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Proposal Design Procedure and Preliminary Simulation of Turbo Expander for
Small Size (2?10 kW) Organic Rankine Cycle (ORC)
Article · November 2014
DOI: 10.1115/IMECE2014-36130
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Proceedings of the International Mechanical Engineering Conference &
Exposition, IMECE2014
November 14-20, 2014, Montreal, Canada
IMECE2014-36130
PROPOSAL DESIGN PROCEDURE AND PRELIMINARY SIMULATION OF TURBO
EXPANDER FOR SMALL SIZE (2-10 KW) ORGANIC RANKINE CYCLE (ORC)
Roberto Capata
Department of Mechanical and Aerospace
Engineering, University of Roma “Sapienza”
Roma, Italy
ABSTRACT
Currently, one of the leading technologies for the
"energy recovery" adopting a Rankine cycle (ORC)
with organic fluids. ORC system operates like a
conventional Rankine cycle, but instead of
steam/water, uses an organic fluid. This change
allows to convert low temperature heat and generate,
where required, electricity. A large amount of studies
were carried out to identify the most suitable fluids,
system parameters and the various configurations. In
reality, most ORC systems are designed and
manufactured for recovery of thermal energy from
various sources but at “large power rating” (exhaust
gas turbines, internal combustion engines, geothermal
sources, large melting furnaces, biomass, solar, etc.)
from where it is possible to produce electric energy
(30kW ÷ 300kW), but for the application of this
system for small nominal power, as well as the
exhaust gases of internal combustion engines (car
sedan or town, ships, etc.) or smaller heat
exchangers, there are very few applications. The aim
of this work is to design a turbo-expander that meets
system requirements: low pressure, small size, low
mass flow rates.
The Expander must be adaptable to a small ORC
system utilizing gas of a diesel engine or small gas
turbine to produce 2-10 kW of electricity. The
temperature and pressure of the exhaust gases, in this
case study (400-600° C and at a pressure of 2 bar),
imposes a limit on the use of an organic fluid and on
the net power that can be produced. In addition to
water, organic fluids such as CO2, R134a and R245fa
have been considered. Once the fluid has been chosen
Gustavo Hernandez
Department of Mechanical and Aerospace
Engineering, University of Roma “Sapienza”
Roma, Italy
operating, the turbine characteristics (dimensions,
temperature, input and output pressure ratio, etc.)
have been calculated and an attempt to find the
"nearly-optimal" has been carried out. The detailed
design of radial Expander is presented and discussed.
An initial thermo-mechanical performance study is
carried out to verify structural tension and possible
displacement. Next step of the research here
proposed will be the CFD simulation to improve or
modify the chosen blade profile.
INTRODUCTION
The Organic Rankine Cycle (ORC) converts thermal
energy to mechanical shaft power.
The benefit of ORC systems is that they recover
useful energy, often as electrical output, from lowenergy sources such as the low-pressure steam
associated with steam-driven turbines for electricity
generation [1,2,3,4,5]. The efficiency of an ORC is
typically between 10 and 20%, depending on
temperature levels and availability of a suitably
matched fluid [1.2].
The properties of the chosen working fluid have a
significant impact on the performance of the ORC
cycle. Appropriate thermodynamic properties can
result in higher cycle performance and low costs. The
ideal organic working fluid should have the following
general characteristics [1,8, 13]:
 High molecular weight;
 Low enthalpy;
 High critical pressure and temperature, to
allow engine operating temperature to
absorb all the heat available up to that
temperature;
Low operating pressure, to avoid explosion
or rupture and avoid negative impact on the
reliability of the cycle;
 Small specific volume, in its gaseous state,
to avoid the need of large and costly
turbines, evaporators, and condensers;
 Higher pressure inside condenser to prevent
air inflow into the system;
 Low heat latency;
 Non-flammable,
corrosive
or
toxic
characteristics;
 Low environmental impact.
