International Research Exchange Meeting of Ship and Ocean Engineering in Osaka, December 1-, Osaka, Japan Comparative Study on Added Resistance Computation Min-Guk Seo, Dong-Min Park, Jae-Hoon Lee, Kyong-Hwan Kim, Yonghwan Kim Seoul National University MHL Marine Hydrodynamics Lab
Introduction Research Background In recent years, discussions at the International Maritime Organization (IMO) have resulted in the development of an Energy Efficiency Design Index (EEDI) to restrict greenhouse gas emissions from ships. http://www.theicct.org/blogs/staff/cutting-carbon-ships
Introduction Research Background The design of ships with less green-house gas is of great interest in naval architecture fields. Ship designers need to find optimum hull forms to minimize the resistance including the added resistance in waves. When a ship navigates in waves, the ship s forward speed decreases compared to that in calm sea because of the added resistance. An accurate computation of added resistance is getting more important for the prediction of power increase on ships in random ocean waves. 3
Methodology Strip Method Rankine Panel Method CFD method Experiment Motion RAOs Force Analysis Near-field Method Far-field Method Force Added resistance S S Time Total force in waves Mean value of total force in waves Steady force in calm water Added Resistance 4
Far-field Method State of the Art Maruo (196) : Propose far-field method Joosen (1966), Newman (1967) : Strip method Gerritsma & Beuklman (197), Salvesen (1978) : Radiated energy method Joncquez et al. (8) : Rankine panel method in time domain Kashiwagi et al. (9) : Enhanced Unified Theory (EUT) + correction in short waves Near-field Method Faltinsen et al. (198) : Strip method, asymptotic approach in short waves Grue & Biberg (1993), Ye & Hsiung (1997), Choi et al. () : Wave Green function method Joncquez et al. (8) : Rankine panel method in time domain Kim & Kim (11) : Rankine panel method in time domain, direct simulation in irregular waves Added Resistance in Short Waves Fujii & Takahashi (197) : Drift force on cylinder + correction coefficient for ship shape, speed Faltinsen et al. (198) : Asymptotic approach in short wave Kuroda et al. (8) : Fujii & Takahashi method + correction
In the Present Study A frequency-domain strip method and a time-domain Rankine panel method are applied to calculate the first-order potential and linear ship responses, as a necessity for the added resistance calculation. Both the near-field method (direct pressure integration method) and far-field method (momentum conservation method, radiated energy method) are adopted for the calculation of added resistance. The established asymptotic approaches are examined to evaluate added resistance in short wavelength. 6
Boundary Value Problem (Rankine Panel Method) Equation of Motion [ M ]{&& x } = { F } + { F } + { F } jk k H. D. j F. K. j Res. j F Res : Restoring force F F.K. : Froude-Krylov force r r r r ( d = x + x ) T R x ( k, j = 1,,...,6) x U o z z = z ( x, y, t) b A, w S F F H.D. : Hydrodynamic force y S B Linearized Boundary Value Problem Governing Equation Body B.C. Kinematic F.S.B.C. Dynamic F.S.B.C. Ñ f = in fluid domain æ x 6 fd j fi = åç n j + x jm j - on SB n j= 1 t n è r r - ( U - ÑF ) Ñ = + + ( U - ÑF ) Ñ on z = t z z z d F fd z d z d z I ö ø r r ( m1, m, m3 ) = ( n Ñ)( U - ÑF) r r r ( m, m, m ) = ( n Ñ )( x ( U - ÑF)) 4 6 f r d F é r 1 ù r - ( U - ÑF ) Ñ fd = - - gz d + U ÑF - ÑF ÑF + ( U - ÑF ) Ñ fi on z = t t ê ë ú û 7
