hydraulic turbines—basic principles and state-of-the-...

85

Hydraulic turbines—basic principles and state-of-the-art computational fluid dynamics applications

P Drtina* and M SallabergerSulzer Hydro AG, Zurich, Switzerland

Abstract: The present paper discusses the basic principles of hydraulic turbines, with special empha-sis on the use of computational fluid dynamics (CFD) as a tool which is being increasingly appliedto gain insight into the complex three-dimensional (3D) phenomena occurring in these types of fluidmachinery. The basic fluid mechanics is briefly treated for the three main types of hydraulic turbine:Pelton, Francis and axial turbines. From the vast number of applications where CFD has proven tobe an important help to the design engineer, two examples have been chosen for a detailed discussion.The first example gives a comparison of experimental data and 3D Euler and 3D Navier–Stokesresults for the flow in a Francis runner. The second example highlights the state-of-the-art of predictingthe performance of an entire Francis turbine by means of numerical simulation.

Keywords: hydraulic turbines, flow prediction, stage simulation, hill chart, Navier–Stokes and Eulercomputations

NOTATION ns specific speedr density (kg/m3)Q guide vane opening (deg)C, c absolute velocity (m/s)W flow coefficientE energy per unit mass (m2/s2)Y head coefficientg gravity (m/s2)v rotational speed (1/s)hat atmospheric pressure head (m)

hd vapour pressure head (m)H turbine head (m)

SubscriptsHs suction head (m)k turbulent kinetic energy (m2/s2)

1 runner inletKc normalized velocity2 runner outletKu normalized circumferential velocityEK leading edgeKw normalized relative velocity

n rotational speed (r/min)Q flowrate (m3/s)

1 INTRODUCTIONR, r radius/radial directionT torque (N m)

The use of hydraulic turbines for the generation of powerU, u circumferential velocity (m/s)has a very strong historical tradition. The first trulyW, w relative velocity (m/s)effective inward flow reaction turbine was developed andZ axial direction/axis of rotationtested by Francis and his collaborators around 1850 in

a absolute flow angle (degrees) Lowell, Massachusetts [1 ]. Modern Francis turbinesb relative flow angle (degrees) have developed into very different forms from the orig-e dissipation rate inal, but they all retain the concept of radial inward flow.f loss coefficient The modern impulse turbine was also developed in theg efficiency USA and takes its name from Pelton, who invented the

split bucket with a central edge around 1880. TheThe MS was received on 20 February 1998 and was accepted after modern Pelton turbine with a double elliptic bucketrevision for publication on 27 July 1998.

including a notch for the jet and a needle control for the* Corresponding author: Sulzer Hydro AG, Hardstrasse 319/Postfach,CH-8023 Zurich, Switzerland. nozzle was first used around 1900. The axial flow turbine

C01898 © IMechE 1999 Proc Instn Mech Engrs Vol 213 Part C

86 P DRTINA AND M SALLABERGER

with adjustable runner blades was developed by the 2 BASIC FLUID MECHANICS OF HYDRAULICTURBINESAustrian engineer Kaplan in the period from 1910 to

1924.Hydraulic turbines are not only used to convert 2.1 Definitions and parameters

hydraulic energy into electricity but also in pumped stor-The torque on any turbomachinery rotor can be esti-age schemes, which is the most efficient large-scale tech-mated from the inlet and outlet velocity trianglesnology available for the storage of electrical energy.(Fig. 1). The resulting equation is known as the EulerSeparate pumps and turbines or reversible machines, soturbine equation and gives the specific energy transferredcalled pump turbines, are used in such schemes. Duringby the runner astheir long history there has been continuous develop-

ment of the design of hydraulic turbines, particularlywith regard to improvements in efficiency, size, power E=

Tv

rQ=U1Cu1−U2Cu2 (1)

output and head of water being exploited. Recently, theuse of modern techniques like computational fluid For hydraulic turbines the degree of reaction is classi-dynamics (CFD) for predicting the flow in these cally defined as the ratio of the static pressure dropmachines has brought further substantial improvements across the runner to the static pressure drop across thein their hydraulic design, in the detailed understanding stage. The Pelton turbine is an impulse stage and hasof the flow and its influence on turbine performance and zero reaction with all the pressure drop occurring acrossin the prediction and prevention of cavitation inception. the stationary components and no pressure drop acrossThe efficient application of advanced CFD is of great the runner. In reaction stages such as Francis andpractical importance, as the design of hydraulic turbines Kaplan turbines a proportion of the pressure dropis custom-tailored for each project. occurs in the rotor and a proportion in the stator.

