The 6th International Supercritical CO2 Power Cycles Symposium

March 27 - 29, 2018, Pittsburgh, Pennsylvania

A preliminary comparison of different turbine architectures for a

100 kW supercritical CO2 Rankine cycle turbine

Martin T. White Abdulnaser I. Sayma

Research Associate Professor of Energy Engineering
Department of Mechanical Engineering Department of Mechanical Engineering
and Aeronautics and Aeronautics
City, University of London City, University of London
Northampton Square, Northampton Square,
London, UK, EC1V 0HB London, UK, EC1V 0HB
martin.white@city.ac.uk a.sayma@city.ac.uk

ABSTRACT
The aim of this paper is to conduct a preliminary comparison of different turbine architectures for a small-
scale 100 kW supercritical CO2 Rankine cycle. The turbine is required to expand supercritical CO2 from
650 °C and 170 bar, down to 50 bar. For such an application, it is not immediately clear which turbine
architecture is the most suitable design when considering both aerodynamic and mechanical design
constraints. Within this paper, three different turbine architectures are considered, namely radial-inflow,
single-stage axial, and two-stage axial turbines. For each architecture, a preliminary design model is
constructed which is based on conventional turbomachinery design parameters such as the loading
coefficient, flow coefficient and degree of reaction. Using this model, a parametric investigation on the effect
of the rotational speed on the required rotor diameter and blade height is conducted and the different turbine
architectures are compared. This is completed with the view of establishing the feasible design space for a
small-scale supercritical CO2 turbine. For all three architectures, it is found that in order to obtain feasible
blade heights it is necessary to maximise the loading coefficient whilst minimising the flow coefficient, and
design the turbine with the minimum allowable diameter. Typically, this results in a turbine design with a
rotor diameter of 30 mm, a rotor-inlet blade height in the range of 1.74 to 2.47 mm, and a rotational speed
between 150 and 250 kRPM for a single-stage radial or axial turbine, and 75 and 175 kRPM for a two-stage
axial turbine. Ultimately, nine candidate turbine designs have been identified, which should be studied
further using more advanced 3D CFD and FEA simulations.

INTRODUCTION
In the past decade, the search for the next generation of high-efficiency thermal power cycles has led to
a significant interest in supercritical carbon dioxide (sCO2) as a working fluid. One of the primary benefits
in operating a thermodynamic cycle with sCO2 is that high efficiency can be obtained at moderate turbine
inlet temperatures (in the region of 500 °C), which makes sCO2 an interesting option for applications such
as nuclear power [1], concentrated-solar power [2] and high efficiency coal-fired power plants [3].
Moreover, sCO2 cycles can also be considered for waste-heat recovery applications for heat-source
temperatures exceeding 450 °C [4]; at this temperature, organic Rankine cycles, which would typically be
considered for waste-heat recovery, are not suitable due to factors such as fluid decomposition and low
efficiency, whilst sCO2 have the advantage of compactness and simplicity compared to steam Rankine
cycles. At present, the primary focus of sCO2 research and development activities has been on medium-
to large-scale applications, with power outputs in the order of 1 MWe. and above, for example in Refs.
[5,6]. However, given the potential thermodynamic benefits, sCO2 cycles can also be considered for small-
scale applications with power outputs in the order of 100 kWe, and systems of this size are already under
investigation [7-9].

1
As recently discussed in Ref. [10], there are a large number of variants of sCO2 cycle, and each variant
has a varying degree of complexity. However, for a small-scale application a simple recuperated cycle,
comprising of compressor/pump, heat-addition heat exchanger, turbine, recuperator and heat-rejection
heat exchanger, is probably the most suitable cycle based on both cost and technical considerations.
Depending on the inlet conditions to the compression process this simple recuperated cycle can either
operate as a Rankine cycle or a Brayton cycle. The effect of the compression inlet temperature 𝑇" , and
compression inlet pressure 𝑝" , on the operating condition and performance of a sCO2 cycle is shown in
Fig. 1. As observed from the analysis shown in Fig. 1, operating with a low inlet temperature to the
compression process corresponds to operating a Rankine cycle, and this can achieve a higher thermal
efficiency than the Brayton cycle operating under the same assumptions. Therefore, operating a Rankine
cycle is preferential from a thermodynamic perspective. However, since the critical temperature of CO2 is
31 °C, it is only possible to operate a sCO2 Rankine cycle in areas with a low ambient temperature.
However, there has been recent research into mixing CO2 with small amounts of other fluids to obtain a
CO2 blend that has a higher pseudo-critical temperature [11,12]. Using a blend could therefore realise the
potential of the sCO2 Rankine cycle in areas with higher ambient temperatures.

