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24~ Symposium on Naval Hydrodynamics Fukuoka, JAPAN, 8-13 July 2002 The Use of a RANS Code in the Design and Analysis of a Naval Combatant Joseph J. Gorski, Henry J. Haussling, Allen S. Percival, James I. Shaughnessy, and Gregory M. Buley (Naval Surface Warfare Center, Carderock Division) ABSTRACT with the entire configuration ~ncluo~ng the propulsor and the scoop preceding it. The overall conclusions from the calculations are that the modifications to the bow dome are an improvement over the original geometry. Additionally, there is no significant separation around the propulsor or in the scoop area leading into the propulsor. However, because the propulsor operates close to the hull the inflow to the propulsor is significantly less than the free stream velocity. Comparisons with experimental data for the final design are also performed for validation purposes demonstrating the accuracy of the RANS predictions. INTRODUCTION The computer advances in the last decade have been a significant catalyst for improving our ability to predict ships flows. The increased computer power has led to Reynolds Averaged Navier-Stokes (RANS) calculations on large grids becoming more routine. It has also led to an increased experience base as it became possible to do more calculations. Good results for a variety of complicated ship flow fields have been obtained with a number of RANS codes (Gorski, 2001b) demonstrating the overall maturing of the capability. Such computations provide an overall picture of the flow field in the immediate vicinity of the ship, which can aid in its understanding as well as a means to do trade off studies to evaluate design Viscous flow calculations using the Reynolds options. Averaged Navier-Stokes (RANS) equations are performed in support of the design effort for the Gov't- 2 geometry of the ONR Surface Combatant Accelerated Hydrodynamics S&T Initiative. The Gov't-2 configuration is a tumblehome geometry with surface piercing bow and ducted propulsors. RANS calculations are used to provide information on the flow created by various bow dome modifications as well as to provide information on the inflow to the propulsor. The bow dome changes are evaluated using bare body calculations. For the propulsor inflow, calculations are performed Because of their demonstrated successes, ITTC (1996) concluded that RANS codes had matured enough to be integrated into the design process for addressing issues associated with resistance and propulsion. Rood (2000) discusses how such codes are starting to revolutionize ship hydrodynamics design and evaluation procedures from traditional towing tank methods to computational based methods, particularly in support of the Navy's new land attack destroyer. RANS codes can be used to predict differences in resistance due to shape and Reynolds number changes as shown by Gorski (1998) for bodies of revolution. Additionally, RAN S codes can contribute in a marine design process, as demonstrated by Gorski and Coleman (2002) for a submarine sail where design decisions were based on the predicted resistance and flow field. For surface ships though, the free-surface predictions with RANS codes have been more problematic (Gorski, 2001b). Although some very good free-surface predictions have been obtained with various codes, and even sinkage and trim predictions have been performed (Subrami et al, 2000), the lack of a robust free-surface capability as part of the RANS prediction process prevents fast and accurate resistance predictions for a variety of speeds. It is expected that this will be overcome. In the meantime RANS codes can still have a significant role in providing propulsor inflow. Depending on the particular design of interest highly viscous and vertical flow can enter a surface ship propeller (Gorski, 2001a). This is especially true for integrated propulsor/hull configurations where the propulsor may be tucked in tight to the hull. It has already been demonstrated that RANS codes have a role to fill in this area for tanker (Valkhof et al 1998) and waterjet (Allison et al 2001) designs and can also provide information on shaft effects on the flow entering the propeller as shown for an aircraft carrier by Gorski et al (20021.
To demonstrate the utility of RANS codes for future Naval combatants, as well as facilitate their use, ONR initiated the Surface Combatant Accelerated Hydrodynamics S&T Initiative. The objective of this effort is to apply verified, validated, and benchmarked computational ship hydrodynamics to the exploration of innovative propulsor/hull concepts and to develop tools and concepts for technology options for DD(X) and beyond. The desire is to use these computational tools to help evaluate 'out of the box' designs so a large experimental program is not needed. Another purpose is to provide a careful validation against the experimental data being generated in order to demonstrate the extent to which the computational codes can reproduce the experimental and actual flow physics. To adequately test the current computational tools a complex surface ship geometry with strong propulsor/hull interaction is desired. To this end a hull form known as Gov't-2 has been designed and built, and a variety of computations and experiments have been performed on it. The Gov't-2 hull form is a tumblehome design with a wave piercing bow and ducted propulsors similar in concept to that shown in Figure 1. Since no traditional model exists for this hull form it needed to be designed, built, and tested as part of the effort. This paper discusses how the use of RANS calculations contributed in the actual design cycle where details of the hull shape were changed based on the predicted results. Comparisons between calculations and measurements for the final built geometry are also shown demonstrating how well the computations reproduced the flow field. Figure 1: Integrated propulsor/hull concept. GOV'T-2 GEOMETRY MODIFICATIONS ~ . As stated previously, the design of the Gov't-2 geometry is based on a tumblehome surface ship configuration with an integrated hull/propulsor 2 combination where the propulsor is a ducted unit merged directly into the hull. Because of the uniqueness of this geometry there is no historical database to aid in the design of this new configuration. Consequently, to aid in evaluating the modifications a significant number of computations are performed, on various modifications to the basic hull form, using several flow solvers including the RANS code UNCLE (Taylor et al, 1991, 1995) and the potential flow codes Das Boot (Wyatt, 2000) and SWAN (Sclavounos, 1995~. The tools used to create and modify the surfaces are