Feasibility analysis and performance characteristics investigation of spatial recuperative expander based on organic Rankine cycle for waste heat recovery

Feasibility analysis and performance characteristics investigation of spatial recuperative expander based on organic Rankine cycle for waste heat recovery

Energy Conversion and Management 121 (2016) 335–348 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www...

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Energy Conversion and Management 121 (2016) 335–348

Contents lists available at ScienceDirect

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

Feasibility analysis and performance characteristics investigation of spatial recuperative expander based on organic Rankine cycle for waste heat recovery Yongqiang Han ⇑, Runzhao Li, Zhongchang Liu, Jing Tian, Xianfeng Wang, Jianjian Kang State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130025, China

a r t i c l e

i n f o

Article history: Received 20 January 2016 Received in revised form 22 April 2016 Accepted 16 May 2016

Keywords: Spatial recuperative expander Variable expansion ratio Organic Rankine cycle Waste heat recovery

a b s t r a c t This paper proposes a new concept of spatial recuperative expander which injects cold refrigerant during exhaust stroke as a measure of direct contact heat transfer. The commercial simulation tool GT-SUIT 7.4 is employed to model and verify the feasibility of spatial recuperative expander. The research contents are comprised of the following aspects: Firstly, the principles and performance characteristics between traditional reciprocating piston expander and spatial recuperative expander have been investigated. Secondly, the potential of spatial recuperation by adjusting cold refrigerant injection timing has been studied. Thirdly, the relation between expander performance and variable expansion ratio under constant operating condition has been discussed. Fourthly, the thermodynamic performance of spatial recuperative expander under various operating conditions has been examined. The simulation results indicate that: Firstly, the torque per unit mass, thermal efficiency, exergetic efficiency, isentropic efficiency and recuperative efficiency of optimum spatial recuperative expander are 51.00%, 6.74%, 20.79%, 5.68% and 11.36% higher than traditional reciprocating piston expander respectively. Secondly, the cold refrigerant injection timing has little influence on recuperative efficiency because the recuperation process can complete within 16.67 ms. Thirdly, different operating conditions correspond to particular optimal expansion ratio. Fourthly, increasing the pump pressure and maintaining appropriate superheated degree can reconcile both power output and thermal economy. While increasing the refrigerant temperature and preserving suitable pump pressure could benefit both recuperative performance and power output. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Low and mediate grade waste heat which reject from conventional thermal power plant, metallurgical plant, cement plant should be utilized efficiently by various technologies, such as turbocompounds, Rankine cycle (RC)/organic Rankine cycle (ORC), combined heat and power (CHP) and thermoelectric generators. Particularly, ORC is an effective measure to recover low grade waste heat for high efficiency and reliability. The selection of heat source, cold sink, refrigerant, types and parameters of expander are the critical task in constructing the entire ORC system [1]. Expander exerts a strong influence on ORC efficiency besides working fluid properties [2–4] because it is the convertor that transforms thermal energy into mechanical work. Generally, the expander types can broadly divide into five categories: (1) reciprocating piston expander, (2) turbine expander, (3) scroll expander, ⇑ Corresponding author. E-mail address: [email protected] (Y. Han). http://dx.doi.org/10.1016/j.enconman.2016.05.042 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

(4) rotary vane expander, (5) swash plate expander. All of them belong to displacement expander except turbine expander. From the first category, reciprocating piston expander is more suitable for on-road vehicle because exhaust temperature usually undergoes wide range fluctuation. Reciprocating piston expander could achieve high expansion ratio to elevate power output and thermal efficiency. Furthermore, it could tolerate droplets formation during expansion process which is superior to impulse turbine [1,5–7]. Yun et al. [8] investigated the effect of arranging two expanders in parallel to enhance the system flexibility for heat source variation. They alleged that parallel expander used in ORC (PE-ORC) has a potential to obtain higher power output and thermal efficiency than traditional ORC configuration. Daccord et al. [1] developed an axial piston expander free of oil lubrication and built the relevant expander test bench. They declared that oil-free axial piston expander is capable of dealing with droplets even under high expansion ratio (>12). They also certified that expander performance enhances with increasing expansion ratio.

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Nomenclature cp cv D E_ x;hot hhot;0 hhot;1 hcold;2 hout;3 hout;3s L mhot _ hot;1 m _ cold;2 m Poutput Q_ hot;1

Q_ rec R S shot;0

specific heat at constant pressure (kJ/(kg K)) specific heat at constant volume (kJ/(kg K)) cylinder diameter (mm) the exergy rate of hot refrigerant (kJ/s) specific enthalpy of hot refrigerant if it was cooled down to the ambient temperature (kJ/kg) specific enthalpy of hot refrigerant (kJ/kg) specific enthalpy of cold refrigerant (kJ/kg) specific enthalpy of outlet refrigerant (kJ/kg) specific enthalpy of outlet refrigerant after undergoing an isentropic expansion process (kJ/kg) connecting rod length (mm) the integrated mass flow rate of hot refrigerant (kg) mass flow rate of hot refrigerant (kg/s) mass flow rate of cold refrigerant (kg/s) average power output per cycle (kW) the heat delivered by hot refrigerant in the expander (kJ/kg) the recuperative thermal energy (kJ/kg) crank radius (mm) stroke (mm) specific entropy of hot refrigerant if it was cooled down to the ambient temperature (kJ/(kg K))

