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Twenty-Third Symposium on Naval Hydrodynamics (2001)
Naval Studies Board (NSB)

Page
820
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Page
820
Front Matter (R1-R19)
Modern Seakeeping Computations for Ships (1-45)
Forces, Moment and Wave Pattern for Naval Combatant in Regular Head Waves (46-65)
New Green-Function Method to Predict Wave-Induced Ship Motions and Loads (66-81)
Validation of Time-Domain Prediction of Motion, Sea Load, and Hull Pressure of a Frigate in Regular Waves (82-97)
Ship Motions and Loads in Large Waves (98-111)
Prediction of Vertical-Plane Wave Loading and Ship Responses in High Seas (112-125)
Basic Studies of Water on Deck (126-142)
Second Order Waves Generated by Ship Motions (143-156)
Prediction of Nonlinear Motions of High-Speed Vessels in Oblique Waves (157-170)
Optimizing Turbulence Generation for Controlling Pressure Recovery in Submarine Launchways (171-180)
Hull Design by CAD/CFD Simulation (181-190)
Steady-State Hydrodynamics of High-Speed Vessels with a Transom Stern (191-205)
Practical CFD Applications to Design of a Wave Cancellation Multihull Ship (206-222)
Simulation of Ship Maneuvers Using Recursive Neural Networks (223-242)
Flow- and Wave-Field Optimization of Surface Combatants Using CFD-Based Optimization Methods (243-261)
Marine Propulsor Noise Investigations in the Hydroacoustic Water Tunnel 'G.T.H.' (262-283)
Propulsor Design Using Clebsch Formulation (284-300)
Unsteady Flow Quantities on Two-Dimensional Foils: Experimental and Numerical Results (301-313)
Hydrofoil Turbulent Boundary Layer Separation at High Reynolds Numbers (314-329)
Pressure Fluctuation on Finite Flat Plate Above Wing in Sinusoidal Gust (330-341)
Control of the Turbulent Wake of an Appended Streamlined Body (342-354)
Investigation of Global and Local Flow Details by a Fully Three-Dimensional Seakeeping Method (355-367)
Prediction of Wave Pressure and Loads on Actual Ships by the Enhanced Unified Theory (368-384)
Frequency Domain Numerical and Experimental Investigation of Forward Speed Radiation by Ships (385-401)
International Collaboration on Benchmark CFD Validation Data for Surface Combatant DTMB Model 5415 (402-422)
Validation of High Reynolds Number, Unsteady Multi-Phase CFD Modeling for Naval Applications (423-440)
Free Surface Viscous Flow Computation Around A Transom Stern Ship by Chimera Overlapping Scheme (441-456)
Anti-Roll Tank Simulations With A Volume of Fluid (VOF) Based Navier-Stokes Solver (457-473)
Validation of Tab Assisted Control Surface Computation (474-484)
Experimental and Numerical Investigation of the Flow Around the Appendices of a Whitbread 60 Sailing Yacht (485-492)
Propeller Wake Analysis by Means of PIV (493-510)
Experimental and Numerical Investigation of the Unsteady Flow Around a Propeller (511-526)
Simulation of Incompressible Viscous Flow Around a Ducted Propeller Using a RANS Equation Solver (527-539)
On Submerged Stagnation Points and Bow Vortices Generation (540-552)
Numerical Prediction of Scale Effects in Ship Stern Flows with Eddy-Viscosity Turbulence Models (553-568)
The Experimental and Numerical Study of Flow Structure and Water Noise Caused by Roughness of a Body (569-578)
Large-Eddy Simulations of Turbulent Wake Flows (579-598)
Instability of Partial Cavitation: A Numerical/Experimental Approach (599-615)
An Unsteady Three-Dimensional Euler Solver Coupled with a Cavitating Propeller Analysis Method (616-638)
On the Flow Structure, Tip Leakage Cavitation Inception and Associated Noise (639-653)
An Experimental Investigation of Cavitation Inception and Development of Partial Sheet Cavaties on Two-Dimensional Hydrofoils (654-669)
Modeling 3D Unsteady Sheet Cavities Using a Coupled UnRANS-BEM code (670-686)
Ship Wake Detectability in the Ocean Turbulent Environment (687-703)
An Experimental and Computational Study of the Effects of Propulsion on the Free-Surface Flow Astern of Model 5415 (704-712)
Breaking Waves in the Ocean and Around Ships (713-745)
Numerical and Experimental Study of the Wave Breaking Generated by a Submerged Hydrofoil (746-761)
The Numerical Simulation of Ship Waves Using Cartesian Grid Methods (762-779)
Radiation Loads on a Cylinder Oscillating in Pycnocline (780-791)
Wave Resistance Computations - A Comparison of Different Approaches (792-804)
Computations of Nonlinear Turbulent Free Surface Flows Using the Parallel Uncle Code (805-819)
Submarine Maneuverability Assessment Using Computational Fluid Dynamic Tools (820-832)
Simulation of UUV Recovery Hydrodynamics (833-847)
Reynolds-Averaged Modeling of High-Froude-Number Free Surface Jets (848-862)
On Roll Hydrodynamics of Cylinders Fitted with Bilge Keels (863-880)
Combining Accuracy and Effciency with Robustness in Ship Stern Flow Computation (882-896)
An Unstructured Multielement Solution Algorithm for Complex Geometry Hydrodynamic Simulations (897-909)
Ship Stern Flow Calculations on Overlapping Composite Grids (910-926)
Study on the Prediction of Flow Characteristics Around a Ship Hull (927-940)
Analysis of Turbulence Free-Surface Flow Around Hulls in Shallow Water Channel by a Level-Set Method (941-956)
A Design Tool for High Speed Ferries Washes (957-967)
Flow Around Ships Sailing in Shallow Water - Experimental and Numerical Results (968-982)
Ship Stability Study in the Coastal Region: New Coastal Wave Model Coupled with a Dynamic Stability Model (983-992)
Waves and Forces Caused by Oscillation of a Floating Body Determined Through a Unified Nonlinear Shallow-Water Theory (993-1005)

