Sensitivity of transcritical cycle and turbine design to dopant fraction in CO2­based working fluids

Supercritical CO 2 (sCO 2 ) 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 CO 2 is close to ambient temperatures in areas with good solar irradiation, dry cooling may penalise the efficiency of sCO 2 power cycles in CSP plants. Recent research has investigated doping CO 2 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 CO 2 /TiCl 4 , CO 2 /NOD (an unnamed Non-Organic Dopant), and CO 2 /C 6 F 6 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 CO 2 with any of the three dopants (TiCl 4 , NOD, or C 6 F 6 ) increases the cycle’s thermal efficiency. The greatest increase in efficiency is achieved with TiCl 4 (up to 49.5%). The specific work, on the other hand, decreases with TiCl 4 and C 6 F 6 , 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 CO 2 /C 6 F 6 turbines.

A B S T R A C T Supercritical CO 2 (sCO 2 ) 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 CO 2 is close to ambient temperatures in areas with good solar irradiation, dry cooling may penalise the efficiency of sCO 2 power cycles in CSP plants. Recent research has investigated doping CO 2 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 CO 2 /TiCl 4 , CO 2 /NOD (an unnamed Non-Organic Dopant), and CO 2 /C 6 F 6 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 CO 2 with any of the three dopants (TiCl 4 , NOD, or C 6 F 6 ) increases the cycle's thermal efficiency. The greatest increase in efficiency is achieved with TiCl 4 (up to 49.5%). The specific work, on the other hand, decreases with TiCl 4 and C 6 F 6 , 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 CO 2 /C 6 F 6 turbines.

Introduction
Supercritical CO 2 (sCO 2 ) power cycles have been investigated for various energy sources such as nuclear, fossil fuels, waste heat and concentrated solar power [1]. Several studies have identified the potential of sCO 2 cycles to outperform traditional steam cycles in concentrated solar power (CSP) plants [2][3][4][5][6][7], potentially making CSP more competitive 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 sCO 2 systems 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 efficiencies. Alternatively, doping CO 2 with an additional fluid to produce a increase the critical temperature of the fluid enable condensation to be achieved using dry cooling. This expands the operation of transcritical carbon dioxide (tCO 2 ) cycles, which compress the fluid in its liquid state and expand it in its supercritical state, into arid environments [9]. The benefit of using CO 2 dopants has been explored in the past. Most recently, Valencia-Chapi et al. [10] quantified the effect of using 12 different CO 2 -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 CO 2 -H 2 S and CO 2 -cyclohexane mixtures, which have higher critical temperatures than pure CO 2 . 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 CO 2 mixture 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 CO 2organic 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 CO 2 with small fractions of dinitrogen tetroxide (N 2 O 4 ) and titanium tetrachloride (TiCl 4 ), 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 temperatures (higher than 40 • C). The dopants were chosen due to their thermal stability and their higher critical temperatures compared to CO 2 . The mass fraction ratios were set to CO 2 -TiCl 4 85%-15% and CO 2 -N 2 O 4 78% to 22% based on a previous optimisation [15]. Cycle optimisation carried out at high turbine entry temperatures of 550 and 700 • C resulted 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 sCO 2 power 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 CO 2 power 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 CO 2 as 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 recuperator 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 CO 2 working 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.  The path to commercial realisation of CO 2 power 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][19][20]. In the case of Novales et al. [19] it was found that sCO 2 Brayton 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 depending 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 TiCl 4 , C 6 F 6 , 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 CO 2 fluid properties during the design process instead of the blends.
The cost and challenges of incorporating CO 2 -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.

Cycle model
In-line with the previous study by Manzolini et al. [14], a simple recuperated tCO 2 cycle 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 tCO 2 cycle and its Temperature-Entropy ( -) 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): wherėp anḋt are the specific compression and expansion work, respectively, and ℎ i is 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): Once the cycle output work capacitẏn is set, the net specific work is used to find the mass flow rate of the working fluid using Eq. (4): Heat loads in the primary heat exchanger, recuperator and cooler are expressed by Eqs. (5) to (7): Cycle thermal efficiency is expressed as the ratio of the net work produced to the heat consumed by the cycle in Eq. (8): The losses within the pump and turbine are approximated by assuming isentropic efficiencies for each component, as expressed by Eqs. (9) and (10): where the subscript 's' denotes the outlet conditions assuming isentropic 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): An internal pinch point is expected in the recuperator, which must be determined to avoid physically impossible (overlapping) temperature profiles. In order to do so, the recuperator is discretised into cells,  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: where is the overall conductance, is the heat load for each cell, and is the log mean temperature difference between its terminals, which is expressed as: 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: where and 4 and 5 are the inlet and outlet total pressures, respectively.
The cycle state points are determined by setting the pump inlet temperature ( 1 ), the turbine inlet temperature ( 4 ), pressure ratio, component efficiencies, and pressure drops. Within this study, 1 and 4 will be set according to the values expected in state-of-the-art drycooled 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.

