluid at the turbine inlet, E2 is the exergy of the working fluid at the turbine outlet, s1 is the entropy of the working fluid at the turbine inlet, s2 is the entropy

of the working fluid at the turbine outlet, and T0 is the environment temperature. The pressure ratio R and the isentropic efficiency t,s of the radial inflow turbine are highly significant indexes for evaluating the turbine performance. The pressure ratio R is expressed as, pt,1

(3)

R = pt,2

Where pt,1 is the total pressure at the turbine inlet, and pt,2 is the total pressure at the turbine outlet. The isentropic efficiency of the turbine t,s is defined as the ratio between the actual enthalpy drop and the isentropic enthalpy drop in the expansion process, calculated by, Wt

h1 - h2

(4)

ηt,s = Wt,s = h1 - h2s Electric power generated by the generator Wg is calculated by, Wg =

∑3 UiAi i=1

(5)

3

Ui refers to the phase voltage of the generator in the actual measurement, and Ai is its corresponding phase current. Generator speed ng is calculated by, 60f

(6)

ng = npg

Where f is generator frequency, and npg is generator pole number. Process 2 - 3 - 4 - 5: Exhausted vapor from the turbine at point 2, is cooled down from superheated vapor into saturated vapor, then continuously cooled down into saturated liquid, finally into subcooled liquid with a certain subcooling by cooling water in the condenser. The heat rejection Qc can be expressed as, (7) Qc = qm(h2 - h5) Where h2 is the enthalpy of the working fluid at the condenser inlet, and h5 is the enthalpy of the working fluid at the condenser outlet. The exergy loss of the condenser Ic is calculated by,

[

Ic = T0qm (s5 - s2) -

]

h5 - h2 TL

(8)

Where s2 is the entropy of the working fluid at the condenser inlet, s5 is the entropy of the working fluid at the condenser outlet, and TL is the cold source temperature. Process 5 - 6: The liquid leaving the condenser at Point 5 is pumped into the evaporator. Under ideal conditions, isentropic compression process of the fluid is expressed as process 5 - 6s. The pump power is calculated by, Wp = qm(h6 - h5) =

Wp,s ηp,s

=

qm(h6s - h5) ηp,s

(9) Where Wp,s is the ideal power of the pump, p,s is the pump isentropic efficiency, h5 is the enthalpy of working fluid at the pump inlet, h6 is the enthalpy of working fluid at the pump outlet for the actual case, and h6s is the enthalpy for the ideal case. The exergy loss of the working fluid pump Ip is given by, Ip = Wp - (E6 - E5) = T0qm(s6 - s5) (10)

Where E5 is the exergy of the working fluid at the pump inlet, E6 is the exergy of the working fluid at the pump outlet, s5 is the entropy of the working fluid at the pump inlet, and s6 is the entropy of the working fluid at the pump outlet. The isentropic efficiency of the working fluid pump ηp,s can be obtained by, ηp,s =

Wp,s Wp

=

h6s - h5

(11)

h6 - h5

Process 6 - 7 - 8 - 1: The evaporator heats the working fluid from the pump outlet to the turbine inlet condition. The process includes three phases, namely preheating, evaporation and superheating. The total amount of heat addition of the working fluid Qe is given by, Qe = qm(h1 - h6) The exergy loss of the evaporator Ie is given by,

[

Ie = T0qm (s1 - s6) -

]

h1 - h6 TH

(12)

(13)

Where TH is the heat source temperature. Cycle efficiency: The thermal efficiency of the system ηth is defined as the ratio between the net power of the cycle to the evaporator heat rate, and it can be given by, ηth =

Wt - Wp Qe

Wt - Wp

= qm(h1 - h6) =

(h1 - h2) - (h6 - h5) h1 - h6

(14) The exergy loss of ORC system Isys is written as [34],

(

Isys = It + Ic + Ip + Ie = T0qm -

h1 - h6 TH

-

)

h5 - h2 TL

(15) The exergy efficiency of ORC system ηex is calculated as follows, ηex =

Wt - Wp

(

TL

Qe 1 - T

H

)

=

(h1 - h2) - (h6 - h5)

