B. Alessandrini, D. Le Touzé, L. Gentaz

Code = EMSHIP S3-3 (Semester S3)

Workload: lectures (30h), practical training (35h)

Number of credits: 6

Objective:

• The goal of this class is to present an overview of the CFD methods for the computation of viscous free-surface unsteady flows for naval applications. The lecture gives exhaustive information concerning the strategies for the discretisation of Navier-Stokes equations and for the representation of the free surface, either by free surface tracking techniques or by free surface capturing techniques. The pros and cons of each strategy are discussed.
• In addition to well established field discretization methods, the SPH (Smooth Particles Hydrodynamics) method is presented. This method has been recently developed for hydrodynamic problems, and solves Navier Stokes or Euler equations on the basis of a set of interpolating kernels moving with Lagrangian control points, thus not relying on any mesh structure. This method is especially efficient for the solution of certain problems of great interest faced by ship designers, such as bow or stern slamming, green water on deck, sloshing flows in LNG tanks, etc…
• Practical projects are proposed to the students, based on the use of a finite difference Navier-Stokes solver especially developed for naval applications, ICARE, and on a SPH code dedicated to free surface flow problems, SPH-Flow. Both softwares are developed by Ecole Centrale de Nantes, with partners such as Hydrocean and, Bassin d’Essais des Carènes, among others.

Contents:

a) VISCOUS FLOW NUMERICAL SIMULATION BY METHODS BASED ON NAVIER-STOKES EQUATIONS

• Navier-Stokes Equations, RANS (Reynolds-Averaged Navier-Stokes) Equations in cartesian coordinates

• Boundary conditions, Free surface conditions, compatibility with no-slip conditions

• Navier-Stokes Equations in curvilinear space, partial and total transformation, metrics

• Conservative formulation

• Case of unsteady computational space, deformation velocities, constraint on generalised metrics

• Mesh Modelling : Finite Element, Finite Difference, Finite Volume, comparison, consistency, stability

• Velocity-Pressure coupling, Checkerboard instabilities, unknowns localization strategies, Rhie and Chow interpolation

• Velocity-Pressure-Free Surface coupling, Large linear systems solving, preconditioning

• Tracking and Capturing method (VOF, Level Set) to compute free surface

• Functional decomposition of RANS Equation to include wave generation and propagation in RANS solvers: the SWENSE (Spectral Wave Explicit Navier-Stokes Equations) principle; advantages compared to usual way to compute wave influence.

b) SPH MESH FREE METHOD:

• General presentation of the SPH method

• Interpolation kernels

• Time marching schemes

• Boundary conditions

• Improvement of accuracy: renormalisation, smoothing, Riemann solver

• Extension to multi-physics simulations, example of fluid-structure modelling using SPH

• Parallelization aspects

c) PRACTICAL TRAINING:

Practical work using a free surface Navier-Stokes solver developed at Centrale Nantes will be proposed to study and compute ship resistance and wave-body interactions cases. It includes the meshing of the fluid domain around the studied structure, study of computation convergence with meshing refinement, comparison of results with experiments or coming from other numerical methods. Bow impact problems will be studied using a SPH meshless method.

Recommended reading

• “Computational methods for fluid dynamics” by J. H. Ferziger and M. Peric, Springer Ed.
• “Smoothed Particle Hydrodynamics, a meshless particle method” by G.R. Liu and M.B. Liu, World Scientific Ed.
• Proceedings of the ONR (Office on Naval Research) conferences

Prerequisites:

Form of exams:

Written exams (2h)+reports of practical training