Three-dimensional (3D) potential flow codes have Typically, at their design points, a Kaplan turbine has abeen used for about 20 years, but their validity is limited reaction of around 90 per cent, a Francis turbine ofto design point operation and requires a lot of empirical around 75 per cent and a pump turbine of around 50interpretation. 3D Euler codes describe the flow field in per cent. At off-design operating points these valuesturbomachines with all typical vorticity effects, but neg- change.lect turbulent and viscous effects. Sulzer Hydro has now The overall efficiency go of a turbine is defined as theapplied a 3D Euler code for advanced runner design for ratio of the power delivered to the shaft to that available10 years. This was developed together with the Swiss in the water entering the turbine:Federal Institute of Technology in Lausanne [2, 3 ] andhas been used for over 70 different contracts, allowing go=

Tv

rgQH(2)

wide experience to be gained. For turbine runners withaccelerated flow the 3D Euler code is an excellent design where the net head H is the difference between the totaltool [4]. It is much faster than a Navier–Stokes code pressure at turbine inlet and turbine outlet.and of very high accuracy, as viscous effects are small For pumps and pump turbines, the flow coefficient Wand confined to thin boundary layers. Nevertheless, the and the head coefficient Y are generally normalized withprediction of runner efficiencies requires a comparison the rotor blade speed, in a similar manner to otherbetween the current 3D Euler result and those of pre-vious designs tested in the laboratory or in the field.

Parallel to the 3D Euler code, 3D Navier–Stokescodes have been applied to the design of componentswith adverse pressure gradients, i.e. impellers in pumpmode [5 ], to the analysis of the losses in turbine compo-nents [6 ], to the prediction of turbine hill charts by calcu-lating the flow in complete turbines from the spiralcasing to the draft tube, and to the prediction of erosioncaused by sand particles [7].

In addition to the discussion of the basic fluid dynam-ics of different kinds of hydraulic turbine, this paperpresents two examples where the application of CFD ledto a better understanding of complex flow phenomena.An improved understanding usually has a direct impacton the design, resulting in geometrical changes of exist-ing components, the replacement of existing componentsby a completely new design and/or the use of new

Fig. 1 Velocity triangles for an axial turbine runnermaterials.

C01898 © IMechE 1999Proc Instn Mech Engrs Vol 213 Part C

87HYDRAULIC TURBINES—BASIC PRINCIPLES AND STATE-OF-THE-ART CFD APPLICATIONS

turbomachines, as 2.2 Types of hydraulic turbomachine

Each type of turbine design can be further classifiedW=

Q

UD2(p/4)(3) according to such criteria as:

Shaft orientation � horizontal axis or verticalY=

H

U2 /(2g)(4) axis

Specific speed � high, medium or lowspecific speedIn hydraulic turbines, the usual performance param-

Operating head � high pressure 200 m<H<eters, such as the flow velocity, C, and the circumfer-2000 mential blade speed, U, are made dimensionless with

� medium pressure 20 m<Hrespect to E(2gH):<200 m

� low pressure H<20 mKc=

CE(2gH)

(5) Type of regulation � single, variable stator vanes,e.g. Francis

� double, variable runner andKu=

UE(2gH)

(6) stator vanes, e.g. Kaplan orvariable needle stroke andvariable number of jetsThe meridional and the circumferential components are

Design concepts � single-stage or multistagedenoted by Kcm

and Kcu

. For both pumps and turbines,� single-volute or double-a useful parameter is the dimensionless specific speed

volutedefined as� single-jet or multijet

ns=v

p1/2Q1/2

(2gH)3/4=

W1/2Y3/4

(7) More details of the regimes of application of the differentturbines can be found in Fig. 2 (see also reference [8]).This figure shows which type of turbine is used forThe specific speed is the main parameter in hydraulic

turbomachinery and is used for classification of turbines different volume flows and head rise and also gives theabsolute power output generated for each category. Afrom turbine head, flowrate and speed.

Fig. 2 Overview of turbine runners and their operating regimes



Fig. 3 Selection diagram for different types of turbine

further diagram showing the different impeller forms and runner [10 ]. It can be seen that the jet acts on severalbuckets at the same time. Much empirical work has beenthe head for a variation in specific speed is given in

Fig. 3. In general, the number of runner vanes or buckets carried out to determine the shape of the bucket foroptimum performance. In general, standard bucketdecreases with increasing specific speed, from about 26

to 18 in a Pelton wheel, from 19 to 11 in a Francis shapes from a family of profiles can be modified for awide range of applications.turbine and from 7 to 3 in an axial turbine.

2.3 Pelton turbines

The impulse turbine extracts energy from the water byfirst converting the available head into kinetic energy inthe form of a high-speed jet discharged from the nozzle.All the pressure drop occurs in the nozzle and the runneroperates at constant static pressure. The jet is directedon to buckets fixed around the rim of a runner, andthese are designed to remove the maximum energy fromthe water. The power of a given runner may be increasedby using more than one jet. A cross-section through atypical vertical unit with six jets is shown in Fig. 4.

The hydrodynamics of the Pelton turbine is simple tounderstand and a one-dimensional steady analysis basedon the velocity triangles provides much insight into thedesign principles. The Pelton turbine remains, however,the most complicated of all types of hydraulic turbo-machinery with respect to detailed flow analysis, as itinvolves a highly three-dimensional, viscous, unsteadyflow with a free surface on a moving boundary, and thisis just on the limit of the capability of the most advancedCFD methods [8, 9].

