13
Axial-flow turbines for low head microhydro systems K.V. Alexander a, * , E.P. Giddens b,1 , A.M. Fuller a a Department of Mechanical Engineering, University of Canterbury, PB 4800, Christchurch, New Zealand b Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand article info Article history: Received 19 December 2007 Accepted 22 March 2008 Available online 25 July 2008 Keywords: Microhydro Hydropower Renewable energy Home energy Low head Remote power generation abstract This paper describes the design of four different specific speed microhydro propeller turbines operating at heads between 4 m and 9 m, and their application to a wider range of heads and outputs by scaling. The features are specifically tailored for ease of manufacture and uniquely resistant to debris blockage. Test machines are described and test results given; hydraulic efficiencies of over 68% have been achieved in all test models despite the fact that these turbines’ blades are planar, further simplifying manufacture. Theoretical models show how closely these flat blades can be made to approach the ideal blade shapes. Outline drawings are given with key dimensions for each reference model, along with the equations for scaling to arbitrary sites. These turbines are the axial flow members of a family of turbines developed to cover the microhydro range from 2 m to about 40 m of head. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction This paper is one of a group of papers describing a University of Canterbury project that sets out to provide a properly configured range of microhydro systems, from radial- to axial-flow designs, based on a modular concept and aimed in particular at third-world sites where regional workshops might be capable of undertaking much of the manufacture themselves. With that in mind, the scope of this paper is a subset of the microhydro project at the University of Canterbury. This paper’s scope is specifically the propeller, or axial-flow, turbines. Future papers will cover the University’s radial- and mixed-flow designs. A particular goal is to provide well- grounded but lowest-cost options for the communities who pos- sess an adequate hydro resource and access to basic fabrication facilities, but who are confined to less reliable, sustainable, or economical power generating technologies due to a lack of design knowledge. Earlier papers have given an overview and justification of the modular approach [1,2] and the analysis leading to the most economic choice of penstock [3]. The selection of the most eco- nomic penstock dictates the turbine size. The combination of dis- charge, available head, and a fixed generator speed allow calculation of the site’s specific speed. If that value falls in the range of this paper’s designs, then one of the turbines described in this paper is likely a suitable choice for development. Microhydro is typically used to describe sites of output below about 20 kW. Above that is minihydro, where the scale of in- vestment is such that professional input is proportionally smaller and there is some advantage in building custom-made systems. The area of particular interest for the project discussed here is specific speeds above those of the Pelton wheel. Pelton wheels are simpler to implement than reaction turbines of similar power output, and are therefore quite popular relative to other types of microhydro machines. However, their applicability is limited to high-head sites. A number of Pelton wheel solutions are already available [4]. This project aims to complement these and other existing microhydro solutions by providing efficient designs for a broader range of sites. The exact scope of this project in terms of head and discharge is shown in Fig. 1 . The development of turbines suitable for operation in the bounded region of Fig. 1 has been the main task of the project, including Francis (radial-flow), mixed-flow, and propeller (axial- flow) machines. 2. Turbine forms and scaling It is well known that different forms of turbine are required for different conditions; the classic range of turbine forms rele- vant to this project is shown in Fig. 2. The forms are classified by their specific speeds, where in this instance the specific speed is defined as * Corresponding author. Tel.: þ64 3 3667 001x7385; fax: þ64 3 364 2078 E-mail addresses: [email protected] (K.V. Alexander), amf88@ student.canterbury.ac.nz (A.M. Fuller). 1 Recently deceased. Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.03.017 Renewable Energy 34 (2009) 35–47

Axial Flow

Embed Size (px)

Citation preview

Page 1: Axial Flow

lable at ScienceDirect

Renewable Energy 34 (2009) 35–47

Contents lists avai

Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Axial-flow turbines for low head microhydro systems

K.V. Alexander a,*, E.P. Giddens b,1, A.M. Fuller a

a Department of Mechanical Engineering, University of Canterbury, PB 4800, Christchurch, New Zealandb Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand

a r t i c l e i n f o

Article history:Received 19 December 2007Accepted 22 March 2008Available online 25 July 2008

Keywords:MicrohydroHydropowerRenewable energyHome energyLow headRemote power generation

* Corresponding author. Tel.: þ64 3 3667 001x7385E-mail addresses: [email protected]

student.canterbury.ac.nz (A.M. Fuller).1 Recently deceased.

0960-1481/$ – see front matter � 2008 Elsevier Ltd.doi:10.1016/j.renene.2008.03.017

a b s t r a c t

This paper describes the design of four different specific speed microhydro propeller turbines operatingat heads between 4 m and 9 m, and their application to a wider range of heads and outputs by scaling.The features are specifically tailored for ease of manufacture and uniquely resistant to debris blockage.Test machines are described and test results given; hydraulic efficiencies of over 68% have been achievedin all test models despite the fact that these turbines’ blades are planar, further simplifying manufacture.Theoretical models show how closely these flat blades can be made to approach the ideal blade shapes.Outline drawings are given with key dimensions for each reference model, along with the equations forscaling to arbitrary sites. These turbines are the axial flow members of a family of turbines developed tocover the microhydro range from 2 m to about 40 m of head.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

This paper is one of a group of papers describing a University ofCanterbury project that sets out to provide a properly configuredrange of microhydro systems, from radial- to axial-flow designs,based on a modular concept and aimed in particular at third-worldsites where regional workshops might be capable of undertakingmuch of the manufacture themselves. With that in mind, the scopeof this paper is a subset of the microhydro project at the Universityof Canterbury. This paper’s scope is specifically the propeller, oraxial-flow, turbines. Future papers will cover the University’sradial- and mixed-flow designs. A particular goal is to provide well-grounded but lowest-cost options for the communities who pos-sess an adequate hydro resource and access to basic fabricationfacilities, but who are confined to less reliable, sustainable, oreconomical power generating technologies due to a lack of designknowledge. Earlier papers have given an overview and justificationof the modular approach [1,2] and the analysis leading to the mosteconomic choice of penstock [3]. The selection of the most eco-nomic penstock dictates the turbine size. The combination of dis-charge, available head, and a fixed generator speed allowcalculation of the site’s specific speed. If that value falls in the range

; fax: þ64 3 364 2078z (K.V. Alexander), amf88@

All rights reserved.

of this paper’s designs, then one of the turbines described in thispaper is likely a suitable choice for development.