The principal component of the ORC system is the
expander. There are different types: Scroll, Vane,
Piston, Screw and Turbine. Most of ORC systems
have been developed with scroll and vane type,
thanks to their better efficiency and low cost, but
researches are made to improve the turbo-expander
[1,3,5].
The aim of the paper is to present or propose a
possible design procedure to develop a typical turboexpander, to cover the gap at small scale and power
range. A research of small ORC systems (between 5
kW and 30 kW) and “micro expander” has been
carried out.
Generally, all ORC systems are designed for
industrial applications, where the amount of energy
produced from industrial processes is greater than 30
kW. Most of the problems of such small scale
systems derive from the economic reasons and
feasibility
and technological limitations. Some
models are available with different features [2,12].
Making a comparison with these applications
available, we set the maximum rotation speed of the
rotor n = 33000 rpm (about 3500 rad/s). As already
mentioned, the main properties of ORC systems is
the use of organic fluids instead of water/steam
normally used in the Rankine cycle; but it is not
unusual to find water as working fluid. As a result,
the systems are called RC as well (because of their
reduced size). The ORC system applications are
many; in reality they are commonly used on:




biomass power plants;
geothermal plants;
solar thermal power stations.
The most application developed for an ORC system
is the so-called "waste heat recovery" [1,3,4,5,
12,13]. The term "waste heat recovery" may be used
to describe the use of any heat rejected to the
environment generally. The ORC system is an
interesting option for heat recovery in the
temperature range between 150° C to 200º C,
especially if no other use for the waste heat is
available on the site.
Our goal is to fill the gap for this range at low
nominal power rating, studying and realizing an ORC
energy recovery system (1÷15 kW) compact enough
to be suitable for vehicular applications.
1. THE ORC RECOVERY ENERGY SYSTEM
1.1 ORC system overview
An Organic Rankine Cycle (ORC) is similar to a
conventional steam power plant, with the exception
of the working fluid, an organic, high molecular mass
fluid with a liquid-vapor phase change, or boiling
point, occurring at a lower temperature than the
water-steam phase change. The low-temperature heat
is converted into useful work that can itself be
converted into electricity [1,3,4,5].
The fluid selection depends on the temperatures of
both the thermal source and thermal sink. The ORC
systems generates electricity using very low-T heat
sources (800-400 K). The layout of the proposed
plant in this work is represented in figure 1.
Figure 1: Layout with R-134a
It is a closed cycle plant composed by four (4)
elementary process:
 S3-S4 Compression on a Pump: liquid
working fluid is pressurized by a feed pump.
 S4-S1 Vaporization on a Boiler: liquid
working fluid absorbs thermal energy and
vaporizes into vapor state. The heat
exchange from the heat carrier fluid to the
working fluid is completed via evaporators.


S1-S2 Expansion on Expander: power
producing process. The heat energy of the
working fluid is converted to the mechanical
energy by an expander; then, an alternator
(not represented) converts the mechanical
energy into electricity.
S2-S3 Condensation on Condenser: heatrejecting process. The vapor fluid condenses
into liquid state.
2. THERMODYNAMIC ANALYSIS OF THE
ORC
2.1 Simulations
This simulation is aimed at a detailed study of the
cycle sensitivity to the different process parameters
variations: a sensitivity analysis provides a very
useful information and suggestions, before
performing an optimization procedure. We will
descrive the following simulation:
 Operating fluid:
R134a organic fluid.
 Case:
ORC plant, R134a, with at least Pnet = 2 kW,
thermal source: Diesel ICE
Data and design constraints
As it has been repeatedly pointed out, the main
objective of this paper is to study the feasibility of an
ORC, which recovers energy from the heat contained
in the exhaust gas of a diesel engine [1,5,9], usually
adopted by commercial passenger sedans (typical
1400 cc Ford engine), to produce electricity. The
engine specifications are known and all exhaust gas
data are available [1]:




mass flow rate [kg/s];
temperature [K];
pressure [Pa];
composition.
