International Journal of

Turbomachinery
Propulsion and Power

Article
Design of a 130 MW Axial Turbine Operating with a Supercritical
Carbon Dioxide Mixture for the SCARABEUS Project †
Abdelrahman S. Abdeldayem 1, * , Salma I. Salah 1,2 , Omar A. Aqel 1 , Martin T. White 1,3 and Abdulnaser I. Sayma 1

1 Energy, Sustainability and Net Zero Research Centre, University of London, London EC1V 0HB, UK;
salma.salah.2@city.ac.uk (S.I.S.); omar.aqel@city.ac.uk (O.A.A.); martin.white@sussex.ac.uk (M.T.W.);
a.sayma@city.ac.uk (A.I.S.)
2 Department of Mechanical Engineering, Centre for Renewable Energy, The British University in Egypt (BUE),
Cairo 11837, Egypt
3 Thermo-Fluid Mechanics Research Centre, School of Engineering and Informatics, University of Sussex,
Falmer, Brighton BN1 9RH, UK
* Correspondence: abdelrahman.abdeldayem@city.ac.uk
† This manuscript is an extended version of our paper published in the Proceedings of the 15th European
Turbomachinery Conference, Budapest, Hungary, 24–28 April 2023.

Abstract: Supercritical carbon dioxide (sCO2 ) can be mixed with dopants such as titanium tetrachlo-
ride (TiCl4 ), hexafluoro-benzene (C6 F6 ), and sulphur dioxide (SO2 ) to raise the critical temperature of
the working fluid, allowing it to condense at ambient temperatures in dry solar field locations. The
resulting transcritical power cycles have lower compression work and higher thermal efficiency. This
paper presents the aerodynamic flow path design of a utility-scale axial turbine operating with an
80–20% molar mix of CO2 and SO2 . The preliminary design is obtained using a mean line turbine
design method based on the Aungier loss model, which considers both mechanical and rotor dynamic
criteria. Furthermore, steady-state 3D computational fluid dynamic (CFD) simulations are set up
using the k-ω SST turbulence model, and blade shape optimisation is carried out to improve the
preliminary design while maintaining acceptable stress levels. It was found that increasing the
number of stages from 4 to 14 increased the total-to-total efficiency by 6.3% due to the higher blade
Citation: Abdeldayem, A.S.; Salah,
aspect ratio, which reduced the influence of secondary flow losses, as well as the smaller tip diameter,
S.I.; Aqel, O.A.; White, M.T.; Sayma,
which minimised the tip clearance losses. The final turbine design had a total-to-total efficiency of
A.I. Design of a 130 MW Axial
92.9%, as predicted by the CFD results, with a maximum stress of less than 260 MPa and a mass
Turbine Operating with a Supercritical
Carbon Dioxide Mixture for the
flow rate within 1% of the intended cycle’s mass flow rate. Optimum aerodynamic performance
SCARABEUS Project. Int. J. was achieved with a 14-stage design where the hub radius and the flow path length are 310 mm and
Turbomach. Propuls. Power 2024, 9, 5. 1800 mm, respectively. Off-design analysis showed that the turbine could operate down to 88% of the
https://doi.org/10.3390/ design reduced mass flow rate with a total-to-total efficiency of 80%.
ijtpp9010005
Keywords: axial turbine; supercritical carbon dioxide; mean line design; CFD; aerodynamic design
Academic Editor: Antoine Dazin

Received: 12 June 2023

Revised: 19 November 2023
Accepted: 28 December 2023 1. Introduction
Published: 2 February 2024
Supercritical carbon dioxide power cycles (sCO2 ) are promising candidates for concen-
trated solar power (CSP) plants [1–3]. Supercritical CO2 power cycles operate between two
pressure limits where both the heat addition and heat rejection pressures are higher than
Copyright: © 2024 by the authors.
the critical point of the working fluid. Consequently, the compression process takes place
Licensee MDPI, Basel, Switzerland. in the supercritical phase using a compressor. The EU-funded SCARABEUS project [4] is
This article is an open access article investigating the applicability of transcritical power cycles operating with CO2 mixtures,
distributed under the terms and where the working fluid is compressed in the liquid phase. This could result in enhanced
conditions of the Creative Commons power generation efficiency and bring the levelised cost of electricity (LCoE) of CSP plants
Attribution (CC BY-NC-ND) license to a competitive level within the renewable energy market [5]. Therefore, several sCO2 -
(https://creativecommons.org/ based mixtures have been proposed to increase the mixture’s critical temperature and
licenses/by-nc-nd/4.0/).

Int. J. Turbomach. Propuls. Power 2024, 9, 5. https://doi.org/10.3390/ijtpp9010005 https://www.mdpi.com/journal/ijtpp

Int. J. Turbomach. Propuls. Power 2024, 9, 5 2 of 17

hence allow for air condensation in a transcritical power cycle for dry regions where water
cooling is not available [4,6].
According to the study presented by Tafur-Escanta et al. [7], blending CO2 with
carbonyl sulfide (COS) increased the efficiency of the cycle to 45.05%, compared to 41.25%
for pure CO2 , while the specific investment cost decreased to 2621$/kWe for the blended
CO2 cycle compared to 2811$/kWe for the pure CO2 cycle. The SCARABEUS consortium
proposed hexafluorobenzene (C6 F6 ), sulfur dioxide (SO2 ), and titanium tetrachloride (TiCl4 )
as possible candidate mixtures [8,9]. The effects of changing C6 F6 and TiCl4 molar fractions
on cycle performance were presented, considering safety and health characteristics [10,11].
The study revealed an absolute efficiency gain of 3% compared to pure CO2 cycles, whilst
the optimum mixture molar fraction ranged from 10% to 20%. The cycle layouts were also
simpler when using mixtures compared to pure CO2 cycles. Doping pure CO2 with 20% to
30% SO2 was investigated by Crespi et al. [9], which resulted in an optimised recompression
cycle with an efficiency of 51% at 700 ◦ C inlet temperature. This corresponds to an efficiency
gain of 2% compared to the recompression cycle operating with pure carbon dioxide.
The SCARABEUS consortium has tested the thermal stability of the three candidate
mixtures for operation at a turbine inlet temperature of 700 ◦ C. According to the test results,
titanium tetrachloride (TiCl4 ) did not thermally degrade at 700 ◦ C. On the contrary, C6 F6
showed signs of thermal degradation for temperatures above 600–625 ◦ C. Unfortunately,
the thermal stability of CO2 /SO2 has not yet been confirmed after long exposure times, but
the experimental investigation is currently underway. Previous studies in the literature
have indicated that CO2 /SO2 is thermally stable at temperatures above 700 ◦ C [12]. In
addition to thermal stability, environmental hazards were considered for the selected
mixtures. TiCl4 has potential limitations due to its high reactivity with moisture in the air
and the formation of HCl and TiO2 , which are both hazardous to human health. For these
reasons, and considering the cycle optimisation analysis, the current study aims to design
the turbine flow path for a CO2 -SO2 precompression cycle layout, which has demonstrated
a superior performance compared to the other mixtures. It is worth mentioning that these
mixtures are to be implemented for closed cycles developed for CSP applications. These
power plants are strategically located in dry regions which are well-ventilated, effectively
mitigating various threats, including the toxicity of SO2 .
Research has determined that turbine performance influences the thermal efficiency
of sCO2 cycles considerably [13–15]. A study by Novales et al. [13] estimated that sCO2
cycles can only compete with state-of-the-art steam cycles if turbine efficiencies are above
92%. They also estimated that a 1% efficiency change in the turbine could result in a
0.31–0.38% change in cycle efficiency. According to Brun et al. [15], a 1% decrease in
turbine efficiency decreased cycle efficiency by 0.5%. Therefore, it is evident that the path
to commercialisation of sCO2 cycles entails a better understanding of turbine design, yet it
remains to be seen what effect CO2 mixtures have on the achievable performance.
Several authors have investigated the design of sCO2 turbines at different scales to
reveal the critical design considerations and the expected efficiency ranges. Zhang et al. [16]
conducted a CFD analysis on a 15 MW single-stage axial turbine, predicting a total-to-static
efficiency of 83.96%. The study also demonstrated the significance of gas bending stresses
on the turbine blades. However, the impact of adding additional stages to the turbine on
the performance was not investigated. On the other hand, Shi et al. [17] predicted a total-
to-total efficiency of 92.12% for a three-stage design for a 10 MW axial turbine. Moreover,
they showed that the turbine can maintain 85% to 92% efficiency while operating at off-
design conditions in the range of mass flow rate from 115 kg/s to 201.3 kg/s. Total-to-total
efficiency above 90% was also predicted by Bidkar et al. [18] for four-stage and six-stage
50 MW and 450 MW axial turbines, respectively. Kalra et al. [19] designed a four-stage
axial turbine for a 10 MW CSP plant. The study focused on practical considerations such
as mechanical integrity, vibrational damping, sealing, shaft assembly, and operational
transients. It highlighted the unique challenges imposed by sCO2 turbines, such as high
Int. J. Turbomach. Propuls. Power 2024, 9, 5 3 of 17

torque requirements, small aerofoil fabrication, aero-design optimisation with mechanically

