Simulation of Wind Speed in the Ventilation Tunnel for Surge Tanks in Transient Processes

Transcription

1 energies Article Simulation Wd Speed Ventilation Tunnel for Surge Tanks Transient Processes Jiong Yang 1, Huang Wang 1,, Wencheng Guo 1,3, *, Weijia Yang 4 Wei Zeng 1 1 State Key Laboratory Water Resources Hydropower Engeerg Science, Wuhan University, Wuhan 43007, Cha; jdyang@whu.edu.cn (J.Y.); wanghuangamy@sa.com (H.W.); wzeng@whu.edu.cn (W.Z.) Changjiang Institute Survey, Planng, Design Research Co. Ltd., Wuhan , Cha 3 Maha Fluid Power Research Center, Department Agricultural Biological Engeerg, Purdue University, West Lafayette, IN 47907, USA 4 Department Engeerg Sciences, Uppsala University, Uppsala SE-751 1, Sweden; weijia.yang@angstrom.uu.se * Correspondence: wench@whu.edu.cn; Tel.: ; Fax: Academic Editor: Juan Ignacio Pérez-Díaz Received: 8 December 015; Accepted: 6 January 016; Publhed: 3 February 016 Abstract: Hydroelectric power plants open-type s may be built mountas subject to provion atmospheric air. Hence, a dpensable. air flow associated with water-level. re a great relationship between wd safe use project vestment s. To obta wd a for a durg transient processes, th article adopts one-dimensional numerical simulation method establhes a mamatical model a wd by assumg boundary conditions air dcharge for a. reafter, simulation wd a, for case a durg transient processes, successfully realized. Fally, effective mechanm water-level a shape (cludg length, al area dip angle) for wd dtribution change process are dcovered. On bas comparon between simulation results 1D 3D computational fluid dynamics (CFD), results dicate that one-dimensional simulation method as proposed th article can be used to accurately simulate wd a durg transient processes. wd s can be superimposed by usg low frequency mass wave (i.e., fundamental wave) high frequency elastic wave (i.e., wave). water-level a al area maly affect amplitude fundamental waves. period a fundamental wave can be determed from water-level s. length has an effect on period amplitude waves, whereas dip angle fluences amplitude waves. Keywords: hydroelectric power plants; ; ; transient process; wd ; numerical simulation; wave superposition 1. Introduction An open-type built a mounta must be connected with atmosphere air by a to realize its functions pressure reduction, as shown 1. In transient processes a hydroelectric power plant (HPP), load rejection load adjustment units can cause water-level s a,, reafter, lead to volume, pressure f air flow changes. As a consequence, gas transforms Energies 016, 9, 95; doi: /en

2 Energies 016, 9, Energies 016, 9, volume, pressure f air flow changes. As a consequence, gas transforms from a static state to an unsteady flow causg high wd flows. se high from wd a static flows state will tonot an unsteady only affect flow causg high structure wd safe flows. use, se but high it also affects wd flows project will not only affect structure safe use, but it also affects project vestment for vestment for provion. Hence, it necessary to carry out a simulation provion. Hence, it necessary to carry out a simulation wd wd durg transient processes to provide a bas for application design durg transient processes to provide a bas for application design s s case s. case s. Mounta Surge Ventilation Upstream reservoir Headrace Penstock Generatg unit Draft tube Downstream reservoir Schematic diagram layout a a a a HPP. a HPP. For For case case a wd a, a, many measurement many measurement methods methods simulation techniques simulation techniques have been have studied. been studied. Davenport Davenport [1], Liu et al. [1], [] Liu et Allegri al. [] et al. Allegri [3] have all et al. proposed [3] have methods all proposed to methods measure to measure wd s wd s a wd. a wd Xu. [4] madexu physical [4] made models physical to models to a a an underground an underground HPP. He measured HPP. He wd measured analyzed wd relation analyzed between wd change process water-level s a. Field tests relation between wd change process s a. experiments are important ways to explore fundamental relationships, but y always dem Field tests experiments are important ways to explore fundamental relationships, but y a great deal time money; hence, many researchers prefer to use numerical simulation always technique. dem Ramponi a great deal Blocken time [5] money; Mo et hence, al. [6] many vestigated researchers wd prefer to use by usg numerical simulation three-dimensional technique. computational Ramponi fluid Blocken dynamics [5] (CFD) Mo method al. [6] vestigated effect turbulence wd models. by usg Zhou etthree dimensional al. [7] studied functional computational mechanmfluid a dynamics system (CFD) for method tailrace by usg effect turbulence CFD. models. three-dimensional Zhou et al. computational [7] studied method functional an accurate mechanm tool, but a it also time-consumg. system for tailrace On or by h, usg CFD. one-dimensional three dimensional numerical simulation computational wdmethod a an accurate, tool, but it for also time consumg. case a On durg or transient h, processes, one dimensional has not been vestigated. numerical Streeter simulation Wylie wd dcussed a transient, flow for a natural case gas pipele a establhed durg its transient basic equations. processes, In th has regard, not been vestigated. y proposed Streeter to use one-dimensional Wylie dcussed method transient charactertics flow (MOC) a [8], natural but gas research pipele object y studied considerably different from a its results cannot be referenced establhed its basic equations. In th regard, y proposed to use one dimensional method directly. In addition, boundary conditions for a are entirely charactertics (MOC) [8], but research object y studied considerably different from a new problems. To determe its results wd cannot be referenced directly. for In addition, case a boundary durg conditions transient processes, th for article a uses one-dimensional are entirely new numerical problems. simulation method establhes ato mamatical determe model wd wd based boundary for conditions case air a dcharge for durg case transient processes, a th. article reafter, uses simulation one dimensional wd numerical simulation method for a establhes durg a mamatical transient processes, model wd successfully based realized. on By comparg boundary conditions results one-dimensional air dcharge simulation for case to a that. three-dimensional reafter, simulation CFD simulation wd through a project case, applicability for a rationality durg transient one-dimensional processes, successfully numerical simulation realized. By as proposed comparg thresults article have one dimensional been verified. Fally, simulation to that effective three dimensional mechanm CFD water-level simulation through a project case, applicability shape rationality (cludg length, al area dip angle) for onward dtribution wd change one dimensional numerical simulation as proposed th article have been verified. Fally, process have been explored from perspective wave superposition. effective mechanm a shape (cludg length, al area dip angle) for onward dtribution wd change process have been explored from perspective wave superposition.. Mamatical Model simulation wd deals with transient flow a gas pipele. mamatical model establhed th based on followg assumptions:

3 Energies 016, 9, Mamatical Model Energies 016, 9, simulation wd deals with transient flow a gas pipele. (1) flow mamatical ormal; () model establhed elasticity th pipe s wall based can be onignored; followg (3) assumptions: flow one (1) dimensional; flow (4) ormal; coefficient () elasticity friction a function pipe s wall can surface s be ignored; roughness (3) flow Reynolds one number dimensional; (when(4) we calculate coefficient transient friction flow, a function steady flow friction surface s coefficient roughness can be used); Reynolds (5) number any ketic (whenenergy we calculate changes along transient pipele flow, can be steady ignored. flow friction coefficient can be used); (5) any ketic energy changes along pipele can be ignored..1. Basic Equations Solution MOC.1. Basic Equations Solution MOC For case unsteady flow pressurized pipele, basic equations clude momentum equation For case contuity unsteady equation; flow pressurized ir expressions pipele, can be basic written equations as follows clude [8]: momentum equation contuity equation; ir expressions can be written as follows [8]: B M p Contuity equation: Contuity equation: B BM A Bx ` Bp 0 (1) A x t Bt 0 (1) p α M pgs θ fb M M Momentum equation: Momentum equation: Bp Bx ` α BM A Bt ` pgsθ B ` f B M M 0 () x A t B DA p DA 0 () p where relevant parameters are defed as follows: B = wave velocity; A = al area where relevant parameters are defed as follows: wave velocity; al area ; M = mass flow; x = position along ax ; p = absolute pressure gas; ; = mass flow; x = position along ax ; p = absolute pressure t = time; α = ertia factor; g = gravitational acceleration; θ = cluded angle between ax gas; t = time; α = ertia factor; g = gravitational acceleration; θ = cluded angle between ax pipele horizontal plane; f = Darcy Webach coefficient friction restance; D = diameter pipele horizontal plane; f = Darcy-Webach coefficient friction restance; D = diameter.. It should be noted that: It should be noted that: (1) M ρva, where v = flow velocity. (1) M ρva, where v = flow velocity. () wave velocity can be determed by usg state equation () wave velocity can be determed by usg state equation B a B p{ρ? p/ ρ λrt ; λrt; where ρ where gasρ density, gas λ density, compressibility λ compressibility coefficient, coefficient, R gas R constant gas constant T T absolute temperature. absolute temperature. (3) (3) When When ax res ax up res along up along direction direction +x, θ, +x, cluded θ, cluded angle between angle between ax pipele ax pipele horizontal plane, horizontal takes aplane, positive takes value. a positive value. (4) (4) default default values values parameters parameters are: are: B = B 340 = 340 m/s, m/s, α α = = 1, 1, f f = 0.015, 0.015, ρ = = kg/m kg/m 3, p 0 = p0 101,35 = 101,35 Pa. Pa. MOC MOC grid grid shown shown.. equations equations positive positive negative negative charactertics charactertics along along with positive charactertic le dx d x dt B dx dt dt α negative charactertic le d x B can be dt α obtaed as follows (expressed by by C` C C, C respectively):, respectively): t P Δt A C + Δx C - Δx B x.. charactertic charactertic grids grids charactertic charactertic les. les. C C` $ α dα M α dp pgsθ fb M M & dm 0 A dt B dt B DA p A dt ` α dp B dt ` pgsθ B ` f B M M DA 0 p % dx dxb dt dt B α α (3) (3)

