multi-objective aerodynamic optimisation of a radial ...409738/v... · turbogrid was applied to...

MULTI-OBJECTIVE AERODYNAMIC OPTIMISATION OF A REAL GAS RADIAL-INFLOW TURBINE

Mostafa Odabaee School of Mechanical and Mining Engineering

The University of Queensland Brisbane, Queensland, Australia

Emilie Sauret Queensland University of Technology

Brisbane, Queensland, Australia

Kamel Hooman School of Mechanical and Mining Engineering

The University of Queensland Brisbane, Queensland, Australia

ABSTRACT Optimisation, robustness and reliability analyses have

increasing importance in turbomachinery. With continuing

progress in numerical simulations, computational-based

optimisation has proven to be a useful tool in reducing the

design process time and expense. This paper describes an

optimisation procedure to modify the geometry of a 7 kW

R245Fa radial-inflow turbine working on heat input at 150ºC

with a pressure ratio of 3.7 to improve aerodynamic efficiency

and satisfy manufacturing constraints. The procedure integrates

the parameterisation of the turbine blade geometry, multi-

objective optimisation, and 3D CFD analysis.

ANSYS-BladeGen was applied to create the 3D geometry

of the flow passage carefully examining the proposed design

against the baseline geometrical data. Generating the required

computational mesh with ANSYS-TurboGrid followed by grid

refinement, CFD simulations are then performed with ANSYS-

CFX in which three-dimensional Reynolds-Averaged Navier-

Stokes equations are solved subject to appropriate boundary

conditions and real gas properties (RGP) where the required

table of properties were generated using REFPROP.

Considering a steady state solution, a high resolution for both

Advection Schemes and Turbulence Numerics were applied

resulting in higher accuracy at the expense of slightly higher

computational cost.

OptiSlang Dynardo was used to conduct a multi-objective

optimisation and to identify the most relevant input parameters

in order to reduce the numerical effort for the optimisation

algorithm. Implementing evolutionary algorithm resulted in a

Pareto front to choose a nominal design for a subsequent

reliability analysis and define previously unknown feasible

design space boundaries.

INTRODUCTION Organic Rankine Power Cycle (ORC) became an important

technology for energy conversion where the low size and

temperature applications are matched with the thermodynamic

properties of organic fluids resulting in small power plants (50-

5000 kW). As ORCs have characteristically low efficiency

levels - due to a low operating temperature – the accurate

design of the turbine/expander is significant in order to improve

the cycle efficiency [1, 2]. Radial turbines benefit the ORCs

with a simple sealing (low degree of reaction), large enthalpy

drop, single-stage design, generally good performance and

affordable price [3-5].

In terms of ORC working fluid selection, the optimisation

of the thermodynamic cycle has been investigated widely [6-8].

Sauret et al. [2] investigated five high-density working fluids

for ORC applications considering realistic radial-inflow

turbines. Preliminary meanline analysis led to turbine designs

for various cycles with about 77% efficiency with difference

rotor diameter/size. Comparing the working fluid

performances, R134a produced 33% more net power than the

lowest performing cycle based on n-Pentane subjects to the

constrains in [2].

Some of those constrains, including the cycle maximum

temperature, will have to be modified a concentrated solar-

thermal power plant. Solar-thermal energy can play a

significant role in generating electrical power by using either

the point-focus or power-tower systems in which the solar-

Proceedings of ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition GT2016

June 13 – 17, 2016, Seoul, South Korea

GT2016-58132

1 Copyright © 2016 by ASME

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thermal energy is concentrated thereby increasing the working

fluid temperature and associated cycle efficiencies. The

Supercritical Carbon dioxide (SCO2) Brayton cycle has

emerged as a promising path for high-efficiency power

production where the turbomachinery for SCO2 Brayton is in

the development phase to reduce the associated technical risks.

This study is conducted to validate the code and optimisation

progress aiming to optimise a supercritical CO2 radial-inflow

turbine which will be designed, manufactured and tested as a

part of the Australian Solar Thermal Research Initiative. Following the ORC cycle optimisation, there is a need for

aerodynamic optimisation of the radial-inflow turbines which

are almost the only choice, with the eventual competition of

screw expanders. The numerical-experimental correlations for

the performance of axial expanders are widely investigated

whereas much less data are available for radial turbines.

Moreover, the majority of data on radial turbines refer to ideal

gas applying Mach compressibility relations. This is not a

satisfactory estimation while dealing with ORC radial turbines

operating close to the saturation line or the critical point.