safe blade design, and high cycle fatigue life of the rotor.
Schmitt et al. [20] designed the first stage of a sCO2 axial turbine by mean line design
and 3D design using a STAR-CCM+ CFD package. They observed that both methods
predict similar vane geometries, but mean line design overestimates the efficiency of the
stage when compared to the CFD analysis. The reason for the discrepancy was attributed
to the inadequacy of the Soderberg loss model to capture all primary losses. They also
observed that the fluid’s high density at the turbine inlet results in short blades relative to
the blade chord length, which promotes secondary flow and tip clearance losses.
To properly model the thermodynamic properties of the selected CO2 mixtures,
Aqel et al. [21] investigated the effect of the choice of the equation of state (EoS) and
its calibration on the turbine design accuracy. The uncertainty in mean diameter and blade
height when using the Peng–Robinson EoS was 2.6% and 4.3%, respectively. However,
most of the deviations stemmed from variations in the turbine boundary conditions as
defined by the cycle model. This indicates that turbine designs for CO2 /SO2 can be de-
signed with reasonable accuracy, even with uncertainty in the fluid model. It is worth
noting that the mixture modelling is most critical when modelling the thermodynamic
cycle, and there is not a large sensitivity when considering the turbine in isolation because
the turbine operates quite far from the critical point of the fluid where non-ideal effects are
most significant. Specifically, the compressibility factor of pure CO2 at the turbine inlet
conditions of 700 ◦ C and 239 bar is 1.054, which indicates a behaviour close to ideal gas
with less dependency on the equation of state and binary interaction parameters [11].
Turbine blades are generated using the preliminary mean line analysis, which can be
used, along with a few assumptions, to generate the 3D blades for the CFD simulations
and structural analysis. A conjugate aerodynamic–structural blade shape optimisation
model can be conducted to improve the 3D blade design assumptions and align the design
to the power cycle requirements [22]. Kalra et al. [19] followed a similar methodology in
designing a four-stage sCO2 expander by generating a mean line flow path followed by a
3D numerical simulation and detailed rotor dynamic analysis.
In this paper, the flow path and aerodynamic design of a 130 MW axial turbine operat-
ing with an 80–20% molar composition of CO2 /SO2 is presented. This design is initiated
utilising mean line design and further refined using CFD simulation. Design constraints
are introduced based on industrial experience to ensure design feasibility in terms of
aerodynamic–mechanical integration. The proposed turbine design is evaluated under
various operating conditions to enhance understanding of the aerodynamic performance at
both design and off-design conditions. More details about the aerodynamic–mechanical
design and integration of this turbine have been published in another publication [23].

2. Design Process
2.1. Meanline Design Model
An in-house mean line design tool is used to develop the turbine flow path [24,25].
Within the tool, the steady-state mass, energy, and momentum equations are solved to
obtain the blade geometry, velocity triangles, and thermodynamic properties for all turbine
stages. The design process starts by defining the boundary conditions, including the total
inlet temperature, the total inlet pressure, the pressure ratio, the mass flow rate, and the
inlet flow angle. Six decision parameters, presented in Table 1, are defined, which include
the loading and flow coefficients ( ψ, ϕ), degree of reaction ( Λ), trailing edge thickness-to-
throat ratio (t/o), pitch-to-chord ratio (s/c), and blade surface roughness. The values for ψ
and ϕ are selected to allow for optimum turbine aerodynamic performance based on the
Smith chart [26]. The trailing edge-to-throat ratio (t/o) is selected to reduce the trailing edge
losses and is set based on the specified range in the literature as indicated in Table 1. The
pitch-to-chord ratio is defined based on industrial recommendations.
Int. J. Turbomach. Propuls. Power 2024, 9, 5 4 of 17
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Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 4 of 18

Table 1. Mean line model design criteria.

Table 1. Mean line model design criteria.
Design
Table Parameter
1. Mean Value
line model design criteria. Design Parameter Value
Design Parameter Value Design Parameter Value
SurfaceParameter
Design roughness (mm) 0.002
Value Degree
Design of reaction Λ
Parameter Value 0.5
Surface
Stage flow roughness
coefficient (mm)
ϕ 0.50.002
[26] Degree
Trailingofedge − to −𝛬throat ratio t/o
reaction 0.5 [27]
0.05
Surface roughness (mm) 0.002[26] Degree of reaction 𝛬 0.5 [27]
Stage loading
flow coefficient𝜙ψ
coefficient 10.5
[26] Trailing
Pitch − edge-to-throat
to − chord ratioratio s/c 𝑡/𝑜 0.05
0.85 [28]
Stage flow coefficient
Stage loading coefficient 𝜓 𝜙 0.5 [26] Trailing edge-to-throat
1 [26] Pitch-to-chord ratio 𝑠/𝑐 ratio 𝑡/𝑜 0.05
0.85[27]
[28]
Stage loading coefficient 𝜓 1 [26] Pitch-to-chord ratio 𝑠/𝑐 0.85 [28]
The number of turbine stages and the number of rotor and stator blades are deter-
The number of turbine stages and the number of rotor and stator blades are deter-
mined Thebased
number on of the defined boundary
turbine conditions ofand decision parameters. arePractically,
mined based on the definedstages
boundaryand the numberand
conditions rotor
decisionandparameters.
stator blades deter-it
Practically,
it
minedis recommended
based on the to restrict
defined the
boundary number
conditionsof blades
and within
decision the range
parameters. of 35 to 100.itThis
Practically,
is recommended to restrict the number of blades within the range of 35 to 100. This range
isrange
ensures
ensures optimal
recommended
optimalto
aerodynamic
restrict
aerodynamic the number design
design that of bladesthat meetsthe
meetswithin
both
both mechanical
mechanical
range of and This
35 rotor
and to 100. rotorrange
dynamic
dynamic
con-
constraints.
ensures To ensure the mechanical strength of the blades, a static bending stress limit of
straints.optimal
To ensure aerodynamic designstrength
the mechanical that meets bothblades,
of the mechanical
a staticand rotor dynamic
bending stress limitcon- of
130 MPa
straints. is set, excluding any stress intensification factor (SIF). Additionally, a slenderness
130 MPaTois ensure the mechanical
set, excluding any stressstrength of the blades,
intensification a static
factor (SIF). bending stress
Additionally, limit of
a slenderness
ratio,
130 MPa defined as the ratio
is set, excluding of stress
the total axial flow path length to the hub diameter, is required
ratio, defined as the ratioany of the intensification
total axial flow path factor (SIF).
length Additionally,
to the hub diameter,a slenderness
is required
to
ratio,be less
defined than as 9 to
the ensure
ratio of structural
the total integrity.
axial flow The
path thermodynamic
length to the
to be less than 9 to ensure structural integrity. The thermodynamic properties and velocity hub properties
diameter, is and velocity
required
totriangles
triangles can be obtained at each boundary for both the stator and rotor, as defined in in
be less can
than 9be
to obtained
ensure at each
structural boundary
integrity. The for both the
thermodynamic stator and rotor,
properties and as defined
velocity
Figure
Figure 1.
triangles 1.canFollowing
be obtained
Following that,atthe
that, the
eachblade geometry
boundary
blade geometry forcancanbebe
both the obtained,
stator and
obtained, including
rotor, as
including blade
defined
blade heights,
in
heights,
annulus
annulus area, chord and axial chord length, blade pitch, and throat-to-pitch ratio (o/c), as as
Figure 1. area,
Following chord and
that, axial
the chord
blade length,
geometry blade
can be pitch, and
obtained, throat-to-pitch
including blade ratio (o/c),
heights,
shown
shown in
annulus in Figure
area, chord
Figure 22 [24,25].
[24,25].
and axial The
Thechordmean
mean linedesign
length,
line design
blademodelmodel
pitch, andgenerates a 1D
throat-to-pitch
generates a 1D geometry forfor
ratio (o/c),
geometry aseach
each
stage,
shown including
in Figure 2 the inlet/outlet
[24,25]. The mean angles,
line the
design stagger
model angle,
generates
stage, including the inlet/outlet angles, the stagger angle, the chord length, the throat thea chord
1D length,
geometry forthe
eachthroat
opening,
stage,
opening, and
including
and thethethetrailing edgethickness.
inlet/outlet
trailing edge thickness.
angles, the The
The number
stagger
number ofof
angle, stages,thethe
the chord
stages, number
length,
number oftheof bladesperper
throat
blades
opening,
stage,
stage, and
andand the
thethetiptrailing
tip clearance
clearanceedge thickness.
values
values arealso
are Theprovided.
also number of stages, the number of blades per
provided.
stage, and the tip clearance values are also provided.

c
c
CW2
U CW2
α2 U Ca2
α2 Ca2
β2
β2

c
c
CW3
CW3 U
Ca3 U β3
β3
C3

Ca3
C3

α3
α3

Figure 1.
Figure 1. Geometry
Geometry of of aa blade
blade cross-section
cross-section where
where CC is is the
theabsolute
absolutevelocity,
velocity,WWisisthe
therelative
relativeve-
velocity,
Figure
locity,1.UGeometry
is the bladeof linear
a bladespeed,
cross-section
Ca is thewhere
absoluteC isaxial
the absolute
velocity, velocity,
Cw is the W is the relative
absolute ve-
tangential
U is
locity,the blade
U isαthe linear
blade speed, C a is
linear velocity the
speed, Cangle absolute
a is theand
axial
absolute velocity,
axial C w is
velocity, the absolute
Cw isangle. tangential velocity,
the absolute tangential α is
velocity, is the absolute β is the relative velocity
the absolute velocity angle and β is the relative velocity angle.
velocity, α is the absolute velocity angle and β is the relative velocity angle.

rtip
rtip

rmean
rmean
rhub
rhub

Figure 2. Axial flow turbine stage showing the stator (S) and the rotor (R) where r is the radius at
Axial
Figure2.2.Axial
Figure flow
flow turbine
turbine stage
stage showing
showing the the stator
stator (S) the
(S) and androtor
the rotor (R) where
(R) where r is ther radius
is the radius
at at
hub, tip and mean sections.
hub, tip and mean sections.
hub, tip and mean sections.
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 5 of 18
Int. J. Turbomach. Propuls. Power 2024, 9, 5 5 of 17