Figure 5 shows an instantaneous snapshot of the flow Fig. 4 Cross-section through a vertical axis Pelton turbinewith six jetsinteraction between the jet and the buckets of a Pelton



contains a rotating component in the same direction asthe runner. For H>Hopt the outlet water rotates againstthe rotational direction of the runner.

2.4 Francis turbines

The modern Francis turbine utilizes purely radial inletflow through stationary guide vanes, but the runners aremixed flow devices with a component of the flow in theaxial direction. The trend from purely radial inflowdevice through mixed flow devices to near axial flowdevices increases as the specific speed is increased. Theflow channel of a modern Francis turbine with a verticalaxis is shown in Fig. 7, comprising a spiral inlet case,stay vanes, guide vanes, runner and draft tube.

The spiral case of a Francis turbine is designed suchthat the velocity distribution in the circumferential direc-tion at the inlet to the stay vanes is uniform and theincidence angle over the height of the stay vanes variesonly little. The main function of the stay vanes is tocarry the pressure loads in the spiral case and turbinehead cover. Their second purpose is to direct the flowtowards the adjustable guide vanes with an optimal inci-dence angle. The adjustable guide vanes are the onlydevice available to control the flow and thus the poweroutput of a Francis turbine. Leakage flow through thegaps between the guide vane tips and facing plates causes

Fig. 5 Visualization of the flow in a Pelton runner efficiency losses and can cause local erosion [7]. Therunner (Fig. 8) consists of a crown and band supportinghighly curved, three-dimensional sculpted blades. ToThe velocity triangles of the water entering and leaving

the bucket in the middle section of its passage through reduce the leakage flow between the runner and thecasing, labyrinth seals at the crown and band are pro-the jet are shown in Fig. 6. At a single value of the jet

velocity or available head, i.e. for U2<U2opt and H= vided. The diffuser downstream of the runner is usuallyan elbow-type draft tube similar to that of KaplanHopt, the optimum exit angle of a2=90° is attained with

the minimum kinetic energy in the flow leaving the turbines. The vortices in the draft tube at off-designconditions often give rise to severe oscillations. A break-bucket. For H<Hopt the relative velocity of the flow

leaving the bucket w2 is reduced and the outlet water down of the loss distribution within a Francis turbine at

Fig. 6 Velocity triangles for analysis of a Pelton bucket



the design point as a function of specific speed ns isshown in Fig. 9. At off-design conditions the lossesattributable to the runner, such as incidence losses, fric-tion inside blade passages and exit swirl losses, stronglyincrease, as do the losses in the draft tube.

Typical velocity triangles for a mean streamline forlow and high ns turbines are shown in Fig. 10. For veryhigh ns the flow in the runner is nearly axial, givingKu1

#Ku2

. With decreasing ns the flow becomes increas-ingly radial with larger differences between inlet andoutlet diameters D1 and D2 and hence between Ku

1

andKu2

. The increasing difference between inlet and outletvelocity U1 and U2 explains the increasing head as nsdecreases.

The flow in a Francis runner is a strongly three-dimen-sional rotational flow. The close proximity of the guidevanes to the highly curved meridional flow channel leadsto a non-uniform meridional velocity at stator outlet. Thisgives rise to a strongly rotational flow at the outlet of thestator vane and a severe three-dimensional flow patterninside the runner. Therefore only fully three-dimensionalmethods will provide effective solutions of the flow in aFrancis runner. As a result of 3D Euler flow computationsthe flow inside the blade channel of a Francis runner ofhigh specific speed close to the suction side and close tothe pressure side can be obtained (Fig. 11). Typically theflow is roughly aligned with the meridional shape on thesuction side of the blade, whereas on the pressure side theflow is forced towards the band. This indicates the strongFig. 7 Cross-section through a typical Francis turbine ofthree-dimensional character and the distinct secondarymedium nsflow of a Francis runner.

Fig. 8 Computer visualization of a typical Francis runner of high specific speed nsC01898 © IMechE 1999Proc Instn Mech Engrs Vol 213 Part C


Fig. 9 Loss breakdown of Francis turbines as a function of ns

Fig. 10 Velocity triangles for Francis turbines (a) with low ns and (b) with high ns

The velocity vectors at the leading edge together with Kaplan concept. Cheaper but not so flexible conceptsare designed as single-regulated turbines. The fixed bladepart of the blading are shown in Fig. 12 for the samepropeller turbine has adjustable stator blades but fixedFrancis runner. The absolute and relative velocity compo-runner blades. In the so-called semi-Kaplan concept,nents are shown and the variation in the flow in the circum-fixed stator blades and adjustable rotor blades are used.ferential direction, especially at the hub, is obvious. The

