Literature Review 1

Design of Wells turbine for conversion of airflow energy for small scale power generation.

TABLE OF CONTENTS NOTATIONS ................................................................................................................... v 1.1.

Aim and Objectives........................................................................................................ 1

Chapter 2: Literature Review ........................................................................................... 2 Working principle of Wells turbine ............................................................................... 3 Basic equations of motion of a rotating system............. Error! Bookmark not defined. Radial Equilibrium Theory ............................................................................................. 6 Types of Wells turbines ................................................................................................. 7 The design and performance variables ......................................................................... 8 Tip speed ratio, λtip ........................................................................................................ 9 Flow ratio....................................................................................................................... 9 Blade solidity, σ ........................................................................................................... 11 2.9 The hub-tip ratio, h............................................................................................................ 13 Aspect Ratio................................................................................................................. 14 The tip clearance ......................................................................................................... 15 The aerofoil profile and thickness ratio, τ ................................................................... 16 Cascade effect ............................................................................................................. 17 The critical speed......................................................................................................... 18 Blade sweep and blade skew ......................................... Error! Bookmark not defined. Previous papers on improvement of Wells turbine ....... Error! Bookmark not defined.

CHAPTER 3: Methodology ...........................................Error! Bookmark not defined. References ...................................................................................................................... 20

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LIST OF FIGURES Figure 1: Power conversion chain for the system ............................................................ 3 Figure 2: Outline of a Wells turbine (Raghunathan et al., 1982). .................................... 3 Figure 3: Forces acting on an airfoil during the suction phase ......................................... 5 Figure 4: Forces acting on an airfoil during the compression phase ................................ 5 Figure 5: Velocity vector at the inlet of the Wells turbineError!

Bookmark

not

defined. Figure 6: Velocity vector at outlet of the Wells turbine ..Error! Bookmark not defined. Figure 7: Flow field along, the blade row represents the turbine. (Raghunathan, 1995) . 6 Figure 8: Performance parameters of the Wells turbine ................................................... 8 Figure 9: Effect of flow ratio on pressure drop: R = 2.8 x 105, h = 0.62........................ 10 Figure 10: Effect of flow ratio on efficiency: R = 2.8 x l05, h = 0.62 ............................ 11 Figure 11: Effect of solidity on the normalized values of pressure drop and efficiency profile (Raghunathan, 1989) ........................................................................................... 12 Figure 12: Effect ' of hub-tip ratio on efficiency: NACA0021 profile (Raghunathan, 1983) ........................................................................................................................................ 14 Figure 13: Effect of blade aspect ratio on efficiency and stall. NACA 0015, h=0.65-0.7 and R= 3×105 (Raghunathan, 1995) ............................................................................... 15 Figure 14: Effect of tip clearance on time averaged efficiency. (Raghunathan 1995) ... 16 Figure 15: 3D blade proposed by Takasaki et al. ........................................................... 17 Figure 16: Representation of Blade sweep (Shehata et al, 2016)Error! Bookmark not defined. Figure 17: Skewed Wells turbine rotors (Starzmann and Carolus, 2013) ............... Error! Bookmark not defined.

ii

Figure 18: Comparison between the optimal shape of the airfoil and the original profile NACA 2421 (Mohamed, 2008) .......................................Error! Bookmark not defined.

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LIST OF TABLES Table 1: Summary of the existing Wells turbine projects (Shehata et al., 2016) ............. 7