According to an analysis conducted by the authors in a previous work, the Aungier

According to an analysis conducted by the authors in a previous work, the Aungier
loss model [29] is one of the most suitable for sCO2 axial turbine design [25]. The mean
loss model [29] is one of the most suitable for sCO2 axial turbine design [25]. The mean
line design tool has been previously verified against multiple cases from the literature.
line design tool has been previously verified against multiple cases from the literature.
This includes cases involving air, CO2 and organic fluids as the working medium. A good
This includes cases involving air, CO2 and organic fluids as the working medium. A good
agreement was obtained for both the geometric parameters as well as the total-to-total
agreement was obtained for both the geometric parameters as well as the total-to-total
efficiency. A maximum percentage difference of 1.5% and 1.2% in the total-to-total and
efficiency. A maximum percentage difference of 1.5% and 1.2% in the total-to-total and
total-to-static efficiencies, respectively, was observed [30].
total-to-static efficiencies, respectively, was observed [30].
2.2. CFD
2.2. CFD Model
Model Definition
Definition
CFD simulations
CFD simulations are areinitiated
initiatedby bygenerating
generatingthe the3D3D blades
blades using
using thethe
meanmean lineline
design
de-
results
sign in addition
results to making
in addition certain
to making geometrical
certain assumptions,
geometrical assumptions, whichwhichcan be further
can eval-
be further
uated andand
evaluated refined in subsequent
refined in subsequent design
design phases.
phases.These
Theseassumptions
assumptionsinclude includethe the leading-
leading-
edge thickness,
edge thickness, inlet/outlet
inlet/outlet wedge
wedge angles,
angles, aerofoil
aerofoil curvature
curvature control points, and
control points, and blade
blade
base fillet. The 2D aerofoil is extruded to form the 3D blade since the mean line design design
indicates relatively
relatively short
short blades.
blades.Specifically,
Specifically,the theratio
ratioofofthetheblade
blade height
heightto the mean
to the mean di-
ameter ranges
diameter ranges between
between 8%8%and 15%.
and TheThe
15%. CFD results
CFD are are
results compared
compared to the mean
to the lineline
mean de-
sign model
design model to verify
to verifythethesuitability of the
suitability applied
of the mean
applied line line
mean loss loss
model. To ensure
model. To ensurea suit-
a
able design,
suitable the predicted
design, the predicted massmass
flowflow
rate rate
for the
for given pressure
the given pressureratio ratio
is compared
is compared with
cyclecycle
with requirements
requirements and the and3Dtheblade design
3D blade assumptions
design assumptionsare adjusted
are adjusted accordingly.
accordingly.The
resulting
The 3D blade
resulting 3D bladegeometry
geometryis then evaluated
is then evaluatedusing finite
using element
finite element analysis (FEA)
analysis to en-
(FEA) to
sure that
ensure mechanical
that mechanicalstresses
stressesarearewithin
withinthe theimposed
imposedlimits.
limits.The The blade
blade base
base fillet can be
modified
modified to tomeet
meetthethestress
stressconstraints,
constraints,alongalong with
withadjusting
adjusting thethe
aerofoil thickness.
aerofoil thickness. Further
Fur-
improvements
ther improvements to theto3Dtheblade geometry
3D blade are achieved
geometry usingusing
are achieved bladebladeshapeshape
optimisation
optimisationwith
the
withgoal
theof improving
goal of improvingthe performance
the performance while while
aligning with the
aligning cycle
with theoperating conditions
cycle operating con-
and safety
ditions andconsiderations.
safety considerations.
A 3D 3D steady-state
steady-state multi-stage CFD model is set up for for aa single
single flowflow passage,
passage, as
shown in Figure
Figure 3. 3.The
Theturbulence
turbulence model is k-ω SST, which is widely
model is k-ω SST, which is widely considered for tur- considered for
turbomachinery
bomachinery simulationssimulations [31].
[31]. Near
Near thethe walls,a ascalable
walls, scalablewallwallfunction
functionmodelmodel is is used,
used,
which
whichemploys
employsequilibrium
equilibrium wall
wallfunctions
functions for for
highhigh
Reynold’s
Reynold’snumber flow. The
number flow.CFD Thesolver
CFD
is ANSYS
solver CFX (2020
is ANSYS CFXR2). TheR2).
(2020 interfaces between between
The interfaces the statorthe andstator
rotorand blades areblades
rotor modelled are
using a mixing plane approach, where the pitch ratios are defined
modelled using a mixing plane approach, where the pitch ratios are defined as the ratio as the ratio between the
number
betweenof blades
the number in the downstream
of blades blade row and
in the downstream the row
blade upstream
and the blade row. blade row.
upstream

Figure 3. Numerical domain of the 14-stage design.

Figure 3. Numerical domain of the 14-stage design.

In the
In the proposed
proposeddesign,
design,thetheratio
ratioofofthe
the rotor
rotor to to stator
stator number
number of blades
of blades fallsfalls within
within the
the range of 0.893 to 0.914. This ratio is sufficiently close to unity, which ensures
range of 0.893 to 0.914. This ratio is sufficiently close to unity, which ensures that modelling that mod-
aelling
singlea single
passage passage
of each ofblade
each blade
row has rowa has a minimal
minimal impactimpact
on theonsolution
the solution accuracy.
accuracy. The
The boundary
boundary conditions
conditions defineddefined formodel
for this this model
are theare thepressure
total total pressure
and theand
totalthe total tem-
temperature
perature
at the inletatofthe
theinlet
firstof the first
stator blade,stator
while blade, while
the static the static
pressure pressureatisthe
is defined defined
outlet ofat the
the
outlet
last of the
rotor. Thelastrotor
rotor. The rotor
blades blades are unshrouded
are unshrouded with a tipgap
with a tip clearance clearance
of 0.07%gapofofthe
0.07%tip
of the tip for
diameter diameter for each stage.
each stage.
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 6 of 18

Int. J. Turbomach. Propuls. Power 2024, 9, 5 6 of 17

Alongside design-point verification, an off-design CFD model is set up to assess tur-

bine Alongside
performance at different operating
design-point verification, conditions. This model
an off-design provides
CFD model insights
is set up tointo the
assess
acceptable turndown capability, defining the operating range without
turbine performance at different operating conditions. This model provides insights into a significant per-
formance
the deterioration.
acceptable turndownThe off-design
capability, simulations
defining are set up
the operating by varying
range withoutthe inlet total
a significant
pressure while maintaining a constant inlet total temperature and
performance deterioration. The off-design simulations are set up by varying the inlet static outlet pressure.
total
The results
pressure are maintaining
while presented using the non-dimensional
a constant form of the
inlet total temperature andmass
staticflow ratepressure.
outlet defined
by Equation
The results are where 𝑚̇ using
(1),presented is the the
mass flow rate, 𝛾 is the
non-dimensional formspecific
of theheat
mass flow𝑅rate
ratio, is the ideal
defined
.
gas constant, 𝑇 is the total inlet temperature, 𝐷 is the hub diameter,
by Equation (1), where m is the mass flow rate, γ is the specific heat ratio, R is the ideal
01 ℎ and 𝑃 01 is the
inlet total pressure.
gas constant, T01 is the total inlet temperature, Dh is the hub diameter, and P01 is the inlet
total pressure.
. √
𝑚̇√𝛾𝑅𝑇01
𝑚𝑅𝑒𝑑 = m γRT (1)
m Red = 𝐷ℎ2 𝑃0101 (1)
2
Dh P01
The mesh quality has been controlled by controlling the global element size while
The mesh
maintaining 𝑦 +quality
valueshas been
on the controlled
walls around 50 bytocontrolling the global
best suit standard wallelement
functions size while
[32]. The
maintaining y + values on the walls around 50 to best suit standard wall functions [32]. The
required number of grid points is identified using a mesh independence study applied to
required number
a single stage of gridefficiency
to obtain points istolerance
identifiedwithinusing 0.02%
a meshcompared
independence studymesh,
to the finest applied as
to a single stage to obtain efficiency tolerance within 0.02% compared to
reported in Figure 4. This mesh size is then applied to the remaining stages. The total number the finest mesh,
as reported
of grid in per
points Figure 4. This
stage, in thismesh
case,size is then
ranges applied
between 3.1toand
the3.7
remaining stages. while
million points, The totalthe
number of grid points per stage, in this case, ranges between 3.1 and 3.7 million points,
total number of grid points of the domain is 47.3 million.
while the total number of grid points of the domain is 47.3 million.

Figure 4. Mesh study of the first stage out of the 14-stage design. The blue line shows the efficiency
variation with
variation with the
the number
numberof
ofgrid
gridpoints
pointswhile
whilethe
thered
reddashed
dashedline
linehighlights
highlights the
the selected
selected mesh
mesh point
point for the
for the study.study.

