Vibration and Fatigue Caused by Pressure Pulsations Originating in The Vaneless Space For A Kaplan Turbine With High Head

 

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Vibration and fatigue caused by pressure pulsations originating in the vaneless space for a Kaplan turbine with high head  Article    Article

in

  Engineering Computations · March 2013

DOI: 10.1108/02644401311314 10.1108/02644401311314376 376

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Vibration and fatigue caused by pressure pulsations originating in the vaneless space for a Kaplan turbine with high head Yongyao Luo

Received 23 September 2011 Revised 15 February 2012 29 March 2012 Accepted 12 April 2012

State Key Laboratory of Hydroscience and Engineering and   Department of Hydraulic Engineering, Tsinghua University,  Beijing, China

Zhengwei Wang and Jing Zhang State Key Laboratory of Hydroscience and Engineering and   Department of Thermal Engineering, Tsinghua University,  Beijing, China

 Jidi Zeng and Jiayang Lin  Fujian Shuikou Hydropower Station, Fuzhou, China, and 

Guangqian Wang State Key Laboratory of Hydroscience and Engineering and   Department of Hydraulic Engineering, Tsinghua University,  Beijing, China Abstract Purpose   – Hydraulic instabilities are one of the most important reasons causing vibrations and fatigues in hydraulic turbines. The present paper aims to find the relationship between pressure pulsations and fatigues of key parts of a Kaplan turbine. Design/methodology/approach  – 3D uns unste teady ady nu nume meri rica call si simul mulat ation ionss we were re pre prefor forme med d fo forr a number of operating conditions at high heads for a prototype Kaplan turbine, with the numerical result res ultss ver verifie ified d by onli online ne moni monitor toring ing data data.. The con contac tactt met method hod and the wea weak k fluid fluid-st -struc ructur turee interaction method were used to calculate the stresses in the multi-body mechanism of the Kaplan turbine runner body based on the unsteady flow simulation result. Findings  – The results show that vortices in the vaneless space between the guide vanes and blades cause large pressure pulsations and vibrations for high heads with small guide vane openings. The dynamic stresses in the runner body parts are small for high heads with large guide vane openings, but are large for high heads with small guide vane openings. Originality/value  – A comprehensive numerical method including computational fluid dynamics analyses, finite element analyses and the contact method for multi-body dynamics has been used to identity the sources of unit vibrations and key part failures. Engineering Computations: International Journal for Computer-Aided Engineering and Software Vol. 30 No. 3, 2013 pp. 448-463 q Emerald Group Publishing Limited 0264-4401 DOI 10.1108/02644401311314376

Keywords Kaplan turbine, Pressure pulsations, pulsations, Multi-body dynamics, Stress S tress,, Fatigue Paper type  Research paper

The authors thank the National Natural Science Foundation of China (No. 50979044) and State Key Laboratory of Hydroscience and Engineering (Grant No. 2009T3) for supporting the present work.

 

