Investigation of the effects of runner gap width on the ﬂow ﬁeld …isromac-isimet.univ-lille1.fr/upload_dir/finalpaper/73... · 2016-01-05 · Investigation of the effects of

Investigation of the effects of runner gap width onthe flow field in the draft tubeBernd Junginger1*, Stefan Riedelbauch1

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2016

InternationalSymposium on

TransportPhenomena and

Dynamics ofRotating

Machinery

Hawaii, Honolulu

April 10-15, 2016

AbstractThe performance of low head turbines, heavily depends on the draft tube. As a result of geometricaland numerical simplifications carried out in the design process to reduce the computational effort, afalsification of the overall flow field can occur. Typical simplifications are the circumferential averagingbetween stationary and rotating parts or the negligence of gaps. The gap between runner and shroudcan however lead to a stabilization of the draft tube flow. Simulations of a 4-blade propeller turbineoperating in a full load operation point with different gap widths are performed to analyzed the effectof the gap flow on the flow field. Two grid densities, one of about 30 million elements and another onewith about 45 million elements, and two turbulence models, the k-ω-SST and the SAS-SST model areapplied for the investigation. For the evaluated operation point a full load vortex develops in the draft tube.Numerical results of the integral quantities, head and torque are validated against results of experimentalmeasurements following the IEC 60 193 performed in the laboratory of the Institute of Fluid Mechanicsand Hydraulic Machinery at the University of Stuttgart. The shape of the vortex rope and the ability ofthe turbulence model to resolve the turbulence quantities are investigated. Also a detailed study of theinfluences of the gap flow on the velocity profiles downstream the runner and the overall draft tube flowfield is carried out.

Keywordspropeller turbine — runner gap — draft tube flow — RANS-LES — full load vortex1Institute of Fluid Mechanics and Hydraulic Machinery, University of Stuttgart, Germany*Corresponding author: [email protected]

1. INTRODUCTIONAll member states of the European Union are advised toachieve a good ecological status for all flowing water by theadoption of the European Water Framework Directive [1]. Theinstallation of hydro power plants in unused dams and weirs isgetting back to the focus of energy provides due to promotionsgiven by the European Union. With the energy revolution inEurope the amount of renewable energy sources like windand photovoltaic are significantly increasing. Hydro powerplants are, due to the good predictability of the energy output,suitable to balance the fluctuations of the electric grid. Therange in which turbines are operated is however getting largerand thus the risk of occurring transient phenomena like vortexropes in the draft tube, cavitation etc. increases. The amountof renewable energy sources in the energy mix of Germanyin the year 2014 was about 26%, whereas about 15% of therenewable energy is produced by hydro power [2].

The overall performance of low head turbines like Kaplan,bulb and propeller, depends on the effectiveness of the drafttube. Simplifications introduced in the design process to re-duce the computational cost may lead to a falsification of theflow field. Typical simplifications are circumferential aver-aging at interfaces between rotating and stationary machineparts and geometrical simplifications like the negligence ofgaps. In general, steady state simulations are performed forthe optimization of the turbine in the design process. Thegap flow between runner and shroud however can lead to astabilization of the draft tube flow.

In this paper a propeller turbine with 4 runner blades is in-

vestigated while focusing on the effects of the gap flow on thedraft tube flow field. Transient simulations with and withoutrunner gap are compared with experimental measurementscarried out in the laboratory of the Institute of Fluid Mechan-ics and Hydraulic Machinery at the University of Stuttgart.The measurements in the laboratory follow the IEC 60 193,which is the standard for model acceptance tests of hydraulicmachines [3]. The model size test rig of the turbine is in-stalled in the closed testing loop. For the investigation a fullload operation point with the following characteristic valuesn′1 = n′1 opt and Q′1 = 1.13 Q′1 opt is evaluated. A full load vor-tex develops in the draft tube for the analyzed operation point,starting from the runner hub. The shape of the full load vortexcan be symmetric or asymmetric [4]. Due to the maximalopening of the guide vane no gap at the trailing edge exists.The investigated normalized gap sizes for the runner gap areτ = 0, τ = 2, and τ = 6.7. The normalized gap size is definedas:

τ =scclD

(1)

containing the runner gap size s, a specific constant for theaxial test rig installed at the Institute of Fluid Mechanics andHydraulic Machinery ccl and the runner diameter D. Themeasured gap size in the experimental setup during the instal-lation process is τ = 1. Due to the deformation of the runnerblades, caused by the head, the gap width is about doublingthe size while operating the test rig, due to the cylindricalshroud contour.

