Experimental study and energy loss analysis of an R245fa organic Rankine cycle prototype system with a radial piston expander

Journal Pre-proofs Experimental Study and Energy Loss Analysis of an R245fa Organic Rankine Cycle Prototype System with a Radial Piston Expander Yongqiang Han, Yiming Zhang, Teng Zuo, Ruolong Chen, Yun Xu PII: DOI: Reference:

S1359-4311(19)36563-9 https://doi.org/10.1016/j.applthermaleng.2020.114939 ATE 114939

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

21 September 2019 26 December 2019 12 January 2020

Please cite this article as: Y. Han, Y. Zhang, T. Zuo, R. Chen, Y. Xu, Experimental Study and Energy Loss Analysis of an R245fa Organic Rankine Cycle Prototype System with a Radial Piston Expander, Applied Thermal Engineering (2020), doi: https://doi.org/10.1016/j.applthermaleng.2020.114939

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1

Experimental Study and Energy Loss Analysis of an R245fa Organic Rankine Cycle Prototype

2

System with a Radial Piston Expander

3 4

Yongqiang Han, Yiming Zhang*, Teng Zuo, Ruolong Chen, Yun Xu

5

State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130025,

6

China

7 8

HIGHLIGHTS

9

 An R245fa organic Rankine cycle system with a radial piston expander is presented.

10

 Performance evaluations of multiple operating parameters are tested.

11

 Moderate filling quantity indicates the best expander performance.

12

 Gross thermal efficiency of the organic Rankine cycle can reach up to 2.02%.

13

 The expander obtains maximum power output 279W with all kinds of energy losses.

14 15

Keywords

16

Organic Rankine cycle prototype system; Experimental study; Radial piston expander; Operating

17

parameters; Energy and exergy analysis; Energy degradation

18 19

ABSTRACT

20

In this paper, an R245fa organic Rankine cycle experimental prototype system with a 5-cylinders

21

radial piston expander is presented to recovery waste heat from exhaust gas of diesel engine. In

22

order to explore the system behavior and research the effective adjustment method, the performance

23

was tested and analyzed with multiple operating parameters: pump speed, generator load, energy of

24

waste heat source and working fluid filling quantity. Moreover, energy and exergy analysis were

25

provided to evaluate the system energy loss. Combining simulation study of expander in GT-SUITE,

26

the internal friction and leakage were calculated to illuminate the energy degradation processes of

27

expansion. The experiments proved the feasibility of radial piston expander for organic Rankine

28

cycle coupled to vehicle engine. The results demonstrate that expander power output can be

29

optimized by adjusting pump speed under different heat sources and moderate filling quantity

30

indicates the largest expander power output. The gross thermal efficiency and exergy efficiency of

31

the organic Rankine cycle system can reach up to 2.02% and 10.5%, respectively. Overall system

32

exergy losses are 4.24-4.63 kW and expander contributes about 1 kW. In the processes of expansion,

33

entropy increment leads to larger energy degradation than working fluid flow loss and mechanical

34

frictional loss. Under the influences of multiple energy losses, the maximum expander mechanical

35

power output 279W can be obtained.

36

1. Introduction

37

With the world widely crisis of fossil fuel and environment pollution, many efforts have been

38

devoted to energy saving and emission reduction of internal combustion engine. Generally, only

39

40-45% of the fuel energy is used as effective power [1]. Most energy is dissipated in the form of

40

waste heat loss. Therefore, there is a growing interest in the field of waste heat recovery and many

41

technologies have been studied such as exhaust turbocharger [2], electric turbo [3], thermoelectric

42

generator [4], Stirling cycle [5], Kalina cycle [6] and Rankine cycle [7]. Bianchi and Pascale [8] * Corresponding author. E-mail: [email protected]

44

Nomenclature

45 46

∆𝐸𝑥

exergy loss [kW]

47

(∆𝐴)

exergy flow [kW]

48

𝐴

exergy value [kW]

49

𝑐𝑜𝑠𝜑

power factor of electromotor

50

𝐸𝑃𝑂𝑈𝐹

expander power output of unit flow working fluid [kJ/kg]

51

𝐸𝑅

expansion ratio

52

𝐻

enthalpy [kJ]

53

ℎ

specific enthalpy [kJ/kg]

54

𝐼

electric current [A]

55

𝑖

number of cylinders

56

𝑀

torque [Nm]

57

𝑚

mass flow rate [kg/s]

58

𝑛

rotational speed [rpm]

59

𝑝

pressure [Pa]

60

𝑄

heat flux [kW]

61

𝑆

entropy [kJ/K]

62

𝑠

specific entropy [kJ/kg-K]

63

𝑇

temperature [K]

64

𝑈

voltage [V]

65

𝑉

volume flow rate [m3/s]

66

𝑉

volume [m3]

67

𝑣

specific volume [m3/kg]

68

𝑊

power [W]

69 70

Greek letters

71

𝜂

efficiency [%]

72

𝜌

density [kg/m3]

73

𝜎

standard deviation

74 75

Subscripts

76

0

environment

77

𝑎𝑣𝑒_𝑔𝑎𝑠

average value of gas state

78

𝑎𝑣𝑒_𝑙𝑖𝑞

average value of liquid state

79

𝑎𝑣𝑒_𝑠𝑎𝑡𝑢𝑟

average value of saturation state

80

𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

cylinder of expander

81

𝑒𝑣𝑎_𝑖𝑛

evaporator inlet

82

𝑒𝑣𝑎_𝑜𝑢𝑡

evaporator outlet

83

𝑒𝑥_𝑔𝑟𝑜𝑠𝑠

exergy of gross

84

𝑒𝑥_𝑛𝑒𝑡

exergy of net

85

𝑒𝑥𝑝

expander

86

𝑒𝑥𝑝_𝑖𝑛

expander inlet

87

𝑒𝑥𝑝_𝑜𝑢𝑡

expander outlet

88

𝑒𝑥𝑝_𝑜𝑢𝑡_𝑖𝑠𝑒𝑛 isentropic expander outlet

89

𝑓𝑙𝑢𝑖𝑑

working fluid

90

𝑓𝑙𝑢𝑖𝑑_𝑒𝑣𝑎

working fluid in evaporator

91

𝑓𝑟𝑖

friction

92

𝑔𝑎𝑠

gas state

93

𝑖𝑛𝑑_𝑒𝑥𝑝

indication of expander

94

𝑖𝑠𝑒𝑛_𝑒𝑥𝑝

isentropy of expansion

95

𝑙𝑖𝑞

liquid state

96

𝑙𝑜𝑠𝑠

energy loss

97

𝑀

mass

98

𝑚𝑒𝑐ℎ_𝑒𝑥𝑝

mechanology of expander

99

𝑚𝑜𝑡𝑜𝑟

motor of pump

100

𝑛𝑒𝑡

net

101

𝑝𝑢𝑚𝑝

pump

102

𝑄

heat

103

𝑠𝑎𝑡𝑢𝑟

saturation state

104

𝑡ℎ_𝑒𝑥𝑝

thermodynamics of expander

105

𝑡ℎ_𝑔𝑟𝑜𝑠𝑠

thermodynamics of gross

106

𝑡ℎ_𝑛𝑒𝑡

thermodynamics of net

107

𝑊

work

109

provided a comparison of existing solutions, organic Rankine cycle, the Stirling engine and the

110

inverted Brayton cycle, to exploit wasted heat. The results showed that organic Rankine cycle

111

obtained the highest electric efficiency values. Gholamian and Zare [9] investigated the performance

112

of different cycles for waste heat recovery and the results revealed the superiority of the organic

113

Rankine cycle over the Kalina cycle in the scope of their study. Thus, the organic Rankine cycle

114

(ORC) system can be perceived as one of the most practical solutions to recovery waste heat.