4 Energies 016, 9, α dm α dp pgsθ fb M M Energies 016, 9, A dt B dt B DA p C (4) $ dx B α & dm C A dt α dp B dt ` pgsθ B ` f B M M dt α DA 0 p % dx dt B (4) By usg tegrated method along charactertic les ( C : A P, C : B P ), we can get equations for C C : α By usg tegrated method along charactertic les ( C` : A Ñ P, C : B Ñ P ), we can C : pp CP CBMP (5) get equations for C` C : C C` p : pc P C P M C B M P (6) (5) : P M B P reafter, tensity pressure C : p P mass C M `flow C B Mat P pot P can be expressed as follows: (6) reafter, tensity pressure C mass flow at pot P can be expressed as follows: P CM pp (7) p P C P ` C M (7) CP CM M P (8) C M P C B P C M (8) 3 C B 3 αb pags θ fb M A M A αb pgs θ fb M B M B B where, CP pa M where, C P p A ` αb A ( A M A p p Agsθ ` f ) t, C B3 M pb MB ( M A M A αb αda q t, C M p B αb p A A M B p p ) t, A αb αda pa A αb αdabgsθ pb ` αb αb C f B 3 M B M. A B αda q t, C B αb p B A... Boundary Conditions Initial Conditions.. Boundary Conditions Initial Conditions..1. Boundary Conditions..1. Boundary Conditions boundary conditions for system, as shown 3, boundary conditions for system, as shown 3, cludes last (i.e., atmospheric air side), connectg pipes cludes last (i.e., atmospheric air side), connectg pipes first (i.e., side). It should be noticed that first (i.e., side). It should be noticed that first last can be considered positive direction first last can be considered positive direction pipele as it assumed th article (i.e., from side towards atmospheric air side). pipele as it assumed th article (i.e., from side towards atmospheric air side). se boundary conditions have been dcussed as follows: se boundary conditions have been dcussed as follows: First J A J v J p J F vz Ventilation L A Water-level z Atmospheric air Last L M L p L t Surge boundary boundary conditions conditions first first a.. (1) (1) Last Last (i.e., (i.e., atmospheric air air side) last last directly directly connected connected to to atmosphere. atmosphere. Its Its pressure pressure to pl identical to atmospheric pressure, i.e., p p0. By usg C L = p 0. By usg C equation, unknown quantity ML M th can be as L th boundary node can be obtaed as follows: M p C 0 M L M (9) L C p 0 C M B C B (9)

5 Energies 016, 9, Energies 016, 9, () Connectg pipes pipes junctions pipes a series (refer to 4) meet contuous mass flow condition. Meanwhile, pressure s just before after junction should be treated, if local loss head neglected. By Byusg CC` C C equations, we can get boundary conditions pipes a series as follows: p P CB 1C p P M CB B1C M ` CP C1 B C P1 (10) C (10) B1 C B1 B` C B M P CP 1 M P C P1 M C M (11) C (11) B1 C B1 B` C B M P1, p P1 C + 1 C - M P, p P boundary boundary condition condition pipes pipes a series. series. (3) First First (i.e., (i.e., side) side) water-level a serves serves as as a source source dturbances. dturbances. Th Th leads leads to to unsteady unsteady flow flow air air a a.. In In th th article, article, we we allow allow water-level a to to be be known, known, i.e., i.e., z = z(t). z(t). process process water-level a can can be be simulated simulated by by usg usg stware stware for for transient transient processes processes a HPP HPP by by neglectg neglectg air air dynamics dynamics.. Next, Next, it it assumed assumed that that itial itial water water level level zero zero upward upward movement movement can can be be treated treated as as positive. positive. It It presumed presumed that that velocity velocity water-level for for case case a a (vz) (v flow rate gas (vj) at first should meet z ) flow rate gas (v J ) at first should meet followg followg relationship: relationship: vf v z va F v J A J (1) (1) z J J where, F al area a ; AAJ J al area first. By substitutg v z dz dz By substitutg vz dt M J ρv J A J Equation (1) by simplifyg resultg M J ρva J J Equation (1) by simplifyg equation, we may get: dt resultg equation, we may get: M J ρf dz (13) dt dz By applyg C` equation, unknown MJ ρf quantity p J at boundary node can be obtaed (13) dt as follows: By applyg C equation, punknown J C P Cquantity B M J p J at boundary node can (14) be obtaed It should as follows: be noticed that re might be some or treatment methods for boundary conditions first a. p J C treatment P CBM method, as adopted th article, can be J (14) used to reflect dynamic nature charactertics air flow. It should be noticed that re might be some or treatment methods for boundary conditions... Initial Conditions first a. treatment method, as adopted th article, can be used to reflect dynamic nature charactertics air flow. For case an ormal (steady) flow, M constant BM 0. tegral Bt... momentum Initial Conditions equation from x 0 at p p 1 to x x at p p yields: M For case an ormal (steady) flow, M constant 0. tegral p pp 1 f B M M DA x es 1 q{e s t (15) s momentum equation from x 0 at p p1 to x x at p p yields:

6 fb M M 1 s e 1 s p ( p x )/ e (15) DA s Energies 016, 9, In Equation (15): s (g xs ) / B. Th equation presents parabolic pressure gradient a steady state. pressure at every durg itial In Equation steady (15): state s should pg xsθq{b satfy th. Th equation. equation For presents case parabolic a horizontal pressure pipele, gradient s 0, s s e 1 ( e 1)/ s 1a, refore, steady state. Equation pressure (15) becomes: at every durg itial steady state should satfy th equation. For case a horizontal pipele, s 0, e s 1 pe s fb M M 1q{s 1, refore, Equation (15) p becomes: p1 x (16) DA If air pipele static p itial p 1 state, f B M n M DA x flow at every equal to zero. (16) As a consequence, pressure at every pipele always equal to atmospheric pressure. If air pipele static itial state, n flow at every equal to zero. As a3. consequence, Solution Model pressure Verification every pipele always equal to atmospheric pressure Solution Solution Model Verification 3.1. In accordance Solution with mamatical model developed Section, simulation wd for case a durg transient processes can be carried out. steps volved In accordance computational with mamatical procedure, model are as developed follows: (1) Section divide, pipele simulation wd to several s. for case space asteps durg time transient steps can processes be denoted canas be carried x out. t, respectively steps volved where x ( B computational /α)/ t. On procedure, bas are itial as follows: condition (1) at divide time t tpipele 0, C P, C M to several s. space steps time steps can be denoted as x C B can be determed, reafter, p P M P at time t t0 t can be determed by t, respectively where x pb{αq{ t. On bas itial condition at time t t 0, C P, C M usg Equations (7) (8). When boundary nodes located last C B can be determed, reafter, p P M P at time t t 0 ` t can be determed by usg, pipes a series first a must be computed, Equations (7) (8). When boundary nodes located last, boundary conditions dcussed Section..1 should be applied. We follow above described pipes a series first a must be computed, boundary procedure for total calculation time set advance. complete simulation process shown conditions dcussed Section..1 should be applied. We follow above-described procedure for 5. total calculation time set advance. complete simulation process shown 5. Load rejection or adjustment unit Calculatg stware for transient process HPP Ventilation for Water-level process Pipele s partition Determation space step Δx time step Δt Boundary conditions Charactertic grids Initial conditions t=t 0 Unknown quantities grid nodes t 0 +Δt Total calculatg time No End Yes complete simulation process process wd wd for for case case a a durg durg a transient a transient process. process. 3.. Model Verification To verify correctness one-dimensional simulation for case wd a, as proposed th article, a project case selected for a comparon between simulation results one-dimensional method that a three-dimensional CFD method.

7 Energies 016, 9, Model Verification To verify correctness one dimensional simulation for case wd a Energies 016, 9, , as proposed th article, a project case selected for a comparon between simulation results one dimensional method that a three dimensional CFD method. layout for for system system process process water-level for casefor a case a are shown are shown 6. basic6. parameters basic are parameters defed as are follows: defed for as follows: for : vertical : pipele vertical L JB pipele = 85 m, LJB horizontal = 85 m, pipele horizontal L BL = pipele 680 m, LBL al = 680 m, area A al = 0 m ; for area A = 0 m ; for case, al case, area al F = area m. F = m. 6. layout for system water-level process for case a (project case). assessment region one dimensional method between first (i.e., Section J, assessment region one-dimensional method between first (i.e., Section J, connectg between ) last (i.e., connectg between ) last (i.e., Section L, exit that connected to atmosphere). three dimensional Section L, exit that connected to atmosphere). three-dimensional CFD method conducts assessment from free water surface a to Section L. In CFD method conducts assessment from free water surface a to Section L. In three dimensional CFD simulation case, volume fluid (VOF) multiphase flow model [9,10], three-dimensional CFD simulation case, volume fluid (VOF) multiphase flow model [9,10], second order realizable k ε turbulence model [11], stard near wall function [1], second order realizable k-ε turbulence model [11], stard near wall function [1], compressible Navier Stokes (NS) equation dpersed by fite volume method (FVM) [13] compressible Navier-Stokes (NS) equation dpersed by fite volume method (FVM) [13] pressure implicit with splittg operator (PISO) algorithm, that are coupled by pressure pressure implicit with splittg operator (PISO) algorithm, that are coupled by pressure velocity [14 17], are adopted. boundary conditions are adopted for preset velocity [14 17], are adopted. boundary conditions a are adopted for preset process, as shown 6, whereas boundary conditions Section water-level process, as shown 6, whereas boundary conditions Section L are fixed to use preset atmospheric pressure (p0). results for dtribution wd are fixed to use preset atmospheric pressure (p (i.e., positive negative extremum envelope 0 ). results for dtribution wd curves along ax ) (i.e., positive negative extremum envelope curves along ax ) processes wd at typical s (i.e., Section J, Section Section B) processes wd at typical s (i.e., Section J, Section L Section B) simulated by usg se two methods are compared shown s 8). Please notice simulated by usg se two methods are compared shown s 7 8). Please notice that: (1) positive wd flows from Section towards Section L, whereas verse flow that: (1) positive wd flows from Section J towards Section L, whereas verse flow negative; () ax length calculated between Section Section L. negative; () ax length calculated between Section J Section L. s show that: (1) accordg to 3D method, absolute values positive s 7 8 show that: (1) accordg to 3D method, absolute values positive negative wd extrema along ax present an almost lear negative wd extrema along ax present an almost lear gradually gradually creasg tendency. amplification positive extremum small while creasg tendency. amplification positive extremum small while amplification amplification negative extremum large (refer to Table 1). Hence, maximum values negative extremum large (refer to Table 1). Hence, maximum values positive negative positive negative wd occur at Section L. For 1D method, dtribution trend wd occur at Section L. For 1D method, dtribution trend wd (extremum) wd (extremum) as that 3D method. positive extreme values at as that 3D method. positive extreme values at Sections J L are respectively Sections J L are respectively higher lower than those estimated by 3D method, whereas higher lower than those estimated by 3D method, whereas absolute values negative absolute values negative wd (extremum) are always higher than those 3D wd (extremum) are always higher than those 3D method. In, re an significantly small difference wd extreme values between 1D 3D methods ( positive difference less than 1.4 m/s 4.86%, negative difference less than 5.76 m/s 8.69%).