The thermophysical
thermophysicalproperties
propertiesofof thethe
sCOsCO 2 mixtures
2 mixtures areare evaluated
evaluated usingusing SIMULIS
SIMULIS [33].
[33].selected
The The selected
equationequation
of stateofisstate is Peng–Robinson
Peng–Robinson in bothinmean
bothlinemean line and
design designCFDand CFD
simula-
simulations
tions for its simplicity
for its simplicity and accuracy
and accuracy [21]. The[21]. Theinteraction
binary binary interaction
parameters parameters for the
for the selected
selected
EoS wereEoS were selected
selected to matchtothose
match those
used forused for theanalysis
the cycle cycle analysis
to ensureto ensure consistency
consistency in the
in the thermodynamic
thermodynamic properties
properties obtained obtained
by bothby both models
models [21,34]. [21,34]. The properties
The properties are in-
are introduced
troduced
to the CFDtomodels
the CFD models
using look-upusing look-up
tables tablesthe
that cover that cover the
expected expected
pressure andpressure
temperatureand
temperature
ranges ranges
with the sizewith the×size
of 500 500 × 500
500ofpoints. The points. The range
pressure pressure range
is set is set between
between 10 bar and 10
300 bar, 300
bar and whilebar,thewhile
temperature range isrange
the temperature set between 400 K and
is set between 4001200
K and K.1200
The K.CFDThe model
CFD
results have been
model results havechecked to ensure
been checked tothat the property
ensure tables cover
that the property thecover
tables globalthe
minimum and
global min-
maximum
imum and values
maximum of the pressure
values of the and temperature
pressure within the solution
and temperature within the domain.
solution domain.
It is worth noting that the CFD model has been verified against both numerical and
experimental results
resultsavailable
availableinin thethe literature,
literature, as illustrated
as illustrated in theinauthors’
the authors’ previous
previous work
work [22,35]. A good agreement was observed between the
[22,35]. A good agreement was observed between the proposed model and the published proposed model and the
published
data in terms data
ofintheterms of the total-to-total
total-to-total efficiency and efficiency and the stator/rotor
the stator/rotor loss coefficients.
loss coefficients. Compared
Compared
to the resultsto of
thearesults
numericalof a CFD
numerical
studyCFD study
of a 15 MWofsCOa 152 MW sCOthe
turbine, 2 turbine, the calculated
calculated deviation
deviation in the total-to-static
in the total-to-static efficiency was efficiency was Compared
0.2% [22]. 0.2% [22]. to Compared to the experimental
the experimental results of a
results
140 kWof a 140
axial airkW axial the
turbine, air turbine,
obtainedthe obtained
deviation in deviation in the total-to-total
the total-to-total efficiency was efficiency
1% [35].
was 1% [35].
 Int.J.J.Turbomach.
Int. Turbomach.Propuls.
Propuls.Power
Power2024,
2024,9,9,xxFOR
FORPEER
PEERREVIEW
REVIEW 77 of
of 18
18
Int. J. Turbomach. Propuls. Power 2024, 9, 5 7 of 17

2.3.
2.3. Blade
2.3.Blade Shape
BladeShape Optimisation
ShapeOptimisation
Optimisation
The
The 3D blade geometrycan
The 3D blade geometry
3D blade geometry canbebefurther
furtherimproved
further improvedthrough
improved throughblade
through blade
blade shape
shape
shape optimisation,
optimisation,
optimisation, as
as
as explained
explained by
by the
the authors
authors in
in aa previous
previous publication
publication [22].
[22].
explained by the authors in a previous publication [22]. The optimisation model The
The optimisation
optimisation model
model uses
uses
uses aa
a set
set
set of decision
of decision
of decision variables
variables
variables represented
represented
represented by by by the
thethe
blade blade
blade aerofoil
aerofoil
aerofoil angle angle
angle
andandand thickness
thickness
thickness distribu-
distribu-
distributions,
tions,
tions, while
whilewhile
the theobjectives
the objectives
objectives andconstraints
and
and constraintsconstraints areintroduced
are
are introduced introduced
to maintain tomaintain
to maintain anefficient
an
an efficient efficientopera-
operation opera-
and a
tion
tion and aa safe
safeand
design. safe design.
Thedesign.
search TheThe search
space search spaceby
space
is defined isisselecting
defined by
defined aby selecting
selecting
certain aa certain
range certain range for
for the range for the
thickness the
and
thickness
thickness andangle
and
angle magnitudes angleatmagnitudes
magnitudes
four different atfour
at four different
different
locations, locations,the
locations,
specifically, specifically,
specifically, theleading
the
leading edge, leading edge,
trailingedge,
edge,
trailing edge,
and twoedge,
trailing andtwo
mid-points,
and twoasmid-points,
mid-points,
shown in Figureasshown
as shown
5. The inFigure
in Figurefor
range 5.5.The
Therange
each range foreach
decision
for eachdecision
decision
variable var-
is defined
var-
iable
around
iable is defined around
the reference
is defined aroundvalue the reference value
using manual
the reference using
value using manual
iterations
manualaimed iterations aimed
at maintaining
iterations at maintaining
a reasonable
aimed at maintaining
aaaerofoil
reasonable
shape,
reasonable aerofoil shape,in
as reported
aerofoil shape, asFigure
as reported
reported inFigure
6. in Figure6.6.

Figure
Figure5.5.
Figure Blade
5.Blade
Blade aerofoil
aerofoil geometry
geometry
aerofoil geometry asas
as defined
defined forfor
for
defined thethe
the optimisation
optimisation model.
model.
optimisation TheThe
The
model. green
green dashed
dashed
green line line
line
dashed
represents
represents the
the aerofoil
aerofoil chord
chord line.
line.
represents the aerofoil chord line.

10
10 96
96
Anglerange
Angle range
88 Thicknessrange
Thickness range 72
72
(mm)
Thickness (mm)

(deg)
Angle (deg)

66 48
48
Thickness

Angle

44 24
24

22 00

00 −−-24
-24
11 22 33 44
Point
Point
Figure6.6.Exemplary
Figure Exemplaryrange
rangefor
fordecision
decisionvariables
variablesof
ofoptimisation
optimisationmodel
modelsearch
searchspace.
space.

Within the
Within optimisationmodel,
the optimisation
optimisation model,the
model, themass
the massflow
mass flowrate
flow rateisis confined
rate confinedto
confined within1%
to within
within 1%of
1% of the
the
cycle design mass flow rate, and the maximum stress is kept
cycle design mass flow rate, and the maximum stress is kept under 260 MPa. This stress under 260 MPa. This stress
limit accounts for
limitaccounts for all
forall stress
stressand
allstress andis
and isisnot
notto
not tobe
to beconfused
be confusedwith
confused withthe
with thestatic
the stress
static
static stress
stress limit imposed
limit
limit imposed
imposed in
the
inthe
in mean
themean line
meanline design,
linedesign, as
design,as the
asthe former
theformer
formerlimitlimit represents
limitrepresents
representsthe the peak
thepeak equivalent
peakequivalent
equivalentstressstress while
stresswhile
whilethe the
the
latterlimit
latter
latter limitisis
limit isan
anaverage
an average cross-sectionstress.
averagecross-section
cross-section stress.AA
stress. Aone-way
one-waylink
one-way linkisis
link isset
setup
set upbetween
up betweenthe
between theCFD
the CFD
CFD
andFEA
and
and FEAmodels,
FEA models,where
models, wherethe
where theCFD
the CFDflow
CFD flowresults
flow resultsare
results aretransferred
are transferredto
transferred tothe
to theFEA
the FEAmodel
FEA modelto
model todefine
to define
define
theaerodynamic
the
the aerodynamicloads.
aerodynamic loads.
loads.DueDueto
Due tothe
to thelimited
the limitedblade
limited bladedeformation,
blade deformation,which
deformation, whichisis
which isfound
foundto
found tobe
to bewithin
be within
within
0.2%
0.2% of
of the
the blade
blade height,
height, there
there is
is considered
considered limited
limited added
added value
value
0.2% of the blade height, there is considered limited added value in studying the effect of in
in studying
studying the
the effect
effect of
of
blade deformation
bladedeformation
blade deformationon on the
onthe flow
theflow
flowfield.field.
field.
The optimisation process
processis
The
The optimisationprocess
optimisation isiscarried
carriedout
carried outusing
out usingaaasurrogate
using surrogatemodel
surrogate model
model toto
toreplace
replace
replace thethe
thephysical
phys-
phys-
CFD/FEA
icalCFD/FEA models
CFD/FEAmodels during
modelsduring the
duringthe optimisation
theoptimisation iterations.
optimisationiterations. The
iterations.The CFD/FEA
TheCFD/FEA
CFD/FEAmodels models
modelshavehave
havebeenbeen
been
ical
used
usedto to solve
tosolve a
solveaaset set
setofof learning
oflearning
learningpointspoints generated
pointsgenerated
generatedusing using a central
usingaacentral composite
centralcomposite
compositedesign design
designof of experi-
ofexper-
exper-
used
ment algorithm
iment algorithm (CCDoE).
(CCDoE). These
These learning
learning points
points are
are used
used to
to construct
construct response
response surfaces
surfaces
iment algorithm (CCDoE). These learning points are used to construct response surfaces
for each
for each output
output parameter.
parameter. Although
Although this this methodology
methodology depends depends on on the
the surrogate
surrogate model
model
for each output parameter. Although this methodology depends on the surrogate model
Int. J. Turbomach. Propuls. Power 2024, 9, 5 8 of 17

accuracy, it allows for increasing the number of iterations during the optimisation process
and achieving lower tolerance. Furthermore, the accuracy of the surrogate model can be
improved by defining a set of refinement points that are solved using the actual CFD-FEA
models until the required tolerance is reached. The details of the optimisation process are
described in the authors’ previous work [22].

