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 Allrights rightsreserved. reserved. Fluid-structure Interaction by the mixed SPH-FE Method with Application to Aircraft Ditching Outline • • Introduction Computational approach • • • Innovations • • • • • • • SPH Coupling with structures Pressure correction Particle regularization Damping Initial particle distributions Periodic boundaries Guided Ditching Tests Conclusions & Perspectives Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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. Copyright © ESI Group, 2011 All rights reserved. Coupling of FE and SPH VPS/PAM-CRASH Contact treatment: Adding dynamic connectivity between a node and a contact segment Copyright © ESI Group, 2011 All rights reserved. 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. Copyright © ESI Group, 2011 All rights reserved. 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. Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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) Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. Damping zone Wedge impact with damping zone near the impact region Contour of the horizontal displacements at the final state for the damping case. Copyright © ESI Group, 2011 All rights reserved. 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) Copyright © ESI Group, 2011 All rights reserved. Non-Uniform Initial Particle Distributions Proposed Solution Weighted Voronoi Tessellation (WVT) Distribution of simulation smoothing(2D) length (2D) Filling Fast and easy to use Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. Non-Uniform Initial Particle Distributions Proposed Solution Weighted Voronoi Tessellation (WVT) Distribution of smoothing length (3D) Copyright © ESI Group, 2011 All rights reserved. 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) Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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…) Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. High-Speed Camera @ 5400 fps Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. GDT selected Results Selected Results – Force Z 10o 30 – 40 – 46 m/s ALU 15 mm Copyright © ESI Group, 2011 All rights reserved. GDT selected Results Selected Results – Force Z 6o 40 m/s ALU 0.8 mm z x Volume cut of trolley & SPH domain Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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] Copyright © ESI Group, 2011 All rights reserved. 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 Copyright © ESI Group, 2011 All rights reserved. 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. Copyright © ESI Group, 2011 All rights reserved. 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.
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