 Open Access
 Total Downloads : 278
 Authors : Shadreck M. Situmbeko, Freddie L. Inambao
 Paper ID : IJERTV5IS070212
 Volume & Issue : Volume 05, Issue 07 (July 2016)
 Published (First Online): 03082016
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Small Scale Axial Turbine Preliminary Design and Modelling
Shadreck M. Situmbeko University of Botswana, Gaborone, Botswana; University of KwaZuluNatal, Durban, RSA;
Freddie L. Inambao University of KwaZuluNatal, Durban, RSA;
Abstract Purpose: This paper presents the preliminary design and modelling of an axial turbine suitable for use in a small to medium level, low temperature, solar thermal, organic Rankine cycle (ORC).The work involves thermodynamic and geometrical design and analyses. Empirical loss correlations are
m mass flow rate (m_dot in EES code) P pressure
PR pressure ratio
Q conductive heat flux
r mean blade radius (m)
used to account for the different kinds of losses. The engineering equation solver (EES) is used to perform the thermodynamic Rr
rotor degree of reaction (also Rs in EES code)
analysis. 2D and 3D computational fluid dynamics (CFD) simulation and the aerofoil design are not done at this stage as they require specialized CFD software. The work is meant to contribute towards the development of optimal costeffective turbine expanders suitable for small to medium sized operation at low to medium temperatures. There is not sufficient evidence to show that significant research and development work has been done with regard to turbomachinery design and development for small to medium size low temperature organic Rankine cycle (ORC) systems. Most turbine manufacturers and developers put more emphasis on larger scale models in the Megawatts (MW) ranges while most researchers who have shown interest in microscale operations in the low temperature applications have concentrated their efforts more on thermodynamic studies regarding the power cycle, and on the proper rules for the selection of the working fluids, with special attention to the power plant efficiency; others have made attempts at adaptation and modification of other equipment, especially positive displacement machines, for use as ORC expanders. A turbine design suitable for small scale and low temperature operation based on the ORC thermodynamic cycle is required because the operating conditions such as speed, flow rate, pressure ratio, etc. are quite different from those of conventional steam and gas turbines; also the properties of the organic fluids used as working fluids are different from those of the conventional steam or fossilfuelgas mixtures.
Keywords: ORC thermodynamic cycle, preliminary design and modelling, thermodynamic and geometrical design, EES
Paper type: Research Paper
Nomenclature
Roman symbols
b blade height
cp isobaric specific heat capacity d mean diameter
e internal energy per unit mass of the medium
G gravitational acceleration, electromagnetic acceleration, etc.
h specific (static) enthalpy (J/kg) I rothalpy
I identity matric equals the kronecker unit tensor k kinetic energy per unit mass of the medium
Rn nozzle degree of reaction

entropy

time

temperature

blade velocity (m/s)
U fluid velocity vector

absolute fluid velocity (m/s) Va axial component of velocity V
Vu tangential component of velocity V

relative velocity of fluid flow to moving blades (m/s)
Ws specific shaft work
w specific shaft work
W t shaft work; turbine work
Greek symbols
absolute flow angle
relative flow angle
partial differential operator
flow coefficient
tt totaltototal efficiency (eta_tt in EES code) ts totaltostatic efficiency (eta_ts in EES code) tangential (circumferential) component
specific mass; density
stress tensor
shaft angular velocity (rad/s)
work coefficient (also blade loading)
mathematical operators
gradient operator
numbers

inlet to machine; inlet to nozzle blades

outlet from machine; inlet to rotor blades

outlet from rotor blades


stagnation state at station 1

stagnation state at station 2
02rel relative stagnation state at station 2 03rel relative stagnation state at station 3
2 static state at station 2 after an isentropic expansion
in the nozzle
3 static state at station 3 after an isentropic expansion through entire stage
3 static state at station 3 after an isentropic expansion in the rotor blades only
03 relative stagnation state at station 3 after an isentropic expansion through entire stage

