Fluid-structure Interaction by the mixed SPH-FE
Method with Application to Aircraft Ditching
Paul Groenenboom
ESI Group
Delft, Netherlands
Martin Siemann
German Aerospace Center (DLR)
Stuttgart, Germany
Conference on SPH and Particle Methods for Fluids and Fluid
Structure Interaction
Lille, France, 21.-22.01.2015
Copyright © ESI Group, 2011.
2011 All
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Fluid-structure Interaction by the mixed SPH-FE
Method with Application to Aircraft Ditching
Outline
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Introduction
Computational approach
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Innovations
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SPH
Coupling with structures
Pressure correction
Particle regularization
Damping
Initial particle distributions
Periodic boundaries
Guided Ditching Tests
Conclusions & Perspectives
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Computational Approach: SPH
The SPH solver within VPS (ESI-Group) is based on the ‘standard’
weakly-compressible SPH algorithm
There are many innovative extensions to improve accuracy and
performance, in particular for fluid-structure interaction simulation
The SPH solver is fully integrated within the explicit Finite Element
Method (FEM) of VPS
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Coupling with structures
SPH is suitable to model violent flow of water.
FEM is best suited to model the (aircraft) structure
A hybrid SPH-FE approach allows to use ‘best of both worlds’ to
model fluid-structure interaction.
VPS/PAM-CRASH software from ESI-Group
The penaly-based contact algorithm between FE and SPH allows
to model fluid-structure interaction.
This approach combines accurary with good CPU performance.
For regions with limited fluid displacements it is possible to use
finite elements for water.
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Coupling of FE and SPH
VPS/PAM-CRASH Contact treatment: Adding dynamic connectivity
between a node and a contact segment
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Coupling of FE and SPH
Ditching simulation of an Airbus 321 model (Courtesy of DLR) involves
sliding interface contact between particles and the aircraft model, and
tied contact of particles with the brick elements for the water.
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Coupling of FE and SPH
It is possible to include tension by definition of a ‘seperation stress’ once
contact has been established – this can model suction effects.
For aircraft ditching suction effects are important for the aircracft
kinematics.
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Innovations: Pressure Correction
Necessity and Requirements
Standard WC-SPH method poor pressure distributions (highfrequency oscillations in time and space)
Established pressure correction methods like density re-initialization
by Shepard filtering and Rusanov flux were recently implemented in
the SPH solver of VPS/PAM-CRASH
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SPH Pressure Correction Methods
Density Re-Initialization using Shepard
Filtering
Density re-initialization method which was derived from an
interpolation technique initially published by Shepard in 1968
SPH notation for the modified density
Since for WC-SPH the pressure is derived from an equation-ofstate, the Shepard filter directly influences the pressure distribution.
The density field is periodically re-initialized at user-defined cycle
frequency f with recommended values of 20 cycles
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SPH Pressure Correction
Rusanov Flux
The Rusanov correction is efficient and robust, but also somewhat
diffusive, numerical approximation to solve Riemann problems
1st order accuracy compared to 2nd order accuracy of Riemann flux
Modified continuity equation
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SPH Pressure Correction Methods
Exemplary effects on pressure field
Pressure field at t = 30ms in 2D NACA flat plate test case
Standard WC-SPH
(no correction)
Shepard filtering
f = 20 Hz
Rusanov flux
ε = 0.5
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Pressure correction: Test Case
Two-Dimensional Rigid Wedge Vertical Impact
Experimental results from Battley et al.
Vertical impact (3 m/s , const.)
Pressure results available for three positions along
center line (keel-chine)
Numerical model
Symmetry
Rusanov flux with ε = 0.5
Smoothing length h = 2 mm (810 000 particles)
Good correlation of peak pressure values
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Innovations: Particle Regularization
During flow or deformation the particle distribution may display some
irregularities with as consequence:
Pressure oscillations
Clumping of particles
Numerical (tension) instability
Counteract by particle regularization methods which aim to yield a
more regular distribution
Effect should be local
Conservation of mass, momentum, and energy
Numerical stability
No significant increase of computational costs
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Particle Regularization
Test case for floating boxes with the VJA algorithm
Particle distribution with contours of the vertical displacement at the final
state for VJA2 (partial view)
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Innovations: Damping zone
Absorbing boundary conditions for pressure are
available.
Absorbing boundary conditions for surface waves
have to be different as they involve gross motion
of the material.
The proposed algorithm is nodal damping in
specific regions
Tested for wave propagation and impact
Damping volume
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Damping zone
Wedge impact with damping zone near the impact region
Contour of the horizontal displacements at the final state for the damping case.
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Non-Uniform Initial Particle Distributions
1.
2.
Define suitable initial particle distributions for SPH fluid impact and flow
simulations.
