TUDelft. Validation of Calculations of the Viscous Flow around a Ship in Oblique Motion. Date Oktober 2004

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1 Date Oktober 2004 Author Address ir. S.L. Toxopeus Delft University of Technology Ship Hydromechanics Laboratory Mekelweg 2, CD Delft Phone: TUDelft Delft University of Technology Validation of Calculations of the Viscous Flow around a Ship in Oblique Motion by Serge Toxopeus Report No P Oktober 2004 The First MARIN-NMRI Workshop in Tokyo Oktober 2004 Page /of 1/1

2 Proceedings of the First MARIN-NMRI Workshop in Tokyo, Japan National Maritime Research Institute, Japan October 25-26,2004

3 Proceedings of the First MARIN-NMRI Workshop in National Maritime Research Institute, Tokyo, Japan October25-26, The important pomts of the model experiment aboutriserusing a de^)-sea basm 1 Kenldchi TAMURA, Kentaro KOKÜBUN, Katsuya MAEDA and Kazuald UOH [NMRI] 2. Model experiment on GTL-FPSO 5 YasuhiroNAMBA,SotaroMASANOBUandShunjiKATO [NMRI] 3. Examination of estimation method of wave loads for a high speed ferry 10 Yoshitaka OGAWA[NMRI], Geert K KAPSENBERG and Frans van WALREE [MARIN] 4. Experimental and numerical study of shipping water on running ship foredeck m regular head seas 14 Katsuji TANIZAWA, IDroshi SAWADA, Masaru TSUJIMOTO, Kunihhxj HOSHINO [NMRI] and Saichi KOSHIZUKA [ The Universify of Tohyo] (Invited lecture'l) 5. Recent Research on seakeepfaig problems at RIAM, Kyushu Universify 22 Prof Masashi Kashiwagi [RIAM, Kyushu Universify] 6. Study for an estimation oftimetofloodof damaged large passenger ship 36 Riaan van't VEER and Jan Otto de Kat [MARIN] 0nvitedlechuie2) 7. Experimental studies on transient motion of a damaged large passenger ship 46 Prof Yoshiho IKEDA, Tom KATAYAMA, Yuji TAKEUCHI [Osaka Pref. Univ.] and Shigesuke ISHIDA[NMRI] 8. Simulation of time-to-flood of a damaged large passenger ship 50 Shigesuke ISHIDA [NMRI], Prof Yoshiho EKEDA, Tom KATAYAMA and Yuji TAKEUCHI [Osaka Pref. Univ.] 9. A model experiment on parametric rolling of a post-panamax contaüier ship in head waves 54 Harukuni TAGUCHI, Shigesuke ISHIDA, Hiroshi SAWADA and Makiko MINAMI [NMRI[ 10. The occurrence and avoidance of parametric roll 58 M. LEVADOU and F. van WALREE [MARIN]

4 11. Practical estimation mefliod for capsizing offlie ritc puree seiner in quartering seas 69 Yoshttalca OGAWA, Sliigesulce ISHIDA [NMRI], Frans van WALREE and Jan Otto de Kat [MARIN] 12. Procedure of safety assessment on high-speed navigation in congested sea area with ship handung simulator M NUMANO and J. FUKUTO [NMRI] 13. Recent CTD research activities at NMRI gj Takanori HINO, Yohei SATO and Nobuyuki HIRATA [NMRI[ 14. Application of OD tofliemanoeuvrability performance of ship 37 Hideki MIVAZAKI, Tadashi NIMURA and Michio VENO [NMRI] 15. Validation of calculations offlieviscousflowaround a ship in oblique motion 91 Serge TOXOPEUS [MARIN]

5 Proceedings of the First MARIN-NMRI Woitehop Date: October 25-26,2004 Venue: Meeting room No.1 on thirdfloor of main building. National Maritime Research Institute, Japan Edited by National Maritime Research Institute, Japan