1. Introduction Kaplan turbines are very efficient over a range of operating conditions since the runner blades are movable and the guide vanes can be turned to any angle to match the blade angle. With increases in unit capacities and runner diameters in recent years, units have experi exp erienc enced ed stab stabil ility ity prob problem lemss suc such h as hydr hydraul aulic ic vib vibrati rations ons and crac cracks ks in the lar large ge hydraul hydr aulic ic tur turbin bines. es. The ene energy rgy tra transfe nsferr in a tur turbine bineis is acc accompa ompanie nied d by pre pressu ssure re pul pulsati sations ons caused cau sed by vort vortice ices, s, cavi cavitati tation on and oth other er com comple plex x flow phe phenom nomena ena in the flow fiel field, d, whi which ch canresu can result lt in exc excess essive ivevib vibrati rations, ons,lea leadin ding g to str structu uctural ral fat fatigu iguee fail failure ures. s. Mos Mostt res researc earch h in the literature has focused on pressure pulsations in the flow path. For example, Wang  et al. (2002) studied the pressure pulsations caused by rotor-stator interactions in the Three Gorgeshydraul Gorges hydraulic ic turbi turbines. nes. Guede Guedess etal. (2002) simul simulated ated unstea unsteady dy rotor-s rotor-stator tator interac interactions tions in a pump-turbine with the unsteady computation results validated by LDV and PIV measurements measur ements.. Muntea Muntean n et al al.. (20 (2004) 04) ana analy lyze zed d th thee flow in th thee sp spir iral al ca casi sing ng an and d di dist stri ribu buto torr of a Kaplan turbine to obtain information on channel vortices at different operating conditions. condit ions. Gehrer etal. (200 (2006) 6) use used d num numeri erical cal flow sim simula ulatio tions ns to opti optimiz mizee Kapl Kaplan an tur turbin binee runner. Liu et al. (2009a, b) predicted the pressure pulsations in the entire flow passage of  a model Kaplan turbine turbine using 3D turbulent turbulent unsteady unsteady flow simu simulation lationss with the predic predicted ted pressure pulsations at different points along the flow passage agreeing well with test datain data in ter terms ms of the their ir freq frequen uencie ciess and andampl amplitu itudes des.. Moty Motycak cak et al al.. (2010) studie studied d runnerrunner-draft draft tub tube e int intera eracti ctions ons of low head hea d Kap Kaplan lan tur turbin bines es bywith numeri num erical cal sim simula ulatio tions ns and mod model el tests. Petit  (2010) compared simulation results experimental measurements for  et al. flow in the U9 Kaplan turbine model, and the numerical results were validated. Howeve How ever, r, few rese research archers ers have cal calcul culated ated the dyn dynami amicc str stress esses es in the tur turbine bine component caused by the unsteady hydraulic loads. For instance, Xiao  et al.   (2007) calculated the dynamic stresses in a Francis turbine runner at partial load, with the results indicating that the dynamic stresses caused by the hydraulic pulses at partial load lo ad are one of th thee im impor portan tantt re reaso asons ns ca caus usin ing g fat fatig igue ue an and d cr crack ackss in th thee ru runne nner. r. Zhou  et al. (2007) computed the dynamic stresses in Kaplan turbine blades for different worki wor king ng con condi diti tions ons to sh show ow th that at th thee dy dyna nami micc st stre resse ssess in th thee bl blad adee are lo low w for approximately optimum operating conditions, but high for low-output conditions with a small blade angle and a high head. Wang  et al.  (2008) studied the dynamic stresses in piston rods caused by unsteady hydraulic loads in a Kaplan turbine with the predicted position of the maximum stress concentration agreeing well with the actual fracture position. However, the runner body of a Kaplan turbine has a very complex mechanism due to the movable blades, so few studies have analyzed the dynamic stresses caused by the unsteady hydraulic load for this multi-body mechanism. In the current paper, the unsteady turbulent flow in the entire flow passage of a Kaplan turbine is simulated using the SST   k   2  v  turbulence model. The calculated pressure pulsation peak to peak values are compared with online monitoring data for a prototype Kaplan turbine to evaluate the robustness of the numerical model. The unsteady pressures on the blades are then used with the contact method in Ansys and the weak fluid-structure interaction method to calculate the stresses in the multi-body mechanism of a Kaplan turbine runner body.

2. Numerical model and theory The analysis analysis models a Kaplan turbine with a 8 m diameter runner. The runner runner has six blades with 24 guide vanes. The runner runner rotational speed is 107.14 rpm. The maximum maximum

