4 CAVITATION AND PRESSURE IMPULSES INDUCED BY THE PROPELLER**

Transcription

1 4 CAITATION AND PRESSURE IMPULSES INDUCED BY THE PROPELLER** The chief ai in thi ection i: to how how the cavitie on a roeller blade working in a wake change volue during one revolution to how how the cavity thereby induce reure iule on the urface of the hull and in the urrounding fluid to how that cavitation i the ot efficient noie generator on board the hi and that it i oible to tudy thi "generator" in a cavitation tunnel before the hi i build At the different radii in the roeller lane the inflow velocity to the roeller will vary with the angular oition of the blade. The velocity i at a iniu when the blade i in the uer oition a indicated in Fig.4.3 and Fig.4.4. If the roeller blade "ee" different velocitie, the angle of attack during one revolution will vary a ketched in Fig.4.3. When it ove toward the to oition, the angle increae, C L increae, the reure on the uction ide decreae and the cavity finally tart to grow. Fig.4.3 illutrate how the thickne of the cavity increae with increaing angle for a contant external reure. The volue of the cavity i tie deendent and it growth a ource of cavitation noie and reure iule. The reure iule caue vibration in larger art of the hi and give crack in the lating. The following contribute eentially in generation of reure iule and noie. 1. Motion and thickne of the blade. Motion and thickne of the cavity 3. Increae in cavity volue with tie 4. olue and volue variation with tie of the ti vortex 5. Lift of the blade 188

2 Fig. 4.1 Wake ditribution for ingle-crew hi without working roeller 189

3 Fig. 4. Different tye of frae in the afterbody 190

4 Fig. 4.3 Blade oition, wake field and cavitation volue 191

5 Fig. 4.4 Growth of cavity volue due to hi wake field 19

6 Fig. 4.5 Predicted full cale wake ditribution 193

7 Fig. 4.6 Cavitation tunnel aft body duy odel 194

8 Fig. 4.7 Axial wake circuferential ditribution 195

9 Fig. 4.8 Cavitation Sketch, 15 degree blade oition 196

10 Fig. 4.9 Cavitation ketch, 30 degree blade oition 197

11 Fig Cavitation ketche, 45 degree blade oition 198

12 Fig Cavitation ketche, 180 degree blade oition 199

13 Fig. 4.1 Cavitation ketche, 345 degree blade oition 00

14 Fig Reult fro reure eaureent 01

15 Fig Exale of ditortion in roeller cavitation 0

16 Fig Different tye of cavitation develoent 03

17 Fig Fig The reure ignal a a function of tie t at the collae of a heet caviy on an ocillting foil 04

18 Fig Scheatic behaviour of a ulating cavity and the radiated reure 05

19 Fig Tyical ignal (t) fro a cavitating roeller. a) Scheatic. b) Exale fro odel tet 06

20 Fig. 4.0 Nuclei content in ea water (fro Iay) 07

21 Fig. 4.1 Non-dienional noie level 08

22 Fig. 4. Preure eaureent reult and concluion 09

23 The reure at an occaional oint on the urface of the hull or in the water induced by the roeller i according to Bernoulli equation: φ 1 i = ρ - t R where t = tie R = reulting velocity φ = velocity otential in the oint due to different contribution a entioned above. The thickne i iulated with ink and ource on the urface of the roeller blade. Thi i illutrated by the following exreion for the induced velocity n noral to the cavity on the blade: τ(r, ϕ,t) τ(r, ϕ,t) n t n n= R + where τ = cavity thickne. The firt art i identical with an exreion already known fro the "frozen" condition. The econd link i an exreion for the dynaic in the roce. Returning to the exreion for the induced reure a ilification i deirable: The reulting velocity i then exreed a: R x ) y z = ( + U +U +U where U x, U y, U z = roeller induced velocity reectively in the x, y and z- direction. The induced velocitie are all relative to, which i the ain velocity. If all U link are equal to 0: = + Ux R If thi i ued in the exreion for i : = i φ ρ - t φ x 10

