Ffth Internatonal Symposum on Marne Propulsors smp 17, Espoo, Fnland, une 2017 RANSE-based Smulaton and Analyss of Scale Effects on Open-Water Performance of the PPTC-II Benchmark Propeller Xao-Qan Dong, We L, Chen-un Yang *, Francs Noblesse Collaboratve Innovaton Center for Advanced Shp and Deep-Sea Exploraton (CISSE), State Key Laboratory of Ocean Engneerng (SKLOE), Shangha ao Tong Unversty, Shangha 200240, Chna ABSTRACT Ths paper presents our numercal study of the scale effects on a tp-rake propeller, the PPTC-II, based on the RANS smulatons usng software FLUENT 6.3. The low Re opton n SST k- model s adopted at, together wth fne prsm grds to resolve the vscous sublayer. At, standard wall functon s adopted. The scale-effect correctons yelded by our RANS smulatons are compared wth those obtaned from the ITTC method. To explan the CFD results, an analyss of sectonal forces s performed. To nvestgate how the tp rake nfluences propeller scale effects, the geometry of PPTC-II s modfed by removng the tp rake only, and the RANSpredcted scale effects for the modfed propeller, PPTC- II-m, are compared wth those for the PPTC-II. The study ndcates that the scale effect on propeller thrust can be as mportant as that on the torque; somehow the RANS- and ITTC-based predctons for full-scale effcency agree qute well; the tp-rake reduces tp loadng and tp vortex strength, and brngs about large dfferences n the scale effects as compared wth the propeller wthout tp-rake. Keywords Propeller; tp rake; open water; scale effect; RANSE 1 INTRODUCTION Theoretcally, the scale effects on propeller open water performance need to be corrected for when predctng the powerng performance of a shp. The emprcal formulae n the 1978 ITTC Performance Predcton Method (ITTC 2014) (referred to as the ITTC method herenafter) have been wdely used for the correcton. In the ITTC method the amounts of correcton to model-scale thrust and torque coeffcents depend on the model- and full-scale secton drag coeffcents at 0.75R, the chord and ptch ratos at the same radus, and the number of blades, where R denotes propeller tp radus. Apparently, the correctons would be the same for two propellers whch dffer n the skew and rake only. Specal tp geometres, such as the tp endplates and tp-rake, are not accounted for n the ITTC method as well. For more accurate predcton of the performance, t s necessary to know how and to what extent the geometrc parameters not consdered n the ITTC method would nfluence the results of scale effect correctons. To elucdate the problem and update the present ITTC method for correctng propeller scale effects when possble, the Propulson Commttees of the 27 th and 28 th ITTC ntated a computatonal campagn n each term of servce usng the PPTC, a conventonal hghly skewed propeller, and the PPTC-II, an unconventonal propeller wth the tp-rake, respectvely. The two test cases were provded by SVA Potsdam, and the data are avalable to the publc at the company's webste. In fact, vscous flow CFD smulaton has been almost the only approach for the research of propeller scale effects snce the last century (Staner 1998). The extensve lamnar flow regon at the Reynolds number of 2~3 10 5 s an ssue whch necesstates the use of very fne prsm grd layers to resolve the vscous sub-layer and the low Re turbulence model at (Kraslnkov et al 2009, Kawamura et al 2009). It was found that the scale effects on propeller thrust and effcency are underestmated by the ITTC method when compared wth the RANS results, especally for hghly skewed propellers (Kraslnkov et al 2009). Alternatve extrapolaton formulae for propeller open water performance were proposed va analyss of RANS smulaton results (Müller et al 2009), where the thrust loadng, skew, and the changes n magntude and drecton of secton force were taken nto account n addton to the geometrc parameters consdered n the ITTC formulae. The comparson for one test case shows that the CFD-based formulae predcts the ncrements n thrust and effcency from model- to full-scale are larger than those predcted by the ITTC method. Propellers wth specal tps may present new challenges to the ITTC method for predctng propeller scale effects. It was found through CFD smulatons that the scale effects on the Kappel and CLT propellers are larger than those on conventonal propellers (Hsn et al 2010). More recently, the RANS approach was employed n selectng optmal endplates of the CLT propeller (Sánchez-Caja et al 2014). Besdes, the RANS tool was also utlzed n the scale effect researches for ducted propellers (Kraslnkov et al 2007) and the rudder bulb (Oh et al 2010). Ths paper presents our numercal study of the scale effects on a tp-rake propeller, the PPTC-II, based on the RANS smulatons usng software FLUENT 6.3. The low Re opton n SST k- model s adopted n, * Correspondence to: cjyang@sjtu.edu.cn.