iv

NOTATIONS Quantity

Symbol

Units

Aerodynamic Efficiency

η

-

Angle of Absolute Velocity

β

Degrees

Angle of Attack

α

Degrees

Angular Velocity

ω

rad/s

Axial Force Coefficient

Cx

-

Axial Velocity

Vx

m/s

Blade Aspect Ratio

AR

-

Blade Circumferential Velocity

U

m/s

Blade Clearance at Tip

τc

m

Blade Height

l

m

Blade Thickness Ratio

τ

-

Chord Length

c

m

Circumferential Force Coefficient

Cθ

-

Circumferential Velocity

Vθ

m/s

Density

ρ

kg/m3

Density of Air

ρ

kg/m3

Drag Coefficient

Cd

-

v

Drag Force

D

N

Energy Dissipation Associated with Drag

Ed

J

Flow Rate

Q

m3/s

Flow Ratio

ϕ

-

Hub to Tip Ratio

h

-

Kinematic Viscosity of Air

υ

m2/s

Kinetic Energy at Exit Plane

Ek

J

Lift Coefficient

CL

-

Lift Force

L

N

Lift Force on Blades

L

N

Mach Number Relative to Blades

M

-

Non-Dimensional Pressure-Drop

p*

-

Number of Blades

N

-

Power Input

Wi

W

Pitch

t

Power Output

Wo

W

Pressure Coefficient

Cp

-

Pressure Drop across the Rotor

Δp

Pa

Pressure head

H

m

vi

Relative Velocity

w

m/s

Rotational Speed

n

rev/min

Rotor Swept Area

A

m2

Reynolds Number

R

-

Speed of of sound

a

m/s

Solidity Ratio

σ

-

Static Pressure

p

Pa

Tip Speed Ratio

λtip

-

Torque

T

Nm

Total Velocity

V

m/s

Turbine Hub Diameter

Dh

m

Turbine Tip Diameter

Dt

m

Turbulence Level at Turbine Inlet

Tu

%

vii

Subscripts h

Hub

m

Maximum value

t

Blade tip

x

Axial direction

0

Isolated airfoil

1

Inlet to plane 1

2

Outlet to plane 1 Peripheral direction

viii

1.1. Aim and Objectives The aim of this project is to investigate and design a Wells turbine for energy conversion for small scale power generation in a household. The objectives of the project are: ✓ Determining the optimum performance parameters of the Wells turbine through calculations. ✓ Design and drawing of the turbine and different components on a suitable 3D platform (Solidworks). ✓ Monitor the aerodynamic performance of the wind turbine with different blade number, using CFD.

✓ Building of a prototype of the Wells turbine. ✓ Comparing the experimental results to that obtained through modelling. The literature review (see section 2.14), it was found that there are a number of researches on the improvement of Wells turbine for maximum efficiency. However, there are not enough studies on the application of Wells turbine for residential applications. In this paper, a model of an optimized Wells turbine will be investigated and designed to convert airflow power for domestic power generation.

1

Chapter 2: Literature Review

2

Working principle of Wells turbine Potential and kinetic energy of air

Wells turbine

Mechanical energy of rotation

Generator

Electrical energy

Figure 1: Power conversion chain for the system Wells turbine is an axial flow reaction turbine mostly used for wave energy extraction from oscillating airflow. The Wells turbine rotor consists of a number of fixed pitch symmetrical airfoil blades set around a central hub. (see Figure 2) Due to the use of symmetrical airfoil blades about the chord line, the turbine rotates in the same direction by cyclically reversing outlet flow. It has a rotational speed limited by the blade tip velocity approaching toward the speed of sound.

Figure 2: Outline of a Wells turbine (Raghunathan et al., 1982).

3

According to the classical airfoil theory, in a fluid flow, an aerofoil at an incidence α, produces a lift force L, normal to the freestream and also a drag force, D in the direction of freestream (Raghunathan et al, 1985). The two forces can be resolved into tangential and axial components Ft and Fx. (refer to Figure 3) For real fluids, increasing the value of α, will result in an increase in both lift and drag, but only up to a certain value of α. At this value, the flow separates from the surface of the airfoil and this angle is called the stall angle. Above the stall angle, there will be a decrease in the lift and drag forces. This is because the flow between adjacent blades in cylindrical or liner series of blades These forces can be resolved into tangential (FT) and axial, (Fx) components as shown below: 𝑭𝑻 = 𝑳𝒔𝒊𝒏 𝜶— 𝑫𝐜𝐨 𝐬 𝜶

(1)

𝑭𝒙 = 𝑳𝒄𝒐𝒔 𝜶 + 𝑫𝐬𝐢 𝐧 𝜶𝝎

(2)

The resultant aerodynamic force, FR due to lift and drag can be calculated as:

𝑭𝑹 = √𝑳𝟐 + 𝑫𝟐

(3)

For a symmetrical aerofoil, the direction of FT is the same for both positive and negative values of a, and therefore the turbine will rotate in the direction of FT and produce power output. The flow between adjacent blades in cylindrical or liner series of blades (cascade) is not necessarily the same as that of isolated airfoils. Each blade has interference on the flow field (cascade effect) around its neighbours (Gareev, A., Kosasih, B. & Cooper, 2013)

4

The Wells turbine may operate with a distorted velocity profile at the inlet due to bends (Raghunathan, Setoguchi and Kaneko, 1989) and may have high levels of inlet turbulence.

