Radial inflow turbines are the preferred architecture for energy extraction from the organic Rankine cycle and the supercritical CO Brayton cycle at smaller scales. For such turbines it is possible for fluid to be delivered to the first stage by either a volute or plenum delivery system. For high pressure supercritical CO turbines, there are no fully documented fluid delivery systems in literature and it remains unclear as to which architecture results in higher performance with the highly dense working fluid. The aim of this paper is to present a performance comparison between a new plenum based fluid delivery system and conventional volute for a 100 kW supercritical CO radial inflow turbine. Numerical simulations of the fluid delivery systems are conducted and compared in terms of flow uniformity, total pressure loss and entropy rise. It is demonstrated that fluid can be delivered to the stator vanes with a plenum style inlet for a radial inflow supercritical CO turbine without re-circulation regions and minimal total pressure loss. Entropy rise for the plenum is reduced more than tenfold in comparison to the volute, however fluid velocities are not matched and there is a periodic variation in in velocity generated by the multiple inlets

Jahn, I. J.

Keep, J. A.

University of Queensland eSpace

20th Australasian Fluid Mechanics Conference
Perth, Australia
5-8 December 2016
Design method and performance comparison of plenum and volute delivery systems for radial
inflow turbines
J. A. Keep1 and I. J. Jahn1
1School or Mechanical and Mining Engineering
University of Queensland, Queensland 4072, Australia
Abstract
Radial inflow turbines are the preferred architecture for energy
extraction from the organic Rankine cycle and the supercritical
CO2 Brayton cycle at smaller scales. For such turbines it is pos-
sible for fluid to be delivered to the first stage by either a volute
or plenum delivery system. For high pressure supercritical CO2
turbines, there are no fully documented fluid delivery systems
in literature and it remains unclear as to which architecture re-
sults in higher performance with the highly dense working fluid.
The aim of this paper is to present a performance comparison
between a new plenum based fluid delivery system and con-
ventional volute for a 100 kW supercritical CO2 radial inflow
turbine. Numerical simulations of the fluid delivery systems are
conducted and compared in terms of flow uniformity, total pres-
sure loss and entropy rise.
It is demonstrated that fluid can be delivered to the stator vanes
with a plenum style inlet for a radial inflow supercritical CO2
turbine without re-circulation regions and minimal total pres-
sure loss. Entropy rise for the plenum is reduced more than
tenfold in comparison to the volute, however fluid velocities are
not matched and there is a periodic variation in in velocity gen-
erated by the multiple inlets.
Introduction
An efficient embodiment of the supercritical CO2 Brayton cy-
cle is a key enabler for the development of concentrating solar
power on a scale of less than 10 MW [4]. Radial inflow turbines
that satisfy these ratings are under 500 mm in rotor diameter
with comparatively small blade inlet heights. This presents a
unique combination of small geometry and very high inlet duct
Reynolds number ( 3×106 , or approximately100 times greater
than air turbomachinery of similar scale), therefore the optimal
design of these turbines remains unclear.
For the efficient operation of a radial inflow turbine stage, fluid
needs to be uniformly supplied to all stator nozzle guide vanes
with uniform pressure and a matched tangential velocity com-
ponent. Volutes are the preferred method to provide the highly
tangential flows as typically required in conventional radial in-
flow turbines. An alternative to this are plenum style inlets. For
the present application of radial inflow turbines, it is unclear as
to which is the preferred method of fluid delivery.
Using conventional machining methods, the relative stack-up
of tolerances is increased at small scale, leading to the potential
for greater deviation from nominal design in components. A
plenum fluid delivery system is of interest in this design space,
as it is less dimensionally critical than a volute.
The aim of this paper is to present a performance comparison
between a plenum based fluid delivery system and conventional
volute for a supercritical CO2 radial inflow turbine with operat-
ing conditions described in table 1. These conditions are repre-
sentative of small scale applications and prefered cycle condi-
tions targeted at a concentrated solar thermal application [3].
Operating Conditions Value Parameter Value
Power 100 kW r1 32.40 mm
Total Pressure 20 MPa Z1 1.25 mm
Total Temperature 833 K α1 80.910
Mass Flow Rate 1 kgs−1
Table 1: Turbine operating conditions and stator geometry pa-
rameters
Design
The aerodynamic objective of a fluid delivery system in radial
turbomachinery is to deliver a uniform flow from the delivery
pipe to the stator inlet. If a high velocity stream is to be de-
livered to the stator inlet, it is important for the flow to match
the stator blade angle in order to minimise incidence losses. By
contrast, if a low velocity stream is delivered, incidence is of
less importance.
Inlet pipe are sized such that Mach number is below 0.1, or
less than the 30 ms−1 as recommended by Southwest Research
Institute [6]. Stator inlet constraints and total inlet conditions
are derived from a 100 kW supercritical CO2 mean-line design
presented by Qi et.al. [8] and listed in table 1.
Plenum
The primary advantage of a plenum fluid delivery system is the
ability to employ a cross section of constant shape, allowing
manufacture in two halves and simplifying assembly of a high
pressure turbine casing. The selected cross section satisfing
these requirements is illustrated in figure 1.
An important consideration with a plenum inlet is jet impinge-
ment into a quiescent body of fluid. In the traditional design
of axial flow turbomachinery inlet plenums, this appears to be
done with the use of diffusers [7]. In the case of supercriti-
cal CO2, the characteristic design of diffusers requires a much
larger space claim than that for air [5], and it would not be prac-
tical to incorporate such features in a compact plenum. An alter-
native to manage the high velocities at the pipe outlet is to offset
inlet pipes as shown in figure 2 thus inducing tangential flow in
the plenum. This also avoids localised impingement of the in-
coming flow on the stator. A asymmetric plenum cross-section
has been selected in order to avoid toroidal vortices from estab-
lishing [2]. Feature sizes of the plenum design are minimised in
order to limit system volume and are listed in table 2.
Feature Value Feature Value
Z0 15.20 mm A0 57 mm2
L0 15 mm Ain 181 mm2
L1 5 mm r0 45 mm
b 50 mm t 4 mm
γ 400
Table 2: Geometric parameters of delivery systems
Volute
Figure 1: Section view of plenum
Figure 2: Plan view of plenum
The volute geometry is developed based on the assumption of
conservation of angular momentum. With this assumption, the
following relationships exist for exit flow angle and area[7].
tanα1 =
ρ1(A1/r1)
ρ0(A0/r0)
(1)
Aθ
rθ
=
m˙
const.ρθ
(
1− θ
2pi
)
(2)
Observing equation 1 and assuming constant density within the
volute, it can be seen that the outlet flow angle (α1) is dictated
by the inlet area (A0) and radius (r0). Assuming constant den-
sity, in order for a constant mass flow to be delivered to the
stator stage a linear decrease in Aθ/rθ with θ is required. Us-
ing the approximation, of constant volute radius (rθ) this gives
a linear reduction in volute sectional area (Aθ) with θ. The plan
shape of the volute as illustrated in figure 4 is mathematically
described by several logarithmic spirals. The tongue thickness,
(t) has been prescribed to limit thermal loads and fatigue. The
inter space between the inner edge of the scroll and the stator
has been set using design guidelines presented in Aungier[2], to
be greater than 1.05r1. This minimises non-uniformities intro-
duced by the tongue. Furthermore to avoid the development of
two opposing toroidal vortices, which increase losses, the vo-
lute outlet is offset with a circular cross-section as illustrated in
figure 3.
Modelling
Both geometries are modeled in three dimensions. The volute
is modeled in it’s entirety from inlet pipe to stator inlet passage.
Owing to rotational symmetry, the plenum is modeled as a half
circumferential section. The geometries were constructed using
CAD and meshed using ANSYS meshing 17.0.