Microhydro is typically used to describe sites of output belowabout 20 kW. Above that is minihydro, where the scale of in-vestment is such that professional input is proportionally smallerand there is some advantage in building custom-made systems. Thearea of particular interest for the project discussed here is specificspeeds above those of the Pelton wheel. Pelton wheels are simplerto implement than reaction turbines of similar power output, andare therefore quite popular relative to other types of microhydromachines. However, their applicability is limited to high-head sites.A number of Pelton wheel solutions are already available [4]. Thisproject aims to complement these and other existing microhydrosolutions by providing efficient designs for a broader range of sites.The exact scope of this project in terms of head and discharge isshown in Fig. 1.

The development of turbines suitable for operation in thebounded region of Fig. 1 has been the main task of the project,including Francis (radial-flow), mixed-flow, and propeller (axial-flow) machines.

2. Turbine forms and scaling

It is well known that different forms of turbine are requiredfor different conditions; the classic range of turbine forms rele-vant to this project is shown in Fig. 2. The forms are classified bytheir specific speeds, where in this instance the specific speed isdefined as

Page 2: Axial Flow

Notation

1 subscript denoting leading edge station2 subscript denoting trailing edge stationf(.) function of stated variablesg gravitational acceleration (m/s2)h subscript denoting location on blade/hub intersection

(Fig. 5)HR head ratio, site/referenceH turbine head (m)j counterk constant for free vortex flowLR length ratio, site/reference_m mass flow rate (kg/s)

N runner rotational speed (rev./min)NS specific speedPi hydraulic power into the turbine from the penstock

(W)Pr power out of the runner (W)PR power ratio, site/referencePd power measured at the dynamometer (W)Q flow rate (l/s or m3/s as noted)QR discharge ratio, site/reference

r general radius (mm)ref subscript denoting parameter of a reference machinesite subscript denoting parameter of machine scaled to

match a real sitet subscript denoting location on blade tip (Fig. 5)Tr runner torque (Nm)va axial flow velocity (m/s)vc circumferential flow velocity (m/s)a angle CCW around scroll casing, from inlet/casing

intersection, as viewed from generator end, for usewith Eq. (26) (degrees)

b blade angle relative to the impeller plane (degrees)d deviation angle (degrees)ht turbine hydraulic efficiency (does not include hm)hm combined bearing, shaft seal, and transmission

efficiencyp 3.14159.q angle clockwise around runner axis from the setup

point ‘‘O’’ (degrees)r density of water (kg/m3)u runner rotational speed (rad/s)j blade set-up angle (degrees)

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–4736

NS ¼NffiffiffiffiffiPrp

H5=4(1)

Note this definition’s departure from Nechleba’s version with theuse of an indirectly calculated powerdthat absorbed by the run-nerdrather than the power measured directly by the dynamom-eter [5, p. 71]. As with Nechleba’s, and other ‘‘practical’’ forms ofspecific speed, it is not a dimensionless number. In this case, the SIunits are

NS¼ðNewtonsÞ1=2

ðsecondsÞ3=2ðmetersÞ3=4

Gross Head, Discharge, Specific Speed a

Pelton W

heel N

s =

36

0.2

kW

Ele

ctic

al O

utp

ut.

1

10

100

1 10Discha

Gro

ss S

ite H

ead

(m

).

Pelton Wheel Region

Microhyd

Power too low to consider

Fig. 1. The site head and discharge ranges definin

Therefore, its use is restricted to comparison with machines char-acterized in the same way. It is worth noting here an interpretationof the term ‘‘specific speed’’ which may help clarify its meaning andrelevance for comparison of hydraulic machines. To paraphrase thesource, ‘‘The specific speed of any turbine equals the speed ofa geometrically similar turbine working under the head of 1 m,when the latter turbine has such dimensions that it delivers underthe head of 1 m a unit of power’’ [5, p. 70]. A definition of NS basedon runner power was adopted because the four reference turbinescovered in this paper were developed in parallel with matchingbearing and transmission designs. As part of each machine’s de-velopment, the efficiency of transmission components has beenmeasured, which allows isolated analysis of hydraulic performance.

t 1550 RPM and Electrical Power Delivered

25 k

W E

lectic

al O

utp

ut.

Hig

hest P

ractical N

s =

600

100 1000rge (l/s)

Minihydro Region

ro Region

Specific Speed too high to achieve

g the microhydro and neighbouring regions.

Page 3: Axial Flow

Fig. 2. The classic figure of turbine forms, with their specific speeds based on thedefinition in Eq. (1).

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–47 37

To facilitate comparison based on hydraulic performance alone, thepower measured by the dynamometer during testing has beendivided by hm, so that the power output reported and used in Eq. (1)is the power extracted from the fluid by the runner, Pr. This leads toslightly high estimates of power and specific speed when com-paring to designs characterized by their output at the dynamom-eter shaft, but has been chosen for the sake of simplicity in thisanalysis and reusability of the data. Pi, the hydraulic power into theturbine, is therefore the maximum power available, and will alwaysexceed a power conversion machine’s output due to efficienciesless than unity.

Pi ¼ rQgH ¼ _mgH (2)

The relationship between the available hydraulic power, efficien-cies, and measured output at the dynamometer is

Pd ¼ hmhtrQgH ¼ hmhtPi ¼ hmPr (3)

To obtain the power transmitted by the runner for hydraulic per-formance comparison, divide Eq. (2) by hm to yield

Pr ¼Pd

hm¼ htPi (4)

80 m

m

100

mm

Pelton N S=36

η=70% N S=60

N S=93

N S=176

N S=242

N S=355

N S=544

0.3 kW Electric

1.3 kW Electric

3 kW Electric

5 kW Electric

1

10

100

1 10Discharg

Tu

rb

in

e H

ead

, H

[m

]

Penstock Nominal Diameters:

Fig. 3. Axial-flow turbine selection char

Substituting Eq. (2) in Eq. (4) and the result into Eq. (1) gives theexplicit form used in this project.

