 Open Access
 Total Downloads : 1577
 Authors : Mr. Vimal Patel, Mr. Himanshu Chaudhari
 Paper ID : IJERTV2IS3540
 Volume & Issue : Volume 02, Issue 03 (March 2013)
 Published (First Online): 21032013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Prediction of HType Darrieus Turbine by Single Stream Tube Model for Hydro Dynamic Application
Dr. S.V. Prabhu, Department of Mechanical Engineering,
Indian Institute of Technology, Bombay, Mumbai400076, INDIA
Mr. Vimal Patel, Department of Mechanical Engineering,
National Institute of Technology, Surat, 395007, INDIA
Mr. Himanshu Chaudhari, Department of Mechanical Engineering,
National Institute of Technology, Surat, 395007, INDIA
Abstract
A Hydrodynamic model that can accurately predict the performance of a device can be used to optimize the design parameters more rapidly and at a much lower cost than carrying out the design studies using scale model tests. Tidal turbine models are principally dependent on the Hydrodynamic models developed for wind turbines. These models are crucial for deducing optimum design parameters and also for predicting the performance before fabricating the Darrieus hydro turbine. The method of analysis used is Single stream tube model in that induced velocity is assumed as a constant and it is obtained by actuator disc theory and blade momentum theory. Single stream tube model can predict the coefficient of performance easily before experiment of the turbine. In this paper Comparison of coefficient of power and coefficient of torque by single stream tube model and experimental result, and its strengths and weaknesses are discussed.
Keywords: Low head power generation, Darrieus turbine, Aerodynamic model, VAWT.

Introduction
The Darrieus vertical axis wind turbine concept attracted considerable research interest in the late 1970s and 1980s, but has never competed successfully with horizontal axis wind turbines. In recent years there has been growing interest in Darrieus straight blade hydro turbine for low head application which is based on Darrieus wind turbine.
Figure: 1: Darrieus Hydro Turbine
In 1974 Templin proposed the single stream tube model which is the first and most simple prediction method for the calculation of Aerodynamic performance characteristics of curve blade Darrieus Vertical axis wind turbine [1].Stream tube models are momentum models based on Glauerts Blade element theory[2]. In stream tube models the change in fluid momentum in the flow direction is equated to the stream wise forces on the aerofoil blades.
In this model the entire turbine is assumed to be enclosed within a single stream tube. The objective of the model is to determine the performance coefficient of rotor.

Nomenclature
A Projected frontal area of turbine
C Blade chord
H Height of turbine blade
L blade lift force N Number of blade R Turbine radius
Re Local Reynolds number WC /
a
a
V Induced velocity
V
V
n
n
C t
C t
V or V Chordal velocity component Normal velocity component
W
W

Wake velocity

Relative velocity
Density of fluid
Azimuth position of blade
Angle of attack
C
C
d
C
C
dor
Blade drag coefficient
Reference zeroliftdrag coefficient


Axial Induction Factor
The axial induction factor, a is the fractional decrease in water velocity between the free stream
C Turbine overall drag coefficient F / AV 2
D D
C Rotor drag coefficient F / AV 2
and the rotor plane, so it is defined as [11],
Nc R
DD D a
C Blade lift coefficient
a
2 R V
sin
(1)
l We can define induction factor by reference [5],
V V
n
n
C Normal force coefficient
C Turbine overall power coefficient= P / AV 3
a a
V
(2)
P o
T B
T B

Turbine overall torque coefficient= T / AV 2 R
C
C
t
t
Tangential force coefficient
Wake velocity Zone
Vw
Induced velocity Free stream
zone velocity zone
Va V

Blade drag force
n
n
F Normal force
t
t
F Tangential force
Disk
Figure: 2: Actuator disc model for Darrieus rotor.
The value for
Va can be obtained by Gluert
Angle of attack is angle between relative
Actuator Disk theory [2], the expression of the uniform velocity through the rotor is,
velocity W and tangential velocity t
V
V
from the following expressions:
is obtained
V V VW
a 2
(3)
tan1 Vn
V
(8)
From equation (1) and (2) we can find induced and
t
wake velocity,
Va V (1 a)
(4)
Substituting the values of (6) and (7) in equation (8), And Nondimensional zing the equation
a
a
tan1
sin
(9)
Vw V (1 2a)
(5)
(R / V ) cos
t n
t n