INTRODUCTION
In this paper we present work done on the research and development of a turbine suitable for a low temperature solar thermal conversion cycle based on the organic Rankine cycle (ORC). The turbine is the single most critical component in a thermal conversion cycle. The ideal solution should be characterized by maximum efficiency, small footprint, and

THEORY OF TURBOMACHINERY
Fluid dynamics and hence turbomachinery theory is based on three fundamental principles of conservation of mass (continuity), conservation of momentum and conservation of energy, represented by the following equations [2]:
conservation of mass (continuity):
+ () = 0 (1)
conservation of momentum:
U + (UU + PI ) G = 0 (2)
t
conservation of energy:
(e+k) + (U (e + P + k) U + Q) G U = 0
minimum shaft speed (Cooper et al, 2010). Although the t
research considered all the three possible architectures: single stage radial turbine cantilever type; single stage radial
(3)
turbine Ninety Degrees InFlow Radial turbine (90o IFR); and single stage axial turbine, this paper only presents findings on the latter.
The turbine design process can be broken down into three stages:

Preliminary Design (PD);

Meanline/Streamline (1D/2D) Analysis and Optimization

Profiling, 3D Blade Design, 3D Modelling and Analysis
Preliminary Design involves finding the optimal flow path, number of stages and distribution of geometrical parameters (heights and angles) based on the given thermodynamic conditions at turbine inlet and outlet. This process can further be subdivided into two tasks:

initial enthalpy drop distribution: this entails determining the optimal number of stages and appropriately distributing the enthalpy drop between them and finding the first approximation of flow path geometry paths; and

adjusting design calculations (inverse calculation task): this entails calculation of turbine main performance characteristics as well as exact thermodynamic and kinetic parameters basing on initial enthalpy drop distribution results.
Initial design parameters are the inlet working fluid conditions (pressure, temperature, and enthalpy), outlet pressure, mass flow rate and rotational speed.
To fully develop a final working turbine model, the following factors are of paramount importance:

manufacturing and material specifications of the rotor and nozzle;

structural and aerodynamic design of the rotor and nozzle; and

specifications of the inlet and outlet parameters such as pressures and temperatures.
The work done by a turbomachine can be represented by the Euler turbine equation which can be written as (Ingram, 2009):
W t = m (r2V2 r1V1) (4)
where m is the mass flow rate, is the shaft angular velocity, r is the mean blade radis, V is the working fluid flow velocity, while subscripts 1, 2 and represent the inlet
and outlet to the machine, and tangential (circumferential) component respectively.
Velocity Triangles and Mollier diagrams are used to aid the analysis of the turbomachinery; typically the velocity triangle is a representation of the equation V = U + W at each station, that is, entry to nozzle, and entry and exit to rotor;
where V is absolute fluid velocity, U is blade velocity and W is relative velocity of fluid flow to moving blades; refer to figure 1:
Figure 1: velocity diagram
The Mollier diagram is a plot of enthalpy against entropy for a process in which one property usually pressure or temperature is kept constant [4]; pertaining to turbine expansion process, the mollier diagram aids in visualizing the isentropic and real expansion processes as well as the stagnation and static states of the working fluid; figure 2 shows a typical expansion process on a mollier diagram.
Thus rothalpy (rotational enthalpy) is conserved between two stations in a rotating reference in any turbomachinery:
I2 = I3 (7)
Stagnation enthalpy is conserved between two points in a fluid flow stream in a nonrotating reference system:
h01 = h02 (8)
The degree of reaction is expressed as the relative pressure or enthalpy drop in the nozzle or rotor blades to that of the stage:
Rotor degree of reaction:
R = static enthalpy drop in rotor stagnation enthalpy drop in stage
Nozzle degree of reaction:
R = static enthalpy drop in nozzle stagnation enthalpy drop in stage


