Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Numerical Study on the Estimation of Hydrodynamic Force Acting on AUV Using CFD Based on N-S
Equation of the Non-Inertial Coordinate System
Siyu CHAN, Hiroyoshi SUZUKI
Department of Naval Architecture and Ocean Engineering, Osaka University
Suita, Osaka, Japan

ABSTRACTa study on the design optimization of an AUV by using computational
fluid dynamic analysis.
But the dynamic mesh tech has its own disadvantages. Firstly, the efficiency is not good. The solving for mesh movement in every time step
consumes a lot of computing resources which results in high time cost.
Secondly, the numerical stability is not good. Calculations are usuallytended to diverge.
So in this work, a new method is developed to estimate the force condition by describing the motion of the object in a non-inertial coordinate
system. When the coordinate system is fixed on the object, the deformation and the displacement of the mesh system can be avoided fundamentally. By doing that, the efficiency of the simulation is greatly improved,
and the numerical stability is also greatly made better.
To evaluate the efficiency and the accuracy of the non-inertial coordinate
system-based method, moving grid and overset mesh are also used tosimulate the same case, and the results are compared.
The open-source software openFOAM is used in this study, ParaView
is used for visualization.

In this study, a PIMPLE algorithm-based solver in a non-inertial coordinate system is developed. The hydrodynamic force acting on an AUVbody that is forced to oscillate in a uniform flow is estimated. Meanwhile,the hydrodynamic force is also estimated and derived by describing themotion in an inertial coordinate system with the moving grid and overset
mesh at the same grid scale. Three results are compared for accuracy
and efficiency. The result shows that under similar accuracy, it is more
efficient to simulate the flow by describing the motion in a non-inertial
coordinate system. Besides, because of the avoidance of the deformationand displacement of the mesh, the non-inertial coordinate system-based
solver has better numerical stability and it is easier to set boundary conditions and the motion.

KEY WORDS: hydrodynamic force, moving grid, overset mesh, noninertial coordinate system

INTRODUCTIONCONTROL EQUATIONS IN NON-INERTIAL SYSTEM

In recent years, ocean exploration has gradually been paid attention toby various countries, and some ocean exploration technologies have also
been well developed. For example, Autonomous underwater vehicles, soknown as AUV, are widely used in this area such as ocean resource exploration and ocean environment exploration. It is one of the unmannedunderwater vehicles which looks like a small submarine or torpedo. They
are always applied to carry out some long-term, routine or dangerous
tasks, such as exploring oil fields, s ea c harts, o ceanographic research,and removing mines. During the mission, it is possible for the AUVs toaccomplish different tasks by following the pre-coded program so that
the AUVs are not connected to a mother ship or operator by a cable.
To meet the requirements for different working conditions, the AUV design should take hydrodynamic performance as an important target. Sofirstly, t he f orce c onditions f or a s ailing A UV s hould b e s tudied. To
know the force conditions, computational fluid dynamics (CFD) is a goodchoice because of the relatively low cost and feasibility. For example,
GAO and PAN (2012) derived hydrodynamic coefficients of a high-speed
AUV by using dynamic mesh tech. And Joung T., Sammut, K.(2009) did

With the assumption of viscous and incompressibility, the control equations of fluid in an inertial coordinate system can be given as(Ren. &Chen., 2004; Wang., 2013):
 →∂−u1−−− a + (→ua · ∇)→ua = f − ∇p + ν∇2→ua∂tρ−∇ ·→ua = 0(1)Where ua is the velocity of the fluid in the inertial coordinate system. And meanwhile, the relationship of the velocity and the acceleration between an inertial and a non-inertial coordinate system
can be explained by the Point Velocity Composition T heorem, and thePoint Acceleration Composition T heorem.
In Fig 1 as an example, X0 , Y0 , Z0 is an inertial coordinate system, andX1 , Y1 , Z1 is a non-inertial coordinate system. Motion of the non-ineital→−system is described by a position vector R and rotational angular velocity

1122