8 Energies 016, 9, Energies 016, 9, method. method. In In,, re re an an significantly significantly small small difference difference wd wd extreme extreme values values between Energies between 016, 9, 1D 95 1D 3D 3D methods methods ( ( positive positive difference difference less less than than m/s m/s 4.86%, 4.86%, negative negative 8 16 difference difference less less than than m/s m/s 8.69%). 8.69%) comparon positive negative (extremum) envelope curves along ax by 1D 3D, simulated by 1D 3D methods. (a) (a) Section Section J J (b) (b) Section Section B (c) (c) Section Section L 8. comparon wd processes typical s as simulated by comparon wd processes typical s as as simulated by by usg 1D 3D methods. usg 1D 1D 3D 3D methods. Table 1. comparon positive negative wd s (extrema) typical s. Table comparon positive negative wd wd s (extrema) typical typical s. Positive Wd Speed Extrema (m/s) Negative Wd Speed Extrema (m/s) Simulation Method Positive Wd Speed Extrema (m/s) Negative Wd Speed Extrema (m/s) Simulation Method Section J B Section L Section J Section B Section L Section Positive J WdSection SpeedBExtrema Section (m/s) L Negative Section Wd J Section Speed Extrema B Section (m/s) Three dimensional Simulation Method L CFD (3D) Three dimensional CFD (3D) Section 9.1 J Section 9.4 B Section 3.8 L Section 56.4 J Section 57.4 B Section L One dimensional (1D) Three-dimensional One dimensional CFD (1D) (3D) One-dimensional (1D) () () In In,, processes processes volved volved wd wd (cludg (cludg period, period, amplitude, amplitude, attenuation attenuation rate, rate, itial itial phase, phase, etc.) etc.) 1D 1D 3D 3D methods methods do do not not differ differ ir ir () In curves curves almost, almost cocide processes cocide with with each volved each or. or. wd wd (cludg wd period, has has similar amplitude, similar rules, rules, when attenuation when we we compare rate, itial compare it it with phase, with etc.) 1D 3D methods a do. not differ. With With ir attenuated attenuated curves almost cocide with each a or. around around its its steady wd steady value, value, has wd similar wd rules, fluctuates when we compare fluctuates gradually it gradually around with around zero. water-level zero. se se results results dicate a dicate that that. wd With wd attenuated depends depends on on water-level a around its steady value, wd fluctuates gradually around zero. se results dicate that wd depends on water-level. negative