115

As the component for power output, expander is critical to the performance of ORC system. The

116

expander technology impacts the amount of mechanical power output [10]. In general, expander can

117

be categorized into two types: the velocity type (such as axial and radial turbine expanders) and the

118

volume type (such as rotary vane expander, screw expanders, scroll expanders and piston expanders)

119

[11]. Dumont et al. [12] depicted larger filling factor, higher pressure ratio and moderate rotate

120

speed of piston expander. Imran et al. [13] provided a comprehensive review of different kinds of

121

volumetric expanders. The advantage of high expansion ratio and low leakage were obvious for

122

piston type but the design was not mature yet. Piston expander was promising and meaningful for

123

research and practical application. Tian et al. [14] presented and tested a novel free piston expander

124

coupling with a linear generator prototype, the maximum peak velocity was about 0.69 m/s and the

125

highest power output 96 W was obtained. Kanno and Shikazono [15] constructed experimental setup

126

with piston and cylinder which mimicked reciprocating expander. Measured indicated adiabatic

127

efficiency of water was about 86%, while that of ethanol was about 82% for the same piston velocity

128

condition. Fukuta et al. [16] designed a novel four cylinders reciprocating expander and examined

129

its performance. The total efficiency of the expander was about 0.4 over the range of rotational

130

speed. Ferrara et al. [17] experimentally analyzed a 9 cylinders reciprocating expander developed

131

from a hydraulic motor and the indicated efficiency was 66%. Considering the possibility of

132

improving the mechanical efficiency, the measured 19% isentropic efficiency would be increased

133

to around 40%. Bianchi et al. [18] presented a full experimental characterization of a micro-scale

134

ORC system driven by a specially designed three cylinders piston expander prototype and facility

135

was provided with an electric boiler as heat source. The maximum ORC gross and net efficiency

136

were 4.5% and 2.2%, respectively.

137

For ORC system performance, the parameters are critical and have been researched extensively

138

combining the first law (energy) and second law (exergy) of thermodynamics analysis. Li et al. [19]

139

introduced a small-scale R245fa ORC system test rig to investigate the performance at different

140

operating conditions. Results showed that both the heat source temperature and ORC pump speed

141

were found to be important parameters in determining system thermal efficiency and the component

142

operations. Gao et al. [20] established a small pumpless ORC system chosen R245fa as the working

143

fluid with scroll expanders and different hot water temperatures were employed to drive the ORC

144

system. The maximum energy efficiency of 2.3% and the maximum exergy efficiency of 12.8%

145

were obtained at the hot water temperature of 90°C. Meanwhile the torque caused by the internal

146

mechanical friction of the expander was measured about 0.4 Nm. Sun et al. [21] conducted the

147

impacts of the operational parameters, including evaporation temperature, condensation

148

temperature, and degree of superheat, on the thermodynamic performances of ORC system. Results

149

showed that, the evaporation temperature and the condensation temperature contributes

150

significantly to the exergy efficiency, whereas the effect of degree of superheat is negligible. Eyerer

151

et al. [22] investigated the applicability of modern fluids R1233zd(E) and R1224yd(Z) as drop-in

152

replacements for R245fa in ORC system. They proved the feasibility of substitution but the

153

maximum power output 326 W was obtained with R245fa. Besides, heat transfer efficiency

154

increased significantly from approximately 38% to 56% with increasing mass-flow rate because the

155

corresponding larger Reynolds number. Mago et al. [23] used exergy topological method to estimate

156

the exergy destroyed in ORC system. The results demonstrated that for basic ORC the evaporator

157

is the component with the highest exergy loss contribution (77%) followed by the expander with

158

21.4%. Moreover, the total system exergy destruction decreased with increasing evaporator pressure

159

and decreasing turbine inlet temperatures. Song et al. [24] presented a stationary compressed natural

160

gas engine-ORC with internal heat exchanger combined system and discussed performances of the

161

ORC system with independently varying engine torque and evaporation pressure. When the

162

evaporation pressure was 3.5 MPa and the engine was operating at the rated condition, the thermal

163

efficiency of the ORC system can reach up to maximum 12.5%. Lin et al. [25] analyzed the dynamic

164

behavior when engine operating condition changes. Applying the PID (Proportion Integration

165

Differentiation) control to regulate the frequency of the pump and the expander, the dynamic

166

evaporation pressure drops relative to steady-state conditions reduced 84% and 78% compared with

167

no parameter was adjusted.

168

Until now, the use of ORC system for internal combustion engine waste heat recovery has mainly

169

been limited to experimental research and a potential for further vehicle applications development

170

can be recognized [26]. Macián et al. [27] discussed a design methodology for the optimization of

171

a bottoming cycle as a waste heat recovering system in heavy duty vehicles. Water and R245fa were

172

selected as working fluids in the proposed solutions and a maximum improvement of 10% in brake

173

specific fuel consumption was obtained. Uusitalo et al. [28] presented an experimental setup consists

174

of large-scale diesel engine and an ORC process utilizing charge air heat in which the turbine-

175

generator was replaced with an expansion valve. They observed that it was capable to increase the

176

power output of the test engine by 2%. Shi et al. [29] conducted an experimental investigation of a

177

CO2-based transcritical Rankine cycle and the estimations results indicated 2.42 kW net power

178

output, 0.077 thermal efficiency and 0.131 exergy efficiency can be obtained. Alshammari et al.

179

[30] manufactured a radial inflow turbine with a novel back-swept blading that was designed

180

specifically for waste heat recovery application. The peak isentropic efficiency of the turbine

181

reached 35.2% and the maximum gross power thermal efficiency of the cycle was 4.3%. AVL [31]

182

developed a Rankine cycle system with ethanol as the working fluid to investigate the fuel economy

183

benefit of recovering waste heat from a heavy-duty truck diesel engine by studying indicated turbine

184

power as a function of the enthalpy drop across the turbine expander. The results demonstrated that

185

3-5% fuel saving is achievable by utilizing this technology. BMW [32] designed the Rankine cycle

186

test bench measurements of the applied car engine coupled with a two separate loops waste heat

187

recovery device which the working fluids were water and ethanol separately. It can be demonstrated

188

that waste heat recovery can produce an additional power output of about 10% at typical highway

189

cruising speeds by means of experimental investigations and simulations. However, alcohol is

190

critical in terms of safety and environmental aspects.

191

Currently, the complete experiment about vehicle exhaust waste heat recovery organic Rankine

192

cycle applications is not popularized. Moreover, it is an area in which little available literature exists

193

to equip a multi-cylinders reciprocating piston expander with prospect for practical application on

194

vehicle engine. An R245fa organic Rankine cycle experimental prototype test bench with a radial

195

piston expander was built in this study to research the system performance and discuss the energy

196

loss. A simulation model of the expander was established in GT-SUITE to study the friction and

197

leakage. The effects of varying operating parameters were tested, such as pump speed, generator

198

load, energy of waste heat and working fluid filling quantity. What’s more, energy and exergy were

199

introduced to analyze all the components and system loss in essence. A detailed discussion of the

200

expansion energy degradation process was presented combining simulation method.