6 The First MARIN-NMRI Worlcshop in Tokyo (Oktober 25-26, 2004) VALIDATION OF CALCULATIONS OF THE VISCOUS FLOW AROUND A SHIP IN OBLIQUE MOTION Serge TOXOPEUS Maritime Researcii Institute Netiieriands (MARIN), Wageningen, The Netherlands. ABSTRACT The capability of the viscous-flow solver PARNASSOS to simulate the flow around a ship in steady oblique motion has been studied. To obtain insight into the reliability and accuracy of the results, grid dependency studies were conducted. Local flow quantities as well as integral variables were compared to measurement values. Two different hull forms were considered: the Series 60 of which extensive flow measurements are available and the KVLCC2M which is the subject of the coming CFD Workshop in Tokyo in KEY WORDS: CFD, RANS, viscous-flow, manoeuvring, hydrodynamic forces, validation. INTRODUCTION For studies into the manoeuvrability of ships only limited use of viscous-flow calculations is nowadays made. One of the major reasons for this is that these calculations involve substantial computing requirements. Another reason is that validation material is sparse and only a few successful demonstrations of the practical application of these calculations are available. Furthermore, in order to study the manoeuvrability of a ship, either time-domain viscous-flow calculations for the ship with active propulsion and steering appendages should be made, or a dedicated mathematical model of the forces on the ship should be derived from viscous flow calculations for steady yaw and drift conditions. Although the first approach theoretically models more accurately the hydrodynamics around the appended ship, the second approach is better suited for practical application at least for the near future. At MARfN, viscous-flow computations are used frequently for the optimisation of hull forms from a resistance and powering point of view. Currently, studies are conducted to extend the capabilities of this solver to also simulate the flow around ships in oblique flow. The first results have already been presented by Toxopeus (2004). Parts of these results are reproduced in this present paper. Besides the possibility to study the detailed flow around the ship in various conditions, this is the first step towards using the viscous flow solver as a tool to predict the forces and moments on manoeuvring ships. Extensive flow field measurements on the well-known Series 60 hull form were conducted at Iowa Institute of Hydraulic Research (IIHR) and the results were made available to the public. Therefore, this case is very suitable for validation studies of viscous-flow calculations. Various researchers have already reported such validation studies, such as Alessandrini and Delhommeau (1998), Cura Hochbaum (1998), Di Mascio and Campana (1999) and Tahara et al. (2002). Validation data is also available for the KVLCC2M hull form which will be used during the coming CFD Workshop in Tokyo in March This paper presents viscous-flow calculations conducted on the Series 60 hull form sailing at a drift angle. In order to examine the reliability of the predicted flow fields and integrated quantities derived from the solution, the discretisation error in the result is studied based on grid refinement. To validate the results, comparisons are made between model measurements conducted at IIHR and simulations of the viscous flow around the model. More detailed comparisons can be found in Toxopeus (2004). Although the full study is not yet finalised, the first results of flow simulations for the KVLCC2M hull form are presented. PARTICULARS OF THE SHIPS AND VALIDATED CONDITIONS Series 60 The first hull form under consideration is the Series 60 with a block coefficient CB of 0.6. The particulars of this hull form are presented below, taken from Longo (1996): Main particulars of Series 60 Designation Model scale (1:40) Full scale Length Lpp m m Beam B m m Draught T m m Blocl< coefficient CB Wetted area S m^ Bilge keels, rudder and propeller were not present during the model tests and are therefore not modelled in the calculations. 91