For classical vertical Kaplan turbines (Fig. 14) thethree-dimensional character of the flow is also evident ininflow and the outflow of the stator is radial, while thevisualization of the flow on the suction side of the bladeinflow and the outflow of the runner is fully axial. Inin the vicinity of the leading edge at a turbine head greatergeneral, steel scroll cases are used for heads between 30than the optimum (see Fig. 13). The flow enters the bladeand 60 m and concrete semispiral casings for headspassage and then deviates strongly towards the band.between 10 and 40 m. The largest Kaplan turbines haveWhile operating at the design flowrate this motion isrunner diameters of up to 10 m. The horizontal bulbaligned roughly parallel to the leading edge. Operation atturbines (Fig. 15) are designed with a horizontal axislower flowrates leads to the occurrence of strong vorticesand have the advantage of a more or less straight flowwhich are contained within the blade passage. Thesepath through the intake and draft tube. The frictioninterblade vortices may induce pressure pulsations.losses are considerably lower in these components thanin the spiral casing and elbow draft tube of the verticalKaplan turbine. In the Straflo turbine design (Straflo=2.5 Axial turbinesstraight flow) the turbine and the generator form an

Axial turbines may be realized in different concepts. The integral unit without a driving shaft. The turbine rotormost flexible in terms of variation in flowrate Q and blades are connected to an outer ring which directly car-turbine head H is the double-regulated turbine with ries the generator rotor poles.

The hub–tip ratio ranges from 0.30 for three-bladeadjustable stator and rotor blades, the so-called full



Fig. 11 Meridional flow in a Francis runner of high specific speed ns

Fig. 12 Euler results for the flow at the leading edge of a Francis runner



Fig. 13 Three-dimensional flow visualization close to the leading edge of a Francis runner. Left: H=1.2Hopt,Q=Qopt ; right: H=1.2Hopt, Q=0.5Qopt

runners up to 0.65 for seven-blade runners. Because of contribution to the losses of a low-head turbine. In caseswhere the draft tube is designed to be close to the stab-the large U variation over the blade span, the velocity

triangles differ strongly between the root and the tip ility limit, the swirl at the runner outlet, especially at thetip section, has to be carefully controlled.section (see Fig. 16). The profiles at the root section have

a large camber and thickness, high turning of the flowand high stresses, while the profiles at the tip sectionhave a small camber and thickness, low turning of the 2.6 Cavitationflow and low stresses.

For the stator vanes of a Kaplan turbine a straight Cavitation occurs in the flow of water when, owing toregions of high-flow velocity, the local static pressureprofile is used, but bulb turbines are designed with coni-

cal vanes. Therefore the swirl at the stator outlet is decreases below the vapour pressure and vapour bubblesappear. Cavitation may occur on the blade suction sur-rotational and the flow in the runner will have a strong

three-dimensional character, which is demonstrated in face in regions of low pressure or at the runner leadingedge at off-design operation. For low-head operation,Fig. 17. The velocity vectors at the leading edge and at

the trailing edge are given in Fig. 18. Again, fully 3D cavitation will be located on the pressure side; for high-head operation it will be on the suction side. Withincomputation methods will be superior to others. The

secondary flows, however, are less pronounced than in vortices such as those induced by the tip leakage flow ofaxial runners or those occurring in the blade passagesFrancis turbines, and therefore axial runner design has

been based on 2D theory for many decades. of a Francis runner at extreme off-design operation andin the draft tube of Francis turbines, cavitation mayThe swirl at the runner outlet strongly influences the

performance of the draft tube, which gives the largest also occur. In hydraulic turbines the most important



Fig. 14 Cross-section of a vertical axis Kaplan turbine

Fig. 15 Cross-section of a horizontal bulb turbine with direct drive

parameter describing cavitation is the cavitation number Kaplan turbines with seven runner blades the value ofs defined by Thoma: s for cavitation onset is typically 0.3–0.5, with 4–5

blades it may be 0.5–2.0 and for runners with threeblades it may vary from 2.0 to 3.0.s=

hat−hv−HsH

(8)The effects of cavitation are harmful, both on per-

formance and on erosion of material. Cavitation erosionIn this dimensionless parameter the pressure marginis caused by the extremely high pressure peaks that occurbetween local pressure and vapour pressure is nor-during the implosion of cavitation bubbles in the vicinitymalized by the turbine head. In order to achieve cavi-of a solid surface. Cavitation imposes restrictions ontation-free conditions, the value of s of the plant mustblade loading and blade design. Modern CFD basedbe larger than the value of s at which laboratory testsdesign methods attempt to avoid cavitation by optimiz-indicate the onset of cavitation. For Francis turbines theing the pressure distribution on the blades to avoid areastypical value of s may vary from 0.04 to 0.09 for lowof high relative velocity [11 ]. In addition the setting levelspecific speed, ns, from 0.09 to 0.20 for medium specific

speed and from 0.20 to 0.30 for high specific speed. For of the turbine relative to the tailwater can be reduced or