201

2. ORC prototype system

202

2.1. Experimental system description

203

The schematic diagram of the ORC prototype system was constructed as shown in Fig. 1. After

204

combustion in the engine, the exhaust gas was imported into the evaporator. A butterfly bamper was

205

equipped between engine and evaporator in order to avoid damage to facility and it was normally

206

open in experiment. Low-boiling organic working fluid was heated to high pressure supersaturated

207

vapor state by high temperature exhaust gas in the evaporator. The working fluid flowed into

208

cylinders and pushed the expander to rotate. The power from the expander was used to turn the

209

generator by belt and produce electricity. Variable number of lamps consumed electricity and

210

changed the load of the generator. The torque of expander depended on the required torque of

211

generator. Theoretically, it was an isentropic process for working fluid in expander with decline of

212

temperature and pressure. However, irreversible entropy increment would occur in practice. After

213

expansion, the working fluid was cooled to liquid state in the condenser. Liquid medium flowed

214

into dry filter to remove water and impurities. The tank was designed to stabilize the pressure of the

215

working fluid and ensure that only liquid could be drawn into the pump. A sight window was

216

installed to observe the state of working fluid. Then, working fluid was pressurized in pump and

217

ready for next working cycle. The pump was driven by an electromotor and pump speed could be

218

adjusted by frequency converter linearly. In this ORC prototype system, various sensors (such as

219

temperature sensors, pressure sensors, flowmeters and torque & speed sensor) were equipped so the

220

system status data can be gathered by high-speed data acquisition cards and displayed in computer

221

instantly to monitor experimental status. Radial Piston Expander

Diesel Engine

Normally Closed Safety Valve Silencer

p

T

p T

Plate Evaporator

T

Tt q

Belt

n

Normally Open Butterfly Bamper

Lamps

…

T

U

… Fuel Consumption Meter

Air Flow Meter

p

222 223

224

Cooling Fans

Fill Port

Plunger Pump

Finned Condenser

Sight Window

I

Dryer

p

U

Air

I

T

Flowmeter Diesel Fuel

Air

Generator

…

M Frequency Converter Electromotor

T

Tank

Data Acquisition Card Computer

Fig. 1. Schematic diagram of the ORC prototype system.

2.2. Experimental setup description

225

Some details of the experimental setup and parts of the ORC prototype system are depicted in

226

Fig. 2. The total volume of experimental setup on the working fluid side was measured 27.0 liters.

227 228

Fig. 2. Experimental setup of the ORC prototype system.

229

The heat source of ORC system was the exhaust gas from a long-haul heavy-duty diesel engine.

230

Main specifications of engine are listed in Table 1. The working condition of engine was monitored

231

and controlled by dynamometer. Besides, the fuel consumption and air flow were measured in real

232

time.

233

Table 1

234

Main specifications of engine. Engine model

CA6DL2.35E3

Number of cylinders

6

Turbocharging

Inter-cooling

Compress ratio

17.0

Displacement

8.6 L

Bore

112 mm

Stroke

145 mm

Fuel system

High pressure common rail

235 236

For safety and efficiency consideration, R245fa (CF3CH2CHF2) was selected as working fluids.

237

In this ORC system, a brazed plate heat exchanger was chosen as the evaporator, and heat insulation

238

cotton was added to reduce the heat loss of the evaporator. An air-cooled finned tube heat exchanger

239

was employed as condenser. One high pressure plunger pump was used to provide the working

240

fluid. The adjusting range of frequency converter is 0-50 Hz and pump speed can be regulated from

241

0 to 1430 rpm gradually. The radial piston expander with 5-cylinders, which are equispaced on the

242

same crankshaft with 72° angel interval, was converted from a pneumatic motor to the ORC power

243

output device. The structure of multi-cylinders can improve stability and continuity of power. More

244

details about the expander can be found in Table 2.

245 246

Table 2

247

Main specifications of radial piston expander.

248

Expander model

QMH050A-L

Number of cylinders

5

Bore

34 mm

Stroke

30 mm

Diameter of main inlet/outlet port

10 mm

Diameter of cylinder branch inlet/outlet port

6 mm

Max. rotational speed

750 rpm

Weight

8.1 kilograms

249

The measuring variables and corresponding measuring devices in this experimental setup are

250

summarized in Table 3. Using the measured values, further parameters such as specific enthalpy

251

and density are calculated in REFPROP. Uncertainties of experimental results are caused by

252

measuring error. In order to reduce random errors, data of ORC steady state test were collected and

253

averaged in about 3-5 minutes after stabilizing. Gaussian law of error propagation [22] is introduced

254

to quantify the uncertainty of derived quantities such as thermal efficiency and assess the influences

255

to final results of experiment. For derived quantity 𝑦 which can be determined from the values 𝑥𝑗

256

with a correlation function in the form of 𝑦 = 𝑓(𝑥1,𝑥2, 𝑥3…𝑥𝑘), the standard deviation of the

257

derived quantity 𝜎𝑦 is described by:

258

𝜎𝑦 = ∑𝑗 = 1

259 260 261 262

𝑘

(

2 ∂𝑓 ∂𝑥𝑗𝜎𝑥𝑗

)

(1)

Taking gross power thermal efficiency of the ORC system as an example, it is calculated as follows: 𝜂𝑡ℎ_𝑔𝑟𝑜𝑠𝑠 = 𝑄

𝑊𝑒𝑥𝑝 𝑓𝑙𝑢𝑖𝑑_𝑒𝑣𝑎

2𝜋

𝑀 × 𝑛 × 60

= 𝜌 × 𝑉 × (ℎ

𝑒𝑣𝑎_𝑜𝑢𝑡

― ℎ𝑒𝑣𝑎_𝑖𝑛)

(2)

Partial derivative with density to pressure is calculated as follows, other further parameters are

263

similar:

264

∂𝜌(𝑝,𝑇) ∂𝑝

=

𝜌(𝑝 + 𝛥𝑝,𝑇) ― 𝜌(𝑝 ― 𝛥𝑝,𝑇) 2 × 𝛥𝑝

(3)

265

Combined with measured data, the maximum expander power, heat absorbed by working fluid

266

and gross power thermal efficiency are 279±8.5 W, 14.3±0.33 kW and 1.94±0.07 %, respectively.

267

By experimental error analysis, relative deviation of gross thermal efficiency is 3.8% and the

268

accuracies are satisfied for present experiment.

269 270

Table 3

271

Types and precision of measuring devices. Measuring variables

Device

Accuracy

Range

Temperature

Thermocouples

±0.18%

0-800 °C

Pressure

Diffused-silicon

±0.2%

0-2.0 MPa

Flow rate of working fluid

Turbine flowmeter

±0.5%

0.1-0.6 m3/h

Torque and speed of

0-10 Nm & 0Torque & speed sensor

±0.5%

expander Electric current

3000rpm Digital multimeter

±2.5%

0-40 A

±0.1%

0-150 kg/h

±0.5%

0-1350 kg/h

Fuel consumption Fuel consumption of engine meter Air inflow of engine

Air flow meter

272 273

To meet the requirements of intensity and sealing detection, high pressure dry air was poured into

274

system to examine the leaking point. After strengthening and seal processing, the pressure drop of

275

prototype system was tiny in pressure retaining test with three hours which was satisfactory for

276

experiment, as shown in Fig. 3.

0.8 0.7 Inflation completed

Pressure (MPa)

0.6 0.5 0.4 0.3

Evaporator inlet pressure Evaporator outlet pressure Condenser inlet pressure Condenser outlet pressure

0.2 0.1 0.0

0

60

120

180

240

Time (min)

277 278

Deflation

Inflation completed Fig. 3. Pressure curve of pressure retaining test.

279

Before filling the working fluid, it is necessary to squeeze out the residual air in ORC test bench.

280

On the one hand, the air is detrimental to ORC performance. On the other hand, chemical reactions

281

would occur between the organic working fluid and the residual moisture in the air, which may

282

cause acid corrosion to the instrument. With the method of vacuuming, the boiling point of water

283

will be lower and it would become easier to be discharged. After completing all previous

284

preparations, the liquid working fluid R245fa was filled by a pump and the performance of the ORC

285

prototype system was tested.

