On the relation between flow behaviour and the lateral force distribution acting on a ship in oblique motion

Transcription

1 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 Universit of Technolog - Ship Hdromechanics Laborator Serge Toxopeus, MSc, MSNAME Maritime Research Institute Netherlands (MARIN) Delft Universit of Technolog - Ship Hdromechanics Laborator Author's Biographies Bart van Oers graduated in 25 from Delft Universit of Technolog, Facult of Mechanical, Maritime and Materials Engineering with a specialisation in Ship Hdrodnamics. Currentl, he is researching the design optimisation of naval surface vessels in the context of his PhD project. Serge Toxopeus graduated in Ship Hdrodnamics from Delft Universit of Technolog at the Facult of Mechanical Engineering and Naval Architecture in 996. 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-ero drift angle. The calculated flow fields were used to investigate flow features relevant to the lateral-force distribution, thus offering insight in the phsics involved in the manoeuvring behaviour of ships. This insight can be used to improve the manoeuvring characteristics in the earl stages of the design process. INTRODUCTION Proper manoeuvrabilit is essential for a ship to perform its task, necessar for both navigation and the avoidance of traffic and natural haards. Designing such a ship, with suitable manoeuvring characteristics, is, however, not straightforward. To be able to do so, it is necessar to predict, with sufficient accurac, the manoeuvring behaviour in the earl design stage. In addition, an understanding of the phsics involved, i.e., what causes the forces acting on the vessel, is necessar to determine relevant design changes. To extend the predictive capabilit and improve the understanding of the flow field, the use of mathematical models with a better prediction of the flow behaviour is necessar and therefore the viscous flow-solver Parnassos (developed b MARIN) was extended to simulate the flow around ships sailing at non-ero drift angle. Promising results with respect to qualit of both field and integrated quantities were obtained (reported in [], [2], [3] and [4]). The present paper addresses the relation between flow field and lateral force distribution of vessels in stationar oblique flow. The flow field around the Esso Osaka for is investigated, highlighting the significant flow features introduced b 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 sstem The origin of the ship-fixed, right-handed sstem of axes used in this stud is located at the intersection of the water-plane, midship and centre-plane, with x directed aft, to starboard and verticall upward. All coordinates given in this paper are made non-dimensional with L pp. All velocities are made non-dimensional with the ship speed V s. Forces and moments are given relative to the origin of the coordinate axes, but in a righthanded sstem 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.

2 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 Renolds-averaged continuit and momentum equations, using full-collocated variables and discretisation. The equations are solved with a coupled procedure, retaining the continuit equation in its original form. For the calculations, the one-equation turbulence model, proposed b Menter [7], was used, while avoiding the use of wall-functions. The Spalart correction (see [8]) of the stream-wise vorticit is included. The results presented in this paper were all obtained on structured grids with H-O topolog, 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 boundar conditions are found in [3] and [4]. Appendages, free surface deformation and dnamic 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 Renolds numbers used in the calculations. Table I: Main particulars Osaka [4] MARIN Ferr * [9] Series 6 [] KVLCC2M [3] Hopper [] C b C m C p C wp L pp /B L pp /T B/T Re * 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= and β=. Viscous effects have the largest influence around the aft bod, which therefore becomes the area of focus of the discussion. Figure through Figure 4 respectivel show the axial flow velocit at the bow, at 25% L pp and 45% L pp 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 awa 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 b changes in flow velocit. The second effect, flow separation, can occur when the streamlines curve towards the hull b 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 propert of a vortex, can change the flow velocit b convecting high-velocit fluid towards a place of lower flow velocit and thereb changing the local pressure. Obviousl, 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. The pressure changes extend downstream towards the forward shoulders, increasing the pressure at the windward side, while reducing it at the leeward shoulder.

3 .2 β = o.2 β = o Leeward Windward Figure : Axial velocit distribution at the bow Further downstream at the aft shoulders, 25% L pp 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 boundar laer shows a large difference in thickness between the windward and leeward side. This difference indicates a delaed 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..2 β = o.2 β = o A Figure 2: Axial velocit distribution at the aft shoulders, 25% L pp aft of midship At 45% L pp aft of midship, shown in Figure 3, large changes occur in the flow field as the viscous effects become more pronounced. The ero drift case reveals the rapid increase in boundar-laer thickness. For drift, the vortex at the leeward side, which developed upstream at the leeward bilge, has detached from the boundar laer near the hull b a combination of an increase in vortex intensit 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 b the transverse flow direction introduced b the receding frame shape, which maintains a constant draft. Due to its convective propert, this vortex increases the flow velocit near the hull, thus compressing the boundar laer 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)..2 β = o.2 β = o B C D Figure 3: Axial velocit distribution at 45% L pp aft of midship