(

TL

(h1 - h6) 1 - T

H

)

(16) 2.2 Grey relational analysis (GRA) As a well-known and highly reliable decision-making method, GRA is a widely-used technique in the grey system [35]. It is also an analytical method to study relations between different parameters. In GRA, each response determined from the experiment is normalized at the range of 0-1. In general, there are three types of equations used for normalization procedure; namely, the lower is the better, the higher is the better, and nominal is the best [36]. In this study, the second equation [37] is used, as described in Eq. (17). yi(k) =

x0i(k) - min x0i(k) max x0i(k) - min x0i(k)

(17)

Where yi(k) stands for the normalization value of grey relational generation, max x0i(k) and min x0i(k) represent the maximum and minimum value of x0i(k), respectively. x0 is the optimum value. After the normalization process, the grey relational coefficient ξi(k) needs to be calculated based on the following Eqs. (18)-(21). Δmin + φΔmax

ξi(k) = Δ0i(k) + φΔmax

(18)

Δ0i(k) = ||y0(k) - yi(k)||

(19)

(20) Δmax = max∀j ∈ imax∀k||y0(k) - yi(k)|| (21) Δmin = min∀j ∈ imin∀k||y0(k) - yi(k)|| Where φ expresses the distinguishing coefficient which is limited in the range 0< φ <1. In GRA, selecting any distinguishing coefficient value between 0 and 1 does not change the order of importance of the parameters. Generally, φ = 0.5 is used [38]. Δ0i is the deviation value between y0(k) and yi(k). y0(k) is the referential sequence and yi(k) is the comparative sequence. Δmax and Δmin are the maximum and the minimum values of the Δ0i, respectively. The overall grey relational grade (γi) is calculated using Eq. (22). 1

n γi = n∑k = 1ξi(k)

(22)

Where n is the number of process responses. A strong correlation between y0(k) and yi(k) is marked by a high grey relational generation grade. If two compared series have the same values, grey relational grade is found to be 1. γi is used to determine the proximity of the compared series value to the reference series value. 3. Experimental system 3.1 Design of radial inflow turbine According to the research background, the heat source temperature is 120 °C, cold source temperature is 20 °C, and the working fluid is R245fa. The thermodynamic calculation [39] of the turbine was obtained based on the laboratory conditions, as follows in Table 1. Table 1 Main design parameters of radial inflow turbine. Parameters

Unit

Values

Inlet pressure Inlet temperature Outlet pressure Expansion ratio Inlet diameter of impeller Rotational speed Mass flow rate Diameter ratio of impeller Outlet external diameter of impeller Outlet internal diameter of impeller Mechanical efficiency Power Width of axial direction Shaft diameter Number of rotor blades Number of nozzle vanes

MPa ℃ MPa — mm rpm kg/s — mm mm — kW mm mm — —

0.635 72 0.166 3.825 50 58500 0.155 0.55 34 19 0.682 2.607 15 10 12 17

A radial inflow turbine consists of a volute, a nozzle, an impeller and a diffuser. The main role of a volute is to evenly distribute flow to the nozzle inlet, and it has an axisymmetric structure. Therefore, the volute is a spiral tube whose section evenly decreases along the flow direction. The cross section of the volute flow passage is a circle. The designed volute is shown in Fig. 2 (a). The role of the nozzle is to convert heat into kinetic energy, and to obtain the flow rate and flow direction required for the rotor inlet. A nozzle is composed of a set number of blades with the same shape,

which are equally spaced on a ring. In this radial inflow turbine, TC-4P blade profile [40] by Moscow Institute of Dynamics is adopted, as shown in Fig. 2 (b). The organic vapor continues doing work by expansion in the impeller, and converts the kinetic energy into mechanical energy for transmission to the generator. The impeller is also a certain set of blades with the same shape, which are uniformly distributed on a disk. According to the principle of one-dimensional flow, based on the reverse design, isosceles trapezoidal design method is proposed to get 3D meridional flow channel of the impeller. The blade shape of the impeller adopts non-developable parabolic surface profile. The developed impeller is shown in Fig. 2 (c). Fig. 2 (d) is the photograph of developed radial inflow turbine.