286

2.3. Simulation model of radial piston expander

287

For further analysis of internal working process, a simulation model of expander is established

288

by commercial software GT-SUITE. GT-SUITE is a highly integrated simulation tool for

289

powertrains and vehicles and its template library is very rich which covers fluid, mechanical,

290

electrical, magnetic, thermal and control components. Graphical user interface of the self-

291

constructed 5-cylinders radial piston expander is shown in Fig. 4 and related formulas are included

292

in the background of software. Leakage module of each cylinder and friction torque module are

293

coupled in this model.

Main Outlet Port

Main Inlet Port Friction Torque Module

Leakage Module

294 295

296

297 298

Fig. 4. Simulation model of 5-cylinders radial piston expander.

2.4. Evaluation indexes

In order to calculate and analyze performance of ORC system, several evaluation indexes are listed as follows.

299 300 301 302 303 304 305 306 307

The heat absorbed by working fluid in evaporator is calculated as follows: 𝑄𝑓𝑙𝑢𝑖𝑑_𝑒𝑣𝑎 = 𝑚𝑓𝑙𝑢𝑖𝑑 × (ℎ𝑒𝑣𝑎_𝑜𝑢𝑡 ― ℎ𝑒𝑣𝑎_𝑖𝑛)

(4)

The electric energy consumption of pump is calculated as follows: 𝑊𝑝𝑢𝑚𝑝 = 3 × 𝑈𝑝𝑢𝑚𝑝 × 𝐼𝑝𝑢𝑚𝑝 × 𝑐𝑜𝑠𝜑 × 𝜂𝑚𝑜𝑡𝑜𝑟

(5)

The power output of expander is calculated as follows: 2𝜋

(6)

𝑊𝑒𝑥𝑝 = 𝑀𝑒𝑥𝑝 × 𝑛𝑒𝑥𝑝 × 60

The theoretical isentropic power of expander is calculated as follows: 𝑊𝑖𝑠𝑒𝑛_𝑒𝑥𝑝 = 𝑚𝑓𝑙𝑢𝑖𝑑 × (ℎ𝑒𝑥𝑝 _𝑖𝑛 ― ℎ𝑒𝑥𝑝 _𝑜𝑢𝑡_𝑖𝑠𝑒𝑛)

(7)

308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329

The thermodynamic power of expander is calculated as follows: 𝑊𝑡ℎ_𝑒𝑥𝑝 = 𝑚𝑓𝑙𝑢𝑖𝑑 × (ℎ𝑒𝑥𝑝 _𝑖𝑛 ― ℎ𝑒𝑥𝑝 _𝑜𝑢𝑡)

(8)

The indicated power of expander is calculated as follows: 𝑊𝑖𝑛𝑑_𝑒𝑥𝑝 =

𝑖 × 𝑛𝑒𝑥𝑝 60

(9)

× ∫𝑝𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟𝑑𝑉𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

The isentropic efficiency of expander is calculated as follows: 𝑊𝑡ℎ_𝑒𝑥𝑝

(10)

𝜂𝑖𝑠𝑒𝑛_𝑒𝑥𝑝 = 𝑊

𝑖𝑠𝑒𝑛_𝑒𝑥𝑝

The mechanical efficiency of expander is calculated as follows: 𝑊𝑒𝑥𝑝

(11)

𝜂𝑚𝑒𝑐ℎ_𝑒𝑥𝑝 = 𝑊

𝑖𝑛𝑑_𝑒𝑥𝑝

The friction torque of expander is calculated as follows: 𝑀𝑓𝑟𝑖 =

(𝑊𝑖𝑛𝑑_𝑒𝑥𝑝 ― 𝑊𝑒𝑥𝑝) 2𝜋 60

(12)

× 𝑛𝑒𝑥𝑝

The expander power output of unit flow working fluid is calculated as follows: 𝑊𝑒𝑥𝑝

(13)

𝐸𝑃𝑂𝑈𝐹 = 𝑚𝑓𝑙𝑢𝑖𝑑 The actual volume expansion ratio of expander is calculated as follows: 𝐸𝑅 =

𝑣𝑒𝑥𝑝_𝑜𝑢𝑡

(14)

𝑣𝑒𝑥𝑝_𝑖𝑛

The net power output of the ORC system is calculated as follows: (15)

𝑊𝑛𝑒𝑡 = 𝑊𝑒𝑥𝑝 ― 𝑊𝑝𝑢𝑚𝑝 The net power thermal efficiency of the ORC system is calculated as follows: 𝜂𝑡ℎ_𝑛𝑒𝑡 = 𝑄

𝑊𝑛𝑒𝑡

(16)

𝑓𝑙𝑢𝑖𝑑_𝑒𝑣𝑎

The heat exergy value of working fluid in evaporator is calculated as follows:

(

𝐴𝑄 = ∫ 1 ―

)𝛿𝑄 = (1 ―

)𝑄

𝑇0

𝑇0

𝑇

𝑇𝑎𝑣𝑒_𝑙𝑖𝑞

𝑙𝑖𝑞

(

𝑇0

)

(

𝑇0

)

+ 1 ― 𝑇𝑎𝑣𝑒_𝑠𝑎𝑡𝑢𝑟 𝑄𝑠𝑎𝑡𝑢𝑟 + 1 ― 𝑇𝑎𝑣𝑒_𝑔𝑎𝑠 𝑄𝑔𝑎𝑠

(17)

The gross power exergy efficiency of the ORC system is calculated as follows: 𝜂𝑒𝑥_𝑔𝑟𝑜𝑠𝑠 =

𝑊𝑒𝑥𝑝 𝐴𝑄

(18)

330 331 332

The net power exergy efficiency of the ORC system is calculated as follows: 𝜂𝑒𝑥_𝑛𝑒𝑡 =

𝑊𝑛𝑒𝑡 𝐴𝑄

(19)

The exergy loss of component is calculated as follows:

333

𝛥𝐸𝑥 = (𝛥𝐴)𝑄 + (𝛥𝐴)𝑊 + (𝛥𝐴)𝑀

334

3. Experimental results analysis

335

3.1. Starting and stopping process of expander

(20)

336

Variations of ORC parameters at cold starting and stopping processes are plotted in Fig. 5 (a) (b).

337

Due to low leakage of piston expander, the pressure differential at both sides of expander can be

338

built up easily and expander started turning without extra starting method when the pressure

339

differential reaches 0.083MPa.

340

After engine and ORC pump shutdown, the expander keeps rolling in 6 minutes and pressure

341

differential decreases gradually in half an hour. In the practical vehicles applications, there should

342

be some extra methods to stop the ORC system immediately, such as a by-pass pipeline with a valve

343

opened timely between inlet and outlet of expander.

0.7

300

Temperature of exhaust gas Expander inlet pressure Expander outlet pressure Expander speed

250

400

0.6 300

150 0.4 100

200

Speed (rpm)

0.5

Pressure (MPa)

Temperature (°C)

200

100 0.3

50

0 0.0

0.5

1.0

0.2 2.0

1.5

Time (min)

344 345

(a)

Temperature of exhaust gas Expander inlet pressure Expander outlet pressure Expander speed

250

348

349

350

400

0.4

100

0.3

50

0.2

0

5

10

15

20

25

0.1 30

300

200

Speed (rpm)

150

Pressure (MPa)

Temperature (°C)

347

0.6

0.5

200

0

500

0.7

300

346

0

100

0

Time (min)

(b) Fig. 5. Variations of ORC parameters at (a). Cold starting process; (b). Stopping process.

