1807404065_1999999096_icmes_2006-oers_toxopeus.pdf

On the relation between flow behaviour and the lateral force distribution acting on a

ship in oblique motion

Bart van Oers, MSc (Hon), GMRINA Delft University of Technology - Ship Hydromechanics Laboratory

Serge Toxopeus, MSc, MSNAME

Maritime Research Institute Netherlands (MARIN) Delft University of Technology - Ship Hydromechanics Laboratory

Author's Biographies Bart van Oers graduated in 2005 from Delft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering with a specialisation in Ship Hydrodynamics. Currently, he is researching the design optimisation of naval surface vessels in the context of his PhD project. Serge Toxopeus graduated in Ship Hydrodynamics from Delft University of Technology at the Faculty of Mechanical Engineering and Naval Architecture in 1996. Since then, he has been working in the Manoeuvring Department of MARIN. Main fields of competence are ship manoeuvring simulations and practical application of viscous-flow calculations for manoeuvring ships.

SYNOPSIS This paper presents the results of a research project focussed on the simulation of the viscous flow fields around five vessels sailing at a non-zero drift angle. The calculated flow fields were used to investigate flow features relevant to the lateral-force distribution, thus offering insight in the physics involved in the manoeuvring behaviour of ships. This insight can be used to improve the manoeuvring characteristics in the early stages of the design process.

INTRODUCTION

Proper manoeuvrability is essential for a ship to perform its task, necessary for both navigation and the avoidance of traffic and natural hazards. Designing such a ship, with suitable manoeuvring characteristics, is, however, not straightforward. To be able to do so, it is necessary to predict, with sufficient accuracy, the manoeuvring behaviour in the early design stage. In addition, an understanding of the physics involved, i.e., what causes the forces acting on the vessel, is necessary to determine relevant design changes. To extend the predictive capability and improve the understanding of the flow field, the use of mathematical models with a better prediction of the flow behaviour is necessary and therefore the viscous flow-solver Parnassos (developed by MARIN) was extended to simulate the flow around ships sailing at non-zero drift angle. Promising results with respect to quality of both field and integrated quantities were obtained (reported in [1], [2], [3] and [4]). The present paper addresses the relation between flow field and lateral force distribution of vessels in stationary oblique flow. The flow field around the Esso Osaka for 10° is investigated, highlighting the significant flow features introduced by the oblique motion. Using the pressure distribution on the hull, the flow aspects relevant to the lateral force distribution are established. As a closure, a comparison is made between the pressure distribution of five vessels to establish the relation between hull shape and manoeuvring characteristics of ships.

APPROACH

Coordinate system

The origin of the ship-fixed, 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. All coordinates given in this paper are made non-dimensional with Lpp. All velocities are made non-dimensional with the ship speed Vs. Forces and moments are given relative to the origin of the coordinate axes, but in a right-handed system with the longitudinal force directed forward positive and the transverse force positive when directed to starboard. A positive drift angle β corresponds to the flow coming from starboard.

Computational background

The calculations were performed with the MARIN in-house flow solver Parnassos, ([5] and [6]). This solver is based on a finite-difference discretisation of the Reynolds-averaged continuity and momentum equations, using fully-collocated variables and discretisation. The equations are solved with a coupled procedure, retaining the continuity equation in its original form. For the calculations, the one-equation turbulence model, proposed by Menter [7], was used, while avoiding the use of wall-functions. The Spalart correction (see [8]) of the stream-wise vorticity is included. The results presented in this paper were all obtained on structured grids with H-O topology, with grid clustering near the bow and propeller plane. More details regarding the computational domain, the implementation of a drift angle in the calculations and the applied boundary conditions are found in [3] and [4]. Appendages, free surface deformation and dynamic trim and sinkage of the vessels were not modelled.

Vessels

Calculations were made of the model scale flows around five ships sailing at a drift angle. Table I shows some main particulars of these ships together with the Reynolds numbers used in the calculations.

