diseño de pequeñas turbinas de agua para granjas y pequeñas comunidades

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MICROFICHEREFERENCELIBRARYA project of Volunteers in Asia

Desiun Of Su Water TUK- for Farms and Small. .Communitie, -4by: MohammadDt,-aliPublished by:Technology Adaptation Program

Massachusetts Institute of TechnologyCambridge, MA 02139 USAPaper copies are $ 7.00.Available from:Technology Adaptation ProgramMassachusetts Institute of TechnologyCambridge, MA 02139 USAReproduced by permission of the TechnologyAdaptation Program, Massachusetts Institute ofTechnology.Reproduction of this microfiche document in z :form is subject to the same restrictions as ti:;seof the original document.


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DESIGN OF SMALL WATER TURBINES FORFARMS AND SMALL COMMUNITIES

Mohammad DuraliProject supervisor:David Gordon Wilson

Spring 1976

TECHNOLOGY ADAPTATION PROGRAMMassachusetts Institute of TechnologyCambridge, Massachusetts 02139


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.

CONTENTS

CONTENTS., *..................... 5LISTOFFIGURES..................... 7PREFACE......................... 9ACXNOWLEDGEMENT. . . . . . . . . . . . . . . . . . . . . 11ABSTBACT........................13CHAPTER 1 INTRODUCTION. . . . . . . . . , . . . . . . . 15

1.1 Background, 101.2 Problem Statement, 101.3 Principles of Our Approach, 11CHAPTER 2 DESIGN OF A CROSS-FLOW (BANKI) TURBINE. . . . 19

2.12.22.32.42.52.62.72.82.92.10

Description, 19Advantages of Bank Turbine, 19Analysis of the Machine, 21Design of the Rotor, 24Losses and Efficiencies, 32Blade Design, 37Sizing of a Cross Flow Turbine,, 46Mechanical Design, 51Evaluation of Efficiencies, 57Radial-Inflow Partial-Admission WaterTurbine, 58

CHAPTER 3 DESIGN OF AXIAL-FLOW TURBINES . . . . . . . . 613.1 Description, 613.2 Advantages, 613.3 Analysis, 633.4 Design of Blades, 653.5 Sizing of the Machines, 68

CHAPTER 4 DISCUSSION ON ADVANTAGES OF DIFFERENT TYPES . 894.1 Improvements on Reaction Machine, 914.2 Off-Design Performance, 92

APPENDIX I TABLE OF PARTS AND WORKING DRAWINGS. . . . . 97APPENDIX II FRICTION LOSS IN NONCIRCULAR CONDUITS . . ..147

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APPENDIX III EFFICIENCIES. . . . . . . . . . . . . m 149APPENDIX IV PERFORMANCE ESTIMATION OF AXIAL-h?LOWTURBINES c . . . . . . . . . . . * .* 153


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LIST OF FIGURES

NUMBER TITLE2-l2-2

Cross-Flow (Banki) Water TurbineVelocity Diagrams of Different Locations inCross-Flow Turbine

2-32-42-5

2-62-72-8

2-9

2-10

2-113-1

3-23-33-4

3-5 Reaction Velocity Diagram 83

Effect of Blade Outlet Angle on StallingVelocity Diagram TerminologyWork Coefficient Iy vsO Relative Inlet FlowAngle 6,Converging Flow Inside the RotorCross-Flow Turbine-Blade TerminologyRatio of Blade Radius of Curvature R andRotor Length L over Rotor Outer Diametervs. Rotor Inner-to-Outer Dia. Ratio m.Ratio of Radius to Hydraulic Diameter R/Dh,and Deflection Angle of the Blade PassageBc vs. Rotor Inner-to-Outer Dia. Ratio m.Number of Blades Z vs. Inner-to-Outer Dia.Ratio m.Radial-Inflow Partial-Admission Water Turbine 59Inlet and &t' -et Velocity Diagrams of Axial-Flow Turbine StageBlade TerminologyImpulse Velocity DiagramB?ade Sections of the Axial-Flow ImpulseTurbine

PAGE2022

262831

353844

44

45

62

666975

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NUMBER TITLE PAGE

3-64-1

Blade Sections of the Axial-Flow Reaction TurbineCharacteristic Curves of Reaction Machine forConstant Flow Rate

8593

4-2 Characteristic Curves of Reaction Machine inConstant Speed 94

APPENDIX II1 Loss Factor for Bends (ASCE, J. Hydraulic Div.,Nov. 65) 148

2

LIST OF FIGURES (Continued)

Friction Factor f vs Re. for Different e/D.(Rohsenow, W.M., and Choi , H.Y., Heat, Ma%,and Momentum Transfer, p. 58)APPENDIX III

1 Scheme of Losses in Water Turbo-GeneratorsAPPENDIX IV

1 Turbine Blade and Velocity Triangle Notation2 Lift Parameter, FL3 contraction Ratio for Traction Profiles4 Basic Profile Loss5 Trailing Edge Thickness Losses6 Profile Loss Ratio Against Reynolds Number Effect7 Secondary Loss-Aspect Ratio Factor8 Secondary Loss-Basic Loss Factor

148

151

156156157157157158158158

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PREFACE

This report is one of a series of publications which describe variousstudies undertaken under the sponsorship of the Technology AdaptationProgram at the Massachusetts Institute of Technology.In 1971, the United States Department of State, through the Agency forInternational Development, awarded the Massachusetts Institute ofTechnology a grant. The purpose of this grant was to provide supportat M.I.T. for the development, in conjunction with institutions inselected developing countries, of capabilities useful in the adaptationof technologies and problem-solving techniques to the needs of thosecountries. At M.I.T., the Technology Adaptation Program provides themeans by which the long-term objective for which the A.I.D. grant wasmade, can be achieved.The purpose of this project was to study alternative water turbinesproducing 5-kw electric power from an available hydraulic head of 10 mand sufficient amount of flow, and to recommend one for manufacture.The work consisted of the preliminary design of different types of waterturbine which could be used for this application. Then one was selectedand designed completely. A complete set of working drawings was producedfor the selected type.Four different types of water turbine were studies: a cross-flow (Banki);two types of axial-flow turbine; and a radial-flow turbine. Each onehas some disadvantages. One of the axial-flow turbine (one with rotorblades having 50% degree of reaction) was chosen for detailed design aspresenting the optimum combination of simplicity and efficiency.In the process of making this T.A.P.-supported study, some insighthas been gained into how appropriate technologies can be identifiedand adapted to the needs of developing countries per se, and it is ex-pected that the recommendations developed will serve as a guide to otherdeveloping countries for the solution of similar problems which may beencountered there.

Fred MoavenzadehProgram Director

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ACKNOWLEDGMENT

This study was sponsored by the M.I.T. Technology AdaptationProgram which is funded through a grant from the Agency for Interna-tional Development, United States Department of State. The viewsand opinions expressed in this report, however, are those of theauthor and do not necessarily reflect those of the sponsors.

Mohammad Durali's financial support during the period of theresearch work has been provided by the Aria Mehr University ofTechnology, Tehran, Iran.

This project was initiated by the T.A.P. program director,Fred Moavenzadeh, in his discussions with a group at the Universidadde Los Andes led by Francisco Rodriguez and Jorge Zapp.

We are grateful for this support and help.

David Gordon Wilson,project supervisordepartment of mechanical engineering

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DESIGN OF SMALL WATER TURBINES FORFARMS AND SMALL COMMUNITIES

Mohammad Durali

ABSTRACT

The purpose of this project was to study alternative waterturbines producing 5-kw electric power from an available hydraulichead of I.0 m and sufficient amount of flow, and to recommend onefor manufacture.The work consisted of the preliminary design of differenttypes of water turbine which could be used for this application.Then one was selected and designed completely. A complete setof working drawings was produced for the selected type.

Four different types of water turbine were studied: a cross-flow (Banki); two types of axial-flow turbines; and a radial-flowturbine. Each one has some advantages and some disadvantages.One of the axial-flow turbines (one with rotor blades having 50%degree of reaction) was chosen for detailed design as presentingthe optimum combination of simplicity and efficiency.

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Chapter 1INTRODUCTION

Not all consumers have easy access to electrical powerproduced by main power plants. Sometimes it is not worthwhile forsmall isolated customers to afford the transmission and maintenancecosts needed if they are to connect to the nearest main power.Until the early 1970's an ideal way to produce small amounts ofelectrical power was to use diesel- or gas-engine-driven generators.But with high energy prices, naturally available power sources aszun, wind, streams, small water fa lls and so forth can often bemore economical, provided a simple and cheap device for each casecan te made.1.1 BACKGROUND

In the country of Colombia in South America most coffee farmsare situated on streams where a head of 10 m can easily be trappedand there is sufficient flow available especially during the timeswhen power is most needed. Although the price of mains electricpower is not very high, the cost of transmission of power from themain power plant to the farms may be extremely high. Because ofthis and also because the demand for electricity is seasonal, manyfarmers prefer to produce their own electricity.1.2 PROBLEM STATEMENT

The effort here is to design a machine which can produce


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5 kw electric power for the cases mentioned before. As thismachine would be used by farmers who on average have littletechnical knowledge, one of the major objects is to avoid verycomplicated structures. Moreover the machine must not need skilledmaintenance. Finally the amortized capital cost for using thismachine should be less than the total cost of using the transmittedpower produced by mains power plants.

