Model to Prototype Correlation of Hydrofoil Assisted Craft

Transcription

1 eg.nr. K / A Nr Pro. K.G.Hoppe 45 Aster treet oerset West 70 el : Fax: Eail: astcc@hysucrat.co Website: Model to Prototype orrelation o Hydrooil Assisted rat by Pro. Dr.-Ing. K.G.W. Hoppe Foil Assisted hip echnologies cc at July 009

2 INDEX. Introduction. Diensional Analysis o hip esistance. Froude's Model est Method in Modern For 4. Hull orrelation 5. Hydrooil orrelation 6. Hydrooil-assisted rat orrelation 7. Exaples o orrelations 8. onclusions and ecoendations 9. eerences

3 . Introduction A hydrooil supported cataaran, known as Hysucat, was developed in the ecturer-esearch- Project at the Mechanical Engineering Departent, Division Marine Engineering at the University o tellenbosch in outh Arica 977/78 ater a qualitative odel test o an existing cataaran odel with a siple hydrooil spanning the tunnel showed up with 40% reduction o the pulling rope resistance in the ree-surace water circulating tunnel. he hydrooil had been designed to carry 50% o the crat s weight at siulated 40 knot top -speed. he strong resistance reducing eect could not iediately be explained especially as the hydrooil had quite a low aspect ratio which usually gives relatively low oil eiciencies. arger odels with hydrooils were tested subsequently and conired the 40% resistance iproveent. his lead to the Hysucat-esearch-Project which was to investigate the Hysucat design theory and optiisation o the Hysucat eect. he design o other Hysucat odels was originally strongly based upon odel tests and an early application to the odel hull o the IM cataaran Doloede was to design and optiise a oil syste or towing tank tests which also indicated a 40% resistance iproveent, see Hoppe []. he correlation o the odel results to the prototype ollowed the standard towing tank ethod used or planing hulls, see Phillilps-Birt. [4] and indicated that the prototype could also be iproved by about 40% due to the hydrooil action. ater studies o hydrooil boundary layer low and aeronautical test data on wing section shapes indicated that the standard towing tank ethod o correlation (with lat plate resistance coeicient data) was not suicient accurate when the saller research odels o cataaran crat were used in which the hydrooils reached eynolds nubers or which lainar and transitional boundary layer low appeared. he present report is intended to explain and suarize the ethods developed and applied to Hysucat towing tank tests which resulted in acceptable predictions o the prototype perorances. A considerable nuber o Hysucat odel tests were conducted since then which approved the elaborated Hysucat correlation by use o prototype eedback data. he largest sea-going Hysucat were the Halter E-at o 45/85t in UA and the hun ak ricat erry o 45/t in Hong Kong, or details and applications see the FAcc website at

4 . Diensional Analysis o the hip esistance 4 Diensional analysis to establish the diensionless groups which are used in the best presentation o the odel and prototype resistance. High-speed crat (Planing rat, Hydrooil rat, E rat, etc.) have no signiicant water line length when running at high speeds and the use o the ship length becoes eaningless. A typical length diension which applies to all crat is needed and was ound by use o the total displaceent o the crat when it is at rest (loating) () g with displaced volue in, = weight o crat in kn, = density o water in kg/ and g = acceleration o earth. he third square root o gives a eaningul and typical length diension which can be used to copare the various dierent types o ships: typic [] () he liting orces which have to carry the total weight o the crat are ade up o hull buoyancy orces and hydrodynaic hull and oil lit orces, as well as by aerodynaic orces (lit and cushion pressure orces). he total drag orce t o the crat is needed to deterine the required power to propel the ship. he hydrodynaic orces are assued to depend on the ollowing ain paraeters, on a typical length typic to describe the body shape as ship and odel have to be geoetrically siilar, the luid density and viscosity, the speed and the acceleration o earth g. urace tension and pressure p and soe sonic speed are let or ore detailed studies. he resistance orce t can now be said to be a unction o these paraeters,,, g () t typic, where is a sybol eaning "soe unction o". I we assue that this unction takes the or o a power law, then it ollows or the resistance a b c typic d c g (4) and we can apply Buckingha's Method, F.M. White 986, o diensional analysis. here are 6 variables and diensions involved, which eans we have to expect 6 - = diensionless independent so-called -groups,,,. he proble can be orulated with a suitable choice o repeating variables as a b c typic d (5)

