Campbell, J

De Vuyst, T

Djordjevic, N

Hughes, K

Vignjevic, R

Brunel University Research Archive

Modelling Transient Fluid Loading on Flexible StructuresKevin HughesJames CampbellTom De VuystRade VignjevicNenad DjordjevicMAFELAP CONFERENCEThe Mathematics of Finite Elements and Applications 14 - 17 June, 2016Brunel University London Overview Introduction / need for Fluid-Structure Interaction codes SPH Overview Contact in SPH Water Modelling Helicopter crash on water Fluid Sloshing• Acknowledgements:o Rade Vignjevic, James Campbell, Tom De Vuyst, Nenad Djordjevic o Omkar Gulavani, David Munro, Lampros Papagiannis, Marcos Acin, Clement Legriel, Esther Comellas, Slavisia Milisavljevic, Luis Rubio Aparici, Paula Serrador, Maria Beneto Garcia, Paul-Andre SomazziModelling Transient Fluid Loading on Flexible Structures 2Brunel University London Extreme fluid-structure interaction There are a number of engineering problems that combine transient non-linear structural and fluid behaviour. Modelling the behaviour present in these events is challenging:• Large structural deformation, including non-linear transient behaviour and potentially material failure,• Complex fluid behaviour,• Fluid-structure interaction3Image source:  http://www.btinternet.com/~derek.mackay/offshore/images/vessels/Modelling Transient Fluid Loading on Flexible StructuresAirbus Ditching in Hudson – Jan 2009Brunel University London Structural modelling- Case Study: Helicopter Impact on water4Differences in load transmission during a “flat” hard surface impact (left) and a fluid surface (right) at 8 m/s [1, 2].[1] Hughes K, Vignjevic R, Campbell J, “Experimental observations of an 8 m/s drop test of a metallic helicopter underfloor structure onto a hard surface: Part 1”, in Proc. IMechE Part G: J. Aerospace Engineering, 221/5 (2007), 661-678[2] Hughes K, Vignjevic R, Campbell J, “Experimental observations of an 8 m/s drop test of a metallic helicopter underfloor structure onto water: Part 2”, in Proc. IMechE Part G: J. Aerospace Engineering, 221(5) (2007), 679-690Modelling Transient Fluid Loading on Flexible StructuresBrunel University London Water modelling• Accurate prediction of structural response is not only limited by structural model itself, but also the ability of the model to accurately describe structural loads arising from fluid.• Several approaches available: Semi analytical fluid models: Von Karman/Wagner theory and developments.  Low cost, does not allow non-linear structural response Lagrangian FE: limited ability to treat large fluid deformation.(Timestep and stability issues) Meshless (SPH):  Mathematical basis of method and treatment of boundary conditions conditions still requires development. Meshed CFD: Known by various names – ALE, CEL, … Based on established CFD methods.  Robust treatment of interaction between fluid and structural solver challenging, as structural model arbitrarily intersects fluid mesh. 5Hughes K, Vignjevic R, Campbell J, De Vuyst, T, Djordjevic N, Papagiannis L“From aerospace to offshore: Bridging the numerical simulation gaps – Simulation advancements for fluid structure interaction problems”, International Journal of Impact Engineering 61 (2013) 48- 63Modelling Transient Fluid Loading on Flexible StructuresBrunel University London Example FSI Case Studies6DambreakFloating bodiesSloshingImpact on water / aircraft ditchingBirdstrike / Ingestion into aircraft enginesModelling Transient Fluid Loading on Flexible StructuresBrunel University London Smoothed Particle Hydrodynamics  (SPH) SPH is a numerical technique for the approximate integration of the governing equations of continuum mechanics.  It is a meshless Lagrangian method that uses pseudo-particle interpolation to compute smooth field variables. Solution variables are held at the nodes (particles), which move with the material.◦ SPH form of the velocity-gradient tensor calculation◦ SPH form of momentum equation7 j j i ijji jm    v v v Wx2 2jii j ijj i jm        σσa WModelling Transient Fluid Loading on Flexible StructuresBrunel University London Coupled FE-SPH Contact The boundary of the SPH domain is not well defined. A contact potential based on the kernel function is used, with FE nodes interacting with SPH particles.  Provides a simple contact treatment allowing large deformations, including material failure. A commonly used alternative to this approach is based on mesh node-to-surface contact algorithms.8),()()( 1hWpWWKnmmf jinavgnjijjiic xxxx De Vuyst, T, Vignjevic R, Campbell J, “Coupling between Meshless and Finite Element Methods”, International Journal of Impact Engineering 31(8):1054-1064, September 2005FE nodesSPH ParticlesModelling Transient Fluid Loading on Flexible StructuresBrunel University London Coupled FE-SPH Contact9De Vuyst T, Vignjevic R, Campbell J, “Coupling between Meshless and Finite Element Methods”, International Journal of Impact Engineering 31(8):1054-1064, 2005• Structure represented with FE mesh• Fluid represented as SPH domain• Use of different ‘best’ solvers for different domains within a single problem• The advantage of this  approach is that contact between the fluid and structure can be simply and robustly treated.  • (Potential for allowing the simulation of fluid ingress following structural failure).Fluid Sloshing in 2DDe Vuyst, “Hydrocode Modelling of Water Impact”, PhD Thesis, Cranfield University, 2003Modelling Transient Fluid Loading on Flexible StructuresDe Vuyst T, Campbell J, Vignjevic R, "A Frictionless Contact Algorithm for Meshless Methods" Computer Methods in Engineering and Science 13(1): 35-48, 2006. Brunel University London Water modelling in SPH Under low velocity (< ≈ 102 m/s) loading conditions the water can be considered incompressible.  However the SPH solver assumes the fluid is compressible, therefore an equation of state (EOS) is required. The Murnaghan EOS is used: The parameters are chosen to give the fluid an artificially low speed of sound, but keep density changes small.  Potential of significant computational cost reduction via CFL condition. This is valid provided the flow velocities are small compared with the speed of sound.10  10BPModelling Transient Fluid Loading on Flexible StructuresBrunel University London Helicopter impact on water A full scale drop test of WG30 fuselage on water was performed within the FP5 CAST programme at CIRA in October 2001.11Modelling Transient Fluid Loading on Flexible StructuresBrunel University London Full scale helicopter simulationExtreme Fluid-Structure Interaction 12Structural Model: 366,194 shell elements 5,206 beam elementsSPH Model 292,800 SPH particles Ran to 87ms in 5 days on 8CPUsFE Model• 234,845 solid elements• Ran to 40ms (negative volume) in 16 CPUs (3.5 days)Vertical Velocity Contours(Blue = -8ms-1, Red = +1ms-1)Brunel University London AccelerometersA3                                                             A13- centre seat railA17 – starboard seat rail13‐10‐5051015202530350 0.02 0.04 0.06 0.08 0.1Z‐Acceleration (g)Time (s)ExperimentFE‐SPHFE‐FE‐200‐10001002003004000 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Z‐Acceleration (g)Time (s)ExperimentFE‐SPHFE‐FEModelling Transient Fluid Loading on Flexible StructuresBrunel University London Sloshing Validation Case StudyUndeformable tank• Excitation amplitude = 0.02m• Excitation Frequency = 0.458 Hz• Water depth = 0.03m• Test duration = 12s• Normalised wave height at centre and tank wall• Reaction force at load cell• Dynamic Relaxation -> Pressure distribution14H. Yeh, J. Yu, S. Gardarsson D. Reed, "Tuned Liquid Dampers Under Large Amplitude Excitation," Journal of Engineering Mechanics, vol. 124, 1998.Modelling Transient Fluid Loading on Flexible StructuresBrunel University London Sloshing Validation Case Study152D SPH model: SPH for tank and fluid (13K particles) Quasi-incompressible viscous fluid Particle-to-particle contact Pressure initialisation (dynamic relaxation) 5 SPH particles in tank thickness Parametric Studies performed:◦ Spatial Resolution (20-50 particles depth)◦ Artificial Viscosity◦ Density Calculation (MLS)◦ Contact Stiffness◦ Wave Height Sensor location3D FE-SPH model: Box modelled with FE Particle-to-surface contact 12 days on standard pcModelling Transient Fluid Loading on Flexible StructuresBrunel University London • (CAVEAT:  No information on filtering applied in test, or positioning of wave sensor location).• Wave heights near tank wall are far less pronounced for 3D results (fewer isolated particles “flying off”), and attributed to differences in contact algorithm and end constraints. a) tank wall b) tank centreTest – Analysis comparison- Wave Height16Modelling Transient Fluid Loading on Flexible StructuresBrunel University London Test – Analysis comparison- Sloshing forceThe magnitude, frequency of the waves (and forces) against time and tank displacement is captured accurately17Brunel University London Summary Coupling a meshless fluid model to a finite element structural model provides a powerfulapproach in simulating complex fluid-structure interaction problems. Permits investigations into predicting free surface motion and removes issues of (mesh)instabilities, but models are computationally expensive For sloshing, coupled approach is capable of accurately predicting fluid motion / time histories Further work required for impact cases, as divergence between test could be due to:• Limitations in structural model (->need for non-linear behaviour under dynamic fluid loads)• Limitations in fluid modelling (is Physics represented correctly?)• (Or a combination of both effects!)• Reliability / repeatability issues in capturing high, amplitude pressureso Van Nuffel et al, “Study on the Parameters Influencing the Accuracy and Reproducibility ofDynamic Pressure Measurements at the Surface of a Rigid Body During Water Impact”,Experimental Mechanics 53(12), 201218Modelling Transient Fluid Loading on Flexible Structures

Modelling Transient Fluid Loading on Flexible Structures

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Modelling Transient Fluid Loading on Flexible Structures

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