Even though conventional piston expanders have made enormous strides in the last few years, researchers still put forth some innovative ideas. For example, Chiong et al. [9] presented a new concept of expansion device which adopts nozzle as a portion of secondary steam cycle. They announced that nozzle piston expander has the potential to increase the power output up to 4.75 kW which is nearly seven times higher than conventional expander. From the second category, impulse turbine has attracted extensive attention due to its high isentropic efficiency and compact design for optimum utilization of space [10,11]. However it cannot bear droplet formation during expansion process which largely constraints thermal efficiency improving [4,12]. Turbine is generally adopted as expander in large-scale Rankine cycle systems [13]. From the third category, scroll expander is also one of the popular expansion devices which usually acts as turbine alternative in small and micro ORC. Because it has relatively high efficiency and the capacity to tolerate droplets [13–15]. However, the low expansion ratio (<5) in a single stage leads to a poor power output [16]. From the fourth category, there are some important advantages of vane expander: high gravimetric specific power, adaptable to wet gas condition and cost effective [17,18]. However, there are no ORC-dedicated vane expanders available. Modified and specially adapted vane expanders are often applied as expansion device in small scale ORC systems [17]. From the fifth category, Galindo et al. [19] investigated the physical parameters influence of the swash-plate expander prototype. They indicated that the real Rankine cycle efficiency is two thirds lower than the maximum theoretical efficiency. However, the major researches about swash-plate expander are still under theoretical investigation. It would take quite a long time to construct mature technique and stable products quality. In summary, reciprocating piston expander is particularly suitable for automotive waste heat recovery and its advantages list as below: 1. Both high power output and thermal efficiency thanks to high expansion ratio (>12). 2. The capacity to handle droplet.

shot;1 T0 T tq T tq;per V0 X

unit

specific entropy of hot refrigerant at expander inlet end (kJ/(kg K)) ambient temperature (K) average torque per cycle (N m) mass torque per unit mass (N m/kg) clearance volume (L) piston position (mm)

Greek letters a hot refrigerant injection timing (°CA) l the ratio of crank radius to connecting rod length q expansion ratio gex expander exergetic efficiency gis;expander the isentropic efficiency of expander grec expander recuperative efficiency gth expander thermal efficiency Abbreviations CHP combined heat and power ORC organic Rankine cycle PE-ORC parallel expander used in organic Rankine cycle RC Rankine cycle

3. Suitable for low mass flow rate. 4. Low and mediate operating speed (<3000 rpm). 5. A simple design and sealing due to relatively low gas pressure and rotational speed. As a result, piston expander would be adopted as the main research subject in this paper. As is well known, adopting recuperator or preheater in ORC system would help improve cycle efficiency and reduce the load of evaporator [20–23]. Yekoladio et al. [20] considered four types of configurations including basic ORC, recuperative ORC, regenerative ORC and regenerative couple recuperative ORC. They claimed that the large temperature difference between heat source and working fluid would cause considerable exergetic destruction. In other words, the various levels of heat source should be utilized at appropriate stages in ORC system. Hence, both recuperation and regeneration are usually taken into consideration in actual application. However, this would increase the system complexity and cost correspondingly which hinders the extensive use in automobile. So it is necessary to simplify the construction of ORC system. This paper presents a spatial recuperative expander to perform waste heat recovery from exhaust. The simulation model is established and verified by software GT-SUITE 7.4. The framework of this paper is shown in Fig. 1. The main contributions of this work list as follows: 1. A new concept of spatial recuperative expander with variable expansion ratio for waste heat recovery has been presented. 2. The power output, thermal economy as well as recuperative performance of spatial recuperative expander under various operating conditions have been investigated. 3. A comprehensive comparison between spatial recuperative expander and traditional reciprocating piston expander has been carried out. 4. Comparative study shows that spatial recuperative expander can achieve better power output and energy conversion efficiency than traditional reciprocating piston expander.

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System flexibility of ORC system

System complexity of ORC system

Problem Expander

Solution

Spatial recuperative ORC

Spatial recuperative expander

Output power

Indicator types

Evaluation indexes

Research contents

Recuperator

Torque per unit mass

Thermal efficiency

Torque

Comparison between spatial recuperative expander and traditional expander

Recuperative performance

Thermal economy

Recuperative performance

Exergetic efficiency

Isentropic efficiency

Variable expansion ratio under normal working condition

Recuperative efficiency

Expander performance under various working conditions

Fig. 1. Framework of the article.

2. Methodology and assumption In the following sections the spatial recuperative expander model would be carefully described and established by GT-SUIT 7.4. Then the established model would be verified from the perspectives of mechanical characteristics and in-cylinder refrigerant state change. Furthermore, six assessment indicators would be introduced in order to evaluate the performance between spatial recuperative expander and traditional expander. And these indexes would be utilized in the subsequent sections. 2.1. Model establishment In this section a spatial recuperative expander model is developed based on ORC. The entire technical configuration of spatial recuperative ORC is shown in Fig. 2. The simulation model mainly focuses on the spatial recuperative expander which as shown in Fig. 3. The specification of spatial recuperative expander lists in Table 1. The main distinguishing characteristic between spatial recuperative expander and traditional expander is that spatial recuperative expander injects cold refrigerant into cylinder during exhaust stroke. As a result, the technical configuration of spatial recuperative ORC is different from traditional ORC. Hot refrigerant injects into cylinder (from ①) during expansion stroke, the high temperature and pressure refrigerant expands as piston moving down to bottom dead center. Expander converts thermal energy to mechanical work during expansion stroke. Cold refrigerant injects into cylinder during exhaust stroke, the hot refrigerant transfers heat to cold refrigerant which plays a role of spatial recuperation. Meanwhile, the hot refrigerant is liquefied by abundant amount of cold refrigerant that may also decrease the push negative work during the refrigerant discharge process. After the fluid exits cylinder through the solenoid valve (③–④), it flows into two directions (⑤ and ⑩). One portion enters the cold refrigerant loop through cold refrigerant solenoid valve (④–⑩) then is cooled to specific temperature at the condenser (⑩–⑪). The cold refrigerant is pressurized to particular pressure by pump (②–③). The other portion enters the hot refrigerant loop through the hot refrigerant solenoid (④–⑤), then is pressurized to a particular value by the pump (⑥–⑦]). Subsequently, refrigerant goes through the preheater and evaporator under constant pressure process (⑦–⑧–⑨). The refrigerant is heated to particular temperature and pressurized to specific