4 -.6 The predicted flow field for drift at the propeller plane, see Figure 4, shows two counter-rotating vortices, which increase the axial flow velocit in the upper part of the propeller disk b convection (E in Figure 4). A more complex flow field is visible for β=. The leeward vortex, reinforced b 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)..2 β = o.2 β = o E F G Figure 4: Axial velocit distribution at the propeller plane 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 (). C p p = () ρ p 2 ½ Vs A β = o A β = o B B C Windward side Leeward side Figure 5: C p distribution at the bow and forward shoulders, β = and β = 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 b the oblique inflow (A in Figure 5). Secondl, 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 ero-drift case (C). These three changes result from displacement effects, i.e. a change in flow direction relative to the local hull curvature.

5 D β = o D β = o E 5 Figure 6: C p distribution at the aft shoulders and stern, windward side, β = and β = Figure 6 and Figure 7 show the pressure distribution at the windward and leeward sides of the stern respectivel. A comparison between β= and β= shows a pressure reduction at the windward aft shoulder, introduced b the flow remaining attached to the hull over a longer distance compared to the ero-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). H β = o G H 5 5 Leeward side F.2 I β = o G Figure 7: C p distribution at the aft shoulders and stern, leeward side, β = and β = 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 propert 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 intensit 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 var substantiall 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 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, V-shaped frames near the bow are onl found on the MARIN Ferr, 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 Ferr and the Series 6 have ver slender bows, reducing flow displacement and thus the influence of the stagnation pressure at the bow. The bow contour of the Ferr is more rounded and this, together with the slight concave shape of the hull aft of the bulb, considerabl reduces the pressure difference between the leeward and windward side of the hull. The flow separates underneath the bow of both the Ferr and Series 6, resulting in a vortex. The ver slender frames, the sharp bow contour and the concave waterlines of the Series 6 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 Ferr, 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 simultaneousl allowing the flow to remain attached at the leeward side, further reducing the pressure. At the stern, see Figure and Figure 2, 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

6 dependent on the frame shape and the contour line of the stern. The Ferr and Hopper, both with pram-tpe 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 bod obviousl 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 Ferr). 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 accompaning vortex reduces the local pressure. However, due to the (upward) cross flow generated b the pram-tpe aft-bod of the Hopper, the vortex is located further awa from the hull surface, resulting in a smaller reduction of the pressure. Together with the relativel 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 Ferr 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 Ferr introduce other effects. At the windward side, the 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 relativel small compared to the pressure distribution on the skeg of the Ferr. In addition to the influences stated above, the longitudinal positions of the forward and aft shoulders and skeg also influence the lateral force distribution b 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 segments, with the segment boundaries located at even stations. The lateral forces Y n acting on these segments are made non-dimensional using the projected lateral area S n 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 b interpolation between 9 and 2 drift angle). Y' Y = (2) ρ n n 2 2 VS s n. Y n ' [-] MARIN Ferr KVLCC2M Osaka Hopper Series stern segment bow Figure 8: Longitudinal distribution of lateral force at 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. 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 velocit. This actuall means that a positive transverse drag is experienced b the ship, as should be expected.

7 Starting with the influence of the bow shape, it was shown in the previous section that the blunt bow vessels have significantl 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 Ferr and Series 6 reduces the transverse drag in segment 9 relative to the vessels with the blunt bows. The relativel small transverse drag of the MARIN Ferr in segment is caused b a combination of the rounded bow contour, the concave hull shape aft of the bulb and the relativel 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 to 4. The higher block vessels all show a positive lateral force in segments 2 to 4, introduced b displacement effects resulting from the increased hull curvature at the aft shoulders. The pramtpe aft bod of the Hopper has an even larger pressure drop, extending over a longer distance explaining the large positive lateral force even in segment. All vessels show the development of flow separation at the leeward side of the stern, with varing influence on the lateral force distribution. The ships with a U-shaped aft bod, the Osaka, the KVLCC2M and the Series 6, 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 to 2. At the extreme end of the stern, different aspects determine the pressure distribution. For the KVLCC2M, and the Osaka the relative vortex intensit determines the pressure distribution in segment. The positive transverse drags (i.e. negative lateral forces) in segments and 2 of the Ferr and the Series 6 can be attributed to the effect of the skeg and the ver narrow and sharp aft bod of the Series 6. The influence of the skeg for the Hopper diminishes b the far larger influence of the pram-tpe aft bod and aft shoulder location, resulting in a net positive lateral force. INFLUENCE OF HULL FORM ON MANOEUVRABILITY The manoeuvrabilit of ships can be divided into two separate qualities: the turning abilit and the directional (or related to that, the course) stabilit. For a good turning abilit, the resistance against turning should be small, the aw moment as a function of drift should be large and the abilit to generate a turning moment (b using a steering appendage such as the rudder) should be large. For a good directional stabilit, the resistance against turning should be large and the aw moment as a function of drift should be small. Therefore, a compromise between the turning abilit and the directional stabilit must alwas be made, unless a ver powerful steering appendage is applied. For most ships except ver slender vessels such as frigates, the required turning abilit is easil met but an acceptable directional stabilit is hard to achieve. For these ships, the directional stabilit can be improved best b reducing the aw moment as a function of drift and increasing the resistance against turning. These effects can be achieved simultaneousl b increasing the drag against cross-flow in the aft ship. Based on experience from manoeuvring tests and clarified b the stud presented in this paper, this can be realised b moving the aft shoulder forward (e.g. b moving the centre of buoanc forward) such that the aft ship becomes more slender or b increasing the pressure at the windward side b appling a sharp skeg. Alternativel, this can be achieved b using V-shaped frames instead of U-shaped frames in the aft ship. Stimulating flow separation and vortex development b reducing bilge radius near the stern will reduce the destabilising awing 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 bod shape: A pram tpe aft bod reduces the transverse drag and increases the destabilising awing moment as a function of drift relative to U and V-shaped frames. V-shaped frames generate slightl more lateral drag than U-shaped frames. The changes above increase in magnitude for the higher block vessels.