NS ¼ N

ffiffiffiffiffiffiffiffiffiffiffiffiffihtrgQ

pH3=4

(5)

In this project, the range of specific speeds is from 60 (high head,small flow, radial-flow) to 540 (low head, large flow, axial-flow). Fora given specific speed the geometrical form of the turbine remainsthe same, but the size may be scaled (Fig. 3). This allows the designfor each specific speed to be scaled to match the available penstockflows and to deliver, from the appropriate heads and discharges, the4 or 5 power bands to cover the 0.2–20 kW range. When scalingfrom a reference machine, the resultant hydraulic efficiency can bepredicted from an empirical function of the physical size (or dis-charge, depending on the model used) of so-called majoration ef-fects [6, p. 765].

Furthermore, these several sizes of the same form can bearranged to deliver at a fixed N. This is apparent from Eq. (1) whereQ and H may be increased while keeping NS and N constant. Aconstant N enables the generation of AC in the standard frequencyof 50 Hz using directly driven 4-pole generators, regardless of in-stallation size.

Once a survey is completed for a particular site, using themethods in [2] and [3], Q and H are known parameters. Now,suppose there is a reference model of known Pr, N, H, Q, NS, and size.For the purposes of illustration, assume the reference machine runsat 1500 rev./min and produces 1 kW at the runner shaft. To pro-ceed, it is necessary to scale that reference machine to an availablesite. Fig. 3 represents the process of scaling to a geometricallysimilar machine, that is, a machine with the same value of NS, butthe calculations to produce such a graphical tool are as follows. Theproject constraints of the scaling operation will be Nsite ¼ 1500 tosatisfy the generator and NS;site ¼ NS;ref to preserve the validity ofthe scaling operations. NS,site, although it is a property of the ma-chine, can be estimated from the site’s parameters. H, Q, and lengthratio, LR, are to be determined. First, compute the site/referenceratios from the given values for P and N.

125

mm

150

mm

175

mm

200

mm

225

mm

250

mm

300

mm

15 kW Electric35 kW Electric: Mini Hydro

100 1000e, Q (l/s)

Turbine Options

t, NS lines are at constant ht ¼ 70%.

Page 4: Axial Flow

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–4738

PR ¼Pr;site

Pr;ref¼ 1kW

Pr;ref(6)

NR ¼Nsite

Nref¼ 1500 rev:=min

Nref(7)

Next, calculate HR, QR, and LR, which, when multiplied by the ref-erence model’s values of H, Q, and any linear dimension, will yieldthe site machine’s values to achieve the stated constraints. Sincescaling is explicitly constrained by dimensional similarity, NS is thesame for site and reference, and Eq. (1) can be solved for HR be-tween the two.

HR ¼�

NR

ffiffiffiffiffiffiPR

p �0:8(8)

Eq. (8), the discharge ratio, is a manipulated form of Eq. (5), forgeometrically similar machines. Here, assume that ht is constantduring this operation, despite having already stated that ht ¼ f(QR),or alternatively: ht ¼ f(LR). Efficiency majoration is included afterscaling as a function of LR in Eq. (11).

QR ¼PR

HR(9)

Eq. (10) relates flow and head variations to the physical scale ratiofrom reference to site.

LR ¼ffiffiffiffiffiffiffiffiffiffiffi

QRffiffiffiffiffiffiHR

ps

(10)

The site machine’s hydraulic efficiency can be majorated from thereference machine’s ht as a function of the size ratio between thetwo using an empirical relation [6, p. 765, Eq. (10)].

Table 1Lab model specifications

Performance and sizing for best models

Specific speed AchievedDesign parameters Pr, kW

Ht, mN, rev./minQ, l/shthm, %hm, %ht, %

Runner parameters Runner OD, mmHub OD, mmSetup angle, degrees

Casing dimensions Draft tube included angle, A, degreesVortex flange-to-outlet throat, B, mmMain casing radius, RCo, mmScrolled casing radius exponential factor, RCpRunner casing ID, ØD, mmExternal draft tube length, E, mmInlet-to-runner centerline offset, F, mmOutlet cone-to-draft tube gap, G, mmMain casing internal length, H, mmInlet centerline-to-vortex flange offset, K, mmVortex flange OD, ØL, mmInlet ID, ØP, mmVortex flange ID radius, RR, mmVortex flange-to-main casing clearance gap, S, mmOutlet throat ID, ØT, mmVortex flange OD radius, RV, mmInlet diffuser plan width, W, mmInlet diffuser full length, X, mmOutlet cone included angle, Z, degrees

ht;site ¼ 1��

1� ht;ref

�L�0:25

r (11)

In line with the modular concept, three different axial-flow (pro-peller) turbine designs have been developed, with a fourth in thefinal stages, each of a different specific speed. This paper focuses onthe turbines in the four higher specific speed ranges (lower heads)of NS ¼ 176, 242, 355 and 544. The actual machines built of eachdesign have been inconsistent in terms of speed and power output,and have been sized to fit a real-world target site and to compli-ment the dynamometer and plumbing facilities available for test-ing. Their specifications are shown in Table 1. For this reason, thefour test models have been scaled, using the exact procedure pre-sented above, to an output of 1 kW and a speed of 1500 rev./min tofacilitate comparison between the designs as shown in Table 2.These normalized results, compiled in Table 2, are the so-calledreferences. These can be scaled to cover heads from 2 m to 20 mdepending on their power output, as seen in Fig. 3.