Besides, most of practical engineering problems need

simultaneous optimisation of multiple objectives related to each

discipline usually known as multi-objective problems where

efficiency, total pressure, static pressure, pressure loss, weight,

stress, etc. are the objectives and variables are related to the

blade profile [9-16]. A numerical optimisation has been

performed by Samad et al. [12] for three objective functions,

namely efficiency, total pressure and torque, with four design

variables of blade stacking line of a low speed axial flow fan

with a fast Non-Dominated Sorting of Genetic Algorithm

(NSGA-II) using three-dimensional Navier-Stokes analysis.

Regression analysis was performed to get second order

polynomial response used to generate Pareto optimal front with

help of NSGA-II and local search strategy with weighted sum

approach to improve Pareto optimal front. The motive of the

optimisation was to enhance the total efficiency and pressure

and to reduce torque resulted in the reduction of separation

zone and increase in blade loading for optimal designed blades

as compared to reference design.

In another study, optimisation of a radial turbine was

performed by Mueller et al. [17] using a differential evolution

algorithm and a database as a compromise between accuracy

and computational cost. The method was validated by running

steady state 3D Navier-Stokes and centrifugal stress

computations. The parametrization of the 3D radial turbine

impeller was based on Bezier and B-spline curves and surfaces

for the control points which were defined on the meridional

contour of blade hub and tip, thickness and blade angle

distribution, and number of blades. The design approach aimed

to improve the total-to-static efficiency and the moment of

inertia of the radial turbine rotor. Results showed that a smaller

blade leading edge height improves both the aero-performance

and moment of inertia and reducing the blade thickness

minimizes the moment of inertia with a marginal impact on the

aero-performance.

Parallel to the above studies, stochastic programming

algorithms or response surface methods are usually used in

turbomachinery design on the applications of the deterministic

optimisation for aerodynamic optimisation [18-20]. Trigg et al.

[21] offers a system approach to the optimisation of 2D blade

profiles using an automatic genetic optimiser to minimize

profile loss. In a comprehensive study [22], Evolutionary

Algorithms (EAs) were applied to multidisciplinary

optimizations of a transonic wing design where the

aerodynamic performances were estimated by using the 3D

compressive Navier-Stokes equations. Due to the tradeoff

between both weight and drag minimization of the wing

structure, the solution was not a single point and Multi-

objective Evolutionary Algorithm (MOEA) successfully

produced a range of solution.

This study presents a multi-objective optimisation for

design of a 7 kW R245Fa radial-inflow turbine from a heat

source at 150ºC with a pressure ratio of 3.7. CFD simulations

are performed in order to provide the Design of Experiments

(DoE) followed by a sensitivity analysis to investigate the most

important optimisation variables within 49 selected parameters

on rotor flow passage. The aim of this optimisation is to

improve the total-to-static efficiency and reduce the thrust

loading of the radial turbine while the impact on the stress and

deformation of the rotor is found to be negligible compared to

the original design.

NUMERICAL ANALYSIS

Turbine 3D Geometry

A subcritical R245FA radial-inflow turbine geometry was

designed by QGECE at the University of Queensland, Australia

to be tested in a power cycle aiming to generate 7 kW power

with total-to-static efficiency of 70%. The 3D geometry is

recreated by ANSYS-BladGen where the 3D nozzle and rotor

blades are created and blade thickness and angle distribution

were applied to generate the geometry. Both geometries were

imported into ANSYS-Geometry in order to define design point

parameters to be discussed in the optimisation method. Table 1

summarizes the geometrical data and operating conditions of

the 7 kW R245FA radial turbine. A 3D view of the fabricated

rotor and stator is illustrated in Figure 1.

Table 1. Operating conditions and geometrical details Parameters Units Values

𝑃𝑡,𝑆,𝑖𝑛 kPa 558

𝑇𝑡,𝑆,𝑖𝑛 C 150

𝑃𝑠,𝑅,𝑜𝑢𝑡 kPa 148.25

𝜔 RPM 30000

𝑟𝑅,𝑖𝑛 mm 52.2

𝑟𝑅,𝑡𝑖𝑝,𝑜𝑢𝑡 mm 28.6

N - 12



Figure 1. A 3D view of fabricated rotor and stator

Mesh

To generate a high quality mesh avoiding negative volumes

which are problematic for traditional mesh generations [23],

ANSYS-TurboGrid was applied to generate the flow passage

meshes for both rotor and stator where the Automatic Topology

and Meshing (ATM Optimized) option was used in stator and

rotor flow passages without the “cut-off squared” option at

trailing edges.