Figure 1. Effect of the inlet conditions of the compression process (inlet temperature 𝑇" , and inlet pressure
𝑝$ ) on the thermal efficiency of a sCO2 cycle, assuming a turbine inlet temperature of 𝑇%& = 650 °C,
pressure ratio of 𝑃𝑅 = 3, compression and expansion isentropic efficiencies of 𝜂",+, = 0.7 and 𝜂-,+, = 0.8
respectively, and a recuperator effectiveness of 𝜖/ = 0.8.

Another advantage of sCO2 is that it has a high density, which facilitates the miniaturisation of system
components, enabling a high power density compared to conventional power plants. Whilst this is
advantageous from the point of view of reducing the size, and cost of the plant, it presents challenges with
regards to turbomachinery design. More specifically, to achieve a high efficiency the turbomachinery
components become very small and must rotate at high speed. This results in low aspect-ratio blades
(blade height to chord ratio), and increased relative clearance gaps, which give rise to increased
secondary flow and over the tip gap losses. Furthermore, the combined effects of a high power density,
high operating pressures, high rotational speeds and small component dimensions mean that the design
of the bearing-shaft arrangement needs to be carefully considered, in addition to considering the axial
thrust that is exerted by the rotor on the bearings. Moreover, for the relatively low pressure-ratio and mass-
flow rate, it is not immediately obvious weather a radial-inflow or axial-flow turbine is the most suitable
design when considering both aerodynamic and mechanical design constraints.
The aim of this paper is to conduct a preliminary comparison of different turbine architectures for a small-
scale sCO2 Rankine cycle system, and establish the feasible design space for different turbine types.
Focus is given here on the turbine based on the premise that the future use of CO2-blends could realise
the potential to operate a Rankine cycle, thus removing the need for a compressor.

THERMODYNAMIC SPECIFICATION AND PRELIMINARY TURBINE SIZING

The results from a thermodynamic analysis of a recuperated sCO2 Rankine cycle are shown in Fig. 2. For

2
this analysis, a compressor inlet temperature of 20 °C is assumed, and the effect of the turbine inlet
temperature 𝑇%& and pressure ratio 𝑃𝑅 on the thermal efficiency 𝜂-0 and turbine inlet pressure 𝑝%& has
been investigated. These calculations have been completed assuming fixed polytropic efficiencies of 70%
and 80% for the pump and turbine respectively, and a recuperator effectiveness of 80%.
It is observed from Fig. 2 that as 𝑃𝑅 increases, 𝜂-0 increases, but at the expense of higher operating
pressures. For 𝑇%& = 650 °C, 𝑃𝑅 = 3 has been selected as this is considered to be reasonable compromise,
corresponding to 𝜂-0 = 28%, and 𝑝%&= 17 MPa. The turbine design specification is summarised in Table 1.

Table 1. Design specification of the sCO2 turbine.

𝑇%& 650 °C
𝑝%& 17.0 MPa
𝑃𝑅 3 -
𝑚̇ 0.65 kg/s
𝑊̇ 100 kW
𝜂-,+, (target) 0.8 -

Figure 2. Effect of pressure ratio 𝑃𝑅 and turbine

inlet temperature 𝑇%& on thermal efficiency 𝜂-0 and
turbine inlet pressure 𝑝%& of a recuperatred sCO2
Rankine cycle (𝑇" = 20 °C, 𝜂",1 = 0.7, 𝜂-,1 = 0.8, 𝜖/ =
0.8).