24 neglecting 1 / which i contant. Only the variable reure i of interet, which lead to the following exreion for the roeller induced reure: = ρ ω - ( φ 1+ φ + φ 3 + φ 4 + φ ) ϕ n x i 5 With reference to the different contribution entioned earlier. ϕ n = angular oition for blade nuber n The roble i now to deterine the ource/ink ditribution and it deendence of the blade oition. Many attet have been ade in order to etiate i for a given roeller and a given wake ditribution. But ince the theory till ha it hortcoing, odel tet and full cale eaureent are required to deterine the relation between i and ϕ n. On Fig.4.5 Fig.4.13 reult fro uch eaureent alying reure cell on a odel of an after body in the cavitation tunnel i hown. To kee control with cavitation and reure iule i one of the chief tak in the deign of a roeller. Two araeter are of ecial interet in reduction of reure iule. Thee are: 1. Proeller geoetry. Wakefield or wake ditribution Different after body hae (Fig.4.) give different wake field. It i not necearily the abolute ean value of the wake w (r,φ ) that i iortant. It follow fro the exreion for n that the derivative of the cavity thickne with tie i ore iortant. Thi indicate that trong gradient in w (r, φ n) ay give large reure iule. Cloely related to the develoent of reure iule i the generation of noie. Preure iule are low frequent while roeller induced noie due to ocillation fro ingle bubble and cluter of ingle bubble covering the entire frequency range. If a cavity on a blade, which ae through a wake eak, i tudied different tye of cavitation will be oberved. The urface ay be covered by a ilvery area or bubble that ae into a cloud looking heet or into cluter of bubble. The cavitie ay a well roll u in auage like vortice. Thi i illutrated in Fig In Fig.4.15 the dynaic in the develoent of cavitation ketched for different alternative. Coon for all cavitie i that they in reality are collection of tiny bubble. One thing i that a cluter of bubble can increae or decreae in volue. Further each bubble a well ay increae and decreae in volue. When a bubble or a cluter of bubble ilode, the local reure ay increae violently. Thi end hockwave toward the urface of the blade and the reure i o high that blade aterial i haered out and finally eroded. Thi roce i accoanied by noie. 11

25 A different echani i that the cluter of bubble divide in two art and induce a jet hitting the urface with very high velocity. Both thee rocee are illutrated in Fig In Fig.4.17 it i illutrated how the reure ignal i when the bubble ilode on the urface of the foil in tie deendent flow. It i oberved that large reure ocillation ay ring u and lat only a few illiecond. Within a given volue of eawater there are an infinite nuber of all bubble filled with ga. Each of the ha a radiu R(t) that varie with the tie t. Due to the variation in volue there i a variation in reure induced by the bubble at a ditance r fro the bubble.. ρq ρ(r R + R (r,t)= = 4 π r r R) (Fitzatrick) where R = radiu of the bubble R = velocity of the urface of the bubble R = acceleration of the bubble urface Q = volue of the bubble r = ditance fro the bubble to a given oint Thi i in linear acoutic and in incoreible flow the claic aroach. In Fig.4.18 the behavior of a ulating cavity that follow thi law been tudied over tie. It i oberved how har to originate and how the bubble collae and arie again. How cluter of uch bubble grow and break off fro the ain cavity when the roeller blade ae through the wake field i hown on the figure 4.14 and When a cluter of uch bubble are ocillating with different hae, violent reure eak a already entioned arie with noie and eroion a a conequence. Thi i illutrated in Fig.4.18 and Fig The following exreion for the radiu of the cavity i often alied: R rel R rel 3 + R rel 1 = - ( σ +C ) (Pleet) where R R rel =, (R 0 = R ax ) R 0 σ = cavitation nuber C (x,t) - 0 = = local reure coefficient ρ 1

26 (x,t) - v σ + C =, exreion for the driving reure ρ or difference in reure between the outide of the bubble (rofile) and the vaor reure v. 13