9 Energies 016, 9, Energies 016, 9, positive wd s (extrema) occur at time fastest water-level drop fastest re,. respectively. For th negative calculation case, positive because wd s fastest water-level (extrema) occur decrease at time greater than fastest fastest crease drop, fastest absolute re, value respectively. negative For wd th calculation extremum case, because greater than fastest that positive extremum decrease greater. than fastest crease, absolute value negative (3) With wd regard to extremum gas compressibility, greater than that 9 shows positive extremum gas pressure change. process Section (3) JWith that regard simulated to bygas usg compressibility, 1D method. It can 9 shows be found that gas pressure gas pressure change has process a slight Section, J that which simulated only fluences by usg gas 1D method. density, hence, It can be found gas compressibility that gas pressure has a slight, can be which ignored. only For fluences conditions gas density, general hence, load adjustment gas compressibility unit, range load changescan small, be ignored. so For above result conditions can always general be applied. load adjustment unit, range load changes On small, basso above above result analys, can always 1D be simulation applied. method, as proposed th article, can accurately On bas simulate above wd analys, 1D simulation method, as proposed a th durg article, can accurately transient process. simulate wd a durg transient process gas pressure change process Section J, as simulated by 1D method Analys Analys Influencg Influencg Factors Factors Effect Effect on on Wd Wd Speed Speed For For system system wd wd results results from from water-level, which, which maly maly depends depends on operatg on conditions operatg conditions transient process transient (i.e., load process rejection, (i.e., load load rejection, crease, etc. load [18 3]). crease, Next, etc. re [18 3]). a certa Next, re fluence a certa shape fluence shape (cludg length, (cludg al area length, al dip angle) area on wd dip angle) on dtribution wd change dtribution process. In th change, process. effects In th, above referred effects (two) above kds referred fluencg (two) kds factors on fluencg wd factors are on analyzed wd by usg are analyzed 1D method, by usg as proposed 1D method, s as proposed above. s basic parameters above. basic parameters are as follows: horizontal are arrangement, as follows: L horizontal = 500 m, arrangement, A = 0 m, F = L 500 = 500 m m,, θ A = 0. = 0 m, F = 500 m, θ = Effect Water Level Water-Level Fluctuation Process a Surge Tank four typical operatg conditions unit unit load load adjustment adjustment [18 3], [18 3], i.e., load i.e., load rejection rejection (LR), (LR), load crease load crease (LI), load (LI), first loadrejection first rejection n crease n crease (LRI), (LRI), load first loadcrease first crease n rejection n rejection (LIR), are (LIR), selected. are selected. Under se Under four se operatg four operatg conditions, conditions, water-level processes processes a a are shown are shown 10a. simulation 10a. results simulation positive results negative positive (extremum) negative envelope (extremum) curves along envelope curves along ax wd ax wdprocesses typical s processes (i.e., typical first s (i.e., last first ) are shown last s ) 10b d. are shown 10 shows 10b d. that: 10 shows that: (1) For case (extremum) envelope curves, absolute positive negative wd (extremum) values along ax present a gradually creasg lear tendency, whereas maximum positive negative wd values occur last. For maximum positive wd wd values, values, values values LIR LIR LI areli high are high low, respectively, low, respectively, whereas whereas values values LR LRI are LRI. are For. maximum For maximum negative negative wd wd values, values, values values LRI LRI LR arelr high are high low, respectively, low, respectively, whereas whereas values values LI LI LIR are LIR are.. plausible plausible cause cause above-described above described results results that that water-level curves curves between between LR LR LRI as well as between LI LIR cocide with each or durg itial period, when positive negative wd extrema occur.

10 Energies 016, 9, LRI as well as between LI LIR cocide with each or durg itial period, when positive negative wd extrema occur. Energies 016, 9, (a) (b) (c) (d) 10. Effect on processes a due to wd 10. Effect on processes water-level a due to wd. (a) processes a under four typical. (a) processes water-level a under four typical operatg conditions; (b) positive negative (extremum) envelope curves along ax operatg conditions; (b) positive negative (extremum) envelope curves along ax ; (c) processes wd at first ; (d) processes ; wd (c) last. processes wd at first ; (d) processes wd at last.

11 Energies 016, 9, () By comparg wd processes first last, first presents Energies smooth 016, 9, 95 curves, whereas last shows an apparent (i.e., superposition phenomenon). For superposition case last, low frequency sub-wave treated () By comparg wd processes first last, first as fundamental wave, which can be derived by usg water-level presents smooth curves, whereas last shows an apparent (i.e., superposition has process as first. high frequency sub-wave phenomenon). For superposition case last, low frequency sub wave treated as wave fundamental that canwave, be derived which can by usg be derived gas by elasticity. usg In th case, wave flowg gas wave has reflected by atmospheric process air as to first outlet.. fundamental high frequency wave sub wave corresponds to mass wave wave that its period can be derived equal by tousg period gas elasticity. water-level In th case, wave, whereas flowg its amplitude gas wave reflected fluenced by atmospheric by both air to outlet. fundamental water-level wave corresponds mass to flow mass wave. its period equal to wave period corresponds to elasticity wave; its period, (4L/B) proportional whereas to its amplitude length fluenced its amplitude by both proportional to gas ertia mass flow. amplitude. wave creases wave corresponds gradually along to elasticity ax from wave; its period first (4L/B) (i.e., proportional to length its amplitude proportional to gas ertia first it zero) towards last decreases gradually over time.. amplitude wave creases gradually along ax from first (i.e., first it zero) towards last decreases gradually over time. 4.. Effect Shape Ventilation Tunnel 4.. Effect Shape Ventilation Tunnel Length Ventilation Tunnel For different Length Ventilation Tunnel lengths (i.e., L = 100, 300, 500, m), simulation results For different positive negative (extrema) lengths (i.e., envelope L = 100, curves 300, 500, along axm), simulation wd results processes positive typical negative s (extrema) (i.e., first envelope curves along last ) ax are shown wd shows processes that: typical s (i.e., first last ) are shown shows that: (1) For cases different lengths, positive (or negative) wd (extreme)(1) For firstcases different, lengths, process positive curves (or negative) cocide wd with each or. (extreme) first, process curves cocide with each or. absolute values positive negative wd (extrema) along ax absolute values positive negative wd (extrema) along ax present a gradually creasg lear tendency. As length creases, absolute values present a gradually creasg lear tendency. As length creases, positive negative wd (extrema) last tend to re. absolute values positive negative wd (extrema) last tend to re. (a) (b) 11. Cont.