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Submarine manoeuvrability assessment using Computational Fluid Dynamic tools D. Bellevre, A. Diaz de Tuesta, P. Perdon (Bassrn d' Essais des Carenes, France) ABSTRACT Tha ks to tha constant increasa in computing power, it is now bacoming possibB to aim at mora and mora ambitious rasults in using Computational Pluid Dy amic. Tha objact of this papar is tha dascription of tha impBmentation of a calc~lahon tool, which should aventually conhibuta to tha sathug up of a quasi-axhaustiva data bank of hydrody amic coafficients of my submarina, for any m mauvars likaly t ba studiad. A mash ganeration tool davalopad in ordar to facilitata tha pra-procassing staga of CPD calculation is prasantad. Than different casas of calculation performad ara dascribad, tha rasults ara comparad to thosa obtainad with towing ta k modal tasts. Tha validity of aach typa of calc~lahon is discussad, with an ovarvi w on tha actual prog ass. A mathamatical m mauvarability modal has baen identifiad f om tha rasults obtainad through calculation. Simulations parfo mad with this modal ara comparad to rasults obtainad at saa. INTRODI CTION It is now possibB to expact rapid rasults for a wida rmga of calculations. CPD (Computational Pluid Machanic) is considarad hara as a'`numarical towing tank", which allows to compara tha rasults with modal tast data. Although tha diract simulahons of manauvars using an unsteady RANSB coda is possibB, it is very tima cons ming md tha usa of a mathamatical modal basad on coafficiants in a quasi steady approach is practically instantanaous and allows a very wida ranga of simulations in a short tima. In order to facilitata tha pra-procassing staga of CPD calculation, a mash ganaration t ol has baen davalopad at Bassin d'assais das carinas. This t ol automatically providas a 3D mash whan cinamatic paramaters (d if t angB, angB of attack, rata of turn in horizontalha tical pi ma) ara given or whan changas in tha gaomat y of tha submarina (L D ratio, m mbar, siza or location of tha appendagas, shapa of dack, ) ara proposad. This avoids tha long and laborious task which consists in ra-mash tha submarsibB for my minor changa in its gaomat y. Purtha mora, using this tool tha grid topology is idanhcal f om ona casa to another so that tha numarical rasults ara mora raliabB, at Bast for comparison pu posas. This study has bean perfo mad on an axisting submarina for which modal tast rasults wera availabB, and calc~lahons hava baen dona on tha basis of usual captiva modal tast: r~ddar affactivanass tasts, obliqua towing tasts, and rotating arm tast in both vertical md horizontal pimas. Tha solver usad was a commercially availabB Raynolds Avaraga Navier-Stokas coda (Nawtonim homogenaous md incomprassibB duid). MESH GENERATION Tha philosophy of tha numaric tool usad to conduct this study is basad on a '`modular" concaption of tha submarina, so that tha shapa, position, or aven a datail m tha mash of aach part of tha ship can aasily ba ch mgad, and ra-inco poratad int tha mash of tha whoB ship. Tha following parag aphs dascriba briady tha chronology of manipulations carriad out to obtain this adaptabB mash. Bodv and deck Tha shapas of tha dack and of tha body of tha submarina ara obtainad f om a CAD fiB. At this staga, tha number, siza md rapartition of tha calls corrasponding to thosa two pa ts of tha submarina ara sat up. Anuend~ Va mean by'`appandagas" tha diraction and diva r~ddars, md tha sail. Tha gaomahic data nacassa y ara, on tha ona h md, tha ganeral charact ristics of tha appendaga (wingspread, chord, ralativa thicknass), and on tha othar h md tha fiBs of Bazier poBs dafining tha thick ass laws at tha basa and in haad of tha appandaga.