27 Scaling of Meaured Noie due to Cavitation The chief intention in thi ection i to how how roeller noie i eaured in a cavitation tunnel and later i caled to full cale noie In a cavitation tunnel or in full cale, it i oible to eaure the ound reure. If the ean reure i taken over the bandwidth a f a in Fig.4.19b, the ound reure on the hi odel i exreed a: ( f ) f f = a f f ( f,a f ) = ρ (r/d ) Where: = characteritic velocity of the odel r = ditance fro the noie ource to a given oint D = characteritic dienion like the roeller diaeter The eaured ound reure in odel i caled to the following ound reure in fullcale: = ( f,a f) r r D D ( ρ ) ( ) ρ If a bubble i growing due to the driving reure, the growth i decribed by: R(t) = ( 3 ) ρ where t i the growing tie. It ha a collae tie given by T c = k 0.5 ρ D ( ) t

28 The frequency in odel and in full-cale i: ρ f T D ρ σ = = f T D ρ ρ σ f f 1 n = λ n where λ = cale n = nuber of revolution A requireent for the caling ade above i that It i alo aued that: σ =σ S J = i equal for odel and full cale. nd It i now oible to cale both ound reure and correonding frequency: The ound reure i norally reented a "root ean quare"-value (r---value) Dienionle the reure i exreed a: K = ρ n r D L P i the baic eaure for ound reure and i defined a follow: L = 0 log db 0 where i the reure at a given oint and 0 i the reference reure. When two level are coared thi i done in the following way: log 1 L = L L 1= 0 In Fig.4.1 we have hown reult fro eaureent of noie fro a cavitating roeller. The roeller wa working in a cavitation tunnel behind a odel of the after body. Frequency and reure i caled to full cale and the reult coared with full-cale eaureent. The eaureent are ade with a certain content of air diolved in the water. In the actual cae, the air content i 40 %. Thi ean that: α = α 15

29 where α = air content α = air content when the water i aturated with air. It i iortant to kee the air content and the nuclei content at a contant level becaue diolved air and ga are the origin of the cavitation bubble. See Fig.4.0. α If the water i dead or low, it will be difficult to generate cavitation at all. The higher α α the earlier the cavitation tart. α The air content and denity of nuclei hould therefore be equal in odel and full cale. The ditribution of bubble ize hould alo be identical. Soe laboratorie do only control the air content. It i clear fro Fig.4.1 that the ratio between velocity and nuber of revolution i aroxiately contant. ( ) n( r ) n Thi ean that the ot iortant odel law i fulfilled. Becaue we have the ae J value in all cae, K T and C L (r) are equal for all nuber of revolution. Conequently, extent of cavitation and noie hould be equal, which the caled ound reure alo indicate. The ound reure i ade dienionle by dividing with ρ n D 16

30 5 LITERATURE Bark, G. On the Mechani of Proeller Cavitation Noie, Diviion of Mechanic, Charer Univerity of Technology, S Gothenburg Brelin, J.P and Anderen, P, Hydrodynaic of Shi Proeller Cabridge Univerity Pre Carlton, J. S "Marine Proeller & Proulion", Bitterroot-Heineann Dickann H.E, Weiinger, J "Beitrag zur Theorie Otialer Düenchrauben Kortdüen" Jahrbuch der STG bd 49,1955 Dyne, G "A Method for the Deign of Ducted Proeller in a Unifor Flow", Meddelanden från STATENS SKEPPSPRONINGSANSTALT Nr Dyne, G "An Exeriental erification of a Deign Method for Ducted Proeller", Meddelanden från STATENS SKEPPSPRONINGSANSTALT Nr Englih, J.W Rowe S.J Soe Aect of Ducted Proeller Proulion" Syoiu of Ducted Proeller", The Royal Intitution of Naval Architect London Suer Gibon, I S,"Theory and Nuerical Analyi of Single and Multi-Eleent Nozzle Proeller" Reort No.LR-579 TU Delft, February Iay W. H, Kavitation Schiffahrt - erlag Hana Kücheann, D.Weber, J "Aerodynaic of Proulion", Publication in Aeronautical Science, Mc Graw - Hill Publihing Coany LTD LONDON Mailge, Ch.1991,"Konzetion und Analye eine integrierten Strahlbetriebe it eine rotationyetrichen Grenzchichteinlauf", Doctor Thei, Techniche Univerität Berlin, Gerany, D83 Minaa, K.J, 1993,"Flow Studie with a Pitot Inlet in a Cavitation Tunnel", Contribution to the 0 The ITTC Workho on Water jet. San Francico, U.S.A, Set.0. Minaa, K. J and Lehn, E "Hydrodynaic Characteritic of Rotatable Thruter". NSFI Reort R-69.78, Minaa, K.J, Jacoben G.M and Okaoto H The Deign of Large Ducted Proeller for Otiu Efficiency and Maneuverability". Syoiu of Ducted Proeller, The Royal Intitution of Naval Architect London Suer Steen and Minaa, Fat 95, Lübeck - Traveünde Svenon, R, 1994,"Waterjet Proulion- Exerience fro High Powered Intallation" International Syoiu on Water jet Proulion - Latet Develoent RINA, London, U.K.No.3 17