5 a b c d typic g (6) 5 a b c d typic t (7) he equations can be written with the diensions o the paraeters involved as M a b d M c M (8) M M a b d M c M (9) a b d M c M (0) oparing alike exponents o both sides we get M 0 = a + d a = -d 0 = -a + b + c - d c = -d 0 = -b - d b = -d which gives d d e d d which indicates a type o eynolds nuber. Equation 8 results in M 0 = a a = 0 0 = -a + b + c + d c = +d 0 = -b - d b = -d

6 6 0 d d g g which is the Froude nuber or Froude displaceent nuber wherein is a signiicant length g g Equation 9 results in M 0 = a + d a = -d 0 = -a + b + c + d c = -d 0 = -b - d b = -d d d t d t d d d c which is the lit or drag coeicient. he ship resistance unction can be written as ollows t, g, 0 () and with g, ' t which gives in coeicient or g, ' ' = [eynolds nuber, Froude nuber] () For the hull and oil lit coeicient a siilar unction is achieved n e F, ''' () Equation and indicate that the resistance and lit coeicients are dependant on two dierent diensionless groups which cannot be satisied in a test on saller odels at the sae

7 7 tie because the kineatic viscosity o the luid or ship and odel reains substantially the sae. A saller odel would have to run aster than the ship speed in order to achieve the sae eynolds nuber, whereas ater Froude's law the odel speed ust be lower than the one o the prototype. Willia Froude developed a ethod 868 which allowed to overcoe the proble with the two scale laws and which is still applied in its principles today and which shall be explained in the ollowing chapter.

8 . Froude's Model est Method in Modern For 8 orresponding to Froude's aw o oparison which Willia Froude stated in 868 and which he achieved by careul and systeatical low observation on odels and ships the two ain resistance coponents, rictional resistance and residuary resistance (ainly wave-aking) obey dierent laws and have to be treated separately, the riction resistance coeicient being dependent on the eynolds nuber and the residuary resistance coponent coeicient on the Froude nuber. orresponding to Froude's hypothesis both resistance coponents do not inluence each other and Equation 4 can be written as ollows and with the rictional resistance coeicient F e n (4) e and the residual resistance coeicient (ainly wave-aking) Fn gives the well known equation (5) F eaning that the total resistance coeicient is ade up o the rictional resistance coeicient which obeys eynolds's law and the residuary resistance which ollows Froude's aw o oparison. In tests with saller geoetrical siilar odels (geosis) it was ound that both laws cannot be ollowed at the sae tie. It was W. Froude 868 who developed the ethod to correlate the odel test to the prototype which in its principle is still used in all towing tanks and which ollows the Froude aw in the odel test and corrects the result or the rictional resistance o the prototype. A geosis odel, in a scale ratio λ, is run in the towing tank at various Froude nubers (F n = F n ) covering the ull speed range o the ship and the odel total resistance recorded. he odel riction resistance is calculated, usually by use o the I-57 odel-ship correlation line, assuing that the rictional resistance is the sae as or a lat plate o siilar length and equal to

9 9 the wetted surace o the odel (ean wetted length and wetted surace o the odel have to be easured as well in the tank tests or each speed). he residuary resistance then becoes: = - with easured and calculated. (6) and then scaled up to the prototype ater Froude's law = (7) he rictional resistance o the prototype is then calculated, using the I-57 odel-to-ship correlation proposal, and added to the residuary resistance to achieve the total prototype resistance at the respective corresponding speeds or which the Froude nubers F n are the sae or odel and ship. (7a) For dynaically supported ships (Planing rat, E rat, Hydrooil rat, Hysucats, etc.) which are lited partly out o the water at speed the wetted surace and the ean wetted length have to be easured careully or each test speed. ainar boundary layer low along the hull has to be prevented to keep the low pattern o odel and ship siilar by use o suicient large odels ( e x 0 6, preerably larger than 5 x 0 6 ) and eicient turbulence stiulators. o ease the work o the towing tank sta a coplete correlation orula or the diensionless resistance coeicients and is developed in the ollowing chapter by use o the correlation actor corr, which is deined by the ollowing equation corr (8)