Based on the information provided in Tab. 1 a preliminary assessment of a single-stage turbine, either
radial-inflow or axial-flow, can be completed using the specific speed 𝜔, :
&
𝜔𝑉̇ 9 (1)
𝜔, = 8 ,
Δℎ,,
where 𝜔 is the rotor rotational speed in rad/s, 𝑉8̇ is the volumetric flow rate at the rotor outlet in m3/s and
Δℎ,, is the isentropic enthalpy drop across the expander, given in J/kg. In general, optimal turbine
efficiency occurs within a certain range of values for 𝜔, , typically 0.1 < 𝜔, < 1.0 [13] (Fig. 3a), and therefore
𝜔 can be found by rearranging Equation 1. This calculation can be completed using the information
provided in Tab. 1, if the total and static conditions at the rotor outlet are assumed equal.
For a two-stage turbine Equation 1 is still valid, but instead applies to each individual stage. In this case
the total enthalpy drop across the entire turbine is equally divided across the two stages, and each stage
is assumed to operate with the same isentropic efficiency (i.e., 𝜂-,+, = 80%). It is assumed that both stages
are mounted on the same shaft, and therefore both stages rotate at the same speed. Therefore, the
second stage will have a higher specific speed than the first, owing to the lower density. In this instance,
the quoted value for 𝜔, refers to the first stage only. For the case study in question, the specific speed of
stage two is then 27% higher than stage one. For a first-stage specific speed below 0.5, the second-stage
specific speed will therefore be below 0.64. Therefore, since this is still within the limits previously stated,
a penalty in the second-stage efficiency is not expected.
The required rotational speed (in kRPM) for a single- and two-stage turbine for 𝜔, ranging between 0.05
and 0.6 is shown in Fig. 3b. For a single-stage turbine to operate at an optimal efficiency, the rotor must
rotate at a speed in the region of a few-hundred kRPM, which introduces challenges with regards to the
mechanical and electrical design of the turbine. Reducing the speed could simplify these aspects, but at
the penalty of a reduced aerodynamic efficiency. Comparatively, a two-stage design facilitates a higher

3
specific speed to be obtained at a lower rotational speed, but at the complexity of requiring multiple stages.
Clearly, a trade-off exists between aerodynamic performance, and mechanical/electrical constraints.

(a) (b)
Figure 3. (a) Effect of specific speed on turbine efficiency for different turbine types, taken from Ref. [13];
(b) the required rotational speed for a single- and two-stage turbine as a function of the desired rotor
specific speed 𝜔, . For the two-stage turbine, 𝜔, refers to the specific speed of the first stage.

RADIAL TURBINE DESIGN

To obtain a preliminary radial-turbine design, a design model has been developed, which is coupled to
NIST REFPROP [14] to obtain the thermodynamic properties of CO2. The selected design parameters are
the rotational speed 𝑁, blade-loading coefficient Ψ, and flow coefficient Φ, which are defined as:
Δℎ%
Ψ= ; (2)
𝑢99
𝑐C8
Φ= , (3)
𝑢9
where Δℎ% is the total enthalpy drop across the turbine, 𝑢9 is the rotor-inlet blade velocity and 𝑐C8 is the
meridional velocity at the rotor outlet. Using the defined target efficiency, the total enthalpy drop across the
turbine can be determined since Δℎ% = 𝜂-,+, Δℎ,, , from which 𝑢9 follows. Moreover, although a small amount
swirl at the rotor outlet is often applied in practice, for simplicity the rotor outlet is designed for zero swirl.
Therefore, the absolute tangential velocity at the rotor inlet 𝑐D9 can be determined since the stage enthalpy
drop reduces to Δℎ% = 𝑢9 𝑐D9. Then, assuming a constant meridional velocity (i.e., 𝑐C8 = 𝑐C8 ), the rotor inlet
velocity triangle is fully defined. Finally, if a loss coefficient is applied to account for losses within the stator,
the density at the rotor inlet and, in turn, the rotor-inlet dimensions (i.e., blade height 𝑏9, and diameter 𝑑9 )
are found.
To design the rotor outlet an additional design parameter must be defined. However, at this stage of the
design process it is not clear whether a 90° radial-inflow turbine, a radial-inflow turbine with a non-zero inlet
blade angle, or even a highly-loaded impulse-type turbine would be the most suitable choice. However,
since the rotor-inlet design is a function of only 𝑁, Ψ and Φ, and is therefore independent of the rotor-outlet
design, a parametric investigation concerning these three parameters can be conducted. For this
investigation constraints were placed on the minimum allowable rotor diameter (𝑑9 ≥ 30 mm), maximum
rotor-inlet absolute flow angle (𝛼9 ≤ 82.5°), and minimum allowable blade height (𝑏9 ≥ 1.25 mm). Of these
constraints, the rotor-inlet blade height is expected to be the most significant, owing to the relative size of
clearance gaps, and values in the region of 1 to 2 mm are currently considered to be close to the limit of
practicality [15,16]. Alongside these constraints, a stator loss coefficient of 𝜁K= 0.075 is assumed. Fixing 𝜁K
means there is no consideration of the effect that changing the rotor-inlet velocity has on the stator
performance, however this is not expected to have a significant effect on the final rotor-inlet dimensions.
Results for three rotational speeds, namely 150, 200 and 250 kRPM, are shown in Fig. 4. These three

