Ships need to be able to maneuver to function properly. They need to accelerate, turn, and stop. For ship designers, many common ways of analyzing maneuverability before a ship is built are either inaccurate or expensive. The primary goal of my research was to provide a computational fluid dynamics tool that is accurate and inexpensive. Leveraging reasonable simplifications in physics, it gives designers an efficient way to determine the maneuvering characteristics of a ship.

This collection of research is a result of my doctoral and postdoctoral activities. Simulations are performed with OpenFOAM, an opensource collection of C++ libraries for simulating a variety of physics. I tend to categorize my research into three areas: high-fidelity scientific studies, practical engineering simulations, and software development. Custom boundary conditions, top-level solvers, and mesh-motion functions are developed by myself to suit particular problems. Typically, grids are generated with the semi-automatic mesh generator native to OpenFOAM, snappyHexMesh. The majority of post-processing is performed with a combination of Gnuplot, Paraview, Python, and Tecplot.

At times, it is necessary to implement highly-resolved simulations to study fluid kinematics in detail. I have investigated boundary layer profiles, turbulent wakes, and viscous stresses for breaking and non-breaking waves using LES and URANS. Great attention to detail must be given to these studies, as they may be sensitive to nearly all aspects of simulation set-up and post-processing.

This on-going work involves the use of LES to study a variety of flow quantities on a square column with rounded corners oriented at 45 degrees. Lift and drag forces, as well as pressure on the column and in the wake, and turbulent kinetic energy are being investigated. Millions of CPU hours have been spent comparing a variety of simulation parameters. These are the most computationally intensive simulations I have performed. Much of the work is being performed with the XSEDE computing grant TG-CTS150061.

- 250,000 CPU hours
- 960 processors
- 11 days of computation
- 0.8 seconds of simulated flow

From the onset of this study, it was known that LES would be the preferred tool of choice. Therefore, all grids were made to ensure y^{+} < 1, since adequate resolution of the boundary layer is crucial to an accurate drag force. Overall, this problem is useful to provide engineering communities with data on a geometry that sits between a circular cylinder and a true square column without rounded corners.

Different parameters studied for this problem:

- Grid resolution
- Domain size
- Boundary conditions
- RANS vs. LES vs. ILES
- Convection schemes
- Structured vs. unstructured grids
- Turbulence modeling
- Wall functions

The purpose of this study was to determine the effects of viscosity at the air-water interface of ship flows. Many naval vessels have transom sterns which can be the source of very different types of flow such as steady waves, unsteady breaking waves, and large areas of recirculation. This research was used to determine if a custom linear free-surface approximation is a reasonable assumption for ship flows, even in the region of a transom stern. Two-dimensional cases of a steady wave, an unsteady breaking wave, and a nearly undisturbed water surface were investigated.

The fully nonlinear air-water interface problem is studied with a volume-of-fluid (VOF) method. This allows for large deformations of the water surface and the ability to measure pressures, viscous stresses, and wave slopes at the exact surface of the water.

Linearized free-surface boundary conditions in conjunction with the URANS equations are used to replicate each study. With this approach, the free-surface is made inviscid, and wave elevations are projected onto a flat free-surface. The linearized URANS method closely predicts wave formations, even the time-averaged wave formation of an unsteady breaking wave. These studies are discussed in detail within my thesis.

Nonlinear VOF solution

Linearized URANS solution with free-surface elevation

Nonlinear VOF solution

Linearized URANS solution with free-surface elevation

Practical engineering questions that typically arise in industrial settings often concern the fluid forces acting on an object. Determining the turning radius of a ship, the thrust required to make an aircraft take flight, or the wave-induced motions of an oil spar are all problems that may need CFD analysis at some point in a design cycle. I often use the RANS equations to perform simulations that address issues such as these.

A large portion of my research is catered towards analyzing the resistance and maneuverability of ships. This requires a mixture off-the-shelf RANS approaches using single or multiphase solvers, and the linearized URANS method which was developed as part of my thesis work. Details about this method can be found in my publications. Results are frequently compared to experiments. Typical quantities measured are forces and moments, wave elevation, and ship motions. These simulations are performed in calm-water and in waves.

Ship maneuvering with linearized URANS

Ship maneuvering with linearized URANS

Gap resonance may occur when multiple objects create a trapped surface of water between them. Heave motion of one or more of the objects produces a wave in this gap. The frequency of heave motion may create a resonant wave where the wave amplitude is many times greater than the heave amplitude. Designing for mitigation of gap resonance is valuable when considering ship-to-ship operations, vessels moored in port, and drillships with moonpools. However, designing for gap resonance may be a goal in energy harvesting applications. The focus of this research is to test several numerical methods against experimental data to determine the accuracy with which they account for resonant wave amplitudes in the gap of a heaving catamaran.