8 Skegs increase the overall lateral drag while reducing the destabilising awing moment Vortex development resulting from flow separation at the leeward side of the stern increases the lateral drag while reducing the destabilising awing moment for U and V-shape aft-bodies. The results above show that the manoeuvring performance of ships is strongl determined b the shape of the aft bod. Therefore, careful attention should be paid to the design of the aft hull form in the earl design stage and guidelines are given. The insight offered b viscous flow simulations contributes to the assessment of manoeuvring characteristics in the earl stages of design. Research to include rotational motion in Parnassos, further improving the predictive capabilit, is currentl under wa. ACKNOWLEDGEMENTS Part of the work conducted for this paper has been funded b 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 b Bart van Oers at MARIN under supervision of Serge Toxopeus. REFERENCES [] Toxopeus, S.L. ; "Simulation and validation of the viscous flow around the Series 6 hull form at drift angle". 7 th NuTTS Numerical Towing Tank Smposium, October 24. [2] Toxopeus, S.L.; "Validation Of Calculations Of The Viscous Flow Around A Ship In Oblique Motion". The First MARIN-NMRI Workshop, pp. 9-99, Toko, Japan, October 24. [3] Toxopeus, S.L.; "Verification And Validation Of Calculations Of The Viscous Flow Around KVLCC2M In Oblique Motion". 5 th Osaka Colloquium, March 25. [4] Van Oers, B.J. An investigation of the viscous flow around a ship in oblique motion. MSc thesis, Delft Universit of Technolog, Facult of Mechanical, Maritime and Materials Engineering, March 25. [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 , Osaka, Japan, Ma 998. [6] Hoekstra, M. Numerical Simulation of Ship Stern Flows with a Space-Marching Navier-Stokes Method. PhD thesis, Delft Universit of Technolog, Facult of Mechanical Engineering and Marine Technolog, October 999. [7] Menter, F.R. "Edd Viscosit Transport Equations and Their Relation to the k-ε Model", Journal of Fluids Engineering, Vol. 9, pp , December 997. [8] Dacles-Mariani, J., Zilliac, G.G., Chow, J.S. and Bradshaw, P. "Numerical/experimental Stud of a Wing Tip Vortex in the Near Field", AIAA Journal, Vol. 33, pp , September 995. [9] Toxopeus, S.L. and Loeff, G.B. "Model Tests with Segmented Ferr", MARIN Report BT, October 999 (Restricted). [] Toxopeus, S.L. "Stud of the flow around a Hopper Dredger at a Drift Angle", MARIN Report No CPM, Ma 25 (Restricted).

9 .5.2. MARIN Ferr.4.2 Series KVLCC2M Esso Osaka Hopper Figure 9: Cp distribution at the bow for different ships sailing at drift angle, windward side

10 MARIN Ferr Series KVLCC2M Esso Osaka Hopper -.2 Figure : Cp distribution at the bow for different ships sailing at drift angle, leeward side

11 ....2 MARIN Ferr Series KVLCC2M Esso Osaka Hopper Figure : C p distribution at the stern for different ships sailing at drift angle, windward side

12 MARIN Ferr Series 6. KVLCC2M Esso Osaka Hopper Figure 2: C p distribution at the stern for different ships sailing at drift angle, leeward side