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wa wate terr head head is is 61 m an and d th thee opti optimu mum m he head ad is 47 m. Th This is lar large ge ca calc lcul ulat atio ion n of th thee flo flow w in a proto pr ototy type pe Kap Kapla lan n tu turbi rbine ne wi with th an 8 m run runne nerr di diam amet eter er as assu sumes mes th that at th thee bl blad adee displacement due to the hydraulic pressure has little impact on the flow compared with the instabilities, so that there is no feedback of the blade displacement on the flow and self-excited oscillations are excluded. The fluid simulation domain extended from the spiral casing inlet to the draft tube outlet as shown in Figure 1. The whole domain was discretized with an unstructured hybrid hyb rid mes mesh h of hex hexahed ahedron ron and tet tetrahe rahedron dron ele element ments. s. The ele element ment siz sizes es wer weree bas based ed on Ma and Zhou’s (2006) recommendation. The final mesh had about 865,000 nodes, with 82,917 nodes inside the spiral case, 460,320 nodes inside the stay and guide vanes, 91,594 nodes inside the runners and 229,972 nodes inside the draft tube. Thee flow thr Th throug ough h the tur turbin binee pas passa sage ge was si simu mulat lated ed usi using ng the in incom compre pressi ssibl blee continui cont inuity ty equa equatio tion n and the Reyn Reynold oldss tim timee avera averaged ged Navi Navier-S er-Stoke tokess equa equation tionss with the   k   2  v    shear shear str stres esss tra transp nspor ortt (S (SST ST   k   2  v  ) turbulenc turbulencee model. The particula particularr impl im plem ement entati ation on of th thee we well ll kno known wn SS SST T k   2  v  mo mode dell is de desc scri ribe bed d in de deta tail il by Me Ment nter er an and d Rumse Ru msey y (1 (1994 994). ). Th This is mod model el acc accoun ounts ts for the tra trans nspor portt of the tu turbu rbule lent nt sh shear ear st stres resss to gi give ve very accurate predictions of the onset and the amount of flow separation under adverse pressure gradients. A second-order Backward Euler scheme was used for the convection terms with a central difference scheme used for the diffusion terms in the momentum equationss (Page et al., 2004). equation The continuity equation was: ›u j  0 ; 1 › x j

¼

 

ðÞ

where   u j   denotes the Rey Reynol nolds ds aver averaged aged vel velocit ocity y comp compone onents nts alo along ng the Cart Cartesi esian an coordinate coordin ate axes, x j. The momentum equation was: ›ui 

r 

›ui 

  þ r u j › x ¼ r  f i  ›t   j

 2

  › p



›

m

þ › x › x i 

 j

›ui  › x j

2



r u 0i u  j0 :

 

ð2 Þ

Here  r  u0i u j0  is the Reynolds stresses for the turbulent flow,   p  is the averaged pressure, r  is   is the fluid density,  m  is the kinetic viscosity of the fluid and   f i i  are the body forces acting on the unit volume fluid. Inlet

Stay vane Guide vane Spiral casing Draft tube

Runner

Outlet

Figure 1. Kaplan turbine flow path

 

Kaplan turbine

The SST  k -v  equations  equations were:

ðr k Þ þ 7 · ðr uk  Þ ¼ 7 ·

›

›t 

  þ   þ mt 

  m

s k

7k

 P k   2 b 0 r kv ;

ðrv Þ 7 · r u v    7 ·   m mt  7v   2 1 ›t    þ ð Þ ¼ v  þ s   þ ð 2 þ a k   P k brv  :

›



 

v 

 2

r 

 F 1

 2

Þ

 

ð3Þ

7k7v 

ð4Þ

s v 2 v 

Here   P k  is the turbulent production defined as:

 ¼  mt S 2 ;

 P k

ð5Þ

 

where:

q   ffi ffi ffi ffi ffi ffi ffi  ¼  ¼

2S iji j S ijij ;   S ijij

S 

 ¼

1 2

1

s v  v 

›ui  › x j

›u j

þ › x

;   a

 ¼  F 1 =s  1 þ4ð1 tanh nh ar arg g1 ;  F 1 ¼   ta

 2

v 



 

 F 1 =s v 2

arg1

Þ



;   s k

i 

 þ ð

  p  ffiffi  ¼   ¼   min

CD kw kw

max

1

k1

 2

 F 1 =s k2

Þ

1   2 F 1 a2 ;   b   F 1 b 1

 F 1 a1

 ¼

 ¼  F  =s   þ ð11 Þ

 ¼

!

;

1   2 F 1 b 2 ;

 þ ð

Þ

!

k 500m   4r k ; ; ; 2 b 0 v  y r  y 2 v  CD kw v2   y kw s v 

  2r   max 7k7v ; 1:0 £ 10 s v  v 2 v 

10

2



with  y  being the distance to the nearest wall. The proper transport behavior is obtained by a limiter to the formulation of the eddy-viscosi eddyviscosity ty defined as: 1k  ¼ maxðra ; a v ; SF  Þ 1

ð6Þ

 

mt 

2

where:

 F 2

tanh nh  ¼  ta

arg ar g 22 ;   arg2

 

 ¼  max

 p  ffiffi !