AXIAL FLOW TURBINE MODEL
(9)
(10)
Figure 2: mollier diagram showing a typical expansion process
Stagnation state is represented by state parameters designated as P0 for stagnation pressure, T0 for stagnation temperature, and h0 for stagnation enthalpy; stagnation pressure is a pressure at a state corresponding to zero velocity, a stagnation state, which is representative of an adiabatic throttling process. The throttling process is a representation of flow through inlets, nozzles, stationary turbomachinery blades, and the use of stagnation pressure as a measure of loss is a practice that has widespread application. Stagnation pressure is a key variable in propulsion and power systems.
The stagnation pressure at a given state is defined by the enthalpy equation:
Description
The fluid flow in an axial turbine is essentially in a direction parallel to the axis of rotation of the machine. Axial turbines usually have several stages such that each stage only handles a moderate pressure or enthalpy drop. Figure 3 shows a single stage axial turbine rotor.
0
0
h = h + V2
2
(5)
where: 0 is the stagnation enthalpy (J/kg); h is the static enthalpy (J/kg); and V is the fluid speed (m/s)
Rothalpy is a function/property that remains constant throughout a rotating machine, that is, in an adiabatic irreversible process relative to the rotating component [5]. It is defined by the equation:
Figure 3: single stage axial turbine rotor
For a single stage the diameter will usually be the same at
I = h + W2 U2
(6)
the turbine inlet and outlet and as such the blade speed
2 2 remains constant along a flow path; and a combined velocity
where h is static enthalpy, W is the relative velocity of the triangle can be drawn as shown in figure 4. fluid, and U is the blade speed.
Figure 4: blade arrangement and velocity triangles
Mathematical Model
With reference to figures 4 and 5 the following set of equations can be written for the single stage axial turbine:
Figure 5: Mollier diagram for an axial turbine stage [6]
The work output per unit mass flow is given by:
w = U (Vu2 + Vu3) = U Va (tan2 + tan3) = U Va
The bladeloading coefficient is used to express work capacity of the stage. It is defined as the ratio of the specific work of the stage to the square of the blade velocity:
2
2
(tan2 + tan3) (11)
= w U
(12)
Working Fluid
Mass flow rate
Inlet Pressure
Inlet Temperature
[kg/s] [Pa] [C] R245fa
0.909
810600
80.99
R134a
0.226
810600
80.99
nbutane
0.420
1010000
80.03
isobutane
0.459
1010000
66.82
Working Fluid
Mass flow rate
Inlet Pressure
Inlet Temperature
[kg/s] [Pa] [C] R245fa
0.909
810600
80.99
R134a
0.226
810600
80.99
nbutane
0.420
1010000
80.03
isobutane
0.459
1010000
66.82
The flow coefficient, , is the ratio of the axial component of the inlet flow velocity to the blade speed:
Table 1: axial turbine model revised inlet conditions
= Va
U
Computer Simulations
(13)
rotor exit temperature (oC)
rotor exit temperature (oC)
Simulations were performed using the engineering equation solver (EES), (Klein, 2014); Soderbergs loss correlations were used (Dixon, 1998). As no convergence could be attained with the given mass flow rates, i.e. from the evaporator model, (Situmbeko and Inambao, 2015), the first simulation was to determine the lowest feasible mass flow rates for all the working fluids by varying the mas flow rates from 0.1 to 2 kg/s; the results showed 0.459 kg/s (instead of 0.241) for isobutene, 0.420 kg/s (instead of 0.207) for n butane, 0.226 kg/s (instead of 0.396) for R134a and 0.909 kg/s (instead of 0.396) for R245fa. Using these new figures the input conditions are modified and then the simulations progressed; the revised inlet conditions are shown in the following table 1:
Three sets of simulations were conducted:
Simulation 1: Rotor exit static pressure was varied within the feasible pressure range and the results are shown in figures 6 and 7; convergence for R245fa could only be attained for pressures 350 to 360 kPa; however, since this range happened to yield higher totaltototal efficiencies, see figure 8, the rotor exit pressure was set constant at 355 kPa for the remainder of the simulations.
60
50
40
30
20
R134a
nbutane isobutane
60
50
40
30
20
R134a
nbutane isobutane
360 380 400 420 440 460 480 500
rotor exit pressure (kPa)
360 380 400 420 440 460 480 500
rotor exit pressure (kPa)
10
0
10
0
51.2
51.2
rotor exit temperature (oC)
rotor exit temperature (oC)
Figure 6: axial turbine model rotor exit – temperature versus pressure
R245fa Simulation 1 Results
R245fa Simulation 1 Results
51.0
50.8
50.6
50.4
51.0
50.8
50.6
50.4
348.0
350.0
352.5
355.0
348.0
350.0
352.5
355.0
rotor exit pressure (kPa)
rotor exit pressure (kPa)
Figure 7: axial turbine model rotor exit – temperature versus pressure for R245fa
Note: The results for nbutane and isobutene appear superimposed in figure 8, although the results for isobutene are slightly superior.
96%
94%92%
90%
88%
86%
84%
82%
80%
78%
76%
R134a
nbutane isobutane R134a (ts)
nbutane (ts)
isobutane (ts)
96%
94%
92%
90%
88%
86%
84%
82%
80%
78%
76%
R134a
nbutane isobutane R134a (ts)
nbutane (ts)
isobutane (ts)
360 380 400 420 440 460 480 500
rotor exit pressure (kPa)
360 380 400 420 440 460 480 500
rotor exit pressure (kPa)
efficiency
efficiency
Figure 8: axial turbine model efficiency versus rotor exit pressure
(ts is for totaltostatic; other series are for totaltototal)
machine speed (rpm)
machine speed (rpm)
With the rotor exit pressure set constant at 355 kPa, the rotor diameter was varied from 26 mm to 160 mm as a way to optimize the machine speed to a lower acceptable level. Results of these simulations are shown in figure 9; from the results it can be seen that any speed between 5000 rpm and
15000 rpm could be considered acceptable; however the speed was set at 20000 rpm as had been done with the radial turbine model (results will be presented in a separate publication). The final optimal results are shown in table 2 and velocity triangles of figures 10 to 13.
70000
60000
50000
40000
30000
20000
R245fa
R134a
nbutane isobutane
70000
60000
50000
40000
30000
20000
R245fa
R134a
nbutane isobutane
10000
0
10000
0
0.026 0.04 0.06 0.08 0.1 0.12 0.14 0.16
rotor diameter (mm)
0.026 0.04 0.06 0.08 0.1 0.12 0.14 0.16
rotor diameter (mm)
Figure 9: axial turbine model machine speed versus rotor diameter
Table 2: axial turbine model simulation results
WF$
m_dot
P_1
P_2
P_3
T_1
T_2
T_3
eta_ts
eta_tt
PR
[kg/s] [Pa] [Pa] [Pa] [C] [C] [C] [] [] R245fa
2.061
810600
356544
355000
80.99
62.67
61.58
0.8397
0.92
1.777
R134a
1.77
810600
356633
355000
80.99
65.28
63.91
0.8348
0.9196
1.896
nbutane
1.627
1010000
355929
355000
80.03
59.83
59.11
0.863
0.9222
2.226
isobutane
1.657
1010000
355998
355000
66.82
46.23
45.48
0.8632
0.9223
2.211
WF$
C_1
C_2
C_3
U
W_2
W_3
Ma_1
Ma_2
Ma_3
Ma_2rel
Ma_3rel
[m/s] [m/s] [m/s] [m/s] [m/s] [m/s] R245fa
44.76
138.2
107.5
55.95
111.9
121.2
0.3478
1.001
0.7809
0.81
0.8803
R134a
48.3
144.6
110.2
60.37
115.1
125.7
0.2932
0.862
0.6586
0.686
0.7509
nbutane
50.37
184.1
156.1
62.97
159.9
168.3
0.2633
0.8666
0.7358
0.753
0.7934
isobutane
49.92
182.6
154.9
62.41
158.6
167
0.2671
0.8772
0.7451
0.762
0.8033
WF$
rpm
d
b
R_s
alpha_1
alpha_2
alpha_3
beta_2
beta_3
[/min] [m] [m] [deg] [deg] [deg] [deg] [deg] R245fa
20000
0.04646
0.00697
0.1133
0
38.88
0
15.97
27.49
R134a
20000
0.05013
0.00752
0.1204
0
40.33
0
16.76
28.71
nbutane
20000
0.05229
0.00784
0.08103
0
32.01
0
12.51
21.96
isobutane
20000
0.05182
0.00777
0.08094
0
31.99
0
12.5
21.95
Figure 10: axial turbine velocity triangles for R245fa Figure 11: axial turbine velocity triangles for R134a
Figure 12: axial turbine velocity triangles for nbutane
Figure 13: axial turbines velocity triangles for isobutene

