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Supercritical CO2 (sCO2) power cycles have gained prominence for their expected excellent performance and compactness. Among their benefits, they may potentially reduce the cost of Concentrated Solar Power (CSP) plants. Because the critical temperature of CO2 is close to ambient temperatures in areas with good solar irradiation, dry cooling may penalise the efficiency of sCO2 power cycles in CSP plants. Recent research has investigated doping CO2 with different materials to increase its critical temperature, enhance its thermodynamic cycle performance, and adapt it to dry cooling in arid climates. This paper investigates the use of CO2/TiCl4, CO2/NOD (an unnamed Non-Organic Dopant), and CO2/C6F6 mixtures as working fluids in a transcritical Rankine cycle implemented in a 100 MWe power plant. Specific focus is given to the effect of dopant type and fraction on optimal cycle operating conditions and on key parameters that influence the expansion process. Thermodynamic modelling of a simple recuperated cycle is employed to identify the optimal turbine pressure ratio and recuperator effectiveness that achieve the highest cycle efficiency for each assumed dopant molar fraction. A turbine design model is then used to define the turbine geometry based on optimal cycle conditions. It was found that doping CO2 with any of the three dopants (TiCl4, NOD, or C6F6) increases the cycle’s thermal efficiency. The greatest increase in efficiency is achieved with TiCl4 (up to 49.5%). The specific work, on the other hand, decreases with TiCl4 and C6F6, but increases with NOD. Moreover, unlike the other two dopants, NOD does not alleviate recuperator irreversibility. In terms of turbine design sensitivity, the addition of any of the three dopants increases the pressure ratio, temperature ratio, and expansion ratios across the turbine. The fluid’s density at turbine inlet increases with all dopants as well. Conversely, the speed of sound at turbine inlet decreases with all dopants, yet higher Mach numbers are expected in CO2/C6F6 turbines.
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Applied Thermal Engineering 190 (2021) 116796
Available online 1 March 2021
1359-4311/© 2021 Published by Elsevier Ltd.
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Applied Thermal Engineering
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Research paper
Sensitivity of transcritical cycle and turbine design to dopant fraction in
CO2-based working fluids
O.A. Aqel , M.T. White, M.A. Khader, A.I. Sayma
Department of Mechanical Engineering and Aeronautics, City, University of London, Northampton Square, London EC1V 0HB, UK
ARTICLE INFO
Keywords:
Transcritical Rankine cycle
Axial turbine
Sensitivity analysis
CSP
CO2-based mixtures
Dry-cooling
ABSTRACT
Supercritical CO2(sCO2) power cycles have gained prominence for their expected excellent performance
and compactness. Among their benefits, they may potentially reduce the cost of Concentrated Solar Power
(CSP) plants. Because the critical temperature of CO2is close to ambient temperatures in areas with good
solar irradiation, dry cooling may penalise the efficiency of sCO2power cycles in CSP plants. Recent
research has investigated doping CO2with different materials to increase its critical temperature, enhance
its thermodynamic cycle performance, and adapt it to dry cooling in arid climates.
This paper investigates the use of CO2/TiCl4, CO2/NOD (an unnamed Non-Organic Dopant), and CO2/C6F6
mixtures as working fluids in a transcritical Rankine cycle implemented in a 100 MWe power plant. Specific
focus is given to the effect of dopant type and fraction on optimal cycle operating conditions and on key
parameters that influence the expansion process. Thermodynamic modelling of a simple recuperated cycle is
employed to identify the optimal turbine pressure ratio and recuperator effectiveness that achieve the highest
cycle efficiency for each assumed dopant molar fraction. A turbine design model is then used to define the
turbine geometry based on optimal cycle conditions.
It was found that doping CO2with any of the three dopants (TiCl4, NOD, or C6F6) increases the cycle’s
thermal efficiency. The greatest increase in efficiency is achieved with TiCl4(up to 49.5%). The specific work,
on the other hand, decreases with TiCl4and C6F6, but increases with NOD. Moreover, unlike the other two
dopants, NOD does not alleviate recuperator irreversibility. In terms of turbine design sensitivity, the addition
of any of the three dopants increases the pressure ratio, temperature ratio, and expansion ratios across the
turbine. The fluid’s density at turbine inlet increases with all dopants as well. Conversely, the speed of sound
at turbine inlet decreases with all dopants, yet higher Mach numbers are expected in CO2/C6F6turbines.
1. Introduction
Supercritical CO2(sCO2) power cycles have been investigated for
various energy sources such as nuclear, fossil fuels, waste heat and con-
centrated solar power [1]. Several studies have identified the potential
of sCO2cycles to outperform traditional steam cycles in concentrated
solar power (CSP) plants [27], potentially making CSP more compet-
itive with solar photovoltaics (PV). It does so by increasing the power
block thermal efficiency while decreasing its complexity and size, thus
lowering the capital cost of the plant. However, one of the challenges
facing sCO2systems for CSP applications persists; the requirement
of wet cooling. Water scarcity necessitates the use of dry cooling,
which prevents condensing cycles, increases the cycle’s compression
work, and limits its efficiency. Consequently, more complex cycles may
be required to reduce compression work and realise higher efficien-
cies. Alternatively, doping CO2with an additional fluid to produce a
Corresponding author.
E-mail address: Omar.Aqel@city.ac.uk (O.A. Aqel).
CO2-based mixture could alleviate the limitations of dry cooling by
increasing the critical temperature of the working fluid.
Firstly, a distinction must be made between a CO2mixture and its
dopant. The latter is any chemical additive that is added to CO2to
produce the former. For instance, a mixture of CO2/TiCl4consists of
CO2as its base fluid and TiCl4as the dopant. The use of dopants is
being explored as means to adapt CO2properties to better suit various
applications, including CSP. In theory, mixing CO2with other fluids
may increase or decrease its critical temperature and pressure, depend-
ing on the added dopant. Dopants with critical temperatures higher
than CO2tend to increase the critical temperature of the working fluid,
whilst those with lower critical temperatures have the opposite effect.
However, this is a general trend that has many exceptions, namely in
the presence of zeotropic mixtures such as CO2-ethane [8].
https://doi.org/10.1016/j.applthermaleng.2021.116796
Received 23 September 2020; Received in revised form 3 February 2021; Accepted 23 February 2021
Applied Thermal Engineering 190 (2021) 116796
2
O.A. Aqel et al.
Nomenclature
Acronyms
AAD Average Absolute Deviation
BIP Binary Interaction Parameter
CSP Concentrated Solar Power
EoS Equation of State
HTM Heat Transfer Medium
LMTD Log-Mean Temperature Difference
MITA Minimum Internal Temperature Approach
NOD Non-Organic Dopant
PHE Primary Heat Exchanger
sCO2Supercritical Carbon Dioxide
SPT Solar Power Tower
TES Thermal Energy Storage
VLE Vapour–Liquid Equilibrium
Greek Symbols
𝜂Efficiency (%)
𝛾Adiabatic coefficient
𝛬Degree of reaction
𝜔Rotational speed (rpm)
𝜔𝑠Specific speed
𝜙Flow coefficient
𝜓Loading Coefficient
Roman Symbols
𝑏Blade height (m)
𝑐Chord length (m)
𝐶𝑝Isobaric heat capacity (J K−1 kg−1 )
Specific enthalpy (J kg−1 )
𝑘𝑖𝑗 Binary interaction coefficient
𝑀Molecular mass (kg−1 mol−1 )
𝑚Mass (kg)
𝑃Pressure (Pa)
𝑄Heat load (W)
𝑅Ideal gas constant (J kg−1 )
𝑟Pressure ratio
𝑆Pitch (m)
𝑆aAllowable stress (Pa)
𝑆eEndurance limit (Pa)
𝑇Temperature (K)
𝑡Thickness (m)
𝑇𝑟Reduced temperature
𝑊Work (W)
Subscripts
𝐻Heat source
𝐿Heat sink
𝑃Pump
𝑠Isentropic
𝑠𝑎𝑡 Saturation
𝑡Turbine
Different dopants have been proposed for different application tem-
peratures. For example, applications for which the heat sink tempera-
tures are well below 31.1 Cmay benefit from dopants that lower the
working fluid’s critical temperature. On the other hand, dopants that
increase the critical temperature of the fluid enable condensation to be
achieved using dry cooling. This expands the operation of transcritical
carbon dioxide (tCO2) cycles, which compress the fluid in its liquid
state and expand it in its supercritical state, into arid environments [9].
The benefit of using CO2dopants has been explored in the past.
Most recently, Valencia-Chapi et al. [10] quantified the effect of using
12 different CO2-based mixtures on a recompression cycle coupled
with line-focusing CSP plants. They found that mixtures increase cycle
thermal efficiency by 3%–4%, depending on the heat sink temperature
and the mode of cooling.
Jeong & Jeong [11] investigated CO2-H2S and CO2-cyclohexane
mixtures, which have higher critical temperatures than pure CO2. They
concluded that these mixtures will deteriorate simple recuperated cycle
efficiency due to the narrowing of the difference between the heat
source and sink temperatures, but will have favourable effects on
a recompression cycle since both compressors will operate near the
critical point and benefit from real gas effects. The phenomenon of real
gas effects in hydrocarbon CO2mixture cycles was studied by Invernizzi
& Van Der Stelt [12] as well. They noted that the mixtures had lower
heat transfer coefficients, which has the adverse effect of increasing the
size and cost of the heat exchangers.