31 van Manen, J.D " Recent Reearch on Proeller in Nozzle" Journal of Shi Reearch, vol.1, no., Terwiga, T.van1993"A Theoretical Model for the Powering Characteritic of Water jet-hull Syte" Proceeding of FAST 93" S.N.A.J. ITTC 1996 Proceeding of the 1t International Towing Tank Conference Trondhei, Norway Seteber 15-1,

32 6 SYMBOLS General = hi eed U A = axial induced velocity in the roeller jet A 0 = dik area or cro ection area of the roeller jet A = roeller dik area or rojected blade area D = roeller diaeter L = length of the duct Ducted Proeller ρ 1 = = reure dro in front of the roeller dik ρ = + UA ( ) = reure ju behind the roeller dik T = A 1 1 ρ = roeller thrut ( + ) = A + U A U A 1 = + U A + δ A + U A = total velocity through the roeller dik A 0 = ( ) δ A = A 0 by the duct U + A A A = velocity through the roeller dik induced T U A 0 = ρa + + δ U A = total thrut of the ducted roeller ρ U A ( ) P= A δ UA = change in energy flux 19

33 η = T0 = P U + A = ideal efficiency C T = T ρ A = thrut loading of the roeller U A 1+ C 1 = induced axial velocity in the roeller jet = T η = = ideal efficiency of ducted roeller τ CT 0 T τ = T 0 U A 1+ = U A δ 1+ + = ideal ratio between roeller thrut and total thrut 1+ τ = 1+ C 1+ C T T = ideal ratio between roeller thrut and total thrut C D f = reitance coefficient of the duct baed on wetted urface 1 + U A Ducted Proeller according to an Manen B RPM HP = S ( 1 w).5 D RPM δ = S ( 1 w) RPM = nuber of revolution r inute 0

34 = hi eed in knot w = wake D = roeller diaeter in feet HP = delivered ower in horeower σ + ρgh 0 v = =cavitation nuber ρ 0 0 = atoheric reure v = reure of aturated vaor h = ditance to the urface 0 S 1 ( ) = w w = wake = hi eed in / Tunnel Thruter ρ 3 P= A Ua = ower delivered to the water in the jet T = ρ A U = ideal thrut 0 a U a = T ρa P = ρa = ideal induced velocity in the jet 1

35 T η = D ( N) P D = factor for thrut gain ζ rot = reure loe due to rotational energy in the jet ζ drag = reure loe due to vicou flow on the blade η = 1 ( τ + ζrot + ζdrag ) Cavitation σ + ρ g h ρ π nd 0 v = = cavitation nuber Water jet Q j = flowrate A j = outlet area 0 = velocity of the craft M j =ρ Q j j = oentu flux at tation j (N) E j ρ Q A = ( ) =energy flux (W) j 1 = inlet velocity ( ) M = M M = ρ Q = total change in oentu flux (N) j 0 j j 0

