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Applied Thermal Engineering 190 (2021) 116796

Available online 1 March 2021

1359-4311/© 2021 Published by Elsevier Ltd.

Contents lists available at ScienceDirect

Applied Thermal Engineering

journal homepage: www.elsevier.com/locate/ate

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 [2–7], 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 )

ℎSpecific 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 [18–20]. 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=ℎ2−ℎ1(1)

𝑤t=ℎ4−ℎ5(2)

where ̇

𝑤pand ̇

𝑤tare the specific compression and expansion work,

respectively, and ℎiis 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=𝑤t−𝑤p(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 =̇

𝑊n∕𝑤n(4)

Heat loads in the primary heat exchanger, recuperator and cooler are

expressed by Eqs. (5) to (7):

𝑞H=ℎ4−ℎ3(5)

𝑞R=ℎ3−ℎ2=ℎ5−ℎ6(6)

𝑞L=ℎ6−ℎ1(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=𝑤t−𝑤p

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=ℎ2s −ℎ1

ℎ2−ℎ1

(9)

𝜂t=ℎ4−ℎ5

ℎ4−ℎ5s

(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

=ℎ5−ℎ6

min ℎ@T5,P2 −ℎ@T2,P2,ℎ@T5,P5 −ℎ@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

4

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 =𝑄∕𝐿𝑀𝑇 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

ℎ−𝑇𝑖

𝑐)−(𝑇𝑖+1

ℎ−𝑇𝑖+1

𝑐)

ln ((𝑇𝑖

ℎ−𝑇𝑖

𝑐)∕(𝑇𝑖+1

ℎ−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=𝑃4∕𝑃5(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=𝛥ℎ𝑜𝑖∕𝑈2

𝑖(16)

𝜙=𝐶𝑎𝑖∕𝑈𝑖(17)

𝛬=𝛥ℎ𝑟𝑖∕𝛥ℎ0𝑖(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 (𝑆a∕𝑆e= 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

5

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,i−̃𝑥1,i

𝑢𝑒

x1,i+̂𝑦1,i−̃𝑦1,i

𝑢𝑒

̂y1,i+

̂

𝑇i−̃

𝑇i

𝑢𝑒

̂

Ti

+

̂

𝑃i−̃

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

6

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[30–33]. 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 +2◦Csub-cooling +5◦Cmargin 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 𝛥𝑝∕𝑝0.015 –

Pressure drop in recuperator 𝛥𝑝∕𝑝0.01 and 0.015 –

High- and Low-pressure sides

Pressure drop in condenser 𝛥𝑝∕𝑝0.02 –

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 (𝑤t−𝑤p) 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 𝑄H∕𝛥𝑇 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=𝐶p∕𝐶v). 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 𝑇1∕𝑇2= 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-ℎdiagram 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.

dℎ=𝑇d𝑠+ d𝑃∕𝜌d𝑠=0

⟶dℎ= d𝑃∕𝜌(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 𝑀∕𝑅𝑇 (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 (𝑏∕𝑐) 2 –

Thickness-to-chord ratio (𝑡∕𝑐) 0.5 –

Pitch-to-chord ratio (𝑆∕𝑐) 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 [36–38].

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):

𝑏∝̇

𝑉∕𝛥ℎ (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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