pressure before entering the expander (⑨–①). During the expansion process, the high temperature and pressure refrigerant injects at a particular timing to acquire required expansion ratio. Until now, the refrigerant undergoes a cyclic process. The thermodynamic properties of refrigerant at these points (from ① to ⑬) are given in Table 2. 2.2. Model validation Before applying the model to perform simulation experiments, the feasibility of this model should be verified first. The model validation is carried out mainly through monitoring mechanical characteristics (crank speed, torque, piston position) and in-cylinder refrigerant state change (refrigerant mass flow rate, dryness fraction and density). From the perspective of mechanical characteristics, since the target crank speed sets as 1500 rpm so the initial speed of dynamometer sets as 1500 in order to minimize the speed oscillation period. The operating condition in model validation is shown in Table 3. The distinct differences between spatial recuperative expander and traditional expander are in bold and underlined. Fig. 4 manifests the crank speed and output torque of initial 30 cycles, the crank speed is moving toward stabilization after the initial four cycles. The shapes of output torque per cycle are basically the same, the slightly differences are mainly due to the minor variation of refrigerant quality injected into the cylinder. Fig. 5 reveals refrigerant mass flow rate of inlet and outlet end during initial 15 cycles. The hot refrigerant injects into cylinder at top dead center and the injection duration is 40 °CA. Owing to the hot refrigerant is superheated steam, the mass flow rate is an order of magnitude less than the cold or outlet refrigerant mass flowrate. According to the experimental results, hot refrigerant can be liquefied rapidly at major operating conditions when the quantity of subcooled refrigerant is six times greater than hot refrigerant. The main effect of cold refrigerant injection can divide into two groups: Firstly, hot refrigerant is liquefied by cold refrigerant that releases latent heat of vaporization. The subcooled refrigerant undergoes heat absorption and temperature increase by direct contact heat exchange with superheated steam. In other words, the expander also acts as recuperator during exhaust stroke which is the reason why called spatial recuperative expander. Secondly, even though the outlet valve opens at bottom dead center, piston moving upwards may pay push work unavoidably due to vapor pressure in cylinder. Once adequate amount of cold refrigerant

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After-treatment

T

C

Cooling water out

Tank

8

Engine exhaust

7 Preheater

6 Pump

Hot refrigerant loop

Evaporator

5 Hot refrigerant solenoid valve 4

Charge air cooler loop

Cooling water in

EGR coolant loop

Cold refrigerant loop 9

13 11

12

EGR valve

Cold refrigerant solenoid valve 10

Tank Solenoid valve 1

3

2

Pump

Condenser

Nozzle

Reciprocating expander

Simulation model

Fig. 2. Schematic of ORC system.

injects into cylinder to liquefy the hot refrigerant, refrigerant state transforms from vapor to subcooled liquid. As long as the hot refrigerant liquefaction rate outstrips cylinder volume decrease rate, spatial recuperative expander pays less push work during exhaust stroke than traditional expander. The stroke of the cylinder is 72 mm and the top dead center and bottom dead center set as 72 mm and 0 respectively. The piston position shown in Fig. 6 reveals that the piston is in good working order. The curve of dryness fraction demonstrates that the hot refrigerant injects into cylinder at top dead center and keeps vapor state throughout expansion stroke. An abundant amount of cold refrigerant injects into cylinder at bottom dead center, refrigerant vapor liquefies gradually during exhaust stroke. Fig. 7 reveals the distinction of refrigerant density between spatial recuperative expander and traditional expander. Superheated refrigerant begins to inject into cylinder at top dead center (0 °CA) and the injection duration is 40 °CA for spatial recuperative expander. Since the clearance volume of spatial recuperative expander is much smaller than traditional expander, so that the refrigerant density is higher at the initial 40 °CA. At the bottom dead center (180 °CA) subcooled refrigerant begins to inject and the duration is 90 °CA. As shown in Fig. 7 the vapor liquefies completely at 270 °CA which is consistent with the hypothesis of spatial recuperative expander. Above all, for both mechanical characteristics and in-cylinder refrigerant state change, there is a good agreement between the values of parameters and practice.

2.3. Performance evaluation indexes There is an optimal expansion ratio to specific operating condition regardless of traditional expander or spatial recuperative expander. That makes it necessary to calculate expansion ratio according to hot refrigerant injection timing. The expansion ratio q is calculated by Eq. (1).



V 0 þ 0:25pD2 S

V 0 þ 0:25pD2 X

ð1Þ

In order to calculate the expansion ratio q, the following parameters would be needed: clearance volume V 0 , cylinder diameter D, stroke S and piston position X. The piston position X is calculated by Eq. (2).

X ¼ R½ð1  cosaÞ þ 0:25lð1  cos2aÞ

ð2Þ

In the above equation the factors X, R, L, l and a stand for the piston position, crank radius, connecting rod length, the ratio of crank radius to connecting rod length and hot refrigerant injection timing respectively. Generally, the expander operates under wide range operating conditions that leads to different refrigerant mass flow into cylinder. So it is necessary to introduce an indicator to evaluate the output power from the same datum level. The output torque produce by a unit mass of hot refrigerant is defined as Eq. (3) [24]:

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Fig. 3. Spatial recuperative expander model based on GT-SUIT 7.4.

Table 1 The specifications of spatial recuperative expander.

Table 2 Thermodynamic propertiesa of refrigerant from ① to ⑬.

Items

Value/description

Point

Temperature (°C)

Pressure (bar)

Engine configuration Target crank speed (rpm) Bore (mm) Stroke (mm) Crank radius (mm) Connecting rod length (mm) Working fluid

Single cylinder 1500 60 72 36 150 R123

① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬

200 50 80 80 80 80 80 120 200 80 50 50 50

30 36 5 5 5 5 30 30 30 5 5 5 36

T tq;per

unit mass

¼

T tq mhot

ð3Þ

T tq;per unit mass , T tq and mhot denote torque per unit mass, average torque per cycle and integrated mass flow rate of hot refrigerant respectively. The isentropic efficiency of the expander indicates the deviation of the actual expansion process that take place from the theoretical isentropic expansion process. The isentropic efficiency of expander is given by Eq. (4) [24,25]:

gis;expander ¼

hhot;1  hout;3 hhot;1  hout;3s

ð4Þ

a The thermodynamic properties of these points vary according to specific operating condition.

gis;expander ; hhot;1 , hout;3 and hout;3s identify the expander isentropic efficiency, specific enthalpy of hot refrigerant, specific enthalpy of outlet refrigerant and specific enthalpy of outlet refrigerant after undergoing an isentropic expansion process respectively. The heat delivered from the working fluid in the expander Q_ hot;1 is given by Eq. (5) [20,24–27]:

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Table 3 Operating conditions between spatial recuperative expander and traditional expander. Item

Case

Spatial recuperative expander

Traditional expander

Hot refrigerant

Temperature (°C) Pressure (bar) Injection timing (°CA) Duration (°CA) Total mass (kg)

200 30 0 40 0.0011948001

200 30 0 30 0.0018805421

Cold refrigerant

Temperature (°C) Pressure (bar)

50

0

36

Injection timing (°CA)

180

0 –

Duration (°CA) Total mass (kg)

90 0.038631007

0 0

Temperature (°C) Pressure (bar) Exhaust valve open (°CA) Duration (°CA) Total mass (kg)

80 5 180 180 0.039826035

80 5 180 180 0.0018805433

0.0001

0.01

Outlet refrigerant

Clearance volume

_ hot;1 ðhhot;1  hout;3 Þ Q_ hot;1 ¼ m

ð5Þ

_ hot;1 represent the heat deliver by hot refrigerant in the Q_ hot;1 and m expander and mass flow rate of hot refrigerant. The thermal efficiency of spatial recuperative expander gth is utilized to evaluate the waste heat exploitation degree. It is equal to the average output power per cycle Poutput divided by the heat delivered by hot refrigerant in the expander Q_ hot;1 , as shown in Eq. (6) [20,24–27]:

Fig. 6. In-cylinder dryness fraction and piston position.

Fig. 4. PID control result.

Fig. 7. In-cylinder refrigerant density between spatial recuperative expander and traditional expander.

P

gth ¼ _output Q hot;1

Fig. 5. Refrigerant mass flow rate of inlet and outlet end.

ð6Þ

The energy balance can be accounted for the first law of thermodynamics using thermal efficiency. However, as the target of spatial recuperative expander is to recuperate the thermal energy

Y. Han et al. / Energy Conversion and Management 121 (2016) 335–348

without assembling additional recuperator. As a result, the recuperative efficiency of spatial recuperative expander grec needs to be defined. It equals to the heat recuperated from the hot refrigerant in the expander Q_ rec divided by the total enthalpy including hot

_ cold;2 hcold;2 , as shown in Eq. (7) _ hot;1 hhot;1 þ m and cold refrigerant m [28]:

Q_

_ m

ðh

h

Þ

rec out;3 cold;2 cold;2 grec ¼ _ ¼ _ cold;2 hcold;2 m _ cold;2 hcold;2 _ hot;1 hhot;1 þ m mhot;1 hhot;1 þ m

ð7Þ

_ cold;2 , hhot;1 , hcold;2 and hout;3 represent mass flow rate of hot _ hot;1 ;, m m refrigerant, mass flow rate of cold refrigerant, specific enthalpy of hot refrigerant, specific enthalpy of cold refrigerant and specific enthalpy of outlet refrigerant respectively. Even though the first law of thermodynamics illuminates the transformation of energy forms, it does not take the inherent qualitative difference between heat and mechanical work into account. The energy forms transformation from heat to mechanical work is an energy quality upgrading process, it must have a downgrading process as compensation to satisfy the second law of thermodynamics. The exergy is defined as theoretical maximum useful work that could be produced if the system is brought into equilibrium with its surroundings. The exergy rate of hot refrigerant E_ x;hot is given by Eq. (8) [20,24–26]:

_ hot;1 ½ðhhot;1  hhot;0 Þ  T 0 ðshot;1  shot;0 Þ E_ x;hot ¼ m

ð8Þ

_ hot;1 ; hhot;1 , hhot;0 , T 0 , shot;1 and shot;0 represent mass flow rate of hot m refrigerant, specific enthalpy of hot refrigerant, specific enthalpy of hot refrigerant if it was cooled down to the ambient temperature, ambient temperature, specific entropy of hot refrigerant at expander inlet end and specific entropy of hot refrigerant if it was cooled down to the ambient temperature respectively. The exergetic efficiency of expander gex is defined as the ratio of average output power per cycle P output to hot refrigerant exergy rate E_ x;hot , given by Eq. (9) [20,24–26]:

P

gex ¼ _output Ex;hot

ð9Þ

Above all, six evaluation parameters have been introduced including T tq , T tq;per unit mass , gth , gex grec and gis;expander . These parameters can mainly divide in three categories: Firstly, total torque T tq and torque per unit mass T tq;per unit mass describe the power output of the expander. Secondly, the thermal efficiency gth and exergetic efficiency gex represent the thermal economy of expander. Thermal economy [29–32] is the subject that the thermodynamics is associated with the economics. It considers energy with not only its ‘‘quantity” (thermal efficiency), but also its ‘‘quality” (exergetic efficiency) as well. The energy analysis and exergy analysis are the fundamental of thermal economy. Thermal efficiency evaluates the waste heat exploitation degree from the perspective of energy conversion and exergetic efficiency describes the perfection degree of heat-work conversion process from the perspective of exergy destruction. Both of them constitute the evaluation indexes of thermal economy. Thirdly, the recuperative efficiency grec and isentropic efficiency gis;expander assess the recuperative performance. These indexes are used for judging expander performance under various working conditions. For more detail information about Eq. (3)–(9) please refer to published literatures [20,24–28]. 3. Results and discussion There are four research contents would be discussed: Firstly, the distinctions of principles as well as performance characteristics between traditional expander and spatial recuperative expander would be compared. Secondly, spatial recuperative performance refer to various cold refrigerant injection timing would be