7 As a first step, tlie calculations are conducted with an undisturbed water surface, i.e. neglecting the generation of waves. The ineasurements were conducted at two different Froude numbers, i.e. Fn=0.16 and Fn=0.3l6. For the validation study of the flow fields presented in this paper, the Fn=0.16 results are used. Boundary conditions The measurements of the mean velocities and pressure fields were conducted with the model restrained from moving in any direction relative to the carriage. For the measurements of the forces and moments, however, the model was free to heave, roll and pitch. Because of the definition of the coordinate system used in the calculations for the present study, the data of the IIHR measurements have been mirrored to allow for easier comparison with the numerical results. This means that in this study, the starboard side is the pressure side and the port-side the suction side. KVLCC2M The second hull form under consideration is the KVLCC2M. The particulars of this hull form are presented below, taken from the website of the coming CFD Workshop in Tokyo, 2005 ( Figure I: Definition of curvilinear coordinate system At the hull surface, no-slip and impermeability boundary conditions are used. The velocities are set to zero (ïï = 0 ) while the pressure is extrapolated from the interior. Symmetry conditions are used on the water surface: ^0, du. <?u 0,^ = 0 Designation Main particulars ofkvlcc2m Model scale Full scale (1:64.4) Because the velocity and pressure behind the ship are unknown, Neumann boundary conditions are applied on the outflow plane: Length Lpp 4.97 m m Beam B m 58,0 m Draught T m 20.9 m Block coefficient CB Wetted area S m^ m^ Bilge keels, rudder and propeller were not present during the model tests and are therefore not modelled in the calculations. ^ = 0,^ = 0 The velocity components in the inflow plane and off-body plane are taken from a potential flow calculation while the pressures in both planes are calculated using the Bernoulli equation. During the viscous-flow calculation however, the velocity normal to the off-body plane is updated to allow for the displacement effect of the viscous boundaiy layer. Conform the specifications for the workshop, the calculations are conducted with an undisturbed water surface, i.e. neglecting the generation of waves. The measurements were conducted with the model restrained fi'om moving in any direction relative to the carriage. NUIVIERICAL PROCEDURES Coordinate system The origin of the right-handed system of axes used in this study is located at the intersection of the water-plane, midship and centre-plane, with x directed aft, y to starboard and z vertically upward. Note that all coordinates given in this paper are made non-dimensional with Lpp unless otherwise specified. All velocities are made non-dimensional with the undisturbed velocity Uq. Solver set-up Use was made of the in-house solver PARNASSOS, see Hoekstra (1999). It solves the discretised Reynolds-averaged Navier-Stokes equations for a steady, three-dimensional incompressible flow around a ship hull, supplemented by a turbulence model. For all calculations, Menter's oneequation turbulence model (1997), extended with the correction for longitudinal vorticity of Dacles-Mariani (1995), was used. The governing equations are integrated down to the wall, i.e. no wall-functions are used. The solver automatically applies grid-sequencing in order to accelerate convergence on the final grid. This technique starts the calculation on a coarse grid (designated istep=8) obtained by taking every 8* stream-wise plane and converges until the maximum changes in the pressure are below a certain limit. Then the grid is refined (istep=4) and the calculation is continued until the required convergence. This procedure is conducted until the solution satisfies the specified convergence criterion on the finest grid (istep=l). 92