36 Suction Force and Reitance of the Inlet Li for an Iered Inlet 1 C Dr = (1 ) 0 = reitance of a har edged inlet ρ 1 FS = ( n 0) dan = A1 1 0 = ideal uction force C DS FS = = ρ 0 A1 1 (1 ) 0 Fluh Inlet ( ) ( ) ( ) u z = + u z + u z = velocity near the inlet 1x 0 fr u (z) = change in velocity due to otential flow u fr (z) = change in velocity due to frictional flow along the hull z Q = u ( z) b( z) dz= volue flow rate at z in the boundary layer 1 1x 0 Q bal = volue flow rate inide boundary layer. Q j = volue flow rate of the jet E ( ) =local energy velocity at tation j: 1 z ρ ρ z = u z + ( ) ( ) ( ) E1 1x = local tatic reure at tation 1. 0 = abient reure in unditurbed flow. u1 x z ( ) = eaured velocity near the inlet δ = 0.37 x R N -1/5 (Prandtl) = boundary layer thickne of the odel 1 7 N δ = 0.16 x R (Wieghardt) = boundary layer thickne of the hi 3

37 x = flow length R N = Reynold nuber baed on flow length in front of the inlet. Moentu Flux and Change of Moentu Flux ( ) = oentu flux at the outlet and at tation 7 7 = ρ 7x M u da da Q = = oentu flux at the outlet and at tation 7 j M7 ρ Qj A j M = M 7 M 1 = change of oentu flux between out and inlet M 1 = oentu flux at the inlet or oint 1 Energy Flux and Lo Coefficient ρ ρ E1 = b1( z) E1( z) u1x( z) dz 0 ( Qj Qbl) + = energy flux at the inlet or at oint 1 (W) Q bl = volue flowrate inide boundary layer Q j = volue flowrate of jet b 1 (z ) = width of the uction area at z E7 ( r) u ( r ) + u ( r ) + ( ( r ) ) = 7 x 7 7Φ 7 ρ = energy velocity at oint 7 ( r ) ( r ) U 7Φ 7 0 = 7 r7 7 ρ dr = reure at oint 7and at radiu r 7 4

38 ρ E ( ) 7 = E7 r7 u7x da7 = energy flux at the outlet (W) E7 Q A 7 ρ Q = = energy flux at the outlet P JSE = E 7 E 1 = change in energy flux between tation 7 and tation 1(W) E E 5 7 ζ 57 = = outlet or diffuor lo coefficient E7 ζ 13 = E E 1 E 0 3 = inlet lo coefficient E ρ = Q = energy flux at oint 0 (W) 0 j 0 1 Q J E3 = QJ ρ = energy flux at oint 3 (W) A 3 Power and Total Head P = ρ g Q h = lifting ower (W) h j j P = P + P + E ζ + ζ E = ρ g Q j H 35 = effective u ower (W ) PE JSE h H = E + E + E + h = total head () ( ζ ) ζ13 j ρ g Q J Cavitation and Ieller Characteritic RPM Q n q = = ecific nuber of revolution 3 H

39 n q RPM Q = = uction nuber 3 4 h 0 v 1 ζ13 h= + E0 hj = uction head ρ g ρ g Q C C Q H Q = = torque coefficient 3 n D = g H 35 ( n D) = reure coefficient η C C π K = Q H = u efficiency Q K Q M = = torque coefficient 5 ρ n D M = torque K T T = = thrut coefficient 4 ρ n D η ρ g Q H 35 = = u efficiency PD : P D PPES = η η int = ower delivered to the haft (W) η int = intallation efficiency ( ). Proeller Induced Preure Iule φ 1 i = ρ - t R = reure induced on the hull fro the roeller t = tie φ = velocity otential due to different contribution. 6