  2 k 500m ; ; b 0 v  y r  y 2 v 

with model parameters defined as: b 0

 ¼ 0 :09;   a1 ¼  5 =9;   b 1 ¼  0 :075;   s k1 ¼  2 ; b 2 ¼  0 :0828;   s k2 ¼  1and s  2 ¼  1 :1682: v  v 

  s v  v1 

 ¼  2;

  a2

 ¼  0:44;

Thee pre Th press ssure ure con condi diti tions ons are at bo both th th thee in inle lett and the out outle lett acc accord ordin ing g to th thee he head ad fo forr ea each ch operating condition and the estimated velocity on each boundary. In the calculations,

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positions of each node in the runner zone mesh rotated at 107.14 rpm with the relative positions this zone unchanged. unchanged. The interfac interfaces es between the guide vanes, the runner and the draft tubee wer tub weree mod modele eled d wit with h sli slidin ding g int interfa erfaces ces wit with h the flux tran transfe sferred rred bet between weennei neighb ghborin oring g zones. For the unsteady calculatio calculations, ns, the time step was 0.0056 s, which is 1/100 of the runner rotational period. This time step is small enough to catch the main pressure fluct flu ctuat uatio ion n fre frequ quen enci cies es su such ch as th thee rot rotati ationa onall fre frequ quen ency cy an and d bl blad adee pas passi sing ng fre frequ quen ency cy as pointed out by Liu  et al.  (2009b) and Xiao  et al.  (2010). The runn runner er hub hub,, blad blade, e, bla blade de lev lever, er, blad bladee lin link, k, cros crossed sed head head,, pis piston ton rod, ret retaine ainerr rin ring g and an d oth other er aux auxil ilia iary ry co comp mpone onent ntss wer weree in incl clud uded ed in th thee run runner ner bod body y me mech chani anism sm as sh shown own in Figure 2. The contact method was used to combine all the parts into a multi-body mech me chan anis ism m wi with th th thee me mesh sh as sh show own n in Fi Figu gure re 3. Th Thee el elem emen ents ts on th thee bl blad ades es an and d th thee hu hub b surf su rface acess we were re id iden enti tical cal in th thee flui fluid d and st struc ructu ture re me mesh shes es.. Th Thee un unst stea eady dy pr pres essur sures es on th thee

runner hub

blade

blade retainer ring

piston rod blade lever

Figure 2. Runner body mechani mechanism sm (cutaway view)

Figure 3. Mesh for the runner body (cutaway view)

blade link  fork ear

cross head retainer ring

 

blades were then input into a weak fluid-structure interaction model to calculate the stresses in the multi-body mechanism of the Kaplan turbine runner body using a code developed devel oped to generate an index for the interfa interfacial cial nodes to transfer the pressu pressure re data at each time step. The tran transie sient nt dyn dynami amicc equ equili ilibri brium um equ equati ation on for the dis displa placeme cements nts in a lin linear ear structure structu re is:

½ M   M {u€ } þ ½C {u_ } þ ½ K   K {u} ¼ { F };

ð7Þ

 

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where [ M   M ] is the mass matrix, [C ] the damping matrix and [ K   K ] the stiffness matrix, {u} the noda nodall dis displa placeme cement nt vect vector, or, {u_ } th thee no nodal dal ve velo loci city ty ve vect ctor, or, {u€ } th thee no noda dall acceleration vector, and { F } the nodal load vector including gravitational, centrifugal and hydraulic forces obtained from the flow simulation. For the linear elastic problem used in the current analysis, the damping matrix [ C ] was assumed to be zero. Equation (7) was discretized using the finite element method and solved using the Newmark method, which is usually used for implicit transient analyses (Bathe, 1996). The dynamic stresses in the runner body were computed based on the fourth strength theory with the von Mises stress used as the equivalent stress.