10 4. Hull orrelation 0 he above described Froude-ethod is used in a odernised or with properly diensionless paraeters in ost towing tanks nowadays. he odel resistance coeicient (or esistance-displaceent ratio) is ( with in N) (9) he odel residuary resistance coeicient is the sae or odel and ship. Equation 7 can be written in coeicient or as (0) and with Equation 6 ollows () he odel riction resistance is () with = wetted surace o odel hull in contact with solid water at speed. he riction coeicient depends on the odel eynolds nuber e and is usually deterined by use o the Model-hip-orrelation-line proposed by the I-57 and reads () og e with e = / and with being the kineatic viscosity o the tank water. It iplies that a ully turbulent boundary layer is necessary which eans eynolds nubers larger than Fro equation ollows (4) (5) he prototype residual resistance becoes now with equation 5

11 (6) he rictional resistance o the prototype ship is A (7) with A being the roughness allowance which accounts or the relatively rougher prototype surace than the one o the odel which should be hydraulically sooth. For the total resistance coeicient corresponding to equation 6 ollows F and the resistance becoes (8) M ] [ which gives with equation 7 A A A (9) With the scale up ratio or Froude s law o coparison = ollows or the total resistance A (0) For the resistance displaceent ratio ( and in Newtons) ollows then with equation 9

12 A A A M M A M M M A with and ) ) /( ( ) ) )( ( ( ) )( ( () with the odel total resistance coeicient being () And with Equation 8 the correlation actor or the hull corr results in A corr ) ( ()

13 he diagra in the sketch below shows the riction coeicient plotted over the eynolds nuber with an exaple o the odel and ship positions and the riction deduction coeicient ( - - A ) (4) indicated. Equation is used to correlate the odel bare hull data to the prototype. ketch : Friction deduction

14 5. Hydrooil orrelation 4 he hydrooil, rudders and siilar appendages in the Hysucat arrangeent or or oil-assisted ships have a relatively sall chord length in coparison to the ship length and their eynolds Nubers are thereor uch saller. In ost odel test series and especially or those research tests in the relatively sall acilities o universities the eynolds Nubers are saller than the ones required or ull boundary layer low over the hydrooils. he oil eynolds Nubers are in the region or transitional boundary layer low or the larger odels at the higher test speeds and in the lainar region or the lower speeds and or saller odels at ost speeds. he hydrooils in the Hysucats carry a load o 60% to 80% o the total crat weight and are ajor contributors to the total resistance o the crat. he accurate correlation o the oil orces is thereor o utost iportance to achieve a proper total resistance prediction. he hydrooils have to be correlated in separation o the hull correlation and the hull correlation orula, equation, needs a ore detailed analysis. he hydrooils on the odel show a dierent low regie than the prototype oils because o the large dierence in eynolds Nubers. he usual correlation based upon the Froude hypothesis in which the riction resistance coponent is scaled ater eynolds' aw and the residuary resistance coponent ater Froude's aw can not be used to extrapolate the oil resistance. As a result o the dierence in the oil low regie the intererence o the oil-hull low ight be changed as well especially when oil low separation o the odel is present but not on the prototype. hose eects cannot easily be accounted or in the extended analysis, but, are believed to be o inor iportance or the crat under consideration. he variation o the drag coeicients as a unction o the eynolds Nuber needs ore detailed attention. Hoerner 965 has collected oil drag coeicients at zero-lit ro any test series and shows a plot over the eynolds Nuber in Fig. o the publication which was reproduced by Kirkan et al. 980 (Fig. ). he drag coeicient o a oil section with a thickness-chord ratio o 0. is shown in Fig., the data points are reproduced ro the above publication. he hydrooil drag consists o a variety o coponents which can be suarised into two ain coponents, the induced drag and the zero-lit drag o. he induced drag is scaled by Froude's law. he zero-lit drag, however, is strongly dependent on the eynolds Nuber and ade up by two ain coponents, the tangential skin riction coponent and the pressure drag coponent due to separation o the boundary layer. he zero-lit drag is thereor also a unction o the oil thickness-chord ratio. ainar low separation occurs when the boundary layer pressure c gradient changes ro negative to positive (at thickest low cross-section). In transitional low the separation point depends strongly on the eynolds Nuber. Four ain eynolds Nuber regions or zero-lit drag can be distinguished:

15 5

16 6 U being the position where the lainar boundary layer changes over to a turbulent boundary layer. A being the position where the lainar or turbulent boundary layer separates ro the wing surace. a) the lainar boundary layer ollows the wing surace b) the lainar boundary layer changes at U to a turbulent one which ollows the wing surace to the trailing edge c) the lainar boundary layer separates at A ro the surace and reains separated ro the surace up to the trailing edge. d) the lainar boundary layer changes to turbulent at U with the turbulent boundary layer ollows the surace up to A ro which point on it separates to the trailing edge. he approxiate eynolds nuber or a, b, c and d are given in the text below. Fig. cheatic presentation o the boundary layer developent and separation on the suction side o a wing. he physical reason o the variation o the oil zero-lit drag can be easier understood by the scheatic boundary layer sketches in Fig. taken ro Eck [5] who sketched these conditions o low observations. In the ollowing the eynolds nuber ranges or the conditions a, b, c, d are given approxiately.

17 a) e 0 5 : he boundary layer low is lainar with separation near the axiu thickness point which leads to high drag coeicients or the thick oil sections. 7 b) 4 x 0 5 e 5 x 0 5 : he boundary layer low transition ro lainar to turbulent is observed with a strong decrease in drag coeicients at the critical eynolds Nuber o transition which is also dependent on the turbulence degree o the inlow and vibrations present on the odel. For eynolds Nubers saller than the one or transition the zerolit drag coeicient varies in proportion to the lainar skin riction coeicients (about parallel to Blasius line). c) d) 7 e 0 : he boundary layer transition point U oves slightly orward along the oilchord and separation appears near to the leading edge ro which point on the boundary layer reains separated to the oil end and the riction drag coeicients increase slightly e 0 : he boundary layer is turbulent ro near leading edge, and turbulent to a id position at which point separation appears and the zero-lit drag coeicient drops with eynolds Nuber proportional to the turbulent riction line (I 57), however, with slightly higher values which are due to the increased oil surace velocities (potential low lines) and the boundary layer separation (near to tail) drag. Kirkan et al. (980) have developed oil-zero-lit drag coeicients DO orulae which best approach the epirical data given by Hoerner (965) or the discussed eynolds Nuber regions and two oil thickness-chord ratios. he orulae are repeated as ollows: a) e : DO DO e e or or 0 (5) c c 0.0 (6) b) 50 4 e : 50 DO 5 : DO e e or c or 0.0 c 0 (7) (8) d) e : 0 : DO c c 4 (9) c) e 0 7 : DO 0.0 e 0.48 c 60 c 4 (40)

18 8 For oil thickness-chord ratios other than the given ones the data are interpolated or extra polated. he oil zero-lit coeicients DO are based upon the wetted surace areas o the oils (not the projected areas as usually applied or hydrooils!) with A b. oil c oil Fig. 4 shows equations 6 to 4 in graphical or together with the sooth turbulent riction line o the I 57 and the lainar riction line corresponding to Blasius as well as the zero-lit drag coeicient or a oil section with 0% thickness chord ratio and another ostly used section with a 7% thickness chord ratio. Here, the drag coeicients are shown in linear scale (not anyore logarithic) to indicate the relative dierences o odel and prototype drag coeicients. op speed eynolds nubers or typical odel and prototype oil values are indicated or a towing tank test with a long odel o a 6 Hysucat or 40 knot top speed. For the odel oil eynolds nubers ro zero to these top speeds lower oil eynolds nubers are encountered.

19 It shows that or a odel the oil boundary layer low alls into the turbulent low regie 6 7 with.40 but the prototype with 4.40 in the ully turbulent range. However, e e at the hup resistance speed which occurs at slightly lower than 50% o the top speed the odel 5 oil alls into the transitional boundary layer low regie with 6.40 whereas the prototype with e 7 e.00 reains in the ully turbulent regie. he above eynolds nubers o the odel are acceptable i the correlation ethod o hapter 5 and 6 is used. ee hapter 7 or details. 9