Inlet pipes to each geometry are modeled with a length greater
than five times the inlet diameter in order to minimise inlet ef-
fects on the area of interest. To ensure comparability, total inlet
cross sectional area of geometries is matched.
The ANSYS CFX 17 solver is used for calculations [1]. Ther-
modynamic and transport properties are incorporate into the
CFD solver through the built-in thermophysical library for CO2.
Figure 3: Section view of volute
Figure 4: Plan view of volute
Boundary conditions are derived from a 100 kW supercritical
CO2 mean-line design presented by Qi et.al. [8], and specified
in table 3. For all simulations, the SST k−ω turbulence model
is used with a 5 % turbulence intensity at the inlet in line with
simulations conducted by Monje et.al. [5].
Surface Type Value
Inlet total pressure 20.0 MPa
Outlet static pressure 17.15 MPa
Upper and lower no-slip wall N/A
Edges rotational periodicity N/A
Table 3: Boundary conditions for CFD simulation
Meshing
Unstructured meshes are used for both plenum and volute ge-
ometries. A grid dependency study comparing three meshes
was completed on the plenum geometry, comparing mass flow
averages for inlet and outlet of total enthalpy and entropy dif-
ference and mass flow. The nominal mesh has approximately
90000 nodes. Results from the dependency study are presented
in table 4, confirming grid independence. The nominal mesh
was selected for further analysis. The same mesh settings were
utilised for automated meshing of the volute geometry resulting
in a mesh with approximately 640000 nodes.
The plenum mesh was refined using 100 inflation layers to
resolve the wall boundaries. This resulted in a typical near
wall cell height of 0.2 mm and a y+ in the range of 1000 to
10000. This is larger than the recommended y+ range for the
turbulence model (30 < y+ < 300)[1], however finer meshes
would prevent solution convergence due to flow instabilities at
the exit of inlet pipes. For the volute mesh convergence was
achieved with a first layer height closer to the desired value
with 6×10−3 mm. Clustering was employed in regions of an-
ticipated flow separation and high pressure gradients. Visuali-
sation of entropy gradient over the domain was used to verify
clustering.
Results
Mesh ∆ s (J/kg.K) h0,total (kJ/kg) h1,total (kJ/kg)
coarse 4.81 8385.1 8385.1
nominal 4.70 8385.1 8385.1
fine 4.25 8385.1 8385.1
Table 4: Results from grid dependence study for plenum mesh,
refinement ratio 2.0
Parameter Volute Plenum
h1,total (kJkg−1) 8385.11 8385.11
∆s (Jkg−1 K−1 ) 8.06 0.49
P1 (MPa) 17.15 19.72
∆P1,total (MPa) 0.83 0.05
m˙ (kgs−1) 1.11 1.11
ηisentropic 73 % 80 %
Table 5: Comparison of exit flow properties for geometries
Utilising the boundary conditions from table 3, exit mass flow
for the plenum and volute geometries are not in close agree-
ment. This is attributed to the difference in effective outlet flow
area (Ae f f =
Aactual
cosα1 ) and difference in total pressure losses be-
tween the two geometries. To allow comparison between the
geometries, exit static pressure for the plenum simulations was
adjusted until mass flow was matched to the volute simulation.
The plenum simulation was adjusted owing to the smaller mesh.
Exit flow properties for each geometry are compared in table 5.
The plenum maintains higher total pressure with lower entropy
rise than the volute, and higher isentropic efficiency.