4
speeds correspond to specific speeds of 0.24, 0.32 and 0.40 respectively. The analysis was also conducted
for 100 and 300 kRPM, however no design could be found that met all of the imposed constraints. In
general, it is observed that increasing Ψ corresponds to a reduction in 𝑑9 , but an increase in 𝑏9. Moreover,
for a specified Ψ, reducing Φ increases 𝑏9 further, but at the cost of increasing 𝛼9 . Ultimately, the result of
this interplay between the design parameters and constraints means that in order to maximise the blade
height, it is necessary to design a turbine with small diameter, and a high absolute flow angle.

Figure 4. Effect of rotational speed, blade-loading coefficient Ψ, and flow coefficient Φ on the rotor-inlet
blade height of a radial-inflow turbine. The red dots correspond to the designs summarised in Tab. 2.

For each rotational speed, the designs that maximise 𝑏9 are summarised in Tab. 2, and these designs are
shown by the red dots in Fig. 4. The velocity triangles for these designs are presented in Fig. 5. From these
results, it is observed that a different type of radial-inflow turbine is required as the rotational speed is
reduced. At 250 kRPM the blade-loading coefficient is below unity, implying a 90° radial-inflow turbine
design. In order to maximise the blade height (𝑏9= 2.13 mm), a flow coefficient of 0.12 is required,
corresponding to 𝛼9 = 82.5°, and a relative flow angle of 𝛽9 = -31.7°, which is within the recommended range
of -40° to -20° [13]. Increasing Φ to 0.16, reduces 𝛼9 by 2.5°, and the 𝑏9 to 1.60 mm. On the other hand,
increasing the diameter to 35 mm, increases 𝛽9 to -74.4°, which is no longer within the recommended limits.
As the speed is reduced to 200 kRPM, it is necessary to have a blade-loading coefficient above unity, and
therefore a rotor with a non-zero rotor inlet blade angle is required. Then, as the rotational speed is further
reduced to 150 kRPM, a high blade-stage loading coefficient, approaching 2, is required to obtain a blade
height close to 2 mm. This implies a highly-loaded rotor, with a degree of reaction approaching zero. In this
case, the rotor is an impulse turbine, with the majority of the expansion occurring in the stator. It is also
noted that for the 150 kRPM design, the feasible design space is not constrained by the minimum diameter
(30 mm), hence the design that maximises the blade height has a slightly larger diameter.

Table 2. Summary of radial turbine rotor design that maximises the rotor-inlet blade height for the three
different rotational speeds considered.
𝑵 [kRPM] 𝚿 𝚽 𝒅𝟐 [mm] 𝒃𝟐 [mm] 𝜶𝟐 [°] 𝜷𝟐 [°] 𝑴𝒂𝟐 Rotor type
Radial 1 150 2.00 0.26 34.00 1.98 82.50 75.25 1.25 Impulse
Radial 2 200 1.45 0.19 30.00 2.09 82.50 66.85 1.03 Backswept
Radial 3 250 0.92 0.12 30.00 2.13 82.50 –31.74 0.81 90° IFR

5
 0.6

0.4

0.2

0.6

0.4

-0.2

0.2

0.6
-0.4

0.4
-0.6

-0.2

0.2
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2
-0.4

-0.6

-0.2

Figure 5. Velocity triangles for the three radial-turbine rotor designs given in Tab. 2. From top to bottom:
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2
design 1 (150 kRPM);
-0.4 design 2 (200 kRPM); design 3 (250 kRPM). The rotor-outlet velocity triangles are
obtained by assuming rotor diameter ratios (𝑑8 /𝑑9) of 0.65, 0.55 and 0.55 for design 1, 2 and 3 respectively.

