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ARCHIVES ANNOUNCEMENTS Home > Archives > Vol 7, No 1 (2017)

Vol7

DOI: http://dx.doi.org/10.1234/ijrer.v7i1

Articles

Study of Integrated Rural Electrification System Using Wind-Biogas Based Hybrid System and Limited Grid Supply System

Dinesh Kumar Yadav, T. S. Bhatti, Ashu Verma

PDF 1-11

Optimum Design and Evaluation of Solar Water Pumping System for Rural Areas

Miqdam Tariq Chaichan, Ali Hussein A Kazem, Moanis M K El-Din, Atma H. K. Al-Kabi, Asma M Al-Mamari, Hussein A Kazem

PDF 12-20

Effect of Rotor Speed on the Thermal Model of AFIR Permanent Magnet Synchronous Motor

Said Abd El-monem Wahsh, Jehan Hassan Shazly, Amir Yassin Hassan

PDF 21-25

Experimental Investigation of metals and Antioxidants on Oxidation Stability and Cold flow properties of Pongamia Biodiesel and its blends

Gaurav Dwivedi, Puneet Verma, mahendra pal sharma

PDF 26-33

Design of Fuzzy and HBCC based Adaptive PI Control Strategy of an Islanded Microgrid System with Solid-Oxide Fuel Cell

Subhashree Choudhury, Pravat Kumar Rout

PDF 34-48

Renewable energy from the seaweed Chlorella pyrenoidosa cultivated in developed systems

Souad Zighmi, Segni LADJEL, Mohamed Bilal GOUDJIL, Salah Eddine BENCHEIKH

PDF 49-57

Optimization of The Fins Dimensions for The Absorber with Fins on a Compact Thermal Solar Collector by Entropy Generation Criterion.

Coffi Wilfrid ADIHOU, Malahimi ANJORIN, C. Aristide HOUNGAN, Christophe AWANTO, Gerard DEGAN

PDF 58-67

Novel Hybrid Evolutionary Game Theory and Differential Evolution Solution to Generator Bidding Strategies with Unit Commitment Constraints in Energy and Ancillary Service Markets

B.Durga Hari Kiran, Sailaja Kumari Matam

PDF 68-79

Vol 7, No 1 (2017) http://www.ijrer.org/ijrer/index.php/ijrer/issue/view/4785074604081177

1 of 4 01/04/2017 10:14

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Multi Level Inverter Based STATCOM for Grid Connected Wind Energy Conversion System

Gundala Munireddy

PDF 80-87

A comparative Study And Evaluation of Improved MAF- PLL Algorithms

mohamed mellouli, Mahmoud Hamouda, Jaleleddine Ben Hadj Slama

PDF 88-95

Design and Analysis of an Integrated Cuk-SEPIC Converter with MPPT for Standalone Wind/PV Hybrid System

K. Kumar, N. Ramesh Babu, K. R. Prabhu

PDF 96-106

Photo-Voltaic Array Fed Transformer-Less Inverter with Energy Storage System for Non-isolated Micro Inverter Applications

K. Mohanasundaram, P. ANANDHRAJ, V. Vimalraj Ambeth

PDF 107-110

Wind-hybrid Power Generation Systems Using Renewable Energy Sources- A Review

Muhammad Shahzad Aziz, Gussan Maaz Mufti, Sohaib Ahmad

PDF 111-127

Performance and Cost Assessment of Three Different Crystalline Silicon PV Modules in Kuwait Environments

Adel Aldihani

PDF 128-136

Dual-Axis Solar Tracker for Using in Photovoltaic Systems Carlos Arturo Robles, Adalberto Ospino Castro, Jose Casas Naranjo

PDF 137-145

Frequency Control of Micro Grid with wind Perturbations Using Levy walks with Spider Monkey Optimization Algorithm

Kayalvizhi Selvam, D.M. Vinod Kumar

PDF 146-156

High Step-Down Dual Output Light Emitting Diode Driver U. Ramanjaneya Reddy, B. L. Narasimharaju

PDF 157-169 Investigate Curvature Angle of the Blade of Banki's Water

Turbine Model for Improving Efficiency by Means Particle Swarm Optimization

Lie Jasa, I Putu Ardana, Ardyono Priyadi, Mauridhi Hery Purnomo

PDF 170-177

Modeling of Wind Energy Conversion System using PSCAD/EMTDC

Asad Ashfaq

PDF 178-187

Assessment of Simulation Modelling and Real-Time

Measurements for 3.15 and 17.28 kWp Solar Photovoltaic (PV) Systems in Malaysia

Banupriya Balasubramanian, Azrul Mohd Ariffin, Samer Husam Al-Zubaidi

PDF 188-199

Assessment of Effect of Load and Injection Timing on the Performance of Diesel Engine Running on Diesel-Biodiesel Blends