Turbine model
To model the turbine, a preliminary mean line turbine design approach was adopted. The target net power for the SCARABEUS plant is 100 MW turbine, for which a multi-stage axial architecture is recommended [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: where and are the specific speed and nominal speed (rpm), respectively. The turbine exhaust volume flow rate is represented bẏ 5 (in m 3 /s) and the isotropic enthalpy drop by ℎ (in J/kg).
The blade-loading coefficient, turbine flow coefficient, and degree of reaction given by Eqs. (16) to (18) are non-dimensional turbomachinery 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: where ℎ is the total enthalpy drop across i th stage of the turbine, is the blade speed of the rotor of the i th stage at the design radius (mean radius is used in this study), is the axial flow velocity at the rotor outlet of the stage and ℎ is the enthalpy drop across the rotor of the i th 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 considerations, 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 ( a ∕ e = 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 ( = 1.5) is assumed. These assumptions are used in Section 3.5 to determine the number of stages in a turbine design case study.

Optimisation model
A MATLAB 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 corresponding 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 thermodynamic 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 ( ) 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 CO 2 cycle was simulated via a REFPROP-based code developed inhouse, while data obtained using Aspen Plus for modelling of CO 2 -TiCl 4 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).

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 CO 2 based power cycles operating within CSP. The main dopant thermophysical parameters of interest are shown in Table 1.
In this study, ij was calculated against regressed Vapour-Liquid Equilibrium (VLE) empirical data and used to tune the mixing models of CO 2 /NOD and CO 2 /C 6 F 6 . Unlike the other two mixtures, the ij value for CO 2 /TiCl 4 was taken directly from literature. This is because the lack of experimental data means any recalibration of ij for CO 2 /TiCl 4 will retain a high uncertainty margin. In such a case, sensible comparison between the original and the new ij values will not be possible.
Determining the value of ij required an optimisation problem. By tuning ij , the calculated VLE lines were manipulated and compared with experimental data to find the best-fit ij 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 experimental 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: where 1 and 1 are the liquid and vapour molar fractions of CO 2 , respectively. The accents (∧) and (∼) indicate the measured and calculated values, respectively. Experimental uncertainty is represented by the term . The number of experiments is denoted by e . A Monte Carlo technique similar to that used by Hajipour et al. [28] was employed to estimate the uncertainties of the binary interaction 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. Phase diagrams for the mixture CO 2 /NOD (left) and CO 2 /C 6 F 6 (right). Lines represent the results of PR EoS with ( ij = 0.0243) and ( ij = 0.0312) for CO 2 /NOD and CO 2 /C 6 F 6 , respectively. Whilst the circles are the experimental data points taken from their respective sources.  [29] In this study, the experimental data were assumed to be normally distributed in accordance with the declared uncertainty (Step 1). Random sampling with replacement was repeatedly conducted for a total of 1000 trials (Steps 2 & 3). Finally, the mode value is taken as ij , while its uncertainty is based on the 95% confidence interval from the mean (Step 4). The regressed VLE lines of CO 2 /NOD and CO 2 /C 6 F 6 are shown in Fig. 4. The values of ij adopted in this study are shown in Table 2.

Optimisation conditions
The pump inlet temperature ( 1 ) 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 • C as it passes through the condenser whilst maintaining a minimum temperature difference of 5 • C [30][31][32][33]. The pump inlet was assumed to be subcooled by 2 • C below the saturation pressure. Consequently, the pump inlet pressure ( 1 ) is defined by the saturation pressure of the fluid at 52 • C. The turbine inlet temperature ( 4 ) 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 ( 4 ) 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 • C heat sink temperature + 10 • C cooler temperature difference + 2 • C sub-cooling + 5 • C margin from the critical temperature). A summary of the assumptions is provided in Table 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 and their expected effect on the cycle and turbine design is considered. 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.