Investigation of the effects of runner gap width on the flow field in the draft tube — 2/9

2. NUMERICAL SETUPThe flow simulations of the propeller turbine are carried outout using the commercial CFD (Computations Fluid Dynam-ics) code Ansys CFX Version 16.0. All presented simulationsare completely transient due to the fact that the shape of a fullload vortex can be asymmetric. The model turbine is installedin the closed loop of the laboratory including an expansiontank downstream the draft tube. The geometry is not sim-plified except for the simulations with a runner gap of τ = 0.Besides investigations of the influence of the runner gap on thedraft tub flow field, the effect of two different turbulence mod-els is evaluated. The compared turbulence models are the k-ω-SST, a standard RANS (Reynolds-Averaged-Navier-Stokes)model and a hybrid RANS-LES (Large Eddy Simulation)model, namely the SAS (Scale Adaptive Simulation) -SSTmodel. The SAS-SST turbulence model is applied for all gapsizes and grid densities, whereas the k-ω-SST is used for thecoarse grid only. The hydraulic contour and the evaluationsspots for the velocity profiles in the draft tube, downstreamthe runner, are illustrated in Fig. 1. For all simulations a mass

Figure 1. Evaluation spots of the gap flowgreen line = L1 black line = L2 red line = L3

flow inlet boundary condition is set originating from the ex-perimental results. A detailed analysis of the effects of thegap flow are performed at the evaluation lines L1-L3, whichare located downstream the runner blades.

A bounded central differencing scheme (BCDS) is usedfor the advenction terms when using a SAS-SST turbulencemodel, whereas a high resolution scheme is applied for thek-ω-SST model [5], [6]. For the temporal discretisation abounded second order Euler backward scheme is used whilefor the spatial discretisation of the turbulence quantities a firstorder scheme is applied [7].

A mesh with about 30 million elements is applied for allgap sizes. The number of elements of the runner domain canvary due to different gap sizes. The number of elements forthe guide vanes and the draft tube are the same for all investi-gations of the coarse grid. For a gap width of τ = 2 , a refinedmesh is investigated. The mesh in the guide vane and therunner domain is equal to the coarse grid. A mesh refinementfrom about 14 million elements to 25 million elements in thedraft tube is carried out. A detailed listing of the analyzedgrids including the number of elements, the averaged y+ andthe number of nodes in the runner gap is shown in Tab. 1.

The crucial mesh locations for resolving effects of the gapflow are the gap itself and the mesh resolution of the runneras well as the draft tube cone. For the resolution of a gapflow the runner gap has to be discretized properly. In Fig. 2the mesh of the gap at the leading and the trailing edge forτ = 2 is illustrated. The number of nodes in the gap is varyingbetween 30 nodes for a gap of τ = 2 and 50 nodes for a gap ofτ = 6.7. In Fig. 3 the mesh at the rotor stator interface between

(a) Mesh in gap at leading edge

(b) Mesh in gap at trailing edge

Figure 2. Mesh in runner gap

the runner and the draft tube domain is shown for the 45Mmesh with a runner gap of τ = 2. The number of cells in radialdirection in the runner domain is a bit lower than in the drafttube domain. To resolve the gap flow a high number of nodesis placed close to the shroud. In the draft tube the resolutionclose to the shroud is a little coarser than in the runner domain,but still sufficient fine to resolve the effects induce by the gapflow. The cell size in streamwise direction at the interfacebetween runner and draft tube is about the same size in bothdomains, to minimize the risk for grid induced interpolationeffects at the interface. Especially in the draft tube domain therequirements for scale resolving simulations are consideredwhile generating the mesh. Under the preconditions of thecomplex geometry in the runner domain an optimized grid isgenerated for the runner to resolve the gap flow. The numberof nodes in the runner gap are derived from earlier studies ofa simplified test case.

3. TURBULENCE MODELINGThe two applied turbulence models are the k-ω-SST and theSAS-SST model. The k-ω-SST turbulence model is a RANSmodel, representing the standard in the design process of turbomachinery. The SAS-SST model, however, is a hybrid modelwhich can switch between RANS and LES like behavior,depending on various influencing variables.