Rajesh Kumar Saluja

PDF 200-213

Solar Manager: Acquisition, Treatment and Isolated Photovoltaic System Information Visualization Cloud Platform

David Omar Guevara, Jesús Israel Guamán, Carlos Luis Vargas, Alverto Ríos Villacorta, Rubén Nogales Portero

PDF 214-223

Photovoltaic Lighting System with Intelligent Control based on ZigBee and Arduino

Ruben Nogales Portero, Alberto Rios

PDF 224-233

Design, Dimensioning, and Installation of Isolated Photovoltaic Solar Charging Station in Tungurahua, Ecuador

Alverto Rios Villacorta, Jesús Israel Guamán, Carlos Luis Vargas, Mario Garcia Carrillo

PDF 234-242

Solar photovoltaic farms suitability analysis: a Portuguese case-study

Mário Baptista Coelho, Pedro Cabral, Sara Rodrigues

PDF 243-254

An Experimental Implementation and Testing of GA based Maximum Power Point Tracking for PV System under Varying Ambient Conditions Using dSPACE DS 1104 Controller

Neeraj Priyadarshi, Arvind Anand, Amarjeet Sharma, Farooque

PDF 255-265

2 of 4 01/04/2017 10:14

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Azam, Vipin Singh, Ravi Sinha

Comparison Study of Solar Flat Plate Collector with Single and Double Glazing Systems

H. Vettrivel, P. Mathiazhagan

PDF 266-274

Simulation of Integrated Biomass Gasification-Gas Turbine-Air Bottoming Cycle as an Energy Efficient System

Hassan Ali Ozgoli

PDF 275-284

Remedy of Chronic Darkness & Environmental effects in Yemen Electrification System using Sunny Design Web

Adel Rawea, Shabana Urooj

PDF 285-291

Performance Evaluation of a Mono-Crystalline Photovoltaic Module Under Different Weather and Sky Conditions

Nouar Aoun, Kada Bouchouicha, Rachid Chenni

PDF 292-297

Performance of Zn-Cu and Al-Cu Electrodes in Seawater Battery at Different Distance and Surface Area

Adi Susanto, Mulyono Sumotro Baskoro, Sugeng Hari Wisudo, Mochammad Riyanto, Fis Purwangka

PDF 298-303

Behaviour of Biogas Containing Nitrogen on Flammability limits and Laminar Burning Velocities

willyanto anggono

PDF 304-310

Fuzzy Logic Controller based PV System Connected in Standalone and Grid Connected Mode of Operation with Variation of Load

BHUKYA KRISHNA NAICK

PDF 311-322

Analysing Wind Turbine States and SCADA Data for Fault Diagnosis

Lorenzo Scappaticci, Nicola Bartolini, Alberto Garinei, Matteo Becchetti, Ludovico Terzi

PDF 323-329

Improvement of Temperature Dependence of Carrier

Characteristics of Quantum Dot Solar Cell Using InN Quantum Dot

Md. Abdullah Al Humayun, Sheroz Khan, A. H. M. Zahirul Alam, Mashkuri bin Yaacob, MohamedFareq AbdulMalek, Mohd Abdur Rashid

PDF 330-335

Technoeconomic Analysis of an Integrated Gasification Combined Cycle System as a Way to Utilise Bagasse

Stavros Michailos, David Parker, Colin Webb

PDF 336-343

A Dynamic Penalty Cost Allocation Based Uncertain Wind Energy Scheduling in Smart Grid

Srikanth Konda, Lokesh Panwar, B K Panigrahi, Rajesh Kumar, Sai Goutham

PDF 344-352

Modelling of Optimal Tilt Angle for Solar Collectors Across Eight Indian Cities

Jims John Wessley, R Starbell Narciss, S. Singaraj Sandhya

PDF 353-358

The Potential of Dark Fermentative Bio-hydrogen Production from Biowaste Effluents in South Africa

Patrick Sekoai, Michael Olawale Daramola

PDF 359-378

Rapid In Situ Transesterification of Papaya Seeds to Biodiesel with The Aid of Co-solvent

Elvianto Dwi Daryono

PDF 379-385

Development of Customized Formulae for Feasibility and Break-Even Analysis of Domestic Solar Water Heater

