Fluid structure interaction analysis of a high-pressure regulating valve of a 600-MW ultra-supercritical steam turbine

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1 Orgnal Artcle Flud structure nteracton analyss of a hgh-pressure regulatng valve of a 600-MW ultra-supercrtcal steam turbne Proc IMechE Part A: J Power and Energy 0(0) 1 10! IMechE 2015 Reprnts and permssons: sagepub.co.uk/journalspermssons.nav DOI: / pa.sagepub.com Xaojng Sun 1,2, Xaowe L 3, Zhongquan Zhen and Dangu Huang 1,2 Abstract A hgh-pressure regulatng valve s one of the most crtcal components n ultra-supercrtcal steam power plants and constantly works under the condton of hgh temperature and hgh pressure. In order to control the flow of steam nto the turbne, the hgh-pressure regulatng valve normally operates at small openngs. Therefore, the phenomena such as whstlng nose and turbulence can be caused by the throttlng effect of the regulatng valve. In addton, the flow-nduced vbraton due to couplng between the flud flow and the movng parts lke valve stem wll also occur. In ths paper, the pressure loss across the hgh-pressure regulatng valve of a 600-MW ultrasupercrtcal steam turbne was assessed wth the ad of computatonal flud dynamcs studes. Furthermore, the dynamc characterstcs and vbraton ampltude of the valve stem were also analyzed by usng flud structure nteracton method. Keywords Ultra-supercrtcal steam turbne, hgh-pressure regulatng valve, numercal smulatons, flud structure nteracton analyss Date receved: 25 September 201; accepted: 22 December 201 Introducton The operatng temperature and pressure of supercrtcal (SC) and ultra-supercrtcal (USC) steam power plants normally need to be above the crtcal pont of water,.e. above the temperature and pressure at whch pont there s no dfference between water gas and lqud water. As a result, ths has the advantage of makng the SC and USC power plants more effcent compared to conventonal coal-fred power plants. Because of ther hgh effcency, relablty and less emsson of ar pollutants, large numbers of SC and USC power plants are beng bult around the world today. 1,2 Especally, n Chna, over 50 USC power generaton unts wth a capacty of 1000 MW have been planned to be nstalled at the ste and wll be put nto operaton wth an attempt to ncrease energy plant effcences and enhance envronmental protecton. 3 As the hgh-pressure regulatng valve s an mportant executve component of the steam dstrbuton system, pressure loss resultng from flow through the valve can drectly mpact the performance and effcency of a steam turbne. Hence, accurate assessment to provde a bass for reducng the pressure drop across the regulatng valve emerged as an mportant area of nqury n the feld of the development of USC steam turbne, but to date there s relatvely lttle research n ths area. The purpose of ths paper s thus to fll ths gap by descrbng a method to calculate the pressure loss across the hgh-pressure regulatng valve of a 600- MW USC steam turbne wth the ad of computatonal flud dynamcs studes. Besdes, the dynamc characterstcs of the valve stem were also analyzed by usng flud structure nteracton method. Governng equatons of flud dynamcs Contnuty, momentum, energy and the state equatons that govern the steam flowng through the 1 School of Energy and Power Engneerng, Unversty of Shangha for Scence and Technology, Shangha, P.R. Chna 2 Shangha Key Laboratory of Power Energy n Multphase Flow and Heat Transfer, Shangha, P.R. Chna 3 The Insttute of Appled Mathematcs and Mechancs, Shangha Unversty, Shangha, P.R. Chna Aerospace Engneerng Department, Unversty of Kansas, Lawrence, USA Correspondng author: Dangu Huang, Unversty of Shangha for Scence and Technology, 516 Jungong Road, Shangha , P.R. Chna. Emal: dghuang@usst.edu.cn