Figure 3: Forces acting on an airfoil during the suction phase

Figure 4: Forces acting on an airfoil during the compression phase 5

Radial Equilibrium Theory According to radial equilibrium theory, it is assumed that the flow is irrotational, axisymmetric and also assuming that the radial component of velocity, Vr is negligible along the flow field but not within the blade rows Considering the radial direction, using the momentum equation, it can be shown that for the radial equilibrium to occur, the pressure force in the radial direction must and the centripetal acceleration are balanced, such that, 𝑽𝜽 𝟐 𝟏 𝝏𝒑 = 𝒓 𝝆 𝝏𝒓

(4)

Figure 5: Flow field along, the blade row represents the turbine. (Raghunathan, 1995)

6

Types of Wells turbines There are different types of Wells turbine that are developed for wave energy devices depending on the available pressure drop in the device; i.

Single plane: single stage with or without guide vanes

ii.

Multiplane: multistage with or without guide vanes

iii.

Contra-rotating

The current applications of Wells turbine are only with OWCs. Shehata et al. has done a thorough research on the existing types of Wells turbines, Table 1 provides a review of some reported projects. Table 1: Summary of the existing Wells turbine projects (Shehata et al., 2016) Devices

Locations

Output

No. of turbines

Diameter

Sakata, Japan

Japan

60 kW

1

1.337 m

Prototype OWC device

Islay,Scotland

75 kW

2

1.2 m

Biplane

Vizhinjam OWC

India

150 kW

1

2m

Monoplane

OSPREY

Dounreay, Scotland

2 kW

4

3m

Contrarotating

Mighty Whale

Japan

120 kW

1

1.7 m

The Pico Power Plant

Azores, Portugal

400 kW

1

2.3 m

LIMPET

Islay,Scotland

500 kW

2

2.6 m

7

Type of turbine Monoplane with guide vanes

Monoplane with guide vanes Monoplane with guide vanes Contrarotating

The design and performance variables

Number of blades Generator characterist ics

Number of planes

Inlet conditions Mach no. Reynolds No.

Blade profile geometry

Wells air turbine

Hub- tip ratio

Speed

Tip clearance

Diameter

Performance Indicators • • • • •

Power output Efficiency Pressure drop Flowrate Operational range

Figure 6: Performance parameters of the Wells turbine

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According to Raghunathan et al (1989), The performance indicators of a Wells turbine are; pressure drop, power, efficiency and variation of power and efficiency with flowrate. The aerodynamic design and performance of a monoplane Wells turbine are dependent on several variable (see Figure 6). Before designing a Wells turbine, it is important to understand each of variables, and the different effects associated to the performance of the turbine. The variables can be expressed as non-dimensional forms; ϕ, σ, h, AR, τ, τc, Tu, f and M

Tip speed ratio, λtip The tip speed ratio is defined as the relationship between rotor blade velocity and relative wind velocity [Equation 5555]. It is the primary design variable around which the optimum rotor dimensions can be determined

𝛌𝒕𝒊𝒑 =

𝝎𝒓 𝑽𝒘

(5)

A higher tip speed demands reduced chord widths leading to narrow blade profiles. This can lead to reduced material usage and lower production costs. Although an increase in centrifugal and aerodynamic forces is associated with higher tip speeds.

Flow ratio The flow ratio, ϕ is a measure of air flow incidence to the blades of the turbine. It is defined as the ratio of the axial velocity, Vx of inlet airflow to the blade circumferential velocity, U at mean radius, 𝛟=

9

𝑽𝒙 𝑼

(6)

The aerodynamic forces on the blades are and therefore the turbine performance is highly dependent on the flow ratio. Figure 7 shows the variation pressure drop with flow ratio.