The first element method was used (for the boundary layer

refinement control) where Reynolds number is 7×107 with near

wall element size specification to meet the y+ requirement (6 to

150) for the turbulence model. The grid-convergence study is

conducted and results are presented in Figure 2.

Figure 2. Results of grid-convergence study

Figure 3. 3D view of mesh generated for a) stator and b) rotor blade flow passage presenting inlet (green), outlet (red), shroud (purple) and periodic surfaces

(yellow)

Considering a constant value of the total-to-static

efficiency, the final total grid number is selected as 1356131

nodes –including 563094 nodes for stator and 793037 nodes for

the rotor where the final mesh analysis of the rotor and stator

flow passages shows 30º for minimum face angle and 155ᵒ for

maximum face angle. Figure 3 illustrates the 3D views of the

generated mesh for the rotor (with tip clearance) and the stator

blade flow passages where Z denotes the rotational axis.

Solver and boundary conditions

The mesh from ANSYS-TurboGrid was imported into

ANSYS CFX 16.1 to conduct the 3D viscous flow simulations

[24]. SST turbulence model was chosen as recommended by

[25, 26]. The basic settings used for the discretisation of the

Reynolds-Averaged Navier-Stokes (RANS) equations - for a

steady state solution - were High Resolution for both Advection

Scheme and Turbulence Numeric resulting in higher accuracy.

The order of accuracy or convergence criteria is 10E-5.

The Real Gas Property (RGP) format table of R245FA is

used in the CFX code. The RGP table is 100x100 size generated

by an in-house MATLAB code automatically writing a RGP file

using NIST REFPROP 9.1 [27] based on the required range of

temperature and pressure. It includes specific enthalpy, speed of

sound, specific volume, specific heat at constant volume,

specific heat at constant pressure, partial derivative of pressure

with respect to specific volume at constant temperature,

specific entropy, dynamic viscosity and thermal conductivity of

R245FA read by CFX solver calculating properties by using

bilinear interpolation. The table size is validated based on

previous studies providing a high accuracy in gas property

prediction and low computational cost/time [28, 29].

The inlet total pressure and inlet total temperature are set at

the inlet of stator flow passage followed by a Frozen Rotor

interface with a fixed pitch value between the outlet of the

stator flow passage and the inlet of the rotor flow passage and

static pressure fixed at rotor exit, see Table 1. The Frozen Rotor

model creates a steady-state solution requiring the least amount

of computational effort where the circumferential variation of

the flow is large relative to the component pitch [24].

SENSITIVITY ANALYSIS

Many meta-model approaches have been used to represent

the model responses by surrogate functions in terms of the

model inputs; however, the application of each approach to the

engineering problems is not clear yet [30]. OptiSlang Dynardo

developed the Meta-model of Optimal Prognosis (MOP) [31] in

which the optimal input variable subspace together with the

optimal meta-model are determined with the aim of an

objective and model independent quality measure called the

Coefficient of Prognosis (CoP).

A global variance-based sensitivity analysis is used for

ranking variables x1, x2, … , x𝑛 with respect to their importance

for a specified model response parameter



𝑦 = 𝑓(x1, x2, … , x𝑛) (1)

𝐶𝑜𝑃 = 100 × (1 − 𝑆𝑆𝐸

𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛𝑠

𝑆𝑆𝑡) (2)

where 𝑆𝑆𝐸𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛𝑠 is the sum of squared prediction errors

which are estimated based on cross validation and giving some

indication of the predictive capability of the surrogate model.

𝑆𝑆𝑡 is the sum squares and equivalent to the total variation [32].

Defining design variable and model responses, the design space

is scanned by Design of Experiments (DoE) which are

evaluated by the solver. This is followed by the model

responses determination and approximation (MOP & CoP)

assessed regarding their quality. As a result of the MOP, an

approximation model is obtained containing the most important

variables.

OPTIMISATION PROCESS

Multi-objective evolutionary algorithm (MOEA) optimisation

procedure is conducted in this study as shown in Figure 4. First

the variables are selected and design space is decided for

improvement of system performance. A sensitivity analysis is

performed to determine the sensitive parameters for each output

parameter and their correlations by using an Advanced Latin

Hypecube Sampling (ALHS) where the correlation errors are

minimized by stochastic evolution strategies recommended

when the number of input variables is less than 50 [33]. The

design points are chosen using DoE and the objective functions

are calculated where CFD solver is applied. Then the prognosis

ability is made through MOP which gives a percentage value of

how good the output value is describable through the input

variables (CoP). After indicating the most important variables

(removing unimportant variables from the model), the

Evolutionary Algorithm (EA) is used to provide a single

optimal solution which called Pareto-optimal solution (Pareto

optimal front) [34]. Evolutionary Algorithms (EA) are

stochastic search methods mimicking processes of natural

biological evolution such as adaption, selection and variation

[35]. The parallel search for a set of Pareto optimal solution is

the main advantage of EA method and in OptiSlang the

Strength Pareto Evolutionary Algorithm 2 (SPEA2) is

implemented; for more details see [32].