Similarly, Xia et al. [13] optimised cycles using different CO2
organic compounds mixtures and identified certain mixtures that may
lead to improved cycle performance. However, hydrocarbon mixtures
are not stable enough for temperatures above 400 C, which is the
expected temperature range of CSP [12], hence alternatives are needed.
Two such alternatives were proposed by Manzolini et al. [14]. By
blending CO2with small fractions of dinitrogen tetroxide (N2O4) and
titanium tetrachloride (TiCl4), the critical temperature of the working
fluid was increased to around 50 C, which enables an air-cooled
condenser to be used in locations with relatively high ambient tem-
peratures (higher than 40 C). The dopants were chosen due to their
thermal stability and their higher critical temperatures compared to
CO2. The mass fraction ratios were set to CO2-TiCl485%–15% and
CO2-N2O478% to 22% based on a previous optimisation [15]. Cycle
optimisation carried out at high turbine entry temperatures of 550 and
700 Cresulted in cycle efficiencies up to 50%, a reduction of 50% and
20% in specific costs of the power block with respect to conventional
steam cycle and sCO2power blocks, and a reduction of 11 to 13% of
levelized cost of electricity (LCoE) with respect to a conventional steam
cycle.
A host of cycle configurations have been studied for CO2power
plants, as noted by Crespi et al. [16]. Among those studied is the simple
recuperated cycle, which consists of a compressor/pump, primary heat
exchanger, turbine, recuperator, and cooler. Its appeal comes from its
use of recuperation to benefit from high turbine outlet temperatures
and improve efficiency whilst maintaining a simple layout, which
translates to lower capital costs. With CO2as its working fluid, a
simple recuperated cycle exhibits significant exergy destruction in the
recuperator as a result of the difference in the heat capacity rates
between the hot and cold streams. Several other cycle configurations
have been devised to reduce recuperator irreversibility. For example,
the recompression and partial cooling achieve this by dividing the recu-
perator into two stages and splitting the flow between them. However,
Manzolini et al. [14] have demonstrated that the use of dopants may
reduce recuperator irreversibility by reducing the heat capacity rate
difference between the hot and cold streams.
The promising results of Manzolini et al. [14] brought forth the
EU funded H2020 SCARABEUS project [17]. The project identifies
blended CO2working fluids as key to making CSP more competitive
against other forms of electrical power generation. The overarching
goal of the SCARABEUS project is to lower the LCoE of CSP plants to
below 96 euro/MWh (30% lower than currently possible). Within the
SCARABEUS project it is necessary to identify optimal cycles and to
design the main system components, including the turbomachinery and
heat exchangers.
Applied Thermal Engineering 190 (2021) 116796
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O.A. Aqel et al.
Fig. 1. 𝑇-𝑠diagram and schematic of a simple recuperated tCO2cycle.
The path to commercial realisation of CO2power cycles requires the
development of key components such as the turbomachinery and heat
exchangers. Previous research has determined that turbine performance
has a significant influence on the overall cycle efficiency [1820]. In
the case of Novales et al. [19] it was found that sCO2Brayton cycles
can only compete with state-of-the-art steam cycles at elevated turbine
efficiencies above 92%. They also estimated that a 1% efficiency change
in the turbine leads to 0.31 – 0.38% change in cycle efficiency depend-
ing on cycle type and conditions. While Allison et al. [20] put the figure
at around 0.5% cycle efficiency for every 1% turbine efficiency.
The aim of the current work is to investigate the sensitivity of key
cycle and turbine design parameters to dopant type and amount within
a simple recuperated cycle layout. The chosen dopants are TiCl4, C6F6,
and an unnamed Non-Organic Dopant (henceforth referred to as NOD).
These are among the dopants selected as preliminary candidates by the
SCARABEUS project. The chemical formula of NOD will not revealed in
this work because it remains confidential within the project consortium.
To the authors’ knowledge, there has not been any prior investigations
of the turbine design sensitivity to dopant fraction. Consequently, this
paper aims to provide a description of the dopant effects, and most
importantly, to determine if turbine design is insensitive enough to
allow the use of pure CO2fluid properties during the design process
instead of the blends.
The cost and challenges of incorporating CO2-based mixtures as
working fluids in power cycles as a whole are not addressed in this
work. This aspect was the focus of other works [14]. Moreover, the
thermal stability of these dopants under high temperature (700 C)
and pressure (25 MPa) conditions requires investigation, but will not
be dealt with here.
2. Methodology
2.1. Cycle model
In-line with the previous study by Manzolini et al. [14], a simple
recuperated tCO2cycle was chosen for the purpose of this study. Cycle
thermodynamic analysis assumes the following:
The changes in kinetic and potential energy are negligible.
Components operate under steady conditions.
The pump and turbine have fixed isentropic efficiencies.
The pressure drop in both sides of a heat exchanger is divided
proportionally to the heat duty.
Heat loss to the surroundings is negligible.
A schematic of the tCO2cycle and its Temperature–Entropy (𝑇-𝑠)
diagram are shown in Fig. 1. The cycle is modelled by applying the first
law of thermodynamics to all equipment. Compression and expansion
work are expressed by Eqs. (1) and (2):
𝑤p=21(1)
𝑤t=45(2)
where ̇
𝑤pand ̇
𝑤tare the specific compression and expansion work,
respectively, and iis the enthalpy at point ‘i’ in the cycle. The
difference between the expansion and compression work is defined as
the net specific work output, and is expressed by Eq. (3):
𝑤n=𝑤t𝑤p(3)
Once the cycle output work capacity ̇
𝑊nis set, the net specific work is
used to find the mass flow rate of the working fluid using Eq. (4):
̇𝑚 =̇
𝑊n𝑤n(4)
Heat loads in the primary heat exchanger, recuperator and cooler are
expressed by Eqs. (5) to (7):
𝑞H=43(5)
𝑞R=32=56(6)
𝑞L=61(7)
Cycle thermal efficiency is expressed as the ratio of the net work
produced to the heat consumed by the cycle in Eq. (8):
𝜂o=𝑤t𝑤p
𝑞H
(8)
The losses within the pump and turbine are approximated by assum-
ing isentropic efficiencies for each component, as expressed by Eqs. (9)
and (10):
𝜂p=2s 1
21
(9)
𝜂t=45
45s
(10)
where the subscript ‘s’ denotes the outlet conditions assuming isen-
tropic compression and expansion.
The recuperator effectiveness determines the ratio of the actual heat
load to the maximum attainable heat load from the stream with the
lowest heat-capacity rate, as expressed in Eq. (11):
𝜖=𝑞R
𝑞R,max
=56
min @T5,P2 @T2,P2,@T5,P5 @T2,P5  (11)
An internal pinch point is expected in the recuperator, which must
be determined to avoid physically impossible (overlapping) tempera-
ture profiles. In order to do so, the recuperator is discretised into cells,
Applied Thermal Engineering 190 (2021) 116796
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O.A. Aqel et al.
Fig. 2. Illustrative example of recuperator discretisation.
as shown in Fig. 2, each with an equal heat load. The pressure drop
is also assumed to be equally divided along all nodes, although this is
not entirely representative since the transport properties of the fluids
and the length of each segment differ. However, because of its trivial
effect on the isobaric heat capacity, the variation in pressure drop is
not expected to notably change the value of the minimum internal
temperature approach (MITA). The first law is then applied between
the nodes to calculate the change in enthalpy based on the exchanged
heat. Finally, the enthalpy and pressure are fed into the Equation of
State (EoS) to calculate the temperature at each node.
The recuperator is sized based on its overall conductance. The
overall conductance is defined for each node as:
𝑈𝐴 =𝑄𝐿𝑀𝑇 𝐷 (12)
where 𝑈𝐴 is the overall conductance, 𝑄is the heat load for each
cell, and 𝐿𝑀𝑇 𝐷 is the log mean temperature difference between its
terminals, which is expressed as:
𝐿𝑀𝑇 𝐷 =(𝑇𝑖
𝑇𝑖
𝑐)−(𝑇𝑖+1
𝑇𝑖+1
𝑐)
ln ((𝑇𝑖
𝑇𝑖
𝑐)∕(𝑇𝑖+1
𝑇𝑖+1
𝑐)) (13)
The error in the calculated MITA is dependent on the chosen number
of cells. It was found that dividing the recuperator into 50 cells results
in <2% error for all mixtures at all blend fractions.
The pressure ratio across the turbine is defined as:
𝑟=𝑃4𝑃5(14)
where and 𝑃4and 𝑃5are the inlet and outlet total pressures, respec-
tively.
The cycle state points are determined by setting the pump inlet
temperature (𝑇1), the turbine inlet temperature (𝑇4), pressure ratio,
component efficiencies, and pressure drops. Within this study, 𝑇1and
𝑇4will be set according to the values expected in state-of-the-art dry-
cooled CSP plants. Whilst the recuperator effectiveness and the turbine
pressure ratio are the two variables that will be tuned to optimise the
cycle thermal efficiency, as will be explained in Section 2.3.