Two topics of special interest:
Particles of non-uniform size
Filling of arbitrary volumes
Proposed Solution Weighted Voronoi Tessellation (WVT)
volume ratio 1:9
Uniform initial distribution (2D)
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Non-Uniform Initial Particle Distributions
Proposed Solution Weighted Voronoi Tessellation (WVT)
Distribution
of simulation
smoothing(2D)
length (2D)
Filling
Fast and easy to use
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Non-Uniform Initial Particle Distributions
Proposed Solution Weighted Voronoi Tessellation (WVT)
0.05 m/s
ca. 1800 ms
g
Distribution of smoothing length (2D)
Gravity load test case (2D) – instable;
Color denotes velocity magnitude
Fast and easy to use
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Non-Uniform Initial Particle Distributions
Proposed Solution Weighted Voronoi Tessellation (WVT)
0.02 m/s
ca. 10 000 ms
g
Distribution of smoothing length (2D)
Gravity load test case (2D) – stable;
Color denotes velocity magnitude
Fast and easy to use
Stable under gravity load
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Non-Uniform Initial Particle Distributions
Proposed Solution Weighted Voronoi Tessellation (WVT)
Distribution of smoothing length (3D)
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Non-Uniform Initial Particle Distributions
Proposed Solution Weighted Voronoi Tessellation (WVT)
z
y
x
Cutting plane
Distribution of smoothing length (3D)
Initial results for guided ditching
simulation (3D)
Significant CPU time savings (>10x through WVT)
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Innovations: Periodic boundaries
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Allows to re-enter particles that have reached a boundary on the opposite side.
Provides a significant reduction of the number of particles required for a moving
object in contact with fluid.
Extended to incorporate translating domains
Extended to allow for inflow with undisturbed flow conditions
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Ditching
aircraft emergency situation that ends with planned impact of the
aircraft on water
Involves complex phenomena (water impact, suction, spray,
cavitation, aerodynamics, structural deformation)
Difficult to test (motion control, scale effects, aerodynamics)
Challenge for simulation (FSI, free surface…)
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Guided Ditching Tests
Test setup (at INSEAN in Rome) :
Simple geometries in aerospace design:panels with skin panel dimensions and thickness
Represent high inertia of aircraft : guided motion
Full-scale ditching conditions (representative impact velocities): sling shot system
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High-Speed Camera @ 5400 fps
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Guided Ditching Tests
Challenges for SPH Model
Large fluid domain due to relative high
forward velocity
Drivers for run time
Fine particle distribution needed to
allow for accurate results
Objectives
60 m/s
- Reduce amount of particles (run time)
- Allow for finer particles in proximity of impacting structure
100 m
5m
10 m
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GDT selected Results
Selected Results – Force Z
10o
30 – 40 – 46 m/s
ALU 15 mm
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GDT selected Results
Selected Results – Force Z
6o
40 m/s
ALU 0.8 mm
z
x
Volume cut of trolley & SPH domain
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GDT selected Results
Selected Results – Strain
6o
40 m/s
ALU 3 mm
S4x
STRAIN YY
3x amplified
S4
S4y
S4
x
y
ESIZE ~10 mm
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GDT selected Results
Selected Results – Strain
6o
40 m/s
ALU 3 mm
STRAIN XX
3x amplified
S1x
S1
STRAIN YY
3x amplified
S1y
S1
S1
x
y
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Suction Force
CN235 sub-scale model
Pressure [Pa]
Pressure [Pa]
Good correlation of pressure results between test and simulation
(overpressure and suction regions)
Time [s]
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Suction Force
CN235 sub-scale model
Comparison suction contact model ON (top) and OFF (bottom)
Suction model OFF
Pitch Attitude [deg]
Suction model ON
Time [s]
Test (No. 25)
Suction model ON
Suction model OFF
Good corellation between test and simulation with suction model ON
High influence on aircraft pitch kinematic
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Conclusions
SPH-FE approach suitable to simulate deformable aircraft ditching
Significant reduction in CPU cost through enhanced modeling
features
Kinematic and structural behavior in good agreement (velocity, force,
strain)
Hydrodynamic behavior (pressure results) still very noisy
The relevance to include suction has been demonstrated.
A simulation study has been presented to demonstrate the
capabilities of the approach.
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Perspectives
•
Further CPU reduction by optimised particle distribution and combination
of SPH with elements for water
•
Transfer knowhow to flexible full aircraft ditching simulation
Bottom view on rear fuselage zone
Copyright © ESI Group, 2011 All rights reserved.
Fluid-structure Interaction by the mixed SPH-FE
Method with Application to Aircraft Ditching
Thanks for your attention
ACKNOWLEDGEMENT
Most of the work presented in this paper has received funding
from the European Commission’s 7th Framework Programme
under grant agreements no FP7-266172 (project SMAES –
Smart Aircraft in Emergency Situations).
Paul Groenenboom
[email protected]
Copyright © ESI Group, 2011.
2011 All
Allrights
rightsreserved.
reserved.