Hydropower Plants - Water hammer
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1 Eviometl Fluid Mecics / Hydopowe Plts 5/6 Hydopowe Plts - Wte mme - Suge tk Suge tk Ilet Glley / edce tuel Pestock Powe sttio Resevoi Muizio RIGHETTI, Rom GABL
2 Wt is??? evey (!!!) cge i te opetio = Pessue wve = Fee sufce -> Reflexio of te WH -> Limittio of te ifluece Suge Tk = volume potetil <-> kietic eegy
3 Diffeeces betwee wte mme d mss oscilltio momete uppe m log peiod (-5 sec) lowe m sot peiod i te ge of secods Pessue wve m Slow cges <- ieti m 3
4 Wy is WH poblem?!!! Pessue > esistce!!! (Cudy 4) cck 4
5 Wy is WH poblem?!!! Pessue < esistce!!! (Cudy 4) 5
6 Wt to do? - slowe cges -> - suge tk - i cmbe - pessue-egultig vlves (Cudy 4) 6
7 WH bsic equtios Fictioless pipe Wlls e igid, costt coss sectio A Iitil pessue upstem ed H Stedy coditios v -> closig vlve suddely t t= Tvels s wvefot wit wve velocity = mteil pmete of te pipe befoe fte (Cudy 4) Cge of te efeece system -> obseve tvels wit te wve 7
8 WH bsic equtios Cge of te efeece system -> obseve tvels wit te wve Resultig foce F o te CV Equl to te cge of mometum iflow outflow velocity Fo wve fot movig dowstem Rge of m/s m/s (Cudy 4) Pessue ed iceses fo eductio i velocity 8
9 Wve Popgtio Time t = e > Time t = L/ (Cudy 4) 4) 9
10 Wve Popgtio Time t = L/ + e Time t = *L/ (Cudy 4)
11 Wve Popgtio Time t = *L/ + e Time t = 3*L/ (Cudy 4)
12 Wve Popgtio Time t = 3*L/ + e Time t = 4*L/ (Cudy 4) 4)
13 Wve Popgtio wit (Giesecke d Heimel 4) 3
14 Wve Popgtio Refectio t te esevoi No fictio! Refectio t te vlve (Cudy 4) 4
15 Wve Popgtio wit fictio Refectio t te esevoi Lowe! Refectio t te vlve (Cudy 4) 5
16 Resevoi <-> Ded ed = - Icidet pessue wve F Reflected pessue wve f wit = f/f (Cudy 4) =!!! Icesig!!! 6
17 Cge of te coss sectio / Juctio Icidet pessue wve Reflected pessue wve A > A v < v (Cudy 4) 7
18 Wve speed = (Fluid Elstic Modulus/ Fluid Desity)^.5 wte t C: elstic pipe Pipe Elstic Modulus d dimete / tickess (Giesecke d Heimel 4) 8
19 Wve speed tick pipe cocete d stel wit oly cocete oly ock wit (Giesecke d Heimel 4) 9
20 How big is te effect of te WH? Joukowski Allievi Metod of ccteistics (MoC) Softwe
21 Joukowski s teoy!! Mx!!! wve speed cge of te velocity [m/s] * [m/s] [m/s^] gvittiol cceletio 9.8 [m/s] eeded we closig time t S < T R
22 Joukowski s teoy icludig closig time Relity: -> Allievi (Giesecke d Heimel 4)
23 How big is te effect of te WH? Joukowski Allievi Metod of ccteistics (MoC) Softwe 3
24 Allievi 4
25 Allievi s ppoc 5 Assumptio No fictio (I E = ) Costt pipe (si α = ) wit fixed boudy coditio (big esevoi) v << D v v λ siα g x p ρ x v v t v = = = = t p ² ρ x v x g t v t ² g x v d x p ρ t v x p v t p ² ρ x v Cotiuity equtio Mometum equtio Vey good expltio i Jege (977)
26 x 6 Allievi s ppoc Iitil vlue cuet vlue Depedig o time t d loctio x (Cudy 4) x L t f x L t f t x ), ( x L t f x L t f g v t x v ), ( Ide: two fuctios f d f e defied, wic - e ssumed s beig complicted pioi d we do t wt it to kow - deped o te boudy coditios - idepedet of time t - f+f= pessue wve
27 7 (Cudy 4) A Resevoi = costt -> Δ ve to be -> f =-f A Allievi s ppoc x L t f x L t f te pimy wve f is fully eflected t A totl eflectio wit evesl of te sig i i i i t f L t f L L t f L t f L t t / fo te fuctio f (t i ) is equl to f (t i -L/) oe peiod T R elie