Some members of the faculty of engineering of the Universidadde Los Andes in Bogota have worked on this problem. They havedeveloped a half-kw cross-flow turbine. They plan to modify thatmodel for hight;r power levels. We have reported our work to thisgroup regularly.

The design o f small water-turbine units has not previouslybeen carried to a high degree of sophistication. This might bebecause of their limited applications. For applications like theone we have (i.e. electricity needed in a period of year when thereis plenty of water) the design of a cheap machine may be a goodsolution to energy problems.1.3 PRINCIPLES OF OUR APPROACH

The effort was put into two different approaches to theproblem.

3) Designing a machine which can easily be manufactured byany simple workshop having enough facilities to weld, drill andcut steel parts. Consequently, the machine can be built locally in


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each farming area. The parts such as bearings, gears, chain,generator etc., can be shipped to each area. In this approach wetried to use materials like angle bars, sheet metal, round bars andso on which do not need much machinery to be used. Casting and othermore complicated processes were excluded.

b) Designing a machine which could be manufactured andshipped to farming locations. This approach a kind of processlayout is going to be arranged for manufacturing the machine. Theproduction methods like casting and molding, and using plastic partsseems to be more economical.

In both cases a) and b), the design has to be within the areaof the industrial capabilities of the country of the user. Thenext chapter contains the design of a cross-flow turbine based onthe "a" assumptions. In the end of Chapter 2 design of a simplerapid inflow turbine is discussed very briefly, Chapter 3 is aboutthe desig? of 2 modified axial-flow turbines with short blades. Thedesign of the two latter types is based on the assumptions made onthe "b" type of approach.


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Chapter 2DESIGN OF A CROSS-FLOW (BANKI) TURBINE

2.1 DESCRIPTIONThis machine was .'irst designed by Dr. Banki over 60 years

ago. Since then some low-power models of this kind have beendeveloped in Europe and have given good performances.

This machine is an atmospheric radial-flow impulse wheelwhich gets its energy from the kinetic energy of an inward jet ofwater. The wheel is simply a squirrel-cage-shaped assemblage ofcurved horizontal blades (Fig. 2-l) fixed between circular endplates to which the shaft is attached. The jet of water coming outof the nozzle passes through the rotor blades twice.

Tine biades have to be designed to direct the flow inward tothe open internal space inside the cage and then to drain it to thetail water outward through another set of blades in another part ofthe inner circumference.2.2 ADVANTAGES OF BANK1 TURBINE

The cross-flow turbine has significant advantages which makeit a suitable solution to our problem. Its simple structure makes iteasy to be manufactured. The atmospheric rotor avoids the need fora complicated and well-sealed housing. The bearings have no contactwith the flow, as they are out of the housing; they can simply belubricated and they don't need to be sealed. And finally, when,


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TAIL-WATER----P-P- --------I_---

-----m--e--

--- -v-----

--- -- -me -- - - - - -

FIG.2-1. CROSS-FLOW (BANKI) WATER TURBINE.


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for a constant head and a given power level a simple fixed rotorcross section is obtained, then for higher power levels one cansimply use a longer rotor.2.3 ANALYSIS OF THE MACHINE

The most useful re7 tion in design of a turbomachine is theEuler equation,

where U stands for rotor peripheral speed, CC is the tangentialcomponent of absolute velocity of the fluid and h, is the stagna-tion enthalpy. Subscripts i and o stand for inlet and outlet ofthe rotor, respectively (Fig. 2-l).

The rotor normally is designed so that the absolute velocityof the fluid leaving the rotor is in the radial direction, so

e. = 0and therefore

icei = gc A bi-oand then the parameter "work coefficient" for the rotor will simplybe


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FIG.2-2. VELOCITY DIAGRAMS OF DIFFERENT LOCATIONS INCROSS-FLOW TURBINE.


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From the first law of thermodynamics,

= = A h, = A (h +" + zg) ,lil i-o i-0

but for water turbines the rate of heat transfer and change instatic enthaipy are very small and for small units like the one weare to study the drop in height from inlet to outlet is negligible,so that,

l3Tm = Ah, =

using the equations we had before,uicei = 3 (Cf - Ci) ,

Yu2 =i $ cc; - 2)or finally u: =k (CIcf,

For an impulse machine the value of 'Y is normally takenequal to 2.0. If the total hydraulic head before the nozzle isAHo and nN be taken as nozzle efficiency (which covers the losscf kinetic energy through the nozzle) then equation (a) can bewritten as follows,

u2= & (2g HorlNcz,


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or C2ui = f (AH, I~ - $ 1 (LJ)

From Eq. (2.1) we find that for a given hydraulic head,choice of the velocity diagrams enables us to determine the rotorspeed and hence rotor dimensions.2.4 DESIGR OF THE ROTOR

The choice of the blade inlet and outlet angles is theimportant part of the design. They have to be chosen so that thejet of water transfers useful work to the rotor in both passesthrough the blades.

Throughout this analysis angles are measured from tangentsto the circles and are positive in the direction of rotation. Alsowe assume that at design point the incidence angle is zero and thedeviation angle is very small so that the design will not be affectedif we assume the derivation to be zero. From Fig. (2-2) by simplegeometry we have for all cases

This is true for all shaft speeds and flow inlet velocities. Butone may question why the inter stage angle of the blades is takenequal to 90" (i.e. the outlet angle of the first "stage" or pass,and the inlet angle of the second stage). The reasoning behind thischoice is as follows.


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Assume zero deviation angle for the flow leaving the bladesin the first pass; therefore, the flow relative velocity angle willbe equal to the blade outlet angle. Now suppose that the angle ofthe blade at the outlet of first pass is bigger than 90' (Fig. 2-3a).As you see there will be negative incidence at the second pass.This time assume 8, < 90" (Fig. 2-3b). In this case positiveincidence will take place. Now as a comparison in Fig. (2-3~) thesituation is shown with B = 90".

Therefore the optimum blade outlet angle has a value around9o". Now assume 6 as deviation angle at outlet of the first pass(Fig. 2-3d). If the blade angle is kept equal to 90" then therewill be an angle of incidence "i" so that i = 6 (in the inlet ofthe second pass). Consequently if the blade's outlet angle isslightly more than 90' (equal to 90 + 6/2) then the incidence willbe near to zero.

Normally the values of deviation angle are of the order of Z"to 8O. Therefore the optimum value for the tlade outlet angle isbetween 91" to 94O. Obviously taking the blade angle equal to 90would not cause much effect on the performance.

Because the cross-flow turbine rotor works totally at atmosphericpressure there is no static-pressure difference from inlet to outletof a blade passage. Therefore the flow through a blade passage doesnot accelerate or diffuse. In fact, blade passages do not fill withwater and flow passes through the blade passage as a jet deflecting


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\02 \ \

(4 (b)

I \

FIG-z-3, EFFECT OF BLADE OUTLET ANGLE ON STALLING.


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along the pressure side of the blade. Consequently the flow will,have a constant relative velocity through the passage (in the absenceof friction) and the maximum flow will be determined by the smallerarea of the passage which is at the inner diameter side of the rotor.

The rotor specifications are then as follows (Fig. 2-4):outlet relative velocity angle (first pass) B, = 90" so fromFig. (2-4a) C, 2 = U2 and the absolute velocity of water leavingthe rotor is in radial direction (Fig. 2-4b) 01~ = 90".

Let us define

(Notice that in this particular case x is equal to the workcoefficient.)and

r2m3- rl

r2 and r 1 are inner and outer radii of the blading respectively,therefore

u2 u3m= 'il = UC l

The above definitions will help us to write simpler geometricrelations.

From Fig. (Z-4a) we have51 Cl cos a1 - cl cos ax f - = = 1

ul ul -cl cos a1 + w1 cos (3, (2.2)


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(4

FIG.2-4. VELOCITY DIAGRAM TERMINOLOGY.


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Also,Crl = Cl sin(IT - al> = Wl sin(?I - 8,)

from (2.2) and (2.3)tan B,x = (tan B, - tan al)

ThereforeB, = tan-'(( 2 1 tan al)

From the outlet velocity triangle (Fig. 2-4a)

(2,3)

(2.4)

c2= wf+u;If we assume no loss of kinetic energy through the blade passage,then the relative velocity of the water has to remain unchangedalong the blade passage, so using Eqs. (2.2) and (2.3) we have

c2 = ulpyi$7 . 0.5)

Butc2 -5z u2 = m 3cos a 2 cos c%2

Combining (2.6) and (2.5) we have,u2 os-lJ$$-j-(2.6)

(2.7)


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From Fig. (2-4b) we have;

u3cos(lT-f3) = - = 14 .rn W3 m tan cx3 (2.8)

but as illustrated before at any condition ~1~ = a2 and if incidenceand deviation angles are assumed to be zero then B, = B, so from(2.8) we have:

1tan a2 = - m cos B1

-1 1u2 = tan m cos B, (2.9)

Therefore we found two values for c12 ' one by using the firs t"stage" geometry (Eq. (2.7)) and the other was found by using thesecond-stage conditions. Putting these two values equal we get anondimensional relation between the design parameters m , x and5 ' as follows:

-1tan (- 1m cosBl)=cos-lJg-Tp

(2.10)


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FIG.2-5. WORK COEFFICIENT$fVS. RELATIVE 1iYLiT FLOW ANGLED,.