Blade Angle of Attack and Relative
The relative flow velocity (W) can be obtained as,
Velocity
W V 2 V 2
(10)
The flow velocities in the upstream and
Inserting the values of Vt
and Vn
, and non
dimensional zing, one can find velocity ratio as, downstream sides of the Darrieus rotor are constant
as seen in figure 3. From this figure one can observe
W R 2
2 R cos 1
(11)
that the flow is considered to occur in the axial direction. The tangential velocity (or chordal
Va Va Va
Local relative water dynamic pressure (q) is given
velocity) component Vt
(or Vc
) in tangential
by:
direction of blade profile and the normal velocity
component Vn is normal to blade profile. Tangential
q 1 W 2
2
(12)
velocity ( Vt ) and Normal velocity ( Vn ) of blade which is given by [3],

Blade Element Force and Drag CoEfficient
Vt R Va cos
Vn Va sin
V
VN W
V V
(6)
(7)
Since the disk acts as a drag device, the source of drag must be a pressure difference across the disk and this drag manifests itself as thrust loading along the axis normal to the disk. Rewriting N2 in terms of
momentum:
T a
.
.
Fx m(V )
(13)
VW
Figure: 3: Flow velocities of Darrieus hydro turbine.
According to glauerts theory [2] the velocity through a wind mill disk V is the arithmetic mean of
a
a
the undisturbed velocity V and the velocity in the wake. The turbine drag D is given by:
D m(V Va )
D 2 AV (V V )
(14)
(15)
Ct Cl sin Cd cos
Cl
a a
DD
DD
The disk drag coefficient C [4] based on dynamic
C C cos C
Cd
sin
pressure and the disk area is defined as:
D
C
DD 1
AV 2
(16)
n l d
W
V
2
2
a
And from equation (13) and (14)
Figure: 4: Normal and Tangential force coefficient on blade
C 4 V 1
(17)
DD V
Assuming that the instantaneous local blade
C
C
C
C
a
DD
DD
V 1 1 C
(18)
element lift and drag coefficints l
and d
are
Va 4
For structural design purpose, a more convenient
function of angle of attack in steady flow, the normal
n
n
force coefficient C and tangential force coefficient
C
C
t
t
drag coefficient D
is based on the ambient
C are given by following expressions:
dynamic pressure [4]:
D
C
D 1
V 2 A
(19)
Ct Cl sin Cd cos
Cn Cl cos Cd sin
(22)
(23)
2 The net tangential and normal forces defined as:
V
V
2
C C D
(20)
Ft Ct
1 CHW 2
2
(24)
D DD V 1
C
Fn Cn
CHW 2
2
(25)
C DD
(21)
D
D
1 2
1 CDD
4
For a given turbine geometry and rotational
Blade element of chord C is subjected to an elemental normal force dN and a forward thrust force dT given by the relation:
speed, turbine power and rotor drag are calculate using the blade element theory [4]. To calculate the
blade element forces, the local Hydrodynamic angle
dFn CnqCH
dFt Ct qCH
(26)
(27)
of attack and the local relative dynamic pressure are required. The resultant velocity vector, relative
The elemental drag at any blade position as shown in figure 5 is:
vector, relative to the moving blade element, is
dD (dF sin dF cos )d
(28)
n t
n t
resolved into two perpendicular components; one parallel to the span wise and other in blade profile plane as shown in figure 4. The velocity component parallel to the blade span wise has no effect on the blade element Hydrodynamic forces.
The total drag value is obtained by integration on a full revolution (0 2). Thus the total drag of a rotor with N blades of constant chord C is given by the relation:
NCH 2 NCHR 2
2
2
t
t
D q Cn sin Ct cos d
0
(29)
T qC d
B
B
2 0
(33)
Torque coefficient is defined as:
V
Blade
B
C
C
T
T
T 1
V 2 AR
2
(34)
flight path
Va
From equation (34) and (33),
T t
T t
NC 2
Stream
C qC d
2 RV 2
(35)
tube 0
Vw
Figure 5: Blade at azimuth position.
The shaft power is then,
B
B
P T
(36)
Drag coefficient is given by,
For straight blade vertical axis rotor of diameter
D and height H only one part of the total wind kinetic
C
C
D
D
D
1 V 2 A
2
(30)
energy flow is converted into useful shaft power. Maximum possible power of the swept rotor area is:
Put the value of drag D from equation (29).
P 1 V 3 A
(37)
2
2
NC 2
max
C q C sin C cos d
(31)
The power coefficient C
p
p
can be defined as the ratio
DD DV 2 n t
0
of actual power P given by equation to the maximum
For numerical integration of the expression of above equation is divided into a finite number of
max
max
value P given by [5],
surface element having equal increments of azimuth
angle .
P
P
P
C
C
p
max
(38)
max
max

