13 International Research Exchange Meeting of Ship and Ocean Engineering in Osaka -1 December, Osaka, Japan Computational Analysis of Added Resistance in Short Waves Yonghwan Kim, Kyung-Kyu Yang and Min-Guk Seo Seoul National University Department of Naval Architecture & Ocean Engineering
Background Energy Efficiency Design Index (EEDI) Restrict greenhouse gas emissions Added Resistance Experiment Numerical Methods CFD RPM Strip Need for analysis of added resistance in short wave due to increase of ship length Investigate the effect of different bow shape to added resistance
State of the Art Experiments Journee (199): Wigley hull Fujii and Takahashi (1975), Nakamura and Naito (1977): S175 containership Kuroda et al. (1): Different bow shapes above the waterline Sadat-Hosseini et al. (13): KVLCC Kashiwagi (13): Modified Wigley hull, Unsteady wave analysis Potential Flow Maruo (196), Newman (1967), Salvesen(1978), Faltinsen et al. (198) Joncquez et al. (8): in time domain Kashiwagi et al. (9): Enhanced unified theory, correction in short waves Kim and Kim (11): in time domain, irregular waves Seo et al. (13): Comparative study for computation methods CFD Added Resistance Orihara and Miyata (3): RANS, FVM, overlapping grid Hu and Kashiwagi (7): CIP, Cartesian grid, immersed boundary Visonneau et al., (1): Unstructured hexahedral grid, mesh deformation Sadat-Hosseini et al. (13): RANS, overset, block structured, Level-set 3
Rankine Panel Method Equation of Motion ( ) T R x [ M ]{ } { F } { F } { F } ( k, j 1,,...,6) jk k H. D. j F. K. j Res. j F Res : Restoring force F F.K. : Froude-Krylov force F H.D. : Hydrodynamic force x U o z z ( x, y, t) A, S F Linearized Boundary Value Problem y S B Governing Equation Body B.C. in fluid domain 6 d j I n m on S n j1 t n j j j B ( m, m, m ) ( n )( U ) 1 3 ( m, m, m ) ( n )( x ( U )) 4 5 6 Kinematic F.S.B.C. Dynamic F.S.B.C. d d ( U ) d ( ) on d U I z t z z d 1 ( U ) d g d U ( U ) I on z t t 4
Added Resistance (RPM) Near-field Method, Direct Pressure Integration Method (Kim & Kim, 11) 1 1 ( 3 4 5 ) ( ( 3 4 5 )) 1 x WL WL F g y x ndl U y x n dl 1 U ( ( 3 4 y 5x)) ndl x WL 1 gz nds I d I d nds S B B B S B I d I d g( 3 4 y 5x) U t x S I d I d U I d nds t t S 1 1 U n ds U n ds x S B 1 x S B I d n1ds n n, n Hn 1 R H ( 5 6) 1 4 5 ( 4 6 ) 46 56 ( 4 5 ) 5
Cartesian-Grid Method Fluid Flow Solver FVM + Fractional step MC limiter Cartesian grid Free surface capturing (THINC / WLIC) Solid Body Treatment u u u * Triangular surface mesh Volume fraction Level-set + Angle weighted pseudo-normal Immersed boundary method n u t u t ** * u t n1 ** n n u u n ds 1 n1 1 n1 f dv n1 1 1 t b n1 ** p nds u nds n1 p nds r 1 r max,min r,, r q x q x / / / i1/ i1/ 1 u 1 t x x Fi x 1 tanh xi i1/ 6
Fx (N) Fx (N) Added Resistance (CFD) 1 1 8 6 4-5 1 15 Time (sec) R_wave 6 5 4 R_calm 3 1 5 1 15 5 3 35 Time (sec) <Wigley III, Fn=.3 > R_wave R_calm R_added 7
Added Resistance in Short Wave Faltinsen et al. (198) 1 U F g I sin ( ) 1 cos cos( ) ndl L g n sin n 1 cos n x cos y 6 sin 1 F d (1 U ) g I BB f ( ) 1 Bf ( ) sin ( )sindl sin ( )sindl B I II Cross-section equal to the waterplane area Fujii & Takahashi (1975), Local steady flow velocity NMRI s method (Tsujimoto et al. (8), Kuroda et al. (8)) Fujji & Takahashi (1975) NMRI (Tsujimoto et al. (8), Kuroda et al. (8)) d I ( kd) I ( ked) e, k e d) K ( k d) g 1 1 d I1 ( kd) K1 ( kd) I1 ( ke 1 1 5 F 1 1 C F, C max[1., 31 B ( ) 68] U n U U n U f 1 e 8
Simulation Conditions <Panel Model for Rankine Panel Method> <Grid Distribution for Cartesian Grid Method> Model L(m) B(m) D(m) C B Series6 1. 14.9 5.7.7 1. 15.39 6.15.8 S175 175. 5.4 9.5.561 KVLCC 3. 58..8.898 <Triangle Surface Meshes for S175 Containership and KVLCC> 9
3 /A 5 /ka Motion Response (S175 Containership).5.5 Exp. (H/=1/1, Fonseca, 4) Exp. (H/=1/4, Fonseca, 4) Cartesian grid method (H/=1/4) Exp. (H/=1/1, Fonseca, 4) Exp. (H/=1/4, Fonseca, 4) Cartesian grid method (H/=1/4) 1.5 1.5 1 1.5.5 1 1.5.5 3 3.5 4 (L/g) 1/ <Heave> 1 1.5.5 3 3.5 4 (L/g) 1/ <Pitch> <Vertical Motion Responses of S175, Fn=.5> 1