Added Resistance (Rankine Panel Method) Near-field Method, Direct Pressure Integration Method (Kim & Kim, 11) r r r F g y x ndl U y x n dl 1 æ F 1 ö = ò r ( z - ( x3 + x4 - x )) - r ( z ( x3 x4 x )) 1 ò ç - + ÑF ÑF - + - x WL WL è ø r æ F 1 ö r - r ò d Ñç - U + ÑF ÑF ( z - ( x3 + x4 y - xx)) ndl è x ø WL r æ 1 ö r - ròò gz nds - ròò ç Ñ ( fi + fd ) Ñ ( fi + fd ) nds è ø SB SB ( f f ) ( ) æ I + d fi + fd ö r - ròò ç g( x3 + x4 y - xx) + -U + ÑF Ñ ( fi + fd ) n1ds t x S è ø B ( f f ) ( f f ) r æ + + ö r - òò Ñç - + ÑF Ñ ( + ) nds ø I d I d r d U fi fd t t SB è æ F 1 ö r æ F 1 ö r -ròò ç - U + ÑF ÑF n ds - r d Ñç - U + ÑF ÑF n ds è x ø è ø SB òò r 1 x SB r r r r r n = x n, n = Hn 1 R é- ( x + x6 ) ù 1 ê ú H = 4 ( 4 6 ) ê x x - x + x ú ê x 4x6 xx6 -( x4 + x ) ú ë û Far-field Method, Momentum Conservation Method (Joncquez, 9) Cd ( Ñ ( fi + fd ) Ñ ( fi + fd ) + k ( fi + fd ) ) r 1 r F = r ò ncdl Cd k r Ñ ( fi + fd )( Ñ ( fi + fd ) nc ) -rò dl Cd k rg r é ( fi + fd ) r ù r + z ncdl r ( U ) ( fi fd ) z ncdl ò + C ò d C ê - - ÑF Ñ + d t ú ë û r r -r ÑF Ñ f + f n + Ñ f + f ÑF n z dl ò [ ( ( ) ) ( )( )] I d c I d c C d : Intersection of the control surface with z = plan n c : Normal vector of the control surface ζ : Wave elevation 8
Strip Method Boundary Value Problem (D) D Wave Green function. Governing equation Ñ f = in fluid domain Free surface B.C. Body B.C. f f + g = on z = t z f n on n = V S B Equation of Motion 6 k = 1 ( ) i t é M jk + A && jk xk + B & å jkxk C jkx ù ë + k û = Fje w A jk : Added mass B jk : Damping coefficient F j : Excitation force 9
Added Resistance (Strip Method) Near-field Method, Direct Pressure Integration Method (Faltinsen et al., 198) ì r g ü F = - z n ds - w M x x + w M ( x - z x ) x ò, x í r ý 1 e 3 e G 4 6 C î þ (1) (1) (1) (1) (1) (1) (1) ì ï f f f f 1 ææ f ö æ f ö æ f ö öü ï + r ò í( x + xx 6 - zx4 ) ( + U ) + ( x3 - xx + yx4 ) ( + U ) + ç + ç + ç ýn1 ds y t x z t x x y z SB ï ç î m m èè ø è ø è ø øïþ Far-field Method 1, Momentum Conservation Method (Maruo, 196) rkr k p ò ( ) F, x = H ( q ) cosq + cos b dq 8p òò ikx cos { b 3 } - -ikx cosq H ( q ) = - wb( x) Ae + iz -ixz e ds S B é ë ù û Far-field Method, Radiated Energy Method (Salvensen, 1978) I * { ˆ D} i F = - k cos b z ( F ) + F + R å, x j j j 7 j= 3, 1 w R z k cos b e ( b b sin b ) dx 7 = - -kds I L 33 w ò + e 1
Added Resistance in Short Waves Faltinsen et al. (198) r F = ò F L n n n 1 r F ndl n 1 é wu ù = rgz I sin ( q b ) [ 1 cosq cos( q b )] ê - + + - g ú ë û = sinq = cosq n = x cosq - y 6 sinq Fujii & Takahashi (197), Kuroda et al. (8) r é1 ù F = ad (1 + au ) ê rgz I BB f ( b ) ú ë û 1 B f ( b ) = é sin ( q - b )sinqdl + sin ( q + b )sinqdlù B ëòi òii û Fujji & Takahashi (197) Kuroda et al. (8) a p I ( kd) p I ( k d) w 1 1 e e d = a d =, k e = p I1 ( kd) + K1 ( kd) p I1 ( ked) + K1 ( ked) g 1+ a = 1+ F 1+ a = 1 + C F, C = max[1., - 31 B ( b ) + 68] U n U U n U f 11
Test Models Principle Particulars and Examples of Panel Model Model Wigley I Wigley III Series 6 C B =.7 Series 6 C B =.8 S-17 Wigley III model Length 1 m 1 m 1 m 11.9 m 17 m Breadth 1 m 1 m 14.8 m 18.76 m.4 m Series 6 (C B =.8) model Draft 6. m 6. m.7 m 7. m 9. m Volume 33.7 m 3 888.9 m 3 64. m 3 1373.3 m 3 413. m 3 S-17 model Center of gravity.67 m.67 m.7 m 6.64 m 8. m 1