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Notice that a1 , x and 6, are related together by Eq. (2.4).Now design curves can be drawn using Eqs. (2.4) and (2.10) which mayhelp to choose the right value of the parameters. Two useful curvesmay be,values of x vs. B, for different values of nozzle angleb,)> and values of x vs. % for different values of m .

Figure 2-5 shows the design curves based on Eq. (2.4).Solving Eq. (2.10) for the value of X we get

\1x = m cosf3 -1 1 I2 -1+1 (2.11)cos tan ( m cos B 11

For any value of m and B, the value of x can be found, orvice versa.2.5 LOSSES AND EFFICIENCIES

In cross-flow machines, blades are normally made of curvedbent strips of thin sheet metal. So small variations in inlet flowangle could cause high incidence losses. Summarily the other lossescan be listed as: hydraulic losses due to skin friction and changeof flow direction in the nozzle and blade passages; losses due toconverging flow in open space inside the rotor; and mechanicallosses.a> Nozzle losses

For nozzle a factor cv which acts as a velocity correctionfactor can be used to define the losses due to skin friction andconverging flow, so


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or

For the loss due to the curved nozzle passage the curve given inAppendix I, will be used, provided a hydraulic diameter isdefined as

Dh = 4 x flow areawetted perimeter (2.12)

If the radius of curvature is R then the curve in Appendix Iprovides the values of loss factor k versus deflection anglefor different values of R/Dh , where

W2% 1oss = 5

and W1 is the mean water velocity through the nozzle. Obviouslythe mean values of R and Dh should be used to get a better 'result.b) Blade losses

I> Hydraulic-friction losses. The coefficient of frictionfor the flow through blade passages can be found based on hydraulicdiameter, and using the curve given in Appendix I. So


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%L w2=oss fhTxz'

subscript h stands for values evaluated on basis of hydraulicdiameter. "L" is the length of the blade passage and W is therelative flow velocity.

II) Losses due to flow direction change, In this case wecan use the curve given in Appendix I, as for the nozzle.4 Losses within the rotor

As seen in Fig. 2-6, the direction of actual velocity leavingdifferent blades converges to one point. This effect will cause achange in flow direction entering the second set of blades.

As seen in Fig. 2-6 from simple geometry, the maximumincidence angle "y" caused by this effect is half of the admissionangle "0". It is assumed that the central stream line remainsundeflected. Also the bigger the admission angle is, the closerthe right-hand side jets will get to the inner surface of the rotorand that will cause negative work on the second pass. Thereforethe angle of admission has to be kept as small as possible. Areasonable range of magnitude for admission angle is between 20* to40". For these values of admission angle the loss due to this effectis very small.d) Efficiencies

Normally the overall efficiency for a water turbine isdefined as;


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F&2-6. CONVERGING FLOW INSIDE THE ROTOR.


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where nh is the hydraulic efficiency of the turbine, and coversall the hydraulic losses across the blading. {See also Appendix11).

AHHloss'h - AHwhere AH stands for difference between hydraulic head of theturbine inlet and outlet.

The term rim or mechanical efficiency covers all the lossesdue to disk friction and bearings and so on and is defined as;

rl, = T - TlossT

where T represents the shaft torque.Finally T-IQ is the volumetric efficiency which covers the

leakages and the flow which passes the turbine without giving anypower

where Q is the volume flow rate.The important part of the evaluation of the efficiency of

a turbine is to find the hydraulic efficiency. This term is very


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sensitive to the blade profile and flow angles (see Appendix III).In order to get the hydraulic effic' &ency of the crossflow turbineusing Eq. (2.15), one has to write all the losses mentioned in thelast section in terms of hydraulic head.2.6 BLADE DESIGN

As mentioned before the rotor in a crossflow turbine con-sists of two end plates to which the blades are joined. anydesigns do not have a through shaft, so that the torque is trans-mitted to the output shaft by the blades, i.e. the blades experienceall the bending moment due to torque transmission, all the bladescome under a relatively higb periodic stress, as at each momentonly a few blades carry the whole flow. Therefore one would liketo avoid long rotor blades and blades with small radial chord.

Stiffer plates may be used to support the blades betweenthe two end plates and so allow longer rotors. Therefore for agiven power level and hence a specified volume flow rate, if therotor can be reinforced with stiffer plates one r-an go forsmaller rotor diameter and longer rotors and hence higher shaftspeed. The cost for these apparent advantages is that of thehigher complexity.

For the type of design we have chosen, we will only beconcerned with rotors having no stiffer plates. Also the bladeprofiles will be segments of a circle. Therefore the blades canbe cut out of thin-wall tubes, or made of strips of thin sheet


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Zr number of bladesdi: inner dia.doz outer dia.L =, length of rotor

FIG.&7. CROSS-FLOW TURBINE-BLADE TERMINOLOGY.


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metal rolled around a pipe. The most important parameter to bespecified is the ratio of inner to outer diameter of the rotor"ml' which affects most of the other rotor parameters, such aslength, number of blades, etc., effect of m on other bladedesign parameters can be found using Eqs. (2.13a) to (2.13f)which relate these parameters. (See Fig., 2-7 for bladenotation.)

0y- 5 =

2y - 4 = B -

dOc sin y = 2

0

s

sin QI

R =2 sinTBc/2)

c cos y + dO sin Q/2 = do - di2

CCT = dl sin n/Z '

(2.13a)

(2J3b)

(2.13~)

(2.13d)

(2.13e)

(2.13f)

The solidity (5 is defined as the ratio of the blade chordto the spacing of the blades on the inner-diameter side of the rotor.

It will be easier to work with the nondimensional forms ofEqs. (2.13a) to (2.13f). Let's define


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then,Y = EIc/2

27-e= B-s

and

2A sin y = sin 4

x5 = 2 sin y

X cosy 4- sin ($/2 = 3 (l-m)

x0 =m sin n/Z '

(2.14a)

(2.14b)

(2.14~)

(2.14d)

(2.14e)

(2.14f)

As discussed in the last section the hydraulic loss throughthe blade passage is a function of the ratio of the radius ofcurvature of the blade camberline (centerline) over the hydraulicdiameter of the passage and the deflection angle of the blade.

Figure 2-8 shows the variation of the ratio of the rotor length andthe blade curvature ratios over the rotor outer diameter versusvalues of rctor inner-to-outer diameter ratio, These curves showthat shorter and more curved blades result from using biggervalues of m.


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As mentioned in Section 2.5 the loss through the bladepassage is a function of the ratio R/Dh and ec , where Dh isthe passage hydraulic diameter and 8 is the blade deflection

Cangle. Bigger values of R/Dh and smaller values of 8c giveus less loss. Both these parameters can be found in terms ofgeometrical parameters introduced in Eqs. (2.13) and (2.14), asfollows:

as defined= 4 x flow

Dh - -.wetted perimeter

but as pointed out before, flow through the blade passage is thedeflection of a jet of water along pressure side of the blade andso the jet thickness is fairly constant. Consequently the hydraulicdiameter of the blade passage can be determined by the inner-diameter side of the rotor. By the aid of Fig0 2-7 we then have

Dh = 4 x (LXS)L + 2s

The reason for defining the wetted perimeter as (L +2s)is that the flow does not fill the passage fully. Only the blade's

pressure side and side walls guide the flow. If Wl is therelative velocity of water through the passage and a is the rotoradmission angle then at the inner-diameter side of the rotor wehave:

Q = WIA a.= 'lL 360-d i


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but as m -5 di/do , then

L = Qci360 IT .Wl m d0

Defining CI E c/s and h = c/d o (Eq. (2.14) therefore,

S C= - =CT k dO0 =

Substituting these into the relation for Dh we have:44 do xx-a-7TmW do 0Dh 360 1=

Q + 2>A3% 7rmW 1 do

Dividing both the denominator and the numerator by doand naming

c E Qa IT d2 W360 01

then we have

c x4--X-Dh = m ad 0


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Also from Eqs. (2.14) we have the definition of

5 +- ,0

orR=tdo ,

Therefore

orRiq =


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FIG.2-8. RATIO OF BLADE RADIUS OF%R"ATURERAND ROTOR LENGTH faOVER ROTOR OUTER DIAMETER VS. ROTOR INNER-TO-OUTER DIA. RATIO m .