2 2 Proc IMechE Part A: J Power and Energy 0(0) valve were smlar to those used n lterature 5,6 and were descrbed n more detal here. In a 3D Cartesan coordnate system, the Naver Stokes (N S) equatons derved for a fxed control volume, n ntegral form, are expressed n conservaton form ZZZ V ZZ! W dv H! ZZ n ds ¼ H! n ð1þ were the control volume boundares, n! was the unt normal vector that ponts outward from the control volume. In addton H ¼!!!!!! F þ G j þ H k!! ƒ!! ƒ!! H ¼ F þ G j þ H k ð3þ!!!, j, k were the unt vectors n the drecton of the x, y and z axes u 3 u! W ¼ v,! u 2 þ P F ¼ uv, w 5 uw 5 E uh v w 3 ðþ uv! G ¼ v 2 þ P,! uw H ¼ vw vw 5 w 2 7 þ P 5 vh wh ! xx ¼ 6 7 ƒ! yx ¼ 6 7 ƒ! zx ¼ 6 7 F 6 xy xz f 5 7 5, G 6 yy yz g 5 7 5, H 6 zy zz h ð2þ ð5þ In equaton (5), f 5, g 5 and h 5 can be expressed as follows f 5 ¼ u xx þ v xy þ w xz g 5 ¼ u yx þ v yy þ w yz h 5 ¼ u zx þ v zy þ w zz The stress tensor components n the above equatons can be wrtten as below xx @y @x yy @y @y zz @y @z xy ¼ yx @x xz ¼ zx @x zy ¼ yz @y In the above equatons,, (u, v, w), E, H, p, T represent densty, the three components of the velocty vector along the three coordnate axes x, y, z, total energy, total enthalpy, pressure and temperature, respectvely. In addton, and k are the coeffcent of vscosty and thermal conductvty, respectvely. In order to close the above equatons, the followng equatons of state are needed p ¼ RT p ¼ ð 1Þ E 0:5 u 2 þ v 2 þ w 2 H ¼ E þ p= where s the specfc heat capacty and R s gas constant. Accordng to Stokes assumpton, l and satsfy the followng relaton 2l þ 3 ¼ 0 The effect of turbulence n ths work s consdered by ntroducng the eddy vscosty coeffcent and coeffcent of turbulence heat transfer, both of whch are obtaned from tme-averaged equatons. As a result, n the momentum equatons has the followng form: ¼ l þ t ð10þ where t s the coeffcent of vscosty of the turbulent flow, l s the coeffcent of vscosty of the lamnar flow and has an exponental relatonshp wth temperature, as shown n equaton (11) 0:75 l ¼ l1 T =T1 ð11þ where subscrpt 1 represents free-stream condton. Smlarly, the coeffcent of thermal conductvty k n the energy equaton ncludes the followng two components k ¼ k l þ k t ð6þ ð7þ ðþ ð9þ ð12þ

3 Sun et al. 3 where k l and k t can be calculated respectvely as Cp k l ¼ l ð13þ ðprþ l Cp k t ¼ t ð1þ ðprþ t where ðprþ l s the lamnar Prandtl number and s taken to be constant at ðprþ t s the turbulent Prandtl number and s taken to be constant at 0.9. In ths way, equatons (1), (6), (7) and () consttute a closure system and thus can be solved under approprate defntve boundary condtons. Model of vbraton The valve stem can be modeled as a cantlevered beam, and the defnte condtons of ts transverse vbraton are shown below 2 þ y ¼ f ðx, x¼0 ¼ ¼ ¼ 0 3 ¼ 0 x¼l ð15þ where E ¼ Pa, ¼ 7: kg=m 3, A ¼ r 2 and I ¼ r =. In addton, y t¼0 ¼ 0 and y f ðx, tþ t¼0 ¼ A. f (x, t) s the transent flow force actng on the stem durng flowng of a workng flud through the valve and s obtaned by solvng the governng equatons descrbed n Governng equatons of flud dynamcs secton. As shown n Fgure 1, the followng hgher order fnte dfference approxmatons can be obtaned _y 1:5 ¼ y 1 y 2 _y 0:5 ¼ y y 1 _y þ0:5 ¼ y þ1 y _y þ1:5 ¼ y þ2 y þ1 ::: 0:5 y ¼ y y 1 y þ0:5 ¼ y þ1 y y 