Rotor Torque and Power CoEfficient
Put value of P and P in above equation,
p t
p t
NC 2
The rotor torque is produced by only the
C qC d
2V 3
(39)
0
tangential component of the force on the rotor blade element and in its elemental form, for a single blade element height H and at d azimuth position of the blade the rotor torque is given by:
Coefficient of power for rotor is obtained by integration on a full revolution (02). The relation with coefficient of torque and coefficient of power are given by:
S t
S t
dT CHRqC d
(32)
C C
(40)
P T
P T
Blade torque varies with blade azimuthally angle
a
a
. The total torque for rotor is obtained by integration on a full revolution (0 2).
We can find coefficient of power from above equation for a given turbine geometry and for each specified value of tip speed ratio R / V

Experimental Setup
The setup consists of a Darrieus rotor and structure. The structure is fabricated using studs and mild steel plates. Geometric details of the rotors considered in the present study are given in Table. 1. Darrieus rotor geometry detail is given. Calculation of performance coefficient is based on data for both blade profiles.
Table: 1: Darrieus rotor geometry detail
Sr No.
Blade Profile
D
(mm)
H
(mm)
C
(mm)
V
(m/s)
1
NACA 0018
250
150
100
0.46
2
NACA 4415
370
150
100
0.395
The hydrofoils used in turbine rotors are made from rapid prototype machine. Fibber Reinforced Plastic (FRP) is used to make hydrofoils. The mild steel plates are held in place by means of washers and nuts for easy replacement of different diameter rotors using same structure. Rotors are mounted on two bearings (UC 204, NTN make). A selfaligned bearing is used as upper side support, to avoid unwanted frictional torque arising due to minor misalignment between upper and lower rotor support shaft. A rope brake dynamometer type arrangement is used for measuring torque and subsequently power developed by Darrieus rotor. The accuracy of spring balance used is 10gms. The ultrasonic flow meter used to measure volumetric flow rate of water though the channel. Velocity of water is calculated using the continuity equation by using cross sectional flow area. Cross sectional flow area is measured by scale with least count of 1 mm. Details of the open channels used in the present study are given in Table.
Table 2: Details of the open channels used
Channel
Channel Width (mm)
Water level (mm)
Average velocity (m/s^2)
Blade Profile used
1
750
300
0.46
NACA 0018
2
750
300
0.395
NACA 4415
To take care about same frictional condition, bearings are always washed in diesel before mounting in experimental setup. This exercise is carried out at the start of the experiment to maintain same mechanical efficiency for every experimental result. Bearings are periodically lubricated by lubricating oil. Single unit rotor experiments are performed with constant velocity given in table.2 for above NACA profiles are used for study effect tip speed ratio on coefficient of power and coefficient of torque. Water level is maintained such that the rotor is always in submerged condition (i.e., just above the top plate of the rotor). To measure the torque, the rotor is loaded gradually to record spring balance reading and angular speed of the rotor. Mostly, each result is repeated thrice.