Auroshis Rout, Sudhansu S Sahoo, Sanju Thomas, Shinu M Varghese

PDF 386-398

Modelling and Simulation of Natural Gas Generator and EV Charging Station: A Step to Microgrid Technology

Jakir Hossain, Nazmus Sakib, Eklas Hossain, Ramazan Bayindir

PDF 399-410

Numerical evaluation of the extinction coefficient of honeycomb solar receivers

Rami Elnoumeir, Raffaele Capuano, Thomas Fend

PDF 411-421

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Designing of Small Scale Fixed Dome Biogas Digester for Paddy Straw

vipan sohpal, Harmanjot Kaur, Dr Sachin Kumar

PDF 422-431

A Comparative Study of Voltage Gain Tolerance in Conventional and Three-Level LLC Converters Against Circuit Variation

Hiroyuki Haga, Hidenori Maruta, Fujio Kurokawa

PDF 432-438

Output Power Loss of Photovoltaic Panel Due to Dust and Temperature

Abhishek Kumar Tripathi, M. Aruna, Ch. S. N. Murthy

PDF 439-442

Modelling and Simulation of Permanent Magnet Synchronous Generator Wind Turbine: A Step to Microgrid Technology

Jakir Hossain, Eklas Hossain, Nazmus Sakib, Ramazan Bayindir

PDF 443-450

Power flow analysis incorporating renewable energy sources and FACTS devices

Suresh Velamuri, S. Sreejith

PDF 451-458

Methane Hydrate Gas Storage Systems For Automobiles Swapnil Tanaji Khot, Sanjay dnyanu Yadav

PDF 459-466

Online ISSN: 1309-0127 www.ijrer.org

[email protected]; [email protected];

IJRER is cited in SCOPUS, EBSCO, WEB of SCIENCE (Thomson Reuters)

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INTERNATIONAL JOURNAL of RENEWABLE ENERGY RESEARCH L.Jasa et al., Vol.7, No.1, 2017

Investigate Curvature Angle of the Blade of Banki's Water Turbine Model for Improving Efficiency by

Means Particle Swarm Optimization

Lie Jasa*

^‡

, I Putu Ardana, Ardyono Priyadi*, Mauridhi Hery Purnomo****

*Department of Electrical Engineering, Udayana University, Denpasar, Bali, Indonesia

**Department of Electrical Engineering, Udayana University, Denpasar, Bali, Indonesia

***Department of Electrical Engineering, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia

****Department of Electrical Engineering, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia ([email protected], [email protected], [email protected], [email protected])

‡Corresponding Author; Lie Jasa, Department of Electrical Engineering, Kampus Unud Bukit Jimbaran Badung, Bali 80623, Indonesia, Tel: +62 0361 703315, Fax: +62 361 703315, [email protected]

Received: 16.09.2016 Accepted:09.12.2016

Abstract-Turbines are used to convert potential energy into kinetic energy. Turbine blades are designed expertly with specific curvature angles. The output power, speed, and efficiency of a water turbine are affected by the curvature angle of the blade because water energy is absorbed by the blade in contact with the water flow. The particle swarm optimization (PSO) algorithm can be used to design and optimize micro hydro turbines. In this study, the blade curvature angle in a Banki’s water turbine model is investigated using the particle swarm optimization algorithm to obtain the highest output power, speed, and efficiency in the water turbine. Mathematical and experimental models are employed to investigate the blade curvature angle.

The result shows that a curvature angle of 15ô provides higher output power, speed, and efficiency than angles of 16ô and 17ô, despite the fact that 16ô is commonly used in commercial production.

Keywords blades, turbine, PSO, hydropower.

1. Introduction

Today, energy resources play an important role in economics, politics, social life, and the sciences. This is especially so in Indonesia where conventional energy resources are decreasing and prices are tending to rise[1].

Renewable energy [2] sources can potentially substitute for conventional energy resources and to smoothly solve these problems [3]. Indonesia has many renewable energy resources, including river water, sea water flow, tides, wind, and geothermal and solar energies, however hydropower plants are predominantly used for renewable energy supply as compared with the other alternatives [4], [5], [6]. One type of hydropower is micro-hydro power, which has become popular since it is simpler in its design, easier and cheaper to operate, faster to install, and has lower environmental impacts than the others [7].

The water turbine is a simple machine usually made of wood or steel with a fixed blade attached to a surrounding wheel [8], [9]. This blade is driven by a stream of water flowing around the wheel. Water pressure on the blade produces torque on the shaft to make the wheel spin [10].