Table I: Main particulars

Osaka [4] MARIN Ferry* [9] Series 60 [1] KVLCC2M [3] Hopper [10]

Cb 0.825 0.570 0.599 0.810 0.878 Cm 0.998 0.981 0.978 0.999 0.996 Cp 0.826 0.756 0.613 0.810 0.882 Cwp 0.889 0.778 0.708 0.905 1.020

Lpp/B 6.129 5.53 7.503 5.522 4.72 Lpp/T 15.633 28.56 18.699 15.386 11.474 B/T 2.551 5.19 2.492 2.786 2.431

Re 7.6·106 3.7·106 2.3·106 3.9·106 7.7·106 * sailing in ballast draught

INFLUENCE OF DRIFT ANGLE ON FLOW AROUND THE ESSO OSAKA

To establish the influence of a drift angle, a comparison is made of the flow fields around the Esso Osaka at β=0° and β=10°. Viscous effects have the largest influence around the aft body, which therefore becomes the area of focus of the discussion. Figure 1 through Figure 4 respectively show the axial flow velocity at the bow, at 25% Lpp and 45% Lpp aft of midship and at the propeller plane. Where applicable, letters are used to indicate relevant parts of the figures. Three dominant effects govern the flow around a ship sailing at a drift angle. The first, the displacement effect, introduces a pressure field around the hull as pressure gradients displace the flow away from (at the bow) and towards the hull (at the forward and aft shoulders) to follow the local hull curvature. These pressure gradients are accompanied by changes in flow velocity. The second effect, flow separation, can occur when the streamlines curve towards the hull by the displacement effect (a pressure reduction at the hull surface) but are unable to follow the curvature of the hull due to an adverse pressure gradient. Flow separation can lead to vortex development. The third effect, the convective property of a vortex, can change the flow velocity by convecting high-velocity fluid towards a place of lower flow velocity and thereby changing the local pressure. Obviously, prediction of the latter two effects requires the use of a viscous flow solver. The main change to the flow field at the bow when sailing in oblique flow is the windward shift of the stagnation point, see Figure 1. The pressure changes extend downstream towards the forward shoulders, increasing the pressure at the windward side, while reducing it at the leeward shoulder.

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Figure 1: Axial velocity distribution at the bow

Further downstream at the aft shoulders, 25% Lpp aft of midship, vortices develop at both bilges, as shown in Figure 2. The vortex shed at the leeward bilge starts further towards the bow, due to the difference in the flow direction relative to the hull curvature. Both vortices remain close to the hull and grow in strength downstream. The boundary layer shows a large difference in thickness between the windward and leeward side. This difference indicates a delayed separation of the flow on a concave, inward-curved surface (refer to A in Figure 2) thus allowing the displacement effect to further reduce the pressure at the windward aft shoulder.

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Figure 2: Axial velocity distribution at the aft shoulders, 25% Lpp aft of midship

At 45% Lpp aft of midship, shown in Figure 3, large changes occur in the flow field as the viscous effects become more pronounced. The zero drift case reveals the rapid increase in boundary-layer thickness. For 10° drift, the vortex at the leeward side, which developed upstream at the leeward bilge, has detached from the boundary layer near the hull by a combination of an increase in vortex intensity and the receding shape of the hull (B). The leeward side also shows a large area of flow separation close to the keel, resulting in the development of an intense vortex (C). This vortex remains close to the hull by the transverse flow direction introduced by the receding frame shape, which maintains a constant draft. Due to its convective property, this vortex increases the flow velocity near the hull, thus compressing the boundary layer and reducing the local pressure. At the windward side, the vortex from the windward bilge ends up alongside the hull, despite the oblique flow direction (D).

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Figure 3: Axial velocity distribution at 45% Lpp aft of midship

The predicted flow field for 0° drift at the propeller plane, see Figure 4, shows two counter-rotating vortices, which increase the axial flow velocity in the upper part of the propeller disk by convection (E in Figure 4). A more complex flow field is visible for β=10°. The leeward vortex, reinforced by the flow separation near the keel, merges with a new vortex shed from underneath the propeller hub, explaining its stretched shape (F). Due to the drift angle, the windward vortex is co-rotating with the leeward vortex, which results in an upward movement of the leeward vortex and a downward movement of the windward vortex (F and G).

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RELATION BETWEEN FLOW AROUND THE SHIP AND PRESSURE DISTRIBUTION

In this section the influence of the flow features on the pressure distribution (the contribution of the friction to the lateral force is negligible) on the hull of the Esso Osaka is discussed, see Figure 5 through Figure 7. Again, letters are used to refer to relevant parts of the figures. The pressure is made dimensionless using equation (1).

