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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 243 Flow- and Wave-Field Optimization of Surface Combatants Using CFD-Based Optimization Methods Y.Tahara1, E.G.Paterson2, F.Stern 2, and Y.Himeno1 (1Osaka Prefecture University, Japan, 2University of Iowa, USA) ABSTRACT This paper concerns flow- and wave-field optimization of surface combatants using CFD-based optimization method. The main focus is placed on development of a high performance optimization module for application to Model 5415 hull form optimization, which is capable in combination with CFDSHIP-IOWA version 3.02, a RANS solver based on higher- order upwind finite difference and a projection method for velocity-pressure coupling. The optimization scheme is based upon the work of part of the present authors wherein tanker hull forms were optimized for minimum viscous resistance. The module is general in formulation, and basically independent from basic flow solver, e.g., different RANS solver or inviscid-panel method can be used with arbitrary combination of constraints and objective function to be minimized. In the following, an overview is given of the present numerical method and results are presented for flow- and wave field optimization of surface combatant Model 5415 hull form. NOMENCLATURE g piezometric pressure gravitational constant G1, G2 , etc equality constraint functions β1, β2 , etc. H1, H2 , etc. design parameter inequality constraint functions ωx L axial vorticity characteristic (ship) length, lift a, b P, Q, R parameters in modification grid clustering and stretching function functions r etc. geometric coefficients grid refinement B(x, z), etc. S modification function, simulation prediction B Rn Reynolds number (=U∞L/v) approximate Hessian matrix CB u, v, w block coefficient fluctuating velocity components Cp pressure coefficient Reynolds stresses U, V, W mean velocity components Cd(f) frictional resistance coefficient UV, UD, etc. uncertainties Cd(p) pressure resistance coefficient U∞ characteristic (freestream) velocity direction vector x, y, z cartesian coordinates D v benchmark data, drag kinematic viscosity E ρ comparison error density F ξ1, ξ2, ξ3 objective function body-fitted coordinates Fn Froude number (= U∞/(gL)0.5) INTRODUCTION 21st Naval surface ships in the Century will be radically different from those currently in the U.S. Navy fleet (e.g., Webster and Mutnick, 1998). As such, much of the current design database, which has been developed over the past 50 years, is not directly applicable, i.e., the new concepts are “out of the box.” Since it will be prohibitively expensive to quickly expand the design database through model studies, there is strong motivation to develop simulation-based design tools. the authoritative version for attribution. Fig. 1 Naval Combatant (US Navy Photo)

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 244 Currently, CFD is used as an analysis tool to study alternative designs. Although extremely valuable, this approach suffers the limitation that it doesn't identify the optimum design. This is the motivation for developing CFD-based optimization tools wherein automatic determination of optimum shape is part of the simulation. To develop a shape optimization tool, 5 components must be built and are common among all the different approaches. First, the optimization problem, which consists of the objective function (e.g., minimum drag), design variables, and constraints, must be formulated. Second, a geometry handler must provide a link between the design variables and a body shape defined by the constraints. Third, a high-performance, general-purpose CFD code is required. Forth, the system must be able to generate or modify the computational grid as the shape evolves. Finally, a method is required to solve the nonlinear optimization problem formed by the objective function and constraints. Some of the earliest work on CFD-based optimization methods was in the aerospace community and focused on optimization of 2D foils for maximum lift-to-drag performance (e.g., Hicks et al., 1974; Hicks and Henne, 1978). Until very recently, the principal obstacle in shape optimization was the large computational cost of evaluating the sensitivity of the objective function to variation of the design parameters. This is typically done through repeated calculation of the flow. Given the development in both CFD methods and high-performance parallel computers, this has obstacle has been greatly reduced. As such, CFD-based optimization methods have seen rapid evolution in the aerospace community including full configurations (Jameson et al., 1998), internal flow systems (Perry et al., 1998), unstructured CFD methods (Elliot and Peraire, 1998), and geometry handler algorithms based upon genetics and mechanics of natural evolution (Zhu and Chan, 1998). In the ship hydrodynamics community, similar development has taken place. However, due to geometry and physics (i.e., free surface) which are more complex than that associated with a wing, development and application has been slower than that in the aerospace community. Application to ships was initiated through the use of solution to the Neumann-Kelvin problem for minimization of wave-making resistance. More recently, advancement of CFD has enabled the use of RANS methods with nonlinear programming for minimization of either viscous resistance or nominal wake distribution (e.g., Larsson et al., 1992; Hamasaki et al., 1996a; Hamasaki et al., 1996b). The recent 3rd Osaka Colloquium (i.e., OC98) on Advanced CFD Applications to Ship Flow and Hull Form Design indicates that optimization methods are actively being developed in the ship hydrodynamics community (Hino et al., 1998; Suzuki and Matsumoto, 1998; Tahara et al., 1998). In general, OC98 showed that optimization methods are capable of stern shape optimization for minimization of viscous resistance. However, large computational cost is still a major issue, but one that can be overcome if parallel high- performance programming technique is adopted. This paper concerns flow- and wave-field optimization of surface combatants using CFD-based optimization method. The main focus is placed on development of a high performance optimization module for application to Model 5415 hull form optimization, which is capable in combination with CFDSHIP-IOWA (Stern et al., 1996; Paterson et al., 1998; Wilson et al., 1998), a general-purpose parallel multi-block RANS code based on higher-order upwind finite difference and a projection method for velocity-pressure coupling. The optimization scheme is based upon the work of part of the present authors (Tahara et al., 1998; Tahara et al., 1999; Tahara et al., 2000) wherein tanker hull forms were optimized for minimum viscous resistance and delivered horse power. The module is general in formulation, and basically independent from basic flow solver, e.g., different RANS solver or inviscid-panel method can be used with arbitrary combination of constraints and objective function to be minimized. In the following, an overview is given of the present numerical method and results are presented for flow- and wave field optimization of surface combatant Model 5415 hull form. COMPUTATIONAL METHOD RANS Equation Solver The primary RANS equation solver in the present study is CFDSHIP-IOWA version 3.02. An overview of the numerical method is given in the following. The non-dimensional RANS equations for unsteady, three-dimensional incompressible flow can be written in Cartesian tensor notation as (1) (2) where Ui=(U, V, W) and ui=(u, v, w) are the Cartesian components of mean and fluctuating velocities, respectively, the authoritative version for attribution. normalized by the reference velocity U∞, xi=(x, y, z) the dimensionless coordinates normalized by a characteristic length L, the piezometric pressure

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 245 Rn=U∞L/v Reynolds number, and normalized by Reynolds stresses normalized by In this study, Reynolds stresses are given by using Baldwin-Lomax turbulence model (Baldwin and Lomax, 1978). Equations (1) and (2) are transformed into nonorthogonal curvilinear coordinates such that the computational domain forms a simple rectangular parallel-piped with equal spacing. The transformation is partial one since it involves the coordinates only and not the velocity components. The transformation is accomplished through the expression for the divergence and “chain rule” definitions of the gradient and Laplacian operators which relate the Cartesian coordinates xi=(x, y, z) to the numerically generated non-orthogonal coordinates ξi=(ξ1, ξ2, ξ3). In this manner, the governing equations (1) and (2) can be written in the form of the continuity and transport equations as follows: (3) (4) The transport equations (4) are reduced to algebraic form through the use of the higher-order upwind difference method. The equations are solved using a projection method for velocity-pressure coupling, and the method of lines. For steady-flow application, time serves as a convergence parameter and the grid is updated at each time step to conform to both the body and free surfaces, where exact nonlinear kinematic and approximate dynamic free-surface boundary conditions are imposed. See Paterson et al., (1998) and Wilson et al. (1998) for more details of the present RANS code. Computational Grids The present body-fitted, structured, multi-block grids are generated using commercial grid generation code GRIDGEN from Pointwise, Inc. For application to Model 5415, patched multi-block grids and boundary conditions are used. Grid clustering can be done as for other hulls, e.g., Series 60 or Wigley hull, however, different topology is required especially for transom. In this case, a separate block is placed in the transom wake. Fig. 2 shows partial views of the present computational grids for Model 5415. In the present study, 5-block grid system is used. Numbers of the grids are as follows: for forebody upper block, 104x25x21 (longitudinal, radial, and girthwise directions, respectively); for forebody lower block, 104x25x30; for afterbody upper block, 47x25x21; for afterbody lower block, 47x25x30; and transom wake block, 30x25x21; i.e., total number is 208,275. This grid is relatively coarse; however, sufficient accuracy in trends of solutions, e.g., resistance, is assured in the precursory work. In fact, for optimization discussed later, smaller number of grids is preferred in order to avoid dramatic increase of computational effort. See Wilson et al. (1998) for more details of the present computational grid. During the optimization, the grid is updated at every optimization cycle as the hull form is modified. This is accomplished by the use of algebraic scheme to increase the computational efficiency. The method is described in the following. After initial grid is generated, the geometrical information is computed and stored in the memory, that is as follows: (5) where P, Q, R are grid clustering and stretching function defined in (ξ1, ξ2, ξ3) directions, respectively. Also, grid points are already defined in computational coordinates, i.e., (6) and hull surface is expressed as (7) On the other hand, the outer boundary is given by the authoritative version for attribution. (8) In the optimization procedure, the hull surface is modified but other computational boundaries, hence all grid points are relocated using P, Q, and R when the surface is modified. Although this is done by iterative manner, which usually converges within 100 iterations, the CPU time required is much less than that for original grid generation. Quality of grid is nearly equal to that of the original, and appears to be applicable to changes in hull surface occurs in the present optimizations.

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 246 Uncertainty Assessment Although CFD uncertainty assessment is not well defined for optimization method, information for the present RANS code must be provided. CFD uncertainty assessment consists of documentation, verification, and validation. An overview of verification and validation for the primary RANS code in the present study is given in the following. Simulation uncertainty is divided into two components, one from numerics USN and the other from modeling USM. The numerical uncertainty in the simulation can be assessed using verification (Stern et al., 1999). Therein USN is estimated for both point and integral quantities and is based upon grid and parametric studies which determine grid USG, iterative USI, and time-step UST uncertainties. A root sum square (RSS) approach is used to combine the components and to calculate USN, i.e., CFD validation follows the method of Coleman and Stern (1997), in which a new approach is developed where uncertainties from both the simulation (US) and EFD benchmark data (UD) are considered. The first step is to calculate the comparison error E which is defined as the difference between the data D (benchmark) and the simulation prediction with S, i.e., E=D-S. The validation uncertainty UV is defined as the combination of UD and the portion of the uncertainties in the CFD simulation that are due to numerics USN and which can be estimated through UV sets the level at which the validation can be achieved. The criterion for verification analysis, i.e., validation is that /E/ must be less than UV. Note that for an analytical benchmark, UD is zero and UV is equal to USN. Validation is critical for making improvements and/or comparisons of different models since USN is buried in UV. A detailed example of the verification procedure for computation of free-surface flow is provided in Rhee and Stern (1998). Although verification and validation results for steady DTMB 5415 simulation have not been fully completed for CFDSHIP-IOWA version 3.02, a status report for version 2.1 is presented and discussed in (Paterson et al., 1998). As an example for application to the practical hull form, results for Series60 CB=0.6 hull are available for the present RANS code in Wilson et al., (1998), where grid convergence was studied by performing steady simulations using three computational in each coordinate direction. Iterative uncertainty USI was assessed through examination of grids with refinement the iteration record of integral and point quantities and was taken as one-half the range of the quantity of interest once initial transients had died out. That is the preferred metric because U SI can be directly evaluated. Finally, it is stated in Wilson et al. (1998) that USN for total resistance coefficient is equal to for the grid whose density is similar to that of the present study. Nonlinear Optimiz ation Proble m A general expression of the optimization problem is as follows: (9) Subject to: (10) are design parameters, F objective function to be minimized, G 1, G2,..Gp equality constraint where functions, and H1, H2,..Hq inequality constraint functions. The design parameters are used to express body geometry, i.e., the solutions of the optimization problem. The objective function gives a value to be minimized, e.g., viscous resistance. Equality and inequality constraints limit the change of values, e.g., displacement or maximum depth, etc. In the present study, design parameters are used to define modification function, the objective function is specific value of flow or wave field, and the equality or inequality constraints are imposed such that the displacement of modified hull is equal to or larger than that of the original. Also, value of flow such as lift or drag can be used in equality or inequality constraint. The present problem is nonlinear, since F, G, and H are nonlinear functions of . Hence, a nonlinear programming algorithm must be introduced to solve the present problem. Nonline ar Programming Algorithm In the present study, equations (9) and (10) are solved by successive quadratic programming (SQP) algorithm, in which the equations are approximated in quadratic form such that Min: (11) the authoritative version for attribution. Subject to:

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 247 (12) is direction vector, and B approximate Hessian matrix of the Lagrangian. In each where optimization cycle (n), optimum is obtained so as to minimize F, and updated by In the present study, the derivative terms in equations (11) and (12) are evaluated by the second-order central finite difference scheme. Part of the present authors compared the convergence characteristics of SQP with that of the successive linear programming (SLP), which is based on extension of affine scaling interior method (Tahara and Himeno, 1998). In the work, the NACA0012 wing section was optimized so as to maximize lift-to-drag ratio (=L/D, i.e., -L/D is minimized) at a fixed incidence angle of 5°, with the constraint such that the cross-sectional area of modified section is same as that of the original. The same RANS equation solver, geometry modification function, and computational grid were used. See Tahara and Himeno (1998) for more details. Fig. 3 shows comparison of convergence history of objective function (-L/D), where faster convergence for SQP is clearly indicated. In the precursory work (Tahara et al., 1998; Tahara et al., 1999; Tahara et al., 2000), the SQP algorithm had been applied to more practical problem for ship design, where tanker stern form was successfully optimized for minimization of viscous resistance and delivered horse power. In the work, however, it also appeared that large computational cost is currently a major issue. That is mainly due to a fact that, for an optimization cycle, at least 2k+1 time computations of F, i.e., execution of RANS solver, are required for evaluations of terms in equations (11) and (12), where RANS solver was initiated with different , i.e., where δ is a-priori given finite-difference step. In the present study, conventional SQP algorithm have been modified and extended for parallel computing in order to overcome the issue related to large CPU time. Fig 4 illustrates the difference of SQP architecture between the present parallel and the conventional serial computations. For the former case, processor 0 controls overall SQP procedure, and processors 1 through m (=2k+1) simultaneously execute CFD method, i.e., evaluation of in the figure. The parallel architecture offers advantage over the serial architecture for considerably higher computational efficiency, i.e., computational speed of the former is nearly m times faster than that of the latter, since most of CPU time is used for CFD method, and communication overhead between the processors is quite small. Furthermore, computational speed for SQP in parallel architecture does not depend on number of design parameters. In the present application of SQP, the parallel computation algorithm was implemented as an independent module, i.e., the optimization method is basically independent from basic flow solver, e.g., different RANS solver or inviscid-panel method can be used with arbitrary combination of constraints and objective function to be minimized, that has been demonstrated as shown in the present results described later. Hull Form Modification Function Choice of hull-form modification function is important in optimization, because the function must have sufficient expressiveness for desired hull modification. In the present study, a 6-parameter function, which is developed in the precursory work by Tahara et al. (1998) is used. Consider a ship fixed in the uniform onset flow U∞ as depicted in Fig. 1. Take the Cartesian coordinate system with the origin on the water plane, x and y axes on the horizontal plane, and z axis directed vertically upward, where x=0 and 1.0 correspond to AP and FP, respectively. Hence, for example, transverse modification is defined as follows: (13) where, y0(x, z) is the original hull surface defined in longitudinal and vertical coordinates (x, z). In this form, depthwise modification of the flat bottom is not considered. B(x, z) is the modification function to provide transverse-directional expansion and reduction ratio for modification region in the range of x2≥x≥x1 and z2≥z≥z1, and that is given by, (14) (15) (16) the authoritative version for attribution. where, B 1(z) and B2(z) are depthwise and longitudinal modification functions, β1, β2,…, βm,…βn the design parameters, and f1, f2,…, fm,…fn the spline

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 248 interpolation functions. B1(z) and B2(z) are defined in the z coordinate and satisfy the following end conditions: (17) The above modification function has continuity in 1st and 2nd longitudinal derivatives at the boundary of definition, and the two independent 1-D functions, defined in the vertical coordinate z, i.e., B1(z) and B2(z), are capable to provide continuous transverse-directional expansion and reduction ratio varying in x-z plane. Note that β1~β3 control cross sectional modification, and β4~β6 longitudinal modification, e.g., the longitudinal locations of peak and bottom the B(x, z) are moved forward or backward. Fig. 6 shows distributions of the present 6 parameter modification function for two combinations of β1~β6. A concept of the present modification function is based on line modification designers do, such that designers try to “push in” or “pull out” a control point of each waterline without discontinuity of curvature at the begin and end points of modification. The location of control points and amount of change are uniquely given by selecting the values of β1~β6. The present function can easily be applied to vertical hull modification by replacing z by y, which is discussed below for stern optimization, i.e., (18) (19) (20) (21) where, z0(x, y) is the original hull surface defined in longitudinal and transverse coordinates (x, y), B(x, y) the modification function to provide vertical-directional expansion and reduction ratio for modification region in the range of x2≥x≥x1 and y2≥y≥y1, B1(y) and B2(y) transverse and longitudinal modification functions which satisfy the following end conditions: (22) RESULTS In the following, results are presented for flow-and wave field optimization of surface combatant Model 5415 hull form, where discussions are focused on stern optimization, sonar dome optimization, and bow optimization, all of which are related to practical design problem. Prior to application of the present method to Model 5415 hull form optimization, the computational efficiency of the present optimization module has been evaluated in comparison with results from the precursory work (Tahara et al., 1998; Kitamura et al., 1997; Tahara et al., 1999), i.e., those concern layout optimization of 2-D tandem hydrofoils under free surface for minimization of wave-making resistance, and stern optimization of tanker hull form for minimization of viscous resistance, in both of which the conventional serial SQP module was used. The comparison of computational speed indicated that the present parallel SQP module is nearly 13 times faster than the serial module. The result has appeared consistent with the earlier discussion on advantage of the present method. Model 5415—Stern Optimization The 1st case is stern optimization for minimization of disturbance on transom wave field. Most recent high-speed fine ships as well as Model 5415 have transom stern in order to obtain wide water plane area to secure sufficient stability. The wide transoms tend to increase disturbance on transom wave field, and that results in increase of hull resistance. The present authors and others (Iwasaki et al., 1996; Tahara et al., 1997) had carried out investigation on transom flow and wave fields using computational and experimental models. In the work, it appeared that transom wave field can be classified as the following 3 types: (A) with dead water zone right after stern end; (B) with no dead water zone, but wave breaking in near wake region; and (C) with neither dead water zone nor wave breaking in near wake region, i.e., free surface is smoothly continuous from the stern end. Also the results indicated that smaller surface pressure gradient near the stern, which results in thinner boundary layer in the region, correlates with less disturbance on transom wave field. In the present study, averaged surface pressure in a control area located near the stern was used as the objective function to be minimized, so that axial surface pressure gradient be larger favorable in the region. This objective function has been shown capable for the present optimization problem as discussed later, rather than objective function directly the authoritative version for attribution.

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 249 given by a value from wave field which often oscillates due to unsteady nature of transom flow fields, that occurs especially for the above-defined type (A) condition. In the present optimization, the earlier discussed parallel SQP module is used in combination with a RANS code, CFDSHIP-IOWA version 3.02. See Paterson et al., (1998) and Wilson et al. (1998) for detailed evaluation of accuracy in prediction of transom flow and wave fields for Model 5415, that had shown sufficient for application to the present optimization. Fig. 7 illustrates the code structure for the present problem. Design parameters modify hull surface in vertical direction by using modification function of equation (18). The surface modification also provides geometrical constraints as G and H. Then grid generator, RANS solver, and post processor are executed to evaluate objective function F. At present, only geometrical constraints are considered in G and H. Computational conditions are as follows: Rn=5x10 6 and Fn=0.28; modification region is given by S.S.0–2 (1≥x≥0.8) and 0.04≥y≥0; and the minimum vertical modification ratio constraint is imposed, i.e., B(x, y)≥0.3. The optimized solution was obtained in 6 optimization cycles. Figs. 8 and 9 show comparison of geometry between for the original and optimized hull forms. In the bodyplan shown in Fig. 8, several S.S. numbers are indicated for reference. Also in Fig. 9, x contours with interval ∆x=0.01 are included for clearer presentation of differences in stern forms. Differences in stern frame lines are obvious, in which maximum differences appear in the region between S.S.0.5 and 1.0. In the region, an inflection point, which does not exist in the original hull form, appears at each frame line. The changes in frame line create concave surface, which is clearly displayed in Fig. 9 for the optimized hull form. The above-mentioned stern modifications have direct influences on the flow field in the near-stern region. Fig. 10 shows comparison of surface pressure (Cp) contours. In the figure, the control area, where the objective function is evaluated, is also indicated. In the area, lower pressure region is extended for the optimized hull form, which is consistent with decrease of objective function. In addition, high pressure region appears around x=0.934 near the center line for the optimized hull form, which results in larger favorable axial pressure gradient from the region towards transom. Differences in surface pressure near the stern leads to significant difference in transom flow and wave fields. Fig. 11 shows comparison of axial-velocity contours near the stern at centerplane. Depth of the stern-end corner (denoted as “A” in the figure for original hull form) is slightly smaller for the optimized hull form. For the original hull form, larger extent of negative contours (i.e., reversed flow region) is seen near the free surface including the region right after the stern end. In authors' earlier work, the wave field is classified as the (A) type, i.e., the free surface is highly disturbed with the reversed flow in the dead water zone beneath the free surface. On the other hand, the optimized transom wave field remains the (A) type; however, the reversed flow region is almost cleared except in the region very close to the transom wall. The above-discussed differences in center plane stern flow field are consistent with those displayed in transom flow and wave fields shown in Figs. 12 and 13, where wave contours and axial-velocity contours are compared, respectively. For the optimized hull form, wave elevation is generally reduced at the transom, and extent of the reversed flow region on the free surface is almost all removed. It is obvious that the optimized hull form has much less disturbance on the transom wave field than the original hull form. Also, it is noteworthy that maximum wave elevation in near wake is the larger for optimized hull form. Lastly, Fig. 14 shows comparison of objective function (Obj.), wave elevation at the transom wall (Fst., defined as the difference in z coordinate between the wave contact point at transom wall centerline and the original stern-end corner denoted as “A” in Fig. 11), frictional resistance coefficient Cd(f), and pressure resistance coefficient Cd(p), all of which are for the optimized hull form and shown in % as compared to those values for the original hull form. Objective function and wave elevation at transom wall are reduced in about 30% and 60%, respectively. Decrease in resistance coefficients are also seen except for frictional part, which is nearly equal to that for the original hull form. The pressure resistance coefficient is reduced in about 5%, and that is mainly related to reduction of reversed flow region in transom flow field and less disturbance on wave field for the optimized hull form. The correlation between resistance and transom wave and flow fields coincides with that found in authors' earlier work (Iwasaki et al., 1996; Tahara et al., 1997). Model 5415—Sonar Dome Optimization The 2nd case is sonar dome optimization. Flow near the hull/sonar-dome junction involves significant longitudinal vortices, which usually remains even in stern flow region at the operation speed. In the present study, the afterbody of sonar dome is optimized so as to minimize the vortices, where magnitude of averaged axial vorticity (ωx) in a control area located at x=0.125 is used as the objective function to be minimized. At present, the optimization was done for Fn =0 condition, and the results were verified for Fn=0.28 condition and used in the following discussion. Note the authoritative version for attribution.

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 250 that the overall trends in solutions have appeared same between for the two conditions, although the magnitude of ωx is generally larger for Fn=0.28 condition. CFDSHIP-Iowa version 3.02 was used as RANS solver. The code structure for the present problem, in which the parallel SQP module is included, is basically same as that for the previous case, i.e., stern optimization. Equation (13) is used for surface modification, i.e., only modification in transverse direction is considered. The modification region covers most of afterbody and part of forebody of sonar dome, and part of sonar-dome/hull junction, i.e., 0.1≥x≥0.01 and −0.04≥z.; and equal-or-larger volume constraint is imposed. Computational Rn based on ship length is 5x106. The optimized solution was obtained in 5 optimization cycles. Figs. 15 and 16 show comparison of sonar dome geometry between for the original and optimized forms, and Fig. 17 comparison of surface pressure (Cp) contours and frictional streamlines. In Fig. 16, y contours with interval ∆y=0.002 are also shown in order to clearly present differences in the geometry. The modification of the dome is mainly seen in the near-tail region, in which the cross sectional area is increased mostly for upper half of the dome. The optimized sonar dome has slightly larger volume than the original. The shape modification causes the larger low pressure area on the dome around x=0.9, which leads to obvious differences in the three-dimensional separation patterns displayed in frictional streamlines. Fig. 18 provides comparison of ωx contours at the control section between for the original and optimized forms. The control area to evaluate objective function is also indicated in the figure. In the present optimization done for Fn=0 condition, the objective function is reduced around 10%, whereas the value evaluated for Fn=0.28 results is reduced around 35%. It is shown in the figure that the vortices for optimized form are more diffused, and the maximum ωx magnitude is clearly reduced. It must be noted that wave profiles on the hull are nearly same between for the original and optimized forms, that may be due to a fact that geometrical changes occurred in the present optimization are relatively small and the locations are at considerably large depths. Although the present optimization method successfully reduced the junction vortices, further extension of the modification function, and inclusion of wave effects in the optimization process are of interest, both of which are issues for future work and partly in progress. Model 5415—Bow Optimization Finally, the 3rd case is bow optimization for minimization of bow wave. For Model 5415 at moderate and high Fn, signature in wave field is remarkable especially in the region near the bow, where wave rises rapidly and shape of the crest is steep. In the present study, the parallel SQP module was applied to minimize the bow wave, in combination with 3-D nonlinear panel method developed by the author (Tahara, 1997; Tahara, 1998), then the results were verified by using a RANS solver, CFDSHIP-Iowa version 3.02, in both of which Fn=0.28 condition was considered. Fig. 19 shows the code structure for the present optimization problem. Design parameters modify hull surface in transverse direction by equation (13), where the modification region is S.S.8–10 (0.2≥x≥0) and z≥−0.35. Only a geometrical constraint is imposed, i.e., displacement of the optimized hull is equal to or larger than that of the original hull. As shown in the author's earlier work (Tahara, 1997; Tahara, 1998), which included comparison of linear and nonlinear theories to predict bow wave, the linear theory generally under predicts the wave elevation near the bow. A nonlinear panel method developed in the work was shown capable for prediction of the wave field around blunt-nose body as well as commercial ships operated at high Fn, that had been accomplished by introduction of the O-type free-surface panels and nonlinear free-surface boundary conditions. Although CFDSHIP-IOWA version 3.02 can be used for prediction of bow wave, the panel method was used in the present optimization, in which evaluation of capability of the present optimization module was somewhat more focused, and at present lower computational effort was preferred. The results were verified by using CFDSHIP-IOWA version 3.02, and presented in the following discussion. Numbers of panels used in the computation are 1600 and 2000 for hull and free surfaces, respectively, that had been found optimum based on panelization dependency tests. Figs. 20 and 21 show computed wave contours and profile for the original hull, respectively, by using the present nonlinear panel method. In Fig. 21, the experimental data are also included for comparison. The present results indicate considerably good agreement with the measurements especially for elevation of bow wave crest, on which focus of the present study is mainly placed. It must be noticed that prediction of the transom wave field is not satisfactory, which is mainly due to the limitation of the inviscid-flow approach. This leads to an important conclusion that, for optimization of transom flow and wave fields, RANS solver must be used as demonstrated in the present work and discussed in the earlier section. On the other hand, the present panel method has been judged capable for the initial validation of present optimization method as far as the authoritative version for attribution.

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Wave profile evaluated by the present panel method for the optimized bow is also included in Fig. 21. Between for the two bows, clear differences in wave profiles are seen in the bow-wave region, i.e., maximum elevation of the bow wave crest is reduced around 20% for the optimized bow. The modification trends in bow shape have been shown remarkable, e.g., a ditch line is created in the mid-girth region, that may not commonly be predicted by the conventional hull form design. As the above-mentioned, the present optimized results were verified by using RANS code, i.e., CFDSHIP-Iowa version 3.02 for Fn =0.28 and Rn=5x106 conditions. See Paterson et al., (1998) and Wilson et al. (1998) for accuracy of the RANS code in prediction of bow wave field for the present ship model. Figs. 24 and 25 show comparison of bow wave elevation, and wave contours near the bow, respectively. Although maximum wave elevation for the original bow was somewhat under predicted due to the relatively coarse distribution of the present computational grid in radial direction, the same trends of results as those discussed above are indicated, i.e., for optimized bow, elevation of the bow wave crest is reduced, which is clearly shown in wave contours as well as profiles. The reduction of bow wave is somewhat smaller than that predicted by the present nonlinear panel method, i.e., about 15% in RANS solutions. The RANS results indicated that, although not shown in the figure, relatively small influences of bow wave reduction are seen on afterbody wave profile, that is also true for the results previously shown in Fig. 21. Lastly, Fig. 26 shows comparison of optimized solutions including integral values, in the similar manner as those used for Fig. 14, i.e., percentage presentation as compared to values for the original bow. Except for objective function (Obj.), values are for verified results by using RANS solver. In the figure, Fmax.-v. is elevation of bow wave crest, which has been reduced about 15% as mentioned above. On the other hand, frictional resistance coefficient Cd(f) has slightly increased, but that is less than 1%. Pressure resistance coefficient Cd(p) has clearly decreased, i.e., that is about 6.5%, which is consistent with the lower wave-making resistance for lower bow wave crest. The above-discussed results have shown that the present method is very promising, and further verification of the results through model tests is of great interest. On the other hand, it is also of interest to replace the panel method by CFDSHIP-Iowa version 3.02, since the RANS solver is more comprehensive, in which viscous and wave making effects are considered in the theory, and capable for accurate prediction of resistance as well as flows especially for hull forms with transom stern. In addition, further investigation must be done on the method to modify the bow shape. All of the above are issues for future work, and in part, currently in progress. SUMMARY AND CONCLUSIONS This paper concerns flow- and wave-field optimization of surface combatants using CFD-based optimization method. The main focus is placed on development of a high performance optimization module for application to Model 5415 hull form optimization, which is capable in combination with CFDSHIP-IOWA version 3.02. The optimization scheme is based upon the work of part of the present authors wherein tanker hull forms were optimized for minimum viscous resistance. The module is general in formulation, and basically independent from basic flow solver, e.g., different RANS solver or inviscid-panel method can be used with arbitrary combination of constraints and objective function to be minimized. In this paper, an overview is given for the present primary RANS equation solver, computational grids, uncertainty assessment for the RANS code, general nonlinear optimization problem, a high performance nonlinear programming algorithm, and the 6 parameter hull form modification function. The results are presented for flow- and wave field optimization of surface combatant Model 5415 hull form, where discussions are made on stern optimization, sonar dome optimization, and bow optimization, all of which are related to practical design problem.. Prior to application of the present method to Model 5415 hull form, the computational efficiency of the present optimization module has been evaluated in comparison with results from the precursory work. The results show that the present parallel SQP architecture offers advantage over the conventional serial SQP architecture for considerably higher computational efficiency, i.e., computational speed of the former is nearly m (=2k+1: k is number of design parameters) times faster than that of the latter. Furthermore, another advantage of the present parallel SQP architecture is such that the computational speed does not depend on number of design parameters. First, results for Model 5415 stern optimization for minimization of disturbance on transom wave field were discussed. The results indicate that the present the authoritative version for attribution.

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 252 method successfully reduced reversed flow region in transom flow field, which relates to less disturbance on transom wave field for optimized stern than that for the original. A concave surface has appeared in optimized stern, which results in larger favorable axial surface pressure gradient in the region. Through evaluation of the results, it has been shown that the correlation of stern modification and flow as well as integral parameters coincides with that found in the authors' earlier work, which concerns experimental and computational studies on transom stern flow and wave fields. Next, Results for Model 5415 sonar dome optimization were discussed, in which minimization of hull/sonar-dome junction vortices was considered. In the present results, modification of the dome is mainly done near the tail end, in which the cross sectional area and volume are increased mostly for upper half of the dome. Although modification of the geometry is relatively small and further improvement on modification function may be required, optimized sonar dome has clearly smaller magnitude of longitudinal vorticity, which relates to reduction of junction vortices. Finally, results for Model 5415 bow optimization were presented and discussed. In the optimization, minimization of elevation of the bow wave crest was considered. The differences in wave profile between for the original and the present optimized bows are clearly seen in the region near the bow, i.e., the elevation of bow wave crest is obviously decreased in the optimized results. The modification trends are notable, i.e., a ditch line has appeared in the mid-girth region, that may not commonly be predicted by the conventional hull form design. In conclusion, the present method has appeared very promising, and will be practical design tool for flow- and wave- field optimization of surface combatants through further improvement and evaluation of the method through comparison of the results with experiments. Importantly, one of the major issues for former CFD-based optimization methods has been overcome by the present high performance optimization module. In addition to issues and extension plans of interest mentioned in the discussions, inclusion of propeller effects, consideration of unsteady ship motions, and extensions of CFD method for full-scale Rn are also of interest, some of which are already in progress. ACKNOWLEDGEMENTS This research was sponsored by the Office of Naval Research grant number N00014–99–1–0232 under the administration of Dr. E.P.Rood whose support is greatly appreciated. The Department of Defense High-Performance Computing Modernization Office (HPCMO) and the Naval Oceanographic Office (NAVO) provided computing resources under the auspices of the DoD Challenge Program. REFERENCES Baldwin, B.S. and Lomax, H., “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper 78–257, 1978, pp. 1–8. Coleman, H.W. and Stern F., “Uncertainties and CFD Code Validation,” ASME J. Fluids Engineering, Vol. 119, 1997, pp. 795–803. Elliot, J., and Peraire, J., “Progress Towards a 3D Aerodynamic Shape Optimization Tool for the Compressible High-Re Navier-Stokes Equations Discretized on Unstructured Meshes,” AIAA-98–2897, 1998. Hicks, R.M., Murman, E.M., and Vanderplaats, B.N., “An Assessment of Airfoil Design by Numerical Optimization,” NASA TM X-3092, Ames Research Center, 1974. Hicks, R.M., and Henne, P.A., “Wing Design by Numeical Optimization,” J. of Aircraft, Vol. 15, 1978, pp. 407–412. Jameson, A., Alonso, J.J., Reuther, J., Martinelli, L., and Vassberg, J.C., “Aerodynamic Shape Optimization Techniques Based on Control Theory,” AIAA-98–2538, 1998. Hamasaki, J., Himeno, Y. and Tahara, Y., “Hull Form Optimization by Nonlinear Programming (Part 3)—Improvement of Stern Form for Minimizing Viscous Resistance -,” J. Kansai Society of Naval Architects, No. 225, 1996, pp. 1–6 [Japanese]. Hamasaki, J., Himeno, Y. and Tahara, Y., “Hull Form Optimization by Nonlinear Programming (Part 4)—Improvement of Stern Form for Wake and Viscous Resistance -,” J. Kansai Society of Naval Architects, No. 226, 1996, pp. 15–21 [Japanese]. Hino, T., Kodama, Y., and Hirata, N., “Hydrodynamic Shape Optimization of Ship Hull Forms Using CFD,” Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan, May 25–27, 1998, pp. 533–541. Iwasaki, Y., Tahara, Y., Okuno, T., Himeno, Y. the authoritative version for attribution.

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 253 and Yamano, T., “Studies on Relationship between Water Surface behind Stern and Stern End Form of Fine Ships,” J. of Society of Naval Architects of Japan, Vol. 180, 1996, pp. 13–20 [Japanese]. Kitamura, T., Tahara, Y. and Himeno, Y., “A Study on Layout Optimization Problem of 2-D Tandem Hydrofoils under Free Surface,” J. Kansai Society of Naval Architects, No. 228, 1997, pp. 67–78 [Japanese]. Larsson, L., Kim, K.J., Esping, B. and Holm, D., “Hydrodynamic Optimization Using SHIPFLOW,” Proceedings of the 5th International Symposium on Practical Design in Shipbuilding (PRADS'92), Newcastle, 1992. Paterson, E., Wilson, R., Stern, F., “Verification/ Validation of Steady Flow RANS for Model 5415,” Proceedings of the 1st Marine CFD Applications Symposium, McClean, VA, May 1998. Paterson, E.G., Wilson, R.V., and Stern, F., “Verification/Validation for Steady Flow RANS Simulation of Model 5415,” 1st Symposium on Marine Applications of CFD, McLean, 1998. Perry, E., Balling, R., Landon, M., and Johnson, R., “Aerodynamic Shape Optimization of Internal Fluid Flow Systems,” AIAA-98–2896, 1998. Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan, May 25–27, 1998. Rhee, S.H. and Stern, F., “Unsteady RANS Method for Surface Ship Boundary Layers and Wakes and Wave Fields,” Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan, May 25–27, 1998, pp. 67–84. Stern, F., Paterson, E.G. and Tahara, Y., “CFDSHIP-IOWA: Computational Fluid Dynamics Method for Surface-Ship Boundary Layers, Wakes, and Wave Fields,” IIHR Report, No. 381, Iowa Institute of Hydraulic Research, Iowa City, IA 52242, USA, 1996. Stern, F., Wilson, R.V., Coleman, H.W., and Paterson, E.G.: Verification and Validation of CFD Simulations, IIHR Report No. 407, Iowa Institute of Hydraulic Research, Iowa City, IA 52242, USA, 1999. Suzuki, K., and Matsumoto, S., “Studies on Inverse and Optimization Problems of Two Dimensional Wing Section Based on Panel Method,” Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan, May 25–27, 1998. pp. 485–498. Tahara, Y., Saitoh, Y. and Himeno, Y., “CFD-Aided Optimization of Tanker Stern Form (1st Report)—Minimization of Viscous Resistance -,” J. Kansai Society of Naval Architects, No. 231, 1999, pp. 29–36 [Japanese]. Tahara, Y., Saitoh, Y., Matsuyama, H. and Himeno, Y., “CFD-Aided Optimization of Tanker Stern Form (2nd Report)—Minimization of Delivered Horse Power -,” J. Kansai Society of Naval Architects, No. 232, 1999, pp. 9–17 [Japanese]. Tahara, Y., Nishida, R., Ando, J. and Himeno Y., “CFD-Aided Optimization of Tanker Stern Form (3rd Report)—Minimization of Delivered Horse Power Using Self-Propulsion Simulator -,” to appear J. Kansai Society of Naval Architects, No. 234, 2000 [Japanese]. Tahara, Y. and Himeno Y., “A Study on Form Optimization Problem Based on CFD for Two-Dimensional Wing Section,” J. Kansai Society of Naval Architects, No. 229, 1998, pp. 27–35 [Japanese]. Tahara, Y., Himeno, Y., and Tsukahara, T., “An Application of Computational Fluid Dynamics to Tanker Hull Form Optimization Problem,” Proceedings 3rd Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan, May 25–27, 1998, pp. 515–531. Tahara, Y. and Iwasaki, Y., “A Study of Transom-Stern Free-Surface Flows by 2-D Computational and Experimental Models,” J. Kansai Society of Naval Architects, No. 227, 1997, pp. 7–19 [Japanese]; also, Proceedings of the 2nd Conference for New Ship & Marine Technology into 21st Century, Hong Kong, June 1998, pp. 83–92 [English]. Tahara, Y., “A Numerical Approach for Steady Ship-Wave Problem Based on Dawson-Type Rankine-Source Method with Non-H-Type-Topology Free- Surface Panels—1st Report: with the authoritative version for attribution.

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 254 Main Emphasis on Application of O-Type-Topology -,” J. Kansai Society of Naval Architects, No. 228, 1997, pp. 79–90 [Japanese]. Tahara, Y., “A Numerical Approach for Steady Ship-Wave Problem Based on Dawson-Type Rankine-Source Method with Non-H-Type-Topology Free- Surface Panels—2nd Report: Application to Blunt-Nose Body and Nonlinear Free-Surface Boundary Conditions -,” J. Kansai Society of Naval Architects, No. 230, 1998, pp. 147–152 [Japanese]. Webster, J., and Mutnick, I., “Future Surface Combatant,” Proceedings 25th ATTC Conference, Iowa City, IA, September, 1998. Wilson, R., Paterson, E., and Stern, F., “Unsteady RANS Simulation of Model 5415 in Waves,” Proceedings of the 22nd Symposium on Naval Hydrodynamics, Washington D.C., August 1998, pp. 532–549. Zhu, Z.W., and Chan, Y.Y., “A New Genetic Algorithm for Aerodynamic Design Based on Geometric Concept,” AIAA-98–2900, 1998. the authoritative version for attribution.

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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 FLOW- AND WAVE-FIELD OPTIMIZATION OF SURFACE COMBATANTS USING CFD-BASED OPTIMIZATION METHODS 261 DISCUSSION H.Chun Pusan National University, Korea 1) Which computer did you use? How long did it take to finish one case of optimum, for example, the bow optimization case? 2) Usually, the hull form for bow optimization would give an undulation (or oscillatory) water lines shape. However, your case does not. Could you explain the reason? AUTHOR'S REPLY 1) All computations were performed on a SGI Origin 2000 system, which is configured with 256 central processing units, 64 GB of distributed shared memory, and 600 GB of disk space. The bow optimization case was completed in about 6 hours. 2) Unlike conventional commercial ships, for which most previous optimization work has been done, Model 5415 has a very characteristic flared bow form with large sonar dome located near the keel. In addition, nonlinear free-surface effects are significant for the conditions considered. Therefore, optimization trends may be different than that shown in previous investigations. On the other hand, the present bow modification appeared in relatively limited region, i.e., midgirth region, where a ditch line had been created. As such, further investigation of the present modification function is currently in progress. Finally, it should be emphasized that CFD-based optimization presents challenges to the verification and validation process and that there is a need for optimization validation data. the authoritative version for attribution.