J. García-Espinosa, A. Coll, E. OñateJ. García-Espinosa, A. Coll, E. Oñateand R. Ribó, D. Sa, C. García, O. Casals, C. Corte, K. Lam

International Center for Numerical Methods in Engineering International Center for Numerical Methods in Engineering (CIMNE)(CIMNE)

Compass Ingeniería y Sistemas SA (CompassIS)Compass Ingeniería y Sistemas SA (CompassIS)

Outline Overlapping domain decomposition level set algorithm

Theoretical backgroung ALE-Navier Stokes iterative-implicit solver Monophase flow adaptation Application example

Boundary layer resolution Anisotropic boundary layer mesh generation Stabilization aspects Fluid flow validation tests Application example

Fluid Structure interaction Development of a new generation GUI Coupling / interpolation algorithm / tools Application example

ODDLS theoretical backgroungALE-Navier Stokes iterative-implicit solverMonophase flow adaptation

Problem Statement: Two fluids Navier Stokes equationsTwo (incompressible) fluids (non homogeneous) Navier

Stokes equations:

With:

And the necessary initial and boundary conditions

0

0

t

t

u

u u u f

u

1 2int 0,t t t T

1 1 1

2 2 2

,, , , , 0,

,

tt t t T

t

xx x x

x

Problem statement: Level set equationLet be Ψ a function (level set), defined as follows:

Therefore we can re-write the density field as:

And finally, obtain an equivalent equation for the mass conservation in terms of Ψ (level set):

1

2

, 0,

, 0

tt

t

xx

x

0 ut 0 ut

1

2

,

, 0

,

d t t

t t

d t t

x x

x x

x x

Problem Statement: ALE* formulation

We may easily re-write the previous equations in an Arbitrary Lagrangian-Eulerian frame:

Where um is the (mesh) deformation velocity of the moving domain:

* The algorithm is Lagrangian for the movement of the ship but the free surface problem (level set) is solved in an Eulerian way

0

0

mt

mt

uu

u

fσuuuu

,Ttttt 0 )()(int 21

Overlapping Domain Decomposition TecniqueLet K be a finite element partition of domain Ω, and

consider a domain decomposition of Ω into three disjoint sub domains Ω3(t), Ω3(t) and Ω5(t):

ΩΩ1 1 (Fluid (Fluid 1)1)

ΩΩ2 2 (Fluid (Fluid 2)2)

)()(\)()(

0),(| ,)( ,0),(| ,)(

534

555333

tttt

tKKttKKt e

e

ee

e

e

xxxx

Overlapping Domain Decomposition TecniqueFrom this partition let us define two overlapping domains

Ω*1, Ω*2 in such a way that

ΩΩ**11

ΩΩ**22

)()(int: ,)()(int: 54*243

*1 tttt

**11

**22

Overlapping Domain Decomposition Tecnique

We can write an equivalent (continuous) problem, using a standard Dirichlet-Neumann domain decomposition technique (using Ω*1, Ω*2 decomposition). The resulting variational problem is (including FIC stabilisation terms):

2 2 22

2 22 2

2 2

2 2 2 2 2 2 2 2

1 2 2

2 2 2

1, , , ,

2

, , , ,

1, , 0

2

MN

t m m

d d

t t

q r q

u v u u v v r h v

t v g s v t v f v

u h

1 1 11

1 11

1 1

1 1 1 1 1 1 1 1

1 2 1

1 1 1

1 2 1

1, , , ,

2

, , ,

1, , 0

2

MN

t m m

d d

t t

q r q

on

u v u u v v r h v

t v g s v f v

u h

u u

ΩΩ**11

ΩΩ**22

Problem statement:Boundary condition at the interfaceDirichlet conditions (compatibility of velocities at the

interface) are applied on Γ*1 (boundary of

And Neumann condition are applied on Γ*2 (jump condition)

t* is evaluated from the resulting velocity and pressure field on Ω*1. Pressure evaluation must take into account the jump condition given by:

Where γ is the coefficient of surface tension, and p1, p2 are the pressure values evaluated on the real free surface interface Γ. These are extrapolated to Γ* to impose the conditions on the defined interfaces.

on 21 nnn pp

*121 on uu

*2

*22 on tσn

Adaptation for solving Monophase Flow

In many cases of interest in naval/marine applications, the aerodynamics effects can be neglected (density and viscosity ratio are about 1000).

