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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 820 Submarine manoeuvrability assessment using Computational Fluid Dynamic tools D.Bellevre, A.Diaz de Tuesta, P.Perdon (Bassin d'Essais des CarÃ¨nes, France) ABSTRACT Thanks to the constant increase in computing power, it is now becoming possible to aim at more and more ambitious results in using Computational Fluid Dynamic. The object of this paper is the description of the implementation of a calculation tool, which should eventually contribute to the setting up of a quasi-exhaustive data bank of hydrodynamic coefficients of any submarine, for any maneuvers likely to be studied. A mesh generation tool developed in order to facilitate the pre-processing stage of CFD calculation is presented. Then different cases of calculation performed are described, the results are compared to those obtained with towing tank model tests. The validity of each type of calculation is discussed, with an overview on the actual progress. A mathematical maneuverability model has been identified from the results obtained through calculation. Simulations performed with this model are compared to results obtained at sea. INTRODUCTION It is now possible to expect rapid results for a wide range of calculations. CFD (Computational Fluid Mechanic) is considered here as a ânumerical towing tankâ, which allows to compare the results with model test data. Although the direct simulations of maneuvers using an unsteady RANSE code is possible, it is very time consuming and the use of a mathematical model based on coefficients in a quasi steady approach is practically instantaneous and allows a very wide range of simulations in a short time. In order to facilitate the pre-processing stage of CFD calculation, a mesh generation tool has been developed at Bassin d'essais des carÃ¨nes. This tool automatically provides a 3D mesh when cinematic parameters (drift angle, angle of attack, rate of turn in horizontal/vertical plane) are given or when changes in the geometry of the submarine (L/D ratio, number, size or location of the appendages, shape of deck,â¦) are proposed. This avoids the long and laborious task which consists in re-mesh the submersible for any minor change in its geometry. Furthermore, using this tool the grid topology is identical from one case to another so that the numerical results are more reliable, at least for comparison purposes. This study has been performed on an existing submarine for which model test results were available, and calculations have been done on the basis of usual captive model test: rudder effectiveness tests, oblique towing tests, and rotating arm test in both vertical and horizontal planes. The solver used was a commercially available Reynolds Average Navier-Stokes code (Newtonian homogeneous and incompressible fluid). MESH GENERATION The philosophy of the numeric tool used to conduct this study is based on a âmodularâ conception of the submarine, so that the shape, position, or even a detail in the mesh of each part of the ship can easily be changed, and re-incorporated into the mesh of the whole ship. The following paragraphs describe briefly the chronology of manipulations carried out to obtain this adaptable mesh. Body and deck The shapes of the deck and of the body of the submarine are obtained from a CAD file. At this stage, the number, size and repartition of the cells corresponding to those two parts of the submarine are set up. Appendages We mean by âappendagesâ the direction and dive rudders, and the sail. The geometric data necessary are, on the one hand, the general characteristics of the appendage (wingspread, chord, relative thickness), and on the other hand the files of Bezier poles defining the thickness laws at the base and in head of the appendage. the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 821 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 âNeumannâ 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). 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 the authoritative version for attribution. Fig 3: intermediate mesh

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 822 Fig 4: finest mesh Fig 5: âforward dive planesâ 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: Îµ) and drift (horizontal plane: Î´) performed during this study. Îµ Î´ values in degrees(Â°) â8 0 â6 +/â0.5 â4 +/â1 â3 +/â1.5 â2 +/â2 â1 +/â2.5 0 +/â3 1 +/â4 2 +/â5 3 +/â6 4 +/â8 6 8 The two cases Îµ=0 and Î´=0 correspond to the same calculation. In the same way, the negative values of Î´ correspond to the same cases as the positive ones, because of the symmetry of the submarine. Rotation (vertical and horizontal planes) 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=Â±11m; Â±13.83m; Â±17.39m; Â±21.97m; Â±27.50 Since the model length was 4.33m, we obtained the following non dimensional rates of turn: the authoritative version for attribution. q(or r)=L/R=Â±0.39; Â±0.31; Â±0.25; Â±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.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 823 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, Î²1 represents the angle of flap of the stern dive planes, and Î± the rudder angle. Î²1 or Î± (degrees) 0 Â± + Â± Â± Â± Â± 5 10 15 20 25 30 CONVERGENCE 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 âresidualâ 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 âresidualâ, above which the calculation is not considered as being converged. 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 ânâ re-used as a base to compute the iteration ân +1â. 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 MESH 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 authoritative version for attribution. 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 of the