Figure 7: Effect of flow ratio on pressure drop: R = 2.8 x 105, h = 0.62 σ = 0.59, NACA0012 blade profile (Raghunathan, 1995) From Figure 7, it can be observed that the pressure-drop and flowrate have a linear relationship except for small flow ratios. This applies in case of monoplane and biplane turbines and also for low or high solidity Figure 8 shows that for a range of values of flow ratio, as the flowrate increases, the aerodynamic efficiency increases, however it starts to decrease beyond this range. This behaviour can be explained by the fact that, at higher values of flow incidence, stalling occurs, and stalling is rather gradual on relatively thicker aerofoils. It can also be observed that when flow ratio is small (ϕ ˂0.05 in case of NACA 0015 for a monoplane turbine), the value of efficiency is negative, and this is because the power of the airflow is absorbed by the rotor. (Raghunathan, 1995)

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Figure 8: Effect of flow ratio on efficiency: R = 2.8 x l05, h = 0.62 σ = 0.59, NACA0012 blade profile (Raghunathan, 1989)

Blade solidity, σ

𝝈=

𝟐𝑵𝒄 𝝅𝑫𝒕 (𝟏 + 𝒉)

(7)

The solidity of the turbine, σ is an important parameter; it is a measure of blockage to air flow within the turbine and of the mutual interference between the blades. (Raghunathan, 1995). It can be varied by changing the radius of the rotor or the number of blades. It is also important for determining the starting characteristics of the turbine (Raghunathan, 1982). It can be shown that pressure drop is proportional to the axial forces acting on the blades. As shown by Raghunathan, 1984, as solidity increases, the axial forces increase causing an increase in pressure drop and power output. Moreover, solidity has a decreasing effect on the aerodynamic efficiency because an increase in σ results in a rise in the exit kinetic energy losses due to swirl. Figure 9 shows the changes on peak efficiencies and pressure-drops with variations in solidity.

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Figure 9: Effect of solidity on the normalized values of pressure drop and efficiency profile (Raghunathan, 1989) The relationships between pressure drop, solidity and efficiency and solidity, can be expressed as: 𝒑∗ =

∆𝒑 𝝆𝝎𝟐 𝑫𝒕 𝟐

(8)

As shown in equation (8) , p* is a non-dimensional pressure drop. 𝒑∗ = 𝟏 − 𝝈𝟐 ∗ 𝒑𝟎

(9)

𝜼𝒎 𝟏 − 𝝈𝟐 = 𝜼𝟎 𝟐

(10)

The pressure-drop and solidity (for CT > 0) can also be expressed as (Raghunathan, 1995): 𝒑∗ = 𝑨𝝈𝟏.𝟔

12

(11)

Where A is a constant. Raghunathan, 1983, suggested through experimental validations, that a value of σ ˂ 0.5 for larger efficiency for a monoplane Wells turbine, however, a low solidity turbine has a poor starting characteristic. To ensure that the turbine is self-starting, a value of σ ˃ 0.6 is suggested experimentally by Raghunthan and Tan, 1983.

2.9 The hub-tip ratio, h

𝒉=

𝑫𝒉 𝑫𝒕

(12)

The hub-tip ratio is an important variable because at a given diameter this ratio affects the volume flowrate through the turbine. The hub-tip ratio also has an influence on the tip leakage losses, the stall conditions, and the capacity to run up to an operational speed. If a turbine is rotating at a given speed, the incidence at the hub is bigger than the incidence at the tip. Stalling: According to Raghunathan and Tan, 1983, the hub incidence increases with the decrease in hub-tip ratio. Thus, the stalling on the blades is predicted to occur earlier near the hub. Leakage Losses: It can be noted, that the ratio of tip clearance to blade height reduces with the reduction in h and therefore decreases relative to leakage losses. Starting Behaviour: The relationship of the hub-tip ratio to the starting behaviour is given in Section 2.12. Efficiency: Figure 11 shows a typical change in the effect of the hub-tip ratio on efficiency.

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Figure 10: Effect ' of hub-tip ratio on efficiency: NACA0021 profile (Raghunathan, 1983) According to Raghunathan et Tan, 1983, the value of h ˂ 0.6 is recommended.

Aspect Ratio

𝑨𝑹 =

𝒍 𝒄

(13)

The primary influence of a decreasing aspect ratio is the delay of stall related with the 'relief effect' due to relatively larger mass flow through the tip. In Figure 11, it can be seen that decreasing aspect ratio AR affects positively, the turbine efficiency and flow ratio at which stalling occurs due to reduced airflow incidence near the hub. Moreover, stronger tip vortices are observed and also the effects of the AR on the turbine can be improved by increasing the tip clearance. For the design of a Wells turbine, the proposed value of AR is 0.5.