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The number of cells in thickness and in chord is now fixed. The number of cells in wingspread will adapt at best the revolution mesh of the mother hull. Combination The principle for the mesh of the submarine for the purpose of maneuverability calculation is the following: the 2D mesh of the body is reproduced by symmetry of revolution around the axis of the ship. The different appendages are afterwards incorporated in the mesh, by locally distorting it. The deck is finally taken into account, by a deformation of the mesh in the concerned areas. Maneuvering To satisfy to the limit conditions of calculation, which are of"Neumann" type, it is necessary to maintain the flow perpendicular to the outlet of the mesh. So the mesh used for calculation in maneuvering (rotation, incidence) is deformed to adapt to this necessity. This operation is fairly quick (one or two minutes). : ~ Hi, Fig 1: deformation of the mesh for a rotation calculation NUMERICAL TESTS Different mesh The size of the mesh is a preponderant factor in the time required and in the quality of calculations. In order to determine a satisfying compromise between those two necessities, tests have been performed with three different mesh sizes. The smallest one, quite coarse, comprises 400.000 cells for the whole submarine. The intermediate one, 800.000 cells, and the finest one, 1.400.000 cells. These numbers correspond to the case where the symmetry related to the vertical plane cannot be used (typically the cases of maneuvering in the horizontal plane). For the other cases, the number of cells is of course reduced by one half. It is obvious that the more the number of cells is important, the longer the calculations are. First, because each iteration takes more time, and then because the calculation needs more iterations to converge. That is why the size of the mesh is a parameter that has to be carefully chosen, before starting of a wide range of calculations. A mesh that includes the forward dive planes requires the use of the finest mesh resulting in a large number of cells. Therefore the impact of fins on the quality of the results has to be evaluated. : Fig 2: coarsest mesh Fig 3: intermediate mesh

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o 2 3 4 6 8 +/-2.5 +1-3 +1-4 +/-5 +1-6 +1-8 The two cases s=0 and 6=0 correspond to the same calculation. In the same way, the negative values of ~ correspond to the same cases as the positive ones, because of the symmetry of the submarine. Rotation (vertical and horizontal planes! Fig 4: finest mesh Fig 5: "forward dive planes" mesh Pure incidence/pure drift Calculation cases have been chosen to coincide with the results of captive model tests available. The following table enumerates the different cases of incidence (vertical plane: s) and drift (horizontal plane: 6) performed during this study. ~ 1 ~ values in degrees(°) -8 1 0 -6 +/-0 5 -4 +/-1 -3 +/-1.5 -2 +1-2 As in previous section, the calculations with yaw and pitch rate have been modeled based on rotating arm test which results were available. During these tests, the radii of rotation were chosen in a geometrical progression between the two extreme positions of the rotating arm carriage. Were retained: R=_1 lm; _13 .83m; _1 7.39m; _21 .97m; _27.50 Since the model length was 4.33m, we obtained the following non dimensional rates of turn: For r)=L/R=_0.39; _0.31; _0.25; _0.16 By convention, we use q to design the rate of turn in the vertical plane, and r for the horizontal one. The following table, exposing the calculation performed, was obtained by combining those values with different incidence (or drift) angle. q (or r) -0.39 -0.31 -12 (g) (g) -10 (D (D -8 5 -4 -2 O 2 4 5 8 10 12 . . -0.2s -0.20 (53 ~ . . . . _ O ,53 ,53 ,53 ,53 ,53 ,53 = 1 1 1 1 1 1 1 T4: 1 ~ 1 1 ~