(a) Volute

(b) Nozzle

(c) Impeller (d) Radial inflow turbine Fig. 2. Photograph of the radial inflow turbine 3.2 Experimental facility of ORC system The schematic diagram of ORC test rig is as shown in Fig. 3. It is mainly composed of heat source cycle, working fluid cycle and cooling water cycle. The heat transfer oil, heated by an electric heater, finishes the heat transfer process with the working fluid in the evaporator, and then returns to the oil tank. The working fluid R245fa is heated into superheated vapor in the evaporator, then enters into the turbine to expand and produce mechanical work. The exhaust vapor from the turbine is condensed in the condenser, then enters the working fluid pump in which the fluid is pressurized, and then it returns to the evaporator. The cooling water, used as the cold source, is stored in the water storage tank and pumped into the condenser through the water pump. The testing rig is presented in Fig. 4.

Fig. 3. Schematic diagram of ORC system

Fig. 4. The testing rig based on the radial inflow turbine The evaporator transfers the thermal energy of the waste heat source to the organic working fluid and heats the liquid organic working fluid into a saturated gas or a slightly superheated gas. The condenser transfers the heat of the completed organic working fluid from the turbine to the cooling water. The process condenses the superheated organic vapor into a saturated liquid or a slightly subcooled liquid. In this platform, plate heat exchangers produced by SWEP (a company which professionally produces heat exchangers in Sweden) are used as the evaporator and condenser. The volume of the organic working fluid channel in the evaporator is 2.13×10-3 m3 and the corresponding value of the condenser is 3.25×10-3 m3, as is shown in Fig. 5 (a). The experimental system adopts the GC-DRY-60 electric heating and heat transfer oil furnace produced by Yancheng Gongchuang Electric Heating Equipment Co., Ltd. An electric heater, a transfer oil tank, an oil temperature control system, a hot oil pump, a liquid level meter and other auxiliary fittings are included in the

facility, as is shown in Fig. 5 (b). Its maximum heating power is 60kW, and the actual required heating can be adjusted by the temperature control system. The canned motor pump connects the pump and the motor. The rotor of the motor and the impeller of the pump are fixed on the same shaft, and the rotor is separated from the stator by a shielding sleeve. There is no dynamic seal on the structure, and only a static seal is provided at the outer casing of the pump. Thus, it is completely leak-free with stable operation, low noise and needless of lubricating oil. The system uses the CAM2/2 canned motor pump produced by Haimetike, as is shown in Fig. 5 (c), with its flow rate being 0.5+1 m3/h, head being 25.5 m, motor power being 3.0 kW, speed being 2690 r/min. The generator, the main facility for the electrical output of the ORC system, is a three-phase AC permanent magnet synchronous generator at high speed (with rated power being 5 kW, rated speed being 12000 rpm). When operated under rated conditions, the generator is with efficiency about 90%, and the output voltage is proportional to the speed. The specially-developed reducer is used to adapt to the turbine and the generator. It adopts a first-class gear transmission with a transmission ratio of 5.304 and external dimensions of 200 mm × 131 mm × 220 mm. The reducer is connected to the turbine through a coupling. Experimental equipment consisting of a turbine, a reducer and a generator is shown in Fig. 5 (d). The radial turbine used in the experiment is shown in Fig. 5 (e). The load is used to consume the electrical energy from the generator. In this experiment, powers of the resistance wires which are used as the load can be adjustable, as is shown in Fig. 5 (f).