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Figure 5: Cp distribution at the bow and forward shoulders, β = 0° and β = 10°

From the pressure distribution at the bow, shown in Figure 5, three things stand out. First is the windward shift of the stagnation point caused by the oblique inflow (A in Figure 5). Secondly, this shift also affects the pressure distribution near the forward shoulders, increasing the pressure at the windward side while reducing it at the leeward side (B). Third, near the bottom the pressure changes are opposite to those occurring at the forward shoulders. At the windward side, a reduction in pressure is visible whereas at the leeward side the pressure increases relative to the zero-drift case (C). These three changes result from displacement effects, i.e. a change in flow direction relative to the local hull curvature.

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Figure 6: Cp distribution at the aft shoulders and stern, windward side, β = 0° and β = 10°

Figure 6 and Figure 7 show the pressure distribution at the windward and leeward sides of the stern respectively. A comparison between β=0° and β=10° shows a pressure reduction at the windward aft shoulder, introduced by the flow remaining attached to the hull over a longer distance compared to the zero-drift case (D in Figure 6). At the bottom of the stern, the vortex developing at the windward bilge has little influence on the local pressure distribution (E).

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Figure 7: Cp distribution at the aft shoulders and stern, leeward side, β = 0° and β = 10°

The area of flow separation responsible for the vortex discussed in the previous section shows up as a pressure reduction visible near the bilge (F in Figure 7). The convective property of the vortex reduces the local pressure and this, together with the flow separation at the stern contour, prevents the shift of the aft stagnation point (G) towards the leeward side. It also limits changes in pressure at the aft shoulder (H). The pressure distribution near the propeller hub (I) is dependent on the position and intensity of vortices on both the windward and leeward side of the hull, as explained in the previous section. In [4] it was shown that the pressure distribution in this area can vary substantially with small changes in drift angle.

RELATION BETWEEN HULLFORM AND PRESSURE DISTRIBUTION

To establish the relation between hull form and lateral force distribution, the pressure distributions on the five hull forms under consideration are compared for 10° drift angle‡. The discussion will focus on the bow and stern areas, as these have the largest contribution to the lateral force. Due to space limitations, the five flow fields could not be included but these have been used to further understand the pressure distributions. Starting at the bow, see Figure 9 and Figure 10, V-shaped frames near the bow are only found on the MARIN Ferry, the other four vessels have U-shaped frames. These differences in frame shape show up as pressure changes around the forward shoulders and near the bottom of the bow, which are more pronounced for the U-framed ships. The MARIN Ferry and the Series 60 have very slender bows, reducing flow displacement and thus the influence of the stagnation pressure at the bow. The bow contour of the Ferry is more rounded and this, together with the slight concave shape of the hull aft of the bulb, considerably reduces the pressure difference between the leeward and windward side of the hull. The flow separates underneath the bow of both the Ferry and Series 60, resulting in a vortex. The very slender frames, the sharp bow contour and the concave waterlines of the Series 60 result in a large high pressure area at the windward side of the bow and a large low pressure area at leeward. Compared to the Ferry, the blunt bows of the Osaka, the KVLCC2M and the hopper dredger introduce a much higher stagnation pressure and stagnation area on the windward side, while simultaneously allowing the flow to remain attached at the leeward side, further reducing the pressure. At the stern, see Figure 11 and Figure 12, the flow features are more complex. A pressure reduction develops at the windward aft shoulder, as was discussed in the previous section. Its longitudinal extent and magnitude are

‡ The pressure distributions for the KVLCC2M in this paper are given for a drift angle of 9°