3. Inlet theoretical design

This project’s objective of producing minimal-maintenance de-signs with long-term resistance to clogging manifests itself in theunique design of most key components. Eliminating the possibilityof clogging has necessitated the removal of any flow-spanningstructure. Hence, stay vanes and inlet guide vanes are left out al-together, runner blade shapes are strongly influenced by theirvegetation-shedding performance, and flow-straightening vanesdownstream of the runner have been designed to be self-cleaning.The main impact of this consideration on the designs presentedhere is that the conditions at the runner are not constrained byguide vanes immediately upstream, but rely solely on the staticgeometry of the casing. As the machines are intended to run ata single setting, with no adjustability, the final geometry of each

176 242 355 5443.07 1.96 1.41 2.829.198 7.07 6.31 3.391605 1989 2986 149146.2 38 32.4 123.970.6 70.8 62.7 60.895.5 95.0 89.2 89.273.9 74.5 70.3 68.2

155 127 101 225100 75 61 13630 30 26 20

16 6 16 7241 370 120 335151 152 102 252– – 0.0024 0.0020155 128 102 227396 465 – –73 71 140 4006 13 5 0362 368 170 1000235 217 44 685250 220 190 256155 162 170 3005 5 5 532 44 60 80103 97 78 2275 5 5 8– – 177 397– – 339 145516 11 16 0

Page 5: Axial Flow

Table 2Table 1 scaled to reference power and speed

Specs when lab models are scaled to a speed/power reference

Scaled design parameters Pr, kW 1 1 1 1N, rpm 1500 1500 1500 1500NS 176 242 355 544Ht, m 5.56 4.31 3.17 2.25Q, l/s 25 32 46 66LR 0.832 1.035 1.411 0.81ht 0.727 0.747 0.727 0.665

Scaled runner Runner OD, mm 129 131 143 182Hub OD, mm 83 78 86 110

Scaled casing dimensions Draft tube included angle, A, deg 16 6 16 7Vortex flange-to-outlet throat, B, mm 201 383 169 271Main casing radius, RC, mm 126 157 144 204Scrolled casing radius exponential factor, RCp – – 0.0024 0.0020Runner casing ID, ØD, mm 129 132 144 184External draft tube length, E, mm 329 481 – –Inlet-to-runner centerline offset, F, mm 61 73 198 324Outlet cone-to-draft tube gap, G, mm 5 13 7 0Main casing internal length, H, mm 301 381 240 810Inlet centerline-to-vortex flange offset, K, mm 196 225 62 555Vortex flange OD, ØL, mm 208 228 268 207Inlet ID, ØP, mm 129 168 240 243Vortex flange ID radius, RR, mm 4 5 7 4Vortex flange-to-main casing clearance gap, S, mm 26 46 85 65Outlet throat ID, ØT, mm 86 100 111 184Vortex flange OD radius, RV, mm 4 5 7 6Inlet diffuser plan width, W, mm – – 250 322Inlet diffuser full length, X, mm – – 478 1179Outlet cone included angle, Z, deg 16 11 16 0

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–47 39

machine has been heavily influenced by experimentation to obtaina satisfactory efficiency. Due to the complex three-dimensionalnature of the flow through the machine, applying conservation ofangular momentum does not reliably predict conditions at therunner. However, the subsequent derivations will show the theo-retical starting point for inlet flow prediction.

The turbine casing is a volume just upstream of the runner,designed with an offset inlet such that the flow acquires angularmomentum about the runner axis while dissipating any circum-ferential asymmetry before entering the runner. The spinning flowapproaching the runner has been assumed to form free-vortex flowto satisfy radial equilibrium, meaning no radial velocity compo-nents are present, and axial velocity is constant throughout thefluid. The latter property allows axial velocity to be written asa function of known parameter Q, in a manipulated form ofQ ¼ V � Area.

va ¼Q

p�

r2t � r2

h

� (12)

Next, the circumferential flow velocity, vc, at any radius from therunner axis is given by the well-known free-vortex relation, derivedfrom the line-vortex solution to radial equilibrium [7, p. 153]

vc ¼kr

(13)

This is the starting point for calculating runner blade geometry asa function of site parameters, design constraints, and casing ge-ometry. Eq. (13) is attractive because a known value for k will allowrunner design to begin.

The torque at any increment of radius rj is produced by reducingthe local circumferential velocity vcj to zero (or close to it). There-fore, the torque at the jth increment of radius is given by

Tj ¼ _mjvcjrj (14)

The torque on the runner as a whole is simply the difference of theangular momentum of the fluid upstream and downstream. Themass flow rate in terms of cross-sectional area through the runnerand axial velocity (which is constant pursuant to the free-vortexassumption) is given by

_mj ¼ rva2prj�rj � rj�1

�(15)

Now, substitute Eq. (15) into Eq. (14).

Tj ¼ rva2prj�rj � rj�1

�vcjrj (16)

This difference equation can be rewritten as a definite integral,where the difference term becomes the infinitesimal radial in-crement, dr. Remove all constants from the integral, substitute k forvcjrj, and integrate radially from hub to tip:

Tr ¼ rva2pkZ rt

r¼rh

rdr ¼ rva2pk�

r2

2

�rt

r¼rh

¼ krvap�

r2t � r2

h

�(17)

Combining all terms following k gives

Tr ¼ k _m (18)

On its own, Eq. (18), like Eq. (13) is not very helpful because k isunknown. However, the shaft power calculated in this mannerequated with the shaft power calculated from potential energy andefficiencies allows a solution for the axial and circumferential flowvelocities just upstream of the runner.

The power produced by the turbine runner, Pr is given by theproduct of the runner torque, Tr, and the runner rotational speed

Pr ¼ TrN60

2p (19)

But the power Pr to be absorbed by the runner is the potentialenergy in the flow, reduced by the turbine efficiency

Page 6: Axial Flow

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–4740

Pr ¼ _mgHht (20)

Using Eq. (18), (19), and (20), and rearranging to solve for k

k ¼ gHht

2p

60N

(21)

Substituting Eq. (21) back into Eq. (13) gives the equation for thecircumferential velocity, vc, at any radius, r, without knowing thevalue of k a priori.

vc ¼1r

gHht

2p

60N

(22)

Now both axial and circumferential flow velocity into the runnerare known. From this, the angle of the flow can be determined atany radius into the runner annulus, allowing the design of blades tomatch.