Table 1. Number of elements and averaged y+ for all turbine components

τ = 0 τ = 2 (30M) τ = 2 (45M) τ = 6.7

Turbine part elements y+ elements y+ elements y+ elements y+

Guide Vanes 5.2M 1.2 5.2M 1.2 5.2M 1.2 5.2M 1.2Runner 11.3M 2.2 11.9M 3.3 11.9 3.3 15.1 3.5Draft tube with expansion tank 14.3M 1.0 14.3M 1.0 25.1M 1.0 14.3M 1.0Total 30.8 - 31.3M - 42.2M - 34.7M -

Nodes in runner gap in radial direction - 30 50

(a) Mesh at interface runner domain

(b) Mesh at interface draft tube domain

Figure 3. Mesh at runner draft tube interface

k-ω-SST The k-ω-SST turbulence model is a two equationturbulence model using the Boussinesq hypothesis for thesolution the turbulent quantities [8]. A sufficient number ofequations is needed to achieve closure of the set of equations,including the Reynolds stress tensor from the averaging pro-cedure. The Boussinesq assumption implies that the Reynoldsstress tensor τi j is proportional to the mean strain rate tensorSi j , which can be written as:

−ρu′iu′j = µt

(∂Ui

∂x j+∂Uj

∂xi−

23∂Uk

∂xkδi j

)−

23ρkδi j (2)

In the k-ω-SST the advantages of the k-ε and the k-ω turbu-lence models are combined by utilizing a blending function toswitch between the two formulations. In the viscous sublayer

the k-ω formulation is applied, hence no additional damp-ing function is necessary. For the core flow the turbulencemodels switches to the k-ε formulation, to avoid the commonk-ω problems of being too sensitive to the inlet free-streamturbulence properties.

SAS-SST The SAS-SST model is a hybrid turbulence modelwith the possibility to switch between RANS and LES. Smallerturbulence scales can be resolved be using the SRS (ScaleResolving Simulation) mode [9]. Therefore an additionalsource term in the transport equation of the turbulence eddyfrequency ω is introduced to the RANS model described like[10], [11], [12]:

∂ρω

∂t+

∂

∂x j

(ρUjω

)= α

ω

kPk − ρβω

2 + QSAS+

+∂

∂x j

[(µ +

µtσω

)ω

x j

]+ (1 − F1)

2ρσω2

1ω

∂k∂x j

∂ω

∂x j

(3)

The source term QSAS is defined as:

QSAS = maxρζ2κS2

(L

LνK

)2

−

−C2ρκσΦ

max(

1ω2

∂ω

∂x j

∂ω

∂x j,

1k2

∂k∂x j

∂k∂x j

),0

] (4)

containing the Karman length scale LvK and the turbulentlength scale L. The Karman length scale is defined as:

LνK = κ

U′

U′′

U′′

=

√√∂2U i

∂x2k

∂2U i

∂x2j

, U′

= S =

√2Si jSi j ,r

Si j =12

∂U i

∂x j+∂U j

∂xi

(5)

The information provided by the Karman length scale isessential for the SAS-SST model to switch into SRS mode andhence for a dynamically adjustment of the resolved turbulentstructures, leading to a LES like behavior [13]. A reducededdy viscosity leads to smaller structures in the turbulentcascade down to grid limit. The turbulent eddy viscosity


is limited by the grid cell size ∆ to control the damping ofthe smallest resolved turbulent fluctuations [10]. From theequilibrium of production and destruction of turbulent kineticenergy a relation of the equilibrium eddy viscosity µt , thevon Karman length scale Lvk and the scalar invariant of theshear rate tensor S can be derived similar to the subgrid scaleeddy viscosity in the Smagorinsky LES model, which has theformulation:

µt ≥ µLESt (6)

Without the limiter of the turbulent eddy viscosity the modeldoes not provide sufficient dissipation. In a comparison ofthe SAS-SST model with DES (Detached Eddy Simulation)-type models, the ability to operate in RANS mode, if thegrid density and the time step are too coarse, is one majoradvantage of the SAS-SST model that can be noted.