Results and Discussion

Angle of Attack
Here Angle of attack for Darrieus otor blade is calculated for different tip speed ratio between 1 and 2 for different azimuth angle of blade between 0 to 2. Blade profile of rotor is taken as NACA0018 for calculation of angle of attack and Geometry detail and velocity is given in table 1. Figure 6 shows the variation in angle of attack as the azimuthally position of blade for different tip speed ratio. The
angle of attack become smaller as the tip speed ratio increases; this can be appreciated in the following graph of the angle of attack variation of a blade in a full revolution.
80
1.2 Tip Seed Ratio
Lift coefficient for azimuth position of blade of 0 to 30 degree there is more variation in the lift of the blade which is shown in figure 8. When the Reynolds number increases there is increment in the lift coefficient of the blade.
1
60 1.4 Tip Seed Ratio
Angle of Attack ()
Angle of Attack ()
1.6 Tip Seed Ratio
40 1.8 Tip Seed Ratio
20 2 Tip Seed Ratio
1 Tip Seed Ratio
0
0.8
Lift Coefficient
Lift Coefficient
0.6
0.4
Re=10000
20
0 100 200 300 Re=20000
40
60
80
Azimuth Angle ()
0.2
0
0.2 0
0.4
Re=40000 Re=80000
5 10 15 20 25 30 35 40
Angle of Attack ()
Figure: 6: Variation of Angle of attack for Different Azimuth angle for Different Tip Speed ratio.

Lift Coefficient
Figure 7 shows lift coefficient versus different angle of attack for different Reynolds number. Here lift coefficient drawn for Blade azimuth position from 0 to 180 degree for blade profile NACA0018. For blade azimuth position from 30 to 180 degree there is no change in the lift of the blade is shown in figure 7.
1.2
Re=10000
Lift Coefficient
Lift Coefficient
0.8 Re=20000
Re=40000
0.4
Re=80000
0
Figure: 8: Variation of Lift Coefficient for different Angle of attack for Different Reynolds Number.

Drag coefficient
Figure 9 shows Drag coefficient versus different angle of attack for different Reynolds number. Here, drag coefficient drawn for Blade azimuth position from 0 to 2 degree for blade profile NACA0018.
2
1.8
Drag Coefficient(Cd)
Drag Coefficient(Cd)
1.6
1.4
1.2
1
0.8 Re=10000
0.4
0.8
1.2
0 20 40 60 80 100 120 140 160 180
Angle of Attack ()
0.6 Re=20000
0.4
Re=40000
0.2
0 Re=80000
0 25 50 75 100 125 150 175 200
Angle of Attack ()
Figure: 7: Variation of Lift Coefficient for different Angle of attack for Different Reynolds Number.
Figure: 9: Variation of Drag Coefficient for different Angle of attack for Different Reynolds Number.
It is noted that Blade azimuth position from 15 to 180 degree there is no change in the drag of the blade but at azimuth position of blade for 0 to 15 degree there is more variation in the drag of the blade. When the Reynolds number increases there is increment in the drag coefficient of the blade that shown in figure 10.
Re=10000 Re=20000 Re=40000 Re=80000
Re=10000 Re=20000 Re=40000 Re=80000
0.25
Drag Coefficient(Cd)
Drag Coefficient(Cd)
0.2
0.15
0.1
0.05
increase but after 50 degree angle of attack lift is decreasing and drag is increasing as shown in figure10.

Comparison between Tangential and Normal force coefficient
Here, the variation of tangential and normal force coefficient with reference to the angle of attack is drawn for bale azimuth position between 0 to degree and Reynolds number of 40000 for blade profile is NACA0018.
2
Tangential force coefficient Normal Force Coefficient
Tangential force coefficient Normal Force Coefficient
1.5
0
0 5 10 15 20
Angle of Attack ()
1
0.5
Tangential force coefficient
Normal force co efficient
Figure: 10: Variation of Drag Coefficient for
different Angle of attack for Different Reynolds Number.
0
0.5
0 50 100 150
Angle of Attack ()
Coefficient of Lift (Cl) Coefficient of Drag (Cd)
Coefficient of Lift (Cl) Coefficient of Drag (Cd)
2
1.5
1
0.5
0
0.5
1
1.5
0 50 100 150 200 250 300 350
Cl Cd
Angle of Attack ()
Figure: 12: Comparison of Variation of Tangential and Normal force coefficient for variation of Angle of attack.