Fig. 16 Velocity triangles over the span of a Kaplan turbine blade: (a) root section; (b) tip section

Fig. 17 Meridional flow in a Kaplan runner

the turbine can be designed with larger diameter and ating an appropriate grid for the complex geometry ofa hydraulic turbine is briefly reviewed. Sections 4 and 5lower flow velocities.demonstrate the ability of state-of-the-art CFD appli-cations to predict not only flow fields but complete hillcharts for Francis turbines.3 GRID GENERATION AND SIMULATION

METHOD

After discussion of the basic fluid mechanics of hydraulic 3.1 Grid generationturbines and the most important design criteria, the fol-lowing sections are devoted to the application of modern Presently there is no unique grid generation approach

that perfectly fulfils all requirements imposed by the vari-3D Navier–Stokes codes, with particular emphasis onthe recently developed stage simulation method. In ous components of hydraulic turbines: spiral casings,

stay vanes and guide vanes, runners and draft tubes.Section 3 the still very time-consuming process of gener-



Fig. 18 Euler results for the flow at the leading edge of a Kaplan runner

As long as the ultimate automatic grid generation tool meshes for geometrically and topologically complexdomains (i.e. mixed H,O,C grids, intersecting butterflyapplicable for any given complex geometry is missing,

tools will be used that are specifically adopted to single grids). In order to avoid highly skewed grid cells themain body of the mesh for a spiral casing (see Section 5)components.

Owing to the geometrical complexity of most of the is constructed using a butterfly arrangement of sub-blocks (a central block surrounded by four outer blocks:hydraulic machinery components under investigation

(i.e. spiral casing), these component grids were generated see inlet section of spiral casing in Fig. 19). To captureall significant flow phenomena the grid resolution has towith the help of ICEM–CFD/P3 and ICEM–CFD/

HEXA which both deliver high-quality block-structured be sufficiently high. On the other hand the available com-

Fig. 19 Grid for an entire Francis runner



puter resources impose severe limitations on the mesh and Sulzer Innotec. Details of the validation of the stagecapability are described by Sick et al. [18].size.

Other grids for guide vane passages and draft tubeshave been generated by applying the grid generation

4 RUNNER FLOW PREDICTIONsoftware TASCgrid which forms part of the CFX–TASCflow software package [12]. An important advan-

4.1 Introductiontage of applying TASCgrid is its ability to parameterizethe basic geometrical description. Thus, it is possible to

The first major breakthrough in the use of CFD methodschange the guide vane angle within certain limits byfor hydraulic turbine design allowed Euler methods tosimply changing the value of a single parameter in thebe used for design of water turbine components and,input file. For most of the sophisticated grid generationcombined with suitable design rules, drastically reducedprograms (ICEM–CFD included) this is still a challeng-the number of model tests needed for the achievementing problem.of a satisfactory design [3]. The relatively simple Eulermethods predict the important features of the flow, suchas incidence levels at runner inlet, pressure levels at3.2 Discretization method and turbulence modelrunner outlet (cavitation) and swirl in the draft tube

All calculations discussed below were carried out using inlet. They are, however, limited in their ability to predictthe CFX–TASCflow software package. This CFD code the losses, as viscous forces are neglected. Whilesolves the 3D Reynolds-averaged Navier–Stokes equa- Section 4 concentrates on the comparison of runnertions in strong conservative form for structured multi- outlet velocity profiles obtained by applying a Euler andblock grids. The system of transport equations is a Navier–Stokes code, the prediction of losses and tur-discretized using a conservative finite element based bine performance will be discussed in Section 5.finite volume method and is solved for the primitive flow This section demonstrates the improvement gained byvariables (pressure and Cartesian velocity components) applying Navier–Stokes codes instead of simple Eulerusing a coupled algebraic multigrid method and a codes. The most significant improvement can be seen bysecond-order accurate skew upwind differencing scheme comparing the runner outlet velocity distributions forwith physical advection correction. The discretization off-design operating points. In particular for the designscheme is second-order accurate in space. Turbulence of draft tubes a reliable knowledge of the velocity profileseffects are modelled using the standard k–e model, the at the draft tube inlet is crucial. The better prediction ofRNG model or the Kato–Launder formulation. velocity profiles is a direct consequence of taking auto-

Liquid and subsonic, transonic and supersonic gas matically into account the losses when applying aflows can be analysed in rotating and stationary coordi- Navier–Stokes flow code. In Section 5 it will be shownnate systems as well as in multiple frames of references. that even the loss distribution is predicted very well.For more than 10 years this software has been appliedto various fluid flow problems [13, 14 ]. Details regarding

4.2 Predicting Francis turbine runner flowthe theoretical basis of the software are reported byRaw [15 ].

The test case considered for the verification of the stageAll calculations were performed applying the CFX–

interface method is a model Francis turbine of highTASCflow code versions 2.6 or 2.7 implemented on an

specific speed (see Fig. 20). The full-scale turbine has aIBM RS/6000 and an SGI Power Challenge carrying 12

runner diameter of 3.4 m and was designed for a headprocessors. Some of the calculations have been carried

of 32.7 m at a nominal flowrate of 90 m3/s with aout in parallel mode using up to four processors.