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Some of these calculations were performed with different mesh, in order to determine the best compromise in term of mesh size between precision and rapidity. Rudder effectiveness The rudder effectiveness is estimated by studying the hydrodynamic coefficients in a straight line, with no incidence, for different plane deflection (or flap angles, if the rudder doesn't move entirely around its axes, as in this case). In the following table, Q~ represents the angle of flap of the stern dive planes, and or the rudder angle. of + 5 CONVERGENCE p~ or or (degrees) 10 1 15 1 20 1 25 1 30 The following graphs show the convergence of a calculation: the curve representing the evolution of the computed values of physical data, like the forces along the x-axis must present a zero gradient at the end of the calculations. The curve "residual" represents the evolution of the difference between the solution computed at stage n, and the one at stage n+1. Depending on the quality of convergence expected, a maximum value is fixed for those "residual", above which the calculation is not considered as being converged. A..,.., I. 5$~t ~ :~.~i; i''' ,... ~55 $5: I: 3.. ~~$f..5) I'.: Ski ::: -$ ~ on >...k - ..~ .. :.~ ~ it ,,. .. ~ ~ - - ~ . ,, ,,,, ~ ~ , .. . ... . . . . . . ~ :. ..~ ~,~ a:'. 5 ,.~,.:.5i5 '5~:5,:~ :55i:' ~ .~, ~ ~ .$v,,.5~ ~ 5~5 ^: in_ ~ ........... ::~1 ·:.. :, ·: I. 5 ., Some calculations required more attention than others before they converge in a satisfactory way. Among the main parameters we modified are the values of the relaxation factor used for the calculations. This relaxation factor represents the proportion of the result of the iteration "n" re-used as a base to compute the iteration "n+1". The larger the factor is, the faster the solution converges, if everything is going all right, but also the higher is the risk of divergence. Indeed, if the first solution computed is radically false, and if the second one is based in a large extent on the precedent, it is very likely to obtain a result even worse. The majority of the problems of this type were met for rotation/incidence cases. They were countered by reducing the relaxation for the first 100 iterations, before setting them back to their usual (default) values. The missing points on the following graphs, showing the calculations results, correspond to the cases where calculation did not converge, despite changes in relaxation factors. Most of them have been encountered for rotations in horizontal plane. EFFECT OF MEStI SIZE Horizontal plane For manoeuvring in horizontal plane, the forward dive planes theoretically do not play a leading role. On the other hand, a very clear difference was observed between the coarsest mesh and the middle one. The comparison with model test results showed that the middle mesh gives results closer to the reality. Tests with the finest mesh still have to be performed. Since it is not possible to use any symmetry in the horizontal plane (which was not the case for vertical plane motions), the size ofthe

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required mesh is at least doubled and therefore, still poses memory capacity problems. e id 0,80 c, 0,60 0,40 +coarsest meshing middle meshing <<,,~,~,<~r model tests ~ / -0,20 Drift (degrees) Fig 6: Pure drift: comparison between two meshes The accuracy of the results seems therefore to be directly related to the size of mesh, and in all likelihood, it will not be judicious to merely compute using the coarsest mesh, even if this would have represented a considerable economy in calculation time. Vertical plane Pure incidence. It appears that the mesh density has a lesser effect on the result accuracy than in horizontal plane. The presence or the absence of the front rudders leads to a difference of 18% on the gradient of the curve of heave force versus incidence, for the pure incidence maneuvering. This results are presented further, in the paragraph "comparison with model test results"(f~g 104. The following graph shows the curves related the drag coefficient as a function of the incidence angle for different meshes. 0,00 -6 -4 -2 - 0 2 4 6 :, Drift (degrees) ° Coarse meshing Middle meshing ED ~ Bme meshing ~0 TO ^~"1 orward planes" meshing , -0,20- Fig 7: drag coefficient in pure incidence manoeuvring The results of the coarsest mesh are quite different from those obtained with the three finer meshes. It is more difficult to obtain precise results for the drag coefficient calculations, because of its nature: the whole drag is the algebraic sum of different drag forces of great absolute value, and of comparable magnitude, but of different signs. A low relative variation of these great values has a very sensible effect on the whole sum, which absolute value is very low. The drag induced by incidence which is more of concern for manoeuvrability purposes does not seem to be much dependent on the refinement of the mesh. Low rotation rates. The difference between the heave force coefficient calculated with the coarse mesh and the finer one is less important when a rotation is introduced in the manoeuvre. The following graph shows that even for a low rotation rate, the difference between the two curves related respectively with the coarse and the "forward plane" mesh is only 10%, against the 18% observed in pure incidence. We do not have yet any satisfying explanation for this difference, but this will allow us to consider that the coarse mesh is sufficient as long as the rotation rate remains inferior or equal to 0,2. It must be noted that during usual situation the non-dimensional rate of turn of a submarine in the vertical plane does not exceed 0,2. 0,2 Incidence (degrees) 4 ~ ~ 12 Coarse meshing; q=0,16 "forward planes" meshing; q=0,16 <~ Coarse meshing; q=0,20 Am "forward planes" meshing; q=0,20 Fig 8: Heave force for rotation in vertical plane (low rotation rates) Higher rotation rates. This good agreement between results corresponding to the two mesh remains valid as long as the rotation rates are not too high. Actually,