3. Results and Discussion

3.1. Flow Path Design
Different CO2 mixtures have been found to be promising to elevate the critical tem-
perature of the mixture. According to design optimisation results previously obtained by
the authors for the three proposed CO2 mixtures, it has been found that similar flow path
geometries are achieved, regardless of the working fluid, although it was found that the
chord length is larger for the TiCl4 designs compared to the SO2 and C6 F6 designs due
to higher bending stresses [22]. However, no significant impact of the working fluid was
observed on the design process or the applied methodology. Among the mixtures, the
CO2 -SO2 mixture has been selected for further analysis based on considerations of thermal
stability, health, and environmental factors, as discussed in the introduction.
The design process of a large-scale axial turbine is carried out based on the specified
boundary conditions and cycle requirements outlined in Table 2. These conditions and
requirements are specifically chosen for the SCARABEUS project. The turbine is designed
to produce 130 MW of power, which corresponds to a cycle net output of 100 MWe for a
concentrated solar power (CSP) plant. The turbine rotational speed is fixed at 3000 RPM to
match the electrical grid frequency requirements (i.e., 50 Hz) since it is not practical to use
a gearbox to decouple turbine and generator speeds at such power scales.

Table 2. Boundary and operating conditions.

Parameter Value Parameter Value

Dopant SO2 Outlet static pressure (bar) 81.24
Dopant molar fraction (%) 20% Mass flow rate (kg/s) 827
Turbine inlet total pressure (bar) 239 Rotational speed (RPM) 3000
Turbine inlet total temperature (K) 973

Initially, the aerodynamic performance of a four-stage design was investigated, which

was intended to limit the peripheral speed of the shaft to 180 m/s. That design achieved
a total-to-total efficiency of 87.5%, as evaluated by the mean line loss model. To enhance
the performance, the number of stages has been increased, whilst constraints have been
introduced to ensure the average rotor static bending stress is less than 130 MPa for all
stages, for rotor blade counts ranging between 35 and 95, and for a slenderness ratio less
than 9.
In view of the fact that turbine designs were evaluated at a constant rotational speed
and loading coefficient of 3000 RPM and 1.0, respectively [25], the number of stages dictates
the peripheral blade speed through the desired stage isentropic enthalpy drop. This, in
turn, directly defines the hub diameter. Increasing the number of stages resulted in smaller
peripheral speed, smaller hub diameter, and larger blade aspect ratio, yielding a higher
total-to-total efficiency, as indicated in Figure 7. It has been observed that increasing the
blade aspect ratio decreases the influence of secondary flow losses, as obtained using the
Aungier loss model. This can be attributed to reducing the ratio between the endwall
boundary layers to the flow path span. Additionally, reducing the hub diameter also
contributes to a decrease in the tip diameter, even with the increased blade length. This
leads to narrower tip clearance gaps, reducing the impact of associated losses on the overall
stage losses [36].
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 9 of 18
Int. J. Turbomach. Propuls. Power 2024, 9, 5 9 of 17

(a) (b)

Figure
Figure7.7.Effect
Effectof
ofthe
thenumber
numberofofstages
stages(𝑛
(n𝑠𝑡st))onon(a)
(a)the
thetotal-to-total
total-to-totalefficiency
efficiency(𝜂(η𝑡𝑡tt))and
andhub
hubdiameter
diameter
(𝐷
(Dℎ𝑢𝑏 ), and (b) peripheral speed for the CO -SO mixture as evaluated by the mean lineloss
), and (b) peripheral speed for the CO 2 -SO 2 mixture as evaluated by the mean line lossmodel.
model.
hub 2 2

The
The loss
loss breakdown
breakdown of the 4-stage,
4-stage, 9-stage,
9-stage, and
and14-stage
14-stagedesigns
designsisisshown
shownininFigure
Figure8,
8,
asasobtained
obtainedusing
usingthe
theAungier
Aungierloss lossmodel.
model.In Inthis
thisfigure,
figure,the
theaverage
averageenthalpy
enthalpyloss
loss coeffi-
coef-
ficient perstage
cient per stageisispresented
presentedfor forthethestator
statorendwall
endwall(SEW),
(SEW),stator
statorprofile
profile(SPF),
(SPF), stator
stator trail-
trailing
ing
edge edge (STE),
(STE), rotor
rotor endwall
endwall (REW),(REW),rotorrotor profile
profile (RPF),(RPF),
rotorrotor trailing
trailing edgeedge
(RTE),(RTE), and
and rotor
rotor tip clearance
tip clearance (RTC).(RTC). It isfrom
It is clear clearthefrom thethat
figure figure
the that the endwall
endwall and tip clearance
and tip clearance losses are
significantly
losses higher in the
are significantly four-stage
higher in the model,
four-stagewhich is due
model, to theislarge
which due hub diameter,
to the large hubwhich
di-
leads towhich
ameter, shorterleads
blades and larger
to shorter relative
blades tip gaps.
and larger relative tip gaps.

0.3

0.25 RTC
coefficient per stage [-]
Average enthalpy loss

0.2 RTE
RPF
0.15
REW
0.1 STE
SPF
0.05
SEW
0
4-stage 9-stage 14-stage

Figure 8. The loss breakdown of the 4-, 9-, and 14-stage models obtained using the Aungier loss
model.

Figure 8. The loss breakdown of the 4-, 9-, and 14-stage models obtained using the Aungier
As a result of such design factors, the number of stages can be increased up to 14
loss model.
stages without exceeding the maximum rotor bending stress and slenderness ratio limits.
Increasing the number
As a result of stages
of such design fromthe
factors, 4 to 14 results
number in ancan
of stages increase in total-to-total
be increased effi-
up to 14 stages
ciency of 6.3%, thus achieving a design total-to-total efficiency of 93.8%,
without exceeding the maximum rotor bending stress and slenderness ratio limits. Increas- as evaluated by
the
ingmean line lossofmodels;
the number this is4due
stages from toresults
to 14 the reduction in peripheral
in an increase speed from
in total-to-total 194 to 107
efficiency of
m/s
6.3%,and hub
thus diameterareduction
achieving from 1.2 toefficiency
design total-to-total 0.62 m. The 14-stage
of 93.8%, as design has by
evaluated a flow path
the mean
length of models;
line loss 1.8 m, although theto
this is due total
theshaft length,
reduction inincluding
peripheralthe bearing
speed fromspan
194 and axial
to 107 m/s gaps,
and
ishub
larger. Further investigations of the rotor dynamic stability, torsional
diameter reduction from 1.2 to 0.62 m. The 14-stage design has a flow path length sizing, and dryof
gas seals
1.8 m, have been
although the conducted and published
total shaft length, includingin athe
separate
bearingpaperspanfocusing
and axialon the integra-
gaps, is larger.
tion of the
Further aerodynamicof
investigations and
themechanical
rotor dynamic systems of thetorsional
stability, turbine [23]. These
sizing, andinvestigations
dry gas seals
have
haveshown an acceptable
been conducted and rotor-dynamic
published in astability
separatefor the proposed
paper focusing on 14-stage design and
the integration of
acceptable shaft end
the aerodynamic andtorsional sizing,
mechanical considering
systems of the the market
turbine [23].availability of a dry gashave
These investigations seal
of a suitable
shown diameter.rotor-dynamic stability for the proposed 14-stage design and accept-
an acceptable
able The
shaftmeridional cross-section
end torsional of the turbine
sizing, considering theflow pathavailability
market is shown inofFigure
a dry 9,
gaswhere
seal ofthea
unfilled and filled shapes represent the stator and rotor blades, respectively.
suitable diameter.
Int. J. Turbomach. Propuls. Power 2024, 9, 5 10 of 17

Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 10 of 18

The meridional cross-section of the turbine flow path is shown in Figure 9, where the
unfilled and filled shapes represent the stator and rotor blades, respectively. Representative
geometrical parameters
Representative for parameters
geometrical the preliminary flow
for the path, as obtained
preliminary using
flow path, the mean
as obtained line
using
design model, are reported in Table 3.
the mean line design model, are reported in Table 3.

Figure
Figure 9.
9. Meridional
Meridional view
view of
of the
the proposed
proposed 14-stage
14-stage flow
flow path
path design.
design.

Table 3. Mean
Mean line turbine design data for the 1st, 7th, and 14th stages.

Parameter
Parameter S1 S1R1 R1 S7 S7 R7 R7 S14 S14 R14R14
Axial
Axialchord
chord (mm)
(mm) 35.53 38.96
35.53 40.43
38.96 40.4344.28 44.28 48.7548.75 53.12
53.12
Hub
Hub radius (mm)
radius (mm) 310.61310.61
Inlet
Inlet tiptip radius
radius (mm)
(mm) 365.17 365.17
366.54 366.54
386.34 386.34
387.54387.54423.51423.51 425.21
425.21
Outlet tip radius
Outlet tip radius (mm) (mm) 366.17 366.17
368.04 368.04
387.21 387.21
389.81389.81 424.74
424.74 428.99
428.99
No. of blades 58 53 53 48 47 42
No. of blades
Tip gap (mm)
58 -
53 0.515
53 -
48 0.546 47 - 42
0.601
Tip gap (mm) - 0.515 - 0.546 - 0.601