2.2. Turbine model
To model the turbine, a preliminary mean line turbine design ap-
proach was adopted. The target net power for the SCARABEUS plant is
100 MW turbine, for which a multi-stage axial architecture is recom-
mended [21]. For such a compressible flow axial turbine, the optimal
specific speed range is from 0.4 to 1.0 (rad/s) [22]. The specific speed
is defined as:
𝜔𝑠=
𝜔̇
𝑉
1
2
5
𝛥ℎ
3
4
𝑠𝑠
(15)
where 𝜔𝑠and 𝜔are the specific speed and nominal speed (rpm),
respectively. The turbine exhaust volume flow rate is represented by
̇
𝑉5(in m3/s) and the isotropic enthalpy drop by 𝛥ℎ𝑠𝑠 (in J/kg).
The blade-loading coefficient, turbine flow coefficient, and degree
of reaction given by Eqs. (16) to (18) are non-dimensional turbo-
machinery design parameters that indicate the required blade speed,
fluid axial velocity, and proportion of expansion that occurs within the
rotor. These parameters are widely used to predict and optimise the
axial turbine’s performance. Optimal values for these parameters are
readily reported within the literature for large-scale turbines operating
with steam or air [23]. These values can be readily used to provide a
preliminary assessment of turbine design. The design parameters are
defined as follows:
𝜓=𝛥ℎ𝑜𝑖𝑈2
𝑖(16)
𝜙=𝐶𝑎𝑖𝑈𝑖(17)
𝛬=𝛥ℎ𝑟𝑖𝛥ℎ0𝑖(18)
where 𝛥ℎ𝑜𝑖 is the total enthalpy drop across ith stage of the turbine,
𝑈𝑖is the blade speed of the rotor of the ith stage at the design radius
(mean radius is used in this study), 𝐶𝑎𝑖 is the axial flow velocity at
the rotor outlet of the stage and 𝛥ℎ𝑟is the enthalpy drop across the
rotor of the ith stage. Further details on the design methodology and a
previous validation study that has been conducted are reported in Salah
et al. [24].
The number of turbine stages is determined by mechanical consid-
erations, namely the maximum allowable stresses on the rotor blades.
Mechanical stresses are approximated by assuming Inconel 740H blade
material. Based on manufacturer’s data, the ultimate tensile strength of
Inconel 740H is 912 MPa at 700 C[25]. Moreover, an allowable stress
limit to endurance strength ratio of (𝑆a𝑆e= 73∕240) is approximated
based on 0.2% creep strain and a 10 000 h fatigue life for an uncooled
turbine. To construct the modified Goodman-line, a safety factor of
(𝑛= 1.5) is assumed. These assumptions are used in Section 3.5 to
determine the number of stages in a turbine design case study.
2.3. Optimisation model
AMATLAB program was developed to study the sensitivity of the
optimal cycle and turbine design to the selected blend. The sensitivity
analysis flowchart in Fig. 3 shows two layers of optimisation corre-
sponding to the dopant molar fraction and the two design variables;
pressure ratio and recuperator effectiveness. The layers are embedded
within each other, meaning that an increment in the dopant molar
fraction restarts the optimisation of the design variables. Once optimum
cycle conditions for a given mixture composition were found, the
program then produces a turbine geometry using the turbine boundary
conditions resulting from the optimal cycle. To calculate the ther-
modynamic and transport properties of the working fluids, Simulis
Thermodynamics – a commercial software – was used [26].
Within Simulis Thermodynamics, the Peng–Robinson (PR) EoS was
selected because it is considered to be a reliable yet simple model that
is fit for purpose [27]. Representation of the mixtures can be achieved
by coupling PR EoS with a mixing model; the Van der Waals model in
this case. To account for non-ideal behaviour, the Binary Interaction
Parameter (𝑘𝑖𝑗 ) was derived from empirical data and used to tune the
mixing model.
Simulis Thermodynamics was validated through a simple recuperated
cycle model for pure compounds and mixtures, respectively. A pure
CO2cycle was simulated via a REFPROP-based code developed in-
house, while data obtained using Aspen Plus for modelling of CO2-TiCl4
mixture was obtained from Manzolini et al. [14]. The present model
showed results consistent with those from REFPROP and Aspen with
percentage variation of 0.5% in efficiency (0.2% nominal efficiency
variation).
Applied Thermal Engineering 190 (2021) 116796
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O.A. Aqel et al.
Fig. 3. Flowchart of optimisation model.
Table 1
Physical and thermodynamic properties of pure compounds (calculated using Simulis Thermodynamics).
Compound Molecular
weight (g/mol)
Acentric
factor
Critical
temperature (K)
Critical
pressure (MPa)
Ideal specific heat at
𝑇r= 2 (J K−1 mol−1)
CO244.01 0.2236 304.2 7.382 47.34
TiCl4189.7 0.2837 639.1 4.661 107.2
NOD 60>0.23>400>7.5>50>
C6F6186.1 0.3953 516.7 3.273 272.1
2.4. Choice of dopants
The mixtures studied in this paper are among the candidates that
have been identified by the SCARABEUS project as potential dopants
for CO2based power cycles operating within CSP. The main dopant
thermophysical parameters of interest are shown in Table 1.
In this study, 𝑘ij was calculated against regressed Vapour–Liquid
Equilibrium (VLE) empirical data and used to tune the mixing models
of CO2/NOD and CO2/C6F6. Unlike the other two mixtures, the 𝑘ij
value for CO2/TiCl4was taken directly from literature. This is be-
cause the lack of experimental data means any recalibration of 𝑘ij
for CO2/TiCl4will retain a high uncertainty margin. In such a case,
sensible comparison between the original and the new 𝑘ij values will
not be possible.
Determining the value of 𝑘ij required an optimisation problem. By
tuning 𝑘ij, the calculated VLE lines were manipulated and compared
with experimental data to find the best-fit 𝑘ij value. An unconstrained
gradient-based optimisation approach was used. The weighted least
mean square method was used as the objective function. Like the simple
least square method, it minimises the residuals between experimental
and calculated data, but it also weighs each residual with the exper-
imental uncertainty of the experimental data. The objective function
is reduced or expanded depending on the availability of experimental
data. The objective function for the optimisation is defined as:
𝑓(𝑘ij) = 1
𝑛e
𝑛e
i=1 ̂𝑥1,ĩ𝑥1,i
𝑢𝑒
x1,i+̂𝑦1,ĩ𝑦1,i
𝑢𝑒
̂y1,i+
̂
𝑇ĩ
𝑇i
𝑢𝑒
̂
Ti
+
̂
𝑃ĩ
𝑃i
𝑢𝑒
̂
Pi(19)
where 𝑥1and 𝑦1are the liquid and vapour molar fractions of CO2,
respectively. The accents () and () indicate the measured and calcu-
lated values, respectively. Experimental uncertainty is represented by
the term 𝑢𝑒. The number of experiments is denoted by 𝑛e.
A Monte Carlo technique similar to that used by Hajipour et al. [28]
was employed to estimate the uncertainties of the binary interac-
tion parameters. The four main steps in applying this technique are:
(1) specification of probability density functions for the uncertain
input variables involved in the study based on the knowledge of their
uncertainty; (2) probabilistic sampling of the uncertainty space; (3)
simulation and calculation of output parameters by passing each sample
set through the model; and (4) statistical analysis of the results to
evaluate the uncertainty of the model outputs.
Applied Thermal Engineering 190 (2021) 116796
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O.A. Aqel et al.
Fig. 4. Phase diagrams for the mixture CO2/NOD (left) and CO2/C6F6(right). Lines represent the results of PR EoS with (𝑘ij = 0.0243) and (𝑘ij = 0.0312) for CO2/NOD and
CO2/C6F6, respectively. Whilst the circles are the experimental data points taken from their respective sources.
Table 2
Optimised BIP with uncertainty intervals.
Mixture 𝑘ij Uncertainty Source of data
CO2/TiCl40.0745 ±0.0456 (57.6%) Taken from Bonalumi et al. [27]
CO2/NOD 0.0243 ±0.0031 (12.8%) Reference not provided
CO2/C6F60.0312 ±0.0104 (33.3%) Calculated from Dias et al. [29]
In this study, the experimental data were assumed to be normally
distributed in accordance with the declared uncertainty (Step 1). Ran-
dom sampling with replacement was repeatedly conducted for a total
of 1000 trials (Steps 2 & 3). Finally, the mode value is taken as 𝑘ij, while
its uncertainty is based on the 95% confidence interval from the mean
(Step 4). The regressed VLE lines of CO2/NOD and CO2/C6F6are shown
in Fig. 4. The values of 𝑘ij adopted in this study are shown in Table 2.