Torque coefficient
Experiment is done for torque coefficient for different tip speed ratio for two different NACA profile. The graph of torque coefficient for two NACA profile, NACA0018 and NACA4415, with
Figure: 11: shows the comparison of the lift and drag coefficient with reference to the angle of attack
Lift and drag coefficient for blade profile NACA0018 for Reynolds number of 40000 is drawn with reference to the angle of attack. As the angle of attack increases, lift and drag coefficient also
reference to the tip speed ratio and with their experimental result is shown. Geometrical data and velocity for both blade profiles are given in table 1. Torque coefficient is accurately predicted by single stream tube model for lower tip speed ration but when the tip speed ratio increases there is more variation in the experimental and analytical result which is shown by figure 13 and figure 14.
0.3
Coefficient of Torque(Ct)
Coefficient of Torque(Ct)
0.25
0.2
0.15
0.1
0.05
0
Experiment Result
Single stream tube model result
Experiment Result
Single stream tube model result
0 0.5 1 1.5 2 2.5
Tip speed ratio
0.35
Coefficient of Power(Cp)
Coefficient of Power(Cp)
0.3
0.25
0.2
0.15
0.1
0.05
0
Experiment Result
Experiment Result
Single stream tube result
Single stream tube result
0 0.5 1 1.5 2 2.5
Tip speed ratio
Figure: 13: Comparison of Experimental and Single stream tube result of for NACA0018
In figure 13 and 14 Variation in torque coefficient with reference to tip speed ratio and their comparison with the experimental result is shown.
Single Stream Tube Result
Experimental Result
Single Stream Tube Result
Experimental Result
)
)
0.12
Coefficcient of Torque ( CT
Coefficcient of Torque ( CT
0.1
0.08
0.06
0.04
0.02
0
0 0.5 1 1.5 2
Tip speed ratio
Figure: 15: Comparison of Experimental and Single stream tube result of for NACA0018
Here, maximum power coefficient developed for blade profile NACA0018 and NACA4415 is 0.3322 and 0.091241042 accordingly, but their experimental result is 0.3215 and 0.0845 accordingly which is more than single stream tube result.
0.1
Coefficient of Power (Cp)
Coefficient of Power (Cp)
0.09
0.08
0.07
Single Stream
Tube Result
Single Stream
Tube Result
0.06
0.05
Experimental Result
Experimental Result
0.04
0.03
0.02
0.01
ee
ee
0
Figure: 14: Comparison of Experimental and
0 0.5 Tip sp 1 d ratio
1.5 2
Single stream tube result of for NACA4415

Power coefficient

Figure 1.15 and 1.16 shows the comparison of power coefficient between experimental result and analytical result with reference to tip speed ratio for two NACA profile, NACA0018 and NACA 4415. Power coefficient is accurately predicted by single stream tube model for lower tip speed ration but when the tip speed ratio increases there is more variation in the experimental and analytical result.


Conclusion and future work
Single stream tube model is simple prediction of coefficient of performance of rotor. Time require for calculation is less. This model can predict the overall performance of low tip speed ration of rotor and a lightly loaded turbine but according to the inquest, it always predicts higher power than the experimental
results. It does not predict the water velocity variations across the rotor. These variations gradually increase with the increase of the blade solidity and tip speed ratio. Single stream tube model does not take into account the difference in the induced velocities between the upstream and downstream halves of the rotor or any difference in velocities across the rotor such as those due to water shear. The main drawback of these models is that they become invalid for large tip speed ratios and also for high rotor solidities because the momentum equations in these particular cases are inadequate.
In future work we can develop another model based on single stream tube model which can be accurately predict the performance coefficient for darrieus rotor for higher tip speed ratio and higher solidity rotor.

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