rotational speed of 166 r/min and a specific speed of 422.The model turbine is a scale model of the originalmachine with a runner diameter of 0.3 m. The experi-3.3 Stage capabilityments were carried out in the hydraulic turbine teststands of Sulzer Hydro in Zurich. Standard measure-For the calculations discussed in Sections 4 and 5 the

so-called stage method developed by Galpin et al. has ment techniques for modern hydraulic practice were usedfor the derivation of all performance parameters.been applied [16 ]. Here the steady state interaction

between stationary and rotating components in a turbo- The velocity near the draft tube outlet was measuredby means of a propeller anemometer. Measurements ofmachine is simulated by a mixing plane between the com-

ponents. Each component is calculated in its own frame the detailed flow velocities were also carried out in thehydraulic turbine test stands of Sulzer Hydro using L2Fof reference and the blade rows can be reduced to single-

blade channels with periodic boundaries. The method is laser velocimetry. Flow traverse planes were establishedat the runner inlet and at the runner outlet by insertionbased on stage simulation ideas of Denton [17 ] which

were extended by Galpin [16 ] and installed into of suitable windows in the casing (see Fig. 20). Flowvelocities at each of these measurement planes wereTASCflow under the partnership of ASC, Sulzer Hydro



Fig. 20 Francis turbine with measurement positions (×) and interfaces (D D D)

obtained at five operating points of the turbine. These that the component interactions are well predicted atboth design and off-design points.operating points were selected to provide a good over-

view of the flow at the best operating point and at a In all operating points the Navier–Stokes solution pre-dicts the velocity profiles for both the swirl componentvariety of different off-design conditions.

During the investigations a series of computations and the meridional component very well. At operatingpoints 1, 2 and 4 the viscous results are clearly in closerwith different levels of complexity was carried out.

Beginning with simple simulation of the flow in the agreement with the measurements than the Euler compu-tations. As regards operating points 3 and 5, viscous andrunner alone and then proceeding with two-component

calculations (distributor–runner and runner–draft tube), inviscid simulation results give comparably good resultswith respect to the measurements. It is hard to decidesimulations for the entire hydraulic turbine were finallywhich one is closer to reality. Nevertheless, it should bearrived at, covering all components starting from theborne in mind that these are part load operating pointsinlet of the spiral casing and ending at the draft tubewhere measurements are difficult to obtain, especially foroutlet. These full machine simulations were performedsmall radii.applying a two-step procedure: in the first step the spiral

casing, including the entire stay vane ring, was simulated;the second step included appropriate passages of the stayvane ring, guide vane ring and the runner as well as the 5 HILL CHART PREDICTION BY STAGEcomplete draft tube. Thus, the two steps overlapped at SIMULATIONSthe stay vanes. Flow conditions extracted from the firststep were used as inlet conditions for the second step. To predict a complete hill chart for a hydraulic turbineMixing interfaces were applied between rotating and the entire machine from the inlet of the spiral casing tonon-rotating components. the outlet of the draft tube has to be modelled. In the

Figure 21 shows the results obtained for the velocity case of a Francis turbine, grids for different guide vanedistribution (meridional and swirl component) at the openings have to be generated.runner outlet for inviscid and viscous cases in compari- In order to reduce the computational effort, the two-son with experimental data. All velocity data for the step procedure described in Section 4.2 was applied.viscous case were extracted from the full stage This is physically reasonable as the flow in the spiralcalculation. casing is a function of the Reynolds number only, just

The comparison of the measured and calculated cir- as the flow in the penstock or the branch pipe. Tocumferential and meridional velocity components at the determine the losses in the spiral casing over the wholerunner outlet demonstrates the reliability of the compu- hill chart it is only necessary to calculate the viscous

flow in the spiral casing at one operating point. Thetational method in detail. The good agreement indicates



Fig. 21 Francis runner. Comparison of non-dimensional meridional velocity, Kcm

, and swirl velocity Kcu

,for five operating points. Operating point 1 is identical to the best efficiency point, while operatingpoints 2–4 reflect different off-design conditions (see sketch in bottom left corner)

losses are then a parabolic function of the volume point) is taken as the initial condition for other operatingpoints. This reduces the number of subsequent itera-flow, Q2 (see reference [19 ] ). For the stage simulation

it is therefore sensible to calculate the flow in the spiral tion steps to 100–300 (1–3 days) depending on theoperating point.casing separately (and in one-half of the symmetric

casing only) to avoid unnecessary large grids for eachoperating point.