-0.6
SINGLE-STAGE AXIAL TURBINE
The aerodynamic design of an axial turbine is very similar to the radial turbine, and can once again be
designed by defining 𝑁, Ψ,-0.4
-0.6 and Φ. The axial
-0.2 0 velocity
0.2 is 0.4
assumed
0.6 constant
0.8 1 𝑐C9 1.2
(i.e., = 𝑐C8 ), and since there
is no change in the meanline radius between the inlet and outlet, there is no change in the blade velocity
(i.e., 𝑢9 = 𝑢8 ). However, unlike the radial turbine, the rotor outlet tangential velocity 𝑐X8 is not assumed to
be zero. Therefore, to complete the design, the degree of reaction Λ is also defined as an input:
ℎ9 − ℎ8
Λ= , (4)
ℎ%9 − ℎ%8
where ℎ9 and ℎ8 are the static enthalpies, and ℎ%9 and ℎ%8 are the total enthalpies at the rotor inlet and
outlet respectively. Both the inlet and outlet conditions are taken at the rotor mid-span. It should be noted
that a non-zero 𝑐X8 allows Ψ to be greater than 2, and that by defining Λ the rotor-outlet velocity triangle
is fully defined and therefore the rotor outlet can be sized.
For the single-stage axial turbine design, another parametric investigation into the effects of the design
parameters on the design of the turbine rotor can be conducted. For this investigation, the same stator
loss coefficient of 𝜁K = 0.075 is assumed. Referring to Fig. 3a, it is observed that, compared to radial
turbines, axial turbines can achieve higher efficiencies at lower specific speeds. However, a preliminary
study found that reducing the rotational speed reduced the maximum possible rotor-inlet blade height; for
example, at 100 kRPM (𝜔, = 0.16) the maximum blade height was only 1.6 mm. For this reason, the
following analysis considers the same rotational speeds as the those considered for the radial turbine,
namely 150, 200 and 250 kRPM.
Since the analysis of an axial turbine is very similar to a radial turbine, it can be inferred from the previous
section that selecting the minimum allowable rotor diameter (𝑑9 = 30 mm), and maximum absolute rotor-
inlet flow angle (𝛼9 = 82.5°), will result in the largest rotor-inlet blade height. Therefore, a parametric
investigation into the effect of Λ on the turbine design, using these values has been conducted, and the
results are presented in Fig. 6. To be consistent with the constraint applied to the rotor-inlet absolute flow
angle, Λ is only varied between 0 and 0.5. This is because Λ > 0.5 corresponds to a rotor-outlet relative
flow angle that is greater than the rotor-inlet absolute flow angle (i.e., 𝛽8 > 𝛼9 ), which would violate the
maximum flow angle constraint (i.e., 𝛽8 > 82.5°).

6
 0.8

Figure 6. Effect of the degree of reaction Λ on the design of a single-stage axial turbine for different
0.6
rotational speeds. Top-left: flow coefficient Φ; top-right: rotor inlet absolute Mach number 𝑀𝑎9 and rotor
outlet relative Mach number 𝑀𝑎8 ; bottom-left: rotor inlet 𝑏9 and rotor outlet 𝑏9 blade heights; bottom-right:
rotor inlet 𝛽9 and rotor
0.4
outlet 𝛽8 relative flow angles.
0.8
0.2

0.6
0

0.4
-0.2

0.8
0.2
-0.4

0.6
0
-0.6

0.4
-0.2
-0.8

0.2
-0.4
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

0
-0.6

-0.2
-0.8

Figure 7. Rotor velocity

-0.8 triangles
-0.4 -0.6 -0.4for -0.2
the three
0 single-stage
0.2 0.4 axial
0.6 turbine
0.8 rotor
1 designs.
1.2 From top to bottom:
design 1 (150 kRPM); design 2 (200 kRPM); design 3 (250 kRPM).
Table 3. Summary
-0.6of single-stage axial turbine rotor designs that maximise the rotor-inlet blade height.