(a) Evaporator and condenser

(c) Pump

(b) Electric heating furnace

(d) Turbine with reducer and generator

1 (e) Radial inflow turbine (f) Loads Fig. 5. Major equipment and apparatus of the ORC system. In the data acquisition systems, following facilities are included, such as a Coriolis mass flow meter, an intelligent liquid turbine flow meter, an elliptical gear flow meter, a temperature sensor, a pressure sensor, an Agilent data acquisition instrument, an electrical parameter meter, and a computer. The Coriolis mass flow meter is installed at the outlet of the pump to measure the mass flow rate of the liquid R245fa. The elliptical flow meter is installed in the heat source cycle to measure the volume flow of the heat transfer oil. An intelligent liquid turbine flow meter is installed in the condensing cycle to measure the flow of cooling water. A temperature sensor and a pressure sensor are separately installed at the inlet and outlet of the main equipment. The Agilent data acquisition device mainly keeps track on the temperature, pressure and working fluid flow in the thermal system. The electric parameter measuring instrument with a 10-second interrecord gap mainly records the frequency, the output voltage, the current and electric power of the generator. The recorded data are summarized on the computer by software to check the performances of the generator. According to the temperature and pressure collected by the computer, the parameters including enthalpy and entropy of the R245fa are obtained through the REFPROP 9.0 issued by NIST. The main experimental testing instruments are listed in Table 2. Table 2 Names and models of testing instrument Measuring object

Instrument

Type

Range

Accuracy

Temperature

Thermal resistance

WZP Pt100

-200~500 ℃

±(0.15+ 0.002t) ℃

Pressure

Diffused silicon pressure transmitter

HX-L61

0~1.6 MPa -100~400 kPa

±0.2%

34970A

——

Data collection

Working fluid flow

Agilent data collector Coriolis flow meter Intelligent liquid turbine flow meter Oval gear flow meter

RHM04 RHE 14 YKLWGY25 YK-LC20

0～24 kg/min

±0.1%

0~10 m3/h

±0.5%

0.4~4 m3/h

±0.5%

Manufacturer

Henan Huixiang Automation System Co., Ltd. United States Agilent Germany RHEONIK Dalian Youke Instrument and Meter Development Center

Rotating speed

Laser tachometer

Electric frequency Current Voltage Electric power Working condition

DT-2857

Electric parameter measuring instrument

8903D

Glass

HMI1TT

2.5~99999 rpm

±0.05%

45~1000 Hz

±1.5Hz

0.1~60 A 5~500 V

±1% ±1%

0.5W~30 kW

±1%

——

——

Guangzhou Lantai Instrument Co., Ltd.

Qingdao Qingzhi Instrument Co., Ltd.

United States EMERSON

In the experimental measurement process, there are measurement errors owing to uncertainty of the measuring instrument, limitations of the experimental conditions and influence of various factors. The accuracy of the sensors used in the experiment is listed in the test equipment table. According to the error synthesis method, there is 1.5% uncertainty of calculating the enthalpy of the available organic working fluid. The calculated parameter uncertainty µw is given by, ∂w

N μw = ∑i = 1(∂xi)2V2xi

(23)

Vxi is the measurement uncertainty of each direct measurement xi, which is synthesized by using the respective Class A and Class B uncertainty components. 4. Experimental results and discussion To investigate the effect of the load power on the performance of each equipment and ORC system, the following operating conditions were used. If other parameters remain unchanged, the load powers of the generator connection in each phase were respectively set as 0.9 kW, 1.1 kW, 1.3 kW, 1.5 kW, 1.7 kW, 1.9 kW, 2.1 kW, 2.3 kW, 2.5 kW, 2.7 kW, when the ambient temperature was set as 21 ℃, the heat transfer oil flow rate was 5.45 m3/h, the pressure was 0.3 MPa, the cooling water flow rate was 4.969 m3/h, and the pressure was 0.19 MPa. Under such conditions, the following factors are analyzed, including the performance of evaporator, condenser, working fluid pump, turbine, thermal efficiency, exergy efficiency and electric power. 4.1 Effects of load power on the performance of the radial inflow turbine The temperature drop and the enthalpy drop of working fluid in the turbine both are related to load power, and the variation is given in Fig. 6. The temperature drop and the enthalpy drop of radial inflow turbine decrease with the increase of load power. When load power exceeds 1.7 kW, the temperature and enthalpy drop for the turbine significantly reduced, as a result of the decline of the turbine speed. When load power is 1.7 kW, the turbine temperature drop is 15.0 °C and the enthalpy drop is 13.9 kJ/kg.

