numerical research on flow characteristics around a hydraulic

Research ArticleNumerical Research on Flow Characteristics around a HydraulicTurbine Runner at Small Opening of Cylindrical Valve

Zhenwei Mo Juliang Xiao and Gang Wang

Key Laboratory of MechanismTheory and Equipment Design of Ministry of Education Tianjin University Tianjin 300072 China

Correspondence should be addressed to Juliang Xiao tianjinxjl163com

Received 14 September 2015 Revised 25 November 2015 Accepted 25 November 2015

Academic Editor David Bigaud

Copyright copy 2016 Zhenwei Mo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We use the continuity equation and the Reynolds averagedNavier-Stokes equations to study the flow-pattern characteristics arounda turbine runner for the small-opening cylindrical valve of a hydraulic turbine For closure we adopt the renormalization-groupk-120576 two-equation turbulence model and use the computational fluid dynamics (CFD) software FLUENT to numerically simulatethe three-dimensional unsteady turbulent flow through the entire passage of the hydraulic turbine The results show that a low-pressure zone develops around the runner blades when the cylindrical valve is closed in a small opening cavitation occurs at theblades and a vortex appears at the outlet of the runner As the cylindrical valve is gradually closed the flow velocity over therunner area increases and the pressure gradient becomes more significant as the discharge decreases In addition the fluid flowvelocity is relatively high between the lower end of the cylindrical valve and the base so that a high-velocity jet is easily inducedThe calculation and analysis provide a theoretical basis for improving the performance of cylindrical-valve operating systems

1 Introduction

Cylindrical valve installed between the stay and guide vaneof mixed-flow hydraulic turbine boasts many advantagessuch as self-closing ability less hydraulic loss effectiveprotection to the distributor small land occupation in fac-tory and small investment So cylindrical valve has beenwidely used in large- andmedium-sized hydropower stationsover sediment-laden rivers For large hydropower stationsinvolving peak load regulation and frequency modulationwhere conventional inlet valve (ball valve and butterfly valve)cannot be installed the installation of cylindrical valve caneffectively protect the distributor and reduce the leakage lossin the stopping process The worldrsquos first cylindrical valvewas made by NEYRPIC Company in France for MonteynardPower Station in 1962 The power station had an installedcapacity of 4 times 83MW and a water head of 137m So farcylindrical valve has been used in over 60 power units in12 hydropower stations in France Canada Portugal and soforth In China Xiaowan Hydropower Station has 6 Francisturbine generator units with a unit capacity of 700MWand Nuozhadu Hydropower Station has 9 hydraulic turbinegenerator units with a unit capacity of 650MW [1]

A runaway transient in a hydraulic turbine is an abnormalprocess that adjusts the hydraulic turbine therefore an in-depth understanding of such transients is vital for the safe andnormal operation of hydraulic turbines When a cylindricalvalve is used to shut down the turbine by forcing the hydraulicturbine to exit the runaway state the water flow surroundingthe runner of the hydraulic turbine is extremely turbulent andaccompanied by strong water impact vibration and noiseThis is especially true when the cylindrical valve is closedin a small opening All of these unstable phenomena canlead to disastrous accidents involving the hydraulic turbineunit [2ndash6] Therefore for proper design of a hydropowerstation a vital prerequisite is the calculation analysis andforecast of the flow field surrounding the runner whenthe hydraulic turbine exit the runaway state Such researchprovides important parameter values that allow the hydraulicturbine to exit the runaway process in a fast safe and stablemanner

When the cylindrical valve is used to shut down theturbine the flow field becomes extremely turbulent Exper-iments modeling this regime are of limited use because themethods used to interpolate between the model turbine andthe prototype turbine are not perfect Shutting down a real

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 6951839 8 pageshttpdxdoiorg10115520166951839

2 Mathematical Problems in Engineering

hydraulic turbine in the runaway state involves a significantrisk which precludes performing such experiments with areal hydraulic turbine Thus we adopt a numerical approachin this study in which we use computational fluid dynamics(CFD) to analyze and study the process of shutting down aturbine with a cylindrical valve

In recent years many research groups in China havenumerically simulated hydraulic turbines A group at theState Key Laboratory of Hydroscience and Engineering ofTsinghua University [7ndash9] studied the rotation rate hydro-dynamic moment and the characteristic runaway curve forrunaway transients in Francis turbines These studies led toa thorough understanding of the flow through the entirepassage of the hydraulic turbine and provided an analysisof the vortex and pressure fluctuations In another work Liet al [10] considered the use of a cylindrical valve for theemergency shutdown of a turbine device and analyzed andcompared the relevant parameters of cylindrical valvesTheseexperiments and the related numerical analysis were carriedout to understand how the shape of the cylindrical valversquoslower end influences the surrounding flow field Wuhrerand Grein [11] calculated and analyzed the hydrodynamicforce at the cylindrical valve of a hydraulic turbine for anoncontinuous flow A group at Tianjin University [12ndash15]carried out a three-dimensional (3D) numerical analysis ofthe entire passage of a hydraulic turbine studied amulticylin-der coordinated control strategy destined to shut down theturbine with the help of a cylindrical valve comparativelyanalyzed analysis of several different shutdown methodsinvolving cylindrical valves with different bottom shapes andfound that the hydraulic characteristics arewell in themannerof the 60 s closing

However these studies did not analyze the flow patternaround the turbine runner when the cylindrical valve isenclosed in a small opening Thus we address this issueherein by performing numerical CFD simulations of a pro-totype cylindrical valve for the Nansha hydropower stationin Yunnan China We focus on analyzing the flow fieldaround the turbine runnerwith the cylindrical valve at a smallopening

2 Description of the Simulation

Figure 1 shows a schematic of the entire flow passage andcylindrical valve of the prototype hydraulic turbine of theNansha hydropower station The photograph of the cylin-drical valve with a unit capacity of 50MW in NanshaHydropower Stations of Yunan China is shown in Figure 2The degree 119890 of the relative opening of the cylindrical valvedetermines how quickly the turbine is shut down and isdefined as the ratio of the distance 119889 between the cylindricalvalversquos lower end and the bottom ring to the thickness of thevalve 119863 119890 = 119889119863 The cylindrical valve is 110mm thick and1405mm high According to the definition of the degree ofrelative opening the cylindrical valvemust limit 119890 to between0 and 127 during turbine shutdown For a small opening0 lt 119890 lt 1 The angle 120593 is the nose angle as shown in Figure 3We acquired screenshots of the cross section for 120593 = 90∘ to270∘ and 120593 = 0 to 180∘ Similarly pictures of the lower end

Runner

Cylindricalvalve

Volute

Stay vane

Guide vane

Draft tube

Figure 1 Schematic of the model components of the turbine and aphotograph of the cylindrical valve

Figure 2 Photograph of the cylindrical valve

of the cylindrical valve with nose angles of 0∘ 90∘ 180∘ and270∘ are also available

3 Numerical Calculation

31 Control Equation When the cylindrical valve is closed foremergency shutdown of the turbine the fluid flows inside theturbine and around the cylindrical valve become a complex3D unsteady incompressible turbulent flows Because therenormalization-group k-120576 turbulence model distinguishesbetween a flow and a swirling flow it can predict theflow pattern near a wall surface relatively well In fact thisapproach has been used in many studies to simulate 3D flowin fluid machinery [16] Thus we also adopt this turbulencemodel for the present study The flow-control equations usedherein for the cylindrical-valve region are the continuityequation

120597119906119894

120597119909119894

= 0 (1)

the momentum equation

119863119906119894

119863119905

= 119891119894minus

1

120588

120597119901

120597119909119894

+

120597

120597119909119895

(]120597119906119894

120597119909119895

minus 1199061015840

119894

1199061015840

119895

) (2)

Mathematical Problems in Engineering 3

1

2

3

4

0∘

90∘

180∘

270∘

Figure 3 Schematic of the hydraulic turbine showing the noseangle

and the renormalization-group k-120576 equation

119863119896

119863119905

=

120597

120597119909119894

[(] +]119905

120590119896

)

120597119896

120597119909119894

] + 119866119896minus 120576

119863120576

119863119905

=

120597

120597119909119894

[(] +]119905

120590120576

)

120597120576

120597119909119894

] + 1198621120576

120576

119896

119866119896minus 1198622120576

1205762

119896

(3)

where 119909119894(119894 = 1 2 3) are the Cartesian coordinates 119906

119894

(119894 = 1 2 3) are the velocity components 119901 is the correctedpressure ] is the kinematic viscosity coefficient 119891

119894is the

mass force and ]119905is the turbulent viscosity coefficient (]

119905=

1198881199061198962

120576) 119888119906= 009 120590

119896= 10 120590

120576= 133 119862

1120576= 144

and 1198622120576= 142 Because the Reynolds stress minus119906

119894119906119895in (2) is

problematic for closure the renormalization group k-120576 two-equation model is used for closure [17]

Since the cylindrical valve of hydraulic turbine is in astate of motion during emergency shutdown process whichcan cause change in the calculation area of the flow fielddynamic mesh technique was used to adapt to this changeThis study divided the motion process of cylindrical valveinto 48 time steps each time step corresponding to a differentdisplacement of the cylindrical valve Firstly the torque 119872of the water flow action on the blade of hydraulic turbine onthe first time step was calculated Then the angular velocityincrement of the blade of hydraulic turbine in each time stepwas obtained according to (4) and the incremental rotationalspeed of the hydraulic turbine was further calculated In thisway the rotational speed of hydraulic turbine on the first timestep can be obtained according to its initial rotational speedIn the same manner the rotational speed on each time stepcan be obtained

119872minus119872119891= 119869Δ120596 (4)

where119872119891is the resistance moment 119869 is the rotational inertia

of the blade of hydraulic turbine Δ120596 is the angular velocityincrement on each time step