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analyzed. Thirdly, the effect of variable expansion ratio would be investigated. Fourthly, the performance of spatial recuperative expander under various operating conditions would be examined. 3.1. Comparison between traditional expander and spatial recuperative expander In this section the distinction between traditional expander and spatial recuperative expander would be discussed. Six cases which represent different working conditions would be introduced and the boundary conditions are shown in Table 4. The distinct differences among various operating conditions are in bold and underlined. Case 1 represents the traditional expander with 0.01 L clearance volume, while case 2 describes the spatial recuperative expander which injects cold refrigerant at the exhaust stroke with identical specifications of case 1. Case 3 and case 4 represent spatial recuperative expander with reduced clearance volume (0.0001 L). The cold refrigerant injection pressure of case 3 and case 4 is 30 and 36 bar respectively which aim at ensuring vapor liquefies quickly and completely. In case 5 the cold refrigerant injection duration prolongs from 60 °CA to 90 °CA. Since the vapor liquefaction may help reduce push work during exhaust stroke, it is interesting to investigate if it may help further improve power output. The cold refrigerant pressure in case 2, 3, 4, 5, 6 are relatively high (30 or 36 bar) which would reduce cyclic net work output for pump work consumption. In case 6 the cold refrigerant injection pressure drops to 5 bar in order to investigate if the expander performance would deteriorate. Case 1 and case 2 represent the traditional expander without cold refrigerant injection and spatial recuperative expander with cold refrigerant injection respectively. The cold refrigerant conducts direct contact heat exchange with hot refrigerant in cylinder which called spatial recuperation. It can replace external recuperator to save installation space. On the other hand, as the large amount of cold refrigerant injects into cylinder which could accelerate hot refrigerant liquefaction. If the hot refrigerant liquefaction rate is superior to cylinder volume decrease rate that may lead to reduction of push work consumption. This is because the vapor pressure at the exhaust stroke is the main source of push work consumption in traditional expander. Sufficient cold refrigerant is needed to ensure the hot refrigerant being liquefied completely. Hence, the cold refrigerant injection pressure of case 2 sets as 36 bar. However, the experimental results of case 1 and case 2 go counter to the hypothesis. From the perspective of power output, the torque per unit mass of case 2 declines 70.74% comparing to case 1 as shown in Fig. 8(a). From the perspective of thermal economy, the thermal efficiency and exergetic efficiency of spatial recuperative expander all inferior to case 1 which represents traditional expander. It means that spatial recuperative expander in case 2 has poor energy conversion efficiency from thermal energy to work. In addition, case 2 does prove that the expander with cold refrigerant injection can recuperate internal thermal energy through direct contact heat exchange. The reason why the power output and thermal economy of spatial recuperative expander contrary to expectation is that the liquid state refrigerant residual from last cycle has negative effects on hot refrigerant expansion ability. The clearance volume for both cases is 0.01 L which means that there are always 0.01 L residual refrigerant in cylinder from previous cycles. Actually, this scale of clearance volume has little effect on traditional expander. However, this scale of clearance volume for spatial recuperative expander is unacceptable. Because a part of superheated refrigerant is liquefied by these residue that have not been used in producing work. As a result, case 3 and case 4 are introduced to investigate the effects of clearance volume on spatial recuperative expander which sets as 0.0001 L. The difference between case 3 and case 4 is the pump

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Table 4 Operating conditions of the six cases. Item

Case

1

2

3

4

5

6

Hot refrigerant

Temperature (°C) Pressure (bar) Injection timing (°CA) Duration (°CA) Total mass (kg)

200 30 0 40

200 30 0 40

200 30 0 40

200 30 0 40

200 30 0 40

200 30 0 40

0.0018832978

0.0026636894

0.0011966004

0.0011969896

0.0011959608

0.001322089

Cold refrigerant

Temperature (°C) Pressure (bar)

0

50

50

50

50

50

0 180

36 180

30 180

36 180

36 180

5 180

Total mass (kg)

0 0

60 0.038200747

60 0.023305006

60 0.02579529

90 0.038630858

90 0.010645409

Temperature (°C) Pressure (bar) Exhaust valve open (°CA) Duration (°CA) Total mass (kg)

80 5 180 180 0.0018833017

80 5 180 180 0.04085465

80 5 180 180 0.024500838

80 5 180 180 0.02699186

80 5 180 180 0.039826326

80 5 180 180 0.010930522

0.01

0.01

0.0001

0.0001

0.0001

0.0001

Injection timing (°CA) Duration (°CA)

Clearance volume (L)

64

Case1 Case3 Case5

6000 48

Efficiency (%)

5000

4000

3000

Case2 Case4 Case6

32

16 2000

1000

0

Torque per unit mass

(b)

Torque (N-m)

Torque per unit mass (N-m/kg)

(a) 7000

Isentropic efficiency

Thermal Recuperative Exergetic efficiency efficiency efficiency

9

3.0

8

2.5

7

2.0

Mass (10-3kg)

Outlet refrigerant

6

1.0

4

0.5

Output torque

Case2 Case4 Case6

1.5

5

3

Case1 Case3 Case5

0.0

Hot refrigerant mass

Fig. 8. Comparison between traditional expander and spatial recuperative expander.

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pressure of cold refrigerant, this would influence the total mass of cold refrigerant into cylinder. As shown in Fig. 8(a) and (b) the performances of case 3 and case 4 are nearly the same because the cold refrigerant injection has little impact on expansion process on the premise of small clearance volume. Furthermore, the gross mass of cold refrigerant have little influence on power output if the gross mass beyond particular threshold value (which make hot refrigerant liquefied completely). Taking case 4 and case 2 as a contrast, it reveals that the clearance volume has a great impact on spatial recuperative expander. The smaller the clearance volume, the better performance spatial recuperative expander can achieve. These stem from the fact that hot refrigerant have to pay a portion of thermal energy to heat up the residue that ought to expand to produce work originally. The less residual refrigerant from last cycle, the more thermal energy can be used to convert into mechanical work. It deserves to note that the residue density of spatial recuperative expander is much greater than those in traditional expander because they are liquid and vapor state respectively as depicts in Fig. 7. So spatial recuperative expander has much more residue than traditional expander even at the same clearance volume which causes serious performance deterioration. It is interesting to research on whether a large amount of cold refrigerant injection into cylinder could further help reduce push work during exhaust stroke. The boundary conditions of case 5 are identical to case 4 except the injection duration prolong from 40 °CA to 90 °CA. As illustrated in Fig. 8(a) and (b), further extend the injection duration does not improve the torque per unit mass, thermal efficiency and exergetic efficiency even though it does slightly elevate the recuperative efficiency. As described in case 3, case 4 and case 5, although the spatial recuperative expander can do an excellent work to produce work and recuperate internal thermal energy. However, the cold refrigerant injection pressure in those three cases are 30 or 36 bar which definitely consume a large amount of pump work. So in case 6 the cold refrigerant injection pressure sets as 6 bar. In case 6 slightly slowdown in torque per unit mass, thermal efficiency, recuperative efficiency and exergetic efficiency are observed. Nevertheless, the gain in pump work reduction may compensate the decline in thermal efficiency and exergetic efficiency when take entire ORC system into consideration. Since the clearance volume of spatial recuperative expander is much smaller than traditional expander, the total mass of hot refrigerant injects into cylinder is fewer than the counterpart. As a result, the total torque output of spatial recuperative expander (such as case 3, 4, 5, and 6) is less than traditional expander (case 1) as shown in Fig. 8(b). Therefore, it is necessary to increase the total mass of hot refrigerant into cylinder to compensate the loss of total power output. Some measures could be taken such as increasing pump pressure, prolonging hot refrigerant injection duration. From what has been discussed above, the conclusions may safely draw that: Firstly, the torque per unit mass, torque, thermal efficiency, exergetic efficiency, isentropic efficiency and recuperative efficiency between traditional expander and optimum spatial recuperative expander are 4603.07 N m/kg vs 6950.65 N m/kg, 8.67 N m vs 8.32 N m, 13.21% vs 19.95%, 40.76% vs 61.55%, 54.53% vs 60.21% and 0% vs 11.36% respectively. Secondly, clearance volume has great influence on power output and thermal economy of spatial recuperative expander. If spatial recuperative expander is adopted, the clearance volume should be as small as possible. Otherwise, expander performance would deteriorate seriously. Thirdly, cold refrigerant injection influences expander performance by reducing push work during exhaust stroke and altering hot refrigerant state due to residue remain in the clearance volume. Fourthly, a sharp reduction of cold refrigerant pressure

would lead to further drop down of power output and thermal economy. However, the saved pump work may compensate the performance degradation of spatial recuperative expander when taking entire ORC system into account. Fifthly, relatively small clearance volume of spatial recuperative expander may decrease total mass of hot refrigerant into cylinder which causes total output power diminishment. It is necessary to increase the amount of hot refrigerant into cylinder to compensate the loss of total power output. The advantages of spatial recuperative expander comparing to traditional expander are as follow: 1. The configuration of ORC system can be simplified by combining the function of conventional piston expander and recuperator. 2. The power output, thermal economy and recuperative performance increase in varying degrees comparing with traditional expander. 3. The flexibility of ORC system enhances which can easily switch modes between basic ORC and recuperative ORC by adopting cold refrigerant injection.

3.2. Analysis of spatial recuperative performance Spatial recuperative expander changes hot refrigerant injection timing to acquire target expansion ratio and alters cold refrigerant injection timing to reach a reasonable compromise between power output and recuperative performance. In this section the cold refrigerant injection timing sweeps from 130 °CA to 270 °CA at 10 °CA interval. The operating condition lists in Table 5. Fig. 9(a) demonstrates that changes of cold refrigerant injection timing have little influence on recuperative efficiency and isentropic efficiency. This is because mixture perform heat transfer in the whole space of the cylinder which is similar to infinite heat exchange area. As a result, the spatial recuperative expander can perform recuperation in a short time. However, when cold refrigerant injection timing retards until 250 °CA, the curves begin oscillate seriously. This may cause by the overlap of cold refrigerant inlet valve and outlet valve occurs at the end of each cycle. As shown in Fig. 9(b), the torque per unit mass increases from 120 °CA to 150 °CA then decreases gradually until 200 °CA. Above 200 °CA this curve drops down rapidly. This phenomenon indicates that slightly advance the cold refrigerant injection timing before bottom dead center help improve power output. This may associate to the further reduction of push work during exhaust stroke which compensates the loss of expansion work. As the piston move downwards near the bottom dead center, the steam in the cylinder has almost fully expanded. The steam pressure is relatively low to produce

Table 5 Operating condition. Item

Case

Value

Hot refrigerant

Temperature (°C) Pressure (bar) Injection timing (°CA) Duration (°CA)

200 30 0 40

Cold refrigerant

Temperature (°C) Pressure (bar) Injection timing (°CA) Duration (°CA)

50 36 Sweep 90

Outlet refrigerant

Temperature (°C) Pressure (bar) Exhaust valve open (°CA) Duration (°CA)

80 5 180 180

Expander

Clearance volume (L)

0.0001

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Fig. 9. The torque per unit mass and isentropic index with respect to various cold refrigerant injection timing.

work but is relatively high to consume push work during exhaust stroke. Therefore, slightly advance cold refrigerant injection timing before bottom dead center can improve power output and thermal economy. Since the isentropic index is inversely proportional to temperature, so the average cycle temperature falls below the minimum value when cold refrigerant injects near bottom dead center (such as 180–220 °CA). Fig. 10(a) depicts dryness fraction with various cold refrigerant injection timing range from 120 °CA to 270 °CA with 10 °CA interval. Even though vapor liquefies completely in these cases, the liquefaction durations are different. When cold refrigerant injection timing is 150 °CA and 270 °CA, the liquefaction duration is 135 °CA and 40 °CA respectively. The liquefaction duration of early injection timing (near bottom dead center) is usually 100 °CA longer than late injection timing (such as 250–270 °CA). In other words, the spatial recuperation process could be completed within 16.67 ms. Fig. 10(b) manifests that a sudden drop in refrigerant temperature as the cold refrigerant injects into cylinder. According to Fig. 10(a) and (b), liquefaction process characterizes that vapor temperature undergoes a significant downwards instantaneously due to abundant amount of subcooled refrigerant injects into cylinder. However, refrigerant state changes does not respond instantly. Refrigerant transforms from vapor to liquid gradually. Besides, the more advance of cold refrigerant timing, the longer the liquefaction duration. From what has been discussed above, the conclusion may safely draw that: Firstly, cold refrigerant injection timing has little influence on recuperative efficiency because the spatial recuperation process complete rapidly generally within 150 °CA at 1500 rpm (16.67 ms). Secondly, the optimal cold refrigerant injection timing is 150 °CA which is slightly advance the bottom dead center. The

Fig. 10. Refrigerant liquefaction process with various injection timing of cold refrigerant.

improvement of torque per unit mass, thermal efficiency and exergetic efficiency may be due to the reduction of push work which compensates the loss of expansive work. Thirdly, the liquefaction duration of early injection timing (such as 150 °CA) would be nearly 100 °CA longer in contrast with the late injection timing (such as 270 °CA). As a result, early cold refrigerant injection timing should correspond to long injection duration to accelerate liquefaction process. On the contrary, the late injection timing should match short injection duration to reduce refrigerant dryness faction and temperature fluctuation that has a negative effect on expander performance. 3.3. Investigation of variable expansion ratio at common working condition The critical temperature and pressure of R123 are 183.681 °C and 36.618 bar respectively. The ORC system adopts subcritical cycle when taking operational safety and low cost into account. On one hand, the average exhaust temperature of heavy duty diesel engine usually does not exceed 350 °C, so it is reasonable to set refrigerant evaporation temperature as 200 °C that takes heat exchanger efficiency and irreversible destruction into consideration. On the other hand, the vapor pressure should be great enough to push piston downwards to produce work. Meanwhile, the refrigerant should be superheated steam at operating pressure, so the pump pressure in this section sets as 30 bar. In other words, the refrigerant temperature and pressure are 200 °C and 30 bar respectively which represent the common working condition of this spatial recuperative expander. The impact of variable expansion ratio would be investigated under this designed working condition with the object of saving computational time.

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Fig. 11. The expander performance with respect to various expansion ratio.

The specific expansion ratio is acquired by adjusting hot refrigerant injection timing. Fig. 11(a) and (b) indicates that the torque per unit mass, thermal efficiency, exergetic efficiency and recuperative efficiency increase linearly with expansion ratio which corresponds with the finding of Peris at al. [33]. The under-expansion loss can be reduced as the expansion ratio increases. As a result, the torque per unit mass, thermal efficiency and exergetic efficiency all increase with expansion ratio until built-in volume ratio of the expander is equal to the system specific volume ratio [34,35]. Generally speaking, the internal volume ratio should match the operating condition with the object of minimizing the under-expansion loss and improving the expander performance [34–37]. From the trend of these four curves, the expander has the potential for further expansion under this condition. Fig. 11 (a) shows that the isentropic efficiency drops slightly with increasing expansion ratio. It deserves to note that the total torque output declines rapidly as the expansion ratio increases. This is because the higher expansion ratio means the earlier hot refrigerant injection timing which encounter higher background pressure in the cylinder. Therefore, the total mass of hot refrigerant into cylinder decrease with increasing expansion ratio that results in power output decline. As previously mentioned, the mass of hot refrigerant should increase as injection timing advance. From what has been discussed above, the conclusion may safely draw that: Firstly, the torque per unit mass, thermal efficiency, exergetic efficiency and recuperative efficiency increase with expansion ratio while the isentropic efficiency decreases slightly. Secondly, the amount of hot refrigerant should increase with expansion ratio to compensate the loss of inlet refrigerant due to high background pressure. Thirdly, sweeping the hot and cold refrigerant injection timing to acquire variable expansion ratio and recuperative performance respectively which is one of the main innovations of this work. Most importantly, the characteristic

Fig. 12. Expander power output and refrigerant mass under various operating conditions.

of reciprocating piston expander guarantees the independence of power output and recuperation processes which operate at expansion and exhaust strokes respectively. 3.4. Research on the expander performance under various operating conditions In this section the performance of spatial recuperative expander under wide range of operating conditions (40 points) would be discussed. The temperature and pressure of hot refrigerant range from 185 °C to 220 °C and from 26 bar to 34 bar respectively. The hot and cold refrigerant injection duration is 40 °CA and 90 °CA respectively. Fig. 12(a) shows that refrigerant pressure should vary with refrigerant temperature to achieve the optimal power output. Generally, the optimal refrigerant pump pressure grows with refrigerant temperature. In the actual application refrigerant

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Fig. 13. Thermal efficiency under various operating conditions.

Fig. 15. Isentropic efficiency under various operating conditions.

evaporation temperature varies within a certain range due to temperature fluctuation of heat source. Especially at vehicle transient working condition. Even though the heat source fluctuates frequently, the pump pressure could be adjusted rapidly to match the refrigerant temperature to acquire required expander performance. The torque per unit mass just describes the power output from the aspect of a unit mass of refrigerant, however, the total torque actually determines the available power output. The output torque under various operating conditions is shown in Fig. 12(b). It reveals that the pump pressure has a significant effect on power output while the temperature of hot refrigerant has a negligible effect. As shown in Fig. 12(c), the higher pump pressure, the more refrigerant enters into cylinder which definitely improve total power output. As a result, it is more reasonable and objective that adopt both torque per unit mass and average torque per cycle to assess the power output performance. As shown in Fig. 13, the thermal efficiency increases with pressure at a given temperature. In addition, thermal efficiency decreases with refrigerant temperature at the same pressure. However, the downwards trends become indistinct as the pressure increasing. Thermal efficiency almost keeps constant at 34 bar regardless of the temperature variation. In summary, raising refrigerant pressure is an effective way to achieve high thermal efficiency under entire operating range. Since the ORC system operates at subcritical state, adopting high critical pressure refrigerant that have the potential to increase pump pressure may help improve thermal efficiency. Comparison between Figs. 12 (b) and 13 can find that appropriately high pump pressure may benefit the total power output and thermal efficiency. Meanwhile,

vapor superheats slightly (such as 190–205 °C for R123) is beneficial for improving thermal efficiency. Exergetic efficiency represents the potential to produce maximum useful work which also characterizes the perfection degree about the conversion process from thermal energy to work. Fig. 14 demonstrates that the exergetic efficiency increases with pressure at specific temperature. On the other hand, exergetic efficiency decreases with increasing superheating degree at a given pump pressure. Especially the downward trend becomes indistinct when the pump pressure is sufficiently high (such as 34 bar). Comparison between Figs. 13 and 14 can find that: Firstly, increasing expander inlet pressure at a given temperature can promote both thermal efficiency and exergetic efficiency. Secondly, increasing refrigerant evaporation temperature at a constant pressure declines both efficiencies because it means consuming more thermal energy to produce nearly the same amount of work. However, it is worth emphasizing that thermal efficiency, exergetic efficiency, recuperative efficiency and isentropic efficiency mentioned in article only refer to expander instead of the entire ORC system (see Fig. 15). The isentropic efficiency decreases with refrigerant pressure at specific temperature. The isentropic efficiency increases with increasing temperature at a given pressure. As shown in Fig. 16 the recuperative efficiency could be raised by means of increasing temperature or decreasing pressure. However, relieving pressure definitely causes thermal economy decline or sacrifice expander power output. The effect of refrigerant temperature and pressure on power output, thermal economy and recuperative performance presents in Fig. 17.

Fig. 14. Exergetic efficiency under various operating conditions.

Fig. 16. Recuperative efficiency under various operating conditions.

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Recuperative performance

Control object

Evaluation index

Recuperative efficiency

Technical measures

Presssure

Conclusion

Thermal economy

Power output

Isentropic efficiency

Torque per unit mass

Torque

Thermal efficiency

Pressure

Temperature

Cover both recuperation and power output

Exergetic efficiency

Temperature

Cover both power output and thermal economy

Fig. 17. Control object and countermeasures.

From what has been discussed above, the conclusion may safely draw that: Firstly, the maximal toque per unit mass achieves 7529 N m/kg when the evaporation temperature and pressure reaches 220 °C and 36 bar. However, the total torque output falls to 9.75 N m due to high background pressure in cylinder which decreases the amount of inlet hot refrigerant. Secondly, the optimal thermal efficiency and exergetic efficiency reach 20.27% and 62.06% at 190 °C, 36 bar. Thirdly, the maximal recuperative efficiency and isentropic efficiency reach 11.87% and 71.71% at 220 °C, 26 bar. Fourthly, different control objectives should adopt corresponding technical measures as shown in Fig. 17. Increasing the pump pressure and maintaining appropriate superheated degree (i.e. 190 °C for R123) could reconcile both power output and thermal economy. While increasing the refrigerant temperature and preserving suitable pump pressure could benefit both recuperative performance and power output. 4. Conclusions This paper proposes a new concept of spatial recuperative expander based on GT-SUIT 7.4. The distinction of principles and performance characteristics between spatial recuperative expander and traditional expander has been discussed. Furthermore, the effect of spatial recuperation and variable expansion ratio have been instigated. At last, the expander performance under various operating conditions has been analyzed in detail. The main conclusions summarize as follows: 1. The torque per unit mass, thermal efficiency, exergetic efficiency, isentropic efficiency and recuperative efficiency of optimum spatial recuperative expander are 51.00%, 6.74%, 20.79%, 5.68% and 11.36% higher than traditional reciprocating piston expander respectively. The clearance volume of spatial recuperative expander should be as small as possible. Otherwise, residual refrigerant from previous cycle would seriously deteriorate the capacity to do work. 2. Cold refrigerant injection timing has little influence on recuperative efficiency because the spatial recuperation process complete rapidly within 150 °CA (16.67 ms) at 1500 rpm. The optimal cold refrigerant injection timing is 150 °CA which is slightly advance the bottom dead center. The improvement of torque per unit mass, thermal efficiency and exergetic efficiency may be due to the reduction of push work which compensates the loss of expansive work. 3. The torque per unit mass, thermal efficiency, exergetic efficiency and recuperative efficiency increase with expansion ratio while the isentropic efficiency decreases slightly. Meanwhile,

the amount of hot refrigerant should increase with expansion ratio to compensate the loss of inlet refrigerant due to high background pressure. The characteristic of variable expansion ratio can improve energy conversion efficiency under various levels of heat source. 4. The maximal toque per unit mass achieves 7529 N m/kg when the evaporation temperature and pressure reach 220 °C and 36 bar. However, the total torque output falls to 9.75 N m because high background pressure in the cylinder decreases the amount of inlet hot refrigerant. Meanwhile, the optimal thermal efficiency and exergetic efficiency reach 20.27% and 62.06% at 190 °C, 36 bar. However, the maximal recuperative efficiency and isentropic efficiency reach 11.87% and 71.71% at 220 °C, 26 bar. These mean that different control objectives should adopt corresponding technical measures. Increasing the pump pressure and maintaining appropriate superheated degree (i.e. 190 °C for R123) could reconcile both power output and thermal economy. While increasing the refrigerant temperature and preserving suitable pump pressure can benefit both recuperative performance and power output. This system is generally applicable to any waste heat recovery system, either stationary or mobile. It can also apply to single heat source with careful consideration. Acknowledgements This work was supported by a grant from the National Natural Science Foundation of China (No. 51576089). And the field work is conducted in State Key Laboratory of Automotive Simulation and Control, Jilin University. The authors thank the laboratory managers and staff workers for their hospitability, time and opinions. The authors are indebted to the reviewers of this article for their invaluable suggestions. References [1] Daccord R, Darmedru A, Melis J. Oil-free axial piston expander for waste heat recovery. SAE technical paper 2014-01-0675. [2] Latz G, Andersson S, Munch K. Selecting an expansion machine for vehicle waste-heat recovery systems based on the Rankine cycle. SAE technical paper 2013-01-0552. [3] Song J, Gu C-W. Performance analysis of a dual-loop organic Rankine cycle (ORC) system with wet steam expansion for engine waste heat recovery. Appl Energy 2015;156:280–9. [4] Li J, Pei G, Ji J, Bai X, Li P, Xia L. Design of the ORC (organic Rankine cycle) condensation temperature with respect to the expander characteristics for domestic CHP (combined heat and power) applications. Energy 2014;77:579–90. [5] Fiaschi D, Manfrida G, Maraschiello F. Design and performance prediction of radial ORC turboexpanders. Appl Energy 2015;138:517–32.

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