CFD Predicting Impact Loading of a Hydrodynamic Wave on a Submarine

Traditionally, submarines are quite stealthy and hydro-dynamically sleek. This is imperative for a vessel designed to operate underwater; however, like surface vessels, a submarine will pitch and roll when it surfaces. This means submarines face similar risks as surface ships when it surfaces in extreme weather conditions.

Dr. Minyee Jiang of the Naval Surface Warfare Center studies the effect of hydrodynamic waves on submarines using computational fluid dynamics (CFD) simulation software.

“Lab experiments are expensive and time consuming,” Jiang said. “CFD simulations of free surface and wave interactions can be used to model the submarine while operating near the free surface.”

For his analysis, Dr. Jiang chose STAR-CCM+. The decision was based on the program’s ability to model higher order irregular Stokes waves and irregular waves as opposed to a basic sinusoidal wave. “These are more realistic,” explains Dr. Jiang. “The program was also chosen for its robust meshing tool which needs little user interaction, and the volume of fluid (VOF) solver which is good for wave-impact and wave-ship interactions.”

The VOF approach assumes that the grid cells near the free surface are filled part way with air and water. Within each computational cell the VOF, pressure, velocity and gravitational force acting on the fluid is calculated. The ocean waves and the free surface are tracked by using the VOF values in the domain. The ship then interacts with this oncoming wave resulting in impact loads on the vessel surfaces which are analyzed,” explains Dr. Jiang.

To perform the simulation, you must first create a mesh for the computational model which will be used to compute the physic variables and properly outline the complex wave field and the vessel geometry.

Due to the viscous fluid traveling around the submarine an appropriately fine grid must be used to resolve the flow physics.  In addition, a small time step size must be used for accurate prediction of the impact loads. Dr. Jiang further explains that, “the time step size and grid size are interrelated for numerical accuracy and stability and a balance must be maintained between them to achieve a practical time step size for running the problem without sacrificing accuracy.   These impact loads are then provided to structural engineers for determining the critical impact loading.”

The initial conditions of the wave field are then specified at the inlet boundaries. During the simulation, the waves are propagated into the computational domain. “The pressure and velocity are solved using a RANS solver and k-ω turbulence model,” said Dr. Jiang.

When compared to lab tests, Dr. Jiang’s results were very accurate, meaning the simulation can now be used to improve the vessel’s design for near surface maneuvers. “External payloads may need to be modified to reduce the impact load. Based on this total impact loading and bending moment, further structural analysis and redesign may be required. Any structure connected to the impacted surface, which exceeds high wave impact loads, needs to be strengthened. Many iterations of CFD wave impact simulation, structural analysis, structure/geometry redesign are required to ensure safe operations.”

Since Archimedes, man has understood the physics of buoyancy. In the 20^th Century the technology took off and led to the submersible marvels we all know today. As simulation technology improves, however, who knows how submarines will change?