together wth fne prsm grds to resolve the vscous sublayer. At, standard wall functon s adopted. The scale-effect correctons yelded by our RANS smulatons are compared wth those obtaned from the ITTC method. To explan the CFD results, an analyss of sectonal forces s performed. To nvestgate how the tp rake nfluences propeller scale effects, the geometry of PPTC-II s modfed by removng the tp rake only, and the RANSpredcted scale effects for the modfed propeller, PPTC- II-m, are compared wth those for the PPTC-II. 2 MUMERICAL MODELING APPROACH 2.1 Governng Equatons The flow around the propeller workng n open water s smulated by solvng the RANS equatons together wth the SST k-model for turbulence closure. The contnuty and momentum transport equatons for an ncompressble flud are wrtten as u x uu 0 u u u 2 u j j j t x x x x 3 x j j j j p uu x j ' ' j x where u and u j (,j=1,2,3) are the velocty components, p s the statc pressure, s the dynamc vscosty of water, ' ' j s the Kronecker delta, and uu s the Reynolds j stress. The transport equatons of the SST k-ω model are wrtten as k k ku k t x x x j j G Y S k k k (2) u t x x x j j G Y S D where k s the turbulence knetc energy, ω s the specfc dsspaton rate, G k and G ω denote the generaton of k and ω respectvely, Γ k and Γ ω denote the effectve dffusvty of k and ω respectvely, Y k and Y ω denote the dsspaton of k and ω due to turbulence, D ω s the cross-dffuson term, Y k and Y ω are user-defned source terms. 2.2 Computatonal Model and Setup The governng equatons are solved numercally by means of FLUENT 6.3, a CFD software package based on the fnte volume method. Snce flow n open water s assumed to be steady and perodc for all blades n the coordnate system fxed to the propeller, a sngle blade passage suffces for the smulaton. As llustrated n Fgure 1, the computatonal doman s a porton of the cylnder whch s coaxal wth the propeller shaft. It s (1) bounded by a par of perodc surfaces whch pass through the shaft axs and make an angle of 360/Z degrees, where Z s the number of blades. The nlet and outlet of the doman are 5D upstream and 10D downstream of the propeller, where D s the propeller dameter. The radal sze of the doman s 10D. As shown n Fgure 2, the perodc boundary surfaces pass through the leadng and tralng edges of adjacent blades, hence the back and face of the adjacent blades, nstead of the same blade, become boundares of the doman. By dong so, prsm layer grds of hgh qualty can be generated easly on blade surfaces, as shown n Fgure 3. Usng the SST k- model for turbulence closure, the boundary layer flow s resolved down to the vscous sub-layer at, whle the wall functon s adopted at. The wall dstance averaged over blade surfaces, y +, ranges 0.64~1.12 at, and 32~62 at. All the boundary surfaces are dscretzed va trangular grds, whle the space outsde the prsm layers s dscretzed va tetrahedral cells. To reduce numercal uncertantes, blade surface grds are geometrcally smlar at both scales, only the thcknesses of the prsm layers are adjusted. The total number of cells s about 4.38 mllon at both scales. Fgure 1 The computatonal doman Fgure 2 Geometry of the sub-doman enclosng the back and face of adjacent blades Fgure 3 Zoom-up vew of blade-surface prsm layer grds
