A Velocity Decomposition Method for Efficient Numerical Computation of Steady External Flows.

Abstract

Modeling forces on surface vessels to determine their hydrodynamic performance in the marine environment is integral to vessel design. Many hydrodynamic solution methods exist, ranging from the geometrically simplified strip theory, to inviscid approaches and fully nonlinear unsteady Reynolds-Averaged Navier-Stokes (RANS) solvers. The former approaches are less expensive, but neglect various aspects of the relevant physics including viscous effects and, often, wave breaking. RANS solvers can include viscosity and handle wave breaking; however, they are generally too expensive to be widely utilized at the design stage. The decomposition method presented in this work provides equivalent accuracy to that of RANS solvers, but with decreased computational expense by combining RANS and potential flow solvers to deliver the benefits of each in a unified methodology.

The decomposition method in this work utilizes a Helmholtz-type velocity decomposition to describe the total velocity field as the sum of an irrotational component and a vortical component. Applying the decomposition to the body boundary condition allows the effects of viscosity to be included in the potential velocity field. The viscous-potential-velocity field then fully represents the real fluid velocity everywhere the vorticity has decreased to a negligible level. The computational domain can therefore be reduced to extend just beyond the vortical region surrounding the body and in the wake, with the viscous potential velocity acting as the inlet and farfield boundary conditions for the total fluid velocity. The potential velocity is determined in the infinite-fluid domain using a boundary-element method, and the RANS equations model the total fluid velocity using a finite-volume method.

The velocity decomposition solver developed in this work has matched the accuracy of a RANS solver in decreased computation time for a variety of steady two-dimensional and three-dimensional, laminar and turbulent, external, incompressible flows. The computation time was reduced between 3% and 68% for the cases studied in this thesis.