WCCM2018 Conference

Advances in the Simulation of Ship Navigation in Brash Ice

J. García-Espinosa, B. Serván-Camas, J. Colom-Cobb, E. Oñate

julio@cimne.upc.edu

Introduction

Scenario 2: Computational model

Multi-body dynamics solver

Scenario 1: Computational model

Demonstration examples

• Different demonstration exercices have been carried out to show the capabilities of the developed computational model

Within this work, the multi-body dynamics library "Open Dynamics Engine" has been integrated in the MPI-domain decomposition-based (HPC-tuned) framework of the fluid flow solver.

• We present here the progress made in the project ‘“Development of new Lagrangian computational methods for ice-ship interaction problems (NICE-SHIP)’ developed by CIMNE under a US Navy Grant issued by ONRG.
• The NICE-SHIP project aims at developing a new generation of computational methods, based on the integration of innovative semi-Lagrangian particle-based and discrete element models for the analysis of the operation of a vessel in an iced sea.

• Case 1: Ellipse crossing a swarm of triangles
• Ellipse 10x5m / Triangular blocks 3m (30x)
• Lagrangian particles: 1.6 Mparticles
• FEM Mesh: 125 Ktriangles
• CPU time: 2 CPUh (75s)

• The Particle Finite Element Method (PFEM, Idelsohn et al., 2004) is a versatile framework for the analysis of fluid-structure interaction problems.
• It combines Lagrangian particle-based techniques with the integral formulation of the Finite Element Method (FEM).
• The latest developed within the framework of the PFEM carried out at CIMNE is based on the X-IVAS (eXplicit Integration along the Velocity and Acceleration Streamlines) scheme.
• The resulting so-called SL-PFEM combines a semi-implicit scheme built over a Semi-Lagrangian (SL) formulation of the PFEM.

Enrichment

Discrete Element Method (DEM)

• Material represented by a collection of spherical particles (not micro, usually cms).
• Rigid particles, soft contacts.
• Particle dynamics based on standard equations of motion.
• Adequate contact laws yield desired macroscopic material behaviour (local contact problem).
• Interacting forces between the particles are evaluated as a local contact problem.
• Contact interaction takes into account friction, cohesion, and the possibility of breakage of cohesive bonds.

• Contact surfaces are estimated based on (approximated) weighted Voronoi diagram (contact areas form a polyhedron: no overlaps, no gaps).
• Cohesive bonds between pairs of particles are broken if normal stress exceeds fracture value.

• Case 2: Spheres colliding
• Spheres diameter 10m
• Lagrangian particles: 0.5 Mparticles
• FEM mesh: 70 Ktetrahedra
• CPU time: 0.5 CPUh (30s)

More recently SL-PFEM has been extended by the authors for the analysis of naval hydrodynamics problems. In particular, in the context of the project "Advanced mumerical simulation of the WAM-V in spray generating conditions" (Navy Grant N62909-12-1-7101).

The Wave Adaptive Modular Vessel (WAM-V, nickname "Spider Boat“) is an innovative class of watercraft developed by Marine Advanced Research.

Nadukandi, P., Servan-Camas, B., Becker, P.A. and García-Espinosa, J. (2017). Seakeeping with the SL-PFEM method. Comp. Part. Mech. 4(3): 321-329.

Motivation

X-IVAS scheme

• Case 3: Ellipsoid crossing a swarn of tetrahedra
• Ellipsoid 20x10m / Tetrahedral blocks 5m (90x)
• Lagrangian particles: 13.6 Mparticles
• FEM mesh: 1.5 Ktetrahedra
• CPU time: 24 CPUh (70s)

Consider the Eulerian description of the incompressible Navier-Stokes equations

• Current retreating of sea ice is enabling an expansion northwards of commercial fisheries and, in time, it will facilitate the exploitation of the mineral and hydrocarbon resources in the Arctic Circle.

Celigueta, M. A., Latorre, S., Arrufat, F., & Oñate, E. (2017). Accurate modelling of the elastic behavior of a continuum with the Discrete Element Method. Computational Mechanics, 1-14.