To visualise flows, and potential regions of re-circulation and
loss generation, streamline plots and pressure contours are
shown in figures 5 and 6. These plots show no significant re-
gions of re-circulation or secondary flow. Both geometries dis-
play the highest rate of entropy generation in the contraction
close to the outlet. The rate of entropy generation in the volute
is significantly larger in this region than for the plenum, with
further entropy generation in the region of the tongue. To ex-
amine outlet flows in greater detail, azimuthal variation in outlet
velocities are compared in figure 7. The volute delivers a higher
velocity magnitude with a larger tangential component. Plenum
radial and tangential velocities exhibit two characteristic peaks
corresponding to the two inlets. For the volute, in the region of
the tongue and for approximately 120◦ thereafter there is fluctu-
ation in outlet velocity, then it remains relatively constant. Ex-
amining the outlet flow angle (α1) in figure 8, it can be seen that
the volute delivers close to design requirement of α1 with minor
deviation in the region of the tongue. This is not the case with
the plenum where large fluctuations in flow angle are present,
and the mean flow angle is significantly lower than the design
requirement.
Discussion
For the scale considered, the numerical comparison of the
plenum and volute show a significantly superior performance of
the plenum. Entropy generation and total pressure loss are both
reduced by a factor of 16. Inspection of the entropy generation
shows that this difference can be attributed to lower velocities
and the elimination of the area discontinuity in the vicinity of
the volute tongue.
However the exit velocities delivered by the plenum are sub-
stantially lower at 61 ms−1 compared with 192 ms−1 and exit
flow direction has an increased radial component. The plenum
exit velocity magnitude is almost invariant, but the flow angle
varies by ±16%. The much reduced velocities at the plenum
exit and the low variations in tangential velocity suggests a dif-
ferent approach to stator design. For example by using stator
blades that are tolerant to variations in incident flow and op-
timised for flow acceleration and flow turning, desired stator
outlet conditions can be attained. Alternative solutions to in-
crease the tangential velocity component are to increase the off-
set of the plenum inlet pipes (b) or to reduce the inlet area (Ain.
Similarly angular periodic variation in flow angle (α1) can be
smoothed through the addition of additional feeder pipes. How-
ever these approaches are not preferred due to additional com-
plexity and limit space that is available in such small turbine
casings.
Close inspection and comparison of the different flow fields
show that the design methods deliver a generally smooth flow.
For both geometries, no significant toroidal vorticies are gen-
erated, showing that the employed geometries operate to de-
sign intent. Additional scope exists to further enhance perfor-
mance through better blending of the inlet pipes and smoothing
of sharp edges, avoidance of flow area discontinuities and to de-
velop stator vanes optimised for the respective flow conditions.
The current work studied a 100 kW scale turbine (inlet radius
< 50mm). It is anticipated that for larger systems 1 MW to
10 MW the performance benefits of the plenum become less
pronounced, but that significant manufacturing advantages re-
main. Furthermore the plenum requires equal or less space
than a compact volute. Considering this in conjunction with the
much simplified manufacturing, this is an additional advantage
for the design of higher pressure turbine casings.
This work has shown that for radial inflow turbomachinery op-
erating with sCO2, which results in very high stage Reynolds
numbers for small geometries, a plenum is the preferred fluid
delivery system, if used in conjunction with nozzle guide vanes.
Conclusions
Both fluid delivery systems deliver a generally smooth flow with
no regions of secondary flow. The numerical comparison of the
plenum and volute show a significantly superior performance
of the plenum with an entropy rise and total pressure loss of ap-
proximately 16 times less than the volute. This difference can
be attributed to the higher velocities in the volute, and higher
isentropic efficiency. Comparing variation in outlet velocity,
it can be seen that the plenum does not deliver the requisite
tangential component of velocity and possess a more sustained
variation with azimuthal angle when compared to the volute. In
order to better understand the impact of stator stage interactions
with a plenum delivery system, it is suggested that further sim-
ulation work be performed with the inclusion of stator vanes.
Acknowledgments
This research was performed as part of the Australian Solar
Thermal Research Initiative (ASTRI), a project supported by
the Australian Government.
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Figure 5: Streamline plots coloured by static entropy gradient to highligh locations of loss generation.
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Design method and performance comparison of plenum and volute delivery systems for radial inflow turbines

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