3.2. Performance influenced by different pump speeds

Pump is a major component consuming energy in ORC system. In this prototype system, the

351

energy loss of pump and electromotor could be friction loss, core loss and eddy current loss mainly.

352

Figure 6 shows the electrical energy consumption at different speeds. No-load conditions mean that

353

the inlet and outlet of pump are open to the environment. On the contrary, the data of loaded

354

conditions are tested in working process under the engine condition, 1330 rpm and 130 Nm. It can

355

be found that 63.6-81.6% electrical energy consumption of the pump and electromotor would be

356

wasted.

90%

180

No-load conditions Loaded conditions Energy consumption ratio

140

80%

120

75%

100 70% 80 65%

60

60%

40

55%

20 0

20

15

25

30

35

40

45

50

50%

Pump electromotor frequency (Hz)

357 358

85%

Energy consumption ratio of no-load to loaded

Electrical energy consumption (W)

160

Fig. 6. Electrical energy consumption of pump.

359

As illustrated in Fig. 7, flow rate increases from 109.6 kg/h to 209.2 kg/h with the increasing of

360

pump speed but the growth rate slows down gradually. The trend of evaporating pressure is similar.

361

The corresponding condensing pressure also increases but very small. As for the evaporator outlet

362

temperature, it decreases from 139.4 °C to 97.1 °C gradually because heat is absorbed by more fluid

363

when the pump speed rises.

2.0

250

Flow rate Evaporating pressure Condensing pressure Evaporator outlet temperature Saturation evaporation temperature

200

200

1.5

0.5

100

50 10

100

Temperature (°C)

1.0

150

Pressure (MPa)

Flow rate (kg/h)

150

15

20

25

30

35

40

45

0.0 55

50

50

Pump electromotor frequency (Hz)

364 365

Fig. 7. ORC parameters at different pump electromotor frequencies.

366

Pump speed is a key adjustment parameter to power output of expander, as reported in Fig. 8. As

367

pump speed increases, more quality of working fluid joins to work, so larger power is available.

368

However when the pump speed is over high, just as the situation at pump electromotor frequency

369

50 Hz, the evaporator outlet temperature is 97.1 °C which is only 4.5 °C higher than saturation

370

temperature so the volume flow rate is small and the capability to work is weak. There exists a

371

maximum power output 215 W when pump electromotor frequency is 30 Hz. 240

500

Expander power Expander speed Expander torque

5.3

400 160 140

350

120

10

372

4.9 4.7 4.5 4.3 4.1 3.9

15

20

25

30

35

40

45

Pump electromotor frequency (Hz)

50

300

55

3.7

Expander torque (Nm)

180

100

5.1

450

200

Expander speed (rpm)

Expander power (W)

220

5.5

373

374

Fig. 8. Power output of expander at different pump electromotor frequencies.

3.3. Performance influenced by different generator loads

375

Shaft power from expander was used to generate electricity and halogen lamps transformed

376

electrical energy into light. A 24 V direct-current generator with a maximum load of 1.5 kW was

377

equipped. The resistance value of one lamp is 11.52 Ω and the generator load was variable by

378

adjusting the number of lamps in parallel.

379

The generator load can adjust operational characteristics of expander-generator obviously as Fig.

380

9. The torque of expander increases gradually with increasing of lamps number. Moreover, it can

381

be concluded that expander speed and torque can be varied freely in its operating range to meet

382

different practical requirements through adjusting flow rate of working fluid and load of expander.

5.5 Torque with   (55 lamps) Torque with   (35 lamps) Torque with 0.768  (15 lamps)

Expander torque (Nm)

5.0 4.5 4.0 3.5 3.0 2.5 300

350

400

450

500

550

Expander speed (rpm)

383 384

Fig. 9. Operational characteristics of expander-generator with different generator loads.

385

The ORC thermodynamic parameters with different generator loads under engine condition, 1330

386

rpm and 130 Nm, is displayed in Fig. 10. The flow rate of R245fa can be adjusted by pump speed

387

effectively and the generator load has little effect to flow rate. When more lamps are connected into

388

the circuit, evaporating pressure tends to be risen by 6.5-12.1% because of the larger load torque

389

requirement, as shown in Fig. 9. Evaporator outlet temperature shows the similar regularity with

390

evaporating pressure which tends to be higher.

2.0

200

1.5

1.0

150 0.5

100

391 392

0

5

10

15

20

25

30

35

40

45

50

300

0.0 55

200

100

Evaporator outlet temperature (°C)

Flow rate with 0.768 Ω (15 lamps) Flow rate with 0.329 Ω (35 lamps) Flow rate with 0.209 Ω (55 lamps) Evaporating pressure with 0.768 Ω (15 lamps) Evaporating pressure with 0.329 Ω (35 lamps) Evaporating pressure with 0.209 Ω (55 lamps) Temperature with 0.768 Ω (15 lamps) Temperature with 0.329 Ω (35 lamps) Temperature with 0.209 Ω (55 lamps)

Evaporating pressure (MPa)

Flow rate (kg/h)

250

0

Pump electromotor frequency (Hz)

Fig. 10. ORC parameters with different generator loads.

393

Fig. 11 illustrates the expander power output with different generator loads. As it is obvious,

394

largest expander power output occurs in case of minimum value of resistance (most lamps). It is

395

because both of the evaporating pressure and evaporator outlet temperature are higher, just as the

396

previous analysis. In order to discuss the maximum expander power output, it will default to adopt

397

the minimum load resistance value 0.209 Ω (55 lamps) in the following analysis.

Expander power outpur (W)

250

Power output with 0.768Ω (15 lamps) Power output with 0.329 Ω (35 lamps) Power output with 0.209 Ω (55 lamps)

200

150

100 10

15

25

30

35

40

45

50

55

Pump electromotor frequency (Hz)

398 399

400

20

Fig. 11. Power output with different generator loads.

3.4. Performance influenced by different waste heat energy

401

By adjusting working conditions of engine, the heat source energy of the ORC system was

402

changed. In order to avoid damaging to the evaporator, the evaporator inlet temperature did not

403

exceed the limit of 230 °C. The four small load working conditions were selected and working

404

parameters are listed as Table 4. The values of exhaust gas waste heat energy describe the energy

405

carried by waste gas in exhaust port compared to the state at environment temperature.

406 407

Table 4

408

Main experimental measured data of engine and exhaust gas. Items

Measured values

Engine speed (rpm)

1330

1330

1650

1960

Engine torque (Nm)

30

130

90

30

Original engine diesel consumption (kg/h)

5.59

7.80

8.89

9.13

Engine-ORC diesel consumption (kg/h)

5.60

7.89

9.07

9.38

Air intake flow rate (kg/h)

409.6

425.8

533.0

628.3

Temperature of exhaust gas (°C)

177.8

217.6

221.9

226.8

Engine power (kW)

4.18

18.11

15.55

6.16

Exhaust gas waste heat energy (kW)

17.84

23.55

30.10

36.31

409 410

As presented in Fig. 12, heat absorbed by working fluid exhibits an increase trend but the growth

411

is not obvious through increasing exhaust gas waste heat energy of engine. This is because the heat

412

absorption capacity of working fluid in the existing flow rate conditions is limited and the heat loss

413

of evaporator tends to be larger when waste heat is more. Heat absorbed by working fluid varies

414

from 13.31 kW under 17.84 kW to 14.16 kW under 36.31kW at pump electromotor frequency 50

415

Hz. Generally, heat absorbed by working fluid manifests an increasing trend with increasing of

416

pump speed because the heat transfer coefficient would enhance with higher flow rate and flow

417

velocity. With the increasing of pump speed, heat absorbed by working fluid increase from 10.45

418

kW to 14.16 kW under waste heat 36.31 kW. The method of reducing heat transfer loss and

419

enhancing heat transfer would be effective to increase efficiency of heat exchanger.