DISCUSSIONS AND CONCLUSIONS

The paper has presented the preliminary design models for axial turbines suitable for a 10 kWe low temperature organic Rankine cycle. The preliminary design has been presented in terms of geometric parameters of flow angles, blade diameters and heights; the preliminary design also includes thermodynamic parameters of stagnation and static pressures, temperatures and enthalpys; the thermodynamic analyses were conducted within the cycle temperature ranges of the evaporator and condenser. Although the presented design models are not complete, this work has shown that small turbines for low temperature cycles are a feasible design option. The turbine preliminary design parameters for the 10 kWe turbine model after parametric optimization are listed in the table 2.
Efficiency: in terms of totaltototal efficiency all the four working fluids performed well of course with varying pressure ratios, mass flow rates and turbines sizes; however when all these factors are taken into account: R245fa requires the least pressure ratio, higher mass flow are and smaller turbine size. R134a performs second best in terms of smaller pressure ratio and smaller turbine size with a remarkable lower (than R245fa) mass flow rate. The performance of the other remaining two working fluids, isobutane and nbutane, is almost a tie, with isobutane having a slighter edge.
In terms of Mach numbers, the flow changes from subsonic to transonic status for all four working fluids but does not extend beyond the sonic stage. This implies that a more detailed study of the blade is required to determine whether the flow passages need to transition from convergent to diergent at any point in the flow passages.
To fully complete the turbine design task it is necessary to employ CFD and FEA analysis and modelling of the detailed blade and nozzle geometry and flow profile design. This would be followed by providing material and manufacturing specifications for prototype construction and testing. AxSTREAM software suite by SoftInWay Inc. is a good package for turbine CFD modelling.
REFERENCES

Cooper, D., Baines, N., Sharp, N. (2010), Organic Rankine cycle Turbine For Exhaust Energy Recovery In A Heavy Truck Engine, Concepts ETI, Inc.

http://web.stanford.edu/~cantwell/AA200_Course_Material/AA200_Co urse_Notes/AA200_Ch_06_The_Conservation_equations.pdf; accessed August 14, 2014

Ingram, G. (2009), Basic Concepts in Turbomachinery, Ventus Publishing ApS, ISBN 9788776814359.

http://dictionary.reference.com/browse/mollier+diagram; accessed February 10, 2015.

http://www.answers.com/Q/What_is_the_rothalpy; accessed February 10, 2015.

Dekker, M (2003), Chapter 7 Axial Flow and Radial Flow Gas Turbines, in Turbomachinery Design and Theory, accessed at http://www.himech.files.wordpress.com/2010/02/dke672_ch7.pdf

Klein S.A., and Alvarado F.L. (2014) Engineering Equation Solver for Microsoft Windows Operating Systems, FChart Software, Middleton, USA.

Dixon S.L. (1978, 1998), Fluid mechanics and thermodynamics of turbomachinery, Elsevier ButterworthHeinemann, 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA, Linacre House, Jordan Hill, Oxford OX2 8DP, UK, ISBN: 0750678704, pp 98100

Situmbeko, S.M. and Inambao, F.L. (2015), Heat Exchanger Modelling for Solar Organic Rankine Cycle, Int. J. of Thermal & Environmental Engineering, Vol. 9 No. 1; pp 716