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Simulation Method

The simulation method, or the computational method employed includes two main elements: 1) the grid generation and 2) the flow solving. The description of the method therefore will be centered around these two topics, which are of equal importance.

Grid Generation and Grid Topology

A structured, curvilinear, body-conforming grid is generated. First, a surface grid is constructed from the designer's blueprint. The forward and midship superstructures are represented by two numerical blocked structures, followed by a flight deck, and a lower missile deck. The numerical model for the surface grid is derived by using the Tai simplification scheme called the area-volume rule for representing the surface components of a ship [10], see Fig.1. Computationally, the model consists of a

Fig. 1—DD-963 ship configuration.

Fig. 2—Ship model with 2-degree pitch (bow down)

serials of rectangular volume blocks in tandem. The ship model is then pitched and/or rolled with respect to the base plane that coincides with the water surface. Pitch was performed about the center of gravity and roll about the ship centerline through the center of gravity. Figure 2 shows the ship attitude (forward portion only) when it pitches two degrees into the water (bow down).

The NASA Ames 3DGRAPE code [11] is used for basic grid generations. A cylindrical grid topology is adopted for its capability to treat a body with a sharp nose. The topology is basically an H-O mixed type, with H-type in the longitudinal plane, and O-type in the crossflow plane. The outer cylindrical surface is set at 2.5 ship lengths from the ship centerline. The most forward plane is set at 1.0 ship length from the bow of the ship, and 3.0 ship lengths for the wake. Assuming symmetry about the centerplane, only half of the ship needs to be modeled in constructing the surface grid. The half model is then unfolded to whole ship in generating the volume grid. This size has been employed in other configurations and proved to be adequate.

An overall coarse grid is generated first by 3DGRAPE using a multi-block procedure. The radial distances are then clustered near the surface and stretched in the outer region for shear layer development. The complete grid has a total of 99×59×57 points with 57 points in the radial direction. This number is larger than those for aircraft because of very low speed freestream involved in the present work. Previous study [12] indicates that when using a compressible flow code at low Mach numbers, an increased mesh density is needed. The details of the grid generation and advantage of the grid topology adapted were discussed in Ref. 8. The grid resolution was enhanced by increasing the number of normal points from previous 51 points to 57 points in the present extension.

Flow Solver

The NASA Langley thin-layer Navier-Stokes code, namely the CFL3D code [13] with multi-zone capability, is used as the basic flow solver. Appropriate modifications to the code for applying specific boundary conditions are implemented. The code is based on a finite volume algorithm with a spatially factored diagonalized, implicit scheme for discretizing the three-dimensional, Reynolds



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