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 CO 2 /C 6 F 6 .
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 CO 2 /TiCl 4 , CO 2 /NOD, and CO 2 /C 6 F 6 , respectively. Among the three blends, CO 2 /TiCl 4 achieves the highest thermal efficiency of 49.5%, followed by CO 2 /C 6 F 6 with an optimal thermal efficiency of 46.5%, while CO 2 /NOD achieves the lowest efficiency of 42.3%. Although not shown in the figure, simulation of an equivelant pure CO 2 cycle achieves thermal efficiency of 44.0%. The 7.2% difference in efficiency between CO 2 /TiCl 4 and CO 2 /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 ( t − p ) 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 CO 2 /NOD, both parameters increase at roughly the same rate, thus maintaining a fairly constant efficiency with dopant fraction. For CO 2 /C 6 F 6 the 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 CO 2 /TiCl 4 , 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 sCO 2 cycle, cycles operating with CO 2 based 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 CO 2 /TiCl 4 , 2.3 to 4.0 times greater for CO 2 /C 6 F 6 , and 1.6 to 1.8 times greater for CO 2 /NOD.
As the recuperator effectiveness increases, the MITA in the recuperator 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 CO 2 /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 -CO 2 /TiCl 4 and CO 2 /C 6 F 6 -are much higher than CO 2 /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.    A survey of the recuperator -diagram 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. CO 2 /NOD exhibits the greatest irreversibility and poorest match of the two streams; similar to pure CO 2 . A proven solution to this issue is the adoption of more complex cycle architectures such as the recompression or partial cooling cycles [16]. The temperature profiles for CO 2 /C 6 F 6 and CO 2 /TiCl 4 , 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 CO 2 /C 6 F 6 and CO 2 /TiCl 4 cycles will reduce the exergy loss along the recuperator length, not just at the pinch point. However, using the O.A. Aqel et al.  same argument, a CO 2 /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 temperature from the analysis gives CO 2 /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 CO 2 / NOD mixture at this composition, and is also trivial for all considered fractions of NOD below (0.4). Considerable condensation occurs in both CO 2 /TiCl 4 and CO 2 /C 6 F 6 recuperators, 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. CO 2 /TiCl 4 exhibits the greatest temperature glide, followed by CO 2 /C 6 F 6 and CO 2 /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 CO 2 /TiCl 4 and CO 2 /C 6 F 6 , but increases for CO 2 /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 CO 2 /TiCl 4 and CO 2 /C 6 F 6 increases 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 CO 2 /NOD mixture, where wider turbines with smaller annulus areas are expected at higher dopant fractions.

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 operational 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 ( HTM ), the cycle heat input ( H ), and the rise in the working fluid's temperature across the PHE ( PHE ).
O.A. Aqel et al. Fig. 11. Variation of turbine specific work, mass flow rate, volume flow rate at turbine outlet, and specific speed with dopant molar fraction. As previously established, CO 2 /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 temperature difference across the PHE. Therefore, greater sensible heat is extracted from the HTM with CO 2 /NOD. This manifests in the overall effect on TES size, which is indicated by the ratio H ∕ PHE , and is the lowest for CO 2 /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 CO 2 /TiCl 4 and CO 2 /C 6 F 6 , respectively. Nevertheless, CO 2 /C 6 F 6 will 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.  Logically, the rise of ambient temperatures above the 40 • C design 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 CO 2 /TiCl 4 and CO 2 /C 6 F 6 because it occurs gradually over the 10 K range. Conversely, the 4% loss occurs within an increment of only 3 K for CO 2 /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.

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): where is the adiabatic coefficient ( = p ∕ v ). 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 CO 2 /TiCl 4 and CO 2 /NOD increase modestly, but significantly decrease for CO 2 /C 6 F 6 . The trend in the adiabatic coefficient of CO 2 /C 6 F 6 is almost coincident with the isoline 1 ∕ 2 = 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 CO 2 /TiCl 4 and CO 2 /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. The expansion ratio of the CO 2 /C 6 F 6 increases 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, CO 2 /C 6 F 6 turbines 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 C 6 F 6 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 pressurevolume ratio, as seen in Eq. (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 CO 2 /C 6 F 6 causes 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 CO 2 /NOD the increase in density is small, thus the specific work increases with the increasing pressure ratio. For CO 2 /TiCl 4 and CO 2 /C 6 F 6 , 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 CO 2 /TiCl 4 , CO 2 /NOD, and CO 2 /C 6 F 6 increase 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 CO 2 /TiCl 4 and CO 2 /C 6 F 6 , and an increase of 12% in specific work for CO 2 /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 -ℎ diagram and in Eq. (24). In Fig. 16, the slope of the isentrope depends on the fluid density while the horizontal   distance between the two ends of the expansion process indicates its specific work.
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 mixtures 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.