8

6

2

0

FltG.2-ANGLE

0 5 ,6 .7 .0 .9 II-9. RATIO OF RADIUS TO HYORAULTC DIAMETER R/Dh g AND DEFLECTOF THE BLADE PASSAGE& VS. ROTOR INNER-TO-OUTER DIA. RATIO

80

60

0IONml.


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I IROTOR ANGLE OF -1

I I I I I.5 .6 -7 .8 .9mFIG.2-10. NUMBER OF BLADES VS. INNER-TO-OUTER DIA. RATIO m.


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The design of the rotors with no stiffer plates is more dominated bymechanical design of the blades than by optimization to get the mini-mum loss. Using Eqs.(2.14a) to (2-14f), the curves shown in Fig.2-10 can be drawn.

These curves show the number of blades for each choice ofsolidity and rotor inner to outer diameter ratio. As the numberof blades is reduced the rotor becomes longer because the throatwidth is lessened (Fig. 2-8). Therefore although the blade chordincreases as the number of blades decreases the blades becomemore flexible in bending. On the basis of stress and stiffnessconclusion, assuming typical material properties and thickness(e.g. 2mm steel plate for the blades), we have let 18 as theminimum number of blades.

When the number of blades is increased, the rotor can beshorter, but the manufacturing difficulties for small workshopsbecome progressively more severe- We have chosen 60 as themaximum desirable number of blades. Points inside the closed curvedrawn in Fig. 2-10, give better designs as far as losses and structuralstiffness are concerned.2.7 SIZING OF A CROSS FLOW TURBINE

For a machlne of this type working under constant head, thevelocity of jet of water leaving the nozzle is fixed (Section 2.4).Therefore the choice of inlet absolute flow angle from the nozzleaffects the size of the rotor, a small nozzle angle being desirable.


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As discussed in Section 2.5, the angle of admission should alsobe kept small in order to reduce the losses within the rotor andlosses due to flow entering the blades in the second pass. Theangle of admission is taken equal to 30 in our machine. The inletabsolute flow angle in a prototype designed by Banki was 16O. Inthat design the flow crosses the rotor on an approximately horizontalline (i.e. the water entrance and draining points are on a horizontalline). He used a cast casing incorporating the nozzle for histurbine.

As we have tried to avoid complex structures and manufacturingprocesses, our design does not have a cast casing like Banki'sdesign had. Rather we used a steel angle framework with sheetmetal covers; there will be a main cover around the rotor whichconfines the water spray, The nozzle will be a separate part fixedto the frame giving a nozzle angle of 30'. That value resultedin the least complexity of the structural design. (See nozzle rotorcombination drawing in Section 2.8.) So with reference to Section2.4 the absolute inlet flow angle "~11" will be 150". Draining willbe vertically downward.

From the fact that the work coefficient is equal to 2.0 wehave %1 2Ul ,

Assuming a total-to-total efficiency of 75% for the turbine(nozzle and rotor), from Eq. (2.1) we get,


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0 (UC*) = 69,20 m2/s2then

u1 = 5.88 m/s

cl = 13088 m/s

-wl = 9.00 m/s .

The choice of shaft speed depends on how large the rotorouter diameter can be and what are the speed limitations for thebearings. As we were to use wooden bearings the sliding velocity:.ztween shaft and bearing bore limited us to a shaft speed of300 rpm. This speed is lower than desirable, because a highgear up ratio is needed to reach the shaft speed to 1800 rpm(generator speed). In future design studies it would be justifiableto specify bearings to run at high speeds.

Therefore specifying N = 300 rpm we get

dO = 0.3743m.

We would like to join the blades to the side plates by rivets(see general arrangement drawing and nozzle-rotor combiExtj.ondrawing in Section 2.81, Therefore we would like to have the leastpossible number of blades in order to get sufficient space forriveting the bent ends of the blades to the side plates. UsingFig. 2-10 in the last section we get m = 0.6 and 24 blades.


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Now using Eqs. (2-13a) to (2-13f) we get the followingresults and blade parameters. First from the velocity diagram(zero incidence) we get

B = 130" 53'and then

8 = 52" 58'CY = 26" 29'R = 0.0956 ms = 0.0293 mC = 0.0843 m

we have previously chosen,Z = 24m = 0.6

The inner diameter of the rotor then will be

di = 0.2246 m .

If 20% extra power is specified to cover the mechanicallosses and the losses in the generator then the output shaftpower has to be 6 Kw. The volume flow rate required will be

Q W= A(U Ce) = 0.0857 m3/s

The length of the rotor then will be


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L= I-&-L-=~adiW 1

O.l64 m

a being the admission angle,Once more recalling the veloci ty triangles shown in Fig. 2-4,

we can write the folPowing relation

WJ C(j) total = A(u Ce) 1st pass + A&J ce) 2nd passor

A@ Ce) = (UICe 1 - u2ce > +2 (U3Ce 3 - u4y3 14

but as we specified,

u 2 = u3 , u1 = u4 , CO2 = c03 = u2

$3, = 2u 1 ' s4 = 0 and AN ce> total = 2Uf

ThereforeAW Ce)

1st pass= 2$ - Ui = 2Ui - m21J: =

2u$ 2- 5 >and

A@ Cal = u; = m2U22nd pass .1


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The above relations show that for a value of m = 0.6 , the energytransferred to the rotor in first pass is 82% of the total energyand only 18% of the total energy is received by the second pass.This means that as hydraulic losses within the rotor and theentrance losses in the second pass do not affect the performance ofthe turbine very much.2.8 MECHANICAL DESIGN

The manufacturing processes under which the turbine is to bemade have been the most dominant parameters in the mechanicaldesign. The general arrangement drawing, scheme of the nozzlerotor combination and an isometric view of the machine are submittedin the following pages. Different parts of the machine are brieflydescribed as follows:Rotor

The turbine has a squirrel-cage-shaped rotor, 380 mm 0-D.and 165 mm long. The optimum speed under the design head of 10 mis 300 rev/min.

It has 24 blades, each blade being simply a circular segment.Blades can be rolled out of 2 mm galvanized steel sheet (see Part 11on the general arrangement drawing). They are joined to the rotorside plates with rivets (Part 12).

The rotor has no drive shaft. Power is transmitted throughthe bearing housing which rotates with the rotor, and the shaftwhich goes through the rotor bearing supports only the rotor(Part 14).


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52 It-1 11_-----I I IiY

-+F


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E-R0 TOR COMB NA TION OFCROSS- FL0 R/RBINE


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ISOMETRIC VIEW OF CROSS-FLOW MACHINE


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BearingsThe bearfng housing, which is a short piece of circular

steel pipe, is weided to a circular plate which is fixed to therotor side plates with rivets (Part 13).

Bearings are made of a special oil-impregnated wood. Althoughthere are some limitations for the maximum permissible speed forthis kind of bearing, its low cost and simplicity makes it suitablefor low-speed applications. Furthermore it does not need lubrication.'jIt works in wet as well as in dry conditions. It requires no seal(Part 15).

In our design the bearing rotates with the rotor, so equalizing.awear on the wooden bearing and increasing the bearing life.

Chain transmissionPower is transmitted from the rotor to the generator by means

of bicycle chain and gears. A 52-tooth gear is fixed to the circularplate which i s welded to tihe bearing housing (Part 21).

The generator has a constant speed of 1800 rev/min. A chainand gear combination is used which gives s speed ratio of about sixfrom turbine to generator.

A complete hub and set of five chain cogs for a bicyclederailleur gear is used for the second speed step up (Part 22).

The unnecessary gears in the gear set are replaced by spacersand only an 18-tooth gear (being driven by a 52-tooth gear on therotor) and a circular plate with a central bore, the same as one ofthe gears, is fixed to the gear set, The latter circular plate is


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be fixed with a 36-tooth gear being used for the second speed-upstep (Part 23). The last gear has 17-teeth and must be fixed tothe generator shaft. For the power level we have in this machinea good lubrication condition should be provided for the chain.

The two-step transmission in this turbine makes it difficultto incorporate an oil bath around the chain. As you will see inChapter 4 this machine would not be selected as the final choice,so we did not do further improvements on its transmission system.In order to increase the life of the chain and sprockets, we recommendthat two chains in parallel be used. Therefore two sprockets shouldbe installed side by side on each shaft,Housing

The housing is completely made of thin galvanized sheet steel.It has a fixed section which covers most of the rotor (Part 31), anda removable door (Part 32), placed in the back of the turbine, forservicing. It has a lifting handle and is fastened to the fixedsection with two simple latches (Parts 34 and 35).Frame

The frame is totally made of angles, welded together. Thegenerator mounting is a steel plate welded to short legs and itssize may vary when using different generators (Part 38).Nozzle

The nozzle is completely made of steel plates, welded together(Part 41). The flow can be changed and set on different valves fordifferent output powers. This is possible by chaning the angle of


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flap (Part 42). The semi-circular channel (Part 43) which is weldedto the flap has holes for different settings.

Warning: never change the flow while the turbine &----in operation-

As the system works under a relatively high head, a changeof flow while the turbine is working can cause "water-hammer" inthe piping which can result in serious damage.