16

16 Temperature drop

Temperature drop(°C)

15 14

14 13 13 12 12

11 0.5

Enthalpy drop(kJ/kg)

Enthalpy drop

15

11

0.9

1.3

1.7

2.1

2.5

10 2.9

Load Power(kW)

Fig. 6. Variation of temperature drop and enthalpy drop of the turbine with load power The pressure ratio is a key index to evaluate the turbine performance. The higher the pressure ratio is, the more efficient heat-power conversion is. The variation of the pressure ratio and the rotational speed of the turbine with the load power is described in Fig. 7. With increase of the load power, the pressure ratio and the rotational speed decrease. However, the pressure ratio is not sensitive to the performance of the load change. When the load power is 1.7 kW, the speed reaches 40284 r/min, and the pressure ratio is 2.23.

2.40

55000

2.34

48000

2.28

41000

2.22

34000

2.16

27000

2.10 0.8

1.2

1.6

2.0

2.4

Turbine Rotational Speed(r/min)

Pressure Ratio

Pressure Ratio Turbine Rotational Speed

20000 2.8

Load Power (kW)

Fig. 7. Variation of pressure ratio and rotational speed of the turbine with load power The variation of isentropic efficiency and the output power of the turbine with load power is demonstrated in Fig. 8. The two parameters initially increase and then decrease with load power. When the optimal load power reaches 1.7 kW, the isentropic efficiency and the output power are 72.1% and 2.24 kW, respectively. The isentropic efficiency of the turbine is mainly affected by its internal leakage and friction loss. When load power is greater than the optimal value, as it increases, the turbine's reverse torque increases. The internal friction loss and the leakage of the turbine are

main contributors to the decrease in the isentropic efficiency.

85

Isentropic Efficiency ηs (%)

80 2.2

75 70

2.0 65 60 55 50 0.5

1.8

Isentropic Efficiency Turbine output power 0.9

1.3

1.7

2.1

2.5

Turbine output power Wt(kW)

2.4

1.6 2.9

Load Power (kW)

Fig. 8. Variation of isentropic efficiency and output power of the turbine with load power 4.2 Effects of load power on the evaporator and condenser performance The variation of the superheating of the evaporator outlet and the subcooling of the condenser outlet with load power is shown in Fig. 9. It can be seen from the figure that the superheating increases at first and then decreases with increase of load power. When load power is lower, the increasing degree is greater. As the former increases to a certain value, superheating starts to decrease, and then a significant inflection point appears. The subcooling does not remarkably change as load power increases, and it maintains a fluctuation around 11 °C. The superheating value is 87.24 °C at load power of 1.7 kW and the subcooling is 10.99 °C.

89

12.0

11.5

85 11.0 83

Subcooling (°C)

Superheating (°C)

87

10.5

81

Superheating Subcooling

79 0.5

0.9

1.3

1.7

2.1

2.5

10.0 2.9

Load Power (kW)

Fig. 9. Variation of superheating of the evaporator and subcooling of the condenser with load power The variation of the heat exchange rate in the evaporator and the condenser with load power is illustrated in Fig. 10. The evaporator heat addition rate Qe and the condenser heat rejection rate Qc

increase with load power. When other operating conditions remain constant, the temperature drop and the enthalpy drop of turbine gradually decline with load power increasing. Meanwhile, the temperature difference of the condenser increases, but the pressure difference decreases. It gives rise to the increase of the heat rejection of the working fluid. As the evaporator outlet temperature increases, the heat transfer temperature difference between the heat source and the working fluid increases, leading to the increase in the heat addition of the working fluid in the evaporator. When load power is 1.7 kW, the values of the heat exchange amount Qe and Qc are 49.24 kW and 48.05 kW, respectively.