For the cooling process, water at 288K and 200 kPa
is chosen for this initial approach (the water is the
most common and available fluid in almost every
system). At the moment, the water side process and
configuration and devices do not concern to this
study.
As general rule, low pressure levels are maintained to
avoid possible explosions or breaking material fails.
On the other hand, this allow to use less resistant and
more economic materials in the manufacture of the
system.
Low temperature levels are maintained lower than
353 K, for the same reason previously explained.
The mass flow rate of process fluid must not exceed
0.5 kg/s (design constraint); the use of big fluid tanks,
which increases the size of the entire plant, is so
avoided.
If it is possible, during the design procedure, we try
to respect the limit the rotational velocity to 30000
rpm (about 3500 rad/s).
Table 1: Thermal Source Main Data
DIESEL:
0.15
Mass flow rate [kg/s]:
845
Exhausts temperature [K]:
200
Pressure [Pa]:
CO=0.041;
Average Composition:
CO2=2.74;
(per cent by volume)
O2=17.14,
CxHy = < 0.03
2.2 Process simulation with PRO/II®
To analyze the ORC plant performance a steady state
simulation of the plant has been performed, with the
PRO/II® Process Simulator. The software has been
developed by InvensysTM and runs in an interactive
Windows-based GUI environment. This steady-state
simulator performs rigorous mass and energy balances
for a wide range of processes.
3. THE PLANT LAYOUT AND SIMULATIONS
RESULTS
Once the system configuration has been chosen, the
simulation was carried out. In these preliminary
simulations all the elements have been studied and
investigated, to analyze their range of use.
Once the “quasi-optimal” operating conditions have
been set, the system was assembled and then
simulated.
This first part was very important, because it allowed
to set and fix some operating parameters for each
component, fundamental requirements for the
subsequent sensitivity analysis.
The COMPONENTS parameters set are:
Expander:
 outlet pressure
 adiabatic efficiency
 estimated outlet temperature.
Figure 2: Expander properties selection
Condenser:
 hot products temperature (outlet temperature
of the working fluid)
Pump:
 outlet pressure
 efficiency.
Figure 3: Pump properties selection
Boiler:
 cold products temperature
temperature of the working fluid).
(outlet
On the other hand, by analyzing the various incoming
and outgoing flows and the stream connections, from
adopted components, the following parameter set has
been set.
Turbine Inlet (S1):
 temperature;
 pressure;
 mass flow rate;
 fluid composition.
Exhaust gas (S7):
 temperature;
 pressure;
 mass flow rate;
 composition
Cooling water (S6):
 temperature;
 pressure;
 mass flow rate.
Hereafter, the results,
of one of the several
simulations carried out, are reported. The value of the
nominal power was done vary from 1 up to 15 kW.
The table provides all the operating parameters of the
system. At the moment cannot be performed reviews
or comparisons with experimental or actual operating
data: in fact, at this range, there are no operating
systems, but only prototypes or test benches. A sort
of evaluation by simulating the same system with
other codes was carried out. This comparison is not
shown, because the authors believe that the attention
can be shifted on the simulation and not to the project
of turbo-expander
The ORC simulations for the working fluids (R-134a)
are presented in Table 2.
Table 2: ORC with R-134a fluid and Pnet = 3 kW
Inlet gas mass flowrate
Inlet gas pressure
Inlet gas temperature
Outlet gas pressure
R-134a mass flowrate
R-134a T at boiler inlet
R-134a T at expander inlet
R-134a T at expander outlet
R-134a T at condenser outlet
R-134a pressure at boiler inlet
R-134a pressure at expander inlet
R-134a pressure at expander outlet
R-134a pressure at condenser outlet
Power output
Power adsorbed by pump
[kg/s]
[kPa]
[K]
[kPa]
[kg/s]
[K]
[K]
[K]
[K]
[kPa]
[kPa]
[kPa]
[kPa]
[kW]
[kW]
4.
