Numerical simulation of hydro-structural coupling for marine propellers

Numerical simulation of

hydro-structural coupling for

marine applications

Guest lecture at the TU Deift,

March21

Paul Groenenboom

E

Conterrfls

° Introduction

D Finite Element Method ° Particle Method (SPH) D Fluid-structure interaction D Benchmarks

° Marine applications

ESI Group 2'

Deift University of Technology

Ship Hydromechanics Laboratory

Library

Mekelweg 2, 2628 CD Deift

The Netherlands

Equations to be solved

Structure:

Kinematics: Newton's laws. Dynamics: Stress-strain relation.

Non-linear behaviour: large displacements, plasticity and failure of material, contact.

Fluid:

Conservation of mass, momentum (energy). Euler or Navier-Stokes.

ESI Group 3

Frame of reference

LAGRANGE:

Nodes have the same motion as the material. Natural system for structures.

No need to interpolate transported properties. Usually not suitable for extreme deformation.

EULER:

Nodes are fixed ¡n space. Natural system for flow of fluids.

Requ ¡red interpolation of transported properties.

Not suitable for structures at small deformations.

Finite Element Method (1)

Equations of mechanics for a (complex) structure. Divide space into a number of small volumes of a simple shape.

Apply variational principle for the energy w.r.t. virtual displacements.

Assume the unknowns may be approximated by simple functions on these volumes.

Solve the resulting (large) set of discrete equations on a computer.

ESI Group

Finite Element Method (2)

Fixed connectivity.

How to account for motion?

Choice of element shape and basic functions. Choice of number, size and distribution of elements.

Check and analyse the results.

ESI Group

IESI GROUP

Solid Elements

ESI Group To discretize bulk materials

Standard: Solid 8 node "brick" elements ' First-order, trilinear isoparametric elements

Single-point integration requires hourglass control SRI (Selective Reduced Integration - i ini. pnt. for

hydrostatic part and 8 i. pnt's for deviatoric part)

also available.

Shell Elements (1)

to discretize structures made of plates and shells

a C° continuity

Number of integration points through the thickness: NINT

ESI Group

Solution ¡n time

Divide the relevant range in time into

a

number of (small) steps.

Update the kinematics and dynamics of

all nodes/particles or particles from one

step to the next.

Investigate the best way to perform this

step.

ESI Group

Explicit integration scheme

I

,

t,_I/2 tn ESI Group

f(t),x,,ï

m-i-kx=f(t) mÏ,+1cc, =f(t) ï,,=m'(j-kx,,) 1,H.I/2 = i lOi

'5

X,.

ÏX,,_112,,._..+I/2

t X,. k in = + &l/2Xn...1F2

IESIGROUP

Explicit integration scheme

'Stab'e time step

L E. p, A

bar spr.flg-flmSS

m = pALJ2

k = EAIL

ESI Group

C[j

isthe speed of sound is the Traversal time

L _L

E/pc

mpllcit integration scheme

f(t),x,k,ï EStGroup ,n+kx=f(t) + kx4.1= f1(t) (2) _{L =} (3) =(m/A72+k)_! +m/Lt2(2X0 -C 12 -C

'6

Comparison of explicit and

imp ici

urne n egration

Number of time steps

Although unconditionally stable, implicit methods needs many time steps in order to trace the physical

phenomena studied

Explicit analysis requires a small time step. This leads to many, but CPU cheap solutions

Equations to be solved

Implicit analysis requires matrix inversion. The solution of NL sets requires iterative solution strategies.

Explicit analysis requires no iteration and no matrix inversion.

ES Group 13

Example: Impact on Beam

Drop of rigid cylinder on supported beam

Impact loading

Elasto-plastic material Spotweld connections

ESI Group 14

PAM-C RASH Applications

Crashworthiness Design

INBAT Project

nnovative Barge Trains for Effective Transporton

Shallow Waters.

5th Framework Programme Project

ESI (roup 15

Mesh plots of a cut-view model at various

moments.