2.5. Optimisation conditions
The pump inlet temperature (𝑇1) was set to 50 C. This was chosen
to be compatible with dry cooling temperatures in hot arid regions,
assuming an ambient dry-bulb temperature of 40 C. The cooling air
is assumed to warm up by 5 Cas it passes through the condenser whilst
maintaining a minimum temperature difference of 5 C[3033]. The
pump inlet was assumed to be subcooled by 2 Cbelow the saturation
pressure. Consequently, the pump inlet pressure (𝑃1) is defined by the
saturation pressure of the fluid at 52 C. The turbine inlet tempera-
ture (𝑇4) was set to 700 C, which is targeted by an advanced CSP
receiver employing sodium salt as its Heat Transfer Medium (HTM).
Additionally, the turbine inlet pressure (𝑃4) was restricted to 25 MPa
as recommended by Dostal et al. [18].
To prevent the dopant from becoming the dominant compound
in the mixture, the maximum molar fraction of the dopant was set
to 0.40. The minimum dopant molar fraction was assumed to be the
value at which the critical temperature of the mixture is equal to, or
slightly exceeds 57 C(40 Cheat sink temperature +10 Ccooler
temperature difference +2Csub-cooling +5Cmargin from the
critical temperature). A summary of the assumptions is provided in
Table 3.
3. Results and discussion
In order to fully capture the effect of mixture composition on the
turbine design, it is helpful to first examine its effect on the cycle
parameters as a whole. Analysis of the results will first investigate
cycle behaviour, with emphasis on turbine boundary conditions and the
expansion process. Then, the change in working fluid characteristics
Table 3
Inputs required for cycle solution.
Controlled parameters
Parameter Range Unit
Dopant molar fraction 𝑋fMax(0.4) %
Turbine inlet temperature (𝑇4) 700 C
Pump inlet temperature (𝑇1) 50 C
Pump isentropic efficiency (𝜂p) 85 %
Turbine isentropic efficiency (𝜂t) 90 %
Generator efficiency (𝜂g) 99 %
Minimum internal temperature approach (MITA) 5 C
Net electrical power (𝑊e) 100 MW
Pressure drop in primary heat exchanger 𝛥𝑝𝑝0.015 –
Pressure drop in recuperator 𝛥𝑝𝑝0.01 and 0.015
High- and Low-pressure sides
Pressure drop in condenser 𝛥𝑝𝑝0.02 –
Dependent parameters
Pump inlet pressure (𝑃1)𝑃sat@(T1+2) MPa
Turbine inlet pressure (𝑃4) Max (25) MPa
Optimised parameters
Pressure ratio (𝑟) 2 to Max (𝑃4)/𝑃1
Recuperator effectiveness (𝜖) 80 to 98 %
and their expected effect on the cycle and turbine design is consid-
ered. After which, turbine geometries for the SCARABEUS project case
study will be discussed in more detail. Henceforth, any observations
on parameter trends will be in reference to the increase in molar
fraction of the dopant, unless stated otherwise. Moreover, a uniform
graphical representation of the three mixtures is adopted throughout
the proceeding sections as introduced in Fig. 5.
The critical loci of the binary mixtures are illustrated in Fig. 5. There
is a notable difference in the shape of the critical locus of each mixture.
The shape indicates the evolution of the Liquid–Vapour coexistence
lines with changing composition. Since the minimum cycle pressure
in a transcritical cycle is determined by the condensation pressure
at the prescribed minimum temperature, the shift in the coexistence
line defines a new equilibrium condensation pressure, which ultimately
influences the cycle’s pressure ratio. In general, as the critical pressure
increases, the vapour pressure of the fluid increases, thus decreasing
the cycle pressure ratio for a fixed maximum turbine inlet pressure.
Whereas an increase in the critical temperature decreases the vapour
pressure of the fluid and increases the cycle’s pressure ratio. The change
in vapour pressure is also proportional to its position relative to the
critical point, and is greatest near the critical point. It is the interplay
between these factors that eventually determines the aggregate change
in vapour pressure, namely the pump inlet pressure.
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Fig. 5. The highlighted segments represent the critical loci corresponding to the blend
fractions studied for each mixture. The point labels indicate the dopant molar fraction
at that point. The same styling convention is used to differentiate the three mixtures
in all subsequent figures.
3.1. Cycle analysis
The pump inlet pressures decrease as the dopant fractions increase
as seen in Fig. 6. Consequently, the decrease in condensation pressure
induces an increase in the cycle pressure ratio in order to achieve higher
levels of cycle thermal efficiency. The fall in condensation pressure is
directly proportional to the increase in pressure ratio; which is greatest
in CO2/C6F6.
The trend in efficiency exhibits an optimal point for each mixture, as
seen in Fig. 7. The dopant molar fractions corresponding to the points
of maximum efficiency are 0.174, 0.264, and 0.167 for mixtures of
CO2/TiCl4, CO2/NOD, and CO2/C6F6, respectively. Among the three
blends, CO2/TiCl4achieves the highest thermal efficiency of 49.5%,
followed by CO2/C6F6with an optimal thermal efficiency of 46.5%,
while CO2/NOD achieves the lowest efficiency of 42.3%. Although
not shown in the figure, simulation of an equivelant pure CO2cycle
achieves thermal efficiency of 44.0%. The 7.2% difference in efficiency
between CO2/TiCl4and CO2/NOD cycles highlights the significant
influence the choice of dopant has on cycle performance. These dopant
molar fractions will later be used to compare the turbine geometries of
the three mixtures.
The trend in efficiency is a consequence of the change in the net
shaft work (𝑤t𝑤p) and the primary heat exchanger heat load, which
in turn is affected by the change in recuperated heat. By inspection of
the rate of change of the two parameters (net specific work and PHE
heat load) with the dopant fraction, the change in efficiency becomes
clearer. For CO2/NOD, both parameters increase at roughly the same
rate, thus maintaining a fairly constant efficiency with dopant fraction.
For CO2/C6F6the PHE heat load decreases at a decreasing rate while
the net specific work decreases at an almost constant rate. Therefore,
the cycle efficiency exhibits an inversion point of maximum efficiency
after which the PHE heat lead decreases at a rate lower than that of the
net specific work, which causes efficiency to drop. The same applies to
CO2/TiCl4, but the drop in efficiency is more dramatic because the net
specific work decreases at an increasing rate.
On the other hand, the trend in the net work is mainly driven
by the change in the specific work, as seen in Fig. 11. Similar to a
pure sCO2cycle, cycles operating with CO2based mixtures are highly
recuperative. As shown in Fig. 7, the recuperated heat is much greater
than the primary heat exchanger load for all mixture compositions. This
is because of the relatively low pressure ratios and specific work across
the turbine, which accompany higher turbine outlet temperatures.
Recuperated heat is 3.2 to 3.5 times greater than the primary heat
exchanger load for CO2/TiCl4, 2.3 to 4.0 times greater for CO2/C6F6,
and 1.6 to 1.8 times greater for CO2/NOD.
As the recuperator effectiveness increases, the MITA in the recu-
perator decreases. Therefore, the recuperator effectiveness is reduced
to maintain a MITA of around 5 C, whilst achieving optimal cycle
thermal efficiency. Fig. 8 shows the reduction in effectiveness with
increasing dopant fractions. It was found that CO2/NOD exhibits an
abrupt fall in recuperator effectiveness for dopant molar fractions
above 0.26, which corresponds to the NOD molar fraction above which
condensation occurs in the recuperator. The same effect is illustrated in
Fig. 7 where the recuperated heat rises abruptly at the same NOD molar
fraction.
The well-matched temperature profiles and higher effectiveness
comes at the cost of larger recuperators. The overall conductance values
of the entire recuperator are indicative of its size and were obtained by
adding the overall conductance of each of its discrete cells (see Fig. 2).
As seen in Fig. 8, the overall conductance of the two heavy mixtures –
CO2/TiCl4and CO2/C6F6– are much higher than CO2/NOD. The trend
in overall conductance with dopant molar fraction is mainly attributed
to the change in the temperature profiles of the two streams, indicated
by the average LMTD, also shown in Fig. 8. The greater the LMTD the
smaller is the recuperator.
Fig. 6. Variation of pump inlet pressure and pressure ratio with dopant molar fraction.
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Fig. 7. Variation of cycle thermal efficiency, net shaft work, primary heat exchanger load, and the specific recuperated heat with dopant molar fraction.
Fig. 8. Variation of recuperator effectiveness and overall conductance with dopant molar fraction.
A survey of the recuperator 𝑇-𝑄diagram for the optimal blend of
each dopant is shown in Fig. 9. It reveals the difference between the
temperature profiles of each blend and the exergy loss (irreversibility)
in the recuperator. CO2/NOD exhibits the greatest irreversibility and
poorest match of the two streams; similar to pure CO2. A proven
solution to this issue is the adoption of more complex cycle architec-
tures such as the recompression or partial cooling cycles [16]. The
temperature profiles for CO2/C6F6and CO2/TiCl4, on the other hand,
are well matched. Therefore, these mixtures work well in a simple
recuperative cycle, and may not require elaborate cycle configurations,
as previously noted by Manzolini et al. [14].