The potential energy in the accumulated water continuously applied to the blade attached to the turbine wheel generates kinetic energy on the turbine shaft [11]. Sometimes the water flows vertically at the top, the middle, or the bottom of the turbine wheel. The curvature angle of the blade is a key issue in the energy conversion process.

One type of water turbine model is called the Banki’s model. The theory behind the Banki’s model, written by Mockmore and Merryfield in 1949, can be found in reference In the Banki’s water turbine, the nozzle[12], whose cross- sectional area is rectangular, discharges a jet into the full width of the wheel, and is oriented at an angle of 16 degrees to the tangent of the wheel’s periphery. More simply stated,

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171 the curvature angle of the blade is 16 degrees. Based on

reference[12], the authors argued that the curvature angle is the key for obtaining the highest possible output power, speed, and efficiency of the water turbine.

This study explores mathematical and experimental design models of the Banki’s water turbine to investigate the performances resulting from 15ô, 16ô, and 17ô blade curvature angles. Our goal is to determine the optimal turbine parameters for achieving the highest possible power output, efficiency, and speed. The mathematical models explored in our research are governed by principles of conservation of mass, momentum, and energy, and are described in detail in section 2. From the mathematical model we use, optimum parameter characteristics are simulated by the particle swarm optimization (PSO) [13], method to obtain the optimal blade curvature angle. Then, experimental design models are used to clarify the blade’s curvature angle obtained by PSO to assess whether or not it yields maximum values for all of the parameters. In order to validate the performance of the each experimental turbine model, it was necessary to utilize the same turbine model parameters, including wheel diameter, thickness, material, number of blades, water discharge, and load generators.

2. The Banki Formula 2.1 Theoretical Background

The Banki’s turbine, as described in[12], consists of a nozzle and a turbine runner. The runner is built of two parallel circular disks joined at their rims with a series of curved blades. The nozzle, whose cross-sectional area is rectangular, discharges a jet of water the full width of the wheel, which enters the wheel at an angle of 16 degrees to the tangent of the wheel’s periphery. The shape of the jet is rectangular, wide, and fairly shallow. The water strikes the blades on the rim of the wheel, as shown in Figure 1, flows over the blade, then leaves it, passing through the empty space between the inner rims, enters a blade on the inner side of the rim, and is then discharged at the outer rim. The wheel is an inward jet wheel. Since the flow is essentially radial, the diameter of the wheel does not practically depend on the amount of water impact, and neither does the desired wheel breadth depend on the quantity of water.

The path of the jet through the turbine is assumed to be that at the centre of point A, as shown in Figure 1, at an angle of α1 tangent to the periphery. So the velocity of the jet path water through the turbine can be written as follows:

𝑉

₁

= 𝐶√2𝑔𝐻

⁽¹⁾

The relative velocity of the water at the entrance, v1, can be found at u1 if the peripheral velocity of the wheel at that point is known. β1 is the angle between the forward directions of the two latter velocities.

A

B H

h2

h1

1 1 U1

v1 V1

2' v

2' U 2' V 2'



2 2' U

C

D

1' '  V1

1' U

2 V1

1'



2 ²

2

1 U

U V² v2

Fig.1. Path of water through turbine^[11]

For maximum efficiency, the angle of the blade should equal β1. Line AB represents the relative velocity of blade v2’ and β2’ represents the peripheral velocity of the wheel at that point. An absolute velocity of the water at the exit of blade v2’ can be determined by v2’, β2’, and v2. The angle between the absolute velocity and the velocity of the wheel at this point is α2’. The absolute path of the water when it is flowing over blade AB can be determined, as can the actual point when it leaves the blade. An absolute velocity V2’ assumes a constant value, so that V1’ can be obtained at point C. This means the absolute velocity V1’ is equal to V2’. Based on this statement, we can state that blade CD is equal to blade AB and α1’= α2’, β1’= β2’, β1= β2.

The efficiency of the output power is given as

HPout= (^ωQu_g¹) (V1cos α1− u1) (1 +ψ cosβ₂/ cosβ₁) (2)

And the input power may be stated as HP_in=^ωQH_g

V¹ v²

V2

U2

U1

v¹

1 ₁

2

2 2

cos 1

1 

V

2

2cos

v

Fig. 2. Velocity diagram ^[11]

Based on Equation (1), we obtain H =_C^V₂¹²_2g And substituting into Equation (3), we obtain HPin= ωQV12/C²2g.