Fig. 5. Runner velocity diagram.

4. Runner blade theoretical design

Remaining consistent with this project’s idea of simple con-struction, the runner is made of a cylindrical hub with flat bladesattached at a specified angle, j. Each blade is set up as shown inFig. 4, so that the hub radius through a reference point ‘‘O’’ also liesin the plane of the blade. Therefore, at point ‘‘O,’’ the blade also liesat the set-up angle, j, to the impeller disk. As a consequence of thisarrangement, the blade angle, b, varies from j where q ¼ 0, tosomething less than j at any angle q, in either direction, around thehub from point ‘‘O.’’ b is defined by the relation

b ¼ tan�1ðtanjcosqÞ (23)

This relation shows that at q ¼ 0, b ¼ j, and confirms that re-gardless of the value of j, b goes to zero when absðqÞgoes to 90degrees.

The runner is designed to spin in the casing at a speed com-patible with the generator, nominally 1500 rev./min. The hub sizecan be varied by the designer taking into account several issuesnamely:

1. The circumferential flow at the hub, as given by Eq. (22), mustbe less than the velocity ur at the hub in order to obtain a non-negative angle of attack along the runner leading edge.

2. Too large a hub-to-tip ratio, while addressing the first issue,results in a high axial flow velocity in the annulus, creatingexcess friction losses and abrupt expansion losses as the hubtruncates just downstream of the blades.

ψ

ψ

θ

β

Runner Blade

BladeSetup Jig

Hub

Reference Point “O”

Hub

Fig. 4. The set-up arrangement for attaching the blade to the runner hub.

3. Too high a hub-to-tip ratio also creates short-span, highlyloaded blades with insufficient area to resist cavitation; thisrequires numerous blades

While addressing the points listed above, a hub-to-tip ratio ofabout 0.6 has been found appropriate. With the hub-to-tip ratio set,a velocity triangle can be drawn at any point on the leading edge ofa runner blade, based on the circumferential velocity, vc, the runnervelocity, ur, and the axial velocity, va, as shown in the velocity tri-angle diagram, Fig. 5. From this, the shock-free (angle of attack¼ 0)leading edge blade angle may be determined. The required angle(relative to the impeller plane) anywhere along the leading edge is

b1 ¼ tan�1

va

ur � vc

(24)

The trailing edge angles are found from the exit velocity triangleshown again in Fig. 5, which embodies the constraint that theexiting flow should have no rotation (i.e. vc ¼ 0). Due to losses ex-perienced in the flow between the leading and trailing edges of therunner, the exiting flow will not exactly follow the blades’ cam-berline at the trailing edge [5, p. 325]. In order for the no-rotationconstraint to be obeyed in reality, the runner blades need to over-turn the flow by a deviation angle, d, of about 5 degrees relative tothe runner compared to what the simplified two-dimensionaltheory would dictate. To be precise, d will vary with r, and can becalculated across the trailing edge [8, p. 31]. Therefore, the equa-tions for blade angle relative to the impeller plane, at the hub andtip, respectively, are

b2 ¼ tan�1 va

ur � 0� d (25)

Given Eqs. (23), (24), and (25) (which, together, embody the flat-blade concept), the free-vortex inlet assumption and the no-rotationexit constraint (with the inclusion of d), the task is to find a bladeshape where b is correct for all points along the blades’ leading andtrailing edges. Realistically, if b can be satisfied at the hub and tip atleading and trailing edges, all intermediate points along the leadingand trailing edges can be found to coexist on a flat blade, as well.This is achieved by choosing a value for j, substituting the result ofEqs. (24) and (25) into Eq. (23) as b, and solving for the angle q fromthe reference point, where the angle b will exist. The four ‘‘corners’’of the blade can thus be defined as shown in Fig. 6. Likewise, valuesof q for any value of r along the leading or trailing edge can becalculated.

Page 7: Axial Flow

Hub

Correct LE Angle

Correct TE Angle

05

10152025303540

Setup Angle = 34.1

Setup Angle = 34.1

Tip

Correct LE Angle

Correct TE Angle

0

5

10

15

20

25

0 20 40 60 80 100

0 20 40 60 80 100

Point "O"

Blade

Hub

θ

Fig. 6. The case where the blade set-up angle is equal to the required angle at the leading edge at the hub (at point ‘‘O’’). All ‘‘corner’’ angles can be achieved.

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–47 41

Using the equations above, several choices are available as tohow to form the blades. These are based on the choice of j. Theoptions are:

1. Choose the blade setup angle j to equal the largest angle of anypart of the blade. This angle is at the leading edge at the hub.This point then is at the reference point ‘‘O.’’ The other cornerpoints are then found from Eq. (23) around the annulus asshown in Fig. 6. The result is a blade that is rather small and hasa swept back trailing edge.

Corr

Corr

05

10152025303540

Corr

Corr

0

5

10

15

20

25

0

0

Point "O"

Hub

Blade

θ

Fig. 7. The case where the blade set-up angle is bigger than the required angle at the leadin

2. Choose the blade setup angle j to be steeper than the largestangle required to match incoming flow at any point along theleading edge. This is shown in Fig. 7. Again all corner angles canbe achieved, but the blade has an even smaller chord anda similar swept back trailing edge.

3. Choose the blade setup angle j to match the required angle at thetip at the leading edge. As shown in Fig. 8 this leaves the angle atthe hub at the leading edge too small; it may even leave thetrailing edge angle too small. The figure shows that at the hub,the blade angle is lower than both the required leading edge and

Hub

ect LE Angle

ect TE Angle

Setup Angle = 41.0

Tip

ect LE Angle

ect TE Angle

20 40 60 80 100

20 40 60 80 100

Setup Angle = 41.0

g edge at the hub. Again all ‘‘corner’’ angles can be achieved, but the blade is narrow.