Heat Addition Rate Qe(kW)

Heat Addition Rate

50.0

49.0

Heat Rejection Rate

49.5

48.5

49.0

48.0

48.5

47.5

48.0

47.0

47.5 0.5

0.9

1.3

1.7

2.1

2.5

Heat Rejection Rate Qc(kW)

49.5

50.5

46.5 2.9

Load Power (kW)

Fig. 10. Variation of heat transfer rate of working fluid with load power 4.3 Effects of load power on the performance of the working fluid pump It can be seen from Fig. 11 that the power consumption of pump is basically constant, around 1 kW. The isentropic efficiency of pump is very low, about 3%, as illustrated in Fig. 11. This is because canned motor pump is used, which is sealed together with the driven motor. The heat dissipation from the motor is absorbed by organic working fluid, so the enthalpy of pump outlet increases, and the isentropic efficiency of pump reduced. The more power the pump consumes, the greater the temperature difference between its inlet and outlet is; therefore, its isentropic efficiency is lower. Moreover, during the experimental process, the system performances under different conditions need to be tested, so the pump performance in actual operation often deviates from the optimal performance. Under the experimental conditions, when load power is 1.7 kW, the pump power is 1.09 kW, and the isentropic efficiency of pump is 3.09 %.

1.3

Pump Power Wp(kW)

3.5

1.2

3.3 1.1 3.1 1.0

0.9 0.5

2.9

0.9

1.3

1.7

2.1

2.5

Pump Isentropic Efficiency ηp,s(%)

3.7 Pump Power Pump Isentropic Efficiency

2.7 2.9

Load Power (kW)

Fig. 11. Variation of power consumption and isentropic efficiency of pump with load power 4.4 Effects of load power on the system performance The variation of the voltage and current of the generator with load power is illustrated in Fig. 12. As load power increases, the voltage gradually decreases, but the current gradually increases. There is a direct proportional manner of change between the voltage and the rotational speed. As load power increases, the generator rotational speed decreases, while the torque increases. Therefore, the generator produces a larger vortex magnetic field which is driven by the increasing current of the stator winding. 12

160

Current (A)

10

140

120 8 100 6

4 0.5

Voltage(V)

Current Voltage

80

0.9

1.3

1.7

2.1

2.5

60 2.9

Load Power(kW)

Fig. 12. Variation of the voltage and current of the generator with load power It can be seen from Fig. 13, electric power reaches the maximum value, 1.424 kW, when load power reaches 1.7 kW. With the increase of load power, electric power of the system shows an upward trend at first and then a downward one. And there is an optimal load power, so that the system has the largest electric power. There is a corresponding optimal rotation speed of the turbine when the power output is maximized. The torque at this rotation speed is the best value under this working condition. In order to reach the optimal match between the turbine and the

electric generator, the load power shall be adjusted so as to make the input torque of the generator intersect with the optimum torque point of the turbine, thus keeping the turbine from being in overload condition or underload condition. Whether the turbine works in overload condition or underload condition depends on whether the output power is greater than the power requirements of the generator. Only when the load power is optimal, will the optimum matching between the turbine and generator and the load be reached, thus maximizing the electric power. 1.5

Electric power (kW)

1.4

1.3

1.2 Electric Power

1.1

1.0 0.5

0.9

1.3

1.7

2.1

2.5

2.9

Load Power (kW)

2.6

9

2.2

8 7

1.8

6

1.4 Thermal Efficiency

5

Exergy Efficiency

1.0

Exergy Efficiency ηex(%)

Thermal Efficiency ηth(%)

Fig. 13. Variation of electric power with load power The variation of the thermal efficiency and exergy efficiency of ORC system with load power is shown in Fig. 14. It can be seen from the figure, the thermal efficiency and exergy efficiency initially increase and then reduce with the increase of load power. When load power is 1.7 kW, two parameters reach the maximum values of 2.52% and 8.09%, respectively. Therefore, in order to improve the performance of ORC system, load power should be controlled near the optimal value.

4 0.6 0.5

0.9

1.3

1.7

2.1

2.5

2.9

Load Power (kW)

Fig. 14. Variation of system thermal efficiency and exergy efficiency with load power The variation of the exergy loss of each equipment with load power is demonstrated in Fig. 15.