12 Energies 016, 9, Energies 016, 9, Energies 016, 9, (c) 11. Effect length (c) on wd ; (a) Positive negative 11. Effect length on wd ; (a) Positive negative (extrema) (extrema) envelope curves along ax; (b) wd processes 11. Effect on wd ; (a) Positive negative envelope curves along length ax; (b) wd processes first first ; (c) wd processes last. (extrema) envelope curves along ax; (b) wd processes ; (c) wd processes last. first ; (c) wd processes last. () As length creases, fundamental waves wd different s rema unchanged because flows different rema ; amplitude () As length creases, mass fundamental waves s wd different s rema () As length creases, fundamental waves wd different s period (4L/B) wave crease remarkably (because longer length, larger unchanged because mass flows flows different ss remarema ; amplitude period rema unchanged because mass different ; amplitude gas ertia ). superposition fundamental wave gas (4L/B) wave crease remarkably (because longer length, larger period (4L/B) wave crease remarkably (because longer length, larger waves leads to rg absolute values wd (extrema). ertia ). superposition fundamental gas ertia ). superposition wave fundamental wave waves leads to rg absolute values wd (extrema). waves leads to rg absolute values wd (extrema) Sectional Area Ventilation Tunnel For Area case Ventilation 4... Sectional Tunnel 4... Sectional Area different Ventilation Tunnel al areas (i.e., A = 10, 15, 0, 5 30 m ), simulation results positive negative (extrema) envelope curves along ax as well as ), For case al areas (i.e., =10, 10,15, 15, 0, For casedifferent different al (i.e., AA= 0, 30 mm ), wd processes typical sareas (i.e., first last ) simulation results positive negative simulation results positive negative(extrema) (extrema)envelope envelopecurves curvesalong along ax axas aswell wellas as have are shown 1. wd processes typical s (i.e., first last ) have wd processes typical s (i.e., first last )are shown have are shown1. 1. (a) (a) (b) (b) 1. Cont.

13 Energies 016, 9, Energies 016, 9, Energies 016, 9, (c) 1. Effect al area on wd. (a) Positive negative 1. Effect al area on wd. (a) Positive negative (extrema) envelope curves along ax; (b) wd processes (extrema) envelope curves along ax; (b) wd processes first ; (c) wd processes last. first ; (c) wd processes last. (c) 1 shows that as al area creases, period fundamental wd 1. Effect al area on wd. (a) Positive negative wave that al area remas unchanged, whereas fundamental amplitude gradually (extrema) 1 shows as creases, period wd envelope curves along ax; (b) wd processes decreases. period wave remas unchanged, whereas its wave remas unchanged, whereas amplitude gradually decreases. first ; (c) wd processes last. amplitude creases gradually to rg ertiaremas as al area creases. Sce period wavedue unchanged, whereas its amplitude decrease amplitude fundamental wave plays a leadg role, absolutewd wd 1 shows that as al area creases, period fundamental creases gradually due to rg ertia as al area creases. Sce decrease (extrema) values are reduced al area creases when we consider wave remas as unchanged, whereas amplitude gradually amplitude fundamental wave plays a leadg role, absolute wd (extrema) values decreases. superposition fundamental period wave waves. remas unchanged, whereas its are creases reduced gradually as al area creases we consider superposition amplitude due to rg ertia when as al area creases. Sce fundamental waves Dip Angle Ventilation Tunnel decrease amplitude fundamental wave plays a leadg role, absolute wd (extrema) values are reduced as al area creases when we consider For different cases dip angles (i.e., θ = 0, 10, 0, 30, 40, 90 ), simulation Dip Ventilation Tunnel waves. Angle superposition fundamental results positive negative (extrema) envelope curves along ax wd, 30, For different cases dip angles (i.e., θ =) 0, 10 are, 0 40, 90 typical s first last shown 13. ), Dipprocesses Angle Ventilation Tunnel(i.e., simulation results positive negative (extrema) envelope curves along ax wd For different cases dip angles (i.e., θ = 0, 10, 0, 30, 40, 90 ), simulation processes typical s (i.e., first last ) are shown results positive negative (extrema) envelope curves along ax wd 13. processes typical s (i.e., first last ) are shown 13. (a) (a) (b) (b) 13. Cont.