The blade, hub, and shaft surfaces are set as statonary noslp walls n the rotatng frame. As shown n Fgure 1, the nlet and far boundary are set as velocty nlets, whle the outlet as the pressure outlet. For a fxed rotaton speed of the propeller, the nlet velocty s specfed accordng to the desred value of, the advance coeffcent. The convecton terms n all the governng equatons are dscretzed wth 2 nd -order upwnd schemes. The SIMPLE scheme s employed for velocty-pressure couplng. 3 RESULTS AND DISCUSSIONS As shown n Fgure 4, the PPTC-II s a four-bladed propeller wth a large tp rake. Its geometrc data are provded by SVA Potsdam and avalable n the publc doman. The geometrc partculars as well as operatng condtons of propeller PPTC-II at model- and full-scale are lsted n Table 1. and ITTC-predcted scale effects on the open water performance. Accordng to the ITTC method, the ncrease n full-scale effcency s manly due to the decrease n torque. On the contrary, the RANS results ndcate that, at, the thrust ncreases by 2~3% (see Fgure 6(a)), however, the torque changes lttle except for =0.7 (see Fgure 6(b)). Amazngly, the ncreases n full-scale effcency predcted n both methods dffer by less than % (see Fgure 6(c)). K T, 10K Q, 0 0.8 0.7 0.6 0.4 0.3 0.2 PPTC-II CFD CFD EFD 10K Q 0 0.1 K T 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 Fgure 5 RANSE-predcted open water performances of PPTC-II at model- and full-scale PPTC-II (ITTC) Fgure 4 Geometrc model of propeller PPTC-II Table 1 Geometrc partculars and operatng condtons of propeller PPTC-II at model- and full-scale Model-scale Full-scale Scale rato 31.428 1 Number of blades 4 Dameter [m] 0.23864 7.5m Chord rato at 0.75R 0.2331 Ptch rato at 0.75R 0.8004 Rate of revoluton (1/s) 18 3.21 Densty of water [kg/m 3 ] 999 1025.87 Knematc vscosty of water [m 2 /s] 1.139 10-6 1.188 10-6 Re at 0.75R, =0.7 5.571 10 5 8.707 10 7 3.1 Scale Effects on Open Water Performance Fgure 5 compares the model- and full-scale open water performances of the PPTC-II predcted by CFD, as well as the model-scale EFD data by SVA Potsdam. Except for =0.1 and =0.9, the CFD results agree well wth EFD data. As s well known, the full-scale effcency s hgher than the model-scale one. However, the ncrease n fullscale effcency s largely due to the ncrease n thrust at =0.1~; at =0.7, t s due to the ncrease n thrust and the decrease n torque, and the latter becomes more mportant as blade loadng decreases. The ITTC-1978 method s also employed to predct the full-scale performance of PPTC-II by usng the RANS results at model-scale. Fgures 6 compares the RANS- 100(K Ts -K Tm )/K Tm (%) 100(K Qs -K Qm )/K Qm (%) 100( 0s - 0m )/ 0m (%) - - - - - - - - - - -3.5-4.0-4.5-5.0-5.5-6.0-6.5-7.0 5.0 4.5 4.0 3.5 0.1 0.3 0.7 (a) thrust 0.1 0.3 0.7 PPTC-II (ITTC) PPTC-II (ITTC) (b) torque 0.1 0.3 0.7 (c) effcency Fgure 6 Comparson RANS- and ITTC-predcted scale effects on the open water performance of PPTC-II
3.2 Analyss of Sectonal Forces To fnd out whether the present CFD results can be explaned from the physcs of flow, and f there are other factors whch nfluence the scale effects n addton to the drag coeffcent, an analyss of hydrodynamc forces s conducted on a sectonal bass for propeller PPTC-II. The pressure and frctonal forces on a blade secton are projected onto drectons normal and tangental to the nose-tal lne and named as secton normal and tangental forces respectvely. Fgures 7 through 9 compare the model- and full-scale normal force coeffcents, K SN, K SN_P, and K SN_F, where the subscrpts P and F denote pressure and frctonal forces respectvely. Smlarly, the tangental force coeffcents are denoted by K ST, K ST_P, and K ST_F respectvely, and the results at model- and fullscale are compared n Fgures 10 through 12. All the sectonal forces are non-dmensonalzed by n 2 D 3, where n and D are the rate of revoluton and the dameter of the propeller respectvely, and s the densty of water. As seen n Fgure 7, the secton normal forces ncrease at manly at outer rad over the range of loadng condtons nvestgated. Lookng further at Fgures 8 and 9, t s obvous that the ncrease n normal force s prmarly