Efficiency is defined by the ratio of the output and input power, η= ^H_H^out

in, η= (2C²u1/V1) (cos α₁− u1/V1) (1 + ψ cosβ₂/ cosβ₁) , When β1 = β2,

η= (2C²u1/V1) (1 +ψ) (cos α1− u1/V1) (3) Assuming that Equation (3) is a function and u1/V1 is an observing variable. The first differentiation of Equation (3) is

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172 equal to zero, and is given by, u1/V1= cosα1/2, Maximum

efficiency is given by η_max= (½C²) (1 +ψ)( cos ²α₁ ) Based on Figure 2, the direction of V2 is not radial when u1 =

½V1α1. The water flow of the outer of rim should be radial.

Therefore, the value of u1 is given by

u1= [_(1+ψ)^C ] (V1cos²α1) (4) When there are no losses on the head due to friction in the nozzle or the blades, ψ and C have unity values.

Variations in the nozzle roughness coefficient C is a quadratic function, as stated at Equation (4). There are two types of hydraulic losses from this nozzle aspect that occur when water is striking the outer and inner peripheries. These losses are relatively small when the blade thickness is sufficiently thin and should not exceed the jet so, as shown in Figure 3. Therefore, the water energy will strike the outer and inner peripheries of the blade. The blade system can provide the optimal blade roughness coefficient ψ, 0.98, when the number and thickness of the blades is accurately obtained.

r1

r2

r1

r2

a

90o 2'



S2

S1

S0 1'



v2'

v2' v1'

1 2 1

1 sin

r vr t

a =r1-r2

Fig. 3. Blade Spacing ^[11]

2.2 Design Construction Formula

Fig. 4. Composite velocity diagram ^[11]

2.2.1 Blade Angle

As stated in Figures 1 and 3, the blade angle β1 can be calculated by u1=¹₂V1cosα1 and tanβ₁= 2 tanα1. Based on Figures 4 and 5, the velocity of V1 ' can be obtained as V₁^′ = [2gh₂+ (V₂^′)²]¹²

Fig. 5. Velocity Diagram ^[11]

2.2.2. Width of the Radial Rim

The thickness of the entrance jet s1 for a distance of blade t can be calculated by

s₁= t sinβ₁ (5)

The inner exit blade spacing s2 for a = r1 − r2 can be obtained by s2= t (r1/r2) where s2= v1s1/v2′ to find the value of β1 requires a velocity v2' influenced by the centrifugal force, and is given by

(v1)²− (v2′)²= (u1)²− (u2′)² (v₂^′) = v₁(^s_s¹

2) = v1(^r_r¹

2) sinβ₁ x²− [1 − (_u^v¹

1)²] x − (^v_u¹

1)²sin²β₁= 0

v₁ u₁=_cos¹

β₁

where x = (r2 / r1)²

Based on Figure 6, the central angle BOC can be calculated by

(v1)²− (v₂^′)²= (u1)²− (u₂^′)² (v₂^′)²= v₁(^s_s¹

2) = v₁(^r_r¹

2) sinβ₁ tanα₂^′ =^v_u²^′

2′

boC = 2 α2’ (6)

2.2.3 Wheel diameter and axial wheel breadth

The wheel diameter can be determined from Equations.

u₁=πD₁N/(12)(60) and D₁= 360C(2gH)¹²cosα₁/πN To find the breadth of the wheel (L), where so = kD1, Equations (26), (27) and (28) may be used.

Q = (^Cs₁₄₄^o^L) (2gH)¹² (7) L = 144 Q N/862H¹²Ck(2gH)¹² (8) where k = 0.075 and 0.10, respectively.

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173

r2 r1

a

Y2 s₀

v’₂ V’2

u’₂ V1

v₁

u₁

V’1 u’₁ v’1 A

B

C

D

1

2'



2'



1' '

1

V2 u2=u1 v₂

2

2

h

h2

h1

Y1

Y ds

BOC

Fig. 6. Path of jet inside wheel ^[11]

2.2.4 Curvature of the blade

The curvature of the blade, as shown in Figure 7, is calculated using Equation (9)

ρ=^[(r_2r¹⁾²^−(r²⁾²^]

1cosβ₁ . (9)

r¹ r²

a

1

C A

B

O 90o

90o



  2

/

Fig. 7. Curvature of the blades^[11]

2.2.5 Central Angle

The central angle, as shown in Figure 7, can be calculated using Equation (10).

tan¹₂δ= cosβ₁/(sinβ₁+^r_r²

1) (10)

In accordance with the construction design equations given above, our calculation results are shown in Table 1, using alpha angles of 15ô, 16ô, and 17ô.