Page 8: Axial Flow

Tip

Required LE Angle

Required TE Angle

0

10

20

30

Blade with Setup Angle = 19.2

Hub

Required LE Angle

Required TE Angle

0

10

20

30

40

0 20 40 60 80 100

-60 -40 -20 0 20 40 60 80 100

Blade with Setup Angle = 19.2Trailing Edge ExtensionSwept Leading Edge Extension

Hub

θ CalcBlade

Swept Leading Edge Extension

Trailing Edge Extension

17°

Fig. 8. The case where the blade set-up angle is equal to the required angle at the leading edge at the tip. Only tip ‘‘corner’’ angles can be achieved; the calculated blade is unable toconnect with the hub. A swept leading edge and trailing edge are added.

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–4742

trailing edge angles. (See below, as in many cases this has shownto be the best choice due to compromises for vegetation shed-ding.) The swept leading edge sheds vegetation in the flow, but asshown in the plots in the figure, makes the leading edge mis-match worse, at least in this theoretical analysis.

-60

0

10

20

30

0

Hub

CalcBlade

Swept Leading Edge Extension

Trailing Edge Extension

Fig. 9. The case where the blade set-up angle is bigger than the required angle at the leadingconnect with the hub at its TE. A swept leading edge and trailing edge.

4. Choose the blade setup angle j to be greater than the requiredangle at the tip at the leading edge. As shown in Fig. 9 thisleaves the angle at the hub at the leading edge too small, butwith the peculiar-shaped triangular blade shown, the trailingedge angle can be achieved. Again in the interests of achieving

Hub

Reqired LE Angle

Required TEAngle

0

20

30

40

-40 -20 0 20 40 60 80 100

Blade with Setup Angle 23.8Swept Leading Edge ExtensionTrailing Edge Extension

Tip

Required LE Angle

Required TEAngle

20 40 60 80 100

Blade with Setup Angle 23.8

edge at the tip. Only tip ‘‘corner’’ angles can be achieved; the calculated blade can just

Page 9: Axial Flow

Penstock/Flow in

SECTION B-BSCALE 1 : 5

Draft tube/Flow out

Runner assembly

Vortex flange

Shaft

Fig. 10. General layout sketch of the turbines.

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–47 43

a sensible blade shape, a swept leading edge and extendedtrailing edge can be added, and a workable solution achieved.Plots in Figs. 8 and 9 show the resulting angle mismatcheswhich occur at the hub.

It is notable that there are actually several different configura-tions which can be used to achieve suitable flow-matching anglesalong both the leading and trailing edges of the runner blade. Themethod chosen for this project, item 3 from the list above, is a de-parture from the theory used to predict the ideal blade shapes,when in fact it produces blade angles close enough to the idealvalues to give acceptable efficiency and excellent vegetationshedding performance. The leading edge swept to more negative q

(upstream) leads to an increase in angle of attack and the expec-tancy of some turbulence on the suction side just downstream ofthe leading edge. The added area at more positive q (downstream)after the trailing edge overturns the fluid trajectory leaving therunner, potentially resulting in energy being returned to the exitingflow. Details of the blade design methodology, including the choiceof setup configuration used throughout this project and the gov-erning practical constraints, are given in Section 6.2.

5. Turbine casing design

A major thrust of the turbine development in this project hasbeen a radical departure from traditional Kaplan inlet configura-tion. The new designs avoid the use of guide vanes or any otherflow-spanning structure that might catch leaves or vegetation. Thisis necessary to eliminate the daily ritual of removing leaves and

blockages common to many microhydro sites. The lack of guidesurfaces has necessitated careful experimentation with casing ge-ometry to achieve desired conditions at the runner.

The traditional Kaplan turbine uses guide vanes to give rotationto the flow immediately upstream of the runner. In the case ofmicrohydro, the scale is sufficiently small that vegetation catcheson the leading edges of such guide vanes and remains there,blocking the flow. A particular motivation in this project has beenthe solution to this problem. The general layout of the casing designis shown in Fig. 10 and the design considerations have been thefollowing:

1. The casing must convert the energy in the flow into an appro-priate circumferential velocity. To achieve this, the inlet has beenoffset to one side. While this has allowed the removal of guidevanes for a single set of operating conditions, it has requiredconsiderable experimentation to arrive at an effective solution.

2. For good efficiency it is important to create an axi-symmetriccircumferential velocity field into the runner. To achieve this,a narrow disk-shaped flow space has been created between thevortex flange and casing end-plate. In this region, the endspacing (dimension ‘‘S,’’ Figs. 11 and 12) has been adjustedempirically to achieve a steady increase in circumferentialvelocity as the flow moves radially inward toward the runner.In the bulk internal volume of the casing and in this region, anysignificant differences in circumferential velocity at a givenradius around the circumference will tend to be damped outdue to the fluid’s viscosity.

3. A further device required in the higher specific speed cases, hasbeen to set up the inlet some distance from the runner so theflow is required to undergo several revolutions before enteringthe disk-shaped space, and is characterized by dimension ‘‘K’’in Figs. 11 and 12. This gives the larger asymmetrical flows anopportunity to even out before entering the runner.

4. The flow field must have a suitable rotational speed to drivea runner at the required 1500 rev./min for the generator. Toachieve this, the size of the inlet piping and its offset have beenadjusted to achieve the circumferential velocity required forthe impeller and the casing diameters needed. The startingpoint for the inlet size and its offset has been the required k inEq. (13) and the flow velocity from the penstock. While theseallow the calculation of an initial value of r (corresponding todimension ‘‘F’’ in Figs. 11 and 12) for the offset, final dimensionshave been arrived at by experiment.