Validation

The effective acceleration field in the fluid domain is obtained from the momentum balance equation of the flow

Uniaxial compression test for 7 Mpa Polycrystal Ice

The final step in our project if the validation phase against experimental data of instantaneous drag force (currently ongoing).

The method selected to take into account the actual interaction between fluid and ice is based on the enrichment of the pressure field in the background mesh (FEM).

Step 1. Velocity is imposed in the particles lying on the solid domain (velocity field is given by solid body dynamics).

Step 2. Enrichment nodes are created at solid interface. Each enriched node is a new degree of freedom for the FEM solver.

The resulting FEM system of equations is:

Step 3. FEM system is assembled using the enriched mesh, but the new degrees of freedom are locally (within every element) collapsed.

Step 4. The dynamics of the ice blocks is evaluated explicitly (using the forces acting on their boundaries).

The fundamental principle of kinematics relates the Eulerian description of the flow with the Lagrangian description as follows

Patrol ship

• Length: 75.5 m / 79.8 m
• Displacement: 1813 t
• Velocity: 8kn

Ice covered waters

• Brash ice channel of 25 m wide
• Ice blocks of average size 0.5-1.0 m
• 300 x 25 ice blocks

where X(λ,t), U(λ,t) are the fluid particle trajectory and velocity.

Proof of concept (unvalidated)

Conclussions

The basic idea of the so-called X-IVAS scheme is to integrate above equations using the following approach:

• De-icing of the existing ice masses allows Arctic trade routes to remain open for longer periods of time. Sailing by northern routes could reduce by 20-30% journey times / fuel consumption and GHG emissions.
• While nobody disputes today that the exploitation of those opportunities must be properly managed in order to preserve the delicate Arctic environment, it is undeniable that reality is that commercial activity and economic development in the Arctic can increase rapidly.
• The potential development of the Arctic and Antarctic regions evidence the need for new procedures for estimating the forces that ice exerts on ice-breakers, polar ships and marine structures, and in general, the need for having advanced computational tools able to help naval architects to design the new generation of vessels to operate in polar regions.
• The goal of NICE-SHIP project is twofold:
• To develop constitutive material models in the context of the Discrete Element Method (DEM), able to simulate the icebreaking process (scenario 1).
• To develop innovative semi-Lagrangian particle-based models (SL-PFEM) for the analysis of the navigation of a vessel in brash ice / broken ice (scenario 2).

• The progress in the development of a computational analysis framework for simulation of different ice navigation scenarios has been presented.
• A SL-PFEM model is being developed to simulate the navigation in brash ice. The interaction between ice-blocks and ship is considered by enriching the FEM pressure field.
• First validation phase and different demonstration tests show promising results. Validation against experimental data on realistic scenarios is ongoing.

Hard ice. 1 meter thick. 6 elements in thickness.

Initial Validation

SL-PFEM model

Step 1: Lagrangian advection of the particles (4th order AB)

• The initial validation exercises carried out included the analysis of the flow about a fixed cylinder. The results using the enrichment have been compared to experimental data and results obtained for the body fitting approach. Forces and Strouhal numbers for different cases (Re up to 1,000,000) have been calculated. An excellent agreement with experimental/numerical data (within experimental/numerical uncertainty) have been found in all the cases.
• In addition, different validation cases, including moving cylinders and plates have been run.

Acknowledgements

Step 2: Project (mapping) the estimate of the velocity (and other information associated with the particles) onto a background FE mesh*

The authors would like to acknowledge the support given to this project (NICESHIP) by the Office of Naval Research Global with the Grant N62909-16-1-2236.

Step 3: Solve the remaining Stokes problem on the background mesh -using the FEM-

Using a backward Euler time integration, and the iterative monolithic approach inspired in the fractional step method, the semi-discrete Stokes system to be solved is

García-Espinosa, J. and Oñate, E. (2003). "An unstructured finite element solver for ship hydrodynamics problems". Jnl. Appl. Mech. 70 (1), 18-26

García-Espinosa, J., Valls, A. and Oñate, E. (2008) "ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems". Int. Jnl. Num. Meth. Eng. 76 (9), 1297-1327

Step 4: Update (correct) the particle velocities

This presentation is available at

Scenario 1: Icebreaking performance in level ice

13th World Congress in

Computational Mechanics