Simulation Results (Rankine Panel Method) Wave Contours (a) Total wave contour (b) Disturbed wave contour S-17 containership, Fn =., λ/l =.7 13
Comparison of Motion Response 3 1.6. Experiment(Journee, 199) Rankine panel method Strip method 4 Experiment(Journee, 199) Rankine panel method Strip method 1. Experiment(Journee, 199) Rankine panel method Strip method 3 x 3 /A 1. 1. x 3 /A 1 x 3 /A.8.4. 1 1.. 3. 3.. 1 1... 1 1.. (a) Heave motion (a) Heave motion (a) Heave motion Experiment(Journee, 199) Rankine panel method Strip method 4 Experiment(Journee, 199) Rankine panel method Strip method. Experiment(Journee, 199) Rankine panel method Strip method x /ka 1. x /ka 3 x /ka 1. 1 1. 1.. 1 1... 1 1.. 14. 1 1.. (b) Pitch motion (b) Pitch motion (b) Pitch motion Wigley I model, Fn =. Wigley I model, Fn =.3 Wigley III model, Fn =.
Convergence Test Convergence Test for Control Surface (Momentum Conservation Method + RPM) Damping zone 3 d CS R/rgA B /L 1 Convergent Control surface -1-1 3 4 6 d CS /l Examples of control surface Wigley III model : Fn =., λ/l =.9 Control surface is placed farther than d cs /λ = 3.
Time signals (Rankine Panel Method) Time-Histories of Surge Force R/rgA B /L 1 1 st -order force nd -order force Mean value of nd -order force (Added resistance) R/rgA B /L 1 1 st -order force nd -order force Mean value of nd -order force (Added resistance) - - -1 6 6 7 7 8 Time (a) Direct pressure integration method -1 6 6 7 7 8 Time (b) Momentum conservation method Wigley III model, Fn =., λ/l = 1. 16
Results of Added Resistance (Wigley I model) 6 6 Experiment (Journee, 199) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM 4 Experiment (Journee, 199) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM R/rgA B /L 4 3 R/rgA B /L 3 1 R/rgA B /L. 1 1.. 6 4 3 1 (a) Rankine panel method Experiment (Journee, 199) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip R/rgA B /L. 1 1.. 6 4 3 (a) Rankine panel method Experiment (Journee, 199) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip. 1 1... 1 1.. (b) Strip method (b) Strip method Wigley I model, Fn =. Wigley I model, Fn =.3 17
Results of Added Resistance (Wigley III model) 6 6 4 Experiment (Journee, 199) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM 4 Experiment (Journee, 199) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM R/rgA B /L 3 R/rgA B /L 3. 1 1.. (a) Rankine panel method. 1 1.. (a) Rankine panel method 6 6 4 Experiment (Journee, 199) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip 4 Experiment (Journee, 199) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip R/rgA B /L 3 R/rgA B /L 3. 1 1.. (b) Strip method Wigley III model, Fn =.. 1 1.. (b) Strip method Wigley III model, Fn =.3
Results of Added Resistance (Series 6 hulls) R/rgA B /L 1 Experiment (Strom-Tejsen et al, 1973) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L 1 Experiment (Strom-Tejsen et al, 1973) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L. 1 1.. 1 (a) Rankine panel method Experiment (Strom-Tejsen et al, 1973) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L. 1 1.. (a) Rankine panel method 1 Experiment (Strom-Tejsen et al, 1973) Momentum Conservation Method + Strip Radiated Energy Method + Strip Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)). 1 1... 1 1.. (b) Strip method (b) Strip method Series6 C B =.7, Fn =. Series6 C B =.8, Fn =. 19