40 τ(r, ϕ n,t) τ(r, ϕ n,t) n= + = exreion for induced velocity n noral to the t cavity and the blade: τ = blade thickne. R = ( U x) U y U z = reulting velocity U x, U y, U z = roeller induced velocity reectively in the x, y and z-direction. = φ - φ i ρ =roeller induced reure t x i= ρ ω - ( φ 1+ φ + φ3+ φ4+ φ5) = roeller induced reure ϕ n x ϕ n = angular oition for blade nuber n. Q ρ (R R + R R) ρ (r,t) = = 4 π r r = reure induced by a bubble at a ditance r R = bubble radiu R = velocity of the bubble urface R = Acceleration of the bubble urface Q = volue of the bubble r = ditance fro the bubble to a given oint R rel = R R 0 = radiu of the cavity R 0 = R ax R rel R rel 3 + R rel σ = cavitation nuber 1 = - ( σ +C ) (Pleet) 7

41 C (x,t) - = = local reure ρ / 0 8

42 Sound reure ( f,a f ) = ρ (r/d ) =ound reure in odel = characteritic velocity r = ditance fro the noie ource to a given oint D = characteritic dienion (roeller diaeter) = ( f,a f) r r D D ( ρ ) ( ) = ound reure in full-cale ρ ρ f T D ρ σ = = f T D ρ ρ σ frequency = ratio between full-cale and odel cale L = 0 log db = eaure for ound reure 0 = reure at a given oint 0 = reference reure. 1 L = L - L 1= 0 log α = air content = exreion for the relationhi between 1 and α = air content near the aturation oint. 9

43 7 INDEX advance ratio, 119 air content, 17 aect ratio, atoheric reure, 6, 50, aziod, 1 blade hae, 6 bow thruter, 39, 130 bubble, 1, 15 bubbleradiu, 13, 9 cavitation,, 77, 8 cavitation noie, 189 cavitation nuber, 6, 41 cavitation tunnel, 6, 1 cavity, 189, 13 change of oentu, 1 change of volue, 189 contra rotating roeller, 14, 8, 94, 96, 11 contraction, 38, 39 Dickann and Weiinger, 1 drag, 39, 3 duct induced velocitie, 13 duct length, 11, 15, 8, 0 duct thrut, 14, 7, 77 ducted roeller, 11, 1, 7, 8, 37, 117 efficiency, 10, 11, 6, 8, 38, 105, 117, 119, 18 ellitical blade hae, 6 fin, free vortex, gain in thrut, 38, 40 houe, 94, 105, 107, 109, 117, 118, 119, 10, 18 hydrofoil boat, ierion, 8 induced drag, induced velocity, 49 interference, 77, 105, 106, 107 internal loe, 38 Kalan, 6, 40, 77 lift, liited ierion, oentu, 3, 49 noie, 41, 49, 130, 1, 13, 16, 17 noieource, 189, 15, 31 nuber of rev, 41, 77, 105, 18, 16, 17 oen water diagra, 6, 105, 10 otiu roeller diaeter, 6 ower, 14, 15, 36, 37, 38, 49, 51, 77, 96, 117, 10, 11, reure ditribution,, 94, 189, 1 rofile drag, roeller arrangeent, 94 roeller dik area, 11, 107 roeller induced velocity, 11, 9 roeller loading, 80 roeller ower, 80, 117 roeller thrut, 10, 11, 14, 15, 7, 39, 77, 107, 117, 18 roeller torque, 36, 77, 18 roulor, 95, 117, 119, 11 ulling roeller, 94, 95, 107, 117, 18 u efficiency, 38 uhing roeller, 95, 18 relative rotative efficiency, 8, 119 reitance, 11, 6, 39, 49, 94, 105, 108, 118, 119, 18 ring vortex, 13 ring vortex cylinder, 13 aturation reure, 6, an, tande roeller, 95 thruter, 37, 40, 77, 117, 1 tie-varying lift, total efficiency, 11 total thrut, 10, 7, 39, 105, 10, 18 tunnel thruter, 10 ventilation, vicou loe, 39, 3 oith Schneider, 8 vortice, wake, 15, 6, 8, 49, 50, 94, 119, 10, 11, 130, wake field, 10 odel tet, 1, 15, 7, 117, 11, 18, 1 30