PRELIMINARY
EXPANDER
OF
DESIGN
0.15
200
845
200
0.38
307
333
315
307
1500
1500
950
950
3.3
0.3
THE
Once the energy recovery system thermodynamic
feasibility has been checked, the next step was to
start to design the expander. In this work it is shown
the general procedure to design a 90° IFR (InwardFlow Radial) turbine. The whole design is based on
the ROHLIK’s procedure for a radial turbine design
[14]. The reasons of this choice depend on the fact
that the procedure defined by Rohlik, is one of the
most detailed and described.
By interviewing with various manufacturers (GE,
Siemens, Green Turbine, etc.), they have confirmed,
as far as possible, the use of this procedure. In
addition, we always remember, that in this field, the
screw and scroll expander have been used. Few
papers describe the use or how to design a radial
stages for a steam expander. Our target is to study the
feasibility of this design procedure.
4.1 ROHLIK’s Work
Adopting Rohlik [14] analytic studies on radial
centripetal turbines performance, optimal geometry
for different applications has been calculated, each
one identified by characteristic parameter called
“specific speed” (Ωs).
Ωs
2
On this
losses:
1.
2.
3.
4.
5.
∗
∗
∗
1
∗
∗
∗
(1)
The goal of this procedure is to obtain maximum
efficiency from each family of turbines analyzed and
tested.
Consequently
the
“quasi-optimal”
configuration of the impeller.
4.2 General Procedure
First of all, we have to define the fluid’s states in it
pass through the turbine (Figure 5):
Then, we have to establish the initial assumptions
made to start the design process:
study, we considered five different types of
stator losses,
impeller losses,
tip clearance losses (gap between impeller
and the machine stationary walls in order to
avoid friction losses),
gas leakage on seals and
kinetic energy losses at outlet.
Then we calculate the efficiency of a different variety
of operating turbines, characterized by a “Specific
Speed (Ωs)” between 0.12 and 1.34.
Figure 5: Turbine general scheme





Figure 4: Distribution of Losses along Envelope of
Maximum Total-to-Static Efficiency
The specific speed value provides a general
indication about the geometry of the turbine: at low
values of this parameter is associated with relatively
small areas of transition, while higher values are
associated with larger areas of transition. In addition,
this characteristic parameter can give an idea of
maximum efficiency that is possible to reach.

The outlet nozzle angle is taken as the
optimal value determined by ROHLIK:
16°;
The meridian diameter of the rotor outlet
section to rotor inlet diameter ratio is:
0,49
(2);
The rotor inlet beta angle is fixed at 90°,
imposed by the material characteristics and
gas temperature:
90°
→
1;
Rotor outlet 2 is assumed zero (axial flow
at outlet)
90°
→
0;
Rotor outlet relative velocity at midspan
(W2mid) is two times the rotor inlet relative
2
(3);
velocity (W1),
With these initial input, the “Spouting Velocity
(CSP)” has been calculated. Assuming an initial R
equal to 0.5, it is possible to calculate T1 and P1, that
represent the inlet fluid conditions.
Now, it is possible to find fluid density on state “1”
(ρ1) and then Q1 Remembering the Euler work
equation and neglecting the dynamic enthalpy, as an
initial approach, the value of peripheral velocity U1
can be obtained:
D2shroud = D2mid +b2; D2hub = D2mid – b2
∙
→
(4)
Then U2hub and U2shroud:
with U1, the rotor inlet diameter has so calculated:
∙
∙
→
(8)
;
(9)
(5)
With 1 and from geometry of the velocity triangle
(Figure 6) we obtain the rest of the kinematic
parameters.
Flow coefficients (ϕ) at outlet section can be
computed. From geometrical considerations, it is
possible to obtain the rest of the operative data for
hub and shroud. After that, it is necessary to verify
the principal limits that ROHLIK indicates on his
work, that are:
0,4 ;
0,7
The ROHLIK’s specific velocity (equation proposed
on Dixon’s book [16]) is:
/
2,11 ∙
/
∙∗
(10)
Figure 6: General inlet velocity triangle
Where c0 is the spouting velocity and:
Then the blade height, at inlet, is computed as:
∙
∙
(6)
∙
Where
is a blockage coefficient that considers
the part of the area occupied by the blade.