Table 1. Calculation results using the construction design

Blade Angle Radial Rim Width

α1 β1 r2 a α2 bOC

15ô 28ô 0.64 r1 0.18 D1 52ô 104ô

16ô 30ô 0.66 r1 0.17 D1 53ô 106ô

17ô 31ô 0.668 r1 0.165 D1 53ô 106ô Blade Angle Wheel Diameter and Axial Wheel Breadth

α1 β 1 D1 L

15ô 28ô (870/N)H^0.5 0.281QN /H until 0.21QN/H 16ô 30ô (866/N)H^0.5 0.282QN /H until 0.211QN/H 17ô 31ô (862/N)H^0.5 0.283QN /H until 0.212QN/H Blade Angle Curvature of

Blade Central Angle

α1 β 1 ρ δ

15ô 28ô 0.334 r1 77ô

16ô 30ô 0.326 r1 74ô

17ô 31ô 0.323 r1 72ô

2.3 Particle Swarm Optimization (PSO) Algorithm

American psychologist Kennedy and electrical engineer Eberhart developed the PSO algorithm based on the behavior of individuals in a swarm of birds [14] The PSO algorithm is an optimization technique and also a kind of evolutionary computation technique. PSO is initialized to a random solution, using an iterative search for the optimal value[15].

Each individual in the group is called a particle in a D- dimension solution space. The position vector of the ith

particle is represented as Xi=(Xi1, Xi2,…Xin). The best position found by the ith particle so far is denoted as Pi=(pi1, Pi2,…Pin), and is known as pBest; Accordingly, the best position found by the whole swarm is denoted as Pg = (Pg1, Pg2,…Pgn), and is known as Gbest. The velocity vector of the ith particle is represented as Vi =(Vi1, Vi2,….Vin). The velocity and position of the ith particle can be defined according to the following equations:

Vin = wVm + c1r1(Pin-Xi) +c2r2(Pgn-Xin) (10)

Xin = Xin + Vin (11)

where w is a constriction factor, c1 and c2 are learning factors, and r1 and r2 are random numbers generated uniformly in the range [0-1].

A linearly decreasing inertia weight was first introduced by Shi and Eberhart in [14]. The linearly decreasing inertia weight is modified as

w(iter) = w_max− (^w^max_iter^{− w}^min

max ) iter (12)

where wmax is the initial inertia weight, wmin is the final inertia weight, itermax is the iteration maximum in the evolution process, and iter is the current value of the iteration. Normally, wmax is set to 0.9 and win is set to 0.4.

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174 The following gives the design step for the improved version

of the PSO algorithm [15],[16]

3. Problem Formulation 3.1 Optimization Formula

The input power and output power equations of the Banki turbine are affected by the value of the parameters H, g, C, ω, ψ, α1, β1, and β2. Constant parameters, such as H, C, and g do not change their values when optimization is performed. The values we can optimize are the values of α1, β1, and β2 with the goal of changing the angle of the corner to affect the efficiency of the turbine. The equation to optimize these parameters is as follows, by maximizing the overall value of equations (3), (1), (4), (2) The values of influence are the equality constraints:

V₁=C(2gH)^1/2 H

g C

Hp_in=WQ(V₁)²/ C²2g V₁

Q C

W g

u₁=(C/

(1+psi) V₁ cos(alfa₁) C

Hp_out=((WQu₁)/

g) x (V₁ cos α₁- u₁).(1+ψ x ( cos β₂/ cos β₁) W

g Q

V1 V₁

u₁

Eff Eff=Hpout / Hpin

V₁



1



1

2

Fig. 8. Proposed Optimization Strategy

The inequality constraints are cos α1min ≤ cos α1 ≤ cos α1 max

cos β1min ≤ cos β1 ≤ cos β1 max

cos β2min ≤ cos β2 ≤ cos β2 max. 3.2 Proposed Method Optimization

According to the block diagram of Figure 8 above, the value of V1 will be influenced by the parameters H, g, and C.

Furthermore, the value of V1 is the input for U1, Hpin, and Hpout. The value of U1 will be determined by the values of the parameters C, ψ, α1, and V1. The Hpin value is determined by the values of Q, C, g, ω, and V1. The Hpout

value will be determined by the values of Q, V1, g, ω, u1, ψ, α1, β1, and β2. The results of a comparison of the Hpin and Hpout values determine the value of the efficiency. We used MATLAB simulation in the optimization process to obtain the maximum value of the efficiency (η) by the value optimized angles α1, β1, and β2.