1 ¼ _y 0:5 _y 1:5 y ¼ _y þ0:5 _y 0:5 y þ1 ¼ _y þ1:5 _y þ0:5 y ¼ y::: þ0:5 y ::: 0:5 Fgure 1. Fnte dfference scheme n space doman. ::: y ¼ y þ1 2 y þ y 1 2 ¼ _y þ1:5 3 _y þ0:5 þ3 _y 0:5 _y 1:5 3 ¼ y þ2 y þ1 þ6y y 1 þy 2 The boundary condtons are gven as follows y 2 ¼ y 1 ¼ 0 y¼a 0 þa 1 xþa 2 x 2 þa 3 x 3 þa x y¼2a 2 þ6a 3 xþ12a x 2 ::: y ¼ 6a3 þ2a x :::: y ð16þ n ¼2a x ¼0 y n ¼ a 0 x ¼ y n 1 ¼ a 0 a 1 þa 2 2 a 3 3 þa x ¼ 2 y n 2 ¼ a 0 2a 1 þa 2 2 a 3 3 þ16a x ¼ 3 y n 3 ¼ a 0 3a 1 þ9a a 3 3 þ1a x ¼ y n ¼ a 0 a 1 þ16a 2 2 6a 3 3 þ256a y n can be calculated only f the value of a s obtaned. As x ¼ 0, y ¼ 0 and y ::: ¼ 0. Then y n and a can be expressed as follows a 2 ¼ 0 a 3 ¼ 0 x ¼ 0 y n ¼ a 0 x ¼ y n 1 ¼ a 0 a 1 þ a x ¼ 2 y n 2 ¼ a 0 2a 1 þ 16a y n ¼ a 0 2y n 1 ¼ 2a 0 2a 1 þ 2a y n 2 ¼ a 0 2a 1 þ 16a a ¼ y n 2y n 1 þ y n 2 1 y n ¼ 2a ¼ 12 ð y n 2y n 1 þ y n 2 Þ 7 _y 1:5 ¼ y 1 y 2 _y 0:5 ¼ y y 1 _y þ0:5 ¼ y þ1 y _y þ1:5 ¼ y þ2 y þ1 ::: 0:5 y ¼ y y 1 :::þ0:5 y ¼ y þ1 y ( y 1 ¼ _y 0:5 _y 1:5 y ¼ _y þ0:5 _y 0:5 y þ1 ¼ _y þ1:5 _y þ0:5 y ¼ y::: þ0:5 y ::: 0:5 y n 1 ¼ y::: n 0:5 ::: y 1:5 ¼ y n 2 y n 1 þ y n 2 2

4 Proc IMechE Part A: J Power and Energy 0(0) ¼ 2 _y n 0:5 þ 3 _y n 1:5 _y n 2:5 3 ¼ 2y n þ 5y n 1 y n 2 þ y n 3 As the result, the equaton (1) becomes y þ y f ðx, tþ ¼ A ð17þ ð1þ In the current research, Wlson-y method s chosen for tme dscretzaton 2 þ y ¼ f ðx, C l ¼ A C r ¼ EI EI C l y þ y ðþ ¼ C r f ðx, tþ ð19þ ðþ y ¼ a 2 y 2 þ a 1 y 1 þ a y þ a þ1 y þ1 þ a þ2 y þ2 where a þ2 ¼ 1, a þ1 ¼, a ¼ 6, a 1 ¼ and a 2 ¼ 1. Based on Wlson-y method, y tþt _y tþt f tþt ¼ q 0 y tþt y t q2 _y t 2 yt ¼ q 1 y tþt y t 2 _y t q 3 y t ¼ f t þ f tþt f t can be substtuted nto equaton (5) and yelds C l q 0 y tþt þ a 2 y tþt 2 þ a 1 y tþt 1 þ a y tþt þ a þ1 y tþt þ1 þ a þ2 yþ2 tþt ¼ C r f t þ f tþt f t þ Cl q 2 _y t þ 2 yt þ q 0y t ð20þ Once y tþt s solved wth qunary dagonal lnear systems, then the followng expressons can be obtaned. Thus, the values of unknown parameters at tme t þ t can be computed y tþt ¼ q y tþt y t q5 _y t þ q 6 y t _y tþt ¼ _y t þ q 7 y tþt þ y t ð21þ y tþt ¼ y t þ 2q 7 _y t þ q y tþt þ 2 y t q 0 ¼ 6 2 t 2 q 1 ¼ 3 t q 2 ¼ 6 t q 3 ¼ t 2 q ¼ 6 3 t 2 q 5 ¼ 6 2 t q 6 ¼ 1 3 q 7 ¼ t 2 q ¼ t2 6 An expermental computer program has been wrtten to valdate the above concepts. The dsplacement, velocty and acceleraton of a rod were calculated under steady-state condtons frst and then the dynamc response of the rod was analyzed. It was found that when ¼ 1., effects of tme step sze were neglgble and uncondtonal convergence occurred. Numercal method and boundary condtons Boundary condtons The body surface boundary condton. The body surface boundary condton of the N S equatons ncludes all of the followng 1. No-slp boundary condton u ¼ v ¼ w ¼ 0 2. Pressure gradent normal to ¼ ¼ 0 n s an outward surface normal. ð22þ ð23þ ð2þ Inlet and outlet boundares. Total pressure, total temperature and mass flow rate were gven at the nlet. The total pressure at the outlet boundary was determned usng the teratve calculaton based on the mass flow rate. In addton, the average densty and velocty at the outlet were extrapolated from the nteror. Mesh generaton The schematc dagram of the hgh-pressure regulatng valve that s beng studed s llustrated n Fgure 2. In the present work, a nested grd approach was mplemented n the numercal scheme n order to decrease the overall computatonal demand but at the same tme for hgh spatal resoluton around the combned body. The flud computatonal doman was dvded nto seven sub-blocks, consstng of manstream ppelne, branch ppelnes (2), valve stems (2), and small gaps between the valve steam and branch ppelne (2). Accordngly, the computatonal grd was generated for each of the blocks and assembled nto a sngle grd. To facltate the use of a nested grd system, the manstream/valve steam ntersecton was represented wth a collar grd whch was then assembled wth the computatonal grd around the