Since the runner is a rotating component rotor-statorinteraction will occur between cylindrical valve and runnerflow fields and between draft tube and runner flow fields Inorder to simulate detailed changes of the flow field over timesliding mesh was used in the front of the runner inlet and theback of the runner outlet (namely the interface of adjacentsubdomains) to complete the data transmission for the entirecomputational domain

32 Mesh and Boundary Conditions For the numerical sim-ulation we created a 1 1 model of a cylindrical valve inthe 3D modeling software UG The computational controlfield is the entire passage from the entrance of the hydraulicturbinersquos spiral casing to the exit of the draft tube Note thatthe creation of the mesh for the flow passage of the hydraulicturbine is an essential part of the entire numerical calculationprocess because the speed accuracy and convergence of theflow-field calculation for the flow passage of the hydraulicturbine are directly related to the quality of the mesh Forthe present work we use ICEM CFD as the preprocessingmodule Considering the specific situations and requirementsfor this work the entire passage of the virtual hydraulicturbine was divided into six regions A structured grid wasused for the region of the cylindrical valve that involvesmotion unstructured grids were used for other regions Thegrid close to the cylindrical valve was densified to improvethe calculation accuracy of the surrounding flow field Thefinal number of computational grid elements was 3 times 108The resulting meshes for the hydraulic turbine runner andcylindrical valve are shown in Figure 4

Because the numerical simulation covers only a limitedcomputational domain specific boundary conditionsmust beapplied at each boundary crossed by the flow in the hydraulicturbine The boundary conditions for the turbinersquos internalflow field mainly involve the inlet outlet and wall boundaryconditions Experience from the Nansha hydropower stationindicates that a cylindrical valve is used to shut down theturbine when the water flow cannot be cut off in time (owingto the runaway phenomenon in the turbine or the break-down of the guide-vane apparatus) Therefore the boundaryconditions should be applied to the inlet outlet and wall ofthe entire flow passage through the spiral casing The outletpressure of the draft-tube outlet gives the outlet pressurecondition and the inlet pressure of the spiral casing givesthe inlet pressure condition On the basis of real operatingconditions of the Nansha hydropower station we use a50m head at the spiral casingrsquos inlet as the inflow boundarycondition with an initial flow speed of 513ms Because theoutlet of the draft tube is directly connected to nearby riversthe outlet is assumed to be at standard atmospheric pressureHowever the effect of gravity on the pressure distribution istaken into consideration because of the considerable heightof the draft tube of the turbine

For the simulation we used the FLUENT software pack-age Numerically calculation of the initial flow field of thehydraulic turbine is a transient problem therefore the firststep is to calculate the initial steady-state flow field andthe result of this calculation is used as the initial conditionfor the next step The finite-volume method (a common


x

y z

(a)x

yz

(b)

Figure 4 Mesh for the (a) hydraulic turbine runner and (b) cylindrical valve

CFD numerical method) is used to discretize the controlequations We use the second-order upwind scheme togenerate the convection term and the second-order central-difference scheme to generate the diffusion and pressureterms of the motion equation To iterate the flow field inthe hydraulic turbine we use the semi-implicit algorithm forpressure-coupled equations to solve the problem of velocityand pressure coupling in the incompressible Navier-Stokesequations [14] This algorithm is widely used to calculate theflow field in fluid machinery and often used to calculate theflow field in hydraulic turbines

33 Model Validation The numerical model was verifiedby testing if its results are independent of the grid via acomparison of results obtained with three different gridsystems with approximately 12 times 108 18 times 108 and 30 times108 grid elements which describe the entire passage of the

hydraulic turbine grid elements In addition the grids aredensified near the cylindrical valve because the fluid fieldmust be accurately represented in this area The calculationresults for the 12 times 108 and 30 times 108 element grid systemsdiffer by less than 5 therefore we use the latter for thecalculation and analysis presented herein Figure 5 shows acomparison of the downpull force with real machine testresults [18] From Figure 5 it can be seen that the downpullforce predicted by the numerical method is in substantialagreement with the real machine test results

4 Analysis of the Results

41 Analysis of the Flow Pattern of the Runner Area Therunner is the crucial factor for determining the internalflow field of the hydraulic turbine during shutdown bythe cylindrical valve Thus a proper understanding of thehydraulic characteristics of the runner area is vital Becausethe rotating runner affects the direction and magnitude ofthe internal flow field of the cylindrical valve these quantitiesare difficult to determine with precision As a result the flowpattern created by the cylindrical valve in the runner area is

times104

Computed resultsTest results

200 10 60 9030 807040 50 100

Closing ()

20

25

30

35

40

45

50

55

60

65

Dow

npul

l for

ce (N

)

Figure 5 Downpull force compared with real machine test results

extremely turbulent In the present work we compare andanalyze the pressure and velocity fields of a cylindrical valvewith 119890 = 03 and 09

As shown in Figures 6 and 7 the pressure is unevenlydistributed over the turbine blades Specifically the blade-inlet area experiences the highest pressures whereas theblade-outlet blade area experiences the lowest pressureTheseresults are consistent with the fact that the runner convertsthe translational kinetic energy of the water flow into therotational kinetic energy of the turbine Furthermore thesmall pressure gradient at the outlet satisfies the outletpressure-gradient requirements When the runner rotatesthe water flow rotating at a high speed generates largecentrifugal forces thereby generating an external pressurethat exceeds the internal pressure With the decrease in thepressure of the flowing fluid the pressure on the impact sideof the blades far exceeds that on the back side of the blades As