The CFD numerical results are compared to the cycle requirements, while several
The CFD numerical results are compared to the cycle requirements, while several
design parameters, such as the outlet wedge angle, the inlet/outlet fillet radius, and the
design parameters, such as the outlet wedge angle, the inlet/outlet fillet radius, and the
suction side (SS) curvature control points, are manually adjusted to control the throat
suction side (SS) curvature control points, are manually adjusted to control the throat
opening and the mass flow rate. The mean line design (MLD) results have been verified
opening and the mass flow rate. The mean line design (MLD) results have been verified
against the CFD results, as shown in Table 4. The obtained deviations in mass flow rate,
against the CFD results, as shown in Table 4. The obtained deviations in mass flow rate,
power, and total-to-total efficiency are 0.51%, 1.38%, and 0.52%, respectively.
power, and total-to-total efficiency are 0.51%, 1.38%, and 0.52%, respectively.
Table 4. Comparison between mean line design and CFD model results.
Table 4. Comparison between mean line design and CFD model results.
Parameter Unit MLD CFD Difference
Parameter
. Unit MLD CFD Difference
m kg/s 827.06 822.9 0.51%
𝑚̇ kg/s 827.06 822.9 0.51%
Power MW 131.9 130.1 1.38%
𝑃𝑜𝑤𝑒𝑟
ηtt %MW 131.9
93.84 130.1
92.90 1.38%
1.01%
η𝜂ts𝑡𝑡 %% 93.84
93.06 92.90
91.95 1.01%
1.21%
𝜂𝑡𝑠 % 93.06 91.95 1.21%
The mass flow averaged relative Mach number at the exit from each blade row is
The mass
compared flow
to the averaged
mean relative
line design Machasnumber
results, shown in at Figure
the exit10.
from each blade
Overall, row is
both models
compared to the mean line design results, as shown in Figure 10. Overall,
show the same trend where the Mach number increases as the pressure decreases because both models
show the same
the speed trenddecreases
of sound where theatMach number increases
the low-pressure stages.asAthe pressure
good decreases
coincidence because
is observed
the speed of sound decreases at the low-pressure stages. A good coincidence
between the results from the two models; however, the velocities obtained using the CFD is observed
between the results
models tend from thehigher,
to be slightly two models; however,
specifically thelast
in the velocities
stages,obtained using
due to the the CFD
cumulative
models tend to be slightly higher,
deviation in the incidence angle. specifically in the last stages, due to the cumulative
deviation in the incidence
The difference betweenangle.
the flow distribution of the first and last turbine stages at the
design point is compared at mid-span in Figure 11. No local regions of supersonic flow,
0.32 no shock losses, exist. Both stages exhibit smooth streamlines without obvious
and hence
Relative Mach number

CFD
separation
0.3 regions at mid-span when operating at the design point, confirming the good
MLD
coincidence between the flow angles and blade angles obtained using the mean line design.
0.28 the stagnation point in the last stage is shifted towards the blade suction side,
However,
showing
0.26 a larger incidence angle in the last stage compared to the first stage. This can be
attributed to the cumulative deviation between the mean line design and CFD results, as
shown0.24in Figure 10.
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
Blade row number

Figure 10. Exit Mach number from each blade row obtained using the mean line design and CFD.
 compared to the mean line design results, as shown in Figure 10. Overall, both models
show the same trend where the Mach number increases as the pressure decreases because
the speed of sound decreases at the low-pressure stages. A good coincidence is observed
between the results from the two models; however, the velocities obtained using the CFD
Int. J. Turbomach. Propuls. Power 2024, 9, 5
models tend to be slightly higher, specifically in the last stages, due to the cumulative
11 of 17
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 11 of 18
deviation in the incidence angle.

0.32

Relative Mach number

The difference betweenCFD the flow distribution of the first and last turbine stages at the
0.3 MLDat mid-span in Figure 11. No local regions of supersonic flow,
design point is compared
and hence
0.28 no shock losses, exist. Both stages exhibit smooth streamlines without obvious
separation regions at mid-span when operating at the design point, confirming the good
0.26
coincidence between the flow angles and blade angles obtained using the mean line de-
sign.0.24
However, the stagnation point in the last stage is shifted towards the blade suction
0 2 a larger
side, showing 4 6 incidence
8 10 12 14 in
angle 16the18last
20stage
22 compared
24 26 28 to the first stage. This
can be attributed to the cumulative Blade row number between the mean line design and CFD re-
deviation
sults, as
Figure
Figure
shown
10.10. Exit
Exit
in Figure
Mach
Mach number
10.
number from
from each
each blade
blade row
row obtained
obtained using
using the
the mean
mean line
line design
design and
and CFD.
CFD.

Relative Mach number

1st stage Last stage

Figure
Figure11.
11.Comparison
Comparisonbetween
between the
the flow field
field obtained
obtainedfor
forthe
the1st1st
andand 14th
14th stages
stages at the
at the design
design point.
point. Thedashed
The red red dashed circles
circles highlight
highlight the incidence
the incidence angleangle fordifferent
for the the different stages.
stages.

TheThemaximum
maximumequivalent
equivalentvon vonMises
Mises stresses
stresses are evaluated
evaluatedfor forthe
thefirst
firstand
andlast
lastturbine
tur-
stages.
bine These
stages. stages
These stagesareare
chosen
chosenbecause
becausethey represent
they represent thethe
extreme
extreme design
designandand
operating
oper-
conditions.
ating To limit
conditions. the peak
To limit the stress values,values,
peak stress adjustments can be can
adjustments made betomade
the blade geometry,
to the blade
such as increasing the outlet wedge angle, increasing the base aerofoil
geometry, such as increasing the outlet wedge angle, increasing the base aerofoil thick- thickness, increasing
the whole
ness, blade
increasing thickness,
the whole bladeor increasing
thickness,theorbase fillet size.
increasing the The
baseeffect
fillet of these
size. Theparameters
effect of
on the
these peak stresses
parameters on theobtained in theobtained
peak stresses first turbine
in thestage
first is summarised
turbine stage is in Table 5, while
summarised in
similar
Table trends
5, while are obtained
similar for the
trends are last turbine
obtained for thestage.
last turbine stage.

Table
Table 5.5.
TheThe effect
effect ofof geometry
geometry tuning
tuning onon the
the peak
peak stressesand
stresses andaerodynamic
aerodynamicperformance.
performance.
.
Model
Model 𝒎̇ m(kg/s)
(kg/s) 𝐏𝐨𝐰𝐞𝐫
Power(𝐌𝐖)
(MW) 𝜼𝒕𝒕ηtt(%)
(%) 𝝈𝑺 σ(MPa)
S (MPa)𝝈𝑹 σR (MPa)
(MPa)
Reference
Referencegeometry
geometry 898.22
898.22 10.07
10.07 93.15
93.15 445.70
445.70 310.64
310.64
Increase outlet wedge
Increase outlet wedge angleangle
846.46 9.60 92.98 333.28 258.38
(decrease throat opening 5%) 846.46 9.60 92.98 333.28 258.38
(decrease throat opening 5%)
Increase the base aerofoil
Increase the(around
base aerofoil 873.38 9.76 92.77 272.13 237.99
thickness 25%)
873.38 9.76 92.77 272.13 237.99
thickness
Increase(around
the whole 25%)
blade
848.72 9.46 92.19 269.86 223.97
thickness (around 25%)
Increase the whole blade
Increase base fillet radius 848.72 9.46 92.19 269.86 223.97
thickness (around 25%) 890.15 9.85 92.86 238.36 264.22
from 1 mm to 2 mm
Increase base fillet radius
890.15 9.85 92.86 238.36 264.22
from 1 mm to 2 mm
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 12 of 18
Int. J. Turbomach. Propuls. Power 2024, 9, 5 12 of 17

It can be seen from the table that decreasing the throat opening by decreasing the
outletItwedge
can beangle
seen decreases
from the table that flow
the mass decreasing
rate as the
wellthroat
as theopening by decreasing
peak stress values of both the
outlet wedge angle decreases the mass flow rate as well as the peak stress
the stator and rotor. Decreasing the throat opening by 5% results in a decrease in the mass values of both the
stator and rotor. Decreasing the throat opening by 5% results in a decrease in the mass flow
flow rate, power, and total-to-total efficiency by 5.8%, 4.7%, and 0.2%, respectively. How-
rate, power, and total-to-total efficiency by 5.8%, 4.7%, and 0.2%, respectively. However,
ever, the reduction achieved in the peak stresses is more significant where the stator and
the reduction achieved in the peak stresses is more significant where the stator and rotor
rotor maximum equivalent stress decreases by 25.2% and 16.8%, respectively.
maximum equivalent stress decreases by 25.2% and 16.8%, respectively.
Further improvements to the blade geometry are achieved through blade shape op-
Further improvements to the blade geometry are achieved through blade shape optimi-
timisation. This design phase seeks to improve the performance within the system con-
sation. This design phase seeks to improve the performance within the system constraints;
straints; however, the performance improvement achievable through blade shape optimi-
however, the performance improvement achievable through blade shape optimisation
sation depends on the reference geometry performance and the flexibility of the model
depends on the reference geometry performance and the flexibility of the model constraints.
constraints. A comparison between the reference and optimised stages is shown in Figure
A comparison between the reference and optimised stages is shown in Figure 12 for the
12 for the first and last stages. The axis represents the axial (Z) and tangential (T) direc-
first and last stages. The axis represents the axial (Z) and tangential (T) directions, while
tions, while the radial direction is selected at mid-span. The results of blade shape optimi-
the radial direction is selected at mid-span. The results of blade shape optimisation have
sation
shownhave shown in
an increase antheincrease in the total-to-total
total-to-total efficiency from efficiency from 90.2%
90.2% obtained forobtained
the initialfor the
blade
initial blade model to 92.9% for the optimised geometry. The optimised
model to 92.9% for the optimised geometry. The optimised geometry for the first stage geometry for the
first
shows stage
onlyshows
slightonly slight when
variations variations whentocompared
compared to the
the last stage. lastisstage.
This This
because is because
turbulence is
turbulence is much lower at the turbine inlet compared to the cumulative
much lower at the turbine inlet compared to the cumulative vortices and incidence effects vortices and
incidence effects due
that are present that to
areflow
present due towithin
deviation flow deviation withinAs
the final stage. thea final stage.
result, As a wedge
the inlet result,
the inlet wedge angle is significantly increased in the last◦ stage from
◦
angle is significantly increased in the last stage from 15 to 26 to account for the larger15° to 26° to account
for
flowthe larger
angle flow angle
deviation from deviation
the blade from theand
angle blade angleflow
reduce andseparation.
reduce flowThisseparation. This
modification
modification
in the last stage in the
haslast stage has
resulted resulted
in an increasein an increase
in the in the total-to-total
total-to-total efficiency
efficiency relative to rel-
the
ative to the reference geometry, which is 0.65% larger than the improvement
reference geometry, which is 0.65% larger than the improvement achieved in the first stage achieved in
the first stage for the same reference
for the same reference blade assumptions. blade assumptions.