4. RESULTSThe main focus of this paper is the gap flow and its effecton the draft tube flow field. Velocity profiles are evaluatedat several spots, downstream the runner, in the draft tube.The positions of the velocity evaluation lines are illustratedin Fig. 1. The green line (L1) is close behind the runnerat the begin of the draft tube. The black line (L2) and redline (L3) are located in the conical part of the draft tube.A detailed study of the numerical results, focusing on theeffects of different gap sizes, the turbulence models and griddensities on the gap flow is carried out. Moreover, the integralquantities head and torque are compared with experimentalresults. The shape of the full load vortex, developing in thedraft tube, is analyzed to evaluate the effects of the gap size,the applied turbulence model and the grid density. Finally, aninvestigation of the resolved turbulent structures in the drafttube is carried out, to identify the impact of mesh density,turbulence model and gap width.

4.1 Integral QuantitiesThe integral quantities head and torque of the runner are vali-dated with experimental results. All evaluated quantities aretime averaged over 60 runner revolutions. The discharge forall numerical setups is as measured in the experiment. Theevaluated numerical quantities head and torque are normalizedusing the results of the measurements (see Tab. 2). The resultswith τ = 0 and τ = 2 overpredict head and runner torque, inde-pendent of the turbulence model and the grid density. For agap size of τ = 6.7 head and torque are underestimated. Withan increasing gap width head and torque are decreasing froman overprediction to an underestimation for both the k-ω-SSTand SAS-SST model. The calculated torque at the runner isdecreasing similarly with an increase of the gap width forboth investigated turbulence models as expected. Owing tothe larger gap size, more fluid can pass the runner throughthe gap between runner and shroud without torque genera-tion. However, the head is differing between the numericalapproaches. The SAS-SST model applied on the coarse grid

provides a head that is at least 2% larger than the head cal-culated applying the k-ω-SST turbulence model. The headdecrease when the SAS-SST turbulence model is applied onthe fine grid. For the torque the result is independent of thegrid density and the applied turbulence model. The results ofthe gap width of the experiment, τ = 2 are overpredicting theresults of the measurements with about 2.6%. The deviationof head and torque are plotted in a graph illustrated in Fig. 4.All quantities indicate the same trend and a similar slope.

-4

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Devia

tion [%

]

Gap Width τ [-]

HeadSST 30MTorqueSST 30M

HeadSAS 30MTorqueSAS 30M

HeadSAS 45MTorqueSAS 45M

Figure 4. Deviation of head and torque for different gapwidths

The influence of the turbulence model and the grid densityon the torque is negligible. As expected the gap size has amajor effect on the torque. For an increasing gap size thetorque is decreasing constantly, due to the gap losses. Owingto the same grid density of the runner and the guide vane grid,further analysis have to be performed to verify the results ofthe simulations.

4.2 Gap FlowThe gap flow is analyzed by time averaged velocity profilesat several evaluation spots. All velocity profiles are timeaveraged over 60 runner revolutions. In Fig. 1 the positionsof the evaluation lines are shown. Line L1 is located aboutD/2 downstream the artificial axis of rotation of the runnerblade, directly behind the runner hub. The evaluation line L2is placed at the begin of the cone about D behind the rotationaxis of the runner blade. L3 is positioned at the end of thedraft tube cone about 2D downstream the trailing edge of therunner blade. At every spot the meridional, circumferentialand radial component of the velocity is analyzed. The timeaveraged velocity profiles of the evaluation lines L1, L2 andL3 are plotted in Fig. 5.

At the evaluation spot of line L1 the effects of the turbu-lence model and the gap are visible. Significant differencesbetween the k-ω-SST and SAS-SST model for the coarsegrid can be noticed in the meridional, circumferential andradial velocity components at a normalized radius of aboutrnorm = 0.1. All simulations applying the k-ω-SST modelhave an increased meridional velocity at rnorm = 0.1 com-pared to those simulations using the SAS-SST turbulencemodel. The circumferential velocity profiles show the sameeffect, meaning the computations with the k-ω-SST model


Table 2. Comparison of integral quantities, head and torque

τ = 0 τ = 2 τ = 6.7

k-ω-SST SAS-SST k-ω-SST SAS-SST SAS-SST k-ω-SST SAS-SST30M 30M 30M 30M 45M 30M 30M

hCFD−hExp

hExp[%] 3.21 5.89 2.44 4.44 1.59 -3.93 -0.16

TCFD−TExp

TExp[%] 4.52 4.35 2.61 2.67 2.63 -3.45 -3.25

-0.1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 1.1 1.2 1.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Meridia

n V

elo

city c

m/c

ref [-

]