Particle Method SPH

Smoothed Particle Hydrodynamics

Meshless method for continuum mechanics Origins ¡n modelling of cosmic physics Significantly enhanced for fluid-flow

Handles free-surface and other interlaces

SPH - fundamental concept

SPH is an alternative numerical method to FEM for simulation of continuum mechanics. Properties (density) can be interpolated within a certain range.

The interpolation points are identified with the

particles with a specified mass.

With SPH there is no need to define a grid The FE connectivity is replaced by a dynamic nearest neighbor search.

There is no need for numerical evaluation of

partial derivatives as with other methods.

ESI Group (20

10

SPH is a new technology for simulation of

large deformation mechanics

Hypervelocity lmpact.

Ballistic Impact Material Forming Liquid sloshing

Impact on water/free surface flow Heart Valve opening

Flow in porous media Industrial Hydraulics Wave interaction

ESI Group 21

Space Debris Im 'act Simulation

References: ESNESTEC, Alenia Spazio

ESI Group

I Kernel approximation

f(x)= ff(x')w(x-x',h)dx'

Vf(x) = ff(x')VW(x-x', h)dx' Particle approximation N :

_L fW(x-x,h)

i=i

Pi)

=

_-x,h)

Ji Pj

ESt Group

> Smoothing function

V' _{Normalization;}

JW(x x',h)dx'=1

Compactly supported

W(x-x')=O

Delta function propert

limW(x- x',h)=ö(x-x')

h - Smoothing length W-Smoothingfuncdon j illustration of a smoothing function a12 [JÈsIGROUP

sp

sc Cocep

IFESIGROUP

Coustrìincthg smoothing functh»D

Constructing smoothing function

The default smoothing function is the cubic spline W4: W(r,h) = C*(1. - 1.5*x**2 + .75*x**3) _{if x < i}

C*O.25*(2 - x)**3 _{if I <x <2}

O.

ifx>2.,

where x=r/h, with the smoothing length h.

ESI Group

Eoup

Fluid Flow Equations

Cäniervation of Mass

dp

t.

Conservation of Momentum

dv

_t-..

_(pj

p

--=m+-Conservation of Energy

Equation of State

_1f

1

L\ PiI

ESI Group

- y)

viwii

13

1.2 0.8 0.6 0.4 0.2 0 0.5 O.Oaum, Kw,wt 1.5 2 2.5 .01 0.2 03 .0.4 .05 06 .5 5

ESI Giou

° Artificial Viscosity

2

/

Ci+Cj

+ 2

+

M3.)

Dissipation term within Governing Eq.

= -

_{( +;}

₊

_H)

=

mi(++iiii)(vi_v).ViWii

ESI Group 27

dv dt

Speca for Shocks

+

h.\(vi_vj).(ri_')) o

f

v _{Conservation equation}

Dp_

&w° Dt Dvcr_1aoe Dt

pa

De O a Dt

I

0.aß

afi .aß

ESI Group

(vv).(rr)<O

(vv).(rr) O

r

S eqmtti

2(V.v)5' &xa _a 3 í28

14

sp foruao or the N-S equat

Density Momentum Energy Strain rate p, f___., pi+pJ Dz ,m1

.LfltJ(I7(.vf)

Meí +J'j Wi Pipi af =

±m

.(JJ-+!L)!i+m (& Dr _{' p p2 f í?} Pj2 r Pi+Pj (fifi)aWJ/IÇ9 Dt 2 _PiPj

' ai

2p,

2f!m (!+!L)(vfl .vL+..&_efl

Dr 2 _{'? p} '

a(

_2p, £: ₌ .V,W,J)Ö" V' Constitutive modeling (Jaumann rate)

V' Strain rate and Rotation

rate

V' _{von Mises flow stress and}

von Mises rule

ESI Group j.aß

-

-=Gë i (a 21è ax° R«8 21,ax ar J = jafi..c1fi Tt;e jJ/3J2

cj5

ESI GROUP

RiI1ae& wth

e1I

ESIGroup 29

I'ESI GROUP

SPH for material with strength

y' Discretized equations

ESI Group

SPH approximations in a two-dimensional space with a circular support domain. ,.

sigoup

_{PAMCRASHI SPH}

_{- Features}

Standard Monaghan formulation mcl.

deviatoric strength.