4. Simulation Result

By the method proposed above in section 3.2, Equation (8) is optimized by MATLAB simulation. The initialization of the parameter values in the PSO algorithm includes the number of birds n = 50, dimensions = 3, steps = 50, c2 = 0.3, c1 = 0.1, w = 0.75 momentum, the angle of α1 (15 ≤ α1 ≤ 17), the angle of β1 (28 ≤ β1 ≤ 31), and the angle of β2 (29 ≤ β2 ≤ 32). The optimization results of Equation (8) are provided in Table 2.

First, PSO simulations were performed with the input values of H and Q, then the PSO calculates the values of α1, β1, β2, V1, Hpin, U1, Hpout, and η. The range of H values is 1 ≤ H ≤ 60 and the Q value is either 30, 35, or 40. Every pair of values of H and Q is given 180 combinations, and for each combination of H and Q, the PSO will produce 30 lines of data. The next step is to identify combinations of H and Q with the highest efficiency (η). Of the 180 combinations, Table 2 shows that only 5 of these were chosen as having the highest η in the PSO simulation results.

Please note that the simulated data generated by the PSO values for 17ô and 16ô angles never appeared. On the basis of these findings, we had to conduct experiments (section 5) to validate the PSO results and prove that the 15ô α1 angle is better than 16ô and 17ô angles.

Table 2. Simulation results of the PSO algorithm

Data 1,0 2,0 3,0 4,0 5,0

H 56,0 47,0 26,0 27,0 58,0

Q 35,0 30,0 35,0 40,0 30,0

α1 15,0004 15,0004 15,0004 15,0002 15,0008 β1 28,1936 29,8677 29,8677 28,8056 29,2837 β2 31,6861 31,8705 31,8705 29,2072 ^30,0975 V1 10,3713 9,5015 7,0669 12,4734 14,9269 Hpin 1960000,0 1410000,0 910000,0 1080000,0 1740000,0

u1 5,0 4,5 3,4 6,0 7,1

Hpout 1738531,6 1250676,3 807173,2 957961,8 1543379,2 η 0,887006 0,887004 0,887004 0,887002 ^0,887000

5. Experimental Results

We constructed prototype turbine models with axles placed on two pillows so the turbine could spin with little friction, as shown in the photographs in Figure 11.

(12)

175

6 Cm 3 Cm 20 Cm 3 Cm 4 Cm

2 Cm 2 Cm

2,7 Cm

2 Cm

6 Cm 3 Cm 20 Cm 3 Cm 4 Cm

2 Cm

2,7 Cm 2 Cm

2 Cm

4 Cm 4 Cm

2 Cm

2,5 Cm

7 Cm 2.8 Cm

2.8 Cm 7 Cm 3,2 Cm

2.2 Cm 2 Cm 2,5 Cm 11 Cm 2,5 Cm

2,5 Cm 16 Cm

Fig. 9. Design shaft of the new micro turbine

Generator Banki Turbin

Pully

Van Belt Nozzle

Pump

Tank Pump

Nozzle Angle

Shaft Angle

Fig. 10. Design model simulation of the micro turbine The prototype models were each made of a waterwheel supported by two pillows placed on the left and right sides of a holder perpendicular to the shafts, with axles made of iron, a pulley as the fan belt connected to the generator, and a water pump to circulate the air from the tank to the nozzle. In this study we used as many as 16 blades with 50 cm wheel diameters and wheels 12 cm thick. The curvature of the waterwheel’s blade angle is the factor responsible for generating a maximum efficiency value (η).

Fig. 11. Model of the turbine prototype

The angle value of α1 = 15ô, obtained from the simulation results in section 4, was tested, as were angles α1 = 16ô and 17ô.

To generate the water flow, we installed 2 pumps (Shimizu, Model PS-116 BIT, U: 1 x 220V 50Hz with Q = 10–24 l/min). Power input was calculated as Pin = Q x ρ x g x h, where Pin = power input (watts), Q = volumetric water flow rate (m³/s) = 0.00064, ρ = density of water (kg/m³) = 1000, g = acceleration due to gravity (= 9.81 m/s²), and h = total energy difference between the upstream and downstream line of wheel (m) = 50 cm = 0.5 m. so, Pin = 1000 kg/m³ x 9.81 m/s² x 0.00064 m³/s x 0.5 m = 3.14 W, as the power input value for the efficiency value results.