Because their profiles are almost parallel, higher effectiveness in
CO2/C6F6and CO2/TiCl4cycles will reduce the exergy loss along the
recuperator length, not just at the pinch point. However, using the
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Fig. 9. Temperature versus heat load profile of the recuperator for each working fluid at optimal dopant fraction. The plots at the top indicate the change in the liquid and
vapour molar fractions of the hot stream along the recuperator.
Fig. 10. Difference between bubble and dew temperatures (temperature glide) for all
compositions of the three mixtures. the highlighted segments represent the range of
molar fractions studied here.
same argument, a CO2/NOD working fluid would not benefit much
from higher effectiveness since it will reduce exergy loss at the pinch
point without affecting the majority of the exergy loss elsewhere in the
recuperator. Therefore, using a high recuperator effectiveness for all
working fluids while discounting the pinch point approach tempera-
ture from the analysis gives CO2/NOD a false advantage. It may also
lead to unobserved temperature profile overlaps and the consequent
misidentification of the optimal dopant fraction and turbine design
point.
Fig. 9 also shows the vapour and liquid compositions of the hot
stream within the recuperator. Condensation does not occur in CO2/
NOD mixture at this composition, and is also trivial for all considered
fractions of NOD below (0.4). Considerable condensation occurs in
both CO2/TiCl4and CO2/C6F6recuperators, where almost 33% and
23% of the heat is exchanged during two-phase flow, respectively. This
phenomenon is directly caused by the mixture’s temperature glide. As
the dew temperature becomes greater than the bubble temperature,
the portion of the recuperation process that occurs in the two-phase
region increases. Fig. 10, shows the temperature glide during heat
rejection for the three working fluids. CO2/TiCl4exhibits the greatest
temperature glide, followed by CO2/C6F6and CO2/NOD. The high
degree of glide in the two heavy mixtures suggests that appreciable
fractionation (where one component is largely in the vapour state,
while the other is still mostly liquid) occurs during cooling, which
might require additional equipment such as vapour–liquid separators
and separate heat exchangers for each component.
As seen in Fig. 11, the turbine specific work decreases for both
CO2/TiCl4and CO2/C6F6, but increases for CO2/NOD; the cause of
which will be explained later. For a fixed electrical power output, the
change in specific work causes an opposite trend in the mass flow rate.
Not only does the turbine exhaust volumetric flow rate depend on the
mass flow rate, but it also depends on its density. For all working fluids,
the volume flow rate decreases with dopant fraction because of the
increase in the fluids’ density.
A zero-dimensional study of the specific speed for the whole turbine
gives an indication of its shape and size. With a fixed rotational speed,
any change in the specific speed will be a result of the change in the
volumetric flow rate or specific enthalpy drop across the turbine. As
seen in Fig. 11 the specific speed of CO2/TiCl4and CO2/C6F6increases
with blend fraction, indicating a reduction in the turbine’s diameter,
accompanied by an increase in the annulus area. The opposite is true
for the CO2/NOD mixture, where wider turbines with smaller annulus
areas are expected at higher dopant fractions.
3.2. Incorporation into solar power tower
To compare the adaptability of the optimal working fluids to Solar
Power Tower (SPT) applications, the cycles were tested for how well
they incorporate a thermal energy storage (TES) system and for their
compatibility with dry cooling. Although SPT plants can directly heat
the working fluid in the receiver, the use of a TES system presents op-
erational and economic advantages. Therefore, it should be considered
when comparing between cycles.
An indicative TES size comparison was obtained by assuming a
constant temperature difference between the heat transfer medium
(HTM) and the working fluid at both terminals of the primary heat
exchanger (PHE). Consequently, the change in the working fluid and
HTM temperatures across the PHE are equal. Moreover, with a constant
HTM specific heat capacity, Eq. (20) describes the relation between
the HTM mass (𝑚HTM), the cycle heat input (𝑄H), and the rise in the
working fluid’s temperature across the PHE (𝛥𝑇 PHE).
𝑚HTM =𝑄H∕(𝐶p𝛥𝑇 PHE)(20)
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Fig. 11. Variation of turbine specific work, mass flow rate, volume flow rate at turbine outlet, and specific speed with dopant molar fraction.
Fig. 12. Thermal energy storage size indication.
As previously established, CO2/NOD is the least recuperative of the
three mixtures because it requires the highest heat input, as seen in
Fig. 12. However, for the same reason, it exhibits the highest tem-
perature difference across the PHE. Therefore, greater sensible heat is
extracted from the HTM with CO2/NOD. This manifests in the overall
effect on TES size, which is indicated by the ratio 𝑄H𝛥𝑇 PHE, and is
the lowest for CO2/NOD. Between the remaining two mixtures, the
ratio is around 1.4 MW/K for the optimal blend fractions of 0.174
and 0.167 for CO2/TiCl4and CO2/C6F6, respectively. Nevertheless,
CO2/C6F6will require larger TES at higher dopant fractions.
Variations in ambient temperature affect the condenser’s ability to
remove heat from the cycle, which will change the temperature of the
working fluid at pump inlet. The more susceptible the performance
of the cycle is to variations in the pump inlet temperature, the less
compatible it is with dry cooling.
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Fig. 13. Change in thermal efficiency with pump inlet temperature variations.
Logically, the rise of ambient temperatures above the 40 Cdesign
point is the main concern, since a drop in ambient temperatures is
likely to improve the cycle’s performance, and can even be mitigated
by controlled cooling, if need be. However, an elevation in the cooling
air temperature cannot be easily mitigated, thus it will affect the
condenser’s performance. Fig. 13 reveals the loss in efficiency as the
pump inlet temperature is increased by up to 10 K. The efficiency for
each temperature increment is obtained by rerunning the optimisation
at the elevated turbine inlet temperatures. Although, all three mixtures
exhibit about 4% loss in efficiency, the effect is less pronounced in
CO2/TiCl4and CO2/C6F6because it occurs gradually over the 10 K
range. Conversely, the 4% loss occurs within an increment of only
3 K for CO2/NOD. This is a consequence of the pump inlet conditions
growing closer to the critical point where the fluid becomes more
compressible, thus requires greater compression work.
3.3. Expansion process
To characterise the expansion process, Figs. 14 and 15 have been
derived by assuming ideal gas behaviour throughout the expansion
process and using the isentropic relations shown in Eqs. (21) and (22):
𝑟=𝑃in
𝑃out
=𝑇in
𝑇out 𝛾
𝛾−1 =𝜈out
𝜈in 𝛾
(21)
𝑤t=𝜂t𝛾
𝛾− 1 𝑃in
𝜌in 1 − 𝑟
1−𝛾
𝛾(22)
where 𝛾is the adiabatic coefficient (𝛾=𝐶p𝐶v). The assumption
of ideal gas behaviour easily permits an investigation of certain flow
features without the aid of a more sophisticated EoS. This assumption
is justified by the near unity (0.95 to 1.1) compressibility factor of all
working fluids at both turbine inlet and outlet.
As shown in Fig. 14, the adiabatic coefficients of CO2/TiCl4and
CO2/NOD increase modestly, but significantly decrease for CO2/C6F6.
The trend in the adiabatic coefficient of CO2/C6F6is almost coincident
with the isoline 𝑇1𝑇2= 1.15, indicating that the decrease in the
isentropic coefficient negates the effect of the increase in pressure ratio
on the temperature drop across the turbine, thus maintaining almost the
same temperature drop for all fractions. In contrast, the temperature
drop increases for CO2/TiCl4and CO2/NOD, suggesting a reduction in
the recuperative capacity of their cycles. This finding agrees with the
trends in specific recuperated heat shown in Fig. 7.
Fig. 14. Maps the effect of dopant fraction on the turbine isentropic volume, tem-
perature, and pressure ratios. The size of the point is proportional to the dopant
fraction.
The expansion ratio of the CO2/C6F6increases at a higher rate
than the other two mixtures because of the more drastic changes in
the pressure ratio and in the adiabatic coefficient. Higher expansion
ratios indicate greater compressibility effects, as confirmed by Fig. 17.
Therefore, CO2/C6F6turbines may be more susceptible to supersonic
flows than the other two mixtures, and are also likely to exhibit larger
blade height variations in multi-stage turbines as the amount of C6F6
increases. This is explored in the next section.
By rearranging Eq. (22), the relation between specific work and
adiabatic coefficient can be described through the work to pressure–
volume ratio, as seen in Eq. (23).
𝑤t
(𝑃 𝜈)in
=𝜂t𝛾
𝛾− 1 1 − 𝑟
1−𝛾
𝛾(23)
The fixed density-specific work isolines in Fig. 14 depict the relative
independence of specific work from the adiabatic coefficient. At its
greatest, the drop in the adiabatic coefficient of CO2/C6F6causes a
mere 3% drop in specific work, whereas its effect on the specific work
for the other two mixtures is less than 1%. Overall, Fig. 14 suggests that
the adiabatic coefficient becomes more significant at higher pressure
ratios. Therefore, if the maximum allowable cycle pressure is increased,
the variances between the expansion processes of the mixtures are
expected to become more pronounced.