Results of Added Resistance (S-17) R/rgA B /L 1 Experiment (Fujii,197) Experiment (Nakamura,1977) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L 1 Experiment (Fujii,197) Experiment (Nakamura,1977) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L 1 Experiment (Fujii,197) Experiment (Nakamura,1977) Direct Pressure Integration Method + RPM Momentum Conservation Method + RPM Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L. 1 1.. 1. 1 1... 1 1.. (a) Rankine panel method (a) Rankine panel method (a) Rankine panel method Experiment (Fujii,197) Experiment (Nakamura,1977) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L 1 Experiment (Fujii,197) Experiment (Nakamura,1977) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)) R/rgA B /L 1 Experiment (Fujii,197) Experiment (Nakamura,1977) Direct Pressure Integration Method + Strip Momentum Conservation Method + Strip Radiated Energy Method + Strip Short wave (Fujii & Takahashi (197)) Short wave (Faltinsen et al. (198)) Short wave (Kuroda et al. (8)). 1 1... 1 1.. (b) Strip method (b) Strip method (b) Strip method S-17, Fn =. S-17, Fn =. S-17, Fn =.. 1 1..
Component of Added Resistance Component of Added Resistance (Direct Pressure Integration Method + RPM) 1 1 1 Experiment (Fujii,197) Experiment (Nakamura,1977) Total (Direct Pressure Integration Method + RPM) Diffraction (Direct Pressure Integration Method + RPM) Radiation (Direct Pressure Integration Method + RPM) 1 Experiment (Fujii,197) Experiment (Nakamura,1977) Total (Direct Pressure Integration Method + RPM) Diffraction (Direct Pressure Integration Method + RPM) Radiation (Direct Pressure Integration Method + RPM) 8 8 R/rgA B /L 6 4 R/rgA B /L 6 4. 1 1... 1 1.. (a) Fn =., S-17 containership (b) Fn =., S-17 containership 1
Conclusions Ø Added resistance on ships in waves is calculated by the two different numerical methods, Rankine panel method and strip method. These are combined with the near-field method and the far-field method. Ø In the case of motion response, the frequency of the peak value in the strip method is slightly moved to the high frequency region. These tendencies are shown in the added resistance results. This means that the motion response crucially affects the prediction of added resistance. Ø In low speed, results of added resistance which calculated by all methods are well agreed with experimental data, while in high speed, there is some discrepancies among computed results, especially peak value frequency of added resistance. In general, Rakine panel method gives better agreement with experimental data than strip method. It is needed to choose proper method by considering ship speed.
Conclusions (cont.) Ø Generally, the added resistances that are calculated by strip methods show good correspondence with the experimental data; however, some discrepancy can be observed when the ship speed is high, and the ship hull is a relatively blunt body. If the ship does not have a blunt shape and high speed, the strip method is a good practical tool for the calculation of added resistance. Ø According to the present case of added resistance in short waves, all methods (Fujii and Takahashi (197), Faltinsen et al. (198) and Kuroda et al. (8)) give reasonable agreements with experimental data for a relatively blunt body, while only the method of Kuroda et al. (8) gives reasonable results for a slender ship. It is necessary to choose a proper method with respect to the shape of the ship. 3
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