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as soon as q>0.25, the curve related to the coarse mesh collapses for the highest incidence angles. o -4 0 ?~ ~~ \ 4} = 1 ' ~ 4 ~ In_ +coarsest meshing; q=0,25 Fry. } "forward planes" meshing; q=0,25 ~ I -0,8 ~ coarsest meshing; q=0,39 -1,2 fffffffff "forward planes" meshing; q=0,39 Fig 9: Pitching moment for rotation in vertical plane (higher rotation rates) 4 0 4 y Incidence (degrees) e 0,04+ e=, =t 0,08~ Ail .^^f~'ffff Coarsest meshing; q=0,16 ~-0,12 "forward planes" meshing; q=0,16 .. (/ off coarsest meshing; q=0,20 ~'ffffff "forward planes" meshing; q=0,20 -0,16 Fig 10: pitching moment for rotation in vertical plane (two different mesh) On the other hand, a very clear improvement is obtained by refining the mesh if we compare the curves related to the pitching moment, even for low rotation rates. For largest incidences, we observe a notable reduction of the values obtained with the small mesh which does not exist for model tests, and which reveals a bad repartition of forces due to the insufficient precision of the cells. COMPARISON WITH MODEL TESTS DATA Pure incidence (without rotations The slope of the curves resulting of calculation, representing the lift coefficient present a satisfying concordance with those of model tests in vertical plane. It is clear that due to the presence of the sail and the deck a submarine is not symmetrical in the vertical plane and therefore a non zero value is expected for heave force and pitching moment at zero incidence angle. This offset is much bigger when for model tests results but is to a great extend related to the experimental set-up (presence of struts) and to the precision limit of strain gauges calibrated for much bigger forces. 0,40 e .. —8 -u,~u Fig 11: Heave force coefficient in incidence ~ _ _ A -0,20 ~ ~.~ +coarse meshing }intermediate meshing ~ Bme meshing Am "forward planes" meshing Model tests Drift (degrees) manocuvring (vertical plane! Pure drift (without rotation) As seen in the section "comparison between meshes", the concordance between model tests and calculation results is very good, as soon as a sufficient refinement of the mesh is adopted. The following graphs show the evolution of the yaw moment as a function of drift angle, for the two meshes already performed, and for the model tests. We see that the slope of the curves is very similar. The shift of values observed is probably due to errors related to test operating. Actually, since the submarine (without propeller) is symmetrical to the horizontal plane, it is logical to obtain a zero value of the yaw coefficient for a zero drift angle, as observed for calculation results, unlike for model test results. non e o e -0,20 E -0,10 -2 ~~>,,, 2 _O,10 \ it, 6 Coarse meshing }middle meshing off model tests Fig 12: yaw moment versus drift angle Dim (d~,~, 1-- 10