5. The draft tube efficiency becomes increasingly significant as thespecific speed gets higher; this component must also cope withmore energetic flow in the runaway condition. Design and ver-ification of the draft tube has been an integral part of the ex-perimental program. For the NS 176 and 242 machines (‘‘lowNS’’), the majority of the draft tube’s expansion is external to themain casing. By contrast, for the NS 355 and 544 machines (‘‘highNS’’), the draft tube expansion occurs within the confines of themain casing, exhaust elbows and other such downstreamplumbing being equal in diameter to that at the main casing exit.

6. A further task has been to design a casing structure than can beeasily built in regional workshops. This has been achieved withcasing concepts that use largely flat plate with simple curves,and components that can be made on a lathe.

7. The design has had to be such that the turbine can easily bedismantled to clear any obstructions that manage to lodge inthe runner. This has led to the form of the casing being that ofthe ‘‘back-pull-out’’ pump, where the shaft bearings and run-ner assembly can be withdrawn without disturbing the inletand outlet pipe connections. To accomplish this, a spacer cou-pling is necessary for the direct-connected transmission to thegenerator and a design consideration is minimising the length

Page 10: Axial Flow

SECTION A-A

GB

H

SE

K

A

RV

T

RRD

L

Z

P

F

RC o

A

A

Fig. 11. Low NS casing dimensioning and orientation guide.

Z

RRRV

RCo

H

B F

S G

W

L

D

K

TA SECTION A-A

A

A

P X

Fig. 12. High NS casing dimensioning and orientation guide.

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–4744

Page 11: Axial Flow

Runnercentreline

Hub boundary

Leading edge Trailing edge

Fig. 13. Axi-symmetric CFD modelling of flow into runner, showing meridional com-ponents upstream of runner.

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–47 45

of the spacer coupling. Dowelling, or some equivalent, is alsoimportant to ensure correct realignment on re-assembly.

8. The design also has to consider the forces of the adjacent pipework on the turbine and allowance made for sufficient strengthof the casing. An alternative is for flexible pipe couplings whichare to be preferred, though are more expensive.

9. Consideration has had to be given to the runaway conditionwhich occurs, for example if there is a loss of electrical load tothe generator. In this instance there is the potential for cavi-tation in the draft tube and destructive forces in the turbine. Ineach design this eventuality has been addressed by a confir-mation test, to verify the integrity of the system left in therunaway condition for several hours.

10. Robustness of the machine is important to cope with handling intransit to the site and for installation with limited resources forlifting. Depending on size, the machine may have to be dis-mantled into small enough components for transport on foot.

11. Pressure testing of the turbine should be undertaken aftermanufacturing and before installation. Proof testing in theoperational mode is normally out of the question.

Key tasks of the research programme have been the construc-tion, modification and testing of casings to achieve these aims, theadjustment of the disk-shaped space and verification of the ap-propriate flow around the lip and into the runner. Fig. 13 shows

Fig. 14. The runners of some of the development tu

a sample of computational flow modelling undertaken for the entryinto the runner of the NS 355 machine.

Generic casings for low and high NS machines are given in Figs.11 and 12 respectively, with dimensions in Tables 1 and 2. Note thatthe main difference is that the low NS designs have a simplerspliced-pipe inlet to the main casing, whereas the high NS designshave a less restrictive rectangular diffuser type inlet, with a fabri-cated circle-to-square flange adapter at the upstream penstockinterface. In addition, the NS 355 and 544 machines’ casings havea scroll shape versus the tubular shape of the other two designs.This introduces the RCp parameter seen in Tables 1 and 2, wherethe NS 355 and 544 casings’ radius from the runner axis is

RC ¼ RCoexpðRCpaÞ (26)

Table 1 contains the casing dimensions of those models tested inthe laboratory, while Table 2 contains the same four machinesscaled to the same 1 kW power output and 1500 rev./min forcomparison and use as reference points for further scaling. It isnoted that the actual manufacturing drawings are necessarily morecomplex and detailed. These figures only give the dimensions ofessential features necessary for the casings’ functionality.

6. Compromises due to project context

The microhydro designs from this paper emphasize some con-ceptual differences between large hydro and microhydro, mainly inthe form of compromises that are made to keep the schemes eco-nomical and reliable with minimal maintenance.

6.1. Reduced efficiency due to simple construction

One driver of this project is that the turbines should be easilymanufactured in regional workshops in third-world countries. Thishas resulted in runners (Fig. 14) and casings designed for simplefabrication using mild steel plate. Volumes and passages aretherefore not as streamlined as would be possible with more so-phisticated manufacturing techniques. Some changes trickle downto affect other components. For example, eliminating the com-plexity of trash racks or other maintenance-intensive supportingstructures has led to the less-than-ideal blade shape illustrated inFig. 8 being utilized throughout. The requirement to freely passdebris has likewise led to the elimination of intake flumes, guidevanes, wicket gates and the like. To be sure, some turbine efficiencyhas been compromised in the design process, but given the context,a few percent of efficiency has been deemed allowable as long asthe final scheme produces the originally predicted power reliably.

rbines in this project: NS 355 (left) and NS 242.

Page 12: Axial Flow

Propeller Turbine Model Hydraulic Efficiency

50.0%

60.0%

70.0%

80.0%

0 100 200 300 400 500 600Specific Speed, Ns

Hyd

rau

lic E

fficien

cy

Ns 176Ns 242Ns 355Ns 544

Fig. 15. Tested model efficiency across propeller turbine range.

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–4746

Even with these manufacturing limitations, it has been an objectof the development program that every turbine should achieve anht of 70% efficiency. The NS 544, the least efficient model, operates ata maximum ht of 68%, while the NS 242, the most efficient model,operates at a maximum ht of 74% (Fig. 15).