Molecular characteristics
As shown in Fig. 17, the molecular weight of the working fluid increases significantly with the addition of C 6 F 6 or TiCl 4 , 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): where the fluid is assumed to be an ideal gas, is the speed of sound (m/s), is the adiabatic coefficient, is the molar weight (kg/mol), and is the ideal gas constant (8.314 J/mol K).
The decrease in the speed of sound is almost identical for the two heavy mixtures CO 2 /TiCl 4 and CO 2 /C 6 F 6 , while CO 2 /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, CO 2 /TiCl 4 is expected to have lower Mach numbers than CO 2 /C 6 F 6 , although it exhibits comparable sound speeds. This contrast is attributed to the particulars of the overall cycle behaviour which limit the pressure drop of CO 2 /TiCl 4 during expansion. Consequently, for the same number of stages, lower Mach numbers are expected in CO 2 /TiCl 4 than 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 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 CO 2 /C 6 F 6 and CO 2 /TiCl 4 , but remains almost constant for CO 2 /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 CO 2 , 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 -profiles and irreversibilities observed in Fig. 9 earlier.

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 optimisation 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 meanline 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 CO 2 and blends. This assumption is deemed sufficient for the objectives of the 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 CO 2 turbines. 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 turbine's rotational speed and annulus area according to Eq. (27): where the coefficient depends on the taper of the blade and is set to 2∕3 assuming a tapered blade [35], b is the density of the blade (appx. 8000 kg/m 3 ), and avg 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 The flow coefficient ( ) and stage geometric relations ( s∕c , b∕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 sCO 2 turbines have been identified in previous publications [36][37][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, ∝̇∕ ℎ As seen in Fig. 20, CO 2 /TiCl 4 requires the longest blades, followed by CO 2 /C 6 F 6 and CO 2 /NOD, which is explained by its higher volume flow rates and lower specific work. Moreover, the blade heights of CO 2 /TiCl 4 and CO 2 /C 6 F 6 increase with blend fraction but decrease for CO 2 /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 increases 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 fraction 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 fraction for all mixtures, suggesting that the turbine flare angle increases with blend fraction. However, CO 2 /C 6 F 6 exhibits the greatest increase.
A schematic of the -diagram 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 compositions, 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 m 3 /s. To put these number into perspective, 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 m 3 /s. Therefore, the contrast between air and CO 2 -based turbines' design space shows in both mass and volume flow rates.
Not only do blended CO 2 cycles outperform pure CO 2 in simple recuperated cycles, they also outperform pure CO 2 in recompression 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 TiCl 4 and C 6 F 6 achieve higher thermal efficiencies even in simpler cycle layouts.

Conclusion
The comparative analysis presented in this paper has investigated the effect of three dopants (TiCl 4 , NOD, or C 6 F 6 ) and their amounts on the optimal thermodynamic cycle conditions and the resulting turbine design for a 100 MW CSP power plant operating with sCO 2 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 CO 2 /TiCl 4 , 0.32 of CO 2 /NOD, and 0.17 of CO 2 /C 6 F 6 . 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 CO 2 , 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 TiCl 4 and C 6 F 6 , but increase with NOD. Moreover, the addition of any of the three dopants increases the pressure, temperature, and expansion ratios across the turbine; except for C 6 F 6 , 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 CO 2 /C 6 F 6 turbines.
By studying a 100 MWe power plant as an example, preliminary turbine 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 bending stresses induced by aerodynamic forces. Modifying the CO 2 working fluid for condensing cycles in CSP applications necessitates dopants heavier than CO 2 to increase its critical temperature. Increasing the density of the working fluid will further exacerbate the blade mechanical 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 CO 2 /TiCl 4 and CO 2 /C 6 F 6 recuperators on heat exchanger design remains to be examined. Moreover, additional equipment may be needed to address the fractionation of CO 2 /TiCl 4 and CO 2 /C 6 F 6 during 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.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.