0.03 0.03

0.02
0.02

0.01
0.01
0
T (m)

T (m)

0
−0.01

−0.01
−0.02

−0.02 −0.03

−0.03 −0.04

Z (m) Z (m)

Figure
Figure 12.
12. Comparison
Comparison between
between reference
reference and
and optimised aerofoil for the 1st and 14th stages.

3.2. Evaluation
3.2. Evaluation ofof Design-Point
Design-Point Performance
Performance
The performance
The performance of of each
each turbine
turbine stage
stage is
is evaluated
evaluated usingusing both
both mean
mean line
line design
design andand
CFD models, as summarised
CFD models, as summarised in Figure 13. A good agreement was obtained
A good agreement was obtained between both between both
models for
models for both
both total-to-total
total-to-total andand total-to-static
total-to-static efficiencies;
efficiencies; however,
however, the the mean
mean line line loss
loss
model predicts
model predicts aa lower
lower total-to-total
total-to-totalefficiency
efficiencythan
thanthe theCFDCFDforformost
mostof of
thethe
stages,
stages,with an
with
average
an difference
average differenceof 1.2%
of 1.2%across
acrossthethe
stages.
stages.The
Theoverall
overalltrend
trendindicates
indicatesa slight
a slight increase
increase in
the total-to-total efficiency with the stage number. It can be observed
in the total-to-total efficiency with the stage number. It can be observed that the differencethat the difference
between the
between thetotal-to-total
total-to-totalandandtotal-to-static
total-to-staticefficiency
efficiency is is high
high forfor each
each single
single stage,
stage, as
as re-
reported in Figure 13, and low for the multi-stage calculation, as reported
ported in Figure 13, and low for the multi-stage calculation, as reported in Table 4. This is in Table 4. This is
because the exit kinetic energy from a single stage is approximately equal
because the exit kinetic energy from a single stage is approximately equal to the exit ki- to the exit kinetic
energy
netic from from
energy the whole turbine.
the whole However,
turbine. However,the ratio between
the ratio betweenthe exit
the kinetic energy
exit kinetic and
energy
enthalpy
and drop drop
enthalpy is much lower lower
is much for theformulti-stage calculation
the multi-stage compared
calculation to a single
compared tostage. As
a single
such, the difference between total-to-total to total-to-static efficiency due
stage. As such, the difference between total-to-total to total-to-static efficiency due to the to the exit velocity
is around
exit velocity1%isfor the entire
around 1% for turbine, compared
the entire turbine,tocompared
10% for a single
to 10%stage.
for a single stage.
Int. J. Turbomach. Propuls. Power 2024, 9, 5 13 of 17
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 13 of 18

ζζ_S-CFD
S (CFD) ζζ_R-CFD
R (CFD) η_tt-MLD
ηtt (MLD)
ηη_tt-CFD
tt (CFD) ηη_ts-CFD
ts (CFD) ηη_ts-MLD
ts (MLD)
0.12 96%

Enthalpy loss coefficient ζ [-]

0.10 92%

Efficiency η [%]
0.08 88%

0.06 84%

0.04 80%

0.02 76%

0.00 72%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Stage count

Figure 13. Comparison between the MLD and CFD total-to-total and total-to-static efficiencies per
Figure 13. Comparison between the MLD and CFD total-to-total and total-to-static efficiencies per
stage, along with the enthalpy loss coefficients obtained using the CFD model results.
stage, along with the enthalpy loss coefficients obtained using the CFD model results.

Investigation of the loss breakdown structure of similar turbine stages has revealed
Investigation of the loss breakdown structure of similar turbine stages has revealed
that endwall losses are the predominant aerodynamic loss in turbines of this scale operating
that endwall losses are the predominant aerodynamic loss in turbines of this scale operat-
within sCO2 [25]. However, near the final turbine stages, where the blades are longer, and
ing within sCO 2 [25]. However, near the final turbine stages, where the blades are longer,
the boundary layers occupy a narrower portion of the flow path, the overall losses are lower.
and the boundary layers occupy a narrower portion of the flow path, the overall losses are
SimilarSimilar
lower. to the total-to-total efficiency,
to the total-to-total the total-to-static
efficiency, efficiency
the total-to-static decreases
efficiency almostalmost
decreases in unison
with the shift in the total-to-total efficiency, which is because all the stages
in unison with the shift in the total-to-total efficiency, which is because all the stages are are designed
with identical
designed velocity velocity
with identical triangles. To further
triangles. understand
To further the distribution
understand of losses
the distribution between
of losses
the turbine stages, the enthalpy loss coefficients obtained using
between the turbine stages, the enthalpy loss coefficients obtained using the CFD model the CFD model results
results are plotted over the efficiency curves in Figure 13. Generally, the losses decrease the
are plotted over the efficiency curves in Figure 13. Generally, the losses decrease with
stagethe
with number, which reflects
stage number, the efficiency
which reflects resultsresults
the efficiency shownshownin Figure 13. Moreover,
in Figure the rotor
13. Moreover,
losses
1 are higher than the stator losses due to the blade rotation and tip
the rotor losses are higher than the stator losses due to the blade rotation and tip clearance, clearance, which
which generates more turbulence. However, the last stator and rotor enthalpy loss coeffi- are
generates more turbulence. However, the last stator and rotor enthalpy loss coefficients
39% and
cients 13% and
are 39% lower 13%than thethan
lower first the
stage,
firstrespectively. This indicates
stage, respectively. that the
This indicates rotor
that thelosses
rotor are
more affected by the development of the flow field and cumulative
losses are more affected by the development of the flow field and cumulative flow angle flow angle deviation
comparedcompared
deviation to the stator losses.
to the stator losses.

3.3.Off-Design
3.3. Off-DesignAnalysis
Analysis
Theperformance
The performanceofofthe theturbine
turbine at at off-design
off-design hashas been
been investigated
investigated usingusing
the the
CFDCFD
model, and the results are reported in Figure 14. The total-to-total efficiency
model, and the results are reported in Figure 14. The total-to-total efficiency is effectively is effectively
constantbetween
constant betweena areduced
reducedmassmass flow
flow raterate
of of 0.0395
0.0395 andand 0.0412.
0.0412. However,
However, the efficiency
the efficiency
sharplydecreases
sharply decreasesatatlower
lowerreduced
reduced mass
mass flow
flow rates.
rates. TheThe off-design
off-design results
results have have shown
shown
thatthe
that theturbine
turbinecancanoperate
operatedowndown to to
88%88% of of
thethe design’s
design’s reduced
reduced mass mass
flowflow
raterate
withwith
total-to-totalefficiencies
total-to-total efficienciesofofover
over 80%
80% andand 81%81%of of
thethe design’s
design’s reduced
reduced mass mass
flowflow
raterate
withwith
total-to-totalefficiencies
total-to-total efficienciesofofover
over 60%.
60%. AA further
further reduction
reduction in the
in the mass
mass flowflow
raterate
leads leads
to a to a
poor performance
poor performance or or even negative power output, output, which
which indicates
indicates that
thatthe
theturbine
turbinerequires
re-
external power to continue running at 3000
quires external power to continue running at 3000 RPM. RPM.

4 100
Total-to-total efficiency
Total-to-total pressure

3 70
Total-to-total
pressure ratio
[%]
ratio [-]

2 40
Total-to-total
efficiency
1 10
0.026 0.03 0.034 0.038 0.042
Reduced mass flow-rate [-]

Figure14.
Figure Theoff-design
14.The off-designperformance
performance maps
maps of of
thethe proposed
proposed turbine
turbine design.
design.
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 14 of 18

Int. J. Turbomach. Propuls. Power 2024, 9, 5 14 of 17

The power produced by each stage at different off-design operating points is reported
in Figure 15a. At the design point, the power produced by each stage is almost the same,
The power
as expected for aproduced
repeatingby eachdesign.
stage stage atHowever,
different off-design operating
a non-uniform power points is reported
generation per
in Figure 15a. At the design point, the power produced by each stage is almost
stage is observed at higher or lower pressure ratios. At higher pressure ratio operating the same,
as expectedthe
conditions, forstage
a repeating stage design.
power increases withHowever, a non-uniform
stage number power
as a result of generation
increasing per
absolute
stage is observed at higher or lower pressure ratios. At higher pressure ratio
velocity magnitudes, which, assuming the same blade outlet angles, increases both axial operating
conditions, the stage power increases with stage number as a result of increasing absolute
and tangential components. When the velocity increases, the fluid density must also de-
velocity magnitudes, which, assuming the same blade outlet angles, increases both axial and
crease, which further compounds this increase in velocity. As such the velocity and power
tangential components. When the velocity increases, the fluid density must also decrease,
increase from stage to stage until reaching a peak value for the last stage. In contrast, at
which further compounds this increase in velocity. As such the velocity and power increase
low pressure values, the velocity decreases and density increases, leading to an accumu-
from stage to stage until reaching a peak value for the last stage. In contrast, at low pressure
lative velocity and power decrease until reaching a minimum power for the last stage. The
values, the velocity decreases and density increases, leading to an accumulative velocity
performance at 83.9% of the reduced mass flow rate shows almost zero power output from
and power decrease until reaching a minimum power for the last stage. The performance
the last stage, which means that this stage is no longer driving the turbine, which causes
at 83.9% of the reduced mass flow rate shows almost zero power output from the last stage,
a sharp drop in overall turbine efficiency. The expansion diagram represented by the en-
which means that this stage is no longer driving the turbine, which causes a sharp drop
thalpy–entropy plane is reported in Figure 15b, which reflects the observations of Figure
in overall turbine efficiency. The expansion diagram represented by the enthalpy–entropy
15a and indicates the excessive entropy generation for reduced mass flow ratios of 93.7%
plane is reported in Figure 15b, which reflects the observations of Figure 15a and indicates
and 83.9% cases.
the excessive entropy generation for reduced mass flow ratios of 93.7% and 83.9% cases.