To avoid this there has. to be a gate valve before the nozzle.The flow must be slowly reduced almost to the shut-off positionbefore changing the flap position,, After setting, the valve mustbe opened gently.

The possibility of installing a surge-tank as a shockabsorber has not been studied, because it would increase the sizeand the cost of the turbine,2.9 EVALUATION OF EFFICIENCIES

Knowing the size of different parts of the turbine thehydraulic efficiency of the turbine can be found. Following themethod given in the last sections we get:

'h = 76%

This efficiency is the total-to-total efficiency and is very closeto our prediction, so the design is acceptable, Taking the effectof the energy loss by drain flow into account we get,

rl t-s = 60%


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If a mechanical efficiency of 94% and a generator efficiencyof 90% is assumed then

andrl t-sm = 56.5%

rl t-su = 51%(See Appendix II.)2010 RADIAL-INFLOW PARTIAL-ADMISSION WATER TURBINEDescription

This type of turbine is a potential alternative to the cross-flow and axial types.

The turbine simply consists of a spiral-shaped distributorwith rectangular cross section which distributes the flow in twoopposite portions of its inner circumference, each one being an arcof 80". The rotor blades are rolled out of sheet metal and arefastened at one end only,around the circumference of the turbinedisk as cantilevers. The flow enters the rotor with a swirlingradially inward motion, passes through the blades while still inthe radial plane, and subsequently is deflected to leave the rotorin the axial direction.Flow Control

This type as described gives the possibility of controllingthe volsume flow to the rotor under constant head. Therefore thevelocity diagrams would keep their design-point geometry andconsequently the turbine would work at its design-point efficiencythrough the whole range of power.


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ROTATABLE SLEEVE

SPIRAL

NOZZLE BLADES

BLADES

FIG.&-11. RADIAL-INFLOW PARTIAL-ADMISSION WATER TURBINE.


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The control of the flow could be easily achieved by reducingthe angle of admission. This could be done by installing a rotatablesleeve between rotor and distributor. The sleeve would have portswhich could be brought more or less into alignment with ports on afixed sleeve to vary the admission area.Dimensions

For specified head (10 m) and power output (5.5 kw) a turbineof this type would have a diameter of about 220 mm when turning at450 rpm. However, with this size of the rotor there would be drain-ing problems on the inner side of the rotor.

Unfortunately, increasing the rotor diameter brings outanother problem which is the spiral geometry and size (see Fig.2). To solve the draining problem by increasing the diameter to340 mm would reduce the axial width of the rotor to 55 mm and thespeed to 300 rev/min.

This would require a spiral distributor of the same width(55 mm). To keep the fluid velocity in the spiral small, the radialdimension of the spiral would have to be increased.Conclusions

A rectangular cross section of the order of 60 x 200 mm wouldresult (in entry port). For the range of specific speed in whichwe are working, dimensions as large as this make the radial inflowturbine unattractive. We have not taken the design further.


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Chapter 3*ESIGN OF AXIAL-FLOW TURBINES

3.1 DESCRIPTIONIn this chapter the task is to design some simple axial-

flow turbines as a solution to the problem. We have chosen todesign machines with high hub-to-tip-diameter ratio which enablesus to use untwisted blades for the blading.

Principally, water flows through a set of nozzle blades(installed all around the circumference of the hub disk), into therotor blades, then passes the rotor blades and through the diffuserto the tailwater. The turbine can be designed as an impulse or areaction machine.3.2 ADVANTAGES

These designs should have comparable advantages with the Bankitype. The design of these machines provides easy manufacturingprocesses if they are to be mass produced (i.e. sand casting andplastic molding).

The blades are made of molded, extruded or cast plasticwhich will give accurate profiles and consequently a better designand off-design performance. Moreover the shaft speed in thesemachines is higher than that of the Banki type and therefore asimpler transmission and a lower gear-up ratio will be needed. Thesemachines can also be used as a drive motor to drive other machinesbesides the generator.


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FIG.S-1. INLET AND OUTLET VELOCITY DIAGRAMS 0FAX.IAL-FLOW TURBINE STAGE.


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3.3 ANALYSISSimilar to the analysis shown for the cross-flow turbine, we

can write Euler's equation to relate different velocity-trianglespecifications together (Fig. 3-l).

h01 - h02 = ulcel - u2ce2 l (3.1)

But if AH0 is the total hydraulic head difference ac'ross therotor then

h01 - h02 = %t AHog (3.2)

where n tt is the total-' co-total efficiency of the turbine (seeAppendix II).

The three parameters: flow coefficient, work coefficientand reaction which specify the type of the velocity diagram andblading are defined respectively as follows:

cX@ -T-

UICel - u2ce2qJ z u2m%l + 532

R E l--=r--

(3.3a)

(3.3b)

(3*3c)


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The analysis is done for the mean diameter,for the usualcase where C remains constant from inlet to the nozzles toXoutlet of the rotor. Now for each design a velocity triangle canbe chosen, hence values of I/J, $ and R can be specified.

A good approach to the design of different machines of thistype with different degrees of reaction is to keep the inlet flowangle to the rotor "ol" constant and to vary the two rtfher parameters(i.e. R and 9).

From (3.2) and (3.3b) we have

u = %t g AHoYJ .

and

Now, choice of shaft speed gives us the mean diameter

dm = 60 UIT @J-)

d = dt+dhm 2and mass flow rate will be

& = WA(U Ce)

where W is the output power of the turbine.

(3.4)

(3.5a)

(3.5b)

(3.6)


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The annulus area then will be

.Aa = (3.7)

where p is the density. Also we know that in terms of hub and tipdiameters the annulus area will be

A =a $ (d: - d; j (3.8)

As mentioned before we try to keep the ratio of hub to tip diameterhigh enough, to be able to use untwisted blades. A reasonablevalue for this ratio is around 0.8.

Now, a choice of velocity triangle gives us the value ofAU ce) and hence from Eq. (3.4), (3.6) and (3.7) the values of.u9L9a are found. Then the shaft speed can be determined and usingZq. (3.5ai gives us the value of mean diameter. Then using Eqs.(3,5bj and (3.8) we can find dh and d, .

If the ratio Of dh/d, is not acceptable a new shaft speedhas to be chosen to optimize the dh/dt ratio.3.4 DESIGN OF BLADES

Figure 3-2 shows the terminology used in this designprocedure. To find blade angles from flow angles we may use theinformation and curves given in Reference (2).I The following tworelations approximate the curves given in Ref. (2) with a good


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BLADE WIDTHr b-0

LEADING EDGE /'\ \\\FLOW INLET \ \ t

STAGGER A JGLE

FLOW OUTLETANGLE /3r

MADE OUTLETAXLE &DEV AT ION ANGL

'NG EDGE

E6

FiG.3-2. RLADE TER lIrJOLOGY.


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accuracy, for incidence and deviation angles.

(3.9)60-X 26 0.08+ ( 300.18_ = c/sc

Please see Fig. 3-2 for information on parameters used in aboveformulae. These two formulae are useful in preliminary design.In Eq. (3.101, ec or blade turning angle is equal to

eC = 6, + Mind + 6, + 6

so the blade angles will be

B2 = B,i-6

Suggested values for leading and trailing edge radii are

r e = (0.03 to o.os>c

(3.10)

It = (0.02 to O.Ol)C


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The design procedure for the blades is to choose a staggerangle "A" and an optimum value for solidity o . The optimumsolidity can be estmated by the Zweiffel criterion for the value ofwidth-to-chord ratio;

bs = 2.5 cos2c12(tgal + tgcx2)

also from Fig. 3-2,

t- = cos xC

(3.11)

(3.12)

from Eqs. (3.12) and (3.11) we find o ,

cl=;.In steam and gas turbines the dimensions of the blades and

the number of the blades are normally determined by choosing areasonable value for chord as far as vibration and stresses areconcerned. In our case, as blades are short, a good choice for thenumber of the blades which gives us a reasonable blade passage seemsto be a good approach.

Then finding the dimensions of the blades we can find theblade shapes by trying different curves for the blade profile.3.5 SIZING OF THE MACHINES

Single-stage axial-flow turbines are normally named on the


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basis of their velocity triangles. Two possible and most commontypes of velocity triangle are: impulse and 50%-reaction.

The design procedure in each case is to guess a value oftotal-to-total efficiency for the turbine. Then the machine willbe designed with respect to the estimated efficiency. Finally forthe designed machine the efficiency will be calculated using themethod given in Appendix III. The design can then be optimized.

