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
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for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, PR China b
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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
15
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
20
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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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
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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
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(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
35
energy has been a hot while difficult topic in the international energy utilization field
36
[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
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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
41
application of ORC systems is continuously expanding to date. Condenser is a critical component in the ORC system. The condenser
43
thermodynamic performance significantly affects the heat-power conversion
44
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
46
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
48
increases [17-19]. The maintenance cost and factory building area of the ORC system
49
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,
58
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
60
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
63
generally flows inside tubes to reduce the charge volume and prevent the organic fluid
64
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
69
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
72
internal diameter, increasing the heat exchange surface roughness and flow turbulence)
73
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
75
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
82
coefficient; meanwhile, separating the condensed fluid can also reduce the flow 5
ACCEPTED MANUSCRIPT resistance. Therefore, the liquid-separated condensation can simultaneously increase
84
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
86
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
103
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
106
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
124
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
129
condenser with counter-flow configuration used in ORC systems. The condenser with
130
once vapor–liquid separation in the organic fluid flow path (tube side) is defined as
131
the “single-stage liquid-separated condensation”, and that with twice vapor–liquid
132
separations is defined as the “two-stage liquid-separated condensation”. This study
133
focused on the optimized liquid-separated thermodynamic states for the single-stage
134
and two-stage liquid-separated condensations. Effects of the heat exchange tube
135
internal diameter, organic fluid mass flux and cooling water temperature rise on the
136
optimized liquid-separated thermodynamic states and heat transfer enhancement
137
effects were also analyzed. The vapor quality is a dimensionless thermodynamic
138
parameter between 0 and 1, which can represent the working fluid thermodynamic
139
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
141
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
147
condensation heat transfer coefficient is shown in Fig. 2. The details have been
148
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
150
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
152
liquid-separated condensers are simple and reliable. Many scholars have
153
manufactured the liquid-separated condenser with more than twice vapor–liquid
154
separations [29-32, 36], including the shell-and-tube condenser with two-stage
155
liquid-separated condensation [36]. Some liquid-separated condensers even have been
156
used in the actual engineering [29].
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2.2 Ranges for the heat exchange tube diameter, organic fluid mass flux and
159
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
162
are 8, 10, 15 and 20 mm. An excessive organic fluid mass flux will significantly
163
increase the pressure drop and even threaten the condenser operational stability [37];
164
thus, the organic fluid mass flux inside the heat exchange tubes is selected as 40–100
165
kg·m-2·s-1. The cooling water temperature rises are selected as 5oC and 15oC as these
166
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
172
major thermophysical properties of nine pure organic fluids are shown in Table 2 [43,
173
44].
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2.4 Heat transfer area calculation model
The condensation temperature remains constant for the pure fluid with liquid-separated
178
thermodynamic performance of the ORC system remains constant as the vapor quality
179
at the liquid-separated unit inlet ( xLSI ) varies. Therefore, this study focuses on the
180
effect of the vapor quality at the liquid-separated unit inlet on condenser heat transfer
181
area for pure organic fluids. The liquid-separated condenser is restricted in the
182
condensation phase change process of the working fluid, and the working fluid is
183
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,
191 192
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
195
the liquid-separated condenser was divided into 50 sections with an equal heat flow
196
interval, as shown in Fig. 3. In each section, the thermodynamic states of the organic
197
fluid and cooling water were determined by their pressures and arithmetic average
198
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
200
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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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 +
211
.
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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
216
logarithmic mean temperature difference remain constant for a given cooling water
217
temperature rise, as the mass flow rate of the organic fluid remains constant.
218
Therefore, the vapor quality at the liquid-separated unit inlet minimizing the
219
condenser heat transfer area is that maximizes the average overall heat transfer
220
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
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condensation:
225
Given the heat exchange tube diameter, organic fluid mass flux and cooling water temperature rise. The liquid-separated condenser heat transfer areas
227
for various vapor qualities at the liquid-separated unit inlet ( xLSI ) were
228
calculated using the model in Section 2.4. The effect of the vapor quality at
229
the liquid-separated unit inlet on the condenser heat transfer area was studied
230
for the given conditions, and the optimized vapor quality at the
231
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
235
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
238
the liquid-separated unit inlet and heat transfer enhancement effects were
239
obtained by analyzing the results.
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The optimization process of the two-stage liquid-separated condensation is
240 241
similar as the abovementioned process. The condenser heat transfer areas of the
242
conventional,
243
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
249
variations in the condenser heat transfer area are similar for nine pure organic fluids
250
with the single-stage liquid-separated condensation. Fig. 4 shows the condenser heat
251
transfer areas of R245fa for various vapor qualities at the liquid-separated unit inlet
252
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
254
condenser
255
liquid-separation for evaluating the heat transfer enhancement effect for the
256
single-stage liquid-separated condensation. As shown in Fig. 4, the condenser heat
257
transfer area first decreases and then increases as the vapor quality at the
258
liquid-separated unit inlet decreases. There is an optimized vapor quality at the
259
liquid-separated unit inlet that minimizes the condenser heat transfer area. For the
260
same vapor quality at the liquid-separated unit inlet, the condenser heat transfer area
261
decreases as the heat exchange tube internal diameter decreases and the organic fluid
262
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
264
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
267
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.
270
The minimized condenser heat transfer area of the single-stage liquid-separated
271
condensation is 18.1% lower than that of the conventional condensation for the heat
272
exchange tube internal diameter of 8 mm, the organic fluid mass flux of 40 kg·m-2·s-1
273
and the cooling water temperature rise of 5oC. In addition, as the heat exchange tube
274
internal diameter and organic fluid mass flux decrease, the optimized vapor quality at
275
the liquid-separated unit inlet remains constant for the single-stage liquid-separated
276
condensation.
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As the cooling water temperature rise decreases, the condensation heat exchange
278
capacity of the organic fluid increases whereas the logarithmic mean temperature
279
difference of the condenser decreases. Given the heat exchange tube internal diameter
280
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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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,
309
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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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
ACCEPTED MANUSCRIPT 356
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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Energy, 2015, 90: 768-775.
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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
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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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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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xLSI,opt
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∆Tcool = 15o C
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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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∆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)
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Fig. 1. Schematic of a counter-flow shell-and-tube condenser with single-stage
595
liquid-separated condensation
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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
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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
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1 2 3
. . .
i
. . .
48 49 50
△Tcond,i+1
Tcool
Heat flow rate, Q
604
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△Tcond,i
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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)
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(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
RI PT
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
ACCEPTED MANUSCRIPT
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℃
RI PT
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.
RI PT
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.