700
Power per stage [MW]

16 650
h [kJ/kg.K]

600
10
550
4
500

−2
-2 450
0 2 4 6 8 10 12 14 200 250 300 350 400
(a) Stage (b) s [J/kg.K]

40
𝑚̇ 𝑒𝑑 = 101.9 % 𝑚̇ 𝑒𝑑 𝑑
Rotor inlet incidence [deg]

20
𝑚̇ 𝑒𝑑 = 101.4 % 𝑚̇ 𝑒𝑑 𝑑

0 𝑚̇ 𝑒𝑑 = 100 % 𝑚̇ 𝑒𝑑 𝑑

−20
-20 𝑚̇ 𝑒𝑑 = 97.8 % 𝑚̇ 𝑒𝑑 𝑑

−40
-40 𝑚̇ 𝑒𝑑 = 93.7 % 𝑚̇ 𝑒𝑑 𝑑

𝑚̇
(c)
−60
-60 𝑒𝑑 = 83.9 % 𝑚̇ 𝑒𝑑 𝑑

0 2 4 6 8 10 12 14
Stage
Figure 15.
Figure Off-designevaluation
15.Off-design evaluationper
perstage.
stage.(a)
(a)Power
Powerdeveloped,
developed,(b)
(b)enthalpy–entropy
enthalpy–entropydiagram,
diagram, and
and
(c)
(c) the
the rotor
rotor inlet
inlet incidence
incidence angle
angle as obtained at different operating inlet total pressures.

The flow
The flow deviation
deviation angle
angle at
at the
the rotor
rotor inlet
inlet is
is shown
shown inin Figure
Figure 15c.
15c. The
Thedeviation
deviation angle
angle
at the design point is around zero, such that the incidence losses are minimised.
at the design point is around zero, such that the incidence losses are minimised. At higher At higher
pressures, the
pressures, the deviation
deviation angle
angle increases,
increases, especially
especially for
for downstream
downstream stages;
stages; however,
however, the
the
efficiency drop
efficiency drop is
is negligible
negligiblebecause
becauseno noflow
flowseparation
separation occurs. AtAt
occurs. lower
lowerpressure ratios,
pressure the
ratios,
incidence deviation angles become much higher and negative (in
the incidence deviation angles become much higher and negative (in the clockwise the clockwise direction
relative to the axial direction), causing flow separation and a significant deterioration in
overall turbine performance.
Int. J. Turbomach. Propuls. Power 2024, 9, x FOR PEER REVIEW 15 of 18

Int. J. Turbomach. Propuls. Power 2024, 9, 5 15 of 17

direction relative to the axial direction), causing flow separation and a significant deterio-
ration in overall turbine performance.
The flow
The flowstructure
structureatat100%
100% andand88%88% of the
of the design
design reduced
reduced massmassflow flow
rate israte is repre-
represented
by the Mach number distribution in Figure 16. At low reduced mass flow rates, rates,
sented by the Mach number distribution in Figure 16. At low reduced mass flow flow
flow separation
separation is observed
is observed starting
starting fromfrom the sixth
the sixth turbine
turbine stagestage
and and propagating
propagating towards
towards the
the final
final turbine
turbine stages
stages as a as a result
result of increasing
of increasing the incidence
the incidence angle.
angle. It hasIt has
beenbeen
found found
thatthat
the
the location
location wherewhere separation
separation first first
occursoccurs
moves moves further
further upstream
upstream towards towards the turbine
the turbine inlet
inlet
as theaspressure
the pressure ratio decreases.
ratio decreases. This explains
This explains the droptheindrop in efficiency
efficiency and in and
stageinpower
stage
power production at lower reduced mass flow rates, as shown
production at lower reduced mass flow rates, as shown in Figures 14 and 15a. in Figures 14 and 15a.

(a) Design point

88% mass
(b) 50% reduced mass flow rate
flow-rate
6th stage
Flow separation

Figure 16. Flow field obtained for the five

five mid-stages: (a) design point and (b) 88% of the
the design’s
design’s
reduced mass flow rate.
reduced mass flow rate.

4. Conclusions
This paper has has presented
presentedthe theaerodynamic
aerodynamicdesign design of of a 14-stage
a 14-stage 130130
MWMW turbine
turbine op-
operating with a CO /SO
erating with a CO2/SO2 2 mixture. 2 mixture. The design process was initiated by
The design process was initiated by defining the aerody- defining the
aerodynamic and mechanical
namic and mechanical constraints
constraints along
along with thewith
cyclethe cycle requirements,
requirements, which werewhich were
used to
used
obtaintothe
obtain
basicthe basic
flow pathflow path through
through mean linemean line design.
design.
The adoption
adoption of aa multi-stage
multi-stage mean mean line
line design
design method,
method, based
based on on the
the Aungier
Aungier loss
loss
model, was
was proven
proventotobe beeffective
effectiveinin predicting
predicting turbine
turbine performance
performance withwith maximum
maximum de-
deviations in efficiency of 1.5% compared to selected verification case
viations in efficiency of 1.5% compared to selected verification case studies. The results studies. The results
obtained
obtained from
from thethe mean
mean line line analysis
analysis demonstrated
demonstrated that that increasing
increasing the the number
number of of stages
stages
from
from 4 to 14 yielded a significant improvement in total-to-total efficiency, increasing from
4 to 14 yielded a significant improvement in total-to-total efficiency, increasing from
87.5%
87.5% toto93.8%.
93.8%.The Theimprovement
improvement waswas
achieved
achieved by increasing
by increasingthe blade aspectaspect
the blade ratio, which
ratio,
reduced the impact
which reduced the of secondary
impact flow losses,
of secondary flowand by reducing
losses, and bythe tip diameter,
reducing the tipresulting
diameter, in
lower tip clearance losses. However, this can introduce challenges related
resulting in lower tip clearance losses. However, this can introduce challenges related to to shaft stability
and
shafthigh bending
stability stresses
and high due to
bending smaller
stresses duehub diameters,
to smaller hublonger flow longer
diameters, paths, flow
and larger
paths,
aspect ratio blades.
and larger aspect ratio blades.
A
A good
goodagreement
agreementwas wasachieved
achievedbetween
between thethe
mean
mean lineline
approach
approachandand the CFD results,
the CFD re-
from which it can be concluded that there is no specific impact of
sults, from which it can be concluded that there is no specific impact of the working fluidthe working fluid on
the design
on the methodology,
design methodology, although
althoughthe working
the working fluidfluid
impacts the design
impacts assumptions
the design assumptionsand
constraints. The difference between the total-to-total efficiency of the mean line design
and constraints. The difference between the total-to-total efficiency of the mean line design
and the CFD model was less than 2%, providing confidence in the mean line design
and the CFD model was less than 2%, providing confidence in the mean line design meth-
methodology for such turbines.
odology for such turbines.
Blade shape optimisation played a crucial role in aligning the turbine boundary
Blade shape optimisation played a crucial role in aligning the turbine boundary con-
conditions with the cycle design conditions by ensuring that the mass flow rate remained
ditions with the cycle design conditions by ensuring that the mass flow rate remained
within 1% of the cycle mass flow rate for the given pressure ratio. The optimisation process
within 1% of the cycle mass flow rate for the given pressure ratio. The optimisation pro-
improved turbine total-to-total efficiency by 2.7%, from 90.2% to 92.9%, while maintaining
cess improved turbine total-to-total efficiency by 2.7%, from 90.2% to 92.9%, while
acceptable stress levels. The performance analysis of the proposed turbine revealed that
stage losses decrease with stage number because of the accompanying increase in blade
Int. J. Turbomach. Propuls. Power 2024, 9, 5 16 of 17

height. The stator and rotor enthalpy loss coefficients of the last stage were found to be 39%
and 13% lower than those of the first stage, respectively. Finally, the off-design analysis
indicated the proposed turbine could run down to 88% of the design’s reduced mass flow
rate with total-to-total efficiencies of over 80%.
Ultimately, this paper has demonstrated the suitability of the proposed methodol-
ogy in designing an axial turbine for the proposed novel working fluid whilst achiev-
ing a total-to-total efficiency of 92.9% and meeting the necessary mechanical and rotor
dynamic constraints.

Author Contributions: Conceptualisation, A.S.A., S.I.S., O.A.A., M.T.W. and A.I.S.; design methodol-
ogy and analysis, A.S.A., S.I.S. and O.A.A.; writing original draft, A.S.A., S.I.S. and O.A.A.; review
and editing, M.T.W. and A.S.A. All authors have read and agreed to the published version of
the manuscript.
Funding: This work was supported by the European Union’s Horizon 2020 research and innovation
programme under grant agreement No. 814985. Funder ID: 10.13039/100010661.
Data Availability Statement: Data supporting this study are available on request. Please contact the
corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.

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