In order to get 5Kw. electrical power from the generatorthe turbine itself will be designed for 10% extra power. So thespecifications of the turbine are 5,5 Kw. output power and 10 m.hydraulic head,a) Design of an impulse machine

Assumptions are a total-to-total efficiency of 0.80 andvelocity-diagram specifications of: work coefficient of 20(implicit in an impulse machine), and flow coefficient of 0.8 (whichgives an acceptable nozzle angle). Also we will specify that theabsolute velocity leaving the rotor is to be in the axialdirection, to minimize leaving losses therefore we have,

AH0 = Ho1 - Ho2 = 10 - $

from Fig. 3-3 we have,

Fig. 3.3. IMI'CLSE VELOCITY DIAGRAM


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Substituting the last two relations into Eqr. (3.4) and rearrangingfor U we have:

u = rl g Hcl++$ n

applying numerical values we have (at mean diameter);

u = 5.90 m/S

soA(UCe) = $U2 = 69.75 m2/s2

Then from Eq. (3.6) the volume-flow rate isQ = 0.0791. m3/s .

lpnnIbaa from the velocity diagram

OL1 = 68.2O

i a2 = O"

and I , = 51.34O\ B2 = 51.34O


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andc1 = 13.26 m/s

w1 = w2 = 7.38 m/s

c2 = 3.54 m/s

The choice of the shaft speed has to be done with regard to thefollowing considerations: a) the value of hub-to-tip diameter ratioshould be around 0.8; and b) a combination ,of two standard availablesprockets can be found which gives us 1800 rev/min on the generatorshaft. The minimum number of teeth for a l/2"-pitch sprocketspinning at 1800 rev/min is 24 teeth. This value is recommendedby almost all manufacturers. Therefore the value of shaft speedgotten by specifying the hub-to-tip diameter ratio should lead toan available number for sprocket teeth.

With regard to the above discussion a shaft speed of 540rev/min gives 80 teeth for the big sprocket, The dimensions of therotor then wili be

d = 0.2087 mm


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anddt = 0.2347 m

dh = 0.1827 mblade height = 0,026O m

The ratio of hub-to-tip diameter ratio is then 0.78 which is in anacceptable range.

Blade design. Nozzle and rotor blades should be designedseparately for this machine as they have different flow inlet andoutlet angles.

First for nozzle blades: by looking through curves andinformation given in Ref. (2) for different blade profiles, forcases having the same deflection and inlet angle, an optimumsolidity of 1,5 and a stagger angle of 45" are suggested. (Wetried several profiles with other staggers but this value gave thebest-looking profile,)

From Eqs. (3.9) and (3.10) we have:

A9 ind = 19.25"

6 = 5*09OThe blade angles are then

i B1 = 19.25OI B2

= 72.29O .


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To choose the number of the blades we have to specify thespacing. From the above specifications we have

b- = cos 45 = 0,71C

C- = 1.5S

(See Fig. 3-21,)In this case a different number of blades were tried, Finally

15 blades seemed to be a good number as it gives a reasonable cross-sectional area for the blades (as we want to use plastic blades, weprefer to have blades with bigger chordal length and hence morecross-sectional area).

With the above specification nozzle blade sizes are asfollows:

S = 0.0434 mmC = 0.0651 mb = 0.0462 mrt = 0.0025 m

9 = 0.0005 m

In the same way calculations for the rotor blades weredone. The results are tabulated in Table 3-1, Also see Fig. 3-4for blade sections.


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B; 6; Z CT AC AOind 8O B; B; S C b rR rt 0

NOZZLE o oo 68.2 15 1.5 45 19.25 5.09 19.25 73.29 43.4 65.1 46.2 2.5 0.5 12.4BLADESROTOR 51.3 51.3 16 1.5 30 5.13 6.27 56.34 57.57 40.7 61.6 53.35 2.5 0.5 21.8BLADES 2

TABLE 3-l: IMPULSE TURBINE BRING DIMENSIONS (DIMENSIONS IN mi)


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NOZZLE BLADES

ROTOR BLADES

- . ---- _

FIG.304. BLADE SECTIONS OF THE AXIAL-FLOW IMPULSE TURBINE.


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Evaluation of efficiencies, With respect to the method givenin Appendix III and information we got about the blades the value ofeach loss parameter can be found.

XPb N NPt XPt Xpr ar X

Nozzles 2.48 0.97 1.13 0.10 4.2 7.20Rotor blades 9.04 0080 1.12 0.10 1.2 20.20

TABLE 3-2: BLADES LOSS FACTORS

Substituting the numerical values for the parameters in theequation for rl and assuming 1 mm. radial clearance for the rotorwe have,

r) t-t = 80.6% .

The assumed value for rltt was 80%; therefore, we are close enoughto the optimum design.

Then from Appendix II we can find other efficiencies. Wespecify that diffuser blades after the rotor will reduce the velocityof the flow down to .75 of its value when it leaves the rotor so,

n = 75%t-s

if mechanical efficiency is 95% and generator efficiency equal to90% then the machine and the unit efficiencies will be;


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11t-sm = 71.0%

rl t-su = 64.1%

Mechanical design. It is not necessary to describe all the detailsof the mechanical design in this report. Therefore only a shortdescription about different parts will be given. In the next pagesthe general-arrangement drawing and turbine section drawing can beseen. The machine is to run a 5Kw., 1800 RPM generator by means ofchain and sprocket transmission. Further descriptions areindividualiy given as follows:Rotor-nozzle combination.-- This combination has high-accuracycomponents to he made of plastic. The rotor (see drawing 1, Part li)has 16 blades. The up-stream nozzle blades (Part 12) with 15 blades,and the downstream diffuser blades (Part 13) are molded into hubswhich act as bearings for the rotor, The nose up-stream of thenozzle blades (Part 14) euides the flow to the nozzles.

These are all ins ,c+Lled in a plastic bush (Part 15). Thisbush gives a smooth inner surface to the duct surrounding the rotor,a feature which will increase the efficiency.

Also this plastic bush allows us to use low-c


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L


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79


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The bushing is fixed to the housing be means of a flangemolded to the upstream end (i.e. nozzle size), which is clampedbetween the flanges of Parts 21 and 22. The nozzle blading isfixed to the bushing by square-cross-section projections in the endof each blade. These match up with slots in the bushing. Afterassembly the blades are fastened to the bushing with resin adhesive.

The nose in front of the nozzle blading -Is also fastened tothe hub of the nozzles by structural adhesive. The diffuserblading is similarly fastened to a flanged bushing, clamped betweenthe flanges of Parts 22 and 23.

The rotor bearings are lubricated with water. Water flowsin through the hole in the front of the nose and lubricates thefront bearing. Then some water flows to the back bearing throughsmall holes in the rotor hub.Housing and frame.-- The housing has three individual sections which*'are bolted together. The upstream section, Part 21, is actually anadaptor. It enables us to connect the turbine to a standard 10"water pipe and flange. The center section (Part 22) encloses theturbine itself and the downstream section (Part 23) is the outletcollector.

Different parts of the housing can be made of rolled steelsheets welded to steel flanges. However, if there are localfacilities for sand casting, Parts 21 and 22 would be better madefrom cast iron.


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The frame (Part 25) is made of steel angles welded together.The turbine is bolted to the frame using some of the flange boltsthrough the housing back plate (Part 24). The upper plate (Part 26)of the frame supports the generator. These are shown in Figure 2,Transmission system. Power is transmitted from the rotor to theoutput shaft by the meansof a coupling disk (Part 31). This diskhas four slots on its circumference which match up with small teethin the bore of the rotor stub shaft.

As the disk is loosely in contact with the rotor it cantransmit only tovque, and no bending moment or thrust force, to theoutput shaft.

The output shaft (Part 32) is supported by a flange bearing(Part 33) which i-b fixed to the housing back plate by bolts. Theflange bearing has a rubber seal in the drain side, which preventswater leaking into the bearing.

The ball bearing in the flange bearing, together with atapered bush and a nut with locking washer, keeps the shaft inthe right position.

In order to raise the rotor speed to the generator speed acombination of two sprockets is used with a tooth ratio of four(Parts 34 and 35). The chain used in this system is standard l/2"chain (bicycle chain). The sprockets have 80 and 24 teeth on therotor and generator shafts, respectzvely.


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We do not recommend the use of standard bicycle sprocketsin this case. To transmit five kw at a speed of 1800 kPM would beloading them up to their maximum strength and would leave no safetymargin.

To fix the larger sprocket to the rotor shaft a split taperbushing (Part 36) is used. This is done to avoid any need forhammering or pressing on the shaft.Using the unit in powers lower than five kw

To run the turbine at a power level less than f ive kw, theflow to the turbine has to be reduced by the means of a valueinstalled at least a meter before the turbine inlet. Obviouslythe turbine will work at its best efficiency when it is run fullyloaded.

Different possibilities for controlling the output powerby installing some kind of mechanism were studied, but all casesresult in a significant increase in size and complexity. I feelthat users would not find these possibilities attractive.b) Design of a reaction machine

This section is concerned with design of a 50% reaction axialturbine. The principles of the calculations are exactly the sameas for the impulse machine. Therefore only the assumptions andtabulated results will be presented. In fact the structure of bothturbines are also the same, so to avoid repeating the mechanicaldrawing of this machine it is not submitted as it is quite similar


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to impulse machine. But a short description of the differences isgiven in the following paragraphs.

The significance of the 50% reaction machine is that itsrotor and nozzle blades will have the same cross section.specify a work coefficient of one,and absolute flow anglerotor to be the same for bothimpulse and reaction turbines.