3. Predicted pressure pulsations The numerical simulations were performed for eight operating conditions with the operating parameters listed in Table I. During the computational process, the pressure data were saved at the recording points shown in Figure 4 inside the distributor, the runner and the draft tube. Two of  the points on the blade pressure side (RP) and the suction side (RS) rotated with the runner in the blade passage, while the other points were fixed along the flow path. In particular, point SV was located between the stay vane and the guide vane. Points GV and HC were located behind the guide vane and at the vaneless space under the head cover. Figure 5 shows the online monitoring system for the Kaplan turbine to record the actual vibrations, throws and pressure pulsations in the unit. The predicted pressure pulsations were analyzed using fast Fourier transforms to calculate the dominant relative frequency (i.e.   f / f n, with   f n   being the runner rotating frequency) and the pulse amplitude at this frequency. The pressure pulsations at HC and RP are shown in Figure 6 in the time and frequency domain for the two typical conditions Cases 3 and 7. For la large rge bl blade ade ang angle less and gu guid idee va vane ne ope openi nings ngs,, Cas Casee 7, th thee pr pres essur suree on HC fluctuates with a dominant frequency of 6   f n   as shown in Figure 6(b) caused by Oper Op erat atin ing g co cond ndit itio ions ns Case Case Case Case Case Case Case Case

1 2 3 4 5 6 7 8

Head He ad (m (m))

Powe Po werr (M (MW) W)

Guid Gu idee va vane ne op opeeni ning ng (% (%))

Blad Bl adee an angl glee ( 8 )

58.5 58.5 58.5 58.5 58.5 58.5 58.5 58.5

60 80 100 120 160 190 210 250

24.1 31.7 37.3 43.9 54.6 60.2 64.0 72.8

2.8 4.8 6.6 8.6 13.3 16.0 18.0 22.5

Table I. Simulation parameters

 

EC 30,3 SV

GV

HC DT1 DT2 DT3

454

DT4

DT5

RS

Figure 4. Locations Locatio ns of record recording ing points for the simulations

RP

interac interactions tions with the passage of the runner blades. The pressu pressure re on RP fluctuates with a dominant frequency of 2  f n  as shown in Figure 6(d). Howe Ho wever ver,, fo forr sm small all blade blade ang angle less an and d sm small all guide guide van vanee op open ening ings, s, Cas Casee 3, the pressur pre ssuree pul pulsati sations ons are acc accomp ompanie anied d by inc increas reased ed turb turbule ulence nce and the domi dominan nantt frequency is about 1.25  f n  as shown in Figure 6(a) and (c). The peak to to peak amp amplit litude udess of the press pressure ure pulsa pulsatio tions ns with with 95 perc percent ent rel reliab iabili ility ty at GV and HC are plotted versus power and compared with the online monitoring data in Figure 7. The simulated results agree qualitatively with the measured data, but with some quantitative differences, which may be partially attributed to differences in the inlet and outlet boundary conditions between the simulations and the real turbine. For turbine tur bine powers powers in the rang rangee of 50-1 50-100 00 MW, the pres pressure sure pulsati pulsations ons in the vaneless vaneless space suddenly increase. Plots of the horizontal vibrations of the upper bracket and the throws of the upper guide bearing and the turbine guide bearing versus power show the same trends with the horizontal vibrations of the upper bracket exceeding the permitted value (120 mm) for loads loads in the range of 50-100 MW as shown in Figure Figure 8. The throw of the turbine guide guide bearing is greater than that of the upper guide bearing, bearing, which indicates indicates that the vibrati vibration on origin originates ates from hydraul hydraulic ic instab instabiliti ilities. es. The turbine shaft, guide bearing bearing and upper bracket bracket were not includ included ed in the multi-body multi-body mechanis mechanism m in the simulations, thus, no simulated results are available for comparison with the throw of the guide bearing and the vibration of the upper bracket.

 

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Figure 5. Online monitoring syste system m for the Kaplan turbine

Th Thee pr pres essu sure re pu puls lsat atio ion n am ampl plit itud udes es at th thee do domi mina nant nt fr freq eque uenc ncy y of 1. 1.25 25   f n   at different diffe rent recording points points for Case 3, where the turbine power is 100 MW, are shown in Figure 9. The results show that the large pressure pulsations in Case 3 with the small guide vane opening originate from the vaneless space between the guide vanes and the runner blades. Vortices develop within the vaneless space for Case 3 as shown in Figure Fig ure 10(a 10(a). ). The movements movements of the vort vortices ices cause pres pressure sure pulsations pulsations alo along ng the flow path and the time variation of the pressure distribution in the vaneless space for Case 3 shown in Figure 11. The pressure pulsation period was 0.8  T  (where   T  is   is the runner runn er rota rotation tional al peri period), od), which ind indica icates tes tha thatt the dom dominan inantt freq frequen uency cy is 1.25   f n. For the same reason, the pressure pulsation amplitudes increase suddenly when the turb tu rbin inee po powe werr is in the ran range ge of 5050-100 100 MW MW.. Fi Figu gure re 10( 10(b) b) shows shows th that at th thee flow in the vaneless space is very smooth in Case 7, so the pressure pulsation amplitudes are quite small.