Figure 4. Overview of the optimisation procedure

Practical optimisation problems include more than on objective

and a large number of variables leading to the general

formulation of the multi-objective optimisation problem:

Minimize: 𝑓𝑚(𝑋), 𝑚 = 1, 2, … , 𝑀

Subject to: 𝑔𝑗(𝑋) ≥ 0, 𝑗 = 1, 2, … , 𝐽 (3)

ℎ𝑘(𝑋) = 0, 𝑘 = 1, 2, … , 𝑛

𝑥𝑖(𝐿)

≤ 𝑥𝑖 ≤ 𝑥𝑖(𝑈)

𝑖 = 1, 2, … , 𝑛

where 𝑥 = (𝑥1, 𝑥2, … , 𝑥𝑛)𝑇 is the vector of design variables and

the constraints of inequality 𝑔𝑗(𝑋) and equality ℎ𝑘(𝑋); all

solutions provide the feasible n-dimensional design space. Each

solution 𝑥 is allocated to a vector 𝑓(𝑋) = 𝑧 = (𝑧1, 𝑧2, … , 𝑥𝑀)𝑇

defining one point of the M-dimensional objective space [32].

When all objectives are equally important the dominance of a

solution is the only way to determine if it is better than others

resulting in the non-dominated subset out of the feasible set of

the solutions. These corresponding points are called Pareto

frontier and the optimisation produces a set of Pareto optimal

solutions. Additional preferences should be considered in order

to select a single solution.

OBJECTIVE FUNCTIONS AND DESIGN VARIABLES

This study aims to enhance the performance of a 7 kW

R245FA radial-inflow turbine and by increasing the total-to-

static efficiency and decreasing the axial force towards the hub

(thrust loading):

𝑒𝑓𝑓𝑇−𝑆 =ℎ𝑡,𝑆,𝑖𝑛−ℎ𝑡,𝑅,𝑜𝑢𝑡

ℎ𝑡,𝑆,𝑖𝑛− ℎ𝑠,𝑅,𝑜𝑢𝑡 (4)

𝐹𝑍 = ∫ 𝑃𝑑𝐴 (5)

where ℎ𝑡,𝑆,𝑖𝑛 represents the total enthalpy at stator inlet, ℎ𝑡,𝑅,𝑜𝑢𝑡

and ℎ𝑠,𝑅,𝑜𝑢𝑡 are the total and static enthalpy at rotor exit. The

calculated thrust loading is considered per single passage, thus,

the total thrust loading is the 𝐹𝑍 multiplied by the number of

rotor blades. This objective is important as the bearing design -

to balance the thrust loads - is one of the significant challenges

for small supercritical CO2 turbomachinery where reducing the

thrust loading improves the design space of bearing [36, 37].

There are two aerodynamic constraints imposed to this

optimisation: mass flow rate needs to be within a certain range

and isentropic Mach number to control the Mach number

profile at blade mid-span on both pressure and suction side of

the blade.

The design variables of the 3D radial turbine rotor are

based on B-spline and spline curves defined by the meridional

contour of the fluid domain, blade camber line at hub, thickness

and angle distribution at hub and tip. The main constraint is that

the optimised rotor blade should fit in similar shroud.

Therefore, the blade camber line at tip is not considered

although the thickness and angle distribution at tip will be

systematically changed. Design variable ranges are precisely

Initial design

ALHS DoE, CFD

MOP, CoP EA,

SPEA2

Pareto optimal

solutions



selected in order to minimize the major impact on mechanical

performance of the turbine (stress and deformation) according

to [16, 17].

The meridional contour of fluid passage is presented in

Figure 5 where half of the interspace between stator exit and

rotor inlet followed by the rotor blade hub and tip camber lines

and rotor outlet are specified by control pints. The quad arrows

represent the displacement direction (r & Z) of selected control

points; red points without arrow are fixed at interspace and

blade tip camber line. There are two single control points (CP1

& CP8) at the leading edge moving only in radial direction in a

limited range and at the outlet edge also changing in radial

direction. The control points at the tip are fixed to avoid

changes on the shroud for the reason mentioned before.