due to the pressure component. It s nferred that the secton angle of attack becomes larger at due to reduced dfferences n the dsplacement thcknesses of boundary layers on the back and face. K SN 0 0.45 0.40 0.35 0.30 0.25 0.20 0.15 =0.1 =0.3 = K SN_F (=0.1) K SN_F (=) 010 005 000-005 -010-015 -020 010 005 000-005 -010-015 -020 (a) =0.1 =0.3 = =0.7 020 015 010 005 000-005 -010-005 (b) Fgure 9 Comparson of the frctonal component of secton normal forces for PPTC-II Fgure 10 shows that the secton tangental forces decrease at from root to tp over the range of loadng condtons nvestgated. It s clear from Fgures 11 and 12 that ths result s almost solely due to the decrease n the frctonal force. 15 10 05 =0.7 025 020 015 010 005 000 K SN_F (=0.3) K SN_F (=0.7) 0.10 5 =0.7 00 = 0 K ST -05-10 =0.3 Fgure 7 Comparson of secton normal forces for PPTC-II -15 =0.1 0 0.45-20 0.40 0.35 =0.1 Fgure 10 Comparson of secton tangental forces for PPTC-II K SN_P 0.30 0.25 0.20 0.15 0.10 5 0 =0.3 = =0.7 Fgure 8 Comparson of the pressure component of secton normal forces for PPTC-II K ST_P 15 10 05 00-05 -10-15 -20 =0.7 = =0.3 =0.1 Fgure 11 Comparson of the pressure component of secton tangental forces for PPTC-II
K ST_F (=0.1) K ST_F (=) 05 04 03 02 01 00-01 -02-03 -04-05 05 04 03 02 01 00-01 -02-03 -04-05 =0.3 (a) =0.1 = =0.7 (b) Fgure 12 Comparson of the frctonal component of secton tangental forces for PPTC-II A further dscusson can be made on how the changes n secton normal and tangental forces due to the scale effect nfluence those n propeller thrust and torque. As llustrated n Fgure 13, the axal and crcumferental force coeffcents of a blade secton are expressed as K K cos K sn SA SN ST (3) K K sn K cos SC SN ST where s the geometrc ptch angle of the blade secton. 10 09 08 07 06 05 04 03 02 01 00 10 09 08 07 06 05 04 03 02 01 00 K ST_F (=0.3) K ST_F (=0.7) magntudes of K SN_P and K ST_F, as well as the ptch angle. But the contrbuton of K SN_P always cancel out that of K ST_F to some extent. Thus the analyss explans the reasons for the scale effects on propeller thrust and torque shown n Fgure 5. The present CFD results and analyss ndcate that t mght be necessary to take nto account the scale effect on the thckness of blade surface boundary layer. Then the predcted scale effect can be equally mportant for both thrust and torque, or even prmarly for the thrust. 3.3 Influence of Tp-Rake on Scale Effects The PPTC-II s a propeller wth the tp rake that s meant to load the tp (hence ncrease the effcency) wthout creatng strong tp vortces. It would be nterestng to make a comparson of the scale effects on propellers wth and wthout the tp rake. Therefore, the blade geometry of PPTC-II s modfed by removng the tp rake, but keepng all the other geometrc parameters untouched. The new propeller s named as, and the RANS smulatons are carred out for t by usng dentcal modelng approach and operatng condtons to those for the PPTC-II. Fgure 14 shows the geometrc model of the. Fgure 14 Geometrc model of propeller Fgure 15 compares the open water performances yelded by RANS smulatons for the at model- and full-scale, whch are qute close to those for the PPTC-II except for extremely hgh/lght loadng condtons (=0.1 and =0.9). 0.8 0.7 0 0.6 Fgure 13 Relaton of the axal and crcumferental forces to the normal and tangental forces of a blade secton Accordng to the results shown n Fgures 7 through 12, the scale effects on K SN_F and K ST_P can be neglected. Then K K cos K K K sn K SA SN _ P ST _ F SC SN _ P ST _ F sn cos where denotes the dfference of full- and model-scale values. Snce K SN_P > 0 and K ST_F < 0, t s clear that K SA > 0; however, the sgn of K SC depends on the (4) K T, 10K Q, 0 0.4 0.3 0.2 0.1 10K Q 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 Fgure 15 RANSE-predcted open water performances of at model- and full-scale Fgure 16 compares the scale effects on propeller thrust, torque, and effcency for the PPTC-II and based on RANS smulaton results. As seen n Fgures 16(a) and 16(b), n lght loadng condtons (= and K T