20 6. Hydrooil-Assisted hip orrelation 0 he above orulae allow the deterination o the zero-lit drag coeicients o the odel which allows the zero-lit drag orce to be calculated which has to be subtracted ro the odel total resistance beore the Froude correlation is applied. he prototype oil zero-lit drag by use o equations 40 and 4 is added to the total prototype resistance. he odel's induced drag is part o the residuary resistance and scaled up by Froude's aw (ultiplied by ). A coplete correlation orula or hydrooil-assisted ships was developed by extending equation 0 to include the above oil correlation x A n oil DO DO A (4) with n being the nuber o oils in the Hysucat arrangeent, x being the last oil, DO = oil zerolit drag coeicient, =odel oil zero-lit drag coeicient and A = oil roughness addition. Do Equation 4 can be sipliied as ollows with correlation actor corr or the Hysucat and gives or the corr corr x oil A DO DO A (4) n with oil being the wetted oil area or each oil ( ) and being the hull wetted area. c boil he inal hydrooil-assist-crat correlation actor to be corr corresponding to equation ollows than corr x oil A DO DO A (4) n and the prototype resistance-displaceent ratio is then = * corr (44) he zero-lit drag coeicient o oil and odel oil are deterined by use o the Kirkan et al.[] equations, equations Equation 4 and 44 are best applied in a coputer progra. An exaple o the correlation result o a 6 Hysucat tested in the towing tank with a odel will be shown in the next chapter.

21 7) Exaples o orrelations In the ollowing soe exaples o odel to ship correlation shall be given using Equation 4 in coparison to the older towing tank ethod which used the I57 odel to ship correlation line or the hulls and or the oils. A odel test series on the early Hysucat H9 with ully asyetrical deep--planing dei-hulls was conducted at the towing tank (9 x 4.50 x.70) o the University o tellenbosch, A. Fig. 5 Hysucat odel H9 In Figure 5 the odel is shown or general understanding with a standard Hysucat oil syste. Fig. 6 gives the odel resistance displaceent ratios ε ro which the input data to the orrelation Progra are derived and which are given in able I. he result o the correlation coputation is given in able II. Fig 6. owing ank esult o H9

22 he results o the correlation coputation is given in able II. In the Fig.4 o the original test report copied on Fig. 7 the new correlation ratios corr are plotted as red crosses on the sae diagra to copare it with old K corr data used in this early odel test. he odel eynolds nubers o the ainoil are also indicated on this diagra. It shows that the oil eynolds nuber at top speed is 5.4*0 5 which is still in the transitional boundary layer range. At hup speed the oil eynolds nuber is.*0 5 which is the range where lainarturbulent boundary layer low is doinant and or which the I57 riction coeicient is not applicable and or which odel speed a reduced odel lit creation can be expected. Inspite o this the correlation actor corr does not dier uch ro the older prediction and the reasons are that the oil orces are very low and have not uch inluence on the hull orces.

23 Fig 7. orrelation actor K corr and corr New and old correlation actors at top speed are nearly identical and this is expected as the oil eynolds nuber is 5.4*0 5 and near to the turbulent boundary layer range which starts with e = 5*0 5. Between hup and top speed the hydrooil operates at eynolds nubers in the transitional boundary layer low range and the zero-lit riction actor as given by Kirkan et al [] has to be used in the correlation calculation in Equation 4. he old ethod over-predicts the prototype by as uch as 0% at 7 knots prototype speed which is a substantial dierence and the new ethod o correlation described in this report is a necessity. here is another proble involved with the low hup speed eynolds nuber o,*0 5. he oil will have a lainar boundary layer ro the nose on to a certain distance downstrea and then the boundary layer will disconnect ro the oil upper surace which will give reduced lit creation. he odel will then sink in deeper and carry ore load with increased odel hull resistance which increases the odel hup resistance and predicts an unrealistic high hup resistance. his was observed on several odels and so ar there is no correlation correction ethod available, except to use larger odels. arger odels also need larger towing tanks which are not available at University s and the increased costs are prohibitive or the relatively sall crat in question.

24 Another exaple shall be applied to a odel test with larger odels which do not all in the eynolds nuber range saller than 5*0 5. uch test series were conducted on the odel o a 7 Hsyucat designed or the ürssen hipyard in Gerany by Pro. Hoppe and tested in the W-Berlin/ Gerany [6]. A photo o the odel is shown in Fig.8 4 Fig. 8 Model o Hysucat H7 he hup speed eyonolds nuber is 6,94*0 5 well in the turbulent boundary layer range. At top speed e =.4*0 6 and well in the turbulent range.

25 5 Fig. 9 H7 odel test result as oputer print-out Fig. 9 gives a copy o one speciic test condition no. 4.00/85 as the trolley onboard print-out or the whole speed range. he odel resistance displaceent ratios are taken ro the table in Fig. 9 and used in the new correlation calculation. he ratios o wetted area at speed and ean wetted length are taken ro Fig.0 and used as Input Data or the correlation progra shown in the able III with the result o the coputation in able I.

26 6 Fig.0 H7 odel wetted length and area ratio at speed Fig. shows the result o the old correlation calculation which treated hull and oil riction correction separately but by use o the I57 line or hull and oils.

27 7 he correlation result o the new coputation or corr is given in able I and the corr data are plotted onto the sae diagra in Fig. arked by a lag sign. It shows that the new correlation data corr agree well with the old ones ε s /ε. Fig. orrelation actor ε s /ε (old) and corr (new) his prediction is ree o scale eects or both ethods. he hup resistance speed has a eynolds nuber o nearly 7*0 5 and there will be little stalling eects on the ainoil with a turbulent boundary layer so that a proper odel oil lit creation can be assued. o be on the sae side the tests were run with a rake-run prior to the inally recorded test run or all lower speeds. he higher turbulent degree assures turbulent boundary layer low well attached to the oil top surace which prevents stalling eects.

28 8 Fro the above the conclusion can be drawn that the odel size is iportant or a precise resistance prediction, there are iniu odel sizes or the various projects based upon the size o the odel oil which should have a eynolds nuber larger than 5*0 5 or the hup speed which appears at a Froude Displaceent nuber around.4. he saller size o the irst odel is typical or University research projects and can deliver good results or the higher speeds. However, the prediction o the hup speed resistance is already aected by scale eects. In this case with an over-prediction o the resistance. For slower speed prototypes and large scale ratios the odel sizes shall be increased. 8) onclusions and ecoendations he report explains the correlation ro odel test to prototype data as it has been used at the towing tank at the University o tellenbosch or any years with good success. On the exaple o two earlier test series on Hysucat towing tank tests it is shown that the conventional correlation ethod which uses the riction actors o the I57 odel to ship correlation line does not give suicient accurate prototype predictions or saller odels and that the use o the presented new correlation ethod gives ore accurate predictions. However, it becoes clear that the size o the hydrooils has to be suiciently larger to operate at odel oil eynolds nubers larger than 5*0 5 in the odel s envisaged speed range ro hup speed to ull speed. he odel ship scale ratio is thereore depending on the hydrooil low conditions. arger and relatively slow prototypes thereore need larger odels than saller and aster crat. In ost towing tanks the trolley top speed is liited and this requires saller odels to be used or ast crat. he presented correlation ethod allows such saller odels but the prediction or the hupspeed resistance can contain scale eects due to the odel hydrooil producing reduced lit due to boundary layer disconnection ro the top surace o the odel oil which would not occur on the prototype oil. As a copensation ethod the turbulence degree in the tank water shall be increased to allow better connected low o the odel oil and proper lit creation. his is possible by running a low-rake prior to the test run or the lower odel speeds.

29 9) EFEENE 9 [] Kirkan, K.. and Kloetzli, J.W. (980), "caling Proble o Model Appendages", A, University o Michigan, Ann Arbor. [] Hoerner,.F. (965), "Fluid Dynaic Drag", Hoerner Fluid Dynaics, Brickton, New Jersey. [] Hoppe, K.G.W. (979), Model tests on IM ataaran Doloede, echnical eport, Bureau or Mechanical Engineering at the University o tellenbosch, A, 5 July 979. [4] Philipps-Brit, D.,AMINA, hip Model esting, International extbook opany td., ondong, 970. [5+ Eck, Bruno (944), echnische troeungslehre, pringererlag Berlin, 944. [6] chwanecke H., Hoppe K.G.W., Nicolaysen k.h. (985), Widerstandsversuche uer Hysucat 7, eil I ragluegelanordnung Avion, Bericht No. 046./985 der ersuchsanstalt uer Wasserbau und chibau, Berlin/Gerany (restricted) *7+ Hoppe, K.G.W., Hysucat 9 owing ank est, esistance, Internal eport, Mechanical Engineering Departent o the University o tellenbosch, outh Arica, August 986.