16

1330-30 (17.84kW) 1330-130 (23.55kW) 1650-90 (30.10kW) 1960-30 (36.31kW)

Heat absorbed by wrking fluid (kW)

14 12 10 8 6 4 2 0

420 421

15

20

25

30

35

40

45

50

Pump electromotor frequency (Hz)

Fig. 12. Heat absorbed by evaporator and working fluid under different waste heat energy.

422 423

The influences of waste heat to ORC parameters are indicated in Fig. 13 (a) (b). With the increase

424

of waste heat, evaporating pressure and evaporator outlet temperature can be higher. At pump

425

electromotor frequency 50Hz, evaporating pressure rises from 0.93 MPa to 1.33 MPa under

426

different waste heat energy. Evidently, energy of heat source is an important factor to influence

427

evaporating pressure. The increase of condensing pressure is much smaller relatively. When there

428

is more waste heat, the volume expansion ratio of the expander will be greatly increased due to the

429

increase in pressure difference between the inlet and outlet of the expander. The maximum volume

430

expansion ratio is 3.99 within the testing range. Additionally, the increasing energy of exhaust gas

431

results to slightly reduction of working fluid flow rate because evaporating pressure, in other words

432

backpressure of the pump, is affected.

Flow rate (kg/h)

200

175

300

Flow rate under 17.84 kW Flow rate under 23.55 kW Flow rate under 30.10 kW Flow rate under 36.31 kW Temperature under 17.84 kW Temperature under 23.55 kW Temperature under 30.10 kW Temperature under 36.31kW

250

200

150 150 100 125

100 10

50

15

20

25

30

35

40

45

Evaporator outlet temperature (°C)

225

0 55

50

Pump electromotor frequency (Hz)

433 434

(a)

6

3.0

Pressure (MPa)

2.0

Expansion ratio under 17.84 kW Expansion ratio under 23.55 kW Expansion ratio under 30.10 kW Expansion ratio under 36.31 kW

5

4

1.5

3

1.0

2

0.5

1

0.0 10

15

20

25

30

35

40

45

50

Expansion ratio

2.5

Evaporating pressure under 17.84 kW Evaporating pressure under 23.55 kW Evaporating pressure under 30.10 kW Evaporating pressure under 36.31 kW Condensing pressure under 17.84 kW Condensing pressure under 23.55 kW Condensing pressure under 30.10 kW Condensing pressure under 36.31 kW

0 55

Pump electromotor frequency (Hz)

435 436

(b)

437

Fig. 13. ORC parameters under different waste heat energy (a). Flow rate and evaporator outlet

438

temperature; (b). Evaporating pressure, condensing pressure and expansion ratio.

439 440

Through the above analysis, it’s easy to draw the conclusion that the increase in energy of waste

441

heat leads to a simultaneous increase in expander power, as shown in Fig. 14. At the same time, as

442

waste heat increases, the maximum expander power point on each curve tends to the higher flow

443

area. When waste heat is 17.84 kW, the maximum power output 152 W locates at pump electromotor

444

frequency 20 Hz. However it becomes 40 Hz when waste heat increases to 36.31 kW. The expander

445

power output can be optimized by adjusting pump speed under different heat sources. In order to

446

ensure the best performance of ORC system, more working fluid is required to absorb heat when

447

more waste energy is detected.

300

Power output Power output Power output Power output

Expander power output (W)

250

under 17.84 kW under 23.55 kW under 30.10 kW under 36.31 kW

200

150

100

50

0

5

10

15

20

25

30

35

40

45

50

55

Pump electromotor frequency (Hz)

448 449

450

Fig. 14. Power output under different waste heat energy.

3.5. Performance influenced by different working fluid filling quantities

451

Working fluid filling quantity would influent the ORC performance and three different initial

452

filling quantities 10, 20 and 26 kilograms were tested. The ORC thermodynamic parameters with

453

different filling quantities under engine condition, 1330 rpm-130 Nm (waste heat energy 23.55 kW)

454

and 1650 rpm-90 Nm (waste heat energy 30.10 kW), are displayed in Fig. 15 (a) (b). Various

455

parameters of working fluid with 10 kilograms are minimum obviously. Flow rates are similar but

456

gap of pressure shows up between the initial filling quantities 20 and 26 kg. The condensing

457

pressures with 26 kilograms working fluid are slightly higher under both of two engine conditions.

458

However, due to the combined influences of working fluid filling quantity, pressure rise by pump

459

and heat transfer process in evaporator, evaporating pressure of 20 kilograms filling quantity

460

surpasses 26 kilograms in the range of high pump speed.

2.0

300 Flow rate with 10 kg Flow rate with 20 kg Flow rate with 26 kg Evaporating pressure with 10 kg Evaporating pressure with 20 kg Evaporating pressure with 26 kg Condensing pressure with 10 kg Condensing pressure with 20 kg Condensing pressure with 26 kg

250

Flow rate (kg/h)

225 200 175

1.5

1.0 150 125 100

0.5

75 50 25

461 462

0

5

10

15

20

25

30

35

40

Pump electromotor frequency (Hz)

(a)

45

50

0.0 55

Pressure (MPa)

275

2.0

250 Flow rate with 10 kg Flow rate with 20 kg Flow rate with 26 kg Evaporating pressure with 10 kg Evaporating pressure with 20 kg Evaporating pressure with 26 kg Condensing pressure with 10 kg Condensing pressure with 20 kg Condensing pressure with 26 kg

150

1.0

100

0.5

50

463

1.5

0

5

10

15

20

25

30

35

40

45

50

Pressure (MPa)

Flow rate (kg/h)

200

0.0 55

Pump electromotor frequency (Hz)

464

(b)

465

Fig. 15. ORC parameters with different filling quantities under (a). 23.55kW; (b). 30.10kW.

466

Shown as Fig. 16 (a) (b), maximum expander powers can be gotten with initial filling quantity

467

20 kilograms under these two engine conditions, 1330 rpm-130 Nm and 1650 rpm-90 Nm, and it

468

can confirm earlier analysis of ORC state parameters. The peak expander powers are 220 W under

469

23.55 kW and 270 W under 30.10 kW. It proves that too much or too little working fluid will both

470

reduce the power of the expander. Additionally, it can be found that with the increasing of filling

471

quantity, the maximum expander power point on each curve tends to the less working fluid flow

472

rate area. Taking Fig. 16 (a) for example, the pump electromotor frequency corresponding to the

473

maximum expander power varies from 40 to 30 Hz when filling more working fluid. It can be

474

inferred that, in practical applications, the lack of the working fluid will lead to the performance

475

degradation of ORC system and the pump speed should increase moderately to compensate.

476

However, there’s no doubt that energy consumption of pump will also increase.

250

Expander power output (W)

Expander power with 10 kg Expander power with 20 kg Expander power with 26 kg 200

150

100

0

5

10

15

20

25

30

35

40

45

50

55

45

50

55

Pump electromotor frequency (Hz)

477 478

(a)

300

Expander power output (W)

Expander power with 10 kg Expander power with 20 kg Expander power with 26 kg 250

200

150

0

5

10

15

20

25

30

35

40

Pump electromotor frequency (Hz)

479 480

(b)

481

Fig. 16. Power output with different filling quantities under (a). 23.55kW; (b). 30.10kW.