FastShip from Proteus Engineering and Mechanical Desktop from AutoDesk, Inc. Discussed in this paper are five hull forms, the final Gov't-2 design and four variants, Concept-2 through Concept-5, which are evaluated with RANS to help obtain the final Gov't-2 design. The ducted configurations discussed, Concept-3 and Gov't-2, are somewhat similar to the hull form shown in Figure 1. The configurations have sonar domes, but no other appendages are included in the calculations. Concept-3 has a simplified docking skeg which ends just forward of the ducted propulsor. Additionally, the hull has been 'scooped' out to provide a smooth hull surface merging into the propulsor ducts, which are embedded in the hull. Concept-3 is the baseline geometry from which the RANS effort was started and Concept-2 is a bare hull version of it. Concept-4 and Concept-5 are attempts to improve the design over Concept-3 and differ from it in several ways. The forebody has been extended forward of the shoulder and the sonar dome has been refaired to reduce the strength of the vertical flow generated there. For the final Gov't-2 design the skeg has been eliminated and the propulsors have been revised and moved forward, inboard, and further into the hull to reduce the propulsors influence on the free surface. Concept-5 is a bare hull version of the final Gov't-2 design. One goal with the Gov't-2 design effort is to keep wave drag low as well as reduce the possibility of propeller ventilation. Potential flow solvers can provide this type of information quite well except where viscous effects may be important, such as in the immediate stern region of the boat. Consequently, most of the design effort for Gov't-2 involves the use of the potential dow solvers because of their overall efficiency compared to RANS codes. During the course of the design investigation the potential flow solvers indicated that there could be deep wave troughs in the immediate vicinity of the propulsors. As a consequence, a considerable effort was undertaken with the potential flow codes to evaluate different positions of the propulsors in order to determine ways to improve the free-surface topography. RANS codes could not be used to provide information on the
movement of the propulsors in a timely manner because of the complications of resurfacing and regrinding the geometry every time the propulsors are repositioned. Although much of this design effort involved the use of the potential flow solvers the RANS codes do have a part in the design process of such geometries and will continue to do so. Because the propulsor is now close to the hull, it is operating in a viscous boundary layer, which is unlike many surface ships where the propeller often operates in a nearly inviscid flow. With the viscous inflow, the flow entering the propulsor is reduced from what it normally would be when operating outside of the boundary layer. Additionally, any vortices or secondary flow generated by the body upstream of the propulsors have the potential to enter the propulsor and affect its performance. Propulsor designers need to know the correct flow entering a propulsor to provide a good design. For such designs it is necessary to perform viscous flow calculations to have any hope of computing the flow field into the propeller accurately. For the purposes of evaluating the design a RANS code is used to compute double hull (no free- surface) or linearized free surface solutions. Discussed here are four main computations performed with RANS during the design process along with the final design prediction. The final design calculations are performed with non-linear free surface modeling. One of these design calculations is done with the hull appended with propulsors to provide information on how the various components interact. The remaining three design calculations are performed on bare hull configurations to evaluate the hullforms themselves and to isolate the effects of the duct on the flow field. By comparing bare hull and appended runs, an assessment can be made of the propulsor's impact on the flow into the scoop/duct and on the nominal wake. The bare hull calculations provide comparisons of the nominal wake and what impact the different bow dome shapes have on the flow into the propulsor. The final Gov't-2 geometry calculations are then compared with the experimentally measured data for the free surface along the hull, wave height behind the hull, and inflow to the propulsor. GRID GENERATION It should be recognized that to perform flow calculations for such complicated geometries is not simply a matter of turning on a particular piece of software. The computation of such flow fields involves a process not unlike that of doing a model experiment and includes: generating the geometry, 3 generating surface and volume grids, carrying out the flow calculation and data reduction. A test of whether a particular code can predict certain measured physics is dependent on all pieces of this process and the grid generation is a significant component of this process. A prerequisite to generating computational grids is the satisfactory specification of the actual geometry. A day spent re-modeling and cleaning up the geometry definition with the CAD software can often save a week in grid generation. Details, such as ensuring there are no gaps in the geometry and trimming surfaces, must be taken care of before the geometry can be used easily with current grid generation software. An experienced grid generator will also consider the topology of the future grid in modeling the geometry and thereby simplify the grid generation (i.e. combine surfaces where applicable and eliminate unnecessary features). For the actual definition of the geometry, a single B-spline surface for each component is preferred. B-splines can model the most complex shapes and provide smooth, continuous definition with well-behaved intersections. In the ICES format, they can be transferred between most CAD and grid generation software packages. When generating the computational grid, a surface grid must first be generated on the body and all surrounding boundaries where boundary conditions are imposed. Then a volume grid is generated providing discrete points in the entire flow domain where the Navier-Stokes equations are solved. For bare hulls this is quite straightforward. However, for appended hulls and structured grids this can be a difficult dilemma. In practice it is often difficult to achieve good grid quality, a sensible amount of time spent, and a practical grid size all at the same time. Experience is very important because trade offs between the three areas must often be made, particularly in a design process. When generating the surface grid it is important to ensure the grid conforms to the actual geometry. Additionally, to help provide accurate predictions, these surface grids must be clustered in areas of high geometry gradients or where the flow is expected to change rapidly. A computed solution can only be as good as the grid on which it is computed If there are high gradients in the flow it is necessary to have enough grid points in these areas to resolve them. If enough grid points are not present, the computation will diffuse these high gradients. Once a flow feature is diffused in this, or any other way, its impact and interaction on the surrounding and downstream flow cannot be predicted accurately. All grids are generated with Gridgen V.13, from Pointwise. A conventional topology is used for all grids: 'O' transversely and 'C' longitudinally. Only