𝑵 [kRPM] 𝚿 𝚽 𝜦 𝒅𝟐 [mm] 𝒃𝟐 [mm] 𝜶𝟐 [°] 𝜷𝟐 , 𝜷𝟑 [°] 𝑴𝒂𝟐

Axial-1 1-0.8 150 2.57 0.30 0.0 30.0 2.26 82.50 76.82 1.26
Axial-1 2 200 1.45 0.23 0.0 30.0 2.27 82.50 72.57 1.27
Axial-1 3 -0.8 250
-0.6
0.92-0.20.190 0.00.2 30.0
-0.4 0.4 0.6
2.40
0.8 1
82.50
1.2
67.39 1.36

7
From Fig. 6 it is observed that for all three rotational speeds, a low degree of reaction is favourable to
increase 𝑏9. Unsurprisingly, the result of having the majority of the expansion within the stator is a high
rotor-inlet Mach number, and a small change in volume through the rotor, resulting in a smaller rotor-outlet
blade height compared to a higher degree of reaction. For each rotational speed, the design that maximises
𝑏9 (i.e., Λ = 0) is summarised in Tab. 3 and the velocity triangles are shown in Fig. 7. The stage loading
coefficients are 2.57, 1.45 and 0.92 for the 150, 200 and 250 kRPM designs respectively. For the 200 and
250 kRPM rotational speeds, these are the same as for the radial turbine. For the 150 kRPM design, the
stage loading for the axial turbine is higher than the radial turbine, owing to the non-zero value for 𝑐D8 . It is
also noted that Λ = 0 corresponds to 𝛽9 = 𝛽8 , and this angle is reduced as the rotational speed is increased.

TWO-STAGE AXIAL TURBINE

For the two-stage axial turbine, the same procedure outlined for the single-stage axial turbine is applied.
The only difference is that the total enthalpy drop is divided equally across the two-stages (i.e., Δℎ,-_`a =
Δℎ% /2). Once the stage enthalpy drop is known, the process outlined in the previous section can be
completed. For this preliminary design, the analysis is only applied to the first stage. This is because the
volumetric flow rate through the machine increases as the pressure reduces. Therefore, the smallest blade
dimensions will be at the rotor inlet of the first stage.
For the two-stage design, the same stator loss coefficient is assumed (𝜁K = 0.075), and three rotational
speeds are considered, namely 75, 125 and 175 kRPM, which correspond to first-stage specific speeds
of 0.16, 0.26 and 0.37 respectively. Following on from the previous discussion regarding the single-stage
axial turbine design, a preliminary study found that reducing the rotational speed below 75 kRPM resulted
in very small rotor-inlet blade heights. Moreover, following from the analysis in the previous sections, it
can again be stated that designs with the minimum rotor diameter (𝑑9 ≥ 30 mm), and maximum absolute
rotor-inlet flow angle (𝛼9 ≤ 82.5°) will correspond to the largest rotor-inlet blade heights. Therefore,
another parametric investigation considering the effect of Λ on the rotor design can be completed. For
brevity, the results from this analysis are not reported in this paper, but ultimately, it is observed that,
unlike the single-stage axial turbine design, a high degree of reaction (Λ = 0.5) results in the largest rotor-
inlet blade height. This is because in the two-stage turbine the enthalpy drop per stage is lower, and
therefore the conditions at the rotor inlet remain subsonic for all values of Λ. However, in the single-stage
design, the rotor inlet conditions are supersonic for Λ < 0.35 (Fig. 6). Since the mass flux (𝜌𝑐) is always at
a maximum at 𝑀𝑎 = 1, the blade height can be maximised by increasing Λ for subsonic designs, and
reducing Λ for supersonic designs. This also explains why 𝑏9 increases for Λ > 0.35 in Fig. 6.
The final designs for the first-stage of a two-stage axial turbine are summarised in Tab. 3. It is noted that
for the 75 kRPM design the rotor has a diameter of 39.26 mm, which is larger than the minimum diameter
of 30 mm. This is because the stage-loading coefficient is capped at 3.0, in accordance with the range of
values typically quoted within the literature (i.e., the Smith chart [13]). The design of the second-stage is
completed assuming the second stage has the same mid-span radius as the first stage, and that the flow
coefficient, loading coefficient and degree of reaction are the same in both stages. This is considered to
be a reasonable assumption for the preliminary design phase, since the second-stage will always have a
larger blade height and is only of secondary interest. However, this assumption should be refined during
future studies.