8 For the present study, all solutions were converged until the maximum change of the pressure coefficient between successive iterations had dropped well below 5-10'^. Iterative convergence errors are therefore assumed to be negligible with respect to discretisation errors. Uncertainty analysis In order to determine and demonstrate the accuracy and reliability of solutions of viscous flow calculations, grid dependency studies are very important. Several methods for uncertainty analysis are available in literature. In the present paper, the method proposed by Ega and Hoekstra (2002) is followed, which amounts to establishing Roache's Grid Convergence Index (GCI) (see Roach (1998)) by a leastsquares method. The full details and background for the followed procedure for the uncertainty study can be found in their paper, but the main idea is as follows: block consists of an inner block and an outer block, see Figure 2. The inner block is the same for all yaw angles and the outer block can deform to allow for the drift angle of the ship. Therefore grids for various drift angles can be made efficiently. Due to the division of the computational domain in an inner and outer block, control of the quality of the grid near the hull is obtained. Use is made of body-fitted, nonorthogonal HO-type grids, which ai'e strongly stretched towards the hull to capture the strong gradients in the boundaiy layer. Richardson extrapolation is used to estimate the value (jjo of a specific quantity for an infinitely dense grid. The numerical prediction error 8; is estimated by: a-h,' The extrapolated value (jio, the constant a and the apparent order of convergence p are found by applying a least-squares method using the grids with different representative grid-cell sizes hi. This method requires at least four geometrically similar grids of various densities. Using the values found from the least-squares method, the uncertainty in the prediction is in the case of grid convergence (p > 0) specified to be as follows, with the factor of 1.25 a safety factor based on experience: U = ^^,-i If divergence or oscillatory convergence is found (p <= 0) then the uncertainty U is found by: U = 3 (max ) - min ((j). Figure 2: Inner (top) and outer (botloin) blocit structure The inner block is generated with a number of cells corresponding to normal MARIN practise in resistance and powering optimisation calculations, see Hoekstra (1999) or Eqa et al. (2002). The size (length, depth and width) of this domain is based on experience with simulations of the viscous flow around a ship sailing with zero drift angle. During the grid generation, first a base-grid is generated using a 3D elliptic grid generator, with a reasonably stretched grid node distribution in the normal direction, j, and the desired node distributions in stream-wise, i, and girth-wise, k, directions. By varying the control parameters in the grid generation process, the deviation from orthogonality is reduced as much as practically possible. Then grid stretching along the surface-normal grid lines is applied to arrive at the desired grid spacing at the hull surface. Once again, 3 is a safety factor based on experience. Based on the uncertainty analysis, it is assumed that the true solution will be bound with 95% confidence by the interval: (1) = ( ),±U It must be stressed that in this paper, only the number of nodes in stream-wise direction was varied. This means that the grids are not geometrically similar. COMPUTATIONAL DOMAIN AND GRID Grid generation To incorporate the drift angle of the ship, the inner block is rotated around the vertical z-axis over the desired yaw angle. Then the outer block is generated around the inner block. The interfaces between the blocks are matching to allow for subsequent merging of the inner and outer blocks. The cell stretching used in the inner block is automatically applied to the outer block as well. The size of the outer blocks is chosen such that the rotated inner block can smoothly be incorporated in the outer grids. This means that increasing drift angles will result in wider domains. The size of the domain is based on the assumption that a solver for potential flow is used to calculate the velocities in the inflow and off-body planes. Before starting the calculations, the separate blocks are merged into one block on the port side of the ship and another block on the starboard side of the ship. For each calculation, separate blocks are used for the port side and starboard side of the computational space. Each 93

9 Series 60 The first grid used in this study incorporates the hull form of the Series 60 for 10 degrees of drift angle. The port-side and starboard blocks together had for the finest grid 289x81x90 nodes in stream-wise, wall-normal and girthwise direction respectively, resulting in a total of over 2 million nodes. Compared to similar studies presented in literature this number of grid nodes is relatively large. The maximum deviation from orthogonality in this grid was 45. The inflow plane was located at 0.65-Lpp forward of midship and the outflow plane 0.82-Lpp aft of midship. The width and depth of the domain were 0.88-Lpp and 0.27'Lpp respectively. Figure 4: KVLCC2M, computational grid, -3 drift In the Figure 3, a top view of the grid (coarsened for presentation puiposes) used for this study is presented. The bow is directed to the left of the figure. REVIEW OF THE CALCULATIONS Series 60 The following calculations were conducted for the Series 60 at 10 drift angle: istep ni nj nk nodes y ^ 9.4'IQ-"^ ^ '* ' "'^ T0' '' 0.30 Figure 3: Series 60, computational grid, 10 drift The reference velocity Uo for the calculations corresponded to a model scale value of m-s"'. With a kinematic viscosity v of 1.138'10''' m^-s"' this results in a Reynolds number of ^ All calculations were conducted with undisturbed water plane. KVLCC2M The grid used in this study incorporates the hull form of the KVLCC2M for 0 and -3 degrees of drift angle (drift angle negative when bow rotated to starboard w.r.t. the incoming flow). For the zero drift case, only the starboard side of the ship is modelled due to the symmetry with respect to the centre-plane. On the flnest grid, the block consisted of 345x81x45 nodes in stream-wise, wall-normal and girth-wise direction respectively. This number of nodes amounts to almost 1.3 million nodes. For the drift calculation, the port-side and starboard blocks together had for the finest grid 345x95x90 nodes, resulting in a total of over 2.9 million nodes. Compared to similar studies presented in literature this number of grid nodes is relatively large. The inflow plane was located at 0.76-Lpp forward of midship and the outflow plane 0.93-Lpp aft of midship. The width and depth of the domain were 0.42-Lpp and 0.36-Lpp respectively. In the following figure, a top view of the grid (coarsened for presentation purposes) used for this study is presented. The bow is directed to the left of the figure. KVLCC2M The following calculations were conducted for the KVLCC2M hull form: drift istep ni nj nk nodes Apmax y ' "* ' ' ' ^ ' 8.0-IQ-' ' "' 0.53 The reference velocity Uo for the calculations corresponded to a model scale value of m-s"'. With a kinematic viscosity v of "^ m^-s"' this results in a Reynolds nmnber of ^ All calculations were conducted with undisturbed water plane. 94