half of the flow field is calculated as port/starboard symmetry is assumed. The far field boundary is one body length away upstream and to the sides. The wake extends 1.75 body lengths downstream. The minimum spacing (initial spacing normal to the body surface) is calculated based on a y+ value of 1, using model scale Reynolds numbers. The grids are broken up into 24-28 approximately equally sized blocks to properly load balance the calculations among the 24-28 processors that are used for the calculations. Bare Hull Configurations The grid generation strategy for the three bare hull grids, Concepts-2, -4, and -5, is the same in order to provide a fair evaluation of the different hull forms and not bias these conclusions because of differences in results due to grids rather than differences in geometries. No changes are needed to the inputs or boundary conditions of the flow solver. These grids all have the same grid dimensions and grid size with approximately 2 million grid points total. In the streamwise direction 257 points are used, 193 of which are on the hull and the remainder are in the wake. In the transverse direction 97 points wrap around the hull and 81 points extend out from the hull in the normal direction. Figure 2 shows the grid near the bow and stern for Concept-2. Hulls Appended with Propulsor The grid for Concept-3 is similar to that for Concept-2, but much more complicated because of the propulsors. The same overall topology is used: 'O' transversely, 'C' longitudinally with a singular pole coming off the transom. Approximately 2.5 million points are used, with the additional half million points primarily in the propulsor region. In order to maintain the boundary layer into and through the duct, a new topology is incorporated into the propulsor region (see Figures 3 and 4~. A half cylinder (180 degree) shaped grid is embedded in the bare hull grid. It conforms to the lower half of the inside of the duct and collapses to a transverse line upstream and downstream. The grid between the half cylinder and the hull conforms to the upper half of the duct, thereby maintaining the necessary grid resolution to carry the detailed boundary layer flow into and through the duct. While it is time consuming, this topology is straightforward and has good grid quality. One problem with the current grid is that good boundary layer resolution is not maintained on the duct walls. This was necessary to meet design deadlines and was felt to be a reasonable trade off as this should not impact the computed flow entering the propulsor significantly. l . i : Figure 2: Concept-2 grid (every other point shown for clarity). 4 . Figure 3: Grid near the propulsor for Concept-3.
Number of points in k (normal) direction Blue : 73 Green: 73 Number of points in j (girth) direction 65 circumferentia 33 radially C Figure 4: Grid in a transverse cut through the propulsor of Gov't-2. In order to do a grid resolution study a finer grid is generated for the Gov't-2 appended hull with approximately 9.5 million points for half the geometry. A cross section of this grid in the propulsor region is shown in Figure 4 with the corresponding number of grid points. A coarser grid is obtained by removing every other point in all three directions providing a resolution of approximately 1.25 million points which is somewhat coarser than that used for Concept-3. A third coarser grid could be obtained by repeating this procedure yielding a grid of approximately 175 thousand points. Transom Stern Issues The transom stern is still a major problem when planning a grid generation strategy. Before generating the grids, the free-surface boundary conditionals) which will be used has to be decided. Concepts 2, 3, 4, and 5 are run with the double-hull or linear free surface boundary conditions. The transom topology used is a continuation of the hull surface grid collapsed to a singular pole at y=z=0. This is simple, easy to generate, and has good grid quality. The non- linear free surface boundary condition has a grid requirement that the double-hull and linear free surface boundary conditions do not. The grid conforms to the changing free surface elevation by moving along the grid's own lines of increasing/decreasing index in the transverse direction. The pole topology cannot be used for the non-linear free surface grids because the singular pole does not allow the grid to move. To alleviate this the Concept-5 bare hull grid is modified to include a cap block extruding off the transom to the downstream boundary. This topology poses some problems because of the jump in grid resolution at the boundary between the cap block and the rest of the grid. Consequently, for the final Gov't-2 appended hull grid a different topology is used where the hull surface grid ends in a small segment of the hull centerline, starting at the free surface and moving a small distance down and forward along the hull. This surface grid can then continue downstream, sharing the symmetry plane with the free surface grid plane. This topology does distort the grid somewhat, but the grid quality is acceptable and it is not a complex topology. The transom stem is also a problem from a boundary standpoint when using the double-hull and linear free surface boundary conditions. For Concepts 2, 3, and 4, the free-surface boundary is modeled by assuming the dynamic free-surface elevation. For Concept 5 the free-surface boundary is modeled at the undisturbed water level. Due to the sharp transom edge the area immediately aft of the transom is very sensitive and a better solution can probably be obtained by estimating the dynamic free-surface level. FLOW SOLVER To compute the viscous flow field the incompressible Reynolds Averaged Navier-Stokes equations are solved using the Mississippi State University code UNCLE (Taylor et al, 1991, 19951. The equations are solved using the pseudo- compressibility approach of Chorin (1967) where an artificial time term is added to the continuity equation and all of the equations are marched in this artificial time to convergence. Only steady state computations are performed for this effort. For the present calculations a thir~order upwind biased discretization, based on the MUSCL approach of Van Leer et al (1987), is used for the convective terms. The equations are solved implicitly using a discretized Newton- relaxation method (Whitfield and Taylor, 1991) with multigrid techniques implemented for faster convergence (Sheng et al, 1995~. The turbulence model used for the present calculations is primarily the q-ce model of Coakley (1983) for evaluating the hull modifications, but the k-e model of Liou and Shih (1996) has been used for the final Gov't-2 predictions that are compared with the experimental data. The free surface implementation uses a surface tracking approach where the water surface is treated like a material boundary and a kinematic s
condition is satisfied there. This boundary then becomes a boundary of the domain and the flow field is _ solved for the water portion of the problem with a dynamic boundary condition applied at the water surface for the Navier-Stokes equations. Usually only inviscid boundary conditions are applied at the water ~l. surface despite the use of a viscous flow solver, but this should have little influence on the large scale waves. Because the water surface is now a boundary to the domain a grid must be generated in the domain using the hull and water surface as its boundaries. Many times one can simply use linearized boundary conditions about the design waterline and get very good results for practical purposes. In this way only a single grid is needed for the problem. If one needs more accurate results a nonlinear formulation is used that iteratively redefines the water surface, based on the calculation, and regenerates the volume grid based on this new surface. Details of the implementation can be found in Beddhu et al (2000~. An important factor in being able to compute and evaluate all the hull modifications of interest is the implementation of a parallel version of the UNCLE code (Pankajakshan et al, 20001. The code uses MPI for message passing due to its portability. To run in parallel the computational grid is decomposed into various blocks, which are sent to different processors. Load balancing is obtained by making the blocks as equally sized as possible. For the present calculations, 24-28 processors are typically used. FLOW SOLUTIONS Three aspects of the flow solutions are discussed. The first involves the bare hull calculations, which provide information on the different bow dome geometries. The second deals with the calculation of the ducted hull configuration, Concept-3, which provides information on the inflow to the propulsor. Both of these efforts are important parts of the design process using the RANS codes. The third part discusses the calculation of the final Gov't-2 geometry and comparisons with the experimental data. Bare Hull Configurations Concept-2 is a bare hull version of the Concept-3 configuration. Although it is called a 'bare' hull it contains the docking skeg as well as the scoop leading into the propulsor. Calculations are performed using the double model approximation with port/starboard symmetry at a Reynolds number of 13.7 million, based on body length. The computed axial velocity contours at several longitudinal locations along the hull are shown in Figure 5. 6 - - - ." T- ~ ~ _: ~ _ Figure 5: Computed axial velocity contours for Concept-2. As seen at the forward location, vortices are formed over the bow dome. These vortices spread and move outboard as they travel downstream. These vortices produce secondary flow outboard along the hull as seen in the cross-sectional plot of Figure 6, which shows one of the axial velocity contour plots with the secondary flow vectors superimposed. Here the port/starboard symmetry plane is at Z=0. These vortices rotate in the same direction as would a forward bilge vortex generated by the hull. Consequently, it is not clear if the vortex system traveling down the length of the hull is entirely from the bow dome or is enhanced by the natural curvature of the hull. In any case, the vortex system moves downstream along the path of the scoops which influence the cross sectional extent of this vertical wake structure. As this vortex structure is accentuated in the scoops, it is seen that low velocity flow is pulled out from the boundary layer and the overall size of the vortex structure appears to increase. Here, green is low axial velocity and red is close to free stream velocity. Additionally, the boundary layer and wake created by the docking skeg is seen in the computation, but does not appear to interact strongly with the flow in the scoops. Although there is low axial velocity flow in the scoops it does not appear to lead to flow separation as shown in Figure 7 via the computed surface streamlines. These surface streamlines appear to be drawn into the scoop area, but there is no indication of flow reversal. The streamlines also flow smoothly around the skeg. It should be noted that there is no propulsion modeling for this calculation. The calculation indicates a vertical flow will enter the propulsor, which may be an area of concern for propulsor design. The vertical flow in and of itself can have some influence on propeller performance due to the local angle of attack imposed on the blades. Of more significance may be the velocity deficit associated with this flow, since the
axial flow entering the propulsor is significantly slower than the free stream value. .01 .02 .03 .05 Ins' _ 0.025 0.05 Figure 6: Axial velocity contours and cross flow velocity vectors for Concept-2. Figure 7: Computed surface streamlines for Concept- 2. As part of the design phase a new bow dome was developed in an attempt to reduce the strength of the vortices created there since they flow downstream directly into the propulsor. To save time only a bare hull computation is performed for this new hull, which also has a lengthened forebody, and is referred to as Concept4. In addition, Concept4 does not contain the scoops or skeg so some insights of their effect on the flow field can also be obtained. Computed axial velocity contours for this configuration at several longitudinal locations are shown in Figure 8. - a__ by_ Bare Hull Ccacopt 4_~ A:; Figure 8: Computed axial velocity contours for Concept4. It should be mentioned that a grid very similar to that used for Concept-2 is used here so that the computed differences should be due to geometry changes and not grid changes. Because the length of the ship has changed, primarily in the section forward of the shoulder, it is difficult to do a one-to-one comparison of the vortices formed by the two bow domes. However, it is evident that with Concept-4 the vortices stay closer inboard, which is a possible indication of less strength as there is less convective spreading of the vortex pair. This is evident all the way to the stern of the hull, although it these downstream locations the lack of a skeg can be keeping the vortices closer together than in Concept-2 where the skeg may push them apart. Additionally, it appears the scoops have a significant influence on the extent of the low velocity flow that would enter the propulsor. For Concept-4, where there are no scoops, the vortices become perturbations to the hull boundary layer at the downstream locations where the propulsors would be. As had been seen in Figure 5, the vortices in the scoop become the dominant feature that enter the propulsor and stand out clearly from the hull boundary layer. Computed surface streamlines over both bows are shown in Figure 9. There is more turning of the bow dome streamlines and subsequent collapse to a limiting streamline for Concept-2 than Concept-4. This again indicates the bow dome vortices generated by Concept4 are an improvement over those computed for Concept-2. A comparison of the axial velocity contours, between the two configurations, near the forward shoulder of the ship is shown in Figure 10. From this location downstream, the lengthening of the ship has no further impact and provides a good comparison location. It is seen that the Concept4 vortex system is inboard of that predicted for Concept- 2. The axial velocity deficit is similar between the two configurations. However, the secondary flow 7
generated by Concept4 is much weaker than that generated by Concept-2. Hence, it appears the bow dome vortices generated by Concept4 are an improvement over those generated by Concept-2. It is not clear whether the axial velocity deficit entering the propulsor is dominated by the bow dome vortices or the scoops. Since the propulsor is embedded in the hull it is felt that the scoops are necessary to provide clean inflow to the propulsor. Consequently, pursuit of improvements to the inflow by minimizing the bow dome vortices seems worthwhile. Conng~6on 2 SduUen it_ Cordiguatlon4 Sodden Figure 9: Computed surface streamlines over the bows of Concept-2 (top) and Concept4 (bottom). CordIguadon 2 Con11gula~don 4 Figure 10: Cross flow velocity vectors and axial velocity contours for Concept-2 (left) and Concept-4 (right). In an effort to obtain some additional flow enhancements, the final configuration calculated with RANS as part of the design process is a modified version of Concept4, referred to as Concept-5. The modifications of Concept-5 are considerably simpler than those performed when going from Concept-2 to Concept-4. Consequently, it is expected the flow changes will also be smaller. The primary enhancements consist of further fairing the bow dome, softening the shoulder in the sectional area curve, and softening the bilge radius approaching the transom knuckle. Very little difference is seen between the viscous boundary layer flow on a bare hull for this new configuration and that of Concept4. A comparison of the axial velocity contours and secondary flow generated by Concepts-4 and -5 just downstream of the bow dome is shown in Figure 11. The flows are quite similar with no detrimental effect on the bow dome vortex from these latest modifications. It should be noted that only the double model solution is shown here. The grid for Concept-5 is similar to that for the previous two bare hulls. With the Concept-5 bare hull calculations, both linear and nonlinear free surface solutions have been obtained with UNCLE v1.2.6. The presence of the free surface has little effect on the bow dome vortices or the viscous flow that would enter the propulsor. Consequently, it is believed that the double model calculations provide useful information on the flow field. 0 962795 0 913421 0 Be4047 0 s, 4672 0 76s2s8 0.7' Ss24 0 66 665 o61 7176 0567802 0s'8428 0 469054 041969 0370306 0320932 0 27 1557 0 222183 0 172809 0 123435 0 07 40511 0~24~87 Concept 4 Figure 11: Comparison of Concept-4 (right) and Concept-5 (left). Concept-3 with Propulsor The bare hull calculations give an indication of some of the flow issues involved with these complex configurations, but do not truly provide the details of 8
the flow into the propulsor which is needed for ithe propulsor design. The Concept-3 calculations provide some of this pertinent information. For Concept-3, the propulsor is embedded in the hull and there is also a hub inside the duct. This ducted geometry provides significant blockage to the flow field and the flow can no longer flow smoothly down the hull as observed for Concept-2. The duct and hub are included in the RANS calculations of Concept-3, but it is necessary to model the thrust through the propulsor as part of the RANS calculation. This is done by using an actuator disk model, which imposes a constant axial force over a plane inside the duct passage. The force is applied at a single axial plane and provides the net effect and not the individual effects of the internal components. The duct and hub are part of the RANS calculation and do not need any additional modeling. The axial force supplies a thrust to the model, but no radial or tangential force components are imposed. The computed axial velocity contours at several longitudinal positions along the body are shown in Figure 12. The flow upstream of the propulsor is nearly identical to that computed for Concept-2 as it should be, since Concept-3 is a ducted version of Concept-2. The Concept4 and -5 bare hull configurations were pursued concurrently with the Concept-3 calculations. It is clearly evident that the vertical structures, and associated velocity defects, flow along the hull and enter directly into the propulsors. In these figures, red is near free stream velocity and blue is low speed flow. This figure indicates that the flow in the entrance region to the propulsor is slower than that farther upstream. This is because of the blockage induced by the propulsor despite the flow being propelled via the actuator disk model. _ _ _ _ ~ _ a_._ a_ _ wen_~ _h Figure 12: Concept-3 Axial velocity contours just downstream of the leading edge of the duct are shown in Figure 13. The flow inside the duct is significantly slower than the free stream with a mean value of roughly 70 percent of ft. This is unlike many conventional surface ships where the propeller is operating in a nearly inviscid free stream flow field. Noticeable in this and the previous figure is the low velocity flow which has been pulled out from the boundary layer due to the vertical nature of the flow entering the propulsor. Also seen in Figure 13 is the outline of the large vertical structure which propagates along the hull with the propulsor clearly in the center of it. The boundary layer on the skeg is also seen, but this seems to have little impact on the propulsor inflow. The axial velocity contour at roughly 70 percent of the propulsor length is shown in Figure 14. Here the flow is somewhat faster than that at the entrance. There is also an interaction between the two propulsors producing the higher velocity flow on the inboard side of the propulsors. The flow at the exit of the propulsor, Figure 15, indicates that the flow velocity is increasing, but is still less than the free stream, which may indicate under propulsion with the actuator disk model. A velocity contour plot further downstream, Figure 16, indicates there is still some wake structure associated with the propulsor, but it is not the significant vertical type structure seen entering the propulsor. Another view of how the axial flow changes through the propulsor is shown in Figure 17, which is a cut along the centerline lengthwise through the propulsor. The axial velocity keeps decreasing as it approaches the propulsor. This is due to a combination of the increasing boundary layer thickness as well as the decreasing depth of the hull. Additionally, it is believed much of the axial velocity decrease is due to the blockage effects of the propulsor. Of significance Computed axial velocity contours for is the low velocity near the hull, which enters the propulsor and could be a cause for concern if it were to separate. As one progresses longitudinally along the propulsor the flow velocity eventually increases as it exits at nearly the free stream velocity. It should be noted that the change in flow from the inlet to the exit of the duct is controlled by mass conservation and the changing duct area. The actuator disk model influences the magnitude of the flow entering the propulsor. Without this actuator disk model there would be significantly lower velocity at the entrance to the propulsor and some possible flow separation. 9
r`L -n no -n nd NSWCCD (6199) Computed Propu~or Inflow (AXEII Velocity Contours) Concept 3 0 0.025 of. ~ _ Z/L Figure 13: Axial velocity at the inflow to the Concept-3 propulsor. no non -0.04 NSWCCD (6/99) Ux 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 PropulsorThrough Flow (Axial Velocity Con~um) Concept 3 0 0.025 0.05 0.075 Z/L Figure 14: Axial velocity contours at 70% of the propulsor length. -0.04 NSWCCD (6199) Computed Propulsor Outflow (Axial Velocity Contours) Concepts 0 0.025 0.05 0.075 Z/L Figure 15: Axial velocity contours at the exit of the Concept-3 propulsor. 1 Ox 1.10 1.05 -0.02 1.00 1 0.95 1 o.so _, 0.85 0.80 0 75 o 04 0.65 0.60 0.55 0.50 0.45 0 40 -0.06 0.35 0.30 10 Ux 1 .10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 , 0.30 O.025 Z/L n rye 0.075 Figure 16: Axial velocity contours downstream of the Concept-3 propulsor.
us 0.8 0.85 o.9 X/L Figure 17: Axial velocity contours on a vertical plane through the centerline of the Concept-3 propulsor. The original version of Concept-3 had an abrupt step from the propulsor to the hull at the exit to the propulsor. This is because of the decreasing draft of the hull at the stern. This step led to significant flow separation at the exit to the propulsor as seen in Figure 18. Consequently, ramps were added to the propulsion exits to provide a smooth transition from the propuslor to the hull. Computed surface streamlines for this configuration are shown in Figure 19. The streamlines clearly enter and exit the propulsor with no apparent separation so exit ramps were also included in the final Gov't-2 design. Also of . . Interest Is the strong turning of the flow around the propulsors both inboard and outboard of them. The strong turning to the outboard side of the propulsors helps give an indication of why the propulsors can have a strong effect on the free surface waves generated near them. The inboard turning of the flow, and its interaction with the skeg, provides a high axial velocity between the propulsors which was indicated in the axial velocity contour of Figure 14. Figure 18: Computed surface streamlines without ramps at the propulsor exit. Figure 19: Computed surface streamlines for Concept-3. The computation for Concept-3 gives some indication of the complexity of the flow field generated by the propulsor/hull interaction. The flow upstream of the propulsor is highly viscous. The subsequent inflow to the propulsor is significantly different than what is found on conventional surface ship configurations. Similarly, the propulsor has a strong affect on the surrounding flow field. The ability to dissect such flow field computations to help understand the underlying flow physics is one of the advantages of RANS calculations where the entire flow field is available for . . . Investigation. GOV'T-2 CALCULATIONS The final Gov-t-2 design consists of the extended forebody of Concept4 with the sonar dome of Concept-5. Additionally, the skeg has been eliminated and the propulsors have been revised and moved forward, inboard, and further into the hull than used on Concept-3. Overall, the computed flow field appears similar to that for Concept-3 already shown in Figure 12 through Figure 19. This hull form was tested at NSWCCD to provide a validation database for the computations. Me asurements consisted of longitudinal wave cuts, stern topography, and velocity measurements of the propulsor inflow. Calculations are performed at model scale corresponding to a Reynolds number, based on model speed and length, of 15.44e+06 and a Froude number of 0.232. Like Concept-3, body force terms are included for propulsion approximately halfway through the propulsor in the streamwise direction. The body force terms model the total thrust of all the blades combined and do not include forces generated by the hub or duct since these are computed directly from the RANS calculation. This is a total blade force and is 11
represented in the code at an axial location, corresponding to a single axial grid plane. The total torque of the unit is negligible so no torque is modeled via body forces. Additionally, the body force is applied uniformly across the disk plane with no attempt to model radial variations in the force model. To better estimate the quality of a solution there have been efforts to develop uncertainty estimates and validation procedures for computations (e.g. ALLA, 1998; Roache, 1998~. This is an area of significant importance as the computational community tries to provide metrics for how good a computation is and more work needs to be done in this area. To this end though it is becoming largely recognized that one cannot declare a particular code validated because a particular solution depends on many factors including: geometry definition, grid quality, turbulence modeling and user experience among other variables. In the current effort an attempt was made to apply the verification and validation procedure of Stern et al (1999~. This requires solutions on three different grids. As already discussed solutions are obtained for the Gov't-2 hull form on three different grids consisting of a fine or large grid containing almost 9.5 million points (after blocking for parallel processing), a medium grid containing about 1.25 million points, and a coarse grid of about 175 thousand points. To implement the procedure correctly all three grids must be in the asymptotic limit of a final grid independent solution. This is not the case for the coarse grid here and uncertainty estimates obtained with it can be erroneous as discussed by Ebert and Gorski (2001~. Consequently, uncertainty estimates are not provided here, but it is still very instructive to look at the grid dependence of the computed solutions. The first comparison shown is for the wave profile on the hull. As shown in Figure 20 the fine grid provides a very good comparison with the measured profile on the hull. Here the bow of the hull is at X/L = O and the stern at X/L = 1. The medium grid captures some aspects of the measured data, but the coarse grid loses many of the details. Longitudinal wave cut data at various locations away from the hull is also available for comparison. At Y/B = 0.66, Figure 21, a comparison similar to that shown for the hull profile is obtained with the fine grid capturing the wave heights well, but the coarse grid has significant damping. Downstream of the hull the computations quickly start to dissipate the computed wave field as the computational grid expands. This dissipation of the computed waw field away from the hull is illustrated further in Figure 22, which provides a comparison of the longitudinal wave cut at Y/B = 2.5. Here it is seen that even the fine grid eventually damps out the wave away from the hull and the coarser the grid the more quickly the waves are dissipated with distance from the hull. new 0.004 n on' Hi o n on; -0.004 Coarse Grid Medium Grid . . - - Fine Grid 0 Measured a a 0 09 0.4 0.6 XJL 0.8 1 Figure 20: Measured and computed wave height on the hull. 0.005 0.004 0.003 0.002 0.001 O -0.001 -0.002 -0.003 -0.004 0 Tank Y/F = 0~6 - Coarse Grid Medium Grid Fine Grid -0.5 0 XIL Figure 21: Computed and measured wave height at Y/B =0.66.
- 0.004 _ _ 0.003 0.001 -0.00 -0.002 -0.003 1 o Tank YE ~ 2~50 | Coar" land Medium Grid Fine Grid Coarso Grld n In .O nS -0.5 0 0.5 1 1.5 ~ in XJL Figure 22: Computed and measured longitudinal wave height at Y/B = 2.5. a) Coarse and Comparisons with free surface heights measured immediately downstream of the hull are shown in Figure 23 for all three grids. Here the computations from the three different grids have been interpolated onto the same "grid" the measurements were obtained on to provide a truer comparison. Each figure has the computed wave heights on top and the measured wave heights on the bottom. The data shows a rooster tail forming immediately aft of the hull with a trough downstream of that. The coarse grid does a very poor job of representing the measured data and significantly under predicts the rooster tail height md following trough depth. The medium grid comparison b) Medium and is better containing much of the correct behavior of the flow, but over predicts the height of the rooster tail and the subsequent trough behind the rooster tail is not as deep as it should be. The fine grid solution is really excellent capturing the flow extremely well. n Ace, The measured axial and secondary flow velocity at X/L = 0.77 is shown in Figure 24, which is in the scooped out area just upstream of the propulsor. This data was taken with a LDV system and axial velocity contours are shown with secondary flow vectors. The dominant feature is the vortex, which is generated at the bow dome, as was shown with the previous computations. This flow is atypical of propeller inflow for conventional ships. There is a large region of low velocity created by the vortex pulling boundary layer flow out away from the hull. Additionally, some high velocity flow is pulled in toward the hull by the vortex. 1.0 1.1 1.2 XJL Medium Grld 0.10 0.05 0.00 -0.10 -0.05 -0.10 c) Fine grid 1.0 1.1 1.2 XIL Figure 23: Computed and measured free surface height in the stern region: a) Coarse grid, b) Medium grid, c) Fine grid. 13
i:) D -~0 ~ ~ -any by: '0.~ -~ Figure 24: Measured velocities at X/L = 0.77. Rae 1 ~:.~ (>sand do ~ ~ 1 raspy i ~ In, @ t>~ i ~~! 1 ~~! 1 'by ' rem '. -~.r~ I.. . . ...... i. .... . , ~ ..~.. . ~ 5.~ ~~ y';:r$ 0~ *~ a) Coarse grid i.it i. .^ -~.O It: The computed flow with all three grids at this location is shown in Figure 25. The solutions from all three grids have been interpolated onto the experimental "grid." The very low velocity predicted next to the hull in the computations is not present in the measurements since the flow could not be measured that close to the hull. The most apparent difference between the computed and measured data is a slight shift of the vortex location. This shift is probably due to the computed vortex not being as strong as the actual b) Medium grid vortex, which can be inferred from the secondary flow vectors. However, the agreement is very good and the predictions are accurate enough to provide cavitation estimates for the propulsor. The solutions just discussed are with the k-£ model. A second calculation performed with the Ace model on the medium grid showed a slightly stronger vortex and shifted the center slightly more toward the experimental data, but the changes are not significant enough to show here. One significant difference between these comparisons and the wave height predictions is the grid dependence of the solution. While the predicted wave heights are very grid dependent the computed axial and secondary flow fields seem more grid insensitive. However, the coarse grid is overly dissipative as seen from the overly thick boundary layer on the hull and the larger low velocity c) Fine grid area due to the vortex as compared to the finer grid solutions and measured data. 14 -. A, _~1i']4 ~ C'£-i ~ `- t40~ t.1,~ 1~.~ Alit · yea . ~ ~ . . . `~;wO 1 ( ~~ ~1 Figure 25: Computed velocities at XIL = 0.77: a) Coarse grid, b) Medium grid, C) fine grid.
CONCLUSIONS The RANS calculations reported here are done as part of the design process for the Gov't-2 geometry of the ONR Surface Combatant Accelerated Hydrodynamics S&T Initiative. The effort demonstrates that RANS computations can be done quickly and accurately enough to provide ship design guidance. Although the free surface is not included in the RANS calculations in the early design phase of this study, the RANS calculations do provide useful insight to aid in the design. Specifically, the RANS calculations provide information on inflow to the propulsor as well as a means to evaluate the different bow dome geometries identified. For these purposes double model calculations provide nearly as much information as a computation with the free surface. One thing that needs to be considered when using RANS for design work is the ability to quickly re-grid the geometry as it changes. The current geometry with its ducted propulsors could not be re-gridded quickly enough when the propulsors are moved. Consequently, there was an emphasis on bare hull calculations. To make RANS a viable design tool the re-gridding of complicated geometries to reflect changes must become more automated or the use of RANS solvers, and their associated flow information, will be limited. An accurate flow prediction method is necessary to provide input for novel surface ship concepts more quickly and more cheaply than possible with conventional build and test procedures. Because of increasing requirements on surface ship performance high fidelity is needed in these computations. To meet these requirements there is a push for integrated hull/propulsor designs which require viscous codes with free surface effects for their prediction which this effort addresses. The comparisons done here with the measured experimental data for the Gov't-2 hull form demonstrate that RANS codes can provide accurate representation of the propulsor inflow as well as the near-field wave heights. Such capability should improve as experience is gained in performing calculations for such hull forms. Consequently, RANS is a viable tool to aide in the design of surface ships. It is important to note that the RANS computations do not provide designs. The computations only provide information on the flow field and a means to evaluate design options. Individual designs are developed based on the experience of the team as well as iterations on various options based on information provided by the computations. It is felt that the best means of evaluating designs currently is the combination of calculations and experiments. The computations provide an overall picture of the flow field and are a good way to gain understanding of the flow physics involved. Additionally, the computations provide a way to evaluate design options more quickly than is possible with physical model testing. However, the computations have some limitations because of grid dependencies and turbulence modeling deficiencies. Experiments on the other hand provide highly detailed flow information, but typically only in specific areas. Consequently, it appears a good approach is to use the computations to help understand the flow physics and interactions of the various components such as the hull and propulsors, as well as to rank order individual modifications. Experiments for the final designs need to be done to both verify that the computational based designs meet the desired goals as well as to get details of the flow in specific areas to validate the computations at these locations. ACKNOWLEDGEMENTS This effort was funded by the Office of Naval Research as part of the ONR Surface Co mbatant Accelerated Hydrodynamics S&T Initiative under the direction of Dr. Edward Rood. The authors would like to thank Ian Mutnick, Toby Ratcliffe and Christopher Chesnakas of NSWCCD for providing the experimental data for comparison. Much useful advice' in the use of the UNCLE code, was also provided by Murali Beddhu, Ramesh Pankajakshan, and Lafette Taylor of MSU. In addition, this work was supported in part by a grant of computer time from the U.S. Army Research Laboratory at Aberdeen as part of the DOD High Performance Computing Challenge Project on Time Domain Computational Ship Hydrodynamics. The authors would also like to thank the U.S. Navy Hydrodynamic/Hydroacoustic Technology Center for the use of its facilities and software licenses. REFERENCES AIAA, "Guide for the Verification and Validation of Computational Fluid Dynamics Simulations", G077- 1998, 1998, American Institute Aeronautics and Astronautics. Allison, J. L., Becnel, A. J., Gorski, J. J., Hoyt, J. G., Purnell, J. G., Stricker, J. G., and Wilson, M. B., "Research in Waterjet Inlet, Hull, and Jet Interactions," Int. Conf. Water~et Propulsion III, Gothenburg, Sweden, 2001. Beddhu, M., Pankajakshan, R., Jiang, M.- Y., Remotigue, M., Sheng, C., Taylor, L., Briley, W.R., and Whitfield, D.L., "Computation of Nonlinear 15
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