Table 3. Summary of the two-stage axial-turbine rotor designs that maximise the rotor-inlet blade height for
the three different rotational speeds considered. The results reported correspond to the first stage.
𝑵 [kRPM] 𝚿 𝚽 𝚲 𝒅𝟐 [mm] 𝒃𝟐 [mm] 𝜶𝟐 [°] 𝜷𝟐 , 𝜷𝟑 [°] 𝑴𝒂𝟐
Axial-2 1 75 3.00 0.26 0.5 39.26 1.74 82.50 75.25 0.67
Axial-2 2 125 1.85 0.19 0.5 30.00 2.40 82.50 66.17 0.61
Axial-2 3 175 0.94 0.13 0.5 30.00 2.47 82.50 –12.44 0.58

8
 COMPARISON OF THE DIFFERENT TURBINE ARCHITECTURES
In the previous sections, three preliminary designs have been obtained for three different turbine
architectures, namely radial, single-stage axial and two-stage axial turbines. In Fig. 8, the nine preliminary
turbine designs are shown, as viewed from the meridional plane. For all three architectures, it is found
that the maximum rotor-inlet blade height increases as the rotational speed is increased. Moreover, to
60
ensure the rotor diameter is greater than 30 mm, the stage-loading coefficient must reduce, and this is
also accompanied by a reduction in the flow coefficient. Comparing the different architectures, it is
50observed that the single-stage axial turbine design can facilitate a slightly larger blade height than a radial
turbine rotating at the same speed. The blade height can be further increased by moving to a two-stage
design, and reducing the rotational speed. It is also found that when moving from a single-stage axial
40design to a two-stage axial design, the degree of reaction changes. More specifically, for the single-stage
turbine a zero reaction (impulse type) design should be selected, whilst the degree of reaction should be
30increased to 0.5 for the two-stage design.

20

10

-10
Figure 8. Comparison between the nine preliminary rotor designs. For the Radial/Axial-1 turbines ‘1’, ‘2’
-20and ‘3’ correspond to rotational speeds of 150, 200 and 250 kRPM respective. For Axial-2 ‘1’, ‘2’ and ‘3’
correspond to rotational speeds of 75, 125 and 175 kRPM respectively.
-30Ultimately, from Fig. 8 it can be observed that most of the designs all have similar dimensions, with an
inlet diameter of 30 mm, and an inlet blade height around 2 mm. With a rotor this small, it is expected that
all of the rotor designs will experience relatively large clearance losses, and increased viscous losses.
-40Unfortunately, existing loss correlations for predicting turbine performance are not validated for sCO2
applications. Therefore, the next stage of this research will require 3D CFD studies of the nine turbine
designs shown in Fig. 8 to assess the aerodynamic performance that can be achieved by each design.
0 20 40 60 80 100 120 140

MECHANICAL AND ELECTRICAL DESIGN CONSIDERATIONS

The challenging operating conditions of a sCO2 cycle mean that alongside considering the aerodynamic
design of the turbine, the mechanical and electrical design must also be considered during the turbine
design phase. This includes decisions such as choosing whether a hermetic turbine-generator assembly
is used, which can be subject to high windage losses owing to the high density, or whether an external
generator is used, in which case suitable shaft seals are required. Moreover, for a directly-coupled turbine
and generator, expensive power electronics are required to match the grid frequency, or alternatively a
gearbox with a high gear ratio is required. However, these challenges, despite their importance, pertain
to any turbine architecture at the given scale.
Of more relevance when comparing different turbine architectures are factors such as the rotor-dynamics,
axial thrust generated by the rotor and the blade stresses. For example, due to the high power density
and high pressure, the stresses on the rotor blade may be too large to use a radial-inflow turbine with a
non-zero blade angle, as in the case for Radial-2 design. Alternatively, due to the moderate tip speed,
which ranges between 235 and 392 m/s for the single-stage turbine designs, means that shrouded rotors
may be considered to improve aerodynamic performance, but may have consequences in terms of the
rotor-dynamics of the shaft. Ultimately, these effects are hard compare at the preliminary level that is
applied within this paper, and can only be compared after more detailed simulations are carried out.
Therefore, an important next step in this research is to conduct rotor-dynamic and FEA simulations of the
nine turbine designs identified, in addition to the already mentioned CFD simulations, to allow for a more
detailed comparison. Moreover, it will be necessary to consider different bearing-shaft arrangements for

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each design, in addition to giving consideration to the thermal management of the assembly to ensure
suitable cooling is available for the bearings and high-speed generator [17].