3 /A 5 /ka Motion Response (KVLCC) 1.6 Exp. (H/L=.1, Lee et al., 13) Cartesian grid method (H/=1/4) 1.6 Exp. (H/L=.1, Lee et al., 13) Cartesian grid method (H/=1/4) 1. 1..8.8.4.4 1 1.5.5 3 3.5 4 (L/g) 1/ <Heave> 1 1.5.5 3 3.5 4 (L/g) 1/ <Pitch> < Vertical Motion Responses of KVLCC, Fn=.14> 11
R/gA B /L Grid Convergence Test (RPM) 6 5 4 /L =.3 /L =.5 <L/Δx = 37> 3 <L/Δx = 59> 1 4 6 8 1 L/x <L/Δx = 95> /A: - -1.6-1. -.8 -.4.4.8 1. 1.6 < Grid Convergence Test of Added Resistance for KVLCC, Fn=.14> 1
Wave Elevation and Pressure Distribution (RPM) Wave Pressure Wave Pressure <λ/l=.4> < KVLCC, Fn=.14> <λ/l=1.> Spatial variation of the physical quantities in short wavelength is more severe. 13
R/gA B /L Grid Convergence Test (CFD) 6 5 4 /L=.5 <L/Δx = 18> 3 <L/Δx = 16> 1 L/x stern =16 L/x stern =8 6 1 18 4 3 L/x bow <L/Δx = 8> < Grid Convergence Test of Added Resistance for KVLCC, Fn=.14> 14
R/gA B /L R/gA B /L Added Resistance (1/4) 1 1 8 Exp. (Fn=.7, Strom-Tejsen et al, 1973) Exp. (Fn=., Strom-Tejsen et al, 1973) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 15 Exp. (Fn=.7, Strom-Tejsen et al, 1973) Exp. (Fn=., Strom-Tejsen et al, 1973) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 6 1 4 5 -..4.6.8 1 /L.5 1 1.5.5 /L <Added Resistance of Series 6, C B =.7, Fn=. > 15
R/gA B /L R/gA B /L Added Resistance (/4) 1 16 1 8 Exp. (Fn=.147, Strom-Tejsen et al, 1973) Exp. (Fn=.165, Strom-Tejsen et al, 1973) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 1 Exp. (Fn=.147, Strom-Tejsen et al, 1973) Exp. (Fn=.165, Strom-Tejsen et al, 1973) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 6 8 4 4 -..4.6.8 1 /L.5 1 1.5.5 /L <Added Resistance of Series 6, C B =.8, Fn=.15 > 16
R/gA B /L R/gA B /L Added Resistance (3/4) 1 1 8 6 Experiment (Fujii,1975) Experiment (Nakamura,1977) Cartesian grid method (H/=1/4) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 15 1 Experiment (Fujii,1975) Experiment (Nakamura,1977) Cartesian grid method (H/=1/4) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 4 5 -..4.6.8 1 /L.5 1 1.5.5 /L <Added Resistance of S175 Containership, Fn=.> 17
R/gA B /L R/gA B /L Added Resistance (4/4) 1 15 8 6 Exp. (H/L=.1, Lee et al., 13) Exp. (H/L=.15, Lee et al., 13) Cartesian grid method (CFD, H/=1/4) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 1 9 Exp. (H/L=.1, Lee et al., 13) Exp. (H/L=.15, Lee et al., 13) Cartesian grid method (CFD, H/=1/4) Short wave (Fujii & Takahashi (1975)) Short wave (Faltinsen et al. (198)) Short wave (NMRI) 4 6 3..4.6.8 1 /L.5 1 1.5.5 /L <Added Resistance of KVLCC, Fn=.14> 18
Wave Contour and Water-Plane RPM CFD RPM CFD <S175 Containership, Fn=.> <KVLCC, Fn=.14> <Comparison of Water-Plane Sections> 19
Conclusions (1/) To predict the reliable added resistance, grid convergence test should be conducted because the added resistance is sensitive to the panel size or grid spacing. Especially, a ship which has blunt bow shape requires finer grid near the ship bow region. According to grid convergence test of Rankine panel method, more panels are required in short wave condition than in long wave condition. Also, it is recommended that panels are concentrated on bow and stern because change of body shape at bow and stern is much more severe than mid-ship region.
Conclusions (/) According to results of added resistance in short wave region, all computational methods gave good results when the vessel has blunt body, while only Cartesian grid method and short wave calculation method proposed by NMRI provided good results when the vessel has slender body. This implies that nonlinear effects which are not included in potential based solver importantly influence added resistance on a slender body in short wavelength. 1
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