Figure 5. Meridional contour of rotor fluid passage

with location of the control points on the hub camber line

As shown in Figure 6 and 7, the blade camber line at hub

and tip is defined by blade angle and thickness distribution

respectively. Blade angle distribution is parametrized by a B-

spline curve with five control points (β1-β5), starting from

leading edge to trailing edge (Figure 6). On both pressure and

suction side of the blade thickness distribution is provided

normal to the camber line at hub and tip defined by B-spline

and six control points (Ti1-Ti6) and two fixed points at the

leading and trailing edge (Figure 7). The control points on

thickness distribution can move in meridional direction while

those on blade angle distribution have fixed meridional values.

Figure 6. Control points defined on the blade angle

distribution at hub and blade tip

The total number of control points is 30 and optimisation

parameters is 49: 15 parameters for hub camber line, 10

parameters for blade angle distribution, and 24 parameters for

blade thickness distribution.

Figure 7. Control points specification on the blade

thickness distribution at hub and blade tip

RESULTS AND DISCUSSIONS

As a result of the CFD simulation, the total-to-static

efficiency convergence, one of the output control parameters, is

shown in Figure 8, reaching a convergent result after nearly 200

iterations while RMS residuals are stable close to 10E-5.

Figure 8. Convergence of the total-to-static efficiency

The total effect sensitivity indices of total-to-static

efficiency are given in Table 2 for different number of samples

obtained by ALHS. One should note that for each sample, as

the variables systematically change, the 3D blade geometry is

recreated. Only if the new geometry successfully passes all

geometrical constraints and mesh quality limits, the CFD

simulation is conducted. The number of succeeded samples is

almost half of the requested samples, as presented in Table 2.

The number of samples generated by ALHS in sensitivity

analysis is increased from 50 to 200 in order to obtain the

minimum required samples and converged CoP values as the

computational cost/time at this stage is noticeable (at least 200

iterations for each sample).



Table 2. Convergence of total sensitivity indices for the most important optimisation variables

No. Samples 50 100 200

No. succeeded samples 29 57 123

Total CoP 92% 69% 69%

CP3r - 10% 13%

CP2r - 13% 7%

𝛽𝑡𝑖𝑝,4 10% 4% 6%

CP3Z 14% 12% 6%

CP4Z 14% - 5%

CP5r - 4% 5%

CP2Z - - 4%

𝛽𝑡𝑖𝑝,2 - - 4%

CP7r & CP8r - 5% 4%

CP4r 14% - 3%

𝛽ℎ𝑢𝑏,4 - - 3%

CP1r - - 3%

Ti tip, m, 4 - 7% 2%

𝛽𝑡𝑖𝑝,3 - 6% 2%

Ti hub, m, 5 10% - 1%

Ti tip, m, 6 - - 1%

Ti hub, 4 - 3% -

CP5Z 30% 5% -

The total effect sensitivity indices are calculated based on

the MOP and by increasing the number of samples up to 200

(123 succeeded samples) the CoP of total-to-static efficiency

becomes steady at 69% and more minor important input

parameters are detected (16 out of 49 primary defined

parameters) compared to 100 and 50 samples. The

approximation functions are illustrated for the two most

important optimisation parameters CP3r and CP2r in Figure 9

indicating that with 123 succeeded samples the general

functional behavior can be obtained.

The optimisation parameters are adjusted to suit the nature

of the problem where the start population size = 1000,

maximum number of generation = 250, number of parents = 10,

number of multipoint crossover = 11, and self-adaptive

mutation is selected. After generating 9900 selected designs for

increasing total-to-static efficiency and decreasing axial force

of the turbine, the Pareto front is provided which estimates the

possibility of 2% improvement in both objectives, see Figure

10. As seen, one solution cannot dominate on the Pareto front

line with respect to both objectives.

The selection of the optimum is finally made between

those individual designs lying on the Pareto front as shown

with a red line in Figure 10, a set of non-dominated solutions.

At this stage the selection of the optimum individual is

completely up to the importance given to one objective

compared to another. In this study, the best design is chosen to

maximize the efficiency of the turbine where the lowest thrust

load could be achieved. Therefore, the turbine design with 70.8

% of efficiency and 133.3 N of thrust loading (for single

passage) is selected as the optimum design.