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 824 required mesh is at least doubled and therefore, still poses memory capacity problems. 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 âcomparison with model test resultsâ (fig 10). The following graph shows the curves related the drag coefficient as a function of the incidence angle for different meshes. 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 dependant 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 âforward planeâ 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. the authoritative version for attribution. 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,

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 825 as soon as q>0.25, the curve related to the coarse mesh collapses for the highest incidence angles. Fig 9: Pitching moment for rotation in vertical plane (higher rotation rates) 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 rotation) 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. Fig 11: Heave force coefficient in incidence manoeuvring (vertical plane) Pure drift (without rotation) As seen in the section âcomparison between meshesâ, 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. the authoritative version for attribution. Fig 12: yaw moment versus drift angle

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 826 Rotation/incidence (vertical plane) We present here the comparison between the results of model tests and calculations with the finest mesh (âforward planesâ mesh), since we saw before that they are sensibly better than the ones with a coarser mesh. Fig 13: Heave force coefficient for combination of pitching rate and incidence Despite the presence of an offset already 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 angles (where forces are the highest), we can notice a slight under estimation of heave forces by calculation. Fig 14: Pitch moment coefficient for combination of pitching rate and incidence The same comments can apply to the pitching moment coefficient (figure 14). The higher 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 increases (at least for combination of incidence and pitch rate close to the natural situation of a free running submarine). Rotation/drift (horizontal plane) The rotation/drift cases posed most of the convergence problems (that is why some of calculation points are missing on the graph above). The calculations are more time consuming in the horizontal plane, because of the lack of symmetry, but this cannot be the only reason for those difficulties. We can suppose that the rotation of the sail in horizontal plane disrupts strongly the flow, and therefore the calculations. More precisely, the chord of the sail can not be considered as small in relation to the radius of rotation and therefore the sail acts as a lifting surface in a curved flow. Fig 15: Sway force coefficient (combination of drift and yaw rate) The results obtained in the horizontal plane are 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 are under estimated for large drift angle. Looking at the yaw moment coefficient we can observe that the overall tendency is well respected. However, a small variation of the gradient can be detected between the different rates of turn. the authoritative version for attribution. Fig 16: Pitching moment coefficient (combination of drift and yaw rate)

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 827 Some options have been thought of to improve these results, such as a local refinement of the mesh in âstrategic areasâ (connection between rudders and body of the submarine, for example), but they have not been performed yet. Rudder effectiveness 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% 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 of the plane (Î²1). 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 âliveâ 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. Fig 18: calculated pressure on suction side (high) and on pressure side (low) of the right dive rudder, with the âalive cellsâ mesh The results obtained with the new mesh (âlive cellsâ mesh) show a remarkable improvement of the concordance the authoritative version for attribution. between calculation and test (approximately 30%), 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).

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 828 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. 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 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. the authoritative version for attribution. Fig 22: Pitching moment induced by yaw

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 829 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. 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. Fig 25: Motions CONCLUSIONS NS calculations have shown their ability to provide relevant results in terms of efforts acting on a maneuvering submarine. 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. the authoritative version for attribution. 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