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Rotation/drift (horizontal plane) Rotation/incidence (vertical plane) The rotation/drift cases posed most of the We present here the comparison between the convergence problems (that is why some of results of model tests and calculations with the calculation points are missing on the graph above). finest mesh ("forward planes" mesh), since we saw The calculations are more time consuming in the before that they are sensibly better than the ones horizontal plane, because of the lack of symmetry, with a coarser mesh. but this cannot be the only reason for those difficulties. We can suppose that the rotation of the 05 .' sail in horizontal plane disrupts strongly the flow, ~ : and therefore the calculations. More precisely, the calculation *~0~ chord of the sail can not be considered as small in -1 5 -10 -0 5 ~;~' 0. 0 0 '5 relation to the radius of rotation and therefore the ~ q=031 .~: OS sail acts as a lifting surface in a curved flow. , ~ ~ , ~ _ ~ c ~ ~ cud ~ lion ~ -15 -2 0 -15 ~ -1 0 -0 5 ~ F ~ ~ O. .0 ~ 0 .5 ~ r=039 ~ -05 Fig 13: Heave force coefficient for combination I. ~0:21 ~ ~ I of pitching rate and incidence ~ r 16 ~ ~ ~] ,.---'', Is j Despite the presence of an offset already -2 addressed, it can be seen that the overall prediction of heave force is quite correct for all combination of rate of turn and incidence. For largest incidence Fig 15: Sway force coefficient (combination angles (where forces are the highest), we can notice of drift and yaw rate) a slight under estimation of heave forces by calculation. The results obtained in the horizontal plane are Amp 03calculation -02 -01 ~ ~ '.' 00 not as good as they were in the vertical plane. - ' Independently from the offset, it can be observed ~~ ~~ that the points do not follow the ideal line. Forces ;. ~ - -01 are under estimated for large drift angle. ~ ~ ~ .. Looking at the yaw moment coefficient we can · ~a- . q=0~39 observe that the overall tendency is well respected. · .' ..' ~~ q-025 -02 However, a small variation of the gradient can be . ~ ~ q=031 ~ detected between the different rates of turn. .' ~~ q-0 16 0 -0~3 Fig 14. Pitch moment coefficient for ~839 ~ a: combination of pitching rate and incidence ;~ I:, The same comments can apply to the pitching calculation ~ ~ - ~ moment coefficient (figure 14). The higher O 3 -0 2 o 1 ~ 0. 0 ~ 1 0 2 ~ 0. 3 0. 4 discrepancy for points at large turning rates can be .- ~ ., explained by the fact that the influence of incidence on pitching moment becomes lower as turning rate L ~ ~-02~ ~ ~ increases (at least for combination of incidence and 1 -03- pitch rate close to the natural situation of a free · Fig 16 Pitching moment coefficient running submarine). (combination of drift and yaw rate)

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Some options have been thought of to improve these results, such as a local refinement of the mesh in "strategic areas" (connection between rudders and body of the submarine, for example), but they have not been performed yet. Rudder effectiveness A: ..~..~ The gap between test and calculation results lead us to try to have the mesh to coincide better with the real geometry of the submarine. Indeed, we observe an overestimation of almost 50 TO of the lift coefficient related to the rudder orientation. The pressure distribution on both sides of the starboard stern plane for the original mesh is presented on the following figure corresponding to 25 degrees deflection ofthe plane (by. On this picture, it can be seen that the pressure distribution over the flap (responsible for the lifting effect) is regularly spread over the span and is also present in the vicinity of the root of the plane. Fig 17: calculated pressure on suction side (high) and on pressure side (low) of the right dive rudder, with the finest mesh. But the real geometry of those rudders is so that when the rudder's flap is inclined, a gap appears between it and the submarine's body, letting the fluid balance in a certain measure this pressure difference observed in calculation results. The easiest way of remedying this problem was to modify a small part of the mesh and transforming the cells corresponding to the gap into "live" cells, which means that they let the fluid go through. The mesh with live cells corresponds to the mesh with forward planes with this slight modification. The following figure shows the results obtained in this way: the depression surface on the suction side is less wide than the one calculated with the former mesh, like the overpressure surface on the pressure side. The heave coefficient resulting in the difference of pressure repartition between the two faces will therefore be less important. This effect can be assimilated to a reduction of the effective span. ,~.,. ..~.. ., ~~..~ ~~.,..~.. ,,.. it.... ~ - - ~ ~ ~ .. .. ... :~.~ ~ |~ :,. ..;.; ,.~...~. ~~ ..... Fig 18: calculated pressure on suction side 5~ ~~ ~~ (high) and on pressure side (low) of the right dive rudder, with the "alive cells" mesh The results obtained with the new mesh ("live cells" mesh) show a remarkable improvement of the concordance between calculation and test (approximately 30°/O), even if the results are not perfect yet, as you can see on the following graph. Those types of calculations have not been performed yet for rudders (because of the mesh size problem for horizontal plane manoeuvring we have already mentioned).