Weto the

The absolute flow leaving therotor will then be in theaxial direction. The firstguess for the total-to-total efficiency is 85%. The result of thevelocity diagram calculation is:

B2 = 68.2

% = O*O"U = 8.84 m/s

A(UC6) = .8 08 m2/s2 or J/KgQ = 0.0704 m3/s3

1=w29,52 m/s

C2 = Cx = Wl = 3.54 m/s

A suitable shaft speed for above results which can give anaccpetable dh/dt is 720 RPM,. Therefore;


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d = 0.2345 mmdt = 0.2615dh = 0.2075 m

blade height = 0.027

5-ldt = 0.79Blade design. For simplicity the rotor-blade section will

be used for both nozzle and rotor blading. But because of differencesbetween number of the blades for the nozzle and the rotor, the solidityof bladings will be different. For preliminary design let's selecta stagger of 45", I.5 blades for nozzle and 16 blades for the rotor.From the Zweiffe l criterion (Eq. (3.11)) for rotor blades we have

b- = O.&l,Salso

b- = cosx= 0.71 .cThen blade dimensions will be as follows (Table 3-3):

Z S b C AR0in 6 0C B1 B2 re rtNOZZLEBLADES 15 48.76 39.3 55,3 20.0 6.4 94.6 20 74.6 2.5 0.5ROTORBLADES 16 45.76 39.3 55.3 20.0 604 94.6 20 74.6 2.5 0.5

TABLE 3-3: REACTION-TURBINE BLADE DIMEKSIONS.


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NOZZLE BLADES

ROTOR BLADES

- -. -.

FIG.3-6. BLADE SECTIONS OF THE AXIAL-FLOW REACTION TURBINE.


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87

rl t-sm = 79.4%. , T-$ su = 71.5%

Mechanical design. The general mechanical design on bothimpulse and reaction machines are the same. Therefore no furtherdetails about this reaction machine will be given, other than tomentlon the differences in size and performance. The output speedof this machine is more than that of the impulse turbine, and theturbine itself is slightly bigger in size, but there is not muchdifference in the total sizes of the units (turbine, frame andgenerator, altogether).

The diffuser blades and axial diffuser in this machine arelonger and give better diffusion, which results in a few pointsincrease in efficiency.

The transmission ratio is 2.5 and the same size chain (l/2")is used with two sprockets having 24 and 60 teeth on the generatorand rotor shafts, respectively.


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Ghapter 4DISCUSSION ON ADVANTAGES OF DIFFERENT TYPES

As seen in the last chapters, each of the studied prototypeshad individually some advantages and some disadvantages. Lookingat the problem from the vieC: of a developing country, the price ofthe turbine, the manufacturing processes under which the turbine isgoing to be made and the type of maintenance and service needed areimportant parameters in the choice of the best machine.

All machines are designed not to need skilled maintenance.Therefore cost and manufacturing requirements have to be discussed.The crossflow turbine gives both possibilities of being manufacturedlocally in farming areas and/or being manufactured in industrialareas and shipped to farms. But axial-flow turbines should bemade centrally and shipped to farms. The type of processes underwhich the cross-flow turbine could be made are mostly intermediateprocesses such as sheet-metals fabrications, but the axial-flowturbines have parts which need more sophisticated processes (i.e.plastic molding, and casting, etc.), To satisfy the goals of theTechnology Adaptation Program it might be preferred to chooseprocesses which provide improvements in industry in the developingcountries. In that case encouraging industries such as plasticmolders may be of great importance.

The amount of labor which has to be put into making eachcross-flow turbine is much higher than what has to be done for the


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axial-flow type. The axial-flow machines would probably be cheaperbecause of automation and their smaller size when produced in largenumbers.

Comparison of the structures of the turbines shows that, thehigh speed of the reaction machine is an advantage over the impulseand cross flow machines, as it provides a lower gear up ratio to theelectrical generator, so that a simple.- transmission and lower forcesin chain and sprockets are entailed.

For the kind of generator speed we have chosen the chainmust work in an oil bath and be well lubricated, otherwise it willnot last long even for the axial flow reaction machine. Thereforethe low speed of cross-flow turbine and its two-step transmissionmkes it unattractive, because a far more expensive transmissionbecoms necessary.

A big portion of the price of each of the units is thegenerator cost. The rest of the construction cost seems likely tobe similar for all units for small scale production. For largescale production the cross flow will be much more costly than theaxial types. This is because the material cost for the axial flowmachines is small but initial investments for molds and dyes arerequired.

Finally the efficiencies of the machines differ. Whilethere is often surplus water flow available a high efficiency machinerequiring a lower water flow will therefore require less costly pipes,channels, values and so forth.


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The following table shows the efficiencies of the differentmachines.

t-tt-st-smt-su

Key :

Cross-Flow Axial-Flow Axial-FlowTurbine76%60%

56.5%51%

Impulse Turbine80%75%71%64%

Reaction Turbine85%

83.5%79.5%71.5%

t-t E total-to-total efficiency of turbine bladingt-s 2 total-to-static efficiency of turbine bladingt-sm Z total-to-static efficiency of machine (shaft power)t-su E total-to-static efficiency of unit (electrical power)

Based on all considerations we chose the reaction machine asthe best solution to the problem.4,l IMPROVEMENTS ON REACTION MACHINE

The preliminary design shown in the last chapter has somequestionable features. Here we try tc improve on that design asmuch as possible. Following are some items which it seems necessaryto cover.

By looking at the general-arrangement drawing submitted inthis chapter (DRN, No, AF301), the difference between the rotor-nozzle combinaticns in two schemes can be seen.


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This improved design provides less hydrostatic force on therotor. The atvlospheric pressure is bypassed through the rotorcentral hole to the other side of the rotor, hence equalizing thepressure on the two sides of the rotor and reducing the axial forceon the rotor. The sliding surfaces between the rotor and diffuserhubs are covered with thin stainless-steel sheets which reduce thefriction and give a long life, (For the high pressure and velocityon sliding surfaces even the best kinds of plastic can not last andthey melt.) Lubrication of these surfaces is possible by the aidof holes in the rotor hub and grooves on the plates. The lubricantwater is supplied from upstream through the holo-s in the stator hub.

The front adaptor in the improved machine is changed. Thenew adapter enables us to connect the turbine to 8" diameter piping.The smaller tube and valve size reduces the cost.

The oil bath in the back of the turbine provides goodlubricating conditions for the chain and sprockets, and henceincreases the transmission system's life.

The blade profiles are also changed. The new blades have asettling angle of 38" and their shapes are also optimized for thebest performance.4.2 Off-Design Performance

The type of flow control we recommend for the machine is touse a gate valve installed one m. ahead of the machine. The basicassumption is that the turbine is going to be run under fairly steady


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180I60

i20loo

8060402000 zoo 400 600 800 1000 1200 1400

SHAFT SPEE R.FIG.401. CHARACTERISTIC CURVES OF REACTION MACHINE FOR CONSTANT FLOW RATE.


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r6

02J00 a0 v 40 45 50 55 60 65 70 75

FLOW RATE m3,lrnFIG.4-2. CE.ARACTERISTIC CURVES OF REACTION MACHINE IN CONSTANT SPEED.

0


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loads. Therefore the required power can be set on the machine andslight changes in frequency up to 5% would be acceptable.

More sophisticated systems to control the turbine will causebig increases in size and price of the machine, which makes themachine unattractive co customers.

Based on this assumption the characteristic curves of theturbine are shown in Figures 4-1 and 4-2. These curves are theoreticalcurves and based on predictions. The off-design performance is predi-cated using the method given in Reference (3), which has been foundto have a high degree of accuracy.


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APPENDIX ITABLE OF PARTS AND WORKING DRAWINGS

Following are the complete working drawings of the modifiedreaction machine. Each drawing has a reference number. Using thesenumbers all information about each part can be found from the tableprovided. Special information on material, type of manufacturingprocess under which the part should be made, or sub-drawings, aregiven under the heading "Remarks."

For the case of complicated parts, drawings for additionalsections or sr;bparts are submitted which are marked by letters "A,""B, (1 I,C," etc., after the master part's reference number. (AF300stands for 'axial-flow reaction turbine.")


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TABLE OF PARTS ANDLIST OF DRAWINGS OF REACTION TURBINE COMPONENTS

PART- IUM~ER , NAME OF PARTIAF311 I, FRONT ADAPTORAF312 ( MIDDLE SECTION

AF313 DRAIN CHUTE'AF313A BACK PLATEAF313B FRONT FLANGEAF313C IAF313D /

CURVED PLATESIDE PLATE

AF313E FRONT PLATE

NUMBERREQ'D MATERIAL REMARKS

1 CAST IRON1 CAST IRON HOLES OF FLANGES SHOULD

BE ALIGNED1 STEEL SEE SUBDRAWINGS1 1 OMM PLATE1 1 5MM PLATE1 8MM PLATE2 5MM PLATE1 5MM PLATE

. . . contl'nued


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TABLE OF PARTS ANDLIST OF DRAWINGS OF REACTION TURBINE COMPONENTS Continued)

NUMBERNAME OF PART REQ'D 1 MATERIALAF314(1 NOSE 1AF314(2

1 ;;;if 1 STATOR BLADING

AF316A ROTOR BLADINGAF316BI

AF316C1 II AF317 NOZZLE AND ROTORBLADE SECTION

131:

GLASS-FIBER-REINFORCEDPOLYESTER THERMOSETPOLYESTER RESINS30% GLASS BY WT.