Once D1 is known, we compute D2mid from initial
assumption, and then with  and D2mid ,U2mid.
From geometry is possible to determine the rest of
the kinematic parameters at mid-span (figure 7)
section.
∙
;
(11)
This specific velocity is considered only as a
“reference value”, to determine how effective our
procedure is; in any case it is a key parameter on this
study. The new reaction degree at mid-span is
calculated and a second iteration is made, to adjust
the parameters values. The number of blades for the
rotor and stator are calculated as follows:
∙
°
20 ∗ cot
(12)
2
(13)
For nozzle calculation we have assumed:
;
1,3 ;
0,85
(14)
(15)
where:
0,004
Figure 7: General Outlet Velocity Triangle
And the blade height, at outlet, is computed as:
∙
∙
∙
The outlet hub and shroud diameter:
(16)
Finally, the value of α0 and velocity components of
the fluid at nozzle inlet have been computed:
∙
∙
∙
∙ ∙
∙
∙
(17)
(7)
(18)
5. EXPANDER DESIGN RESULTS
Using the procedure, briefly described, the main
geometric parameters for the design of the expander
impeller have been derived. The following results,
are obtained after an accurate "optimization" (maybe
it would be better to define it as iterative optimization
process) of the results, by varying the initial
parameters:
Table 3: Expander design results
Basic Thermodinamic Data
333
T0 [K]
1500
P0 [kPa]
0,0052
Q0 [m3/kg]
327
T1 [K]
1363
p1 [kPa]
0,0057
Q1 [m3/kg]
315
T2 [K]
950
p2 [kPa]
0,0085
Q2 [m3/kg]
Rotor Geometry
0,041
D1 [m]
0,002
b1 [m]
0,020
D2mid [m]
0,006
b2 [m]
0.014
D2hub [m]
0,026
D2shroud [m]
13
Z rotor
Velocity Triangles
42500
 [rpm]
94,5
V1 [m/s]
26,0
W1 [m/s]
90,8
U1 [m/s]
16
1[°]
90
1 [°]
1
1
0,286
1
27,0
V2mid [m/s]
52,0
W2mid [m/s]
44,5
U2mid [m/s]
90
2mid [°]
31
2mid [°]
0
2mid
0,61
2mid
27,0
V2shroud [m/s]
63,6
W2shroud [m/s]
57,6
U2shroud [m/s]
90
2shroud [°]
25
2shroud [°]
0
2shroud
0,47
2shroud
V2hub [m/s]
W2hub [m/s]
U2hub [m/s]
2hub [°]
2hub [°]
2hub
2hub
Nozzle Geometry
D1sta [m]
D0 [m]
b0 [m]
α0 [°]
V0 [m/s]
Zstator
27
41,5
31,4
90
41
0
0,86
0,045
0,058
0,002
21
45,9
11
6. FIRST SIMULATION
Once the procedure of impeller design have been
completed, a drawing, both in 2D and 3D, was
realized. The 3-D geometry of the turbine was
created using a dedicated commercial software
(ANSYS Blademodeler®) in which all the
geometrical data is inserted. The variation of the beta
angle () along the rotor was establish by a spline
curve for every layer (mid, hub and shroud) that can
be configured and modified in the program. The
blade profile chosen for both, the rotor and stator,
was a general NACA profile.
A thermal stress, that varies depending Z coordinates
(axial direction) has been applied. For the
temperature trend, an equation, to achieve the
maximum temperature at the inlet fluid section, and
the minimum one at the outlet, has been used; it is
shown here follows:
T = TIN - z·(1000)
(19)
with z in millimeters.
The results of the distribution of the thermal load is
reported in figure 9. The last consideration is the
material used. In this case a structural steel have been
used, available in the software library, which
corresponded to our hypothesis.