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r r \ 050 ~middle meshing "forward planes" meshing 0 25 "alive cells" meshing ~ ~ ^~ model tests -30 ~" ' :~ _ _ -0.25 1 -I.. -11, ~, t ~ -0 50 Fig 19: Rudders effectiveness PREDICTION OF SUBMARINE BEHAVIOUR In order to evaluate the benefit of numerical calculation in the prediction of submarine manoeuvrability, a mathematical model has been derived from the results of the calculation. All the derivatives usually obtained through captive model tests have been identified from the results of calculations, except for rudder and stern plane effectiveness derivatives, for which prediction appeared to be poor. Fins effectiveness derivatives used in the following simulations have been derived from captive model tests. In the horizontal plane, the lack of accuracy of yaw rate influence on the sway forces lead to a bad estimation of the stability indices. In this particular case, the submarine is predicted as being course stable though sea trials (and model tests) indicated slight course instability. L/R ''' /~ 5 In 15 20 7~ 30 Fig 20: Non dimensional yaw rate versus rudder deflection On the same figure it can be seen that the estimation of non-dimensional rate of turn for intermediate rudder deflection is quite correct while greater discrepancy arise for larger deflection angles. In addition to the under estimation of sway forces for large drift angles, the relatively simple mathematical model used in this case can also explain those latter discrepancies. More precisely non-linear derivatives used to describe the coupling effect between planes deviation and local incidence were voluntary omitted. In the vertical plane, the prediction of the submarine behaviour is globally better. The figure 21 display the maximum non-dimensional pitch rate obtained during stern plane deflection trials (stern plane angle being average between deflection to dive and deflection to rise). It can be observed that the behaviour of the submarine is well represented. The non-symmetry of the behaviour of the submarine in the vertical plane is more important for the simulation, but sea trials results show some discrepancy Kiss simulation - dive simulation - rise sea trials - dive ..... .,., ~ ,i~ A,. .. ~.i .~ 0 5 10 15 20 25 Fig 21: Non dimensional maximum pitch rate vs. mean stern plane angle deflection A step further was the simulation of six degrees of freedom manoeuvres. For this purpose, a reduced set of out of plane derivatives has been identified from NS calculation. .^r~ —simulations ~ sea trials 0.08 006 petit mai Ilage mailIage moyen captive mode' tests 004 0.02 0004 ~ 000 200 , . . ./ At/ 400 600 800 Fig 22: Pitching moment induced by yaw

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The simulation is performed using time histories of actuator positions measured at sea as inputs. The maneuver considered consists in a stern plane deviation, followed 30 seconds later by a rudder deviation in conjunction with forward plane deviation. In addition to rudder and stern plane motion, the propeller is stopped. Such a maneuver, which can be considered as a recovery maneuver for dive plane jam, emphasizes the well known coupling effects between yaw and pitch. Fig 23: Simulation inputs (planes deviation) Motions predicted by the simulation are compared in the time domain to full scale tests. For this complex maneuver, the dynamic of the submarine is qualitatively well predicted as shown on figure 24 where the rates of turn simulated are compared to measurements. By_ ~~ roll rate - sea trials Troll rate - simulation pitch rate - sea trials pitch rate - simulation c' yaw rate - sea trials —yaw rate - simulation Fig 24: Rates of turn It is clear that for time domain simulation, the small errors encountered during the prediction of forces and consequently on components of acceleration is magnified by the integration. Therefore, motions calculated during simulation differ significantly from those measured at sea. On figure 25, a factor two is observed on the pitch angle and also on the depth changing between simulation and sea trials. ~ roll - sea trials —roll - simulation pitch -sea trials simulation >> depth sea trials Depth simulation CONCLUSIONS . ~, ..... : :: ..... Fig 25: Motions ... NS calculations have shown their ability to provide relevant results in terms of efforts acting on . . a maneuvering su Marine. Pure drift and incidence forces are very well predicted by NS calculations even with a relatively simple mesh. As soon as a rotation is introduced, the quality of the results becomes more dependent on the parameters of the calculation. This study showed that the use of a finer mesh was absolutely necessary. Vertical plane rotation prediction is quite satisfying on the basis of the calculations already performed. Horizontal plane rotation would require an even finer mesh than the vertical plane in order to simulate more accurately the details of the appendages. Indeed, an oversimplified geometrical description of the planes led to bad results in terms of rudder efficacy prediction. Results have already been improved thanks to an easy manipulation of the existing mesh. Some more efforts are to be made in this direction. Relevant comparisons (on a relative basis) between different alternative shapes are already being made and very interesting results have been obtained which enable the evaluation of novel appendage configurations without having to engage in costly systematic experimental tests. In the end, this study should allow us to obtain accurate absolute values of the hydrodynamic coefficients of the submarines as well as a description of the mechanism of the generation of these forces on the different elements of the submarine. Indeed, one of the great advantages of using computational fluid dynamic tools is that in addition to an estimation of global forces, it provides a precise evaluation of local consequences of some geometrical modifications, which would