Radius R/Rref [-]

τ=0, SST 30Mτ=0, SAS 30Mτ=2, SST 30Mτ=2, SAS 30Mτ=2, SAS 45M

τ=6.7, SST 30Mτ=6.7, SAS 30M

(a) L1 cm

-1.3-1.2-1.1

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Circum

fere

ntial V

elo

city c

u/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(b) L1 cu

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Radia

l V

elo

city c

r/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(c) L1 cr

-0.1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 1.1 1.2 1.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Meridia

n V

elo

city c

m/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(d) L2 cm

-1.3-1.2-1.1

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Circum

fere

ntial V

elo

city c

u/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(e) L2 cu

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1R

adia

l V

elo

city c

r/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(f) L2 cr

-0.1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 1.1 1.2 1.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Meridia

n V

elo

city c

m/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(g) L3 cm

-1.3-1.2-1.1

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Circum

fere

ntial V

elo

city c

u/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(h) L3 cu

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Radia

l V

elo

city c

r/c

ref [-

]

Radius R/Rref [-]


τ=6.7, SST 30Mτ=6.7, SAS 30M

(i) L3 cr

Figure 5. Velocity profiles downstream the runner at evaluation spots L1, L2 and L3

have a higher counter rotating circumferential velocity com-ponent at rnorm = 0.1. The opposite effect can be observedfor the radial velocity profiles at the position rnorm = 0.1. Asignificant higher radial velocity can be noticed for the sim-ulations with the applied SAS-SST model compared to thesimulations with the k-ω-SST. The velocity profiles of the finegrid density differ from the coarse mesh. In the meridionaland the circumferential velocity component the differencesto the SAS-SST model are rather small. However, the radialvelocity at rnorm = 0.1 is smaller than those of the coarse grid,

independent of the applied turbulence model.

Influences of the gap on the velocity profiles can be ob-served in all three velocity components in the coarse mesh.The differences of the meridional velocity components aresmall. Thus, for the largest investigated gap width a clearreduction of the meridional velocity at rnorm = 0.1 can benoticed compared to the velocity profiles with a gap size ofτ = 0, independent of the applied turbulence model. For a gapwidth of τ = 2 a smaller decrease of the meridional velocity isoccurring than for a larger gap width of τ = 6.7. Additional


to the reduction of the meridional velocity at rnorm = 0.1 anincrease of the meridional velocity can be observed close tothe shroud. The meridional velocity of the simulation, whenapplying the SAS-SST model, is clearly increasing close tothe shroud (rnorm = 0.9) in comparison to the results of thek-ω-SST model and the other investigated setups. The sim-ulation with a runner gap size of τ = 6.7 and the SAS-SSTturbulence mode is the only simulation that is not followingthe tendency of a rather straight meridional velocity distribu-tion to a smaller normalized radius. The tendency that themeridional velocity is decreasing with an increasing gap size,which is visible at rnorm = 0.1, cannot be seen in the velocityprofile close to the shroud. All velocity profiles are more orless on an equal level except the largest investigated gap sizeof τ = 6.7.

Similar tendencies as represented in the meridional ve-locity profiles can be noticed in the circumferential velocitydistributions at evaluational line L1. Differences between theanalyzed turbulence models are visible at rnorm = 0.1, as inthe meridional velocity. The absolute value of the circumfer-ential velocity is higher for the simulations using the k-ω-SSTmodel than for those computed with the SAS-SST model.Influences of the gap width on the absolute value of the cir-cumferential velocity can also be observed. The tendency thatthe absolute value of the circumferential velocity is decreasingfor an increasing gap size can be noticed for both investigatedturbulence models. The described effect, however, is strongerdeveloped while applying the k-ω-SST model. Moreover, asmall shift of the spot of the highest absolute value to a largerradius rnorm can be noticed between the coarse and the finemesh. The effects of the gap flow close to the shroud areclearly visible in the circumferential velocity distributions incomparison to the meridional velocity components. A localminimum is moving to smaller radii with an increasing gapwidth. The local minimum of the circumferential velocity forsimulations applied the SAS-SST model is always smallerthan the minimum for computations with the k-ω-SST model.An effect of the grid density on the position and value of thelocal minimum close to the shroud cannot be noticed. For thelargest gap size of τ = 6.7 the velocity distributions are slightlyoscillating which means that several local minima exist. Thiseffect is visible for both investigated turbulence models. Dif-ferences of the gap width and the turbulence model can alsobe seen in the radial velocity profiles. The global maximum ofthe radial velocity components are positioned at rnorm = 0.1.The maximal radial velocity for simulations applying the k-ω-SST model is decreasing for an increasing gap width. Forsimulations using the SAS-SST model the maximal radialvelocity is increasing for an increasing gap size. Moreover,a significant difference in the maximum value of the radialvelocity can be observed. The maximum of the radial velocitycomponent of simulations with the SAS-SST model is abouta factor two of the maximum radial velocity compared tosimulations applying the k-ω-SST model. A reason for thedifferences between the turbulence models could be the totallydifferent flow field in the draft tube. Owing to significantly