10 GRID DEPENDENCY STUDY Series 60 Based on the results of the calculations using different grid densities, the discretisation error in the solution can be examined. In Figure 5, the value of the longitudinal velocity u is presented against the transverse position with respect to the centreline. The figure contains the results for a transverse cut close to the bilge and is located at x=0.3 (i.e. aft of midship) and z= This figure shows that the results on the finest grid are not yet grid-independent. But it is encouraging that the differences between successive numerical solutions decrease with increasing mesh density (within 3.3%) definitions used by Longo, Y is made non-dimensional with 0.5-p-Uo-S and N with 0.5-p-Uo'Lpp'. The relative step-size indicates the coarseness of the grid with respect to the finest grid. Theoretically, the discretisation error (in stream-wise direction) disappears if the solution is extrapolated to zero relative step-size. The extrapolated value is the value that should be compared to the experiments. The horizontal dashed lines in the figure indicate the uncertainty interval. The figure illustrates that for the transverse force as well as the yawing moment the difference in the results for progressively finer grids reduces to less than 2.5%. The figure also shows that extrapolation of the results from grid dependency studies to zero for this type of computations is not trivial. Although the differences between the solutions for the yaw moment are relatively small and large for the transverse force, the uncertainty interval for the yaw moment is large due to the fact that oscillatoiy convergence was found. This illustrates that for these cases, the uncertainty estimation method is not well suited. It should be noted however, that only grid refinement in longitudinal direction was applied bull surface -0,015-0,017-0,019-0,021 ) Ycfd Y' exp extrap 0.2-0,023 L Figure 5: Comparison grid density and experimental data, x=0.3, z=-0.048, longitudinal velocity In Figure 6 the differences between the calculated longitudinal velocity and the experimental values are given for the four grids. Especially for this transverse cut, which is placed directly through the vortex originating from the bilge, the solution still changes with increasing mesh density. However, once again the differences between successive solutions decrease with increasing mesh density Figure 7: Grid dependency of integrated variables 0,10 The table below shows the quantitative results of the uncertainty analysis, with (j), the solution on the finest grid, ifo the estimated value using extrapolation to an infinitely fine mesh, U the uncertainty and p the apparent order of convergence: Quantity 1^1 U P X' ' -4,63-10-' 34% 0,43 Y' "^ -1,75-10'^ 1.2% 1.85 Z' ^ 4,93-10"^ 0.7% 1,52 K' 7.IM0-' 7,05-10-' 1,3% 1.02 Figure 6: Difference in longitudinal velocity between calculations and experiments, x=0.3, z= M' ' -8,16-10-' 94% Divergence N' - -9,91-10-'' 30% Oscillatory convergence Also the dependency of the integrated forces on the ship for the various grids has been studied. In Figure 7, the nondimensional transverse force Y and yawing moment N for the different grid densities are given. Corresponding to the KVLCC2M, zero drift case The following figures illustrate the longitudinal velocity u and transverse velocity v behind the stern of the KVLCC2M for the straight-ahead condition for the four different grids. 95