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bring to light phenomena which arc so far poorly understood. To gain eonfidenoe in this n w tool, calculations arc now systematically perfo mad in parallel with captive model tests. At this stage, the math matinal models used for the pu pose of m meuvering simulations arc the same as those developed for captive model tests analysis. M!e do think that a earef I analysis of the huge quantity of data provided by each NS calculation will be of help to improve existing empirical prediction methods, and fiom a more general point of view to improve the understanding of physics involved in submarine m mew en hi in. 11 11 RE DEVELOPMENT The present study showed some difficulties for prediction of rudder efficacy derivatives and for y w induced forces. To overcome those problems, we plan to perform calculations of a single dapped rudder to date mme the neeessa y mo mt of refinement in the mesh to allow for m accept bie prediction. This calculation will be based on m existing set of test data for which geometrical details such as root gap were explored. M!e arc confident that horizontal plane forces associated with y w motions will be correctly calculated once sufficient mesh sizes will be m mageabie. Once the overall prediction of hyd odynamie forces will be considered as being correct, specific aspects arc to be studied. Among those aspects, the induenoe of test inshumeutation (stings, suppo on-v struts, etc..) on towing tank md rotating a m tests will be considered. Calculations will be performed with md without shut and for different strut an my ment. Also, specific effort will be devoted to emphasize the induenoe of propulsion on m meuverability. One additional perspective for further studies in m meuverability is the direct simulations of m meuvers using the unsteady low capabilities of the RANSE codes.

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DISCUSSION U. Bulgarelli Instituto Ncziorule per St di ed E perienze di A chitetturc Nacelle, Italy To apply CFD to study of m meuverability you should already developed unstecdy Na vier states code, bee mse the phenomenon under m- e n anon is completely unstecdy is f is true? AUTHOR'S REPLY The quasi steady approach we used to investigate the capacity of RANS code for submarine m moeuvrability studies hr. two cdv Stages: Using CFD cclcubtions es c mom ert al towing tmkgavetheopport nitytouse mexistingset of tools to quickly derive time domain simulations of m uloeu.~ et fi om cclcubtion of forces Results of calculation were du ectly c mparable to existing model tests data Ed could therefore lead, to c certain extend, to validation Although unstecdy ph nom ffk~ ar he during m moeuvres, the quasi steady cpproachhcs demon trcted for c long time its capacity to provide pertinent simulations of He behaviour of submarines ion conventional m Hoed n et For most cases, the dynamic of the submarine is relatively slow compared to the dynamic of unstecdy phenomena concerned Ed the see trials don't really show some major i fluency of unsteadiness A other problem of unsteadiness, which is not solved, is that the solution of steady flow cclculationc moot fheoreticcllybe consideredas the me m force acting on He body on which separation c mses un te tdiness in She flow (es it would be me tech d in c towing t mk or m c rotating arm facility) The calculations performedhehe show d how ver some concord mce with measurements DISCUSSION IK H Kim Naval Surface Warfare C nter, Carderock Division, USA When simulating the deflection of fin/control surface, how do you h mdle She gap betw en the body cod fins? AUTHOR'S REPLY During simulations of rudder effectiveness for c fl mped rudder, we discovered large discrepancy betw en calculation Ed model te ts Previous cclcubtions for all movable surfaces did 't show such problems Ed w w nt to the conclusion that the mesh of the geometry of the su face Ed especially She root (including gaps) should be improved To solve His problems, w considered that the cells located et the ro ot are active The difference betw en the two meshes is show on figme 17 Ed I g of our paper Although encouraging, the results obtained are not completely satisfactory Ed m me work ht. to be done in fi is field We plarmed to do more extensive cclcubtion of isolated fins m order to comparetocavitationtum Itests Theobjective is to define what is She "minimum acceptable" degree of refinement of She mesh for rudder effectiveness prediction bearing in m Ed that in our meshing method, the refinement of the mesh in the vicinity of planes ht. c greet impact on She overall size of She mesh for the whole submarine DISCUSSION I-Y tioh Naval Surface Warfare C nter, Carderock Division, USA How do you pl m to do unstecdy maneuvering predictionusmg CFD? AUTHOR'S REPLY It is the Id feasible to perform unstecdy m moeuvrmg prediction using CFD For this purpose, it is possible to use the "deforming mesh" option of unstecdy RANS codes for which unstecdy ~ Ice ht i on are performed et each time step, c new mesh being t tom tti tlly generated taking into account the dynamic of the submarine es w ll es the ch m e. in control su face deflection Bcssin ht. already used this kind of approach in c simplified way (without

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solving the equation of the d. cmic of the body) for c cycloidal f uster AD) or for c c on- em Oral propeller on c inclined shaft (3 D) How ver, it is clear Nat At the moment, the 3D case of c m moeuvring submarine would requite too much computation time to be of c practical use On the of her, h Ed He possibility for validation are reduced for such m approach Ed co fidence hr. still

Representative terms from entire chapter:

vertical plane