Figure 9. Approximation function in the subspace of

the most important parameters for 200 samples

Figure 10. Objective Pareto plot (red line) with initial

turbine design (blue point) and optimum design (Green point)

Once the single solution is selected as a result of the

optimisation process, the optimum design is used in a CFD

simulation in order to create the 3D geometry and validate the

performance. These geometrical parameters are listed in Table 3

where geometrical parameters and the difference ratio between

the optimum and original designs are presented, resulting in

different hub curvature and expansion ratio. Figure 11 shows

the Mach number distribution of original and optimum designs

on the pressure side of the rotor blade. Both designs provide an

almost identical distribution while the hub surface area of the

optimum design is reduced by less than 1% compared to that of

the original design. This results in less thrust loading and

similar efficiency while the optimization estimation was 2%



improvement in both efficiency and thrust loading, as shown in

Figure 10. It is interesting to observe that by fixing the shroud

curvature profile the performance enhancement is limited and

control points on hub curvature - such as CP3r and CP3Z - have

more influence compared to those control point on blade

thickness and angle distribution, such as Titip,m,4 and 𝛽𝑡𝑖𝑝,2.

Table 3. Convergence of total sensitivity indices for the most important optimisation variables

Initial design Optimised

design

Opti/Ini

CP3r 40.6 mm 35.06 mm 0.86

CP2r 47.65 mm 45 mm 0.94

𝛽𝑡𝑖𝑝,4 -55.24 deg -53 deg 0.95

CP3Z 1.17 mm 2.59 mm 2.21

CP4Z 4.87 mm 6.98 mm 1.43

CP5r 23.75 mm 26.28 mm 1.1

CP2Z 0.088 mm 0.088 mm 1

𝛽𝑡𝑖𝑝,2 -3.04 deg -3.04 deg 1

CP7r & CP8r 15.67 mm 15.98 mm 1.02

CP4r 32 mm 29.56mm 0.92

𝛽ℎ𝑢𝑏,4 -40.28 deg -32.5 deg 0.8

CP1r 52.23 mm 52.23 mm 1

Ti tip, m, 4 24.24 mm 24.24 mm 1

𝛽𝑡𝑖𝑝,3 -28.29 deg -28.29 deg 1

Ti hub, m, 5 38.98 mm 38.98 mm 1

Ti tip, m, 6 32.73 mm 32.73 mm 1

Figure 11. Mach number distribution on rotor blade of the optimised design (left) and initial design (right).

CONCLUSION This paper describes an optimisation procedure to improve

the geometry of a 7 kW R245Fa radial-inflow turbine. The

procedure integrates the parameterisation of the turbine blade

geometry, 3D CFD analysis, and multi-objective optimisation.

ANSYS-BladeGen was applied to create the 3D geometry

of the flow passage carefully examining the proposed design

against the baseline geometrical data. Generating the required

computational mesh with ANSYS-TurboGrid followed by grid

refinement, CFD simulations are then performed with ANSYS-

CFX in which three-dimensional Reynolds-Averaged Navier-

Stokes equations are solved subject to appropriate boundary

conditions and real gas property (RGP). OptiSlang Dynardo

was used to conduct a multi-objective optimisation and identify

the most relevant input parameters (16 out of 49) in order to

reduce the numerical effort for the optimisation algorithm.

Implementing Evolutionary Algorithm resulted in a Pareto front

to choose a nominal design with 2% higher total-to-static

efficiency and lower thrust loading compared to those of the

initial turbine design. To validate the result, a CFD simulation

of the predicted optimised turbine design was conducted and

the aerodynamic performance of the optimum design was

investigated. The results showed the amount of performance

enhancement is limited and control points on hub curvature

have more influence compared to those control point on blade

thickness and angle distribution while the shroud curvature

profile was unchanged.

ACKNOWLEDGMENTS This research was performed as part of the Australian Solar

Thermal Research Initiative (ASTRI), a project supported by

the Australian Government, through the Australian Renewable

Energy Agency (ARENA).

NOMENCLATURE ALHS Advanced Latin Hypecube Sampling

CoP Coefficient of Prognosis

CP Control point

DoE Design of experiments

EA Evolutionary Algorithm

eff Efficiency

f Objective function

𝐹𝑍 Axial load/force, N

h Enthalpy, kJ/kg

Ini Initial design

LE Leading edge

m Meridional length, %

MOP Metamodel of Optimal Prognosis

N Number of rotor blades

Opti Optimised design

�̇�𝑚 Mass flow rate, kg/s

r Radius/radial, mm

SPEA2 Strength Pareto Evolutionary Algorithm

SS Sum squares

T Temperature, ºC

Ti Thickness, mm

TE Trailing edge

Z Axial direction

Greek symbols β Blade angle, deg

ω Rotational speed, RPM

Subscripts E Error

in Inlet

hub Hub

out Outlet



R Rotor

s Static

S Stator

t Total

T-S Total to static

tip Tip/Shroud

REFERENCES

[1] Fiaschi, D., G. Manfrida, and F. Maraschiello, Design

and performance prediction of radial ORC

turboexpanders. Applied Energy, 2015. 138(0): p. 517-

532.