482

4. Energy loss analysis

483

4.1. Energy and exergy analysis of system

484

Various forms of energy can be converted between each other. Their qualities are discrepant and

485

it can be quantified by exergy. Exergy is defined to describe the maximal theoretical value that can

486

be converted to useful work. Different from energy analysis which is focusing on the quantity,

487

exergy analysis pays attention to the quality of energy. In order to evaluate the efficiency and

488

irreversibility of the system, energy and exergy analyses are introduced according to the first and

489

second laws of thermodynamics.

490

Fig. 17 illustrates the expander power output, electrical energy consumption of pump and net

491

power output with filling quantities 26 kilograms and waste heat 36.31 kW. Corresponding gross/net

492

power thermal efficiency and exergy efficiency of the ORC system are reported in Fig. 18. It can be

493

found that there is no obvious change in gross power thermal efficiency, which means the ratios of

494

heat-work conversion are similar. The net power thermal efficiency reduces gradually with the

495

increasing of pump electromotor frequency because much electrical energy consumed by pump-

496

electromotor. Maximum gross power thermal efficiency and net power thermal efficiency are 2.02%

497

and 1.27%, respectively. For ORC system, the energy is transferred from low quality heat energy to

498

high quality mechanical energy. Exergy efficiency is used to calculate the capacity to transfer from

499

heat exergy into actual mechanical power output. Since it does not take account of the unavailable

500

energy of heat, the values of exergy efficiency are much more than thermal efficiency but similar

501

variation tendencies exist between them. The maximum values, 10.5% and 6.82%, are achieved for

502

the gross power and net power exergy efficiency, respectively.

350

Expander power output Electrical energy consumption of pump Net power output

300

B

A

C

Power (W)

250

200

150

100

50

20

25

35

40

45

50

Pump electromotor frequency (Hz)

503 504

30

Fig. 17. Expander power, electrical energy consumption of pump and net power output.

15% Gross power thermal efficiency Net power thermal efficiency Gross power exergy efficiency Net power exergy efficiency

12%

Efficiency

9%

6%

3%

0% 15

505 506

20

25

30

35

40

45

50

55

Pump electromotor frequency(Hz)

Fig. 18. Thermal efficiency and exergy efficiency of the ORC system.

507

In order to discuss the energy dissipation and exergy loss particularly, three operating conditions

508

(point A, B, C in Fig. 17) are selected for further analysis. The energy dissipations to environment

509

of each component in conditions A, B and C, calculated based on the first law of thermodynamics,

510

are plotted in Fig. 19. The energy dissipations to environment are mainly caused by evaporator,

511

followed by condenser. About 98 % energy of system is lost by the two heat exchangers. In contrast,

512

the energy dissipations of expander and pump are much smaller. In these conditions, the total system

513

energy 30.1-32.3 kW are wasted. Methods to enhance heat transfer performance, adopt regenerative

514

cycle and decrease degree of subcooling at the condenser outlet would be effective to reduce heat

515

loss of heat exchangers.

Energy dissipation of evaporator and condenser (kW)

Evaporator Condenser

20 18 16 14

Expander Pump 56.3%

54.8%

54.0%

43.3%

43.8%

1.6

42.0%

1.2

12 10 8

0.8 2.0% 1.6%

6

1.3%

4 2 0

A

0.4%

0.3%

0.2% B

0.4

C

0.0

Energy dissipation of expander and pump (kW)

2.0

22

516 517

Fig. 19. Energy dissipation of each component in conditions A, B and C.

518 519

The actual temperature-specific entropy (T-s) diagram of cycles A, B and C is shown together in

520

Fig. 20. Entropy is a key parameter to characterize the randomness of system in thermodynamic

521

study. All the actual spontaneous working process is accompanied by entropy increment which

522

causes proportional exergy loss, in other words irreversible loss. The entropy increment of expander

523

can be observed visually in Fig. 20. In addition, for condenser, the entropy of working fluid

524

decreases and resulting in an increase entropy for cooling air. Ultimately, the total entropy of

525

condenser still keeps increasing.

250

ORC in condition A ORC in condition B ORC in condition C

Temperature (℃ )

200

150

Expander Evaporator

Exhaust gas

100

Working fluid

50

Condenser

Pump

Cooling air 0 1.0

1.2

1.4

1.6

1.8

2.0

Specific entropy (kJ/kg-K)

526 527

Fig. 20. Actual temperature-specific entropy (T-s) diagram in conditions A, B and C.

528

According to thermodynamics, all the connections between the investigated system and

529

surroundings can be summarized as: heat, work and mass flow. So the exergy loss of component is

530

calculated based on exergy balance function as Eq. (20) and partition of exergy flows for each

531

individual component are shown in Table 5. Specially, the heat released from evaporator to

532

environment, power output of expander and electric power input of pump need to be considered.

533 534

Table 5

535

Partition of exergy flow for each component. Partition of Evaporator

Condenser

Expander

Pump

0

0

0

0

― 𝑊𝑒𝑥𝑝

𝑊𝑝𝑢𝑚𝑝

exergy flow Exergy flow of heat (𝛥𝐴)𝑄 Exergy flow of

𝑇0

∫(1 ― 𝑇 )𝛿𝑄 0

𝑙𝑜𝑠𝑠

work (𝛥𝐴)𝑊 Exergy flow of mass flow (𝛥𝐴)𝑀

∑(𝛥𝐻 ― 𝑇

0

× 𝛥𝑆)

∑(𝛥𝐻 ― 𝑇

0

× 𝛥𝑆)

∑(𝛥𝐻 ― 𝑇

0

× 𝛥𝑆)

∑(𝛥𝐻 ― 𝑇

0

× 𝛥𝑆)

536 537

Fig. 21 displays the exergy loss of each component. The main contributions of exergy losses are

538

given by evaporator and condenser for all the conditions. Heat transfer process from high

539

temperature to low temperature is the major reason of heat exchangers exergy loss. Combining with

540

the ORC temperature-specific entropy (T-s) diagram in Fig. 20, the larger temperature difference

541

between working fluid and cooling air produces higher condenser exergy loss 1.82kW in condition

542

A. The exergy loss of expander makes up the third proportion with 21.1-23.5%, varying from 0.98

543

kW to 1.01 kW. As for the direct result of overall system exergy loss in conditions A, B and C, it

544

increases from 4.24 to 4.63 kW. The temperature difference for heat-transfer and capacity for heat-

545

work conversion could be optimized to reduce the irreversible loss.

546

By contrasting Fig. 19 and Fig. 21, it can be found that the exergy losses of heat exchangers are

547

much less than energy dissipations because the exergy is only a portion of heat energy. On the

548

contrary, exergy losses of expander and pump are larger than energy dissipation. For one thing, the

549

energy loss of expander and pump comes from useful work, or exergy. For another, the processes

550

of expansion and compression result in extra entropy production and exergy loss.

2.5

Evaporator Condenser 2.0

Exergy loss (kW)

37.9%

Expander Pump 43.6%

43.6%

39.2%

1.5

29.9%

30.6%

1.0

22.8%

23.5%

21.1%

0.5

0.0

A

3.7%

2.3%

1.7%

B

C

551 552

553

Fig. 21. Exergy loss of each component in conditions A, B and C.

4.2. Friction and leakage analysis of expander

554

The results obtained from system exergy loss analysis shows obvious shares of expander exergy

555

loss. The main loss possibilities of expander, friction and leakage, are analyzed by means of

556

simulation in this subsection.

557

Expander power output of unit flow working fluid, defined by Eq. (13), was introduced to discuss

558

the actual work capability of expander carried by the working fluid of the same quality. The

559

influence of expander inlet temperature and evaporating pressure tested with different operating

560

parameters mentioned in subsections 3.2-3.5 are plotted in Fig. 22. As it is described, expander inlet

561

temperature plays a more important role and the effect of evaporating pressure is not obvious. The

562

maximum value 6.03 kJ/kg locates at the point with maximum temperature 152.8 °C.