121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06

(a)

121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06

(b)Figure 6 Pressure distributions of a runner observed from the isometric (a) and bottom (b) views The degree of the relative opening of thecylindrical valve is 03

983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06

(a)

983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06


shown in Figures 6(b) and 7(b) a low-pressure zone developson the back side of the blades creating a negative pressureSuch low-pressure zones are propitious for the cavitationphenomenon

As shown in Figures 8 and 9 the flow velocity in therunner area increases when the cylindrical valve is closedand the degree of relative opening decreases In addition thepressure gradient in the runner area becomes more apparentas the flux decreasesWhen the runner rotates at high speedsa secondary flow is likely to form in the runner area As shownin the plane sketch of the runner blades (Figures 8(a) and9(a)) the secondary flow lines are seriously distorted andthe flow pattern is extremely turbulent Owing to the impactcreated by the large angle of attack at the inlet a channel

vortex forms between the blades because of the secondaryflow and backflow between the flow passages As shown inthe water-flow vector diagram of the runner outlet (Figure 9)a huge swirling flow forms at the runner outlet with a highouter speed and low inner speed and these angular velocitiesincrease as the degree of the relative opening of the cylindricalvalve decreases Because the vortex is off center we deducethat a larger off-center vortex should form at the turbinersquosdraft-tube inlet because of the transfer of water The channelvortex and the runner vortex exert a significant stress on therunner blades which shifts the blades thereby intensifyingblade cavitation and pressure pulsation As the amplitude ofthe blade vibration increases spots cracks and even sponge-like damage may appear on the surfaces of the runner blades


931e + 01

885e + 01

838e + 01

792e + 01

745e + 01

699e + 01

652e + 01

605e + 01

559e + 01

512e + 01

466e + 01

419e + 01

373e + 01

326e + 01

279e + 01

233e + 01

186e + 01

140e + 01

932e + 00

466e + 00

195e minus 03

(a)

700e + 01

665e + 01

630e + 01

595e + 01

560e + 01

525e + 01

490e + 01

455e + 01

420e + 01

385e + 01

350e + 01

315e + 01

280e + 01

245e + 01

210e + 01

175e + 01

140e + 01

105e + 01

700e + 00

350e + 00

195e minus 03

(b)

Figure 8 Velocity vector diagram of a runner in the x-y plane and at the outlet when the degree of the relative opening of the cylindricalvalve is 03

731e + 01

694e + 01

658e + 01

621e + 01

585e + 01

548e + 01

512e + 01

475e + 01

439e + 01

402e + 01

366e + 01

329e + 01

292e + 01

256e + 01

219e + 01

183e + 01

146e + 01

110e + 01

732e + 00

366e + 00

108e minus 02

(a)

500e + 01

475e + 01

450e + 01

425e + 01

400e + 01

375e + 01

350e + 01

325e + 01

300e + 01

275e + 01

250e + 01

225e + 01

200e + 01

175e + 01

150e + 01

125e + 01

100e + 01

751e + 00

501e + 00

251e + 00

108e minus 02

(b)


42 Distribution of the Flow Field around a Cylindrical ValveBecause the water flow near the lower end of the cylindricalvalve is turbulent we amplify this area to analyze the pressureand velocity fields Cross-sectional views for nose angles of 0∘90∘ 180∘ and 270∘ are shown in Figures 10 and 11 for 119890 = 03and 09 respectively

As shown in Figures 10 and 11 the inner and outerpressures greatly differ at and next to the throttling pointwhich is between the lower end of the cylindrical valve andthe bottom ring This creates a pressure gradient along theintervening path This result indicates that a considerablehydraulic loss occurs at the lower end of the cylindricalvalve when enclosed in a small opening Furthermore ajet-prone condition is created because of the small degreeof opening and the large flow velocity Consequently the

pressure on the cylindrical valve should decrease accord-ingly

A low-pressure zone which apparently forms at the outletof the cut-off section of the cylindrical valve is a bubble-generating area The inner surface of the valve is likely tobe impacted by the local water flow thereby generatingcavitation noise and vibration The bursting bubbles in thismanner would lead to the long run to corrosion of the valvesurface over the long run further amplifying cavitation andcavitation erosion

5 Conclusion

In this work we calculated and analyzed the flow field aroundthe runner of a small-opening cylindrical valve for a turbine


124e + 06111e + 06984e + 05854e + 05725e + 05595e + 05466e + 05336e + 05207e + 05776e + 04minus518e + 04minus181e + 05minus311e + 05minus440e + 05minus570e + 05minus699e + 05minus828e + 05minus958e + 05minus109e + 06minus122e + 06minus135e + 06