It is important for these cases to adapt the ODDLS technique to solve monophase problems, reducing the computational cost and capturing the free surface with the necessary accuracy and maintaining the advantages of the proposed method.

In these cases, the computational domain is reduced to the nodes in the water plus those in the air being connected to the interface (Ω*1). The later nodes are used to impose the pressure and velocity boundary conditions on the interface.

PT-215 Mega-yacht (Isonaval)

Isonaval PT-215 This example shows the application of the presented technique to the analysis

of a 135’ mega-yatch designed by Isonaval. The general characteristics of this yacht are shown in the following table:

Main Characteristics

Length overall 135’ (41,2 m)

Moulded Draft 2.48 m

Moulded Beam 9.5 m

Construction depth 4.5 m

Design Speed 14.5 Kn

Isonaval PT-215 analysesThe analyses consisted of the towing of the hull at different

speeds (still water) at real scale. Analyses were carried out in parallel to experimental test in

towing tank. The objective of this parallel work was to complete the information from the towink tank (such as real scale behaviour, streamlines for bilge keels arrangement, local phenomena, …)

Characteristics of calculations: 2 sets of analyses were performed: fixed ship and free to sink and

trim. 5 different speeds were run for every set of analysis with an

unstructured 2.4 million linear tetrahedra mesh. Two more meshes of 3.7 and 6.3 million linear tetrahedra were

used to study the influence of the mesh density in the results (run for the fixed ship cases).

The model geometry includes keel and bow truster tunnel, but no other appendages.

All the cases were run using an ILES-type turbulence model.

Isonaval PT-215Streamlines (V = 14.5 kn):•Mesh of 2.4 million tetrahedra•Pressure map on hull and (limiting) streamlines

Isonaval PT-215b After the study of the PT-215 hull, a new requirements from the owner

arose: extend the LOA from 135’ to 148’. Therefore, the hull was extended amidships and a stern platform was modified and slighly enlarged. In parallel, the platform base was modified, including a slight wedge to reduce the dynamic trim angle.

The final general characteristics are shown in the following table:Main Characteristics

Length overall 148’ (45.1 m)

Moulded Draft 2.45 m

Moulded Beam 9.5 m

Construction depth 4.5 m

Design Speed 14.5 Kn

Isonaval PT-215b analysesThe analyses consist of the towing of the hull at different

speeds (still water). No parallel experimental study were done this time!

Characteristics of the analyses:1 set of analyses were performed, leaving the ship free to

sink and trim.5 different speeds (12 kn, 13 kn, 14 kn, 14.5 kn and 15 kn)

were run for every set of analysis with an unstructured 2.5 million linear tetrahedra mesh.

Two more meshes of 4.5 and 6.4 million linear tetrahedra were used to study the influence of the mesh density in the results (run for the full set of speed cases).

The model geometry includes keel and bow truster tunnel, but no other appendages.

All the cases were run using an ILES-type turbulence model.

Isonaval PT-215 Snapshot of the results (V = 14.5 kn):•Mesh of 4.5 million tetrahedra•Left: (dynamic) pressure map on free surface•Down: pressure field on hull

The results showed that the contractual speed could be achieved without increasing the power!

Anisotropic boundary layer mesh generationStabilization aspectsFluid flow validation tests

Resolution of the boundary layerObjective: Improvement of the resolution of the

boundary layer, by generating an adapted (anisotropic) mesh in the boundary layer area.

The existing (frontal method) mesh generator for the generation of unstructured tetrahedral meshes of the GiD pre-processor has been adapted.