[2] Sauret, E. and A.S. Rowlands, Candidate radial-inflow

turbines and high-density working fluids for

geothermal power systems. Energy, 2011. 36(7): p.

4460-4467.

[3] Lei ZHANG, Weilin Zhuge, Yangjun Zhang, Jie Peng,

The influence of real gas effects on ice-orc turbine

flow fields. in Proceedings of ASME Turbo Expo:

Turbine Technical Conference and Exposition. 2014.

Düsseldorf, Germany.

[4] Young Min Yang, Byung-Sik Park, Si Woo Lee, Dong

Hyun Lee, Development of a turbo-generator for orc

system with twin radial turbines and gas foil bearings.

in ASME ORC: 3th International Seminar on ORC

Power Systems. 2015. Brussels, Belium.

[5] Sauret, E. and Y. Gu, Three-dimensional off-design

numerical analysis of an organic Rankine cycle radial-

inflow turbine. Applied Energy, 2014. 135(0): p. 202-

211.

[6] Saleh, B., Koglbauer G., Wendland M., Fischer J.,

Working fluids for low-temperature organic Rankine

cycles. Energy, 2007. 32(7): p. 1210-1221.

[7] Tao, G., W. Huaixin, and Z. Shengjun. Fluid Selection

for a Low-Temperature Geothermal Organic Rankine

Cycle by Energy and Exergy. in Power and Energy

Engineering Conference (APPEEC), 2010 Asia-

Pacific. 2010.

[8] Facoa J and Oliveira A. Analysis of energetic, design

and operational criteria when choosing an adequate

working fluid for small ORC systems. in Proceedings

of the ASME 2009 international mechanical

engineering congress & exposition. 2009. Lake Buena

Vista, Florida, USA.

[9] Mack, Y., Goel T., Shyy W., Haftka R., Surrogate

Model-Based Optimization Framework: A Case Study

in Aerospace Design, in evolutionary computation in

dynamic and uncertain environments, S. Yang, Y.-S.

Ong, and Y. Jin, Editors. 2007.

[10] Casey, M., F. Gersbach, and C. Robinson, An

Optimization Technique for Radial Compressor

Impellers, in ASME Turbo Expo 2008: Power for

Land, Sea, and Air. 2008, ASME: Berlin, Germany. p.

pp. 2401-2411.

[11] Qiang, Z. and M. Chaochen. Multiple-objective

aerodynamic optimization design of a radial air

turbine impeller. in Remote Sensing, Environment and

Transportation Engineering (RSETE), 2011

International Conference on. 2011.

[12] Abdus Samad, Kwang-Yong Kim, and K.-S. Lee.

Multi-objective optimization of a turbomachinery

blade using nsga-ii. in 5th Joint ASME/JSME Fluids

Engineering Conference. 2007. San Diego, California

USA.

[13] Ronan M. Kavanagh, Geoffrey T. Parks, and M.

Obana. Multi-objective optimisation of the humid air

turbine. In ASME Turbo expo 2007: Power for Land,

Sea and Air. 2007. Montreal, Canada.

[14] Schiffmann, J. and D. Favrat, Design, experimental

investigation and multi-objective optimization of a

small-scale radial compressor for heat pump

applications. Energy, 2010. 35(1): p. 436-450.

[15] Dirk Roos, Kevin Cremanns, and t. Jasper, Probability

and variance-based stochastic design optimization of

a radial compressor concerning fluid-structure

interaction, in VI International Conference on

Adaptive Modeling and Simulation. 2013: Parice,

France.

[16] Mohsen Modir Shanechi, Mostafa Odabaee, and K.

Hooman. Optimisation of a High Pressure Ratio

Radial-Inflow Turbine: Coupled CFD-FE Analysis. in

ASME Turbo Expo 2015: Turbine Technical

Conference and Exposition. 2015. Montreal, Quebec,

Canada.

[17] Lasse Mueller, Zuheyr Alsalihi, and T. Verstraete,

Multidisciplinary Optimization of a Turbocharger

Radial Turbine. Journal of Turbomachinery, 2012.

135(2): p. 9.