(a) 120593 = 0∘

974e + 05858e + 05742e + 05625e + 05509e + 05393e + 05276e + 05160e + 05434e + 04minus729e + 04minus189e + 05minus306e + 05minus422e + 05minus538e + 05minus655e + 05minus771e + 05minus888e + 05minus100e + 06minus112e + 06minus124e + 06minus135e + 06

(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘

Figure 10 Pressure distributions around a cylindrical valve for various nose angles 120593 and 119890 = 03


(a) 120593 = 0∘minus107e + 06

983e + 05880e + 05778e + 05675e + 05572e + 05470e + 05367e + 05264e + 05162e + 05592e + 04minus434e + 04minus146e + 05minus249e + 05minus351e + 05minus454e + 05minus556e + 05minus659e + 05minus762e + 05minus864e + 05minus967e + 05

(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘



By analyzing the pressure and velocity fields of such a valvewe find that a low-pressure zone develops on the runnerblades cavitation erosion occurs on the blades and a vortexforms at the runner outlet The velocity distribution map ofthe runner area shows that the flow velocity near the runnerincreases upon closing the cylindrical valve In additionthe pressure gradient increases as the flux decreases Whenthe runner rapidly rotates secondary water is likely to flowthrough the runner area As shown in the plane sketchesof the runner blades the secondary-flow line is seriouslydistorted and the flow pattern is extremely turbulent Theinner and outer pressures greatly vary at and next to thethrottling point which is between the lower end of thecylindrical valve and the bottom ring revealing a pressuregradient along the intervening path This result indicatesthat a considerable hydraulic loss occurs at the lower endof the small-opening cylindrical valve In addition a jet-prone condition occurs because of the small degree of relativeopening and the large flow velocity

Conflict of Interests

The authors declare no conflict of interests regarding thepublication of this paper

Acknowledgments

This work was sponsored by the Key Technologies RampD Pro-gram of Tianjin under Grant no 09ZCKFGX03400 and bythe Youth Scholar Foundation (B type) of Tianjin Universityunder Grant no TJU-YFF-08B24

References

[1] S B Wu ldquoResearch on cylindrical valve at Nuozhadu hydro-power plantrdquoMechanical amp Electrical Technique of HydropowerStation vol 31 no 2 pp 13ndash15 2008

[2] Z Q Tian and J W Liu ldquoStudy on hydraulic stability of francisturbine of Three Gorges Power Stationrdquo Yangtze River vol 31no 5 pp 1ndash3 2000

[3] M Q Ji and J L Yuan ldquoTurbine and its characteristicsrdquo Hei-longjiang Science and Technology of Water Conservancy vol 4pp 134ndash134 2009

[4] Y D Zhao H J Hong and Y Li ldquoDiscussion on anti-runawaydesign for units of Binling hydropower stationrdquo NorthwestHydropower vol 1 pp 47ndash51 2009

[5] G Q Ma H J Duan G F Liu et al ldquoAnalysis of cylinder valveinstallation at Wunonglong hydropower stationrdquo NorthwestHydropower vol 3 pp 69ndash72 2011

[6] Z Q Wang ldquoSimple explanation on runaway protection ofhydro-generator unitrdquo Hubei Water Power vol 6 pp 72ndash732011

[7] W R Strub and R E Mawhinney ldquoRing gates for La grande-2turbinesrdquoWater Power vol 31 pp 11ndash13 1979

[8] Y L Wu S H Liu and Z D Qian Shuilijixie Jisuan LiutiDonglixue Water amp Power Press Beijing China 2007

[9] SH Liu L Zhang Y LWuXW Luo andMNishi ldquoInfluenceof 3D guide vanes on the channel vortices in the runner of aFrancis turbinerdquo Journal of Fluid Science and Technology vol 1no 2 pp 147ndash156 2006

[10] J W Li S H Liu D Q Zhou and Y L Wu ldquo3D unsteadyturblulent simulation of the runaway transients of the francisturbinerdquo Journal of Hydroelectric Engineering vol 27 no 6 pp148ndash152 2008

[11] W J Wuhrer and H L Grein ldquoRing gate as turbine emergencyshut-down devicerdquoHydraulic Engineering vol 6 pp 1085ndash10901990

[12] I S Veremeenko and S D Kostornoy ldquoComputation of hydro-dynamic forces at the ring gate of a hydraulic turbinerdquoTyazheloeMashinostroenie vol 10 pp 5ndash7 1992

[13] C L Guo J L Xiao andGDWang ldquoNumerical simulation forcharacteristics of ring gate during emergency shut-down waterprocessrdquo Journal of Tianjin University vol 42 no 11 pp 1022ndash1027 2009

[14] M Li J L Xiao G Wang andW K Song ldquoThree-dimensionalunsteady numerical simulation of ring gate emergency shut-down for hydraulic turbinerdquo Journal of Hydroelectric Engineer-ing vol 31 no 2 pp 228ndash234 2012

[15] J Xiao E Zhu and G Wang ldquoNumerical simulation of emer-gency shutdown process of ring gate in hydraulic turbinerunawayrdquo Journal of Fluids Engineering vol 134 no 12 ArticleID 124501 2012