Figure 7: 3D sketch for the expander stator and
impeller
Once the drawing has been completed, the mesh has
been provided. The mesh is composed of 20179
triangular elements (as shown in figure 8)
Figure 9: Thermal load distribution on the impeller.
Figure 8: Impeller mesh
Then, a first and preliminary thermo-structural
simulation has been performed. In our case it was
divided into three successive steps: simple structural
stress, thermal stress and, finally, a global stress, sum
of the previous ones.
In details, the centrifugal stress has been obtained
applying a rotational speed of 3500 rad/s, with the
rotational axis coinciding with the inner cylindrical
surface one.
6. DISCUSSIONS AND RESULTS
As expected, the central part of the rotor is the most
stressed part, due to the centrifugal forces combined
with the thermal load.
Finally, to determine if we are working in safely
conditions, we compute the safety factor (as the yield
stress of the material divided by maximum equivalent
stress). Operating in this way, we obtain satisfactory
results. The value so obtained is close to limit
conditions, but still under the limit imposed by the
material strength.
The following figure illustrate the global stress and
the displacement of the rotor.
Figure 10: Maximum global stress
Figure 12: Final global stress using safety factor
CONCLUSIONS
The objective of this work, as has been mentioned
before, was to verify the feasibility of the system and
to study the opportunity to make a turbo-expander for
these low power rating (2-15 kW).
The authors would like to emphasize this, precisely,
"peculiarities" of their work: study and submit a
design for a small turbo expander for ORC systems.
This analysis was divided into several stages.
A preliminary simulation of the ORC system
performance by the PRO/II® software, varying the
main operative parameters and considering the R134a, as working fluid.
The design procedure of the radial expander has been
completed under a set of specifications, derived by
the previous simulations. In this procedure many
others constraints has been added, always keeping in
mind the main goal of the project: realize a compact
waste energy recover systems, using an “ad hoc”
studied and design turbo expander.
Figure 11: Equivalent Von Mises stress
Finally
the
main
preliminary
geometrical
characteristics have been calculated, and a
preliminary 3D geometry has been created.
Consequently, at this moment, a thermo-structural
analysis has been performed, using FEM methods.
The analysis bring the authors to adopt the material
and to verify, for this specific step of the design
procedure, the structural resistance of the impeller.
The future step will be the CFD analysis, to verify,
and if necessary, modify the blade profile, to
optimize the impeller efficiency.
Once all simulations and expander design are
completed, the final step will be to build a prototype
and test it.
NOMENCLATURE
A
area [m2]
b
Blade height [m]
c
velocity [Dixon reference]
CFD
Computational Fluid Dynamics
D,d
Diameter [m]
ICE
Internal Combustion Engine
GUI
Graphical User Interface
n
rotational speed [rpm]
ORC
Organic Rankine Cycle
p
Pressure [Pa]
P
Net power [W]
Q
Volumetric flow rate [m3/kg]
Grade of reaction
R
U
Blade speed [m/s]
V
Real fluid velocity [m/s]
T
Temperature [K] or [°C]
W
Relative fluid velocity [m/s]
Z
Number of blades
Greek



ψ
ρ
ω
s
angle [°]
angle [°]
Flow coefficient
Stage Loading
Density [kg/m3]
Rotational speed [rpm]
Rohlik specific speed
Subscripts
1
inlet
2
outlet
cond
condenser
REFERENCES
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Turbine Hybrid Veichle Lethe@ At Udr1: The OnBoard Innovative Orc Energy Recovery System –
Feasibility
Analysis”,
IMECE2012-85237,
proceedings of the ASME International Mechanical
Engineering Congress and Exposition IMECE2012,
9-15 November, 2012, Houston, TX, USA.
[2] Johnson I., and Choate W. T., “Waste Heat
Recovery- Technology and Opportunities in U.S.
Industry”, Prepared by: BCS, Incorporated; March
2008
[3] A. Rettig, M. Lagler, T. Lamare, S. Li, V.
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2011.
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(2011) 3301.
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Expander for an ORC Applicable to a Passenger Car
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Korea.
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of
Cogeneration
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