Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Self-Propelled Maneuvering Underwater Vehicles
Self-Propelled Maneuvering Underwater Vehicles
Pages 478-489
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From page 478... ...
The numerical approach used to solve the three-dimensional time-dependent Navier-Stokes equations is discussed in Section 2; Iwo propulsor treatments are available, a body force propulsor and an actual rotating propulsor, and these two propulsor treatments are described in Section 3. The 6-DOF computational approach is discussed in Section 4, turbulence modeling in Section 5, and results and concluding remarks are given in Sections 6 and 7.
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From page 479... ...
There are numerous ways of developing this flux vector, and the formulation used early on [4J in this maneuvering underwater vehicle research was the flux difference split scheme of Roe U.Q1 for the first-order contribution and a hybrid numerical flux vector for the higher-order contribution that was patterned after the flux vector developed for compressible flow Am. An advantage of this hybrid flux is that the formulation leads more or less naturally to the limiting of characteristic variables which is important for compressible flows 479
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From page 480... ...
Therefore, some considerable time after the first version of this incompressible code was written it was determined to investigate the sort of results that could be obtained for second and third-order flux vectors by the more classical van Leer MUSCL-type of numerical flux vector formulation UP The nonlimited form of the dependent variable extrapolation method of Anderson, Thomas, and van Leer UP was found to work rather well for this incompressible formulation and the numerical results were found to be extremely close to the results provided by the hybrid numerical flux vector Id. The numerical flux currently used UP is based on Roe's approximate Riemann solver Uld, which in the interest of reduced floating point operation count is written for this one-dimensional example (Eq.
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From page 481... ...
This 481 coefficient information was used to determine the components of the body force vector and then distribute these components to the center of the cells in this cell-centered finite volume scheme in the region where the propulsor was located. 3.2 Actual Rotating Propulsor The method used to include an actual rotating propulsor is one that has been continually developed and also used for a number of years, primarily for compressible flows -.
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From page 482... ...
Solution of these equations yields the linear velocities of the vehicle u, v, w and the angular velocities of the vehicle p, q, r in the body fixed frame of reference.
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From page 483... ...
5.0 TURBULENCE MODEL Turbulence models used in this work include the Baldwin-Lomax mixing length model ~ the Launder-Sharma Low-Reynolds number k-c model and a Low-Reynolds number nonlinear k-e model based on the work of Nisizima and Yoshizawa, Speziale, and Myong and Kasagi [by. The bulk of the initial work was done with the algebraic mixing length model typified by the eddy viscosity AT = Ql~ I ~ I Here, a representative length scale is determined empincally, and it is combined with vorticity, ce, to provide a representative velocity scale.
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From page 484... ...
484 6.0 RESULTS Throughout this research effort, computations were earned 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 WOOF computation in order to predict the trajectory of the submarine.
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From page 485... ...
The computation of the ~ajecto~y of Me fully appended vehicle with an actual rotating propulsor was Gained out in the same fashion as the trajectory calculation for the body force propelled vehicle, except in this case a complete steady state solution does not exist due to the rotating propulsor. Rather, a periodic solution at zero angle of attack and drift is first obtained and then the Navier~tokes/~DOF computation was initiated.
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From page 486... ...
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.
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. The work involved a team of rather significant size Hat was composed of researchers at both the Applied Research Laboratory at Penn State University and the Computational Fluid Dynamics Laboratory at Mississippi State University.
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From page 488... ...
K., Thomas, J L., and van Leer, 8, "Companson of Finite Volume Flux Vector Splittings for He Euler Equations," AIAA Journal.
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From page 489... ...
and Briley, W R., "Parallel Solution of Viscous Incompressible Flow on Multi-Block Structured Grids Using MPI." Accepted for Parallel Computational Fluid Dynamics - Implementations and Results Using Parallel Computers, Edited by S
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