[16] C L Guo G D Wang and J L Xiao ldquoNumerical simulationfor hydraulic characteristics of cylindrical valve in runawayprotection processrdquo in Proceedings of the Asia-Pacific Power andEnergy Engineering Conference Wuhan China March 2009

[17] J-F Huang L-X Zhang and S-H He ldquoNumerical simulationof 3-D steady and unsteady flows in whole flow passage ofa francis hydro-turbinerdquo Proceedings of the Chinese Society ofElectrical Engineering vol 29 no 2 pp 87ndash94 2009

[18] ZWMo J L Xiao andGWang ldquoEvaluation of hydrodynamicforces on turbine ring gate during emergency shutdown pro-cessrdquo Advances in Mechanical Engineering vol 7 no 5 pp 1ndash102015

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hydraulic turbine in the runaway state involves a significantrisk which precludes performing such experiments with areal hydraulic turbine Thus we adopt a numerical approachin this study in which we use computational fluid dynamics(CFD) to analyze and study the process of shutting down aturbine with a cylindrical valve

In recent years many research groups in China havenumerically simulated hydraulic turbines A group at theState Key Laboratory of Hydroscience and Engineering ofTsinghua University [7ndash9] studied the rotation rate hydro-dynamic moment and the characteristic runaway curve forrunaway transients in Francis turbines These studies led toa thorough understanding of the flow through the entirepassage of the hydraulic turbine and provided an analysisof the vortex and pressure fluctuations In another work Liet al [10] considered the use of a cylindrical valve for theemergency shutdown of a turbine device and analyzed andcompared the relevant parameters of cylindrical valvesTheseexperiments and the related numerical analysis were carriedout to understand how the shape of the cylindrical valversquoslower end influences the surrounding flow field Wuhrerand Grein [11] calculated and analyzed the hydrodynamicforce at the cylindrical valve of a hydraulic turbine for anoncontinuous flow A group at Tianjin University [12ndash15]carried out a three-dimensional (3D) numerical analysis ofthe entire passage of a hydraulic turbine studied amulticylin-der coordinated control strategy destined to shut down theturbine with the help of a cylindrical valve comparativelyanalyzed analysis of several different shutdown methodsinvolving cylindrical valves with different bottom shapes andfound that the hydraulic characteristics arewell in themannerof the 60 s closing

However these studies did not analyze the flow patternaround the turbine runner when the cylindrical valve isenclosed in a small opening Thus we address this issueherein by performing numerical CFD simulations of a pro-totype cylindrical valve for the Nansha hydropower stationin Yunnan China We focus on analyzing the flow fieldaround the turbine runnerwith the cylindrical valve at a smallopening

2 Description of the Simulation

Figure 1 shows a schematic of the entire flow passage andcylindrical valve of the prototype hydraulic turbine of theNansha hydropower station The photograph of the cylin-drical valve with a unit capacity of 50MW in NanshaHydropower Stations of Yunan China is shown in Figure 2The degree 119890 of the relative opening of the cylindrical valvedetermines how quickly the turbine is shut down and isdefined as the ratio of the distance 119889 between the cylindricalvalversquos lower end and the bottom ring to the thickness of thevalve 119863 119890 = 119889119863 The cylindrical valve is 110mm thick and1405mm high According to the definition of the degree ofrelative opening the cylindrical valvemust limit 119890 to between0 and 127 during turbine shutdown For a small opening0 lt 119890 lt 1 The angle 120593 is the nose angle as shown in Figure 3We acquired screenshots of the cross section for 120593 = 90∘ to270∘ and 120593 = 0 to 180∘ Similarly pictures of the lower end

Runner

Cylindricalvalve

Volute

Stay vane

Guide vane

Draft tube

Figure 1 Schematic of the model components of the turbine and aphotograph of the cylindrical valve

Figure 2 Photograph of the cylindrical valve

of the cylindrical valve with nose angles of 0∘ 90∘ 180∘ and270∘ are also available

3 Numerical Calculation

31 Control Equation When the cylindrical valve is closed foremergency shutdown of the turbine the fluid flows inside theturbine and around the cylindrical valve become a complex3D unsteady incompressible turbulent flows Because therenormalization-group k-120576 turbulence model distinguishesbetween a flow and a swirling flow it can predict theflow pattern near a wall surface relatively well In fact thisapproach has been used in many studies to simulate 3D flowin fluid machinery [16] Thus we also adopt this turbulencemodel for the present study The flow-control equations usedherein for the cylindrical-valve region are the continuityequation

120597119906119894

120597119909119894

= 0 (1)

the momentum equation

119863119906119894

119863119905

= 119891119894minus

1

120588

120597119901

120597119909119894

+

120597

120597119909119895

(]120597119906119894

120597119909119895

minus 1199061015840

119894

1199061015840

119895

) (2)


1

2

3

4

0∘

90∘

180∘

270∘



119863119896

119863119905

=

120597

120597119909119894

[(] +]119905

120590119896

)