4. Runner body dynamic stresses Thee st Th stre ress ss di dist stri ribut butio ion n in th thee ru runne nnerr bod body y me mech chani anism sm for Cas Casee 3 is sh shown own in Figure 12(a). The maximum stress in the runner body mechanism is located at the key slot because the blade torque is transferred to the blade lever by the key. Figure 12(b) shows that the maximum stress in the blade is near the blade root which agrees with wit h gen general eral kno knowle wledge dge on stat static ic stre stress ss dis distri tribut butions ions in Kap Kaplan lan tur turbin binee bla blades des.. The maximum stress in the hub is located at the bottom of the large pivot hole, which is the bearing surface of the blade pivot, as shown in Figure 12(c). Figure 12(d) shows

 

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6 f n

1.25 f n

(a)

1.25 f n

Figure 6. Pressure pulsations in the time and frequency domain at HC and RP

Figure 7. Comparison Comparis on of simulat simulated ed and measur measured ed press pressure ure pulsation amplitudes

(b)

2 f n

(c)

(d)

Notes: (a) Pressure on HC, Case 3; (b) pressure on HC, Case 7; (c) pressure on RP, Case 3; Notes: (a) (d) pressure on RP, Case 7

Note: H = 58.5 m Note: H

 

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Note: H = 58.5 m Note: H

Figure 8. Measured motions of key components in the turbine

Figure 9. Amplitudes corresponding to the dominant frequency 1.25  f n  for Case 3

that the maximum stress in the piston rod is near the lower retainer ring slot root, which agrees well with the actual fracture position for the piston rod as shown in Figure 13. Thee dy Th dyna nami micc st stres resse sess at th thee no node dess wi with th th thee ma maxi ximu mum m st stre ress ss in th thee ke key y sl slot, ot, blad bl ades es,, hu hub b an and d pi pist ston on ro rod d ar aree pl plot otte ted d inFig inFigur uree 14 fo forr Ca Case sess 3 an and d 7. In Ca Case se 3, th thee ru runn nner er body bo dy me mech chani anism sm is lo loade aded d by th thee un unst stead eady y pr press essure uress wi with th a dom domin inant ant fr freq eque uenc ncy y of 1.2 1.25 5  f n in the six blades. The pressure pulsations on each blade are conside considered red independent independent with a 608  phase difference between each blade, hence, the domin dominant ant frequency for the dyna dy nami micc st stre ress sses es inthe ke key y sl slot ot,, hu hub b an and d pi pist ston on inCas inCasee 3 is7.5 f n, wh whil ilee th that at in th thee bl blad ades es is 1. 1.25 25 f n, wh whic ich h is th thee sa same me as th thee do domi mina nant nt pr pres essu sure re pu puls lsat atio ion n fr freq eque uenc ncy y at po poin intt RP in this th is ca case se.. On th thee ot othe herr ha hand nd,, th thee do domi mina nant nt fr freq eque uenc ncy y fo forr th thee dy dyna nami micc st stre ress sses es in th thee ke key y

 

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(a)

Figure 10. Velocity vectors in the vaneless space between the guide vanes and the runner blades (vertical section)

(b)

Note: (a) Case 3; (b) Case 7 Note: (a)

 

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40.0T 

40.5T 

 

 