The algorithm implemented in this work is able to generate “a posteriori” boundary layer mesh of prisms or tetrahedra.

The philosophy of the method is based on Y. Ito and K. Nakahashi (2002) work, but adapted to the specific requirements of the GiD system.

Meshing the boundary layer: steps

Meshing the boundary layer: steps

Meshing the boundary layer: steps

Boundary layer mesh: stabilization aspectsFinite Calculus (FIC) method is used to stabilize Navier

Stokes equations. The stabilized FIC form of the governing differential equations is as follows:

Characteristics lengths hm, hd and hψ must reflect the anisotropy of the mesh, since they are related to the discrete balance domain size.

mtr uu

udr

fσuuuur mtm

021

021

021

d

m

rr

rr dd

mm

h

h

rhr

First validation: Turbulent flow in a pipe

First element thickness 2.3·10-5 m Ratio boundary layer thickness / D

= 0.004 Ratio first element thickness / D =

0.001 Turbulence model: k-ε low-Re

Boundary layer mesh: KVLCC2 Flow about KVLCC2 tanker ship (validation study based on data

available at Gothemburg 2000 Workshop website) Wind tunnel tests were carried out for a model at scale 1:116,

resulting in a model of length 2.76 m. The velocity of the air at the inlet is 25 m/s, being the density and viscosity ρ=1.01 Kg/m³ and μ=3.045·10-5 Kg/ms, respectively.

Estimated viscous sub-layer thickness 4.0·10-5 m

Study at real scale (L = 320 m), Re = 2.03·109. Estimated viscous sub-layer thickness is 3.0 e-5 m

k-ε low-Re, Spalart Allmaras and ILES models predicted too low Cf values. k-ε low Rea and Spalart Allmaras seems to be overdiffusive and mesh density is too coarse for ILES approach.

k-ω SST seems to behave better that others in this case. However it is noticeable that k-ω gives a closer value to Cf friction line for the case at scale 1/116. Similar results have been obtained in other cases (in particular NT-130 case shown afterwards).

NT-130 semi-planning’craft (Navtec)

NT-130We will apply the presented technique to the analysis of a

semi-planning hull. The general characteristics of this boat are shown next.

Main Characteristics

LOA 14.0 m

Moulded Draft

1.05 m

Moulded Beam

3.54 m

Design Speed 14 Kn (Fn = 0.65)

NT-130 Still Water Analyses

The first example consist of the towing of the hull at different speeds (still water).

Characteristics of the analyses:2 sets of analysis were done: fixed ship and free to sink

and trim.4 different speeds were run. All the cases were run

twice, using different meshes of 2.0 and 3.2 million linear tetrahedra (isotropic) and 3.4 million linear tetrahedra (anisotropic).

Additional cases with different (isotropic) meshes ranging from 1.5 to 16 million linear tetrahedra were used to study the influence of the mesh density in the results.

NT-130 Still Water Analyses: Dynamic Sinkage and Trim effect Fn=0.6

5

Fn=0.55

NT-130 Still water Drag / Towing force

NT-130 Still Water AnalysesSnapshot of the results (V = 12kn):•Mesh of 16 million tetrahedra•Left: (dynamic) pressure•Down: velocity modulus

NT-130 Results / Mesh dependency

Development of a new generation GUICoupling / interpolation algorithm (library)

Development of a new GUI for FSIMain Objectives To develop a framework to integrate different analysis solvers Able to manage in an efficient way geometry and data for FSI and

multi-physics solvers User-friendly and easy to use (as much as possible). Utilities to

guide the user in the insertion of the data (wizards, links between data, error reporting, simplification of data tree, …)

Allowing fully integration of fluid, structure and multi-physics solvers in the same GUI

To develop a strategy (and tools) to minimize the effort required for the integration / communication of different (existant) solvers

Resulting in a package of high quality (focussed in commercialization) Other aspects:

Tools to help in the definition of materials, properties, … Parametric modeling tools Reporting tools (quasi-automatic) Library to create self-training tools Translation management tools