5.1 Numerical hill chartThe outlet of the spiral casing simulation is chosen tobe downstream of the stay vanes so that the flow at the

The hill chart for a high specific speed Francis turbineinlet to the stay vane cascade is correctly modelled. Thehas been determined experimentally on a model test rig.boundary conditions for the stage including the distribu-The turbine efficiency has been evaluated for more thantor, runner and draft tube consist of tangential and200 operating points, which yields a good approximationradial velocity components (defining the swirl ) in a refer-of the turbine performance for the operating range ofence plane upstream of the distributor (as calculated ininterest.the spiral casing analysis) and average constant pressure

To calculate the turbine efficiency from the numericalin an outlet plane downstream of the draft tube exit (thissimulation data, the following procedure is applied toallows for the typical non-uniformities of the flow at theeach operating point:draft tube exit).

The solution of the first simulation (best efficiency 1. The spiral casing (casing and stay vane ring) and stage



(distributor, runner and draft tube) calculation results The qualitative agreement of both hill charts isimpressive. All general features are captured by the simu-are examined together in order to evaluate the totallations. The best efficiency point is identical in the twopressure loss over the entire machine.hill charts and all gradients show a very similar behav-2. The power delivered by the runner is calculated asiour. Please note that the two scales Ku and Kc

m

are inthe product of rotational speed and torque on theabsolute rather than in relative terms in order to be ablerunner. Both pressure and viscous forces acting onto check the correct location of the best efficiency point.the runner surfaces (blades, hub and shroud) contrib-Quantitatively there is some discrepancy in the steepnessute to the torque.of the gradients, in particular for high values of Ku .3. Efficiencies are determined for each component, i, by

A detailed comparison for the three different guideapplyingvane openings under investigation can be obtained fromFigs 24 to 26. For each guide vane opening the nor-g

i=

p: tot,i,in−p: tot,i,outDp: tot,em

(9)malized efficiency is plotted as a function of Ku . It canbe seen that the shape of the efficiency curves for allwith Dp: tot,em being the difference in total pressure overthree guide vane openings is predicted correctly. Forthe entire machine. Note that for the runner the worksmall openings the best efficiency point occurs at low Kudone, which is evaluated in step 2, has to be takenvalues (high head). At large openings the high efficiencyinto account.region occurs at high Ku values ( low head). This typical4. Component losses are defined by f

i=1−g

iand

characteristic of a high specific speed turbine is perfectlyadded to give the entire loss appearing in the machinerepresented in the analysis.ftot=∑

ifi. The resulting overall efficiency is defined

Two weaknesses of the present analysis should beby gem=1−ftot. mentioned. Firstly, whereas the relative shape of the hillOwing to the high demand in computer memory and chart is perfectly simulated, the absolute level of the cal-CPU time, the number of operating points that could be culated efficiency is about 3 per cent lower than thatsimulated was restricted. In the present case 14 operating measured. This is attributed to the use of a coarse grid.points were chosen, with three different guide vane open- A check of one operating point calculated with a finerings (volume flowrates) and six different heads mesh produces a reduction in friction losses.investigated. Further improvements are expected if the near-wall

A comparison between experimentally and numeri- regions are treated by advanced turbulence formul-cally evaluated hill charts only makes sense if the number ations such as two-layer and Reynolds stress models.and distribution of data points is identical. For this pur- Calculations for individual components have shown thatpose the experimental hill chart shown in Fig. 22 is based the application of two-layer models increases the accu-only on the experimental data corresponding to the racy of loss prediction but also increases the compu-operating points that were also calculated. Figure 23 tational time.shows the resulting hill chart based on the 14 operating Secondly, the rate of convergence is rather poor for

high Ku values at small guide vane openings. Largepoints from the stage calculations.

Fig. 22 Hill chart based on 14 experimentally obtained efficiency values ($ data points)



Fig. 23 Hill chart based on 14 numerically obtained efficiency values ($ data points; D D D constant guidevane opening)

Fig. 26 Turbine efficiency for Q=33° (design mass flow)Fig. 24 Turbine efficiency for Q=25°

separation zones occur in the draft tube in this case. Thisis probably the reason why the steep gradients of themeasured efficiency curves could not be reproduced inthe numerical analysis. However, it is known from themodel test that the turbine exhibits a very rough andunstable operational behaviour at Ku�1.5, especiallyfor small openings. The unstable conditions make itdifficult to compare the time-averaged data of stronglyunsteady experimental signals with numerical data of abasically steady analysis.

This is confirmed by comparison of measured and pre-dicted diffuser efficiency of the draft tube (see Fig. 27).At high values of Ku , where the flow separates, thenumerical simulation currently overestimates the off-

Fig. 25 Turbine efficiency for Q=40.5° design performance of the draft tube.



2 Gode, E. and Rhyming, I. L. 3-D computation of the flowin a Francis runner. Sulzer Tech. Rev., 1987, (4).

3 Keck, H., Goede, E. and Pestalozzi, J. Experience with 3DEuler flow analysis as a practical design tool. In Proceedingsof IAHR Symposium, Belgrade, September 1990.