higher values of the radial velocity components for the SAS-SST compared to k-ω-SST model the shape of the vortex ropecan be derived close behind the runner.

The differences between the turbulence models are morecharacteristic further downstream at evaluation line L2. Aclear differing between the k-ω-SST model and the SAS-SSTmodel applied on the coarse mesh can be observed in themeridional, the circumferential and the radial velocity compo-nent. The differences in the meridional velocity componentbetween the different numerical setups is more developed atthis evaluation spot. The influence of the gap size on themeridional velocity profiles can be observed, similar as il-lustrated for evaluation line L1, independent of the appliedturbulence model. Whereas the stagnation region illustratedin the meridional velocity distribution for simulations withan applied k-ω-SST model has not increased much, a clearenlargement of the stagnation region can be observed for thesimulations using the SAS-SST turbulence model. In com-parison with evaluation spot L1, the stagnation region forcomputations with the applied SAS-SST model has increasedfrom rnorm = 0.1 to rnorm = 0.3. Even though the simulationof the fine mesh is carried out with the SAS-SST model, theoverall meridional velocity profile is better fitting to simula-tions using the k-ω-SST model. This can be observed in thesize of the stagnation region developing for the different nu-merical setups in which the vortex rope develops. Outside thestagnation region, the overall meridional velocity of computa-tions using the SAS-SST model is on a higher level comparedto simulations applying the k-ω-SST model The difference inthe absolute value of the maximum circumferential velocityhas significantly increased in comparison to the evaluationspot closer downstream the runner. For simulations using theSAS-SST model applied on the coarse grid no real peak inthe circumferential velocity distribution develops. Influencesof the gap can also be observed in the velocity distributionsclose to the shroud. Despite of the large gap size of τ = 6.7the effect of the gap flow is smoothed out in comparison toevaluation line L1. The effects of the gap width can still beseen in the velocity plots as described for evaluation line L1.The velocity profile evaluated for the fine mesh resemblesthe results of the velocity profiles of the coarse grid with thek-ω-SST model. In the radial velocity distribution the sameeffects can be noticed. The peak that was present in the radialvelocity distribution at evaluation line L1 has smoothed outfor all simulations of the coarse grid with the k-ω-SST modeland the computation of the fine grid with the applied SAS-SST model. In the computations of the coarse grid with theSAS-SST model a peak in the radial velocity distribution stillexists, even though the maximal radial velocity has decreased.Effects of the gap size on the velocity profile can be seen,however, the differences of the velocity profiles start to blurfor the various gap sizes. The velocity distributions illustratedin Fig. 5 give a good indication of the vortex shape developingin the draft tube.

Even though the evaluation spot L3 is about 2D awayfrom the trailing edge of the runner blade, the influences of


the gap size are still clearly visible. The effects can be seen inparticular in the meridional and the circumferential velocitycomponents for both turbulence models applied on the coarsemesh. As seen for evaluation lines L1 and L2 clear differencesbetween the turbulence models can be identified. A real peakof the maximum meridional velocity can neither be detectedby computations using the k-ω-SST model nor by simulationwith a SAS-SST turbulence model. A larger influence of thegap width on the meridional velocity profiles can be observedespecially when applying the k-ω-SST model on the coarsegrid. The meridian velocity profile of the fine mesh resemblesthe results of the coarse mesh with the applied k-ω-SST model.The nonuniform velocity distributions are smoothed more andmore. The circumferential velocity distributions at evaluationspot L3 are similar to the meridional velocity profiles. In theradial velocity distributions the effects generated by the runnerare smoothed out completely. Only the velocity profile of thefine mesh is on another level than those of all other simulationusing the coarse mesh.