Development of a new GUI for FSI A new toolkit (Tcl-Tk) for managing CAE information has been developed (for

GiD pre/postprocessing system) CAE Information is stored in a XML database

XML is endorsed by software market leaders, it supports Unicode and it is a W3C recommendation. The syntax rules are very simple, logical, concise, easy to use. The XML documents are human-legible, clear

and easy to create. The information is stored in plain text format. It can be viewed in all major of browsers and it is designed to

be self-descriptive. The elements in a XML document form a tree-structure that starts at “the root” and branches to “the leaves”

with different relationships between the nested elements. It allows to efficiently aggregate elements. XML elements are defined using generic tags and can have attributes, which provide additional information

about elements.

The new Toolkit takes advantage of this hierarchical XML structure to convert automatically the XML database to a physical tree on the GiD window.

Data tree and menus are simplified/organized based on previous configuration / selection done by the user

Geometry data is organized in groups and/or layers. The system allows easy and efficient integration of data for different solvers. A library for communication / interpolation of solvers based on TCL-IP sockets

has been developed

XML-file containsDefinition of data entries (general data, conditions, materials, …) TCL procedures that execute commands when necessaryXpath instructionsTree structure generated from XML

database

XML-based GUI

Toolkit for CAE GUI

Start data window allows to select the main characteristics of the analysis. The XML-based data tree is adapted accordingly.Tree is dynamicaly adapted based on the data already inserted by the user.

Communication/Interpolation libraryA C++ library has been

developed for communicationof different solvers (C and FORTRAN interface).

Information is interchangedat memory level, based on TCL_IPsockets.

Different solvers may be connected inparallel.

Library incorporates automatic mesh interpolation tools (advanced element octtree search algorithm) and allows mesh updating.

Require minimum adaptation of the solvers (dynamic library).

FSI comm library

Update mesh

Solve fluid(time t)

Read new mesh A

Update Mesh B Transfer fluid forces to mesh

B

Update meshSolve struct.(time t)

Transfer structure

velocity to mesh A

Update mesh

Solve fluid(time t+dt)

Update mesh Solve

struct.(time t+dt)

Transfer structure

velocity to mesh A

Itera

te to

bal

ance

in

tera

ction

forc

es

(initi

ally

ext

rapo

late

)

Read new mesh A

Update Mesh B Transfer fluid forces to mesh

B

NT-130 in head waves

NT-130 Head Waves Analyses

This example consist of the FSI analysis of the hull structure at different speeds in head waves.

Characteristics of the analyses:The analyses were carried out with the ship free to sink

and trim.4 different speeds were run for every set of analyses

with two meshes: 2.9 and 3.4 million linear tetrahedra mesh (fluid).

The structure of the ship was modelled using and 30 000 six nodes (composite) shell triangles and 2 100 beam elements.

The analysed wave length range from 1.0 to 1.5 x LOA (about critical values for slamming).

NT-130 Head waves analysis

NT-130 Head Waves

Fluid dynamics analysis (right)Structural response (down)

ConclusionsThe present work describes the ODDLS methodology for

the analysis of naval problems. The method is based on the domain decomposition technique combined with the Level Set technique and a FIC stabilized FEM.

The ODDLS approximation increases the accuracy of the free surface capturing as well as the solution of the governing equations in the interface between two fluids.

ODDLS method has also been integrated with an ALE algorithm for the treatment of the dynamic movement of a body/bodies (ship).

The boundary layer treatment is based on the generation of an anisotropic mesh.

The work has included the development of a FSI framework (GUI+comm libs for GiD) for integration of existing solvers.

Different examples have shown practical application of the methodology.

AcknowledgmentsThis work has been partially supported by CENIT

2007-2024 BAIP 2020 Isonaval S.A. (Spain): PT-215 analysesNavtec Ltd. (Chile): NT-130 analyses

For further informationhttp:///www.compassis.comemail: info@compassis.com