CONCLUSIONS
In this paper, the design of the turbine for a small-scale (100 kW) supercritical CO2 Rankine cycle with a
turbine inlet temperature of 650 °C has been evaluated. To identify the most suitable designs, design
models for radial-inflow, and single- and two-stage axial turbines have been developed, which use, as
inputs, the loading coefficient, flow coefficient, and degree of reaction. The objective of the design study
is to identify turbine designs that result in feasible blade heights. It is found that to obtain optimal
efficiencies, a single-stage turbine must rotate at speeds in excess of a few hundred kRPM, and for the
three different turbine architectures considered the resulting turbine has a diameter of 30 mm, and a
minimum rotor blade height in the range of 1.74 to 2.47 mm. More generally, it is found that to obtain a
feasible blade height, it is necessary to design the turbine with a high loading coefficient, and low flow
coefficient, corresponding to a high absolute flow angle. Moreover, when considering axial turbines, an
impulse-type turbine, with a low degree of reaction, is most suitable for a single-stage design, and this
results in supersonic conditions at the rotor inlet. On the other hand, for a two-stage axial turbine, a higher
degree of reaction is more suitable, whilst conditions at the rotor inlet remain subsonic.

REFERENCES
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NOMENCLATURE
𝛼 absolute flow angle, ° 𝑝 pressure, Pa
𝛽 relative flow angle, ° 𝑃𝑅 pressure ratio
𝜖/ recuperator effectiveness 𝑇 temperature, K
𝜁K stator loss coefficient 𝑢 blade velocity, m/s
𝜂 efficiency 𝑤 relative velocity, m/s
𝛬 degree of reaction 𝛥ℎ% stage enthalpy drop, J/kg
𝛷 flow coefficient 𝛥ℎ,, isentropic enthalpy drop, J/kg
𝛹 blade-loading coefficient
𝜔 rotational speed, rad/s Subscripts
𝜔, specific speed, rad/s θ tangential
𝑏 blade height, m 0 total conditions
𝑐 absolute velocity, m/s 1 turbine inlet
𝑑 diameter, m 2 rotor inlet
ℎ enthalpy, J/kg 3 rotor outlet
𝑚̇ mass-flow rate, kg/s c compression process inlet/compressor
𝑊̇ power, J/s is isentropic
𝑉̇ volumetric-flow rate, m3/s m meridional
𝑀𝑎 Mach number p polytropic
𝑁 rotational speed, RPM th thermal

BIOGRAPHY

Dr Martin White is a Research Associate within the Turbomachinery and Energy

Systems research group at City, University of London. He obtained his PhD from
City in October 2015, and his MEng in Mechanical Engineering from the University
of Southampton in 2015. His primary interest is in understanding and characterising
the performance of turbomachines accounting for real-gas effects.

Professor Abdulnaser Sayma is a Professor of Energy Engineering, at City,

University of London since 2013, and the leader of the Turbomachinery and Energy
Systems research group. He obtained his PhD from the University of Manchester in
1994 and worked as a Rolls Royce research fellow at Imperial College London before
becoming a professor of CFD at University of Sussex in 2006. His main research area
is the development of compressible flow CFD methods for turbomachinery
applications and the development of turbo compressors and expanders with current
emphasis on micro-gas turbines and organic Rankine cycles. He has been leading a
team developing a micro-gas turbine powered by concentrated solar power using a
solar dish system (OMSoP), and currently leads the SolGATS project for integrating
solar powered micro-gas turbines with thermal-energy storage. He is also leading
EPSRC funded research on fundamental studies on organic Rankine cycle expanders
(NextORC).

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