5 Sun et al. 5 Table 1. Maxmum flud exctng force and resultng shear stress for varyng percentage openng of the valve. Fracton of valve openng (f) Maxmum flud exctng force (N) Resultng shear stress (N/m 2 ) f ¼ ,775 f ¼ ,663 f ¼ ,03 f ¼ ,691 f ¼ ,99 f ¼ ,295 f ¼ ,700 f ¼ ,675 Fgure 2. Schematc dagram of the smulated hgh-pressure regulatng valve. Fgure 3. A vew of the surface grd for a hgh-pressure regulatng valve confguraton. Fgure. The grd generated to fll the nteror of the computatonal doman. valve stem. As a result, the total number of grd ponts was about one mllon. Besdes, both algebrac methods and hyperbolc partal dfferental equaton methods were used for surface grd generaton and feld grd generaton. The grd was locally refned at places where the soluton was expected to exhbt sharp features. The computatonal grds adopted are shown n Fgures 3 and. Numercal results and dscusson Usng the numercal method descrbed above, the flow-nduced vbraton of the ntake valve stem of a 600-MW USC steam turbne was analyzed for a number of dfferent flow condtons usng a self-developed code. The SC steam condtons were used at the nlet to the turbne. In addton, the valve openng was defned as d ¼ f d max, n whch d max s the openng when the valve s fully opened and f s fracton of valve openng. Dfferent cases of valve openng, namely f ¼ 1.0, 0.5, 0.70, 0.625, 0.55, 0.5, 0.5, 0.325, were smulated n order to dentfy ts nfluence on the falure mechansm of a steam valve stem and the pressure loss across the valve. Analyss for flud exctng force and resultng shear stress It was assumed that there was no collson between valve stem and surroundng. Then, the maxmum flud exctng force and the resultng shear stress on the root of the valve stem were calculated and summarzed n Table 1. As shown n Table 1, the values of the flud exctng force are frst ncreased wth the ncreasng of f rangng from 0.35 to 0.7 and then start to decrease when the value of f reaches 0.5 and 1.0. As the percentage openng of the valve s progressvely ncreased further, a reducton n the extent of the contact area between the flow and the valve stem mght be expected and thereby the mpact force of flow of superheated steam aganst the valve stem can be reduced obvously. In addton, t can also be seen from Table 1, that the maxmum shear stress on the stem s much smaller than the allowable shearng stress of the stem materal (about 0 MPa). Analyss for steam-flow-excted vbratons Fgures 5 to 13 are graphc llustratons of characterstc vbraton of the smulated valve stem for dfferent valve openngs. As can be seen from the above fgures, the valve at moderate degree of openng (f ¼ 0.5, 0.55, 0.625, 0.7) s subjected to relatvely large vbraton ampltudes whch has a maxmum value of 0.25 mm. In contrast,

6 6 Proc IMechE Part A: J Power and Energy 0(0) Fgure 5. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ 0.25 and n the supercrtcal flow state. Fgure 6. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ and n the supercrtcal flow state. Fgure 7. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ 0.5 and n the supercrtcal flow state.