=0.7), there are large dfferences between PPTC-II and n the scale effects on propeller thrust and torque. Fgure 16(c) shows that the scale effect on propeller effcency s generally larger for PPTC-II than for by %~1%. 100(K Ts -K Tm )/K Tm (%) - - - - 0.1 0.3 0.7 ncrease n secton tangental force close to the tp are both dfferent from the case of PPTC-II. The tp rake actually reduces the loadng close to the tp, especally when the angle of attack s small. By comparng Fgures 19 and 20, the pressure felds n the cross sectons mmedately downstream of the tp tralng edge, t s clear that the tp vortces of PPTC-II are much weaker (due to reduced tp loadng) than those of. K SN 0 0.45 0.40 0.35 0.30 0.25 0.20 =0.1 =0.3 = - 0.15 0.10 =0.7 (a) thrust 5 - - 0.1 0.3 0.7 0 (a) total 100(K Qs -K Qm )/K Qm (%) - - - -3.5-4.0-4.5-5.0-5.5 K SN_P 0 0.45 0.40 0.35 0.30 0.25 0.20 =0.1 =0.3 = -6.0-6.5-7.0 0.15 0.10 =0.7 5.0 4.5 4.0 3.5 (b) torque 5 0 (b) pressure component Fgure 17 Secton normal forces for 100( 0s - 0m )/ 0m (%) 20 15 10 05 =0.7 0.1 0.3 0.7 (c) effcency Fgure 16 Comparson of RANS-predcted scale effects on the open water performances of PPTC-II and Fgures 17 and 18 show the results of sectonal force analyss for propeller. By comparng Fgures 17(a) and 17(b) t s obvous that the frctonal force contrbutes lttle to the secton normal force, whch s the same as for the PPTC-II. However, as shown n Fgure 17(b), K SN_P decreases from postve to negatve value as ncreases, whch explans the results at = and =0.7 for n Fgures 16(a) and 16(b). Fgures 18(a) and 18(b) ndcate that, the frctonal force s not the only contrbutor to the secton tangental force, especally close to the tp. Ths s dfferent from the results for PPTC-II (see Fgures 10 and 11). Besdes, as shown n Fgures 17 and 18, the monotonc ncrease n secton normal force as well as the sharp K ST K ST_P 00-05 -10-15 -20 20 15 10 05 00-05 -10-15 -20 = =0.3 =0.1 (a) total =0.7 = =0.3 =0.1 (b) pressure component Fgure 18 Secton tangental forces for
dentfed wth and wthout the tp rake, but not on 0. To account for the tp rake and predct the scale effects on K T and K Q more accurately, the exstng ITTC method mght need to be updated. (ITTC) (a) (b) Fgure 19 RANS-smulated pressure felds n the cross secton 05D downstream of the tralng edge of tp. PPTC-II, =0.7. 100(K Ts -K Tm )/K Tm (%) - - 0.1 0.3 0.7 - - - (a) thrust 0.1 0.3 0.7 - - (a) (b) Fgure 20 RANS-smulated pressure felds n the cross secton 05D downstream of the tralng edge of tp., =0.7. Fnally, the scale effects predcted by the ITTC method are compared wth those by RANS smulatons n Fgure 21. Smlar to the comparson made for the PPTC-II n Fgure 6, the dfferences between ITTC and RANS results are large for K T, but relatvely small for K Q. The ITTCpredcted ncreases n the full-scale effcency of PPTC- II-m are stll qute close to the RANS predctons, but are all hgher than the latter. 4 CONCLUSIONS Based on the RANS smulatons, the scale effects on propeller open water performance have been numercally studed for PPTC-II, an ITTC benchmark propeller, and, a modfed verson of the PPTC-II by removng the tp rake. By analyzng the RANS-based blade secton forces, and comparng the scale effects predcted by RANS wth those by the ITTC-1978 method, the followng conclusons are drawn, 1) The scale effect on propeller thrust can be as mportant as that on the torque, whch seems to be the result of reduced boundary layer thckness on full-scale blade surfaces. On the contrary, the scale effect correcton for K T s one magntude smaller than that for K Q accordng to the ITTC method. 