120597119896

120597119909119894

] + 119866119896minus 120576

119863120576

119863119905

=

120597

120597119909119894

[(] +]119905

120590120576

)

120597120576

120597119909119894

] + 1198621120576

120576

119896

119866119896minus 1198622120576

1205762

119896

(3)


119894


119894is the


119905=

1198881199061198962

120576) 119888119906= 009 120590

119896= 10 120590

120576= 133 119862

1120576= 144


119894119906119895in (2) is



119872minus119872119891= 119869Δ120596 (4)








x

y z

(a)x

yz

(b)







times104


200 10 60 9030 807040 50 100

Closing ()

20

25

30

35

40

45

50

55

60

65

Dow

npul

l for

ce (N

)





121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06

(a)

121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06


983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06

(a)

983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06






931e + 01

885e + 01

838e + 01

792e + 01

745e + 01

699e + 01

652e + 01

605e + 01

559e + 01

512e + 01

466e + 01

419e + 01

373e + 01

326e + 01

279e + 01

233e + 01

186e + 01

140e + 01

932e + 00

466e + 00

195e minus 03

(a)

700e + 01

665e + 01

630e + 01

595e + 01

560e + 01

525e + 01

490e + 01

455e + 01

420e + 01

385e + 01

350e + 01

315e + 01

280e + 01

245e + 01

210e + 01

175e + 01

140e + 01

105e + 01

700e + 00

350e + 00

195e minus 03

(b)


731e + 01

694e + 01

658e + 01

621e + 01

585e + 01

548e + 01

512e + 01

475e + 01

439e + 01

402e + 01

366e + 01

329e + 01

292e + 01

256e + 01

219e + 01

183e + 01

146e + 01

110e + 01

732e + 00

366e + 00

108e minus 02

(a)

500e + 01

475e + 01

450e + 01

425e + 01

400e + 01

375e + 01

350e + 01

325e + 01

300e + 01

275e + 01

250e + 01

225e + 01

200e + 01

175e + 01

150e + 01

125e + 01

100e + 01

751e + 00

501e + 00

251e + 00

108e minus 02

(b)






5 Conclusion




(a) 120593 = 0∘


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘



(a) 120593 = 0∘minus107e + 06


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1

2

3

4

0∘

90∘

180∘

270∘



119863119896

119863119905

=

120597

120597119909119894

[(] +]119905

120590119896

)

120597119896

120597119909119894

] + 119866119896minus 120576

119863120576

119863119905

=

120597

120597119909119894

[(] +]119905

120590120576

)

120597120576

120597119909119894

] + 1198621120576

120576

119896

119866119896minus 1198622120576

1205762

119896

(3)


119894


119894is the


119905=

1198881199061198962

120576) 119888119906= 009 120590

119896= 10 120590

120576= 133 119862

1120576= 144


119894119906119895in (2) is



119872minus119872119891= 119869Δ120596 (4)








x

y z

(a)x

yz

(b)







times104


200 10 60 9030 807040 50 100

Closing ()

20

25

30

35

40

45

50

55

60

65

Dow

npul

l for

ce (N

)





121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06

(a)

121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06


983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06

(a)

983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06






931e + 01

885e + 01

838e + 01

792e + 01

745e + 01

699e + 01

652e + 01

605e + 01

559e + 01

512e + 01

466e + 01

419e + 01

373e + 01

326e + 01

279e + 01

233e + 01

186e + 01

140e + 01

932e + 00

466e + 00

195e minus 03

(a)

700e + 01

665e + 01

630e + 01

595e + 01

560e + 01

525e + 01

490e + 01

455e + 01

420e + 01

385e + 01

350e + 01

315e + 01

280e + 01

245e + 01

210e + 01

175e + 01

140e + 01

105e + 01

700e + 00

350e + 00

195e minus 03

(b)


731e + 01

694e + 01

658e + 01

621e + 01

585e + 01

548e + 01

512e + 01

475e + 01

439e + 01

402e + 01

366e + 01

329e + 01

292e + 01

256e + 01

219e + 01

183e + 01

146e + 01

110e + 01

732e + 00

366e + 00

108e minus 02

(a)

500e + 01

475e + 01

450e + 01

425e + 01

400e + 01

375e + 01

350e + 01

325e + 01

300e + 01

275e + 01

250e + 01

225e + 01

200e + 01

175e + 01

150e + 01

125e + 01

100e + 01

751e + 00

501e + 00

251e + 00

108e minus 02

(b)






5 Conclusion




(a) 120593 = 0∘


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘



(a) 120593 = 0∘minus107e + 06


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










x

y z

(a)x

yz

(b)







times104


200 10 60 9030 807040 50 100

Closing ()

20

25

30

35

40

45

50

55

60

65

Dow

npul

l for

ce (N

)





121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06

(a)

121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06


983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06

(a)

983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06






931e + 01

885e + 01

838e + 01

792e + 01

745e + 01

699e + 01

652e + 01

605e + 01

559e + 01

512e + 01

466e + 01

419e + 01

373e + 01

326e + 01

279e + 01

233e + 01

186e + 01

140e + 01

932e + 00

466e + 00

195e minus 03

(a)