40.3T 

40.8T 

slo slot, t, hub and pis piston ton in Case 7 is 1  f n  or 6  f n  and that in the blades is 24  f n, due to the rotor-stator rotor-st ator interactions from the 24 guide vanes. Table II lists the predicted mean and peak to peak amplitudes (with 95 percent reliability) of the dynamic stresses. This Th is ta tabl blee sh show owss th that at th thee me mean an dy dyna nami micc st stre ress sses es fo forr th thee ke key y sl slot ot,, bl blad ades es an and d hu hub b va vary ry littl li ttlee for di diff ffere erent nt gui guide de van vanee ope openi nings ngs.. How Howeve ever, r, the me mean an dyn dynam amic ic st stres resses ses in the pi pisto ston n rod ro d ar aree ve very ry la larg rgee wi with th th thee sm smal alll gu guid idee va vane ne op open enin ing g an and d sm smal alll wi with th th thee la larg rgee gu guid idee va vane ne opening. Similarly the peak to peak amplitudes of the dynamic stresses are low with the large guide vane opening, but high with the small guide vane opening. The amplitude of  the dynamic stresses stresses reaches 60.9 MPa for Case 3, which is very high for the piston rod. The Kaplan turbine is run in the automati automaticc generation control (AGC) mode with the operating conditions varying with the power demand. According to analyses of the online monitoring monitoring data for a whole year, the turbine was run with operating conditions conditions similar simil ar to Case 3 (with the power being being 50-100 MW and the head being being 55-61 m) about 30 percent of the total running time. Thus, the mean and variable dynamic stresses in the piston rod were very large for long period of time, resulting in fatigue in the piston rod resulting in failure, as shown in Figure 13. Other key parts of the runner body have opera op erated ted fo forr mo more re th than an 15 ye years ars wi with thout out any cra cracks cks du duee to th thee rel relati ativel vely y lo low w dynamic stresses in the other components.

Figure 11. Time variation of the pressure distribution in the vaneless space for Case 3 (cross-section)

 

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460

(a)

Figure 12. Stress distributions for Case 3

(c)

 

(d)

Notes: (a) Notes:  (a) Runner body mechanism (cutaway view); (b) blades; (c) hub; (d) piston rod

cross head broken piston rod end dropped retainer rings

Figure 13. Fractured Fractu red piston rod

(b)

 

Kaplan turbine

461 7.5 fn

6 fn

(a)

(b)

1.25 fn 24 fn

(c)

7.5 f n

(e)

 

(d)

1 f n

(f) (continued )

Figure 14. Dynamic stresses at the nodes with the maximum stresses for Cases 3 and 7

 

EC 30,3

462

7.5 f n

1 f n

(g)

Figure 14.

(h)

Notes: (a) Key slot for Case 3; (b) key slot for Case 7; (c) blades for Case 3; (d) blades for Notes: (a) Case 7; (e) hub for Case 3; (f) hub for Case 7; (g) piston rod for Case 3; (h) piston rod for Case 7

Key slot Blades Hub Piston rod Oper Op erati ating ng co condi nditi tion onss Me Mean an Am Ampl plit itude ude Me Mean an Am Ampl plit itude ude Me Mean an Am Ampli plitu tude de Mean Mean Amp Ampli litu tude de

Table II. Predicted mean and amplitudes of the dynamic stresses

Case 3 Case 7

148.2 128.3

33.5 8.0

98.1 93.9

10.9 1.4

98.7 91.3

23.2 2.1

103.9 48.6

60.9 27.5

Note:  Unit: MPa

5. Conclusions Thee pre Th press ssur uree pu puls lsati ations ons in a Ka Kapl plan an tu turb rbin inee we were re pr predi edict cted ed us usin ing g nu nume meri rical cal simulations, with the robustness of the method verified by comparisons with the online monitor mon itoring ing dat data. a. Vortices Vortices in the vanele vaneless ss spa space ce between between the guide guide vanes vanes and the blades blades lead le ad to la large rge pr pres essu sure re pu puls lsati ations ons an and d vi vibra brati tion onss fo forr sm small all gu guide ide van vanee op openi enings ngs and hi high gh head he ads. s. Th Thee co cont ntact act me meth thod od was th then en us used ed to co comb mbin inee allthe pa parts rts of th thee run runner ner bod body y in into to a multi-body mechanism with the weak fluid-structure interaction method used to calcul calc ulate ate th thee st stre resse ssess in th thee ru runn nner er bo body dy.. Th Thee res resul ults ts sh show ow th that at th thee dom domin inant ant frequencies and amplitudes of the dynamic stresses in the runner body mechanism are closely related with the pressure pulsations in the blades. The mean and variable dynam dy namic ic st stre resse ssess in th thee pi pist ston on rod are ver very y la large rge fo forr sm small all gu guid idee va vane ne ope openi ning ngss and hi high gh heads, which would create fatigue in the piston rod. References Bathe, K.J. (1996),  Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ. Gehrer, A., Schmidl, R. and Sadnik, D. (2006), “Kaplan turbine runner optimization by numerical flow simulation (CFD) and an evolutionary algorithm”,   Proceedings of the 23rd IAHR  Symposium on Hydraulic Machinery and Systems, Yokohama. Guedes, A., Kueny Guedes, Kueny,, J.L., Ciocan, G.D. and Avellan, F. (2002), “Unste “Unsteady ady rotor-stator analysis of a hydraulic pump-turbine – CFD and experimental approach”,  Proceedings of the 21st IAHR  Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland .

 

Liu, S.H., Li, S.C. and Wu, Y.L. (2009a), “Pressure fluctuation prediction of a model Kaplan turbine by unsteady turbulent flow simulation”,  Journal of Fluids Engineering , Vol. 131 No. 10, pp. 101102 (1-9).

Kaplan turbine

Liu, S.H., Mai, J.Q., Shao, J. and Wu, Y.L. (2009b), “Pressure pulsation prediction by 3D turbulent unsteady flow simulation through whole flow passage of Kaplan turbine”,  Engineering  Computations, Vol. 26 No. 8, pp. 1006-25. Ma, W.S. and Zhou, L.J. (2006), “The effect of grid on the result of CFD simulation of turbine”,  Journal of Hydroelectric Engineering , Vol. 25 No. 1, pp. 72-5 (in Chinese). Menter, F.R. and Rumsey, C.L. (1994), “Assessment of two-equation models for transonic flows”, AIAA Paper, Colorado Springs, CO, pp. 94-2343. Motycak, L., Skotak, A. and Obrovsky, J. (2010), “Analysis of the Kaplan turbine draft tube effect”,  Proceedings of the 25th IAHR Symposium on Hydraulic Machinery and Systems, Timisoara. Muntean, S., Balint, D. and Susan-Resiga, R. (2004), “3D flow analysis in the spiral case and distributor of a Kaplan turbine”,  Proceedings of the 22nd IAHR Symposium on Hydraulic  Machinery and Systems, Stockholm. Page, M., Theroux, E. and Trepanier, J.Y. (2004), “Unsteady rotor-stator analysis of a Francis turbine”, Proceedings of the 22nd IAHR Symposium on Hydraulic Machinery and Systems, Stockholm. Peti Pe tit, t, O., O., Mu Mulu lu,, B. B.,, Ni Nilss lsson on,, H. an and d Ce Cerv rvan antes tes,, M. (2 (2010 010), ), “C “Com ompa pari rison son of nu nume meric rical al an and d experimental results of the flow in the U9 Kaplan turbine model”,  Proceedings of the 25th  IAHR Symposium on Hydraulic Machinery and Systems, Timisoara. Wang, Z.W., Zhou, L.J. and Huang, Y.F. (2002), “The rotor-stator interaction flow simulation on three gorges hydrau hydraulic lic turbin turbines”, es”, Proceedings of the 21st IAHR Symposium on Hydraulic  Machinery and Systems, Lausanne, Switzerland . Wang, Z.W., Luo, Y.Y., Zhou, L.J., Xiao, R.F. and Peng, G.J. (2008), “Computation of dynamic stresses in piston rods caused by unsteady hydraulic loads”,  Engineering Failure Analysis , Vol. 15 Nos 1/2, pp. 28-37. Xiao, R.F., Wang, Z.W. and Luo, Y.Y. (2007), “Dynamic stress analysis of Francis turbine with partial load”,  Journal of Hydroelectric Engineering , Vol. 26 No. 4, pp. 130-4 (in Chinese). Xiao, Y.X., Wang, Z.W., Yan, Z.G., Li, M.A., Xiao, M. and Liu, D.Y. (2010), “Numerical analysis of  unsteady unstea dy flow under high-head high-head operatin operating g conditi conditions ons in Francis turbine”, turbine”,   Engineering  Computations, Vol. 27 No. 3, pp. 365-86. Zhou, turbine L.J., Wang, Z.W., Engineering Xiao, R.F. and Luo, Y.Y. (2007), of dynamic blades”, Computations , Vol. “Analysis 24 No. 8, pp. 753-62. stresses in Kaplan

Corresponding author Zhengwei Zheng wei Wang can be contact contacted ed at: wzw@ma [email protected] il.tsinghua.ed hua.edu.cn u.cn

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