The effect of the density at turbine inlet is evident in Fig. 15. Whilst
ignoring the effect of the change in the adiabatic coefficient on specific
work, which has been shown to be trivial, higher densities result in
lower specific work for a given pressure ratio. In the present study, both
density at turbine inlet and pressure ratio increase with dopant molar
fraction, but to varying degrees. For CO2/NOD the increase in density
is small, thus the specific work increases with the increasing pressure
ratio. For CO2/TiCl4and CO2/C6F6, however, there is a significant
increase in density which causes a decrease in the specific work, even
though the pressure ratio increases. For comparison, the densities of
CO2/TiCl4, CO2/NOD, and CO2/C6F6increase by 74%, 11%, and 91%,
whilst the pressure ratios increase by 28%, 35%, and 76%, respectively.
The outcome is a 27% and 19% decrease in specific work for CO2/TiCl4
and CO2/C6F6, and an increase of 12% in specific work for CO2/NOD.
These results demonstrate the dependence of specific work on both
density and pressure ratio, which are in turn dependent on the dopant
molar fraction.
The same phenomena may also be observed through the slope of the
expansion isentrope in a 𝑃-diagram and in Eq. (24). In Fig. 16, the
slope of the isentrope depends on the fluid density while the horizontal
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Fig. 15. Maps the effect of dopant fraction on the working fluid’s density at turbine inlet, pressure ratio, and turbine specific work. The size of the point is proportional to the
dopant fraction.
Fig. 16. Compares between the expansion process for three different amounts of dopant fractions. The solid line (-) indicates low dopant fraction, the dashed line (- -) indicates
medium dopant fraction, and the dot–dash (-.) line indicates high dopant fraction.
distance between the two ends of the expansion process indicates its
specific work.
d=𝑇d𝑠+ d𝑃𝜌d𝑠=0
d= d𝑃𝜌(24)
As the molar fraction of the dopant increases, the slope and lower
end of the expansion process changes according to the turbine inlet
density and pressure ratio, respectively. Since the density of all mix-
tures increases with blend fraction, their expansion follows a steeper
isentrope. Simultaneously, the increasing pressure ratio extends the
vertical length of the line. The combined movements of the two effects
ultimately determines the horizontal distance (enthalpy drop). The
same effect may be attained by lowering the turbine inlet temperature
and moving closer to the Andrew’s curve where densities are higher.
3.4. Molecular characteristics
As shown in Fig. 17, the molecular weight of the working fluid in-
creases significantly with the addition of C6F6or TiCl4, but only slightly
with NOD. Higher molecular weights are known to decrease the heat
transfer coefficient and increase the size of the heat exchangers [34].
Since the turbine inlet temperature is constant, and the effect of the
isentropic coefficient is minor, the increase in molecular weight leads
to an increase in density and a decrease in the speed of sound according
to Eqs. (25) and (26):
𝑎=𝛾𝑅𝑇 𝑀(25)
𝜌=𝑃 𝑀𝑅𝑇 (26)
where the fluid is assumed to be an ideal gas, 𝑎is the speed of sound
(m/s), 𝛾is the adiabatic coefficient, 𝑀is the molar weight (kg/mol),
and 𝑅is the ideal gas constant (8.314 J/mol K).
The decrease in the speed of sound is almost identical for the two
heavy mixtures CO2/TiCl4and CO2/C6F6, while CO2/NOD exhibits a
less dramatic change in the speed of sound. As a general rule, the
reduction in the speed of sound in conjunction with the increase in
pressure ratio may lead to an increase in Mach numbers and the
creation of supersonic flows.
Counter intuitively, CO2/TiCl4is expected to have lower Mach
numbers than CO2/C6F6, although it exhibits comparable sound speeds.
This contrast is attributed to the particulars of the overall cycle be-
haviour which limit the pressure drop of CO2/TiCl4during expansion.
Consequently, for the same number of stages, lower Mach numbers
are expected in CO2/TiCl4than the other two mixtures. However,
as will be seen in the next section, subsonic flow requirements are
not the determining factor for the number of turbine stages, rather it
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Fig. 17. Variation of molecular weight, ideal specific heat capacity, compressibility factor at turbine inlet, and speed of sound at turbine inlet with dopant molar fraction.
is the maximum allowable blade stress. Therefore, it is unlikely that
supersonic flow conditions will present issues for any of the blends.
The ideal heat capacity, also shown in Fig. 17, is also effected
by the dopant molar fraction. It increases for mixtures of CO2/C6F6
and CO2/TiCl4, but remains almost constant for CO2/NOD. Ideal heat
capacity depends on the molecular complexity of the fluid (number
of atoms per molecule and their configurations). From a molecular
perspective, this trend may be attributed to the increasing complexity
of the mixture molecules with the addition of the dopants. Since NOD
has a similar complexity to that of CO2, there is no tangible change in
the mixture’s ideal heat capacity.
The ideal heat capacity has profound implications on recuperative
cycles. Higher values reduce the difference between the heat capacities
of the low- and high-pressure streams of the recuperator. The relative
difference between the two has a direct effect on the pinch point
temperature and the compatibility of the temperature profiles; i.e. the
lower the difference the better the recuperation. The trend in ideal
specific heat explains the 𝑇-𝑄profiles and irreversibilities observed in
Fig. 9 earlier.
3.5. Mean-line turbine design
The results presented in this section are intended to compare the
general trends in the turbine design with dopant molar fraction. Moving
into the mean-line design of an axial turbine requires the definition of
certain parameters, which are summarised in Table 4. The selection of
these parameters was based on common design practices that yield high
turbine efficiencies [23]. No attempt has been made to modify these
parameters to optimise the turbine designs. Rather, the assumptions
were made with the intent of providing a common basis for comparing
turbine geometries, regardless of the blend. Further turbine optimisa-
tion is required before optimal designs for specific blends are compared,
which will be considered in future work.
Within the current paper, as noted in Table 4, the turbine mean-
line design relies on the assumption of a fixed turbine efficiency. This
was selected since, in our opinion, there remain uncertainties in the
suitability of existing loss correlations for operating with both CO2and
blends. This assumption is deemed sufficient for the objectives of the
Table 4
Turbine design parameters.
Parameter Value Units
Rotational speed (𝑁) 3000 RPM
Turbine efficiency (𝜂t) 90 %
Loading coefficient (𝜓) 1.65 –
Flow coefficient (𝜙) 0.23 –
Degree of reaction (𝛬) 0.5 –
Aspect ratio (𝑏𝑐) 2 –
Thickness-to-chord ratio (𝑡𝑐) 0.5
Pitch-to-chord ratio (𝑆𝑐) 0.85 –
current study, which is focused more on the overall cycle and general
effect of the blend the turbine design, rather than identifying optimal
turbine geometries.
As mentioned previously, the number of axial turbine stages is
governed by the mechanical integrity of the turbine blades. Both rotor
blade centrifugal and gas bending stresses were calculated for all
possible mixture compositions. Unlike steam or gas turbines, centrifugal
stress is not the dominant source of mechanical stress in CO2turbines.
As seen in Fig. 18, gas bending stresses are greater by an order of
magnitude.
In general, the tensile centrifugal stress is determined by the tur-
bine’s rotational speed and annulus area according to Eq. (27):
𝜎𝑐𝑡 = 2𝜋𝐾 𝑁2𝜌b𝐴avg∕3600 (27)
where the coefficient 𝐾depends on the taper of the blade and is set to
2∕3 assuming a tapered blade [35], 𝜌bis the density of the blade (appx.
8000 kg/m3), and 𝐴avg is the average annulus area between rotor inlet
and outlet.
The rotational speed was fixed to a relatively moderate value of
3000 RPM to allow direct connection to a 50 Hz synchronous electric
generator, without the need for a gearbox. On the other hand, the
annulus area is narrower than that of gas turbines because of the low
volumetric flow rate of the working fluid. Both of these factor reduce
the significance of centrifugal stresses.
Gas bending stress may be expressed as a function of the fluid
density, stage enthalpy drop, flow coefficient, and stage geometric
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Fig. 18. Maximum allowable blade mechanical stresses based on number of turbine
stages. The numbers denote the number of turbine stages corresponding to the plotted
points and the point size is proportional to the dopant fraction.
Fig. 19. Transformation of rotor blade profiles based on dopant molar fraction.
relations:
𝜎gb =4𝜋𝜑𝑁
60 𝑟s∕c𝑟b∕c 2
𝑧𝜌𝛥ℎ 𝜎gb 𝜌𝛥ℎ (28)
The flow coefficient (𝜙) and stage geometric relations (𝑟s∕c,𝑟b∕c ) were
chosen based on gas turbine best practices, thus are not the cause
for the high stresses. The strong aerodynamic stresses are likely to
be caused by the fluid’s high density and the stage enthalpy drop.
Since the density is imposed by optimal cycle conditions, the stress
may otherwise be alleviated by increasing the number of stages to
reduce the enthalpy drop per stage. As seen in Fig. 18, at least 4 stages
are required to remain below the maximum design stress. The figure
also shows that higher dopant fractions produce greater gas bending
stresses. However, the difference between the stresses for all fractions
reduces with increasing number of stages. One could argue that the
number of stages is no longer affected by the blend fraction for axial
turbine with three or more stages. The severity of aerodynamic stresses
in sCO2turbines have been identified in previous publications [3638].