700e + 01

665e + 01

630e + 01

595e + 01

560e + 01

525e + 01

490e + 01

455e + 01

420e + 01

385e + 01

350e + 01

315e + 01

280e + 01

245e + 01

210e + 01

175e + 01

140e + 01

105e + 01

700e + 00

350e + 00

195e minus 03

(b)


731e + 01

694e + 01

658e + 01

621e + 01

585e + 01

548e + 01

512e + 01

475e + 01

439e + 01

402e + 01

366e + 01

329e + 01

292e + 01

256e + 01

219e + 01

183e + 01

146e + 01

110e + 01

732e + 00

366e + 00

108e minus 02

(a)

500e + 01

475e + 01

450e + 01

425e + 01

400e + 01

375e + 01

350e + 01

325e + 01

300e + 01

275e + 01

250e + 01

225e + 01

200e + 01

175e + 01

150e + 01

125e + 01

100e + 01

751e + 00

501e + 00

251e + 00

108e minus 02

(b)






5 Conclusion




(a) 120593 = 0∘


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘



(a) 120593 = 0∘minus107e + 06


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06

(a)

121e + 06

106e + 06

921e + 05

779e + 05

636e + 05

494e + 05

351e + 05

209e + 05

667e + 04

minus756e + 04

minus218e + 05

minus360e + 05

minus503e + 05

minus645e + 05

minus787e + 05

minus930e + 05

minus107e + 06

minus121e + 06

minus136e + 06

minus150e + 06

minus164e + 06


983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06

(a)

983e + 05

880e + 05

778e + 05

675e + 05

572e + 05

470e + 05

367e + 05

264e + 05

162e + 05

592e + 04

minus434e + 04

minus146e + 05

minus249e + 05

minus351e + 05

minus454e + 05

minus556e + 05

minus659e + 05

minus762e + 05

minus864e + 05

minus967e + 05

minus107e + 06






931e + 01

885e + 01

838e + 01

792e + 01

745e + 01

699e + 01

652e + 01

605e + 01

559e + 01

512e + 01

466e + 01

419e + 01

373e + 01

326e + 01

279e + 01

233e + 01

186e + 01

140e + 01

932e + 00

466e + 00

195e minus 03

(a)

700e + 01

665e + 01

630e + 01

595e + 01

560e + 01

525e + 01

490e + 01

455e + 01

420e + 01

385e + 01

350e + 01

315e + 01

280e + 01

245e + 01

210e + 01

175e + 01

140e + 01

105e + 01

700e + 00

350e + 00

195e minus 03

(b)


731e + 01

694e + 01

658e + 01

621e + 01

585e + 01

548e + 01

512e + 01

475e + 01

439e + 01

402e + 01

366e + 01

329e + 01

292e + 01

256e + 01

219e + 01

183e + 01

146e + 01

110e + 01

732e + 00

366e + 00

108e minus 02

(a)

500e + 01

475e + 01

450e + 01

425e + 01

400e + 01

375e + 01

350e + 01

325e + 01

300e + 01

275e + 01

250e + 01

225e + 01

200e + 01

175e + 01

150e + 01

125e + 01

100e + 01

751e + 00

501e + 00

251e + 00

108e minus 02

(b)






5 Conclusion




(a) 120593 = 0∘


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘



(a) 120593 = 0∘minus107e + 06


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










931e + 01

885e + 01

838e + 01

792e + 01

745e + 01

699e + 01

652e + 01

605e + 01

559e + 01

512e + 01

466e + 01

419e + 01

373e + 01

326e + 01

279e + 01

233e + 01

186e + 01

140e + 01

932e + 00

466e + 00

195e minus 03

(a)

700e + 01

665e + 01

630e + 01

595e + 01

560e + 01

525e + 01

490e + 01

455e + 01

420e + 01

385e + 01

350e + 01

315e + 01

280e + 01

245e + 01

210e + 01

175e + 01

140e + 01

105e + 01

700e + 00

350e + 00

195e minus 03

(b)


731e + 01

694e + 01

658e + 01

621e + 01

585e + 01

548e + 01

512e + 01

475e + 01

439e + 01

402e + 01

366e + 01

329e + 01

292e + 01

256e + 01

219e + 01

183e + 01

146e + 01

110e + 01

732e + 00

366e + 00

108e minus 02

(a)

500e + 01

475e + 01

450e + 01

425e + 01

400e + 01

375e + 01

350e + 01

325e + 01

300e + 01

275e + 01

250e + 01

225e + 01

200e + 01

175e + 01

150e + 01

125e + 01

100e + 01

751e + 00

501e + 00

251e + 00

108e minus 02

(b)






5 Conclusion




(a) 120593 = 0∘


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘



(a) 120593 = 0∘minus107e + 06


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











(a) 120593 = 0∘


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘



(a) 120593 = 0∘minus107e + 06


(b) 120593 = 90∘


(c) 120593 = 180∘


(d) 120593 = 270∘






Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









numerical research on flow characteristics around a hydraulic

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