dependent on the frame shape and the contour line of the stern. The Ferry and Hopper, both with pram-type aft bodies, show a larger pressure reduction over a longer distance compared to the U or V shaped frames due to an increase in hull curvature relative to flow direction. A more full aft body obviously increases hull curvature and hence the pressure reduction at the windward aft shoulder (compare for instance the results of the full-bodied Hopper with those of the slender Ferry). The influence of stern shape also influences viscous effects. Flow separation occurs at two locations near the stern, at the stern contour and near the bottom of the leeward aft shoulder. At the second location, the accompanying vortex reduces the local pressure. However, due to the (upward) cross flow generated by the pram-type aft-body of the Hopper, the vortex is located further away from the hull surface, resulting in a smaller reduction of the pressure. Together with the relatively blunt waterlines in the aft ship, this results in a shift of the aft stagnation point towards the leeward side. None of the other vessels shows this shift. The larger skeg of the Ferry prevents the leeward shift of the stagnation point, despite having a similar hull shape as the Hopper. In addition to the effect discussed above, the skegs of the Hopper and the Ferry introduce other effects. At the windward side, they displace the flow, increasing the local pressure. At the leeward side, a vortex develops at the start of the skeg, increasing in strength downstream. This vortex reduces the pressure at the leeward side of the skeg, contributing to a higher negative lateral force at the stern. Due to the strong reduction in sectional area in the aft ship of the Hopper, the flow around the windward side of the stern is accelerated and therefore the pressure on the skeg on windward is relatively small compared to the pressure distribution on the skeg of the Ferry. In addition to the influences stated above, the longitudinal positions of the forward and aft shoulders and skeg also influence the lateral force distribution by changing the hull curvature and the longitudinal position of pressure changes.

RELATION BETWEEN PRESSURE DISTRIBUTION AND THE LATERAL FORCE DISTBUTION

To establish the consequences for the lateral force distribution along the length of the ship, the ship is divided into 10 segments, with the segment boundaries located at even stations. The lateral forces Yn acting on these segments are made non-dimensional using the projected lateral area Sn of each segment according to equation (2). Figure 8 shows the calculated longitudinal distributions for the five vessels (the results for the KVLCC2M were obtained by interpolation between 9° and 12° drift angle).

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Figure 8: Longitudinal distribution of lateral force at 10° drift angle

Figure 8 shows that the largest magnitude of the lateral force is generated at the bow and forward shoulders, i.e. in segments 9 and 10. Furthermore, it shows that the five foremost segments, for all ships, contribute to the lateral force, while the aft segments experience either negative lateral forces as well as positive forces, depending on the hull form. It should be noted that the overall lateral force is negative due to the positive transverse velocity. This actually means that a positive transverse drag is experienced by the ship, as should be expected.

Starting with the influence of the bow shape, it was shown in the previous section that the blunt bow vessels have significantly larger pressure gradients at the bow, explaining the large transverse drag (i.e. large negative lateral force) at the bow and forward shoulders. The flow separation at the slender bows of the Ferry and Series 60 reduces the transverse drag in segment 9 relative to the vessels with the blunt bows. The relatively small transverse drag of the MARIN Ferry in segment 10 is caused by a combination of the rounded bow contour, the concave hull shape aft of the bulb and the relatively shallow draught (low aspect ratio). Moving aft, the reduction of the pressure at the windward aft shoulder is responsible for the positive lateral forces seen for segments 1 to 4. The higher block vessels all show a positive lateral force in segments 2 to 4, introduced by displacement effects resulting from the increased hull curvature at the aft shoulders. The pram-type aft body of the Hopper has an even larger pressure drop, extending over a longer distance explaining the large positive lateral force even in segment 1. All vessels show the development of flow separation at the leeward side of the stern, with varying influence on the lateral force distribution. The ships with a U-shaped aft body, the Osaka, the KVLCC2M and the Series 60, all develop an intense vortex at the leeward side, which reduces the local pressure and thus results in small or negative lateral forces in segments 1 to 2. At the extreme end of the stern, different aspects determine the pressure distribution. For the KVLCC2M, and the Osaka the relative vortex intensity determines the pressure distribution in segment 1. The positive transverse drags (i.e. negative lateral forces) in segments 1 and 2 of the Ferry and the Series 60 can be attributed to the effect of the skeg and the very narrow and sharp aft body of the Series 60. The influence of the skeg for the Hopper diminishes by the far larger influence of the pram-type aft body and aft shoulder location, resulting in a net positive lateral force.