Fig. 19 illustrates the meridional profiles of the turbine rotors for
the range of blend fractions considered and may be studied to draw a
comparison between two trends: (1) the different turbine geometries of
the three dopants; (2) and the varying turbine geometries of the same
mixture, but with changing dopant fractions.
For a fixed loading coefficient and rotational speed, the diameter of
the turbine becomes a sole function of the enthalpy drop. Therefore,
Table 5
Comparison of design and performance parameters of 100 MWe pure sCO2and tCO2
power plants operating with different mixtures.
Working fluid CO2CO2/TiCl4CO2/NOD CO2/C6F6
Dopant molar fraction 0 0.174 0.264 0.167
Thermal efficiency (%) 41.7 49.5 42.3 46.5
Recuperator effectiveness (%) 98.5 95.9 98 93.1
Recuperator heat load (MW) 398 844 389 799
PHE inlet temperature (K) 762 823 687 819
PHE heat load (MW) 242 204 239 217
Turbine
Mass flow rate (kg/s) 902 1393 738 1054
Exhaust volume flow rate (m3/s) 7.03 6.88 5.11 5.31
Inlet temperature (K) 973 973 973 973
Outlet temperature (K) 817 869 817 877
Enthalpy drop (MJ/kg) 186 88.8 163 120
Mean diameter (m) 1.09 0.753 1.02 0.873
Axial length (m) 0.32 0.61 0.27 0.38
CO2/NOD turbines, which experience higher enthalpy drops per stage,
require wider turbines than CO2/C6F6or CO2/TiCl4. On the other
hand, the blade height is influenced by the volume flow rate and
enthalpy drop of the turbine in accordance with Eq. (29):
𝑏̇
𝑉𝛥ℎ (29)
As seen in Fig. 20, CO2/TiCl4requires the longest blades, followed
by CO2/C6F6and CO2/NOD, which is explained by its higher volume
flow rates and lower specific work. Moreover, the blade heights of
CO2/TiCl4and CO2/C6F6increase with blend fraction but decrease for
CO2/NOD blends.
Since the blade aspect ratio is fixed, the chord length becomes
linearly proportional to the blade height. Therefore, the chord length
increases with blade length, and the axial length of the turbine in-
creases by consequence. Accordingly, in a transcritical cycle, one might
expect the turbine to have a wider diameter and shorter length for
mixtures that increase its specific work.
As previously noted, the expansion ratio increases with blend frac-
tion for all mixtures. This is demonstrated in Fig. 21, which plots the
normalised heights of the turbine rotor blades, where the change in
blade height is proportional to the expansion ratio across the turbine.
The change in blade height with each stage increases with blend frac-
tion for all mixtures, suggesting that the turbine flare angle increases
with blend fraction. However, CO2/C6F6exhibits the greatest increase.
A schematic of the 𝑇-𝑠diagram and turbine flow paths meridional
view corresponding to the optimal points are illustrated in Figs. 22 and
23. The cycle and turbine parameters corresponding to the composi-
tions, pressure ratio, and recuperator effectiveness that yield optimal
cycle efficiency are summarised in Table 5. Although there are notable
differences between the four working fluids, they share comparably
high mass-flow rates in the order of 1000 kg/s, and relatively low
volumetric flow rates below 10 m3/s. To put these number into per-
spective, the H-100 gas turbine manufactured by Mitsubishi has a
similar capacity of around 100 MW, and exhausts about 300 kg/s of
air at approximately 550 C. Assuming ideal gas and ambient pressure
conditions, this translates to 700 m3/s. Therefore, the contrast between
air and CO2-based turbines’ design space shows in both mass and
volume flow rates.
Not only do blended CO2cycles outperform pure CO2in sim-
ple recuperated cycles, they also outperform pure CO2in recompres-
sion plants. Modelling of recompression cycle with similar boundary
conditions, equipment efficiencies, 89% recompressor efficiency, and
0.79 split fraction yields an overall thermal efficiency of 43.4%. This
comparison suggests that dopants like TiCl4and C6F6achieve higher
thermal efficiencies even in simpler cycle layouts.
Applied Thermal Engineering 190 (2021) 116796
15
O.A. Aqel et al.
Fig. 20. Variation of mean diameter and rotor blade height at last stage with dopant molar fraction.
Fig. 21. Normalised stage-wise rotor blade height for the range of dopant molar fraction.
Fig. 22. Schematic of the 𝑇-𝑠diagram for the dopant fraction and cycle conditions that yield optimal thermal efficiency. The critical point is indicated by a red dot.
Applied Thermal Engineering 190 (2021) 116796
16
O.A. Aqel et al.
Fig. 23. Comparison of turbine flow paths meridional view corresponding to the design point that yields optimal thermal efficiency for pure CO2and CO2-based mixtures. Left
to right: Pure CO2; CO2/TiCl4; CO2/NOD; CO2/C6F6.
4. Conclusion
The comparative analysis presented in this paper has investigated
the effect of three dopants (TiCl4, NOD, or C6F6) and their amounts
on the optimal thermodynamic cycle conditions and the resulting tur-
bine design for a 100 MW CSP power plant operating with sCO2
blends. Increasing dopant molar fraction was found to increase the
pressure ratio for all blends. The maximum achievable efficiencies
were found to be 49.5%, 46.5%, and 42.3% for molar fractions of
0.21 of CO2/TiCl4, 0.32 of CO2/NOD, and 0.17 of CO2/C6F6. The
adoption of molecularly complex dopants has been shown to alleviate
the irreversibilities in the recuperator and enables condensing cycles
to be realised with dry cooling. This could lead to higher thermal
efficiencies compared to equivalent cycles operating with pure CO2,
which achieves an efficiency of 44.0%, but at the cost of possibly larger
recuperators.
In terms of turbine design, the specific work was found to decrease
with increasing fraction of TiCl4and C6F6, but increase with NOD.
Moreover, the addition of any of the three dopants increases the pres-
sure, temperature, and expansion ratios across the turbine; except for
C6F6, which exhibits an almost constant temperature ratio. The fluid’s
density at turbine inlet increases with all dopants as well. Conversely,
the speed of sound at turbine inlet decreases with all dopants, yet
higher Mach numbers are expected in CO2/C6F6turbines.
By studying a 100 MWe power plant as an example, preliminary tur-
bine sizing data was presented. This serves to investigate the sensitivity
of the turbine design to the blend and molar fraction before moving
onto a more detailed turbine design optimisation stage. Since heavier
working fluids reduce the specific work, they increase the mass flow
rate into the turbine, which in turn requires larger flow annuli. On the
other hand, the turbine mean diameter is smaller for heavy working
fluids. Therefore, assuming a fixed number of stages and the same
design inputs, they require narrower but longer turbines compared to
the lighter dopant (NOD).
Blade mechanical stresses were found to be dominated by gas bend-
ing stresses induced by aerodynamic forces. Modifying the CO2working
fluid for condensing cycles in CSP applications necessitates dopants
heavier than CO2to increase its critical temperature. Increasing the
density of the working fluid will further exacerbate the blade mechani-
cal stresses. Dedicated optimisation studies of turbine design should be
undertaken to lower the aerodynamic stresses by adding more blades or
increasing blade chord or thickness. Ultimately, a compromise between
turbine size, mechanical strength, and aerodynamic efficiency can be
made.
The topic of power cycles operating with CO2-based mixtures still
requires further study. An informed decision of the most suitable
dopant must account for techno-economic considerations. The effect
of the relatively high temperature glides in CO2/TiCl4and CO2/C6F6
recuperators on heat exchanger design remains to be examined. More-
over, additional equipment may be needed to address the fractionation
of CO2/TiCl4and CO2/C6F6during heat rejection, which may increase
the plant size and cost. Another, deciding factor pertaining to fluid
selection is off-design analysis, which is increasingly important in the
design of CSP plants which are subject to daily and seasonal variations.
CRediT authorship contribution statement
O.A. Aqel: Conceptualization, Methodology, Software, Formal anal-
ysis, Investigation, Writing - original draft, Visualization. M.T. White:
Conceptualization, Methodology, Software, Investigation, Writing - re-
view & editing, Supervision. M.A. Khader: Software, Writing - review
& editing. A.I. Sayma: Writing - review & editing, Supervision, Funding
acquisition.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgement
This project has received funding from the European Union’s Hori-
zon 2020 research and innovation programme under grant agreement
No. 814985.
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... Another important characteristic for the selection of the dopants is the working fluid thermal stability with expected values, for the highest efficiency applications, up to 700 • C. Excluding the inorganic compounds class, perfluorocarbons compounds are suggested by preliminary activities of the SCARABEUS project and other research studies [24][25][26][27]: they are characterised by good solubility into CO 2 , good molecular complexity, low-toxicity and low-flammability [28] and they are potentially thermally stable and chemically inert at temperatures higher than 400 • C [25,[29][30][31][32]. On the other hand, they are very expensive fluids and with a high global warming potential (i.e. 6630 for tetrafluoromethane CF 4 , 11,100 for Hexafluoroethane C 2 F 6 or 9550 for Octafluorocyclobutane C 4 F 8 [33]). ...