11 In these figures comparisons are made between the results of the different grids at a transverse cut located at x=0.48 and z= It is seen that for y > 0.01, the results are more or less grid-independent. However, closer to the centreline, the solution still changes considerably between the second finest grid and the finest grid. Noteworthy is the change of the transverse flow direction between y < u(cr(l,i.slep=l) 11 (crd,isiep=z) u (urd,istc[i=4) 11 fi:l(i;isli.-[v=8) Figure 10: Discretisation of stern and location of ineasio-ements (white dot) 0.04 Figure 8: Grid dependency of axial velocity behind stern, x=0.48,z=-0.05, 0 drift v(cfd,istep=l) V ((;fd,isll-p=2) V (trd,islei)=4) V (crd,i.tep=81 The dependency of the integrated variables on the grid density in stream-wise direction is also studied. In this case, not only the total forces (subscript t) but also the separate components due to pressure (subscript p) as well as due to friction (subscript f) are considered. Figure 11 presents the results for the longitudinal force X and vertical force Z graphically. In this case, the forces for the KVLCC2M are made non-dimensional using 0.5-p-Uo-Lpp-T, conform specifications for the CFD Workshop cfd extrap O.IIIO , Figure 9: Grid dependency of transverse velocity' behind stern, x=0.48, z=-0.05, 0 drift The reason for this grid dependency is the resolution of the grid between the aft part of the ship and the position at which the solution is resolved. If insufficient grid cells are present, the transition between the no-slip boundary condition and free-stream condition at the solution position is too abrupt and the development of the flow is not well modelled. In Figure 10, the position of the measurements is compared to the grid for the finest mesh. It is seen that only two grid nodes are present between the no-slip hull-surface and the measurement position. For the coarser grids, one (for istep=2) or even no node (for istep=4 and istep=8) is present and subsequently interpolation between discrete results at neighbouring grid nodes will result in inaccurate predictions of the flow at the measurement position. It is therefore proposed to use grid refinement at the stern to resolve the velocities at the measurement position more accurately cfd - extrap ,1125 0,1120-0,010 _0,1115 ' -0,015 ' 0,1110 0,1105-0,020 0, Figure 11: Grid dependency of integrated variables, 0 drift 96