Expander Power Output of Unit Flow Working Fluid (kJ/kg)

160

6.040 5.537

Expander inlet temperature (°C)

150

5.035 4.532

140

4.030 3.527

130

3.025 2.523

120

2.020

110 100 90 80 0.7

0.8

1.0

1.1

1.2

1.3

1.4

Evaporating pressure (MPa)

563 564

0.9

Fig. 22. Expander power output of unit flow working fluid.

565

Combined with the simulation mode of radial piston expander as Fig. 4, the temperature, pressure

566

of inlet port and expander speed are set on the basis of experimental data. The state of outlet port is

567

extracted to verify the accuracy of model. Through comparing the simulation results and

568

experimental data of all the 84 points mentioned in Fig. 22, the maximum relative error absolute

569

value of outlet port enthalpy is 6.4%. The results indicate that the simulation model of the radial

570

piston expander is reasonable.

571

Shown as Fig. 23, the friction torque of expander is strongly influenced by evaporating pressure.

572

The friction torque increases from 2.44 Nm to 6.38 Nm with the increasing of evaporating pressure.

573

It is no doubt that working fluid with larger evaporating pressure carries more energy to work.

574

However, because of the corresponding increase in stress between moving parts, the resulting

575

frictional torque also increases obviously. Therefore, as shown in Fig. 22, the evaporating pressure

576

plays a minor role in the expander power output of unit flow working fluid. Displayed in Fig. 24,

577

the mechanical efficiency of expander is mainly affected by friction torque and expander actual

578

work capability of unit working fluid. The maximum value of mechanical efficiency is 62.6% in the

579

region of low friction torque.

Friction Torque (Nm)

160

6.400 5.905

Expander inlet temperature (°C)

150

5.410 4.915

140

4.420 3.925

130

3.430 2.935

120

2.440

110 100 90 80 0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Evaporating pressure (MPa)

580 581

Fig. 23. Friction torque of expander.

Mechanical Efficiency (%)

160

62.60 58.91

Expander inlet temperature (°C)

150

55.23 51.54

140

47.85 44.16

130

40.48 36.79

120

33.10

110 100 90 80 0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Evaporating pressure (MPa)

582 583

Fig. 24. Mechanical efficiency of expander.

584

Although low leakage is one of the significant advantages of piston expander, it still makes sense

585

to analyze the consequent influences of expander performance. A single lumped nozzle leakage

586

model is used to calculate the leakage module for each cylinder, and the equivalent leakage area in

587

this module is adjustable to meet the actual measured working fluid flow. As plotted in Fig. 25, the

588

maximum equivalent leakage area of 4.77 mm2 in single cylinder can be gotten in the region of low

589

expander inlet temperature. It may be caused by microscale expansion and contraction of parts at

590

different temperatures. Looking at all the data calculated, the maximum leakage rate is 5.91% which

591

means the expander performance influence of leakage is limited.

160

Equivalent Leakage Area in Single Cylinder (mm2)

4.780 4.182

Expander inlet temperature (°C)

150

3.585 2.987

140

2.390 1.792

130

1.195 0.5975

120

0.000

110 100 90 80 0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Evaporating pressure (MPa)

592 593

594

Fig. 25. Equivalent leakage area in single cylinder.

4.3. Energy degradation of expansion process

595

The duty of expander is to transfer working fluid flow energy into mechanical energy. Energy

596

loss is inevitable due to the difference of energy qualities between them. Fig. 26 shows the energy

597

degradation processes of expansion in condition A, B and C. Theoretical isentropic powers, the

598

largest potential powers under assumed isentropic expansion process, are prominent for each

599

condition. However, due to the irreversibility of the actual expansion process, thermodynamic

600

powers reduce obviously and the largest isentropic efficiency 64.8% is gotten in condition A.

601

Indicated power means the power delivered to the pistons in cylinders which deducts the flow

602

energy loss such as external throttling loss and internal leakage loss. Condition A shows the

603

minimum indicated power on account of the largest inlet volume flow rate 3.36m3/h and largest

604

leakage rate 5.2% occurred in this condition. Actual mechanical power equals to the difference of

605

indicated power and frictional loss. The frictional loss increases from condition A to condition C

606

because of increasing evaporating pressure. Therefore, the mechanical efficiency reduces from

607

condition A 51.0% to condition C 46.5%. In total, the entropy increment leads to the largest energy

608

degradation in all the three conditions. The second largest loss is the flow loss for high flow velocity

609

condition (condition A) and frictional loss for high evaporating pressure condition (condition B and

610

C). Under the influences of multiple factors, the maximum expander mechanical power output 279

611

W can be obtained in condition B. 2000

Power (W)

1500

1000

Theoretical isentropic power Thermodynamic power Indicated power (Simulation) Actual mechanical power 1428

1409

1359

881

785 681

585

569

531

500

279

271

272

Energy degradation (W)

0

612 613

614

-200 -400 -600 -800

Entropy increment loss Flow loss Frictional loss A

B

C

Fig. 26. Energy degradation of expansion in conditions A, B and C.

5. Conclusions

615

This study presents an experimental investigation on an organic Rankine cycle waste heat

616

recovery prototype system with a 5-cylinders radial piston expander and R245fa is selected as

617

working fluid. The energy recovery effects of system were tested with small load working

618

conditions of a diesel engine and the influences of varying operating parameters were evaluated

619

with quantitative method, such as pump speed, generator load, energy of waste heat and working

620

fluid filling quantity. Besides, the energy losses of system were discussed with the method of energy

621

analysis, exergy analysis and simulation. The summarized conclusions are listed as follows:

622

(1) Pump speed would be an effective method to optimize expander power output. More energy

623

of waste heat leads to higher expander power and the suitable pump speed corresponding to

624

maximum expander power output tends to increase with more waste heat. Under the same

625

waste heat, the maximum expander power can be gotten with moderate filling quantity 20

626

kilograms but the price is relative higher pump speed.

627

(2) In the range of discussion, the ratios of heat-work conversion are similar with different pump

628

speeds. The maximums of gross power thermal efficiency and exergy efficiency are 2.02%

629

and 10.5%. The exergy loss of system is mainly caused by evaporator and condenser. For

630

expander, it contributes 21.1-23.5% of the overall system exergy loss which is much higher

631

than its proportion of energy dissipation.

632

(3) Expander inlet temperature is the key state parameter to expander power output of unit flow

633

working fluid and the maximum 6.03 kJ/kg can be gotten. Combining simulation study of

634

expander, the friction torque of expander varies from 2.44 Nm to 6.38 Nm with the increasing

635

of evaporating pressure and low leakage of piston expander can be proved. In the whole

636

processes of expansion, entropy increment leads to larger energy degradation than working

637

fluid flow loss and mechanical frictional loss. Finally, the expander achieves maximum

638

power output 279 W with all kinds of energy losses.

639 640

In this experimental study, the expander, pump-electromotor and heat exchangers were refitted

641

from industrial grade products which means the efficiency would be relatively low to be used in

642

automobile. In further study, the dedicated expander for organic Rankine cycle system with

643

excellent high temperature and pressure resistance, low friction and throttle loss, high expansion

644

ratio and isentropic efficiency should be researched. Furthermore, method to enhance heat transfer

645

performance of evaporator and recycle the heat release of condenser should also be adopted.

646

Acknowledgements

647

This work was supported by the Technology Development Program of Jilin Province [grant

648

numbers 20180519005JH]; the Science Fund of State Key Laboratory of Engine Reliability [grant

649

numbers skler-201706]; and the Graduate Innovation Fund of Jilin University [grant number

650

2017125].

651

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