14 Energies 016, 9, Energies 016, 9, (c) 13. Effect 13. Effect dip angles dip angles on wd on. wd. (a) Positive (a) Positive negative negative (extrema) (extrema) envelope curves along ax; (b) wd processes envelope curves along ax; (b) wd processes first first ; (c) wd processes last. ; (c) wd processes last. From spection 13, we can fer that dip angle effect similar to that length From as described spection hereunder: 13, we can fer that dip angle effect similar to that length as described (1) For hereunder: different cases dip angle, positive (or negative) wd (1) (extrema) For different first cases are dip angle, process positive curves cocide (or negative) with each wd or. absolute values positive negative wd (extrema) along ax (extrema) first are process curves cocide with each or. present a gradually creasg lear tendency. As dip angles crease, absolute values absolute values positive negative wd (extrema) along positive negative wd (extrema) last tend to re. ax present () a As gradually dip angle creasg creases, lear tendency. fundamental As wd dip angles waves crease, absolute period values positive waves negative different wd s (extrema) rema unchanged; last tend to wave re. amplitude creases () because As dip gas angle ertia creases, direction fundamental augmented wd by weight waves component period gas when waves dip angle different res. s superposition rema unchanged; fundamental wavewaves amplitude leads creases to re because gas ertia absolute wd direction values augmented (extrema) at by weight. component gas when dip angle res. superposition fundamental waves leads to re absolute wd 4.3. Summary for Influencg Factors Effect Analys values (extrema) at. From perspective wave superposition ory, Sections reveal effective 4.3. Summary mechanm for Influencg Factors Effect a Analys as well as shape (cludg length, al area dip angle) for onward dtribution wd change From perspective wave superposition ory, Sections reveal effective processes a. as well as mechanm al water-level area a maly affect as well amplitude as shape fundamental (cludg length, waves. al period area fundamental dip angle) wave for onward can be determed dtribution by usg wd change processes. a length. water-level can greatly affect period amplitude as well as al area waves, whereas dip angle maly fluences affec amplitude wave amplitude. fundamental waves. On period bas fundamental results described wave above, can be we determed can deve some by usg appropriate water-level measures that. can length be adopted for practical purposes to can reduce greatly affect harm high period wd amplitude a. waves, whereas optimization, dip angleregardg fluences type load adjustment wave amplitude. as well as crease al area for a, most effective way to reduce wd. On bas results described above, we can deve some appropriate measures that can be adopted 5. Conclusions for practical purposes to reduce harm high wd a. optimization, regardg type load adjustment as well as crease al area for a aim th article was to adopt a 1D numerical simulation method to establh, most effective way to reduce wd. mamatical model system to derive a wd 5. Conclusions simulation method. reafter, from perspective wave superposition, effective mechanm s a shape for onward dtribution aim th article wd was tochange adopt processes a 1D numerical are dcovered. simulation major method conclusions to establh can be mamatical summarized model as follows: system to derive a wd simulation method. reafter, from perspective wave superposition, effective mechanm water-level s a shape for onward dtribution wd change processes are dcovered. major conclusions can be summarized as follows:

15 Energies 016, 9, (1) one-dimensional simulation method, as proposed th article, can be used to accurately simulate wd a durg transient processes. () wd can be superimposed by usg low frequency fundamental waves as well as high frequency waves. fundamental waves can be derived by usg water-level a. It has process to that first, whereas waves can be derived by usg gas elasticity correspond to reflected wave flowg gas by atmospheric air enterg outlet. fundamental wave corresponds to mass wave; its period equal to period water-level a its amplitude fluenced by water-level mass flow. wave corresponds to elasticity wave; its period (4L/B) proportional to length its amplitude proportional to gas ertia. amplitude a wave creases gradually from first (i.e., first zero) to last along ax gradually decreases over time. (3) water-level a al area greatly affect amplitude fundamental waves. period a fundamental wave can be determed by usg water-level. length can be used to greatly affect period amplitude waves, whereas dip angle fluences wave amplitude. simulation wd can be used to provide a good reference for design purposes. As a result, hydroelectric power plants can be operated safely energy production would become more stable over time. To summarize, simulation results a project case have been compared to results prototype measurements,, ir comparon establhes a good agreement. In any future work, we would conduct transient (model) experiments wd s for a to furr validate simulation method as proposed th article. Acknowledgments: Th work was supported by National Natural Science Foundation Cha (Project no ) Cha Scholarship Council (CSC). Author Contributions: Jiong Yang Huang Wang performed programmg works, simulations dcussions, wrote manuscript; Weijia Yang Wei Zeng conducted part case studies dcussions; Wencheng Guo engaged dcussion, coordated ma me th paper reved manuscript. All authors superved approved fal version manuscript. Conflicts Interest: authors declare no conflict terest. References 1. Davenport, A.G. Past, present future wd engeerg. J. Wd Eng. Ind. Aerodyn. 00, 90, [CrossRef]. Liu, Z.J.; Dong, T.T.; Fu, Z. Wd wd control system based on PMAC controller. Mechatronics 013, 3, Allegri, J.; Dorer, V.; Carmeliet, J. Wd measurements buoyant flows street canyons. Build. Environ. 013, 59, [CrossRef] 4. Xu, J.X. Experimental vestigation on wd traffic cave tailwater. J. Tianj Univ. 1994, 7, Ramponi, R.; Blocken, B. CFD simulation cross- flow for different olated buildg configurations: Validation with wd measurements analys physical numerical diffusion effects. J. Wd Eng. Ind. Aerodyn. 01, , [CrossRef] 6. Mo, J.O.; Choudhry, A.; Arjomi, M. Effects wd changes on wake stability a wd turbe a virtual wd usg large eddy simulation. J. Wd Eng. Ind. Aerodyn. 013, 117, [CrossRef] 7. Zhou, J.J.; Yang, J.D.; Wang, H. Study on function mechanm system for tailrace. Ch. Rural Water Conserv. Hydropower 01, 7, Streeter, V.L.; Wylie, E.B. Fluid Transients; McGraw-Hill: New York, NY, USA, 1978.

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