28 Allievi s ppoc L tall T =,, 3,... fü B x = L Oly t te mi peiods d t B L x ( x, t) f t f t g L x v( x, t) v f t f t L x L x f, f, g v v f f,, f (t ) f (t L / ) -> oly f A B (Cudy 4) 8
29 Allievi s ppoc Iitil vlue f, f, g v v f f,, cuet vlue t time= *L/ f f,, g v v f f,, pevious vlue t time= *L/ f f,, g v v f f,, equl v v g f (,,v,v ) is ow fuctio depedig o oly kow vlues 9
30 Allievi s ppoc A v v st equtio g d equtio eeded fo exmples: v v B A B T T T T s s closig opeig v g (Cudy 4) 3
31 3 Allievi s ppoc v g g v wit pessue tio pipelie ccteistic tio of excess to stedy pessue Allievi s equtio (clssicl fom) -t eflectio t = T d eflectio t = T st eflectio t = T
32 Coectig Allievi wit Joukowski 3 s T T st eflectio t = T Abupt closue g v v g L / T T S by t = (Jege 977) pipelie ccteistic g v tio of excess to stedy pessue Remembe:
33 Fst closig T S T TS T g g v v g g v v t t T R T R 3T R 4T R 5T R 6T R T R T R 3T R 4T R 5T R 6T R 33 Slow closig d opeig TS T T S / T (t) (t) T R t t 4 T R 3T R 4T R 5T =T R s T R 5 T R 3T R 4T R 5T =T R s
34 Slow closig 34 T R T R 3T R 4T R 5T R T S m T R T R 3T R 4T R 5T R T S m T / T S S T T Asymptotic beviou S T T η S T T η S T T η η m m m m m m symptotes / fil vlue m m S m m T T T T T T S S m m m m m
35 Execise to Allievi L, d, s, Q Pipe: Dout=,4 m Tickess mm E(steel)=,* N/m E(wte)=,6* 9 N/m L= 4 m H= m Q =,6 m³/s Vlve: ζ = 384 x -,5 +,5 (x positio of te vlve; = ope, = closed)??? Joukowski (t) 35
36 How big is te effect of te WH? Joukowski Allievi Metod of ccteistics (MoC) Softwe 36
37 Clcultio MoC Cotiuity equtio descibig tsiet flow i closed coduits = ypebolic ptil diffeetil equtios Mometum equtio? solve? Metod of ccteistics (MoC) L + ukow multiplie * L = wit f.fictio fcto 37
38 Clcultio MoC wt ve totl deivtive if, tis is stisfied te Elimite te idepedet vible x -> Odiy diffeetil equtio depedig o t 38
39 Clcultio MoC fo ptil diffeetil equtio vlid eveywee i te x-t ple odiy diffeetil equtio vlid oly o stigt lie, if is costt = ccteistic lies (Cudy 4) 39
40 fute o i time Exmple MoC Regio II: imposed by te dowstem coditio bck Regio I: depedig oly o te iitil coditios excittios o bot sides: (Cudy 4) 4
41 Clcultio MoC fo wted kow fictio losses (depedig o Q P ) fist ode ppoximtio: (Q is costt fom A to P fo tis tem) stisfctoy esults /sot computtiol itevl eeded 4 (Cudy 4)
42 Clcultio MoC positive ccteistic equtio wit egtive ccteistic equtio two equtios = two ukows: H P d Q P H P bsed o oe ccteistic equtio boudy coditios fute dvced metods -> Cudy (4) (Cudy 4) 4
43 How big is te effect of te WH? Joukowski Allievi Metod of ccteistics (MoC) Softwe 43
44 Softwe Hydulic System EPFL Wte Hmme d Mss Oscilltio (WHAMO) 3. AFT Impulse moe ifomtio: Gidoui et l. (5) 44
45 Exmple WANDA 45
46 WANDA wokflow Most of te time! 46
47 WANDA 47
48 Refeeces Cudy, M. Hif: Applied Hydulic Tsiets. Spige, New Yok Heidelbeg Dodect Lodo, 4. DOI:.7/ Gidoui MS, Zo M, McIis DA, Axwoty DH. A Review of Wte Hmme Teoy d Pctice. ASME. Appl. Mec. Rev. 5;58(): DOI:.5/.885. Giesecke, J.; Heimel S.: Wssekftlge Plug, Bu, Betieb. Spige, Beli Heidelbeg, 4. DOI:.7/ Jege, Cles: Fluid Tsiets i Hydo-Electic Egieeig Pctice. Blckie, Glsgow Lodo, 977. WANDA Use mul 4.3, Deltes, Delft Hydulics, 4. (Gidoui et l 5) 48
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