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 830 bring to light phenomena which are so far poorly understood. To gain confidence in this new tool, calculations are now systematically performed in parallel with captive model tests. At this stage, the mathematical models used for the purpose of maneuvering simulations are the same as those developed for captive model tests analysis. We do think that a careful analysis of the huge quantity of data provided by each NS calculation will be of help to improve existing empirical prediction methods, and from a more general point of view to improve the understanding of physics involved in submarine maneuverability. FUTURE DEVELOPMENT The present study showed some difficulties for prediction of rudder efficacy derivatives and for yaw induced forces. To overcome those problems, we plan to perform calculations of a single flapped rudder to determine the necessary amount of refinement in the mesh to allow for an acceptable prediction. This calculation will be based on an existing set of test data for which geometrical details such as root gap were explored. We are confident that horizontal plane forces associated with yaw motions will be correctly calculated once sufficient mesh sizes will be manageable. Once the overall prediction of hydrodynamic forces will be considered as being correct, specific aspects are to be studied. Among those aspects, the influence of test instrumentation (stings, supporting struts, etc..) on towing tank and rotating arm tests will be considered. Calculations will be performed with and without strut, and for different strut arrangement. Also, specific efforts will be devoted to emphasize the influence of propulsion on maneuverability. One additional perspective for further studies in maneuverability is the direct simulations of maneuvers using the unsteady flow capabilities of the RANSE codes. the authoritative version for attribution.

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 831 DISCUSSION U.Bulgarelli Instituto Nazionale per Studi ed Esperienze di Architettura Navale, Italy To apply CFD to study of maneuverability you should already developed unsteady Navier states code, because the phenomenon under investigation is completely unsteady. Is this true? AUTHOR'S REPLY The quasi steady approach we used to investigate the capacity of RANS code for submarine manoeuvrability studies has two advantages: Using CFD calculations as a numerical towing tank gave the opportunity to use an existing set of tools to quickly derive time domain simulations of manoeuvres from calculation of forces. Results of calculation were directly comparable to existing model tests data and could therefore lead, to a certain extend, to validation. Although unsteady phenomena arise during manoeuvres, the quasi steady approach has demonstrated for a long time its capacity to provide pertinent simulations of the behaviour of submarines ion conventional manoeuvres. For most cases, the dynamic of the submarine is relatively slow compared to the dynamic of unsteady phenomena concerned and the sea trials don't really show some major influence of unsteadiness. An other problem of unsteadiness, which is not solved, is that the solution of steady flow calculation can not theoretically be considered as the mean force acting on the body on which separation causes unsteadiness in the flow (as it would be measured in a towing tank or in a rotating arm facility). The calculations performed here showed however some concordance with measurements. DISCUSSION K-H.Kim Naval Surface Warfare Center, Carderock Division, USA When simulating the deflection of fin/control surface, how do you handle the gap between the body and fins? AUTHOR'S REPLY During simulations of rudder effectiveness for a flapped rudder, we discovered large discrepancy between calculation and model tests. Previous calculations for all movable surfaces didn't show such problems and we went to the conclusion that the mesh of the geometry of the surface and especially the root (including gaps) should be improved. To solve this problems, we considered that the cells located at the root are active. The difference between the two meshes is shown on figure 17 and 18 of our paper. Although encouraging, the results obtained are not completely satisfactory and more work has to be done in this field. We planned to do more extensive calculation of isolated fins in order to compare to cavitation tunnel tests. The objective is to define what is the âminimum acceptableâ degree of refinement of the mesh for rudder effectiveness prediction bearing in mind that in our meshing method, the refinement of the mesh in the vicinity of planes has a great impact on the overall size of the mesh for the whole submarine. DISCUSSION I-Y.Koh Naval Surface Warfare Center, Carderock Division, USA How do you plan to do unsteady maneuvering prediction using CFD? AUTHOR'S REPLY It is already feasible to perform unsteady manoeuvring prediction using CFD. For this purpose, it is possible to use the âdeforming meshâ option of unsteady RANS codes for which unsteady calculation are performed at each time step, a new mesh being automatically generated taking into account the dynamic of the submarine as well as the changes in control surface deflection. Bassin has already used this kind of approach in a simplified way (without the authoritative version for attribution.

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. approach and confidence has still SUBMARINE MANOEUVRABILITY ASSESSMENT USING COMPUTATIONAL FLUID DYNAMIC TOOLS 832 shaft (3D). However, it is clear that, at the moment, the 3D case of a manoeuvring submarine would require too much solving the equation of the dynamic of the body) for a cycloidal thruster (2D) or for a conventional propeller on a inclined computation time to be of a practical use. On the other, hand the possibility for validation are reduced for such an