In the total system exergy loss, the turbine is the component with the lowest exergy loss, followed by the working fluid pump. The exergy loss of the evaporator accounts for the largest proportion, followed by the corresponding value of the condenser, and both of them increase with load power. The total system exergy loss increases with load power from 13.12 kW to 14.12 kW. When the optimal load power reaches 1.7 kW, the exergy loss of the evaporator, condenser, pump, turbine and total exergy loss are 7.98 kW, 4.05 kW, 1.02 kW, 0.62 kW and 13.67 kW, respectively. In this case, the exergy loss contribution of each equipment are ie=58.38%, ic=29.62%, ip=7.46%, it=4.54%, respectively. 15 Evaporator Condenser Pump Turbine Total Exergy Losses

Exergy Losses (kW)

12

9

6

3

0 0.5

0.9

1.3

1.7

2.1

2.5

2.9

Load Power (kW)

Fig. 15. Variation of exergy loss of each equipment with load power 4.5 Grey relational analysis of load power on the system performance According to grey system theory, grey relational grade reflects the correlation grade between compared series of parameters and reference series of load power in the system. The higher grey relational grade is, the closer proximity of their changes is and the closer interrelation is [41]. Grey relational grades ( γ ) of parameters are shown in Fig. 16. It can be seen that for electric power, there is the highest grey relational grade of 0.632 when all criteria are considered equally in import. Therefore, electric power has the closest correlation with load power in comparison with any other parameters. As shown in the Fig. 16, compared with the exergy efficiency, the thermal efficiency maintains a higher relational grade.

0.70

0.66 0.619

0.62 

0.596 0.58

0.606

0.603 0.601

0.612 0.613

0.624 0.601

0.632 0.612

0.564

0.54

t ur

bi n

et e tur mper a tu bi n t ur e e nt r e dr ha op bi n lp t ur ep r e s y dr o t ur bi ne s ur p ro bi n e i s ta ti o e r a t io e nt na l t ur r o pi c s pe e d bi n e ff ic eo ut p i e nc y ut s up po w e erh r ea t he a s ubc i ng oo ta he a ddi t i l i ng on tr e je ra t pu c ti on e mp p ra t ise um e nt r o p p po w ic e e r f e l e fi c i e t he c t r i c nc y rm po w al e x e e ffi c e r i en rg y cy e ff i ci e nc y

0.50

Fig. 16. Grey relational grades of parameters. According to the above analysis, it can be found that load power has different effects on the ORC system performance. Therefore, the load power of the generator should be as close as possible to the optimal power of the turbine. When the turbine works near the best operating point, the system performance is optimal. 5. Conclusions This paper carried out the experimental study on the effects of different operating loads on system performances. Based on the first and second laws of thermodynamics, many parameters were evaluated, such as the system thermal efficiency, exergy efficiency, exergy loss, and so on. The following conclusions were obtained:  According to experimental results, when load power is 1.7 kW, rotational speed, pressure ratio, isentropic efficiency and output power of the turbine are 40284 r/min, 2.23, 72.1% and 2.24 kW, respectively. And electric power, thermal efficiency and exergy efficiency of the ORC system reach the maximum values, 1.424 kW, 2.52% and 8.09%, respectively.  Exergy analysis of ORC system shows that under the experimental conditions, the exergy loss of the evaporator is the component with the highest exergy loss contribution, followed by the condenser. While the turbine is the lowest contributor to the total exergy loss, followed by the working fluid pump. When the optimum load power is 1.7 kW, the exergy loss rate of each equipment is ie=58.38%, ic=29.62%, ip=7.46%, it=4.54%, respectively.  Under the experimental conditions, following factors increase with the increase of load power, including the heat exchange rate, the isentropic efficiency of pump, the pressure ratio of turbine, the generated current, and the total exergy loss, while these factors decrease with load power, such as the power consumption of pump, the temperature drop of turbine, the enthalpy drop, the rotational speed, and the power generation voltage. When load power is optimal, the isentropic efficiency of turbine, output power, electric power, thermal efficiency, and exergy efficiency reach the maximum values. By grey relational analysis, it is concluded that electric power has the closest correlation

with load power, with its grey relational grade being 0.632. Compared with the exergy efficiency, the thermal efficiency maintains a higher relational grade.  In the design of the ORC system, the appropriate permanent magnet generator and load power should be selected for the expander. Load power of the generator should be as close as possible to the optimal power of the turbine, through which the turbine works near the best operating point. Thus, system performance is optimal. As the load power increases, the isentropic efficiency of the working fluid pump slightly rises, and the pump is working with low isentropic efficiency at the same time. It is of great value to further optimize the working fluid pump of the ORC system.