12 Quantitatively, the results are presented in the table below (with the pitch moment M made non-dimensional 0.5-p-Uo-Lpp'-T). Quantity ^0 U P Xp' '' "' 153% Oscillatory convergence Xf' -7.3M0'' "' 0.7% 1.92 X,' "' "' 39% Divergence Zp' "' "' 0.1% 1.54 Zf' "'' "'' 3.2% 1.20 z; "' "' 0.1% 1.52 Mp' "^ "^ 1.6% 1.15 Mf' "' "*' 1.1% 1.86 M,' "^ "^ 1.5% 1.15 using plane was assumed. The influence of this assumption has to be examined in further studies. In Figure 12 through Figure 14, the calculated longitudinal velocity flelds based on the finest grid for several transverse planes are given together with the velocity field obtained from the experiments. Note that the calculated results have been projected on the measurement points and therefore some irregularities that are present in the measurement data are introduced in the simulation results. The dashed lines represent the measurements and the continuous lines represent the calculations. It is found that with the grid geometry used, the longitudinal force due to the pressure cannot be resolved accurately. Since this component is in the same order of magnitude as the friction component, the total longitudinal force is also inaccurately predicted. An increase of the grid density at the bow and stern will result in a better description of the hull form and the local velocity gradients and subsequently to a more accurate prediction of the longitudinal force. Figure 12: Axial velocity conlours, x=0.3, 10 drift C0N4PARIS0N WITH EXPERIMENTS Series 60 Already in the previous sections, the results of the calculations have been presented along with results of the experiments. As can be observed in Figure 5 and Figure 6 with the transverse cut, the results of the calculations for the finest grid are quite close to the measurements. The table below presents the maximum differences obtained from the comparison of the transverse cuts: Figure 13: Axial velocity contours, x=0.5, 10 drift AUma.xl y AUm Z istep=l istep=2 istep=4 istep= Figure 14: Axial velocity contours, x=0.7, 10 drift These results show that for istep=l, the maximum error in the longitudinal velocity at the transverse cut at x=0.3 is less than 5% of the undisturbed velocity. The results show that the vortex from the bilge in the calculations is slightly shifted away from the hull, resulting in relatively large differences when subtracting the experimental results from the calculations. Qualitatively, the physics of the flow are well represented. Quantitatively, the comparison of the integral forces in Figure 7 shows that for the istep=l results a good correlation of the yaw moment with the measurements is found. However, a deviation of the side force from the experimental values is also present. A reason for the discrepancy between the simulations and the experiments can be that the experiments were conducted with the model free to trim and sink while the calculations were done with the ship on even keel. Furthermore, differences may be introduced because in the calculations an undisturbed water The correspondence between the measurements and the simulations is very promising and the majority of the calculated contour lines follow the contours from the experiments closely. The calculated velocity profile at the keel is very close to the measured profile while the position and magnitude of the vortex developing at the keel is well predicted. The strength of the vortex from the bow area is slightly less than found during the measurements and the location is somewhat shifted downward and further away from the ship. KVLCC2M, zero drift case Comparisons between the longitudinal and transverse velocities obtained from the calculations and from the measurements at x=0.48/z=-0.05 are given in Figure 15 and Figure 16. It is seen that the physics of the flow are captured but some discrepancies are seen close to the centre line, especially in the transverse velocity. In further research.

13 additional calculations will be done with a refined grid in order to investigate whether this is caused by the poor grid resolution at the stern. The prediction of the longitudinal force is rather poor. The resistance force from the simulation is 46% lower than the measured resistance. As already suggested, grid refinement around the bow and stern will improve the prediction. 11 (cfd,istcp=l) a (osp.mirtored)l KVLCC2M, -3 drift case Only integral variables are available from the measurements for the -3 drift case. The table below presents the comparison between the simulated and experimental results. Quantity Pressure Friction Total Exp Error X' '' "^ "^ "^ 11% Y' '' "' "' "^ -22% Z' ' "'' "' - - K' "'' "' "'' - - M' "^ "' "^ - - N' "' "' "' "' 19% During the experiments, also a 3 drift angle condition was tested. When assuming a symmetric flow around the ship model for equal positive or negative drift angles, these results may also be used to compare to the simulation results. This leads to the following comparison: 0.04 Quantity CFD Exp (-3 ) Error Exp (3 ) Error X' "^ "^ 11% "^ 10% Figure 15: Axial velocity at x=0.48/z=-0.5, 0 drift Y' "' "^ -22% "^ -21% 0.05 V (cfd.islgp^l) V (e\p,niinorój) N' "' "' 19% "' 2.8% Apparently, the yawing moment measured during the test with -3 drift angle differs significantly from the result for 3 drift angle. This comparison leads to more favourable error values, but still large discrepancy is found in the transverse force. For practical application the predictions should be improved. > Figure 18 presents the axial velocity contours at x=0.48. The asymmetry in the flow due to the drift angle is clearly present Figure 16: Transverse velocity at x=0.48/z=-0.5, 0 drift Figure 18: Axial velocity contours, x=0.48, -3 drift Figure 17: Axial velocity contours atx=0.48, 0 drift Figure 17 presents the axial velocity contours at x=0.48. The horizontal line in the figure represents the transverse cut at z=-0.05 at which the velocities were resolved. 98

