A Novel Approach to High Speed Collision Avril Slone University of Greenwich
Motivation High Speed Impact Currