Optimized liquid-separated thermodynamic states for working fluids of organic Rankine cycles with liquid-separated condensation

Optimized liquid-separated thermodynamic states for working fluids of organic Rankine cycles with liquid-separated condensation

Accepted Manuscript Optimized liquid-separated thermodynamic states for working fluids of organic Rankine cycles with liquid-separated condensation Ji...

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Accepted Manuscript Optimized liquid-separated thermodynamic states for working fluids of organic Rankine cycles with liquid-separated condensation Jian Li, Qiang Liu, Zhong Ge, Yuanyuan Duan, Zhen Yang, Jiawei Di PII:

S0360-5442(17)31635-3

DOI:

10.1016/j.energy.2017.09.115

Reference:

EGY 11609

To appear in:

Energy

Received Date: 17 April 2017 Revised Date:

17 August 2017

Accepted Date: 24 September 2017

Please cite this article as: Li J, Liu Q, Ge Z, Duan Y, Yang Z, Di J, Optimized liquid-separated thermodynamic states for working fluids of organic Rankine cycles with liquid-separated condensation, Energy (2017), doi: 10.1016/j.energy.2017.09.115. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1

Optimized liquid-separated thermodynamic states for working fluids

2

of organic Rankine cycles with liquid-separated condensation Jian Lia, Qiang Liua, b, Zhong Gea, Yuanyuan Duana,∗, Zhen Yanga, Jiawei Dia

3 4

a

5

for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, PR China b

6

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Key Laboratory for Thermal Science and Power Engineering of MOE, Beijing Key Laboratory

Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum, Beijing 102249, PR China

8

Abstract: Liquid-separated condensation is an emerging enhanced heat transfer

9

method that simultaneously increases the condensation heat transfer coefficient and

10

reduces the pressure drop. This method was applied to shell-and-tube condensers used

11

in organic Rankine cycle systems. The optimized liquid-separated thermodynamic

12

states of organic fluids which maximize the average condensation heat transfer

13

coefficients were studied for the single-stage and two-stage liquid-separated

14

condensations. Effects of the heat exchange tube diameter, organic fluid mass flux and

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cooling water temperature rise on the optimized liquid-separated thermodynamic

16

states and heat transfer enhancement effects were also analyzed. Results show that the

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minimized condenser area decreases by 10.2%–18.1% for the single-stage

18

liquid-separated condensation and 14.5%–25.0% for the two-stage, compared to the

19

conventional condensation. Optimized liquid-separated thermodynamic states of nine

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organic fluids were also obtained. Reducing the heat exchange tube diameter, organic

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fluid mass flux and cooling water temperature rise, the decrement in the condenser

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area increases. Increasing the liquid-separation stage is beneficial for reducing the

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Corresponding author. E-mail addresses: [email protected] (Y. Duan). 1

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condenser area. The optimized vapor quality at the liquid-separated unit inlet remains

24

constant as the heat exchange tube diameter and organic fluid mass flux decrease.

25

While, it decreases as the cooling water temperature rise decreases.

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26 27

Key words: Organic Rankine cycle; Liquid-separated condensation; Heat transfer

28

enhancement; Organic fluid; Condensation; Parameter optimization

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Nomenclature heat transfer area (m2)

c

specific heat (kJ·kg-1·K-1)

d

diameter (m)

G

mass flux (kg·m-2·s-1)

h

Subscripts

M AN U

A

critical state

con

conventional condensation

cond

condenser or condensation

specific enthalpy (kJ·kg-1)

cool

cooling water

m&

mass flow rate (kg·s-1)

g

vapor

Nu

Nusselt number

i

inside the heat exchange tube

Pr

Prandtl number

in

inlet

p

pressure (kPa)

LSI

liquid-separated unit inlet

reduced pressure, p p c

LSI_1

first liquid-separated unit inlet

heat flow rate (kW)

LSI_2

second liquid-separated unit inlet

Re

Reynolds number, ρvd µ

l

liquid

T

temperature (oC)

m

average

U

overall heat transfer coefficient

max

maximum

Q

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p*

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c

2

ACCEPTED MANUSCRIPT min

minimum

v

velocity (m·s-1)

O

organic working fluid

x

vapor quality, mg

o

outside the heat exchange tube

∆h

specific enthalpy variation (kJ·kg-1)

opt

optimized

∆T

temperature difference (oC)

out

outlet

p

isobaric process

Greek symbols

pp

pinch point

α

sat

g

l

(W·m-2·K-1) viscosity (Pa·s)

ρ

density (kg·m-3)

δ

wall thickness (m)

λ

thermal conductivity (W·m-1·K-1)

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Abbreviations

GWP

global warming potential

ODP

ozone depletion potential

ORC

organic Rankine cycle

EP

1

heat exchange tube wall

Introduction

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wall

µ

30 31

saturated condition

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heat transfer coefficient

SC

(m +m )

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(W·m-2·K-1)

Medium to low temperature (<350°C) heat sources widely and largely exit in the

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renewable energy and waste heat resources. The efficient utilization of this thermal

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energy has been a hot while difficult topic in the international energy utilization field

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[1-4]. Organic Rankine cycle (ORC) is a heat-power conversion technology that is

37

based on the principle of the Rankine cycle and uses low boiling point organic fluids

38

as working fluids [5]. ORC presents a great potential to efficiently utilize the medium 3

ACCEPTED MANUSCRIPT 39

to low temperature thermal energy due to the advantages of high efficiency, stability,

40

simplicity, flexibility, safety and wide installation capacity range [5-15]. The

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application of ORC systems is continuously expanding to date. Condenser is a critical component in the ORC system. The condenser

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thermodynamic performance significantly affects the heat-power conversion

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efficiency of the ORC system [8, 16]. Moreover, the condenser critically affects the

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economic performance of the ORC system, and the condenser purchased cost can

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exceed 35.8% of the total purchased equipment cost for a water-cooled ORC system

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[17]. The condenser purchased cost generally increases as the heat transfer area

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increases [17-19]. The maintenance cost and factory building area of the ORC system

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also increase as the condenser heat transfer area increases [17-20]. Improving the

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condenser heat transfer performance is an important approach to reduce the heat

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transfer area, thereby reducing the total investment and operation cost of the ORC

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system.

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Currently, shell-and-tube condensers are widely used in ORC systems [11, 14, 17,

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19, 21-23]. Many scholars used the heat transfer models of shell-and-tube condensers

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to analyze the ORC system thermo-economic performance [11, 14, 17, 19, 22, 23].

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Some scholars tried to reduce the heat transfer area of the shell-and-tube condenser by

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optimizing the tube layout, number of tube passes, tube diameter, shell diameter,

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baffle spacing and baffle cut [24-27]. Walraven et al. [21] also adopted the method of

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simultaneous design in the system and component levels to design the shell-and-tube

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condenser. In generally, minimizing the heat transfer area is the crucial objective for

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the design of the shell-and-tube condenser. For the shell-and-tube condensers used in ORC systems, the organic fluid

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generally flows inside tubes to reduce the charge volume and prevent the organic fluid

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from leaking, and the cooling water flows outside tubes. The specific heat capacity

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and density of the organic fluid are small, and the flow velocity inside tubes is low to

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guarantee the operational safety and stability of the condenser. While, the specific

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heat capacity, density and mass flux of the cooling water are relatively large.

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Therefore, the convective heat transfer coefficient inside tubes is generally much

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lower than that of outside tubes. Improving the condenser heat transfer performance

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needs to increase the convection heat transfer coefficient inside tubes. However,

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conventional enhanced heat transfer methods (e.g., reducing the heat exchange tube

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internal diameter, increasing the heat exchange surface roughness and flow turbulence)

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generally significantly increase the pressure drop during condensation [18, 28],

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thereby increasing the pump power and even degrading the ORC system

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thermodynamic performance by deviating the actual system operating condition from

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the design condition.

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Liquid-separated condensation is an emerging enhanced heat transfer method

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that separates the condensed fluid from the vapor–liquid mixture during condensation

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to reduce the condensing film thickness on the cooling surface and increase the vapor

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quality inside tubes [14, 29-32]. This method utilizes the excellent heat transfer

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performance of high-quality vapor to maintain a high condensation heat transfer

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coefficient; meanwhile, separating the condensed fluid can also reduce the flow 5

ACCEPTED MANUSCRIPT resistance. Therefore, the liquid-separated condensation can simultaneously increase

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the condensation heat transfer coefficient and reduce the pressure drop [30-32]. The

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liquid-separated condensation is a promising method to effectively improve the heat

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transfer performance of shell-and-tube condensers used in ORC systems.

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Conventional enhanced heat transfer methods can be used in combination with the

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liquid-separated condensation to attain the advantages superposition.

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The liquid-separated condensation method was proposed by Peng et al. [33].

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Peng et al. [29] studied the physical mechanisms of increasing the heat transfer

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coefficient and reducing the pressure drop for the liquid-separated condensation. Wu

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et al. [30] designed an air-cooled condenser with liquid-separated condensation, and

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their results showed that the condenser heat transfer area could decrease by 37%

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compared with that of the conventional fin-and-tube condenser. Luo et al. [18],

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Hua et al. [31], Zhong et al. [32] and Luo et al. [34] focused on the air-cooled

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condenser with liquid-separated condensation and verified its advantages in

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increasing the heat transfer coefficient and reducing the pressure drop compared to the

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conventional condensers. Mo et al. [35] studied the effective control method for the

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vapor–liquid

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separation

in

the

air-cooled

condenser

with

liquid-separated

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condensation. The liquid-separated condensation also shows the advantages of

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enhancing the heat transfer performance in shell-and-tube condensers. Li et al. [14]

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introduced the liquid-separated condensation into the shell-and-tube condenser used

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in ORC systems, and their results showed that the ratio of the total heat transfer area

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to the net power output could decrease by 28.3% at most for ORC systems using 6

ACCEPTED MANUSCRIPT R600/R601a mixtures with liquid-separated condensation, compared to the

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conventional condensation. Li et al. [36] experimentally measured the performance of

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a shell-and-tube condenser with liquid-separated condensation, and the results showed

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that the heat transfer coefficient could increase by 25.1% compared to the

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conventional condensation.

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The thermodynamic state of the working fluid during the vapor–liquid separation

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(“the liquid-separated thermodynamic state” hereinafter) directly determines the

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liquid-separated unit (vapor–liquid separator) location in the condenser, thereby

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determining the flow path and structure designs of the liquid-separated condenser.

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Moreover, the liquid-separated thermodynamic state also significantly affects the heat

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transfer enhancement effect of the liquid-separated condensation [14]. Therefore,

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determining the optimized liquid-separated thermodynamic state that maximizes the

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average condensation heat transfer coefficient is important. However, the existing

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studies about the liquid-separated condensation are mainly based on the fixed

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liquid-separated unit locations, and the studied condensers are generally air-cooled

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condensers. The effect of the liquid-separated thermodynamic state on the condenser

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heat transfer area is unclear, and the studies on the shell-and-tube condenser with

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liquid-separated condensation are insufficient. Furthermore, the condenser parameters

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(e.g., the condenser flow path, heat exchange tube internal diameter, working fluid

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mass flux, and cooling water temperature rise) significantly affect the condenser heat

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transfer performance. Effects of these parameters on the optimized liquid-separated

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thermodynamic states and heat transfer enhancement effects are still indeterminate for

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the liquid-separated condensation. In this study, the liquid-separated condensation was applied to the shell-and-tube

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condenser with counter-flow configuration used in ORC systems. The condenser with

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once vapor–liquid separation in the organic fluid flow path (tube side) is defined as

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the “single-stage liquid-separated condensation”, and that with twice vapor–liquid

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separations is defined as the “two-stage liquid-separated condensation”. This study

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focused on the optimized liquid-separated thermodynamic states for the single-stage

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and two-stage liquid-separated condensations. Effects of the heat exchange tube

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internal diameter, organic fluid mass flux and cooling water temperature rise on the

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optimized liquid-separated thermodynamic states and heat transfer enhancement

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effects were also analyzed. The vapor quality is a dimensionless thermodynamic

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parameter between 0 and 1, which can represent the working fluid thermodynamic

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state during condensation. Thus, the vapor quality of the working fluid at the

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liquid-separated unit inlet ( xLSI ) was used to represent the liquid-separated

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thermodynamic state in this study.

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2

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2.1 Liquid-separated condenser

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Methodology

Fig. 1 shows a schematic of the counter-flow shell-and-tube condenser with

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single-stage liquid-separated condensation, and its schematic for increasing the

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condensation heat transfer coefficient is shown in Fig. 2. The details have been

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described by our previous work [14]. For the pure organic fluid, using the 8

ACCEPTED MANUSCRIPT liquid-separated condenser in the ORC system will nearly not change the performance

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of other components, and the system thermal performance will also nearly not change.

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In addition, the equipment manufacturing and operating maintenance of

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liquid-separated condensers are simple and reliable. Many scholars have

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manufactured the liquid-separated condenser with more than twice vapor–liquid

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separations [29-32, 36], including the shell-and-tube condenser with two-stage

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liquid-separated condensation [36]. Some liquid-separated condensers even have been

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used in the actual engineering [29].

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2.2 Ranges for the heat exchange tube diameter, organic fluid mass flux and

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cooling water temperature rise

The heat exchange tubes in the liquid-separated condenser are smooth tubes and

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the tube diameters are shown in Table 1. The heat exchange tube internal diameters

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are 8, 10, 15 and 20 mm. An excessive organic fluid mass flux will significantly

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increase the pressure drop and even threaten the condenser operational stability [37];

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thus, the organic fluid mass flux inside the heat exchange tubes is selected as 40–100

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kg·m-2·s-1. The cooling water temperature rises are selected as 5oC and 15oC as these

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values are common in the ORC wet cooling system.

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2.3 Working fluids

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R227ea, R236ea, R245fa, R600, R600a, R601, R601a, R1234yf and R1234ze(E)

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are selected as the working fluids, because previous studies have shown that they can 9

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obtain the attractive thermodynamic performance in ORC systems [8, 38-42]. The

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major thermophysical properties of nine pure organic fluids are shown in Table 2 [43,

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44].

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2.4 Heat transfer area calculation model

The condensation temperature remains constant for the pure fluid with liquid-separated

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thermodynamic performance of the ORC system remains constant as the vapor quality

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at the liquid-separated unit inlet ( xLSI ) varies. Therefore, this study focuses on the

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effect of the vapor quality at the liquid-separated unit inlet on condenser heat transfer

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area for pure organic fluids. The liquid-separated condenser is restricted in the

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condensation phase change process of the working fluid, and the working fluid is

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saturated vapor ( x = 1 ) at the condenser inlet. Operating parameters for the

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liquid-separated condensers are listed in Table 3.

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To simplify the calculation model of the condenser heat transfer area, the following assumptions are made:

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Liquid-separated condensers are in a steady state,



Pressure drop and heat dissipation of the organic fluid and cooling water are

neglected ,



Pressure of the organic fluid remains constant during the vapor–liquid separation,

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condensation (the pressure drop is neglected); thus, the

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Organic fluid is the saturated vapor ( x = 1 ) at each flow path inlet, 10

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To calculate the liquid-separated condenser heat transfer area, each flow path of

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the liquid-separated condenser was divided into 50 sections with an equal heat flow

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interval, as shown in Fig. 3. In each section, the thermodynamic states of the organic

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fluid and cooling water were determined by their pressures and arithmetic average

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temperatures. Thermodynamic properties of fluids were calculated using REFPROP

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9.1 [44]. The liquid-separated condenser heat transfer area is the summation of each

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section heat transfer area.

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Organic fluid mass flux inside tubes remains constant in each flow path.

The energy balance of each section in the liquid-separated condenser is

& O∆hO,i = m & cool∆hcool,i . Qi = m 202

The cooling water mass flow rate is

m& O ∆hO,cond

hcool,pp − hcool,in

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m& cool = 203

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EP

Qi . U i ∆Tm,i

∆ Tm,i =

∆ Tmax,i − ∆Tmin,i

ln ( ∆Tmax,i ∆Tmin,i )

(3)

.

(4)

Fouling resistances of the liquid-separated condenser are neglected, and the

overall heat transfer coefficient of the i th section is calculated as [37]

1 1 do δ wall do 1 = + + , Ui αi di λwall dm αo 207

(2)

The logarithmic mean temperature difference of the i th section is

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.

The heat transfer area of the i th section is

Acond,i =

204

(1)

where dm = ( do − di ) ln ( do di ) . 11

(5)

ACCEPTED MANUSCRIPT The convection heat transfer coefficient is calculated as α = Nu

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calculated from the Churchill–Bernstein correlation as [45]

0.62 Re1/2 Pr1/3 1 + ( 0.4 Pr )2/3   

Nu , is calculated from the Shah correlation as [46]

Nu = 0.023Re Pr

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1/4

  Re 5/8  1 +      28200  

4/5

.

(7)

The pure organic fluid flows inside the horizontal tubes, and its Nusselt number,

0.8 L

213

(6)

The cooling water flows outside tubes, and its Nusselt number, Nu , is

Nu = 0.3 +

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.

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d

where ReL = Gdi

µl .

0.04  3.8 x 0.76 (1 − x )  0.8 (1 − x ) + , p*0.38  

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λ

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0.4 l

(8)

The liquid-separated condenser heat transfer area is calculated as n

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Acond = ∑ Acond,i .

(9)

i =1

For the liquid-separated condenser, its heat exchange capacity and overall

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logarithmic mean temperature difference remain constant for a given cooling water

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temperature rise, as the mass flow rate of the organic fluid remains constant.

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Therefore, the vapor quality at the liquid-separated unit inlet minimizing the

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condenser heat transfer area is that maximizes the average overall heat transfer

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coefficient for the liquid-separated condenser.

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2.5 Optimization process and details For a specific pure organic fluid with the single-stage liquid-separated 12

ACCEPTED MANUSCRIPT 224

condensation: 

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Given the heat exchange tube diameter, organic fluid mass flux and cooling water temperature rise. The liquid-separated condenser heat transfer areas

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for various vapor qualities at the liquid-separated unit inlet ( xLSI ) were

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calculated using the model in Section 2.4. The effect of the vapor quality at

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the liquid-separated unit inlet on the condenser heat transfer area was studied

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for the given conditions, and the optimized vapor quality at the

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liquid-separated unit inlet ( xLSI,opt ) was also determined. 

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With varying conditions (the heat exchange tube diameter or organic fluid mass flux or cooling water temperature rise), the liquid-separated condenser

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heat transfer areas for various vapor qualities at the liquid-separated unit

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inlet were calculated for the new given conditions. 

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The effects of the heat exchange tube internal diameter, organic fluid mass flux and cooling water temperature rise on the optimized vapor qualities at

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the liquid-separated unit inlet and heat transfer enhancement effects were

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obtained by analyzing the results.

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The optimization process of the two-stage liquid-separated condensation is

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similar as the abovementioned process. The condenser heat transfer areas of the

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conventional,

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condensations were compared.

single-stage

liquid-separated

244 245

3

Results and Discussion 13

and

two-stage

liquid-separated

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3.1 Single-stage liquid-separated condensation As the vapor quality at the liquid-separated inlet, heat exchange tube internal

248

diameter, organic fluid mass flux and cooling water temperature rise vary, the

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variations in the condenser heat transfer area are similar for nine pure organic fluids

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with the single-stage liquid-separated condensation. Fig. 4 shows the condenser heat

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transfer areas of R245fa for various vapor qualities at the liquid-separated unit inlet

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with the single-stage liquid-separated condensation, and the cooling water

253

temperature rise is 5oC. The right vertical coordinate ( xLSI =1) in Fig. 4 represents the

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condenser

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liquid-separation for evaluating the heat transfer enhancement effect for the

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single-stage liquid-separated condensation. As shown in Fig. 4, the condenser heat

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transfer area first decreases and then increases as the vapor quality at the

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liquid-separated unit inlet decreases. There is an optimized vapor quality at the

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liquid-separated unit inlet that minimizes the condenser heat transfer area. For the

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same vapor quality at the liquid-separated unit inlet, the condenser heat transfer area

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decreases as the heat exchange tube internal diameter decreases and the organic fluid

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mass flux increases. While, as the heat exchange tube internal diameter and organic

263

fluid mass flux decrease, the decrement in the condenser heat transfer area increases

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and the heat transfer enhancement effect of the single-stage liquid-separated

265

condensation improves. For example, when the organic fluid mass flux is 100

266

kg·m-2·s-1 and the cooling water temperature rise is 5oC, the minimized condenser

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heat transfer area of the single-stage liquid-separated condensation is 15.6% lower

transfer

area

of

the

conventional

condensation

without

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ACCEPTED MANUSCRIPT than that of the conventional condensation for the heat exchange tube internal

269

diameter of 20 mm and is 16.4% for the heat exchange tube internal diameter of 8 mm.

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The minimized condenser heat transfer area of the single-stage liquid-separated

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condensation is 18.1% lower than that of the conventional condensation for the heat

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exchange tube internal diameter of 8 mm, the organic fluid mass flux of 40 kg·m-2·s-1

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and the cooling water temperature rise of 5oC. In addition, as the heat exchange tube

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internal diameter and organic fluid mass flux decrease, the optimized vapor quality at

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the liquid-separated unit inlet remains constant for the single-stage liquid-separated

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condensation.

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As the cooling water temperature rise decreases, the condensation heat exchange

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capacity of the organic fluid increases whereas the logarithmic mean temperature

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difference of the condenser decreases. Given the heat exchange tube internal diameter

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and organic fluid mass flux, the condenser heat transfer area increases as the cooling

281

water temperature rise decreases. Fig. 5 shows the condenser heat transfer areas of

282

R245fa for various vapor qualities at the liquid-separated unit inlet with the

283

single-stage liquid-separated condensation as the cooling water temperature rises are

284

5oC and 15oC, and the heat exchange tube internal diameter is 10 mm and the organic

285

fluid mass flux is 70 kg·m-2·s-1. Compared to the conventional condensation, the

286

decrement in the single-stage liquid-separated condenser heat transfer area increases

287

as the cooling water temperature rise decreases; thus, the comparative advantage of

288

the single-stage liquid-separated condensation strengthens. For example, Fig. 5 shows

289

that the minimized condenser heat transfer area of the single-stage liquid-separated

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15

ACCEPTED MANUSCRIPT condensation is 13.9% lower than that of the conventional condensation for the

291

cooling water temperature rise of 15oC and is 17.0% for the cooling water temperature

292

rise of 5oC. Furthermore, the optimized vapor quality at the liquid-separated unit inlet

293

decreases as the cooling water temperature rise decreases for the single-stage

294

liquid-separated condensation. As shown in Fig. 5, the optimized vapor quality at the

295

liquid-separated unit inlet of R245fa is 0.35 for the cooling water temperature rise of

296

15oC and is 0.33 for the cooling water temperature rise of 5oC.

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In conclusion, the single-stage liquid-separated condensation is more suitable to

298

enhance the condensation heat transfer for the low heat exchange tube internal

299

diameter, organic fluid mass flux and cooling water temperature rise. Table 4 lists the

300

optimized vapor qualities at the liquid-separated unit inlet and maximum condenser

301

heat transfer area decrements for nine pure organic fluids with the single-stage

302

liquid-separated condensation. For the given parameters ranges, the optimized vapor

303

quality at the liquid-separated unit inlet ( xLSI,opt ) is 0.31–0.38 for nine pure organic

304

fluids with the single-stage liquid-separated condensation, and the minimized

305

condenser heat transfer area is 10.2%–18.1% lower than that of the conventional

306

condensation. In addition, the average maximum condenser heat transfer area

307

decrement for various heat exchange tube diameters and working fluid mass fluxes,

308

from the largest to the smallest is: R245fa, R236ea, R601, R601a, R227ea,

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R1234ze(E), R600, R600a, R1234yf. This sorting is valid for the cooling water

310

temperature rises of 5oC and 15oC.

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3.2 Two-stage liquid-separated condensation Given the heat exchange tube internal diameter, organic fluid mass flux and

314

cooling water temperature rise, two optimized parameters are provided for the

315

two-stage liquid-separated condensation, namely, the vapor qualities of the organic

316

fluid at the first and second liquid-separated unit inlets ( xLSI_1 and xLSI_2 ). For

317

various heat exchange tube internal diameters, organic fluid mass fluxes and cooling

318

water temperature rises, the variations in the condenser heat transfer area are similar

319

for nine pure organic fluids as the vapor qualities at the first and second

320

liquid-separated unit inlets ( xLSI_1 and xLSI_2 ) vary. Fig. 6 shows the condenser heat

321

transfer areas of R245fa for various vapor qualities at the first and second

322

liquid-separated unit inlets ( xLSI_1 and xLSI_2 ) with the two-stage liquid-separated

323

condensation, when the heat exchange tube internal diameter is 10 mm, the organic

324

fluid mass flux is 70 kg·m-2·s-1, and the cooling water temperature rise is 5oC. In Fig.

325

6, xLSI_1 = 1I xLSI_2 = 1 represents the conventional condenser heat transfer area,

326

xLSI_1 = 1U xLSI_2 = 1 (except

327

liquid-separated condenser heat transfer areas, and others represent the two-stage

328

liquid-separated condenser heat transfer areas for various vapor qualities at the first

329

and second liquid-separated unit inlets ( xLSI_1 and xLSI_2 ). Given xLSI_1 ( xLSI_2 ), the

330

condenser heat transfer area first decreases and then increases as xLSI_2 ( xLSI_1 )

331

decreases. As shown in Fig. 6, the two-stage liquid-separated condenser heat transfer

332

area decreases more than 20% for xLSI_1 = 0.3 − 0.7 I xLSI_2 = 0.1− 0.6 , compared to

333

the conventional condensation. The minimized condenser heat transfer area is 23.6%

xLSI_1 = 1I xLSI_2 = 1 ) represents the single-stage

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17

ACCEPTED MANUSCRIPT 334

lower than that of the conventional condensation at xLSI_1 = 0.5 I xLSI_2 = 0.31 . Compared to the conventional condensation, the heat transfer area decrement of

336

the two-stage liquid-separated condensation increases as the heat exchange tube

337

internal diameter and organic fluid mass flux decrease; while, the optimized vapor

338

qualities at the first and second liquid-separated unit inlets ( xLSI_1,opt and xLSI_2,opt )

339

remain constant. As the cooling water temperature rise decreases, the heat transfer

340

area decrement of the two-stage liquid-separated condensation increases, and both the

341

optimized vapor qualities at the first and second liquid-separated unit inlets ( xLSI_1,opt

342

and xLSI_2,opt ) tend to decrease. Table 5 lists the optimized vapor qualities at the

343

liquid-separated unit inlets and maximum condenser heat transfer area decrements for

344

nine pure organic fluids with the two-stage liquid-separated condensation. For the

345

cooling water temperature rise of 15oC, the minimized condenser heat transfer area of

346

the two-stage liquid-separated condensation is 14.5%–20.7% lower than that of the

347

conventional condensation. The optimized vapor quality at the first liquid-separated

348

unit inlet ( xLSI_1,opt ) is 0.53–0.55, and the optimized vapor quality at the second

349

liquid-separated unit inlet ( xLSI_2,opt ) is 0.31–0.35. For the cooling water temperature

350

rise of 5oC, the minimized condenser heat transfer area of the two-stage

351

liquid-separated condensation is 17.5%–25.0% lower than that of the conventional

352

condensation. The optimized vapor quality at the first liquid-separated unit inlet

353

( xLSI_1,opt ) is 0.49–0.52, and the optimized vapor quality at the second liquid-separated

354

unit inlet ( xLSI_2,opt ) is 0.3–0.34. In addition, the average maximum condenser heat

355

transfer area decrement for various heat exchange tube diameters and working fluid

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18

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mass fluxes, from the largest to the smallest is also: R245fa, R236ea, R601, R601a,

357

R227ea, R1234ze(E), R600, R600a, R1234yf.

358

3.3 Comparison of the conventional, single-stage liquid-separated and two-stage

360

liquid-separated condensations

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Fig. 7 shows the condenser heat transfer areas of R245fa with the conventional,

362

single-stage liquid-separated and two-stage liquid-separated condensations, and the

363

heat exchange tube internal diameter is 10 mm and the organic fluid mass flux is 70

364

kg·m-2·s-1. Although the complexity of the condenser design increases as the

365

liquid-separation stage increases, the decrement in the condenser heat transfer area

366

also increases. Given the same heat exchange tube internal diameter, organic fluid

367

mass flux and cooling water temperature rise, the minimized condenser heat transfer

368

area of the two-stage liquid-separated condensation is 4.7%–8.5% lower than that of

369

the single-stage liquid-separated condensation. Furthermore, the condenser heat

370

transfer area decrement of the two-stage liquid-separated condensation increases as

371

the heat exchange tube internal diameter, organic fluid mass flux and cooling water

372

temperature rise decrease, compared to the single-stage liquid-separated condensation.

373

Increasing the liquid-separation stage is more suitable to enhance the condensation

374

heat transfer for the low heat exchange tube internal diameter, organic fluid mass flux

375

and cooling water temperature rise.

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376 377

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Conclusions 19

ACCEPTED MANUSCRIPT In this study, the liquid-separated condensation was introduced into the

379

shell-and-tube condenser with counter-flow configuration used in ORC systems. The

380

optimized liquid-separated thermodynamic states and heat transfer enhancement

381

effects of the single-stage and two-stage liquid-separated condensations were obtained.

382

The effects of the heat exchange tube internal diameter, organic fluid mass flux and

383

cooling water temperature rise on the optimized liquid-separated thermodynamic

384

states and heat transfer enhancement effects were also analyzed. Main results are

385

detailed below.

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For given parameter ranges, the optimized vapor quality at the liquid-separated

387

unit inlet is 0.31–0.38 for the single-stage liquid-separated condensation. The

388

minimized condenser heat transfer area is 10.2%–18.1% lower than that of the

389

conventional condensation. For the two-stage liquid-separated condensation, the

390

optimized vapor quality at the first liquid-separated unit inlet is 0.49–0.55 and that is

391

0.3–0.35 for the second liquid-separated unit inlet. The minimized condenser heat

392

transfer area is 14.5%–25.0% lower than that of the conventional condensation. Given

393

the same heat exchange tube internal diameter, organic fluid mass flux and cooling

394

water temperature rise, the minimized condenser heat transfer area of the two-stage

395

liquid-separated condensation decreases by 4.7%–8.5%, compared with that of the

396

single-stage liquid-separated condensation.

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Reducing the heat exchange tube internal diameter, organic fluid mass flux and

398

cooling water temperature rise, the decrement in the condenser heat transfer area

399

increases. Increasing the liquid-separation stage is beneficial for reducing the 20

ACCEPTED MANUSCRIPT condenser heat transfer area. The optimized vapor quality at the liquid-separated unit

401

inlet remains constant as the heat exchange tube internal diameter and organic fluid

402

mass flux decrease; while, it decreases as the cooling water temperature rise

403

decreases.

404

Acknowledgements

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This work was supported by the National Natural Science Foundation of China

406

(Grant Nos. 51236004, 51506223 and 51621062); and the Science Foundation of the

407

China University of Petroleum, Beijing (Grant No. 2462014YJRC021).

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Organic Rankine Cycle utilizing high and low temperature energy of an LNG

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ORC (organic Rankine cycle) power plant based on R245fa working fluid.

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Energy, 2015, 90: 768-775.

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[44] Lemmon EW, Huber ML, Mclinden MO. NIST reference fluid thermodynamic

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gases and liquids to circular cylinder in cross flow. ASME J. Heat Transfer, 1977,

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pipes. Int. J. Heat Mass Transfer, 1979, 22(4): 547-556.

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TABLE CAPTION LIST

540

Table 1. Heat exchange tube diameters

542

Table 2. Thermophysical properties of the selected working fluids

543

Table 3. Operating parameters of the liquid-separated condensers

544

Table 4. Optimized vapor qualities at the liquid-separated unit inlet and maximum

545

condenser heat transfer area decrements for nine pure organic fluids with the

546

single-stage liquid-separated condensation

547

Table 5. Optimized vapor qualities at the liquid-separated unit inlets and maximum

548

condenser heat transfer area decrements for nine pure organic fluids with the

549

two-stage liquid-separated condensation

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ACCEPTED MANUSCRIPT Table 1. Heat exchange tube diameters

551

Symbol

1

2

3

4

Internal diameter (mm)

di

8

10

15

20

External diameter (mm)

do

9.6

12

18

24

552

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Table 2. Thermodynamic properties of the selected working fluids [43, 44]

Working fluid

Tc / oC pc / MPa ODP GWP100

R227ea

101.8

2.93

0

R236ea

139.3

3.50

R245fa

154.0

R600

* * * * µg,sat ×105 µl,sat ×105 / λg,sat ×102 / λl,sat ×102 /

* Prg,sat

* Prl,sat

W·m-1·K-1 W·m-1·K-1

Pa·s

3220

1.18

22.33

1.41

5.91

0.77

4.53

0

1370

1.10

35.76

1.49

7.78

0.68

5.82

3.65

0

1030

1.04

38.23

1.33

8.65

0.76

5.89

152.0

3.80

0

~20

0.75

15.11

1.71

10.27

0.81

3.63

R600a

134.7

3.63

0

~20

0.76

14.34

1.74

8.75

0.81

4.04

R601

196.6

3.37

0

~20

0.71

20.88

1.47

10.95

0.83

4.46

R601a

187.2

3.38

0

~20

0.74

20.60

1.55

10.55

0.82

4.49

R1234yf

94.7

3.38

0

4

R1234ze(E) 109.4

3.64

0

6

*: T = 30 o C

SC

1.26

14.65

1.45

5.67

0.94

3.66

1.25

18.80

1.41

6.78

0.89

3.89

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ACCEPTED MANUSCRIPT Table 3. Operating parameters of the liquid-separated condensers Parameter

Symbol

Value

Condenser minimal temperature difference (oC)

∆Tcond,min

5

&O m

1

vo

0.5

Tcool,in

20

Organic fluid mass flow rate (kg·s-1) Fluid velocity outside the tube (m·s-1)

SC

Cooling water inlet temperature (oC)

Tcool,pp −Tcool,in

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Cooling water temperature rise (oC) Cooling water pressure (MPa)

Mass flux inside tubes (kg·m-2·s-1)

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30

5, 15

pcool

0.101

G

40-100

ACCEPTED MANUSCRIPT 560

Table 4. Optimized vapor qualities at the liquid-separated unit inlet and maximum

561

condenser heat transfer area decrements for nine pure organic fluids with the

562

single-stage liquid-separated condensation

Working fluids

565

xLSI,opt

∆Acond Acond,con

R227ea

0.35

13.9%–15.3%

0.38

11.2%–12.3%

R236ea

0.33

15.4%–17.5%

0.36

12.5%–14.2%

R245fa

0.33

15.6%–18.1%

0.35

12.8%–14.7%

R600

0.33

12.6%–15.8%

0.36

10.3%–12.9%

R600a

0.34

12.6%–15.3%

0.37

10.2%–12.5%

R601

0.31

13.3%–17.5%

0.34

11.1%–14.4%

R601a

0.32

13.4%–17.3%

0.34

11.1%–14.2%

R1234yf

0.36

13.0%–14.5%

0.38

10.4%–11.6%

R1234ze(E)

0.35

13.6%–15.4%

0.38

11.0%–12.4%

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∆Acond Acond,con

EP

564

xLSI,opt

AC C

563

∆Tcool = 15o C

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∆Tcool = 5o C

31

ACCEPTED MANUSCRIPT Table 5. Optimized vapor qualities at the liquid-separated unit inlets and

566 567

maximum condenser heat transfer area decrements for nine pure organic fluids with

568

the two-stage liquid-separated condensation

xLSI_1,opt / xLSI_2,opt

∆Acond Acond,con

R227ea

0.52/0.33

19.5%–21.6%

0.55/0.35

15.9%–17.5%

R236ea

0.51/0.32

21.4%–24.3%

0.54/0.33

17.7%–20.0%

R245fa

0.50/0.31

21.7%–25.0%

0.53/0.32

17.9%–20.7%

R600

0.51/0.32

17.5%–22.1%

0.54/0.33

14.5%–18.2%

R600a

0.51/0.32

17.6%–21.5%

0.54/0.34

14.5%–17.6%

R601

0.49/0.30

18.3%–24.1%

0.53/0.31

15.4%–20.2%

R601a

0.50/0.30

18.5%–23.9%

0.53/0.32

15.5%–19.9%

R1234yf

0.52/0.34

18.3%–20.5%

0.55/0.35

14.9%–16.6%

R1234ze(E)

0.52/0.33

19.1%–21.6%

0.55/0.35

15.6%–17.6%

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EP

570

xLSI_1,opt / xLSI_2,opt

AC C

569

∆Tcool = 15o C

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∆Tcool = 5o C

32

ACCEPTED MANUSCRIPT

FIGURE CAPTION LIST

571

Fig. 1. Schematic of a counter-flow shell-and-tube condenser with single-stage

573

liquid-separated condensation

574

Fig. 2. Schematic of the single-stage liquid-separated condensation that increases the

575

condensation heat transfer coefficient

576

Fig. 3. Schematic of the method for calculating the liquid-separated condenser heat

577

transfer area (taking a flow path as an example)

578

Fig. 4. Condenser heat transfer areas of R245fa for various vapor qualities at the

579

liquid-separated unit inlet with the single-stage liquid-separated condensation when

580

the cooling water temperature rise is 5oC: (a). di = 8 mm; (b). di =10 mm; (c).

581

di =15 mm; (d). di = 20 mm

582

Fig. 5. Condenser heat transfer areas of R245fa for various vapor qualities at the

583

liquid-separated unit inlet with the single-stage liquid-separated condensation when

584

the cooling water temperature rises are 5oC and 15oC

585

Fig. 6. Condenser heat transfer areas of R245fa for various vapor qualities at the first

586

and second liquid-separated unit inlets ( xLSI_1 and xLSI_2 ) with the two-stage

587

liquid-separated condensation

588

Fig. 7. Condenser heat transfer areas of R245fa with the conventional, single-stage

589

liquid-separated and two-stage liquid-separated condensations (a: Conventional

590

condensation; b: Single-stage liquid-separated condensation; c: Two-stage

591

liquid-separated condensation)

AC C

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ACCEPTED MANUSCRIPT

Fig. 1. Schematic of a counter-flow shell-and-tube condenser with single-stage

595

liquid-separated condensation

SC

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1200

1

2〞 Single-stage liquid-separated condensation

1000 Vapor-liquid separation

800

=0 x LS I

2

600 Conventional condensation 400

R245fa di=10 mm △Tcool=5oC

G=70 kg·m-2·s-1

3〞

0 0

20

40

60

80

SC

200

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.5

Heat transfer coefficient, Ucond(W·m-2·K-1)

598

100

120

140

Heat flow rate, Q(kW)

Fig. 2. Schematic of the single-stage liquid-separated condensation that increases the

601

condensation heat transfer coefficient

M AN U

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ACCEPTED MANUSCRIPT

1 2 3

. . .

i

. . .

48 49 50

△Tcond,i+1

Tcool

Heat flow rate, Q

604

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△Tcond,i

SC

Temperature, T(oC)

Tcond

Fig. 3. Schematic of the method for calculating the liquid-separated condenser heat

606

transfer area (taking a flow path as an example)

M AN U

605

607

AC C

EP

TE D

608

36

ACCEPTED MANUSCRIPT

55

(a)

50 45

35 30 25

0.2

0.3

0.4

0.5

0.6

0.7

0.8

RI PT

40

20 0.1

0.9

1.0

Vapor quality at the liquid-separated unit inlet, xLSI

609

45 40

30 25

(b)

M AN U

50

TE D

Condenser heat transfer area, A cond(m 2)

55

35

G=80 kg·m-2·s-1 G=90 kg·m-2·s-1 G=100 kg·m-2·s-1

G=40 kg·m-2·s-1 G=50 kg·m-2·s-1 G=60 kg·m-2·s-1 G=70 kg·m-2·s-1

60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Vapor quality at the liquid-separated unit inlet, xLSI

EP

610

G=80 kg·m-2·s-1 G=90 kg·m-2·s-1 G=100 kg·m-2·s-1

G=40 kg·m-2·s-1 G=50 kg·m-2·s-1 G=60 kg·m-2·s-1 G=70 kg·m-2·s-1

SC

Condenser heat transfer area, A cond(m2)

60

60 55

(c)

50 45 40 35 30

25 0.1

611

G=80 kg·m-2·s-1 G=90 kg·m-2·s-1 G=100 kg·m-2·s-1

G=40 kg·m-2·s-1 G=50 kg·m-2·s-1 G=60 kg·m-2·s-1 G=70 kg·m-2·s-1

AC C

Condenser heat transfer area, A cond(m 2)

65

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Vapor quality at the liquid-separated unit inlet, xLSI 37

1.0

ACCEPTED MANUSCRIPT G=40 kg·m-2·s-1 G=50 kg·m-2·s-1 G=60 kg·m-2·s-1 G=70 kg·m-2·s-1

65 60

(d)

55 50

40 35 30 0.2

0.3

0.4

0.5

0.6

0.7

0.8

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45

25 0.1

0.9

1.0

Vapor quality at the liquid-separated unit inlet, xLSI

612

Fig. 4. Condenser heat transfer areas of R245fa for various vapor qualities at the

M AN U

613

G=80 kg·m-2·s-1 G=90 kg·m-2·s-1 G=100 kg·m-2·s-1

SC

Condenser heat transfer area, A cond(m 2)

70

liquid-separated unit inlet with the single-stage liquid-separated condensation when

615

the cooling water temperature rise is 5oC: (a). di = 8 mm; (b). di =10 mm; (c).

616

di =15 mm; (d). di = 20 mm

EP

618

AC C

617

TE D

614

38

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35

30

25

△Tcool=15oC

20

15 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Vapor quality at the liquid-separated unit inlet, xLSI

619

Fig. 5. Condenser heat transfer areas of R245fa for various vapor qualities at the

M AN U

620

△Tcool=5oC

RI PT

di=10 mm, G=70 kg·m-2·s-1

SC

Condenser heat transfer area, A cond(m 2)

40

621

liquid-separated unit inlet with the single-stage liquid-separated condensation when

622

the cooling water temperature rises are 5oC and 15oC

AC C

EP

TE D

623 624

39

ACCEPTED MANUSCRIPT di=10 mm

0.932.00

△Tcool=5 C

0.8

G=70 kg·m-2·s-1

33.00

31.00

28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00

32.00

0.7 0.6

29.00

0.5 0.4

Acond(m2)

0.3 0.2 31.00

31.00

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

SC

0.2

Vapor quality at the first liquid-separated unit inlet, xLSI_1

Fig. 6. Condenser heat transfer areas of R245fa for various vapor qualities at the

M AN U

626

34.00

30.00

0.1 0.1

625

35.00

o

RI PT

Vapor quality at the second liquidseparated unit inlet, xLSI_2

1.0

627

first and second liquid-separated unit inlets ( xLSI_1 and xLSI_2 ) with the two-stage

628

liquid-separated condensation

EP AC C

630

TE D

629

40

ACCEPTED MANUSCRIPT di=10 mm, G=70 kg·m-2·s-1 △Tcool=5℃

35

△Tcool=15℃

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30

25

20

15

a

b

SC

Condenser heat transfer area, Acond(m2)

40

c

Fig. 7. Condenser heat transfer areas of R245fa with the conventional, single-stage

633

liquid-separated and two-stage liquid-separated condensations (a: Conventional

634

condensation; b: Single-stage liquid-separated condensation; c: Two-stage

635

liquid-separated condensation)

TE D EP

637

AC C

636

M AN U

631 632

41

ACCEPTED MANUSCRIPT

Highlights  Liquid-separated condensation is applied to shell-and-tube condensers in ORC.  Effect of cooling water temperature rise on liquid-separated states is analyzed.

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 Optimized liquid-separated thermodynamic states are obtained for organic fluids.  Liquid-separated condensation can reduce area by 25% compared to conventional

AC C

EP

TE D

M AN U

SC

type.