Fig. 3 Flow Angle β=tan–¹(W/U), Anisotropic Model, Re=4.2×10⁶, α=10°.

Fig. 4 Boundary Layer Normal Stress Profiles, x/L=0.4,Φ=100°, Anisotropic Model, Re=4.2×10⁶, α=10°.

Fig. 5 Boundary Layer Shear Stress Profiles, x/L=0.4,Φ=100°, Anisotropic Model, Re=4.2×10⁶, α=10°.

Throughout this research effort, computations were carried out in order to validate the code as each additional computational capability and improvement was added. These test cases have ranged from steady state laminar flow over a flat plate to unsteady turbulent flow about a fully appended submarine configuration that included sail, sail plane, four stern appendages, and an actual rotating propeller; and, the coupling of this unsteady flow computation to the 6-DOF computation in order to predict the trajectory of the submarine. The computations performed between these two extremes were cases where analytical solutions or experimental data were available for comparison whenever possible. The solutions were carried out on multiblock grids with structured subgrids, and nearly all of these grids were built using EAGLEView [34]. Moreover, all of the grids were tight with y⁺ values near surfaces of order one.

The ultimate objective of this work, which was the prediction of the trajectory of fully appended self-propelled maneuvering vehicles, involved more complicated flow fields and configurations than those corresponding to the experiments for which measured data were available. Nevertheless, the approach taken, whenever data and time permitted, was to perform rather critical comparisons with the experimental data that were available. For steady state flows, comparisons have been made between numerical results and experimental data that include one or more of the measurements of pressure, skin friction, and/or boundary-layer velocity profiles for geometric configurations that include SUBOFF [35], inflected stern [36], 6:1 prolate spheroid [37], and wing-body junction [38]. These numerical and experimental comparisons are included in [ 4, 18, 19, 20, 39, and 40]. For unsteady flows, comparisons with experimental pressure and velocity measurements have been made with the so-called flapping foil experiment [41]. the 6:1 prolate spheroid in pitch, plunge, and roll maneuvers [42 and 43], an impulsively started cylinder [44], and isolated rotating propellers [45 and 46]. These numerical and experimental comparisons are included in [ 21, 39, 47, 48, and 49]. The quality of agreement for all of the steady and unsteady flow comparisons have been considered reasonable to excellent.

The computations mentioned above that have been carried out for comparisons with experimental data have involved an enormous number of calculations and essentially all of these calculations were performed on workstations that included SGI 75 MHz R8000 processors and IBM RS/6000 Model 560 and 590 processors. Examples of processing speed are given in [20] and include an example of the computation of a