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Under the background of carbon reduction, the development of efficient power conversion system has drawn more important attention. The advantages of high efficiency and compactness have triggered increasing industrial interests in the applications of supercritical carbon dioxide power system for broad heat sources. However, when the supercritical carbon dioxide power cycle is coupled with different heat sources, there exist both general problems mainly associated with the supercritical carbon dioxide cycles and unique problems due to the heating processes of supercritical carbon dioxide. Moreover, the multiscale features of the supercritical carbon dioxide power system lead to significant challenges to theoretical analysis and engineering design. This review work provides the recent advances of supercritical carbon dioxide power systems, especially for the applications in heat sources of nuclear, solar and fossil fuel. With a focus on the category of general problems and unique problems, the current studies concerning the coupling of supercritical carbon dioxide power cycle with a specific heat source are further divided into three scales of system, component and process. The designs of the reactor core in nuclear, the receiver in concentrated solar power plant and the boiler in coal-fired power plant are discussed in detail at the scales of system, component and process. Future research directions for supercritical carbon dioxide power system are identified at different scales and more accurate integrated modelling for the coupling of supercritical carbon dioxide power cycle with specific heat sources are encouraged. The present work will benefit the in-depth understanding and further promotion of supercritical carbon dioxide power systems in industrial applications.
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The development of alternative working fluids has become a difficult and never-ending task, and thus driven a tremendous progress of the organic Rankine cycle (ORC) technology. In the past 25 years, the promotion of zeotropic working fluid has provided a new opportunity to further improve the performance of ORC. However, a critical performance comparison between zeotropic mixtures and pure working fluids in ORC systems is still rare, due to a lack of reasonable framework of comparative analysis and confused original data. Particularly, it is controversial whether zeotropic mixtures are promising alternatives when considering economic factors. In such a situation, a quantitative performance evaluation of zeotropic mixtures is necessary to quickly understand the current research progress and assess new research results. This paper presents a data-based evaluation of comprehensive performance of zeotropic mixtures. The available data is collected, screened, and classified from 361 published papers. 1312 available data of thermodynamic performance calculation and application aspects is obtained from 94 papers for in-depth analysis. The comparison between theoretical calculation and application shows that organic Rankine cycle using zeotropic working fluids have potential for wide application. However, there are many problems need to be solved in theory and application, such as thermodynamic cycle construction, key device design, composition shift, dynamic performance and control strategy and so on.
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The application of Organic Rankine cycle (ORC) units in concentrating solar power systems is a very promising solution. However, fluctuations in the available solar energy often force solar-based ORC systems to operate at part-load conditions. An innovative methodology for finding robust design solutions of such ORC systems, based on the minimization of the expected Levelized Cost of Energy (LCOE), is therefore proposed. The expected variations in the ORC heat source and heat sink are considered during the design stage by adopting a multi-scenario approach. The proposed methodology has been tested by referring to a medium-scale ORC unit and by considering different working fluids. As cases study, the direct coupling of the ORC unit with a solar field and the integration of a Thermal Energy Storage system have been investigated. The comparison of the results obtained by using a multi-scenario and a single-scenario approach highlights a reduction of the actual LCOE. The ORC configuration obtained by adopting a multi-scenario approach is characterized by lower performance under design conditions, but it is less sensitive to variations in the main inputs during off-design operating periods. This fact is particularly noteworthy for the case with the direct coupling of the solar field.
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This paper discusses the adoption of CO2 mixtures for improving the thermal-to-power efficiency conversion in solar tower plants and reducing the Levelized Cost of Electricity. Two different fluids are considered for blending the CO2: N2O4 and TiCl4. The main advantage of the innovative mixtures relies in a higher critical temperature with respect to pure CO2, which allows condensing cycles even at relatively high ambient temperatures typical of solar plants locations. Thermodynamic results show that the innovative cycles can achieve conversion efficiencies as high as 43% and 50% at 550 °C and 700 °C maximum temperature respectively, outperforming the reference CO2 cycle by 2 points percent. In addition, the simpler lay-out and the liquid compression reduce the power block capital costs below 700 $/kW. Detailed solar plant annual simulation is performed to assess the overall solar to electricity efficiency which can be around 21% for the innovative fluid, corresponding to 10% increase with respect to state-of-the-art solar plant. The higher performance and lower costs lead to a Levelized Cost of Electricity reduction of 10% with respect to conventional steam cycle power block.
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The competitiveness of concentrated solar power technology in the near-future electricity generation scenario, requires a substantial reduction of the Levelized Cost of Energy which can be achieved with an increase of the energy conversion efficiencies while maintaining or reducing the investment costs. This paper discusses the use of pure Dinitrogen tetroxide N2O4, and N2O4/CO2 mixture, as working fluids in supercritical Brayton cycles applied to solar tower power plants. When N2O4 is combined with CO2, the resulting mixture has a compara- tively higher critical temperature than pure CO2, allowing a condensing cycle even at the fairly high ambient temperatures of desert areas, where solar power plants are typically installed. This allows the adoption of simpler cycle configurations than the one used in sCO2 cycles (cost reduction) while achieving very high ther- modynamic efficiency (47% at 700 °C). The N2O4/CO2 mixture with optimized composition, integrated in a solar tower unit, increases the solar-electric efficiency by 1% with respect to commercial plants based on steam cycle with 550 °C maximum temperature (22.3% vs. 21.3%). At 700 °C, the overall solar-electric efficiency can reach 24.5% which is slightly higher than supercritical CO2 cycles, yet with a foreseeable reduction of the investment costs as consequence of the simpler plant lay-out.
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Supercritical CO2 cycles have been said to be a good alternative to the Rankine Cycles for Concentrating Solar Power plants of the future. The next generation molten salts will be able to achieve 700 °C, which is a suitable temperature for Supercritical CO2 cycles. However, there is a big uncertainty about the efficiencies of the cycle components, which could make these cycles unviable. A sensitivity analysis of the energy efficiency of the Recompression Cycle and Partial Cooling Cycle, regarding turbomachinery isentropic efficiencies and Recuperator effectiveness variations, has been carried out to show that the Recompression Cycle’s energy efficiency is considerably more sensitive than the Partial Cooling Cycle’s. From the sensitivity analysis, it can also be concluded that the Recompression Cycle is the best performing cycle for most of the studied cases, with energy efficiencies in the range between 32.97% and 51.91%. Exergetically, the Recompression Cycle is also more suitable in most situations, and the exergy analysis on cycle components shows that irreversibilities occur mainly in the Recuperators, which means that future research should focus on methods to reduce irreversibilities in these components. The state-of-the-art of Supercritical Rankine Cycle plant net energy efficiencies currently reach 45.60% for fossil fuel plants. Although Supercritical CO2 cycles are a simpler and more compact alternative, this work concludes that only the optimized Recompression Cycle with turbomachinery isentropic efficiencies over 92% and Recuperator effectiveness over 95% are able to obtain similar or higher efficiencies than actual Supercritical Rankine Cycles. Furthermore, the sensitivity analysis plots permit the areas to be mapped where each of the optimized two-cycle efficiencies can compete with the Supercritical Rankine Cycles regarding the turbomachinery isentropic efficiencies and Recuperator effectiveness.
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The application of CO2 power cycles has proved to be particularly advantageous to exploit high-temperature heat sources (500–800 °C) in the case of available low-temperature heat sinks (15–25 °C). Otherwise, the efficiency of these cycles is strongly reduced when cold sink temperatures are higher than 25 °C. This is the case, for example, of solar applications installed in desert areas whose cold sink is represented by available hot air. Due to these high temperatures of the cold sink, CO2 is inevitably compressed in the supercritical phase thus preventing its more efficient pressurization in the liquid phase. One of the solutions envisaged to overcome this problem consists of adding to CO2 a small amount of one or more chemicals, resulting in a mixture with a critical temperature higher than the one of pure CO2 (about 31 °C). This preserves the working fluid compression in its liquid phase, even in the case of cold sinks with temperatures greater than 25 °C. This research aims to show that the addition to CO2 of a specifically selected second component enables to increase the critical temperature up to 45 °C with relevant improvements of cycle efficiency with respect to pure-CO2 power cycles. In particular, after summarizing the most relevant criteria to be accounted for when selecting CO2-additives, the paper warns about the thermodynamic effects deriving from adding to CO2 a second component characterized by a much more high critical temperature, such as the occurrence of infinite-pressure critical points and multiple-phase liquid-liquid and vapor-liquid critical points. Moreover, the paper specifically analyses the thermodynamic properties of CO2-TiCl4 mixtures which, depending on the content of TiCl4, may lead to a mixture characterized by the sought higher critical temperature. While studying this mixture, it has been observed that it presents multiple-phase critical points. For the sake of completeness, the paper also shows how do enthalpy and specific volume change in response to pressure variations in the event of either liquid-liquid or vapor-liquid critical points. This research finally shows the comparison between performances of power cycles which use, as working fluid, either pure CO2 or the specifically designed CO2-TiCl4 mixture. As expected, the TiCl4 addition brings about a significant efficiency gain.