6.2. Runner blade practical design

In developing runners for this project it was decided early onthat options 1 and 2 from the list in Section 4 gave blade shapesthat, while possible, were unsatisfactory in that their chord was tooshort, the area per blade too small, and many more blades would berequired to reduced blade loading to levels below those causingcavitation. The starting point for experimentation has been option3 shown in Fig. 8. The arguments in favour of this choice are:

� A CFD study of the 3D flow into the runner annulus shows thatthere is a considerable radial component to the flow near the hubwhere the leading edges are located (see Fig. 13). The effect is toreduce both va and vc in Fig. 5, lowering the required leadingedge angle at the hub to a value much closer to what is actuallybuilt. As a consequence the blade angle mismatch at the hub isnot as significant as shown in the theoretical model of Fig. 8.� These blades have been found by experiment to work as

required [9, p. 141–143].

-100

-80

-60

-40

-20

0

20

40

60

800 20 40 60 80 100 120 140

Labaratory Models

Ns 176Ns 242Ns 355Ns 544

Fig. 16. Runner blade true shapes

� They are a reasonable area, so that a small number of blades issufficient; this makes manufacture easier.� The hub-to-tip ratio is reasonable, being close to that of Kaplan

turbines.� Efficiencies of 70% are achievable; the losses introduced by the

compromises are perhaps less of a problem than building andmounting multiple, small, odd-shaped blades.� The added logarithmic spiral leading edge works effectively in

shedding vegetation, though it may cause some small stalledregions near the hub so some losses will result.� The mismatch of the angles at the trailing edge effectively adds

more deviation (d) to the blades and consequently has thepotential to create a small reverse circumferential velocity inthe core of the discharge flow. Again this loss appears small.

Experimental work with leaves and the swept leading edge hasshown that a constant spiral angle of about 17 degrees is requiredas shown in Fig. 8. The leading edges should be sharpened, withmaterial taken off the suction face; the sharp edges can be seen insome cases in the photographs of Fig. 14, the same as is representedon the leading edge of the profile shown in Fig. 5. The process ofshedding vegetation is that any leaves wrapping themselves overthe leading edge are either cut immediately or they slide out to thetip where they catch between the tip and the casing and are slicedup by the sharp edge.

-100

-80

-60

-40

-20

0

20

40

60

800 20 40 60 80 100 120 140

References: 1 kW, 1500 RPM

Ns 176Ns 242Ns 355Ns 544

for the four specific speeds.

Page 13: Axial Flow

K.V. Alexander et al. / Renewable Energy 34 (2009) 35–47 47

An important consideration in the manufacture of the runners isthe correct attachment angle of the blades. In Fig. 4, the fixture formounting the blades is shown, as is the point on the blade thatmust be lined up on the radius through the reference point ‘‘O’’ onthe hub. The dimensions for the runners for the four specific speedsare shown in Table 1, and the templates for the blades at laboratorymodel and 1 kW reference scale are shown in Fig. 16. Note thatalthough the hub-to-tip ratio is not constant across all four designs,the runners’ swept diameter increases with specific speed at con-stant power output, confirming the prediction that higher specificspeed machines, and therefore lower power-density machines, arenecessarily larger when compared to low-specific speed machines.

6.3. Higher cost due to low power density of low head

For sites of a given power, as the site head reduces, the flowmust increase. This is indicated by Eq. (2). This means that as sitehead reduces, the penstocks [3] and turbines need to become largerto carry the increased flow, and although the penstocks are shorter,the larger components inevitably make the installations more ex-pensive. So, on a per kilowatt basis, the installations for these lowhead sites are quite likely more expensive than higher head sites.This is one of the reasons why this low head area has remainedundeveloped. Note that in the commercial sector, low head appli-cations such as tidal barrages and marine stream power generationcannot typically compete with higher head hydro plants. One no-table exception may be Toshiba’s Hydro-eKIDS scheme, marketedfor use in irrigation channels [10]. Therefore, it must be appreciatedthat at a low head site, the installation is going to be more costly (in$/kW terms) than at a higher head site of equivalent power.

7. Conclusions

These four turbine types have been built and tested, at one scale.The test unit efficiency results for each machine’s final configuration

are given in Fig. 15 showing that a finite number of designs may beused to cover a broad range of sites. Nominally, there is sufficientinformation in this paper for these propeller turbines to be built, inessence covering 28 of the possible 38 units shown in Fig. 3.However, at this stage working drawings are only available at thefour scales of the tested models and the one full-scale machine thathas been implemented in practice. Work is proceeding on furtherdesigns.While it is expected that slightly better efficiencies could beachieved with more refinement in the runner design, this paperpresents practical, working, and economic turbine solutions for lowhead microhydro systems, especially when they are matched withthe modular components described in the other papers in thisseries [2,3,11].

References

[1] Blakely RJ, O’Connor KF. Present and potential use of micro-hydro-electricschemes in remote locations. October. Auckland: New Zealand EnergyResearch and Development Committee 1981.

[2] Alexander KV, Giddens EP. Microhydro: cost-effective, modular systems forlow heads. Renewable Energy 2008;33(6):1379–91.

[3] Alexander KV, Giddens EP. Optimum penstocks for low head microhydroschemes. Renewable Energy 2008;33(3):507–19.

[4] New Zealand. Demonstration project profile: remote area power supply: microhydro/diesel hybrid, Project summary 22. Wellington: Energy Efficiency &Conservation Authority; 1994.

[5] Nechleba M. Hydraulic turbines: their design and equipment. Prague: ARTIA;1957.

[6] White FM. Fluid mechanics. 5th ed. Boston: McGraw-Hill; 2003.[7] Dixon SL. Fluid mechanics: thermodynamics of turbomachinery. 2nd ed.

Oxford: Pergamon Press; 1975.[8] Hothersall R. Hydrodynamic design guide for small Francis and propeller

turbines. Vienna: United Nations Industrial Development Organization; 2004.[9] Parker GJ, Faulkner SA, Giddens EP. A low head turbine for microhydropower.

RERIC International Energy Journal 1993;15(2).[10] <http://www.toshiba.co.jp/f-ene/hydro/english/newtech/newproducts/doc5.

htm>.[11] Bryce P, Giddens EP. Malfunction protection for electrical equipment used in

micro hydro plants. Water Power & Dam Construction Supplement 1985;37(11):5–8.