AF3l8A DIFFUSER BLADING 1 GLASS-FIBER REINFORCEDAF318B POLYESTER THERMOSETPOLYESTER RESINS30% GLASS BY WT.AF319 DIFFUSER-BLADESECTIONAF320 BUSH 1 GLASS-FIBER REINFORCEDPOLYESTER THERMOSET.POLYESTER RESINS30% GLASS BY WT.

REMARKSSEE ADJACENT TABLE FORPROFILE COORDINATESSEE AF317 FOR BLADESPROFILE.

THE 1.5MH STAINLESS-STEELSHEET SHOULD BE JOiNED TOSLIDING SURFACE BY METAL-BONDING. EPOXY.SEE ADJACENT TABLE FORBLADE PROFILZ.THE 1.5MM STAINLESS STEELSHEET SHOULD BE JOINED TOSLIDING SURFACE BY METAL-BONDING EPOXY.SEE ADJACENT TABLE FORBLADE PROFILE.

. ..continued


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TABLE OF PARTS AND ILIST OF DRAWINGS OF REACTION TURBINE COMPONENTSContinued)

PART j NUMBERNU%EER i NAME OF PART IREQ'D MATERIAL REMARKSAF321A 1 SLOTTED DISK 1 ALUM1NWAF321B ' KEY 2 HARD STEEL

-AF322 1 SHAFT 1 STAINLESS STEEL,11 HUB ASSEMBLY

AF323A HUB HOUSING 1 CAST STEELAF323B FRONT CAP 1 1.5MM STEEL SHEETAF323C BALL BEARING 1 M.R.C. BEARING 206-SX EQUIVALENT STANDARDADAPTER AND NUT G-Y PARTS WITH THE SAME SIZECAN ALSO BE USED.AF323D SEAL 1 GARLOCK 78, 0542

COMP NO. 26448-35DES. GRP. D.

AF323E* (3/16"~32)~5/16" 3 ROUND HEADi BOLT

II

. ..continued*no drawing; standard component


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TABLE OF PARTS kNDLIST CT DRAWINGS OF REACTION TURBINE COMPONENTS Continued)

PART NUMBERNUMBER NAME OF PART REQ'D MATERIAL REMARKS

AF324 BIG SPROCKET 1 BROWNING 4OP60 NO. OF TEETH 60TYPE 4 PITCH l/2"BUSHING Pl PITCH CIRCLE DIA. 9.554FOR TYPE 40 CHAIN

AF325 SMALL SPROCKET 1 BROWNING 4024 NO. OF TEETH 24PITCH l/2PITCH DIA. CIRCLE 3.831

AF326* CHAIN

-I--

FOR TYPE 40 CHAIN -1 BROWNING NO. 40 l/2" PITCHNO. 40 A.S.R.C.

. ..continued*no drawing; standard component


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PART 1 INUKBER fNUKBER 1NAXE OF PARTAXE OF PART I REQ'D-_-I - IFRAME 1SIDE ANGLES 2+2

I 21 iF327C TOP PLATE 1#1 IF327D 1,j

BAR 2#j AF327D ,1 AF327E ]

SIDE ANGLES 2+2TOP ANGLE II 2iTOP PLATE

1 ;i,,DATION PLATEAF327E 1 FOUNDATION PLATE 4

MATERIALATERIAL REMARKEMARKSTEELTEEL80X80X8 L0X80X8 L80X80X8 L0X80X8 L80MM PLATE0MM PLATE40x8 FLATBAR0x8 FLATBAR1OMM PLATE

2 OFF AS DRAWNOFF AS DRAWNOPPOSITE HANDPPOSITE HAND

I

1OMM PLATE Ij AF328I / OIL BATHIj AF329 ' OIL-BATH COVERI

2 AND 3MF1STEEL SEAMWELDEDSHEETS-2MM STEEL SHEET

. ..continued


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NAIVE OF PART8; AF330* j GENERATORI III

jf 1i i1

AF331A*i (5/8"~12)~2 l/2" BOLTAF331B *[ 5/8"x12 NUT

/ AF331Cj 5/8" LOCK WASHER1 AF332A"I (l/2%12) l-1/2" BOLTj AF332B*/ 1/2"x12 NUT1 AF332C*[ l/2" LOCK WASHERI IIAF333A*; (9/16"xl2)x2" BOLT

AF333B* (9/16"xl2)xNUTAF333C *j 9/16" PLAIN WASHERA:Z33D*/ 9/16" LOCK WASHER, _AF334 *I ALIGNMENT-PINAF335A"I (3/8%16) 2" BOLTAF335B*/ 3/8" PLAIN WASHERAF335C* (3/8'k16) WING NUT

II-*no drawing; standard compcnent

NUMBERREQ'D,_--

1

202020

4444444--4121

--

MATERIAL REMARKSWiNCO INC.SERIES 5KS4G-3 4 POLE, 5KW, 115/230 VOLTS21.7 AMP.60 CYCLE

1800 R.P.M.1 PH.

HEXAGON HEADEDI

HEXAGON HEADED

HARD STEEL IHEXAGON HEADED

. ..End


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105I


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f

co


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WI


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CURVED PLATE

=0


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111


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s


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-7

-


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0.02.55.07.510.015.020.025.030.035.040.050.060.070.080.090.0ZE120:o130.0140.0150.0160.0

2xax25:531.536.045.051.056.562.066.070.077.082,O87.091.595.098.0100.0101.5102.5103.0103.5104.0


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I -


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II


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IOS


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m7 I


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AROTOR BLADING_


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0.01.02.53.755.06.2510.012.515.017.520.022.525.030.032.535.037.538.7540.041.2542.543.544.545.546.547.548.7550.0

Yc mmE52:oE54:75S510.011.512.513.2513.8514.013.8513.2512.612.011.2510.59.128.627.756.75x52100.0

Xt mm I t mm0.03.06.0

129::15.018.021.024.027.030.031.533.036.037.539.042,O45.0E51:o54.057.060.0- l

0.00.760.86i-y81:431.762.022.523.283.784.134.344.344.434.594.544.284.134.033.532.832.170.0


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-cuLc0-


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t/Ir,\t

R/=1.0 mmRf=0.2 mm

X mm0.0K50:751.5i-i6:0

1E15:o18.021.024.027.030.033.036.039.042.045.048.051.054.057.060.0

t mm0.00.690.841 , Of,1.521.962.382.743.303.734.054.284.434.504.474.334.083.373.312.842.331.791.250.730.280.0


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--


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i 220

SHAFT


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I I I I

HUB HOUSING (1 of 2


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I


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135a


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I--


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?Tr


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, t

-a---------m-- ---- ---.-A------ e--m---

-.I--v-----------

--

FRAME (plan view) 2 of 2


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IIIIIIIIIIIIIIII


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402 -i

TOP ANGLE

I IQ00


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I I

II I I


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a

I8


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Y \8G9

1 \\

\ \\


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35 I

II

0

ALIGNMENT-PIN--


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APPENDIX IIFRICTION LOSS IN NONCIRCULAR CONDUITS

Pressure drop due to flow through a non-circular cross-section bend can be found from;

where K is the loss factor, v the average flow velocity and pis the mass density. K is a factor of hydraulic diameter of thecross-section and the radius of the bend, as well as the deflectionangle of the bend (Fig, I-l),

The hydraulic diameter is defined as;

ADh 5 4 x flow areawetted perimeter '

and then pressure drop due to friction loss can also be expressedin terms of Dh' as:

where L is the length of the conduit and fh is the frictionfactor on the basis of hydraulic diameter. Obviously Re andE/D should be defined as,

v DhRe E 7 and E/D F $-then fh can be found using Fig. I-2.

147


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0.20

0.15

0

FIG. 7. LOSS FACTOR FOR BENDS.(ASCE,J.HYDRAULIC DIV.,NOV. 65)I 20

1 VALUES OF R/a

i

DEFLECTION ANGLE

e. .004I0.003--- -- IO3 IO4 IO5 IO7

Re = VII/vFIG, 2. FRECTlON FACTOR f VS. Re. FOR DIFFERENT e/D. (W.M.Rohsenew andH.Y.Choi, Heat,Mass and Momentum Transfer P 58 1


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APPENDIX IIIEFFICIENCIES

The total-to-total efficiency of a turbine is defined as

?J E turbine output powertt enthalpy drop from inlet total pressureand temperature to outlet total pressureThis definition of efficiency is concerned with the blading hydrauliclosses.

The total-to-static efficiency of a turbine isdefined as,

diseño de pequeñas turbinas de agua para granjas y pequeñas comunidades

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