4.3 Vortex RopeThe full load vortex arises from a low pressure zone down-stream the runner hub. The vortex rope is visualized by usinga pressure isosurface for all investigated numerical setups witha runner gap width of τ = 2 (see Fig. 6).

(a) 30M k-ω-SST

(b) 30M SAS-SST

(c) 45M SAS-SST

Figure 6. Shape of the vortex rope in the draft tube for the30M (k-ω-SST and SAS-SST) and the 45M (SAS-SST) meshwith a normalized runner gap width of τ = 2 colored withviscosity ratio 0-2000

A clear difference in the shape of the vortex can be ob-served between the three setups. For the simulation applyingthe RANS turbulence model on the coarse grid a straight vor-tex rope develops in the middle of the draft tube. When theSAS-SST model is applied on the coarse grid a different vortexshape is provided. The vortex rope is developing in a shape ofa corkscrew, similar to a part load vortex. Thus the stagnationregion in the middle of the draft tube is significantly bigger forthe SAS-SST model then for the k-ω-SST for the same mesh,as illustrated in Fig. 5. The developing vortex when using thefine grid with the SAS-SST turbulence model, is a combina-tion of the predicted vortex shapes of the k-ω-SST and theSAS-SST model applied on the coarse grid. Moreover, thevortex rope of the fine grid appears to predict more detailedvortex structures. Small vortex streaks develop from the mainvortex. Owing to several streaks more vortex cores exist. Theposition of the main vortex is not stable in the middle of thedraft tube, however, the movement is not as big as displayed inthe coarse grid with the SAS-SST model. Optical evaluationsof the vortex rope at test rig indicate that the vortex shaperesolved by the fine grid is in rather good agreement. Furtherexperimental validation of the vortex shape is projected in thefuture to verify this conclusion.

The influence of the runner gap on the developing vortexrope, for the investigated gap sizes, is negligible. Due tothe different shapes of the vortex rope the swirling flow isevaluated further by the usage of a vector plot. In Fig. 7 avector plot on a cutting plane through the draft tube cone atthe position of evaluation line L2 is illustrated.

Only one cylindrical shaped vortex core, positioned inthe middle of the draft tube can be seen in the vector plot ofthe k-ω-SST model. Even though the cutting plane is aboutone runner diameter D downstream the runner the wake ofthe runner blades are still visible, both at center close to thevortex core and at the shroud. In the plot visualizing theresults of SAS-SST model applied on the coarse grid an ovalshape vortex core is shown, together with a smaller counterrotating vortex. The vortex core is not positioned in the centerof the cutting plane. In the vector plot of the fine grid themain vortex consists of several small vorticies. The shape ischanging its appearance throughout the rotation, due to thedeveloping vortex streaks. The number of vortex streaks andthus the number of vortex cores is varying.

The influence of the gap width on the vector plot is neg-ligible. The main influence coefficient on the appearance ofthe vector plot and hence on the velocity distribution in theevaluated cutting plane is the turbulence model and the griddensity, as seen in Fig. 5.

4.4 Turbulence QuantitiesThere are several possibilities to resolve the turbulence quan-tities. One option to evaluate the turbulence quantities is theusage of the velocity invariant Q (Q=0.5(Ω2-S2) with the ab-solute value of the strain rate S and the absolute value of thevorticity Ω [7], [14]. In Fig. 8 a comparison of the turbulencequantities of the three investigated cases with a runner gap


(a) 30M k-ω-SST

(b) 30M SAS-SST

(c) 45M SAS-SST

Figure 7. Vector plot at a cutting plane located at evaluationspot L2 for the 30M (k-ω-SST and SAS-SST) and the 45M(SAS-SST) mesh with a normalized runner gap width of τ = 2colored with the velocity 0-5

of τ = 2 is illustrated. The ability of the SAS-SST model toresolve smaller flow structures is obvious when comparingFig. 8 (a) and Fig. 8 (b). The k-ω-SST turbulence model isonly capable to resolve large turbulent structures developingin the draft tube. However, the SAS-SST model applied onthe coarse grid is able to resolve small flow structures in thedraft tube cone. In the draft tube diffuser the resolution ofthe flow structures is increasing when applying the SAS-SSTturbulence model which is also indicated by the increase ofthe viscosity ratio. Differences of the resolution of the flowstructures between the k-ω-SST and SAS-SST model appliedon the coarse grid may occur due to different flow fields in thedraft tube. An improvement of the resolution of the turbulencestructures can be noticed when applying the SAS-SST on thefine mesh. In the draft tube cone as well as in the draft tube