A velocity potential approach is used where the Laplace equation satisfies the conservation of mass in the domain. On the free-surface, an unsteady, combined free-surface boundary condition is satisfied. This is an inviscid formulation of the problem. The study is also performed with the linearized URANS method. The conservation of mass and momentum are satisfied with the continuity equation and URANS equations, respectively. The inviscid potential method is seen to overpredict the resonant wave amplitude in the gap. The viscous linearized URANS data agree very well with the experimental results over the entire range of heave periods.

Unique problems may require software development of existing tools. In addition, software is developed for the pursuit of more accurate or efficient solutions to day-to-day problems compared to existing tools. Often, a new method to simulation necessitates development of multiple sections of a code library, but they can be broken down into three key components: boundary conditions, top-level flow solvers, and mesh motion logic.

Using a finite volume method to solve free-surface problems in a velocity potential framework required the development of the combined free-surface condition - a combination of the classical kinematic and dynamic free-surface boundary conditions in a single equation. This was used to investigate gap resonance from an inviscid perspective. Using C++, a new boundary condition was made to solve the problem using the open source physics simulation software, OpenFOAM. Promising results to this problem motivated the pursuit of a viscous free-surface solver, and eventually led to the development of the linearized URANS method. The same combined free-surface condition was used with an inlet condition to model an unsteady, propagating wave in MATLAB.

A large portion of my PhD work was dedicated to the development and testing of the linearized URANS method for simulating ship maneuvering. This research is motivated by the need for high fidelity hydrodynamics tools that can efficiently compare several concepts of ship hulls. Model tests and fully nonlinear CFD are suitable for detailed design. However, the resources required with these methods (time, space, CPU, cost, etc.) are not conducive to an iterative approach to design. The ability to quickly obtain solutions to transient maneuvering simulations allows naval architects to begin evaluating important characteristics such as fuel efficiency, turning diameters, and straight-line stability at a stage in design where changes to the hull form are less costly.

Method (grid) | Pure sway | Pure yaw |
---|---|---|

Lin. URANS (coarse) | 11.5 | 10.4 |

Lin. URANS (medium) | 56.3 | 35.8 |

Lin. URANS (fine) | 221.9 | 196.0 |

Fully nonlinear CFD | 322 | 322 |

CPU hours per PMM period

Yaw moment during pure yaw

Linearized URANS accurately predicts forces

Linearized URANS - waves present

Double-body - no waves

Method (grid) | Pure sway | Pure yaw |
---|---|---|

Lin. URANS (coarse) | 11.5 | 10.4 |

Lin. URANS (medium) | 56.3 | 35.8 |

Lin. URANS (fine) | 221.9 | 196.0 |

Fully nonlinear CFD | 322 | 322 |

CPU hours per PMM period

Yaw moment during pure yaw

Solutions to the viscous unsteady Reynolds-averaged Navier-Stokes (URANS) equations provide accurate predictions of the forces acting on a ship. Linear dynamic and kinematic free-surface boundary conditions greatly reduce the CPU requirements compared to fully nonlinear CFD methods. This strategy results in transient maneuvering simulations that are up to 30 times faster than multiphase approaches. While heavily tested for maneuverability analysis, the method is also applicable to gap resonance, submarines near the air-water interface, wave energy devices, etc.

Solutions to the viscous unsteady Reynolds-averaged Navier-Stokes (URANS) equations provide accurate predictions of the forces acting on a ship. Linear dynamic and kinematic free-surface boundary conditions greatly reduce the CPU requirements compared to fully nonlinear CFD methods. This strategy results in transient maneuvering simulations that are up to 30 times faster than multiphase approaches. While heavily tested for maneuverability analysis, the method is also applicable to gap resonance, submarines near the air-water interface, wave energy devices, etc.

Double-body - no waves

Linearized URANS - waves present

Linearized URANS accurately predicts forces

Linearized URANS accurately predicts forces

Dynamic computational meshes are valuable advancements to simulating physics. Problems can be solved in various frames of reference, objects can move in response to the forces acting on them, and rotating machinery can be embedded in a surrounding mesh. I regularly develop mesh motion functions to solve unique problems. The linearized URANS method required logic to dictate the motion of propellers, rudders, and maneuvers in an inertial, Earth-fixed reference frame.

Custom propeller crashback motion function