2) Although the correctons for K T and K Q by the ITTC method dffer largely from those by the RANS method, the correctons for 0 by the two methods agree qute well at least n the cases of PPTC-II and. Further nvestgatons are necessary to fnd out f ths s just a concdence. 3) The tp rake serves to reduce the hydrodynamc loadng close to the tp. At small angle of attack where the propeller s desgned to work, large dfferences n the scale effects on K T and K Q are 100(K Qs -K Qm )/K Qm (%) 100( 0s - 0m )/ 0m (%) - - - -3.5-4.0-4.5-5.0-5.5-6.0-6.5-7.0 5.0 4.5 4.0 3.5 (ITTC) (ITTC) (b) torque 0.1 0.3 0.7 (c) effcency Fgure 21 Comparson of RANS- and ITTC-predcted scale effects on the open water performance of REFERENCES Hsn, C.-Y., Chang, K.-K., Ch, R.-C. & Chen, P.-F. (2010). Desgn and Analyss of the End Plate Effect Propellers, Proceedngs of the 28 th Symposum on Naval Hydrodynamcs, Pasadena, CA, USA. Internatonal Towng Tank Conference (2014). 1978 ITTC Performance Predcton Method, ITTC - Recommended Procedures and Gudelnes, 7.5-02-03-01.4, Revson 03. Kawamura, T. & Omor, T. (2009). Reynolds Number Effect on Propeller Performance n Open Water, ournal of the apan Socety of Naval Archtects and Ocean Engneers 10, pp.29-36.
Kraslnkov, V. I., Sun,. Y. & Halse, K. H. (2009). CFD Investgaton n Scale Effect on Propellers wth Dfferent Magntude of Skew n Turbulent Flow, Proceedngs of the 1 st Internatonal Symposum on Marne Propulsors, Trondhem, Norway. Kraslnkov, V. I., Zhang, Z., Hong, F., Ponkratov, D. V. & Sun,. Y. (2007). Steady Analyss of Vscous Flow around Ducted Propellers: Valdaton and Study on Scale Effects, Proceedngs of the 9 th Internatonal Conference on Fast Sea Transportaton, Shangha, Chna. Müller, S. B, Abdel-Maksoud, M. & Hlbert, G. (2009). Scale Effects on Propellers for Large Contaner Vessels, Proceedngs of the 1 st Internatonal Symposum on Marne Propulsors, Trondhem, Norway. Oh, S., ang,., Rhyu, S., Hoshno, T. & Seo,. (2010). Some Applcatons on Extrapolaton Method of Rudder Bulb Performance as an Energy-Savng Devce, Proceedngs of the 11 th Internatonal Symposum on Practcal Desgn of Shps and Other Floatng Structures, Ro de anero, Brazl. Sánchez-Caja, A., González-Adald,., Pérez-Sobrno, M. & Splä, T. (2014). Scale Effects on Tp Loaded Propeller Performance Usng a RANSE Solver, Ocean Engneerng 88, pp.607-617. Staner, M. (1998). The Applcaton of RANS Code to Investgate Propeller Scale Effects, Proceedngs of the 22 nd Symposum on Naval Hydrodynamcs, Washngton DC, USA. DISCUSSION Queston from Stephan Helma What s the reason that the secton force was splt nto components normal and tangental to the nose-tal ptch lne and not normal and parallel to the hydrodynamc nflow? Authors closure Accordng to potental flow theory, the secton lft s the only force perpendcular to the resultant nflow whch s composed of the undsturbed nflow and the nduced veloctes. Inversely the resultant nflow drecton can be found once the secton force (wthout vscous component) s known. In vscous flow, however, t would be napproprate to do so snce the vscous force contrbutes (negatvely) to the lft. In fact, we tred to determne the nflow drecton by solvng the Euler equatons, but found erratc behavors n secton lft drecton at nner rad (close to the hub), whch was probably because the grd qualty was not good enough n that regon. For ths reason, we eventually chose to use the nose-tal lne for our analyss of the secton forces.