(a) 30M k-ω-SST

(b) 30M SAS-SST

(c) 45M SAS-SST

Figure 8. Isosurface of the velocity invariant Q=1 coloredwith the viscosity ratio 0-500 for the 30M (k-ω-SST andSAS-SST) and the 45M (SAS-SST) mesh with a normalizedrunner gap width of τ = 2

diffuser smaller flow structures are resolved which can alsobe seen in the decrease of the viscosity ratio. Only in the tran-sition area between cone an diffuser, where flow separationsdevelop an increase of the eddy viscosity respectively, theresolved flow structures can be observed. Due to the scaleadaptive approach of the SAS-SST model the capability toresolve small turbulence structures for an adequate mesh den-sity has to be higher. The resolution of the flow structures ofthe fine grid indicates that the SAS-SST model works well.An effect of the gap width on the flow structures in the drafttube cannot be observed.

5. SUMMARY AND CONCLUSIONSimulations of a full load operation point of an axial propellerturbine are performed with normalized gap sizes of τ = 0 -6.7. The investigations are carried out on two different griddensities, one with about 30 million elements and anotherone with about 45 million elements. The k-ω-SST and theSAS-SST turbulence model are applied for the analysis.

An influence of the turbulence model, the gap width andthe grid density on the analyzed quantities head and torquecan be noticed. Both evaluated quantities are overestimatingthe experimental results for gap sizes from τ = 0 to τ = 2,independent of the applied turbulence model. Both quantities


are reduced with an increasing gap width. For a gap size ofτ = 6.7 torque and head underpredict the measurements. Theinfluences of the gap flow on velocity profiles evaluated atthree spots behind the runner can be observed. Moreover,influences of the turbulence model and the grid density canalso be noted. Significant differences of the shape of the fullload vortex rope in the draft tube can be noticed between theevaluated turbulence models and grid sizes. A straight vortexrope develops when the k-ω-SST is applied on the coarse grid.While, a vortex rope reassembling a corkscrew occurs forsimulations using the coarse mesh and the SAS-SST model.The developing vortex rope, when computing the fine gridwith a SAS-SST turbulence model is a combination of thevortex ropes of the coarse grid. The vortex rope of the finegrid is visualized in more detail including small vortex streaksdeveloping from the main vortex core. Influences of the gapsize on the vortex rope can be neglected. The SAS-SST modelis capable to resolve smaller turbulent flow structures thanthe k-ω-SS model. A better resolution of the turbulent flowstructures in the entire draft tube is only possible when theSAS-SST model applied on the fine grid.

Even though the SAS-SST model is capable to resolvesmaller turbulent structures, the model has some limitationswhich can be seen in the results of the 30M grid. For flowswith moderate instabilities the SAS can stay in RANS mode,and hence can lead to a wrong flow field, while more turbulentquantities are resolved in the draft tube than using a standardRANS model. This can be a cause for the large deviationbetween the SAS-SST model applied on the 30M mesh com-pared to the the k-ω-SST model applied on the same griddensity [7]. The SAS-SST model is the savest of the hybridRANS-LES turbulence model for a scale resolving simula-tion. DES or SBES (Stress Blended Eddy Simulation) do notrequire as large flow instabilities as the SAS-SST model toswitch to LES-mode might lead to equal or better resolvedresults on the same grid density.

6. FURTHER WORK

To compensate for the lack of experimental results, additionalinvestigations on the model turbine are projected. Laser-Doppler-Velocimetry measurements are planed in the drafttube to verify the velocity profiles of the numerical results.Moreover, high-speed videos of the vortex rope and dynamicpressure measurements in the draft tube are projected for fur-ther validation. Further computations applying the fine meshto get a better understanding of the mesh influence on theresults are planned. Additionally other hybrid RANS-LESmodels are applied for a further investigation of the effectsof the turbulence model on the simulation results. Studies ofother operation points (e.g. part load) are also scheduled toinvestigate the effect of the runner gap on the developing flowfield in the draft tube.

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