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Fig. 7 Trajectory and Flow Field about SUBOFF Configuration with Sail, Sail Planes, and Stern Appendages with Body-Force Propulsor.

Fig. 8 Multiblock Grid for SUBOFF Configuration with Sail, Sail Planes, Stern Appendages, and Propeller.

balance and the rapid deceleration of the vehicle was eliminated. This trajectory computation continues to be carried out but the additional CPU time required for the rotating propulsor computation limits the number of body lengths that can be computed in a reasonable amount of computer time. It is estimated that 1000 CPU hours on the IBM Model 590 is required to complete five body lengths of travel. Whereas, this is a large amount of computer time, it is anticipated that a five body length computation can be carried out overnight using the parallel version of the code. The parallel computation of this trajectory calculation is just now being initiated. The vehicle trajectory that has been computed thus far is shown in Fig.9.

All of the above calculations were performed using an algebraic turbulence model and are currently being repeated using k–ε and nonlinear k–ε turbulence models.


A physics-based method was presented for the maneuvering prediction of self-propelled underwater vehicles. The method is based on coupling the numerical solution of the three-dimensional time-dependent incompressible turbulent Navier-Stokes equations with the numerical solution of the equations of motion of the vehicle. The computational methods were previously verified independently on numerous test cases, and also verified in the coupled mode. The Navier-Stokes/6-DOF coupled code was applied to the trajectory calculation of two fully appended submarine configurations that differed only in their propulsor units. One had a body force propulsor and the other had an actual rotating propeller.

This research effort was of three and one-half years duration and was sponsored by the Office of Naval

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