4 Sallaberger, M. J. Quasi-three-dimensional and three-dimensional flow calculation in a Francis turbine. IGTIpaper 96-GT-38, Birmingham, 1996.

5 Goede, E., Sebestyen, A. and Schachenmann, A.Navier–Stokes flow analysis for a pump impeller. InProceedings of 16th IAHR Symposium, Sao Paulo, Brazil,14–19 September 1992.

6 Drtina, P., Gode, E. and Schachenmann, A. Three-dimen-sional turbulent flow simulation for two different hydraulicturbine draft tubes. In Proceedings of 1st EuropeanConference on Computational Fluid Dynamics, Brussels,Fig. 27 Draft tube efficiencyBelgium, 7–11 September 1992.

7 Drtina, P. and Krause, M. Numerical prediction of abrasion6 CONCLUSIONfor hydraulic turbine guide vanes. In Proceedings ofIMACS-COST Conference on Computational FluidAs is to be expected for turbomachines with such a longDynamics, Lausanne, 1995.

history, the design of hydraulic turbines still relies heavily 8 Casey, M. V. and Keck, H. Hydraulic turbines. Handbookon experience gained in earlier designs. 3D Euler codes of Fluid Dynamics and Fluid Machinery (Eds J. A. Schetzprovide a systematic tool for the application of this know- and A. E. Fuhs), 1996 (John Wiley).how to new designs. Nowadays, however, the use of 9 Janetzky, B., Gode, E., Ruprecht, A., Keck, H. andmodern stage simulation methods in 3D viscous Scharer, Ch. Numerical simulation of the flow in a Pelton

bucket. Submitted to XIX IAHR Symposium, Singapore,Navier–Stokes codes is transforming the analysis of tur-1998.bine designs. Details of flow separation, loss sources and

10 Bachmann, P., Scharer, Ch., Staubli, T. and Vullioud, G.loss distribution in components, matching of componentsExperimental flow studies in a 1-jet model Pelton turbine.at design and off-design, and low pressure levels with riskIn Proceedings of IAHR Symposium, Belgrade, 1990.of cavitation are now amenable to analysis with CFD.

11 Drela, M. Two-dimensional transsonic aerodynamic designIn each numerical investigation a significant amount ofand analysis using the Euler equation. GTI Report 187, 1986.

time has still to be spent with grid generation and grid 12 TASCflow User Manual, Theory Documentation—Versionmodification. Often this effort prevents the integration of 2.5, 1995 (Advanced Scientific Computing Limited,sophisticated Navier–Stokes simulations into the design Waterloo, Canada).procedure. For this reason 3D viscous calculations for 13 Casey, M. V., Borth, J., Drtina, P., Hirt, F., Lang, E.,complete turbines are not yet a standard design step for a Metzen, G. and Wiss, D. The application of computationalnew hydraulic turbine. Advanced automatic grid gener- modeling to the simulation of environmental, medical and

engineering flows. 18th Workshop Proceedings. Speedupation tools are needed that generate high-quality meshesJ., 1996.(block-structured hexahedron or mixed elements) on the

14 Wehrli, M., Borth, J., Drtina, P. and Lang, E. Industrialbasis of 3D CAD data for all essential components.application of computational fluid dynamics for mass trans-Together with the application of parallel computers (par-fer processes. 19th Workshop Proceedings. Speedup J., 1997.allelized codes are already available), the generation of

15 Raw, M. J. A new control-volume-based finite-element pro-numerical hill charts will become feasible for standardcedure for the numerical solution of the fluid flow and

design tasks. scalar transport equations. PhD thesis, University ofWaterloo, 1985.

16 Galpin, P. F., Broberg, R. B. and Hutchinson, B. R. Three-ACKNOWLEDGEMENTSdimensional Navier–Stokes predictions of steady staterotor/stator interaction with pitch change. In Proceedings

The authors gratefully acknowledge the helpful dis- of 3rd Annual Conference of the CFD Society of Canada,cussions with Dr M. V. Casey, Sulzer Innotec, and Banff, Alberta, Canada, 25–27 June 1995.Dr H. Keck, Sulzer Hydro, during the preparation of 17 Denton, J. D. The calculation of three-dimensional viscous

flow through multistage turbomachines. Trans. ASME,this paper. Thanks are also due to Dr M. Sick for herJ. Turbomachinery, 1992, 114, 18–26.contribution, in particular with the stage calculations.

18 Sick, M., Casey, M. V. and Galpin, P. Validation of a stagecalculation in a Francis turbine. In Proceedings of 18th

REFERENCES IAHR Symposium, 1996.19 Drtina, P. and Sebestyen, A. Numerical prediction of

hydraulic losses in the spiral casing of a Francis turbine.1 Francis, J. B. Lowell Hydraulic Experiments, 5th edition,In Proceedings of XVIII IAHR Symposium, 1996.1909 (Van Nostrand, Princeton, New Jersey).


hydraulic turbines—basic principles and state-of-the-...

Documents