Cartesian coordinates in i D, 2D, 3D. Choice of momentum formulations. Choice of smoothing kernels.

Two types of NN search. Variable smoothing length.

Artificial viscosity: standard FE or M-G Anti-crossing force option.

Symmetry planes

ESI Group (32

IESIGRoup PAM-CRASHISPH _- Features (2)

SPH - Features (3)

Moving Least Squares option (order O or 1) Special version for axial symmetry

Special version for porous media flow and two-phase flow (coupled to finite element solution)

ESI Group

17

Material models: JWL(detonation),

Hydrodynamic-EP, Johnson-Cook, SESAME Lib.,Mumaghan

Free material surface correction. Material interface treatment.

Coupling to PAM-SOLID FE through contact algorithms.

Particle generation from solids ¡n generis Post-processing by standard PAM-VIEW.

Advantages

a Lagrangian method suitable for large deformations of solids, liquids and gas.

Pre&post-processing same as for PAM-SOLID FE

Straightforward coupling to finite elements. Proven capability for Hyper-velocity impact and ballistic applications.

Suitable for liquids with free surlaces or

interfaces (sloshing and mixing) a Fluid-structure interaction (coupling)

ESI Group

Disadvantages

V' Comparatively lower accuracy; V Boundary deficiency;

V' Particle inconsistency; V Tensile instability.

ESI Group 36

Notable modifications

ESI Group y' _{Monaghan XSPH (anti-crossing)} d v+et m

(

_{Liu W. K.'s modification (RKPM, 1996)}

V Kuhnert's FPM (with _{ESI-Group...)} I Chen J. K.'s correction (CSPM, 1999)

I Monaghan's tensile stability modification (2001) y' Liu M. B.'s generalization (FPM, ₂₀₀₃₎

I

Others (MLSSPH, ASPH, etc.)

SPH Apphcatìon Example

Using Smoothed Particle Hydrodynamics for the water

ESI Group 38

The example of a bursting dam has been given by Monaghan, Bonet and Hyncik.

A rectangular column of water is confined between a

vertical wall and the floor. At t=O the gate is removed instantaneously and the water is allowed to collapse

under gravity,

The SPH simulation is performed in 2D with 3249 particles, using the Murnaghan model for the liquid. The results are compared against the experiments by

Martin and Noice, and against the SPH simulation by Monaghan (1994) ESI Group i 39 Contours of the horizontal velocity at various times

Bursting dam

ESI Group 1 40

20

!Eao

Bursting dam

cied dip1.et a

Bursting dam

.35 crtst'8pfl eBU1tB daa.fctaap. dLa daa.fctIaaghan 0H Z I-423 : : 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.0 ca1ed t1 ESt Group

Fluid Mixin

Mixing of water at different densities

under gravity

ESI Group (42)

PAM-CRASH Contact treatment: Adding dynamic

connectivity between a node and an element

Penalty method

Fluid-structure interaction

ESI Group TN (,JA _jB).jA Sfl = f (5T o}dV -sri + a frc ö(7N)2d1' = O

22

PAM-CRASH FE contact interface: Nodes to Surface: (Master-Slave, node to segment) Surface to Surface: (Master-Slave, segment to segment)

It is also possible to tie a node to a surface.

Fluid-structure interaction

Water entry of cylinders

Aircraft ditching Helicopter drop Bird strike Cardiovascular flow í oup

23

IESIGROUP

Fluid-structure interaction

SPH Application Example

Car entering water pool

24

SPH (Smooth Particle Hydrodynamics)

Benchmark test of car vs. water-filled barrier

courtesy H-Y Clzoi - Hong-1k University, Seoul, Korea

ÈsI GROUP

'-l

--:

Fuel sloshing

9

Fluid

SPH and FEM for ship hydrodynamics