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8 Figure 11: Effect of blade aspect ratio on efficiency and stall. NACA 0015, h=0.650.7 and R= 3×105 (Raghunathan, 1995)

The tip clearance Compared to a conventional turbine, the Wells turbine is far more sensitive to tip clearance. Figure 12, shows that a reduction in tip clearance advances the stall but improves the cyclic average efficiency due to reduced leakage losses. In contrast, a turbine with a relatively large tip clearance can run over a much larger range of flowrate without stalling. Therefore there are no significant benefits to be obtained for τc, > 0.02. Therefore, values of a tip clearance ratio τc ˂ 0.02 are suggested for design.

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Figure 12: Effect of tip clearance on time averaged efficiency. (Raghunathan 1995)

The aerofoil profile and thickness ratio, τ The airfoil thickness is very important as it controls the aerodynamic force coefficients on an isolated aerofoil, stall angles and turbine weight. It can be noted that the effect of aerofoil thickness on the aerodynamic performance and the effect of the Reynolds number are both coupled since they influence together the separation on the airfoil (Raghunathan and Tan, 1983). Based on the experimental investigation of Raghunathan and Tan, 1983, it can be observed that, the maximum values of aerodynamic force coefficients and the stall normally increase with Reynolds number. From the results the blade profiles NACA 0021 (τ =0.21) lead to the best performance for original Wells turbines . The results show that for small-scale turbines, a thicker profile is recommended, and it also improve the starting characteristics of the turbine. However, the test are based on isolated aerofoil and do not take into account the joint interference effects of blades in a cascade. (Raghunathan, 1985). Takasaki et al., studied the effect of 3-dimensional (3D) blade on the characteristics of Wells turbine, with the aim to reduce flow separation on the suction surface near the tip. An experimental investigation by model testing under steady flow conditions was done

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to improve the peak efficiency and stall characteristics. The blade proposed used a constant chord length with radius while the blade profile changes progressively; NACA0015 was used at the hub, NACA0020 at the mean radius and NACA0025 at the tip. The proposed model (see Figure 13) resulted in an improved efficiency compared to the original blade design with an improvement in efficiency and the postponement of severe stalling.

Figure 13: 3D blade proposed by Takasaki et al.

Cascade effect The cascade lift and drag can be quite different compared to that of isolate airfoils, because of mutual interference between each blade. The interferences occur due to the mutual velocities induced by the blades. and wakes produced by the blades. For a Wells turbine, the interferences can be quite significant due to the high solidity rotors. An important effect of the adjacent aerofoils is the increase and reduction of the chordwise component of the velocities on the upper and lower surfaces respectively, developing an increase in circulation and consequently, an increase in lift produced by the aerofoil. (Raghunathan, 1995). According to Weinig et al. (1935), a simple method to assess the interference effects can be based on a potential flow analysis of flat plate aerofoils in a cascade. It was found that,

17

for an airfoil in cascade, the value of C1 can be corrected for cascade effects by a factor of k such that, 𝑪𝟏 = 𝒌 𝑪𝟏𝒐

(14)

Where, factor k for a cascade of stagger angle, π/2 is expressed as,

𝒌= (

𝟐𝒕 𝝅𝒄 ) 𝒕𝒂𝒏 ( ) 𝝅𝒄 𝟐𝒕

(15)

However, the drag cannot be predicted by the potential flow analysis and it can be assumed that, 𝑪𝒅 = 𝑪𝒅𝒐

(16)

Starzmann and Carolus assessed systematically the effect of cascade solidity and hub-totip ratio on the aeroacoustics performance of Wells turbine rotors by numerical simulations and model scale testing. It was found that maximum values of total-static peak efficiency and low sound emission can be attained by choosing moderate values of cascade solidity and hub-to-tip ratio. However, for a maximum range of operation without stall, high hub-to-tip ratio together with high solidity are suggested. The disadvantage is a slightly larger rotor diameter related to lower cascade solidity

The critical speed The tip speed ratio is defined as the relationship between rotor blade velocity and relative wind velocity [Equation 23]. It is the primary design variable around which the optimum rotor dimensions can be determined

𝛌𝒕𝒊𝒑 =

18

𝝎𝒓 𝑽𝒘

(17)

This can lead to: • reduced material usage and lower production costs. Although an increase in centrifugal and • aerodynamic forces is associated with higher tip speeds.

19

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