Fluid-structure Interaction by the mixed SPH-FE Method with Application to Aircraft Ditching

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Delft, Netherlands Martin Siemann German Aerospace Center

Methods for Fluids and Fluid Structure Interaction Lille,

1 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, Copyright ESI Group, All rights reserved.

Introduction Computational approach SPH Coupling with structures Innovations Pressure correction Particle regularization Damping Initial particle distributions

2 Introduction Computational approach SPH Coupling with structures Innovations Pressure correction Particle regularization Damping Initial particle distributions Periodic boundaries Guided Ditching Tests Conclusions & Perspectives Fluid-structure Interaction by the mixed SPH-FE Method with Application to Aircraft Ditching Outline

3 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

4 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.

5 Coupling of FE and SPH VPS/PAM-CRASH Contact treatment: Adding dynamic connectivity between a node and a contact segment

contact between particles and the aircraft model, and

6 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.

7 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.

8 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

9 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

10 SPH Pressure Correction Rusanov Flux The Rusanov correction is efficient and robust, but also somewhat diffusive, numerical approximation to solve Riemann problems 1 st order accuracy compared to 2 nd order accuracy of Riemann flux Modified continuity equation

NACA flat plate test case Standard WC-SPH (no

11 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

Pressure correction: Test Case Two-Dimensional Rigid Wedge Vertical Impact Experimental results from Battley et al. Vertical impact (3 m/s, const.

12 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 ( particles) Good correlation of peak pressure values

13 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

14 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)

15 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

16 Wedge impact with damping zone near the impact region Damping zone Contour of the horizontal displacements at the final state for the damping case.

17 Non-Uniform Initial Particle Distributions Define suitable initial particle distributions for SPH fluid impact and flow simulations. Two topics of special interest: 1. Particles of non-uniform size 2. Filling of arbitrary volumes Proposed Solution Weighted Voronoi Tessellation (WVT) volume ratio 1:9 Uniform initial distribution (2D)

18 Non-Uniform Initial Particle Distributions Proposed Solution Weighted Voronoi Tessellation (WVT) Distribution Filling of simulation smoothing (2D) length (2D) Fast and easy to use

19 Non-Uniform Initial Particle Distributions Proposed Solution Weighted Voronoi Tessellation (WVT) 0.05 m/s ca ms g Distribution of smoothing length (2D) Gravity load test case (2D) instable; Color denotes velocity magnitude Fast and easy to use

20 Non-Uniform Initial Particle Distributions Proposed Solution Weighted Voronoi Tessellation (WVT) 0.02 m/s ca ms g Distribution of smoothing length (2D) Fast and easy to use Gravity load test case (2D) stable; Color denotes velocity magnitude Stable under gravity load

21 Non-Uniform Initial Particle Distributions Proposed Solution Weighted Voronoi Tessellation (WVT) Distribution of smoothing length (3D)

22 Non-Uniform Initial Particle Distributions Proposed Solution Weighted Voronoi Tessellation (WVT) y z x Cutting plane Distribution of smoothing length (3D) Initial results for guided ditching simulation (3D) Significant CPU time savings (>10x through WVT)

Provides a significant reduction of the number of particles required for a moving

23 Innovations: Periodic boundaries 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

cavitation, aerodynamics, structural deformation) Difficult to test (motion

24 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 )

thickness Represent high inertia of aircraft : guided motion

25 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

26 High-Speed 5400 fps

27 Challenges for SPH Model Guided Ditching Tests Large fluid domain due to relative high forward velocity Fine particle distribution needed to allow for accurate results Objectives Drivers for run time 60 m/s - Reduce amount of particles (run time) - Allow for finer particles in proximity of impacting structure 100 m 5 m 10 m

28 GDT selected Results Selected Results Force Z 10 o m/s ALU 15 mm

29 GDT selected Results Selected Results Force Z 6 o 40 m/s ALU 0.8 mm z x Volume cut of trolley & SPH domain

30 GDT selected Results Selected Results Strain 6 o 40 m/s ALU 3 mm S4x S4 STRAIN YY 3x amplified S4 S4y ESIZE ~10 mm y x

31 GDT selected Results Selected Results Strain 6 o 40 m/s ALU 3 mm STRAIN XX 3x amplified S1x S1 STRAIN YY 3x amplified S1y S1 S1 y x

32 Suction Force CN235 sub-scale model Good correlation of pressure results between test and simulation (overpressure and suction regions) Pressure [Pa] Pressure [Pa] Time [s]

Suction Force CN235 sub-scale model Comparison suction contact model ON (top) and OFF (bottom) Suction model ON Suction model OFF Pitch Attitude [deg] Good

33 Suction Force CN235 sub-scale model Comparison suction contact model ON (top) and OFF (bottom) Suction model ON Suction model OFF Pitch Attitude [deg] Good corellation between test and simulation with suction model ON High influence on aircraft pitch kinematic Time [s] Test (No. 25) Suction model ON Suction model OFF

34 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.

elements for water Transfer knowhow to flexible full

35 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

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

36 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 FP (project SMAES Smart Aircraft in Emergency Situations). Paul Groenenboom pgr@esi-group.com Copyright ESI Group, All rights reserved.

SPH: Why and what for?

SPH: Why and what for? 4 th SPHERIC training day David Le Touzé, Fluid Mechanics Laboratory, Ecole Centrale de Nantes / CNRS SPH What for and why? How it works? Why not for everything? Duality of SPH SPH