[18] Pierret, S. and R.A. Van den Braembussche,

Turbomachinery Blade Design Using a Navier–Stokes

Solver and Artificial Neural Network. Journal of

Turbomachinery, 1999. 121(2): p. 326-332.

[19] Sasaki, S. Obayashi, and H.J. Kim, Evolutionary

Algorithm vs. Adjoint Method Applied to SST Shape

Optimization., in In The Annual Conference of CFD

Society of Canada. 2001: Waterloo.

[20] Shahpar. A Comparative Study of Optimisation

Methods for Aerodynamic Design of Turbomachinery

Blades. in ASME Turbo Expo 2000: Power for Land,

Sea, and Air. 2000. Munich, Germany.

[21] Trigg, M.A., G.R. Tubby, and A.G. Sheard, Automatic

Genetic Optimization Approach to Two-Dimensional

Blade Profile Design for Steam Turbines. Journal of

Turbomachinery, 1999. 121(1): p. 11-17.

[22] Oyama, A. Multidisciplinary Optimization Of

Transonic Wing Design Based On Evolutionary

Algorithms Coupled With CFD Solver. in Proceedings

of European Congress on Computational Methods in

Applied Sciences and Engineering. 2000.

[23] ANSYS 15.0 Theory Guide.



[24] Ansys 16.1 CFX-Solver Theory Guide. 2015.

[25] Rocha, P.A.C., Rocha H. H. B., Carneiro F. O. M.,

Vieira da Silva, M. E., Bueno A. V., k–ω SST (shear

stress transport) turbulence model calibration: A case

study on a small scale horizontal axis wind turbine.

Energy, 2014. 65(0): p. 412-418.

[26] Louda, P., Savcek P., Fort J., Furst J., halama J., Kozel

K., Numerical simulation of turbine cascade flow with

blade-fluid heat exchange. Applied Mathematics and

Computation, 2013. 219(13): p. 7206-7214.

[27] Lemmon, E.W., M.L. Huber, and M.O. McLinden,

NIST Standard Reference Database 23: Reference

Fluid Thermodynamic and Transport Properties-

REFPROP, Version 9.1,. 2013, National Institute of

Standards and Technology, Standard Reference Data

Programm, Gaithersburg.

[28] Seong Gu Kim, Yoonhan Ahn, Jekyoung Lee, Jeong Ik

Lee, Yacine Addad, Bockseong Ko, Numerical

investigation of a centrifugal compressor for

supercritical co2 as a working fluid. in Proceedings of

ASME Turbo Expo 2014: Turbine Technical

Conference and Exposition. 2014. Düsseldorf,

Germany.

[29] Odabaee, M., E. Sauret, and K. Hooman, CFD

Simulation of a Supercritical Carbon Dioxide Radial-

Inflow Turbine, Comparing the Results of Using Real

Gas Equation of Estate and Real Gas Property File, in

The 2nd Australasian Conference on Computational

Mechanics. 2015: Brisbane, Australia.

[30] Roos, D., T. Most, J. F. Unger, J. Will, Advanced

surrogate models within the robustness evaluation, in

Proc. Weimarer Optimierungs- und Stochastiktage.

2007: Weimar,Germany,.

[31] Most, T. and J. Will, Metamodel of Optimal Prognosis

- an automatic approach for variable reduction and

optimal metamodel selection, in Proc. Weimarer

Optimierungs- und Stochastiktage 5.0,. 2008: Weimar,

Germany,.

[32] Dynardo GmbH, W., Methods for multi-disciplinary

optimization and robustness analysis. 2015.

[33] Huntington, D.E. and C.S. Lyrintzis, Improvements to

and limitations of Latin hypercube sampling.

Probabilistic Engineering Mechanics, 1998. 13(4): p.

245-253.

[34] Collette, Y. and P. Siarry, Multiobjective Optimization:

Principles and Case Studies. 2003, New York:

Springer.

[35] Coello, C., Carlos L., Gary B., Van V., David A.,

Evolutionary Algorithms for Solving Multi-Objective

Problems. 2007: Springer.

[36] Iverson, B.D., Conboy, t.M., Pasch, J.J, Kruizenga,

A.M., Supercritical CO2 Brayton cycles for solar-

thermal energy. Applied Energy, 2013. 111(0): p. 957-

970.

[37] Ahn, Y., Bae, S., Kim, M., Cho, S., Baik, S., Lee, J.,

Cha, J., Review of supercritical CO2 power cycle

technology and current status of research and

development. Nuclear Engineering and Technology,

2015. 47(6): p. 647-661.



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