Acknowledgements This work was supported by the Scientific and Technological Planning Projects of Henan Province, China (No.162102310504), Funding Plan for Key Research Projects of Henan Province Higher Education Institutions in 2018 (No. 18B620002), Funding Plan for Key Research Projects of Henan Province Higher Education Institutions in 2019 (No.19A480005). The financial support is gratefully acknowledged. References [1] Kang SH. Design and experimental study of ORC (organic Rankine cycle) and radial turbine using R245fa working fluid[J]. Energy, 2012, 41(1):514-524. [2] Karimi S, Mansouri S. A comparative profitability study of geothermal electricity production in developed and developing countries: exergoeconomic analysis and optimization of different ORC configurations[J]. Renewable Energy, 2018, 115:600-619. [3] Rayegan R, Tao YX. A procedure to select working fluids for Solar Organic Rankine Cycles (ORCs)[J]. Renewable Energy, 2011, 36(2):659-670. [4] Uris M, Linares JI, Arenas E. Techno-economic feasibility assessment of a biomass cogeneration plant based on an Organic Rankine Cycle[J]. Renewable Energy, 2014, 66(66):707-713. [5] Hemer MA, Manasseh R, Mcinnes K L, et al. Perspectives on a Way Forward for Ocean Renewable Energy in Australia[J]. Renewable Energy, 2018, 127:733-745. [6] Liu P, Shu G, Tian H, et al. Engine load effects on the energy and exergy performance of a medium cycle/organic Rankine cycle for exhaust waste heat recovery[J]. Entropy, 2018, 20:137. [7] Quoilin S, Broek M V D, Declaye S, et al. Techno-economic survey of Organic Rankine Cycle (ORC) systems[J]. Renewable & Sustainable Energy Reviews, 2013, 22(22):168-186. [8] Mahmoudi A, Fazli M, Morad M R. A recent review of waste heat recovery by Organic Rankine Cycle[J]. Applied Thermal Engineering, 2018, 143: 660-675. [9] Shao L, Ma X, Wei X, et al. Design and experimental study of a small-sized organic Rankine cycle system under various cooling conditions[J]. Energy, 2017, 130:236-245. [10] Jiménez-Arreola M, Pili R, Wieland C, et al. Analysis and comparison of dynamic behavior of heat exchangers for direct evaporation in ORC waste heat recovery applications from fluctuating sources[J]. Applied Energy, 2018, 216:724-740. [11] Feng YQ, Hung TC, Wu SL, et al. Operation characteristic of a R123-based organic Rankine cycle depending on working fluid mass flow rates and heat source temperatures[J]. Energy Conversion and Management, 2017, 131:55-68. [12] Kang SH. Design and experimental study of ORC (organic Rankine cycle) and radial turbine

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Wp: work done by pump (W) Wt,s: isentropic turbine power (W) Wp,s: isentropic pump power (W) Wg: electric power (W) y: the normalization value of grey relational generation Abbreviations ORC: Organic Rankine Cycle GRA: grey relational analysis Subscripts 1-6: state point 0: environment H: heat source L: cold source p: pump t: turbine m: mass flow s: isentropic e: evaporator c: condenser th: thermal ex: exergy sys: the ORC system Greek letters ηt,s: isentropic efficiency of turbine (%) ηp,s: isentropic efficiency of pump (%) ηth: thermal efficiency of the system (%) ηex: exergy efficiency of the system (%) µ: calculated parameter uncertainty ξ: grey relational coefficient Δ: deviation value φ: identification coefficient γ: grey relational grade

Highlights  A small radial inflow turbine is self-designed and the testing rig is built.  The variation of system performance with operating load power is studied.  The best matching relation among radial inflow turbine, generator and load is investigated.  By grey relational analysis, it is concluded that electric power has the closest correlation with load power.

Declaration of Interest Statement

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.