INFLUENCE OF HULL FORM ON MANOEUVRABILITY

The manoeuvrability of ships can be divided into two separate qualities: the turning ability and the directional (or related to that, the course) stability. For a good turning ability, the resistance against turning should be small, the yaw moment as a function of drift should be large and the ability to generate a turning moment (by using a steering appendage such as the rudder) should be large. For a good directional stability, the resistance against turning should be large and the yaw moment as a function of drift should be small. Therefore, a compromise between the turning ability and the directional stability must always be made, unless a very powerful steering appendage is applied. For most ships except very slender vessels such as frigates, the required turning ability is easily met but an acceptable directional stability is hard to achieve. For these ships, the directional stability can be improved best by reducing the yaw moment as a function of drift and increasing the resistance against turning. These effects can be achieved simultaneously by increasing the drag against cross-flow in the aft ship. Based on experience from manoeuvring tests and clarified by the study presented in this paper, this can be realised by moving the aft shoulder forward (e.g. by moving the centre of buoyancy forward) such that the aft ship becomes more slender or by increasing the pressure at the windward side by applying a sharp skeg. Alternatively, this can be achieved by using V-shaped frames instead of U-shaped frames in the aft ship. Stimulating flow separation and vortex development by reducing bilge radius near the stern will reduce the destabilising yawing moment while increasing the transverse drag for U-shaped and V-shaped frames.

CONCLUSIONS

Using the results of calculations for several different ships, the influence of the hull form on the flow around five different ships was studied, relating the hull form and the manoeuvring performance of the ship. The following qualitative conclusions are drawn. Influence of the bow shape: • Sharp, vertical frames generate more transverse drag than slender, shallow draught, V-shaped frames. • Concave waterlines reduce the transverse drag compared to convex waterlines. Influence of the aft body shape: • A pram type aft body reduces the transverse drag and increases the destabilising yawing moment as a

function of drift relative to U and V-shaped frames. • V-shaped frames generate slightly more lateral drag than U-shaped frames. • The changes above increase in magnitude for the higher block vessels.

• Skegs increase the overall lateral drag while reducing the destabilising yawing moment • Vortex development resulting from flow separation at the leeward side of the stern increases the lateral drag

while reducing the destabilising yawing moment for U and V-shape aft-bodies. The results above show that the manoeuvring performance of ships is strongly determined by the shape of the aft body. Therefore, careful attention should be paid to the design of the aft hull form in the early design stage and guidelines are given. The insight offered by viscous flow simulations contributes to the assessment of manoeuvring characteristics in the early stages of design. Research to include rotational motion in Parnassos, further improving the predictive capability, is currently under way.

ACKNOWLEDGEMENTS

Part of the work conducted for this paper has been funded by the Commission of the European Communities for the Integrated Project VIRTUE. This project is part of the Sixth Research and Technological Development Framework Programme (Surface Transport Call). Another part of the project was conducted as an MSc thesis project carried out by Bart van Oers at MARIN under supervision of Serge Toxopeus.

REFERENCES

[1] Toxopeus, S.L. ; "Simulation and validation of the viscous flow around the Series 60 hull form at 10° drift angle". 7th NuTTS Numerical Towing Tank Symposium, October 2004.

[2] Toxopeus, S.L.; "Validation Of Calculations Of The Viscous Flow Around A Ship In Oblique Motion". The First MARIN-NMRI Workshop, pp. 91-99, Tokyo, Japan, October 2004.

[3] Toxopeus, S.L.; "Verification And Validation Of Calculations Of The Viscous Flow Around KVLCC2M In Oblique Motion". 5th Osaka Colloquium, March 2005.

[4] Van Oers, B.J. An investigation of the viscous flow around a ship in oblique motion. MSc thesis, Delft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering, March 2005.

[5] Hoekstra, M. and Eça, L. "PARNASSOS: An Efficient Method for Ship Stern Flow Calculation", Third Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, pp. 331-357, Osaka, Japan, May 1998.

[6] 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 1999.

[7] Menter, F.R. "Eddy Viscosity Transport Equations and Their Relation to the k-ε Model", Journal of Fluids Engineering, Vol. 119, pp. 876-884, December 1997.

[8] Dacles-Mariani, J., Zilliac, G.G., Chow, J.S. and Bradshaw, P. "Numerical/experimental Study of a Wing Tip Vortex in the Near Field", AIAA Journal, Vol. 33, pp. 1561-1568, September 1995.

[9] Toxopeus, S.L. and Loeff, G.B. "Model Tests with Segmented Ferry", MARIN Report 15295-1-BT, October 1999 (Restricted).

[10] Toxopeus, S.L. "Study of the flow around a Hopper Dredger at a Drift Angle", MARIN Report No. 18349-8-CPM, May 2005 (Restricted).

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