14 CONCLUSIONS Simulations of the viscous-flow around two different hull forms have been conducted. In order to determine the grid dependency several grid densities were used for some of the calculated conditions. Although still notable differences between the two finest meshes for the Series 60 were found, detailed comparisons with experimental data show that the physics of the flow are well predicted even when looking at discrete positions in the flow fleld. However, for the second hull form, the KVLCC2M, strong grid dependence was found at the propeller plane. This is caused by poor grid resolution between the hull surface and the propeller plane. Qualitatively, promising results are obtained. For practical purposes however, the accuracy of the results should be improved. For the current calculations, the predicted yaw moment is close to the measurements but the side force is under-predicted. Reasons for these discrepancies might be the neglect of trim and sinkage for the Series 60 and of the water surface deformation. For the KVLCC2M, this is probably also caused by insufficient grid resolution at the bow and stern. This should be studied in future research. Tahara, Y., Longo, J. and Stern, F. "Comparison of CFD and EFD for the Series 60 CB=0.6 in steady drift motion". Journal of Marine Science and Tecimoiogy, pages 7:17 30, Toxopeus, S.L. "Simulation and Validation of the Viscous Flow around the Series 60 Hull Form at 10 Drift Angle". 7th NitTTS Numerical Towing Tank Symposiui?i, Hamburg, October REFERENCES Alessandrini, B. and Delhommeau, G. "Viscous free surface flow past a ship in drift and in rotating motion". 22'"' Symposium on Naval Hydrodynamics, pages , August Cura Hochbaum, A. "Computation of the turbulent flow around a ship model in steady turn and in steady oblique motion". 22'"' Symposium on Naval Hydrodymainics, pages , August Dacles-Mariani, J., Zilliac, G.G., Chow, J.S. and Bradshaw, P. "Numerical / experimental study of a wingtip vortex in the near field". AIAA Journal, Vol. 33, pp , September Di Mascio, A., and Campana, E.F. "The numerical simulation of the yaw flow of a free surface ship". 7"' International Conference on Nuitierical Ship Hydrodynamics, pages , July E9a, L., Hoekstra, M., and Windt, J. "Practical grid generation tools with applications to ship hydrodynamics". 7"' International Conference on Grid Generation and Computational Field Simulations, February Epa, L. and Hoekstra, M. "An evaluation of verification procedures for CFD applications". 24"' Symposium on Naval Hydrodynamics, July Hoekstra, M. Numerical Simulation of Ship Stern Flows with a Space-Marching Navier-Stokes Method. PhD thesis. Delft University of Technology, Faculty of Mechanical Engineering and Marine Technology, October Longo, J.F. Effects of Yaw on Model-Scale Ship Flows. PhD thesis. University of Iowa, May Menter, F.R. "Eddy viscosity transport equations and their relation to the k-s model". Journal of Fluid Engineering, Vol. 119, pp , Roach, P.J. Verification and Validation in Computational Science and Engineering. Hermosa Publishers,

15 Page 1 of 1 Heer, P.W. de From: Heer, P.W. de Sent: Tuesday, November 09, :15 AM To: 's.l.toxopeus@marin.nr Subject: paper MARIN-NMRI Workshop Hallo Serge, Ik heb hier het paper "Validation of Calculations of the Viscous Flow around a Ship in Oblique Motion" voor me liggen datje gebracht hebt op the First MARIN-NMRI Workshop in Tokyo dit jaar Mijn vraag is nu: Ik heb voor de output van papers nodig een kopie van de Kaft + de daarop volgende pagina's inclusief de inhoudsopgave. Ik weet niet of het proceeding digitaal of als hardcopy is uitgebracht maar ik wil graag van die pagina's een kopie. Je mag het ook morgen aan Tom van Terwisga meegegeven want die komt dan toch naar Delft. Heb je vragen laat het weten. Alvast bedankt Piet 11/9/2004