Each turbine model was tested with curvature angles of α

= 15ô, 16ô, and 17ô. The values of the other parameters were kept exactly the same in all models. Using a water pump to generate water flow to the nozzle, we changed the angle of the nozzle and measured the current I (amperes), voltage V (volts), and rpm. The power generated was calculated from P

= I x V (watts).

An output efficiency graph can be drawn for the angle (θ) within the range 0ô–50ô. Figure 12 shows a comparison of the efficiency output for blade angle curvatures (α) of 15ô, 16ô, and 17ô, respectively. The parameters of a water flow velocity of 0.00064 m³/s, a 50 cm diameter water wheel, 16 blades, and a 12 cm-wide water wheel were the same in all models. The goal was to carefully investigate the effect of the curvature blade angle (α) on water wheel efficiency.

Experiments were performed sequentially for each wheel at a certain curvature angle α to determine their influence. The value of the curvature of the blade angles (α) selected for testing was based on the results of the PSO (section 3). The best angle (α) according to our PSO is 15ô. According to the results of the plans [12], 16° was the optimum, and 17ôwas the authors optimal experimental result by their own research. Our experimental results verified our results that a water wheel with a blade curvature angle (α) of 15ô produces the highest nozzle angle (θô) efficiency in the range 25ô < θô

< 45ô, compared with water wheel angle curvatures of 16ô and 17ô.

Fig. 12. Efficiency of the relative water wheel nozzle angle θ Figure 13 shows the power output produced by the water wheel with a 15ô blade curvature angle, which is higher than the output by water wheels with the blade curvature angles of 16ô or 17ô. The chart patterns formed by the power output are similar to the efficiency pattern. This is because efficiency is the ratio of the output power to the input power. In this case, the input power is constant.

0 5 10 15 20 25 30 35 40 45 50

0 5 10 15 20

Theta (degree)

Efficience

16o 17o 15o

(13)

176 Fig. 13. Power output of the water wheel vs nozzle angle θ

The RPM output can be ascribed to the nozzle angle θ.

In Figure 14 we can see that the RPM output value increases with an increasing nozzle angle from 10ô to 30ô. These results show that a 15ô blade curvature angle (α) yields a higher RPM than the water wheels with 16ô and 17ô blade curvature angles (α). Other parameters were held constant in the three experiments.

Fig. 14. RPM of the water wheel vs the nozzle angle θ The improved results obtained with a 15ô blade curvature angle α compared with 16ô and 17ôblade curvature angles α include (1) RPM value, (2) output power, (3) output current, and (4) voltage output. We can conclude that water wheels with a 15ô blade curvature angle have higher efficiency compared with those with 16ô and 17ô blade curvature angles. Thus this study contradicts the research results of[12], which concluded that a 16ô blade curvature angle was optimal.

6. Conclusion

The angle of the blade greatly affects water wheel efficiency where the blade is in direct contact, such that the thrust of water causes the wheel to spin. A 15ô blade curvature angle is shown to produce higher efficiency values when compared with curvature angles of 16ô [12]and 17ô. By utilizing the PSO algorithm to find the optimal blade curvature angle, the water wheel is proven to generate higher output power and higher RPM with its nozzle set at this angle (θ) value.

The energy generated by the water wheel with a 15ô blade curvature angle proved to be higher than those with curvature angles of 16ô [12] and 17ô. These results were obtained from a mini-generator operating with a water wheel-mounted fixed load, for which the output current and voltage were measured. The output power of each model

were calculated, and the calculation results provide the evidence that the 15ô blade curvature angle (α) produces the highest energy, when compared with angles of 16ô and 17ô.

Acknowledgements

The authors wish to convey their gratitude to the Ministry of Ristekdikti, Indonesia, which providing financial research Hibah Bersaing via LPPM Udayana University 2015-2016 contract No. 311-19/UN14.2/PNL.01.03/2015.

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PDF International Journal of Renewable Energy Research - UNUD

Vol7

Table of Contents

Articles

Investigate Curvature Angle of the Blade of Banki's Water Turbine Model for Improving Efficiency by

Means Particle Swarm Optimization

Lie Jasa*

, I Putu Ardana**, Ardyono Priyadi***, Mauridhi Hery Purnomo****

𝑉

= 𝐶√2𝑔𝐻

, I Putu Ardana, Ardyono Priyadi*, Mauridhi Hery Purnomo****