7 Sun et al. 7 Fgure. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ 0.5 and n the supercrtcal flow state. Fgure 9. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ 0.55 and n the supercrtcal flow state. Fgure 10. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ and n the supercrtcal flow state.

8 Proc IMechE Part A: J Power and Energy 0(0) Fgure 11. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ 0.7 and n the supercrtcal flow state. Fgure 12. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ 0.5 and n the supercrtcal flow state. Fgure 13. Ampltudes n tme (left) and frequency (rght) domans for the end-pont vbraton of the smulated valve stem when f ¼ 1.0 and n the supercrtcal flow state.

9 Sun et al. 9 f the valve openng s too narrow (f < 0.5) or too wde (f > 0.7), the ampltude of the end-pont vbraton of the valve stem then becomes relatvely small (less than 0.1 mm). In addton, the above results also ndcate that the smulated valve stem vbrates at a low frequency whch s all smaller than 30 Hz. In most cases, especally at the condton of valve large openng, the vbraton of the valve stem appears to be the most obvous at a frequency of 30 Hz, whch corresponds to half of ts natural vbraton frequency. It s common phenomenon for SC steam turbne rotors that low and half frequency vbraton can be caused by steam-nduced vbraton exctaton force. However, the results obtaned n ths work confrm that the vbraton of valve stem also have smlar frequency characterstcs. The vbraton ampltudes of the valve stem s central part, where collson between the valve stem and the outer crcumferental wall s most lkely to occur, were also calculated for dfferent valve openngs and presented n Table 2. It can be seen from Table 2 that when f ¼ 0.55 and 0.5, the maxmum vbraton ampltudes of the valve stem s central part are all consderably large and reach 0.12 mm and 0.1 mm, respectvely. Accordng to the orgnal desgn concept of a 600-MW SC steam turbne, the clearance between the valve stem and crcumferental wall was desgned to 0.15 mm. Therefore, consderng the exstence of sudden mechancal perturbatons, the collson between the valve stem and crcumferental wall s hghly lkely to occur when f ¼ 0.55 and 0.5. Specal attenton should be pad to the safe operaton of valves when the valve openng vares from 50% to 60% of capacty. Analyss for operatng characterstcs of ntake valve under SC and USC condtons The total pressure drop l across the ntake valve was numercally calculated n ths work. The defnton of l s gven as below l ¼ðP 0,n P 0,out Þ=P 0,n 100 % where P 0,out s the average total pressure at outlet (¼ P Q out, P 0,out, =Qout ), P 0,n s the average total pressure at nlet, P 0,out, s the pressure n one cell at the outlet boundary, Q out s the total mass flow rate through the outlet boundary and Q out, s the mass flow rate through the cell at the outlet boundary. For SC case, nlet boundary condtons were nlet total pressure P 0,n ¼ 2.13 MPa, nlet total temperature T n ¼ 39 K and mass flow rate Q n ¼ /2. For USC case, nlet boundary condtons were nlet total pressure P 0,n ¼ 2.52 MPa, nlet total temperature T n ¼ 73 K and mass flow rate Q n ¼ /2. Therefore, the resultng nput parameters used for the smulatons were summarzed n Table 3. P out =P n 0:95 was obtaned through teratve calculatons based on flow rate. As a result, the total pressure drop across the ntake valve for dfferent valve openngs under SC and USC steam condtons was computed and presented n Table. Table 3. Input parameters used for the supercrtcal and ultra-supercrtcal cases. Input parameters Supercrtcal case Ultra-supercrtcal case Mach number, Ma Velocty, U n (m/s) Densty, (kg/m 3 ) Temperature, T (K) Pressure, P (MPa) Velocty of sound, c (m/s) Reynolds number, R e Table 2. Vbraton ampltudes of the smulated valve stem s central part at dfferent valve openng ratos. Fracton of valve openng (f) The maxmum vbraton ampltude (mm) Table. Total pressure drop across the ntake valve for dfferent valve openngs under supercrtcal and ultra-supercrtcal steam condtons. F Supercrtcal case Ultra-supercrtcal case Ma Pressure drop (%) Ma Pressure drop (%) Ma: Mach number.

10 10 Proc IMechE Part A: J Power and Energy 0(0) It should be noted that the changes n valve openng affect the varaton of flow rate and back pressure. However, both flow rate and back pressure were actually unknown parameters at ths stage of smulaton. Consequently, the varaton of flow rate n the present study was realzed by adjustng the Mach number of the flud, whereas back pressure was assumed unchanged. Although the accuracy and precson of the results obtaned n Table mght be compromsed by usng ths approach, the followng general trend of varaton n the pressure drop across the ntake valve under SC and USC condtons can stll be observed n Table. 1. Under both SC and USC operatng condtons, the pressure drop across the ntake valve generally ncreases as the valve openng decreases; and 2. For any gven valve openng, the values of the pressure drop across the ntake valve obtaned at SC condtons are close to that acheved at USC condtons. Conclusons Based on the above numercal study, the man fndngs drawn from these results are as below 1. Maxmum flud exctng force ntally ncreases wth ncreasng valve openng rangng from to On the contrary, t starts to decrease, as the valve openng further ncreases from 0.5 to 1.0; 2. When the valve s at moderate degree of openng (f ¼ 0.5, 0.55, 0.625, 0.7), the ampltude of vbraton of the end-pont of the valve stem can become relatvely large and has a maxmum value of 0.25 mm. On the other hand, ts vbraton ampltude s small at the other openng ratos. In addton, our results proved that the vbraton frequency of valve stem has the same characterstcs as that of steam turbne rotor, as both of them vbrate at low frequences or half of ther natural frequences; 3. The trend n the varaton of pressure drop across the ntake valve for the SC case s same wth that of the USC case. Moreover, the values of the calculated pressure drop are also qute close for both cases and are all ncreased wth decreasng the valve openng;. The numercal results suggested that the alternatng shear stress actng on the valve stem s relatvely small and s only 1/0 of allowable stress of the valve stem materal. It s thus reasonable to beleve that a falure n the valve stem durng operaton s hardly caused by fatgue alone; and 5. When f ¼ 0.55 and 0.5, the valve stem s central part also has the maxmum vbraton ampltude. Therefore, the valve stem vbrates so severely that the probablty of collson between the stem and ts surroundngs s extremely hgh. Acknowledgements We would lke to thank all of our colleagues and other personnel of the Shangha Unversty for Scence and Technology wth whom we have had a chance to nteract, and who have kndly shared ther experences wth us. In partcular, we would lke to thank the management of the Shangha Unversty for Scence and Technology for ther commtment. In addton, ths work s supported by Natonal Natural Scence Foundaton of Chna (No ). Conflct of nterest None declared. Fundng Ths work s supported by Natonal Natural Scence Foundaton of Chna (No ). References 1. Beer JM. Hgh effcency electrc power generaton: the envronmental role. Prog Energy Combust Sc 2007; 33: Franco A and Daz A. The future challenges for clean coal technologes : jonng effcency ncrease and pollutant emsson control. Energy 2009; 3: Yang Y, Wang L, Dong C, et al. Comprehensve energybased evaluaton and parametrc study of a coal-fred ultra-supercrtcal power plant. Appl Energy 2013; 112: Dong J and Lu Y. Numercal smulatons of the flow feld nsde hgh pressure combned valve of a 600MW ultra-supercrtcal steam turbne. Turbne Technol 2009; 51: (n Chnese). 5. L L and L X. Numercal smulaton of gusts over multelement arfols and ther flow control. Acta Aerodyn Sn 2013; 31: (n Chnese). 6. Zhang H and L X. Numercal smulaton of unsteady gust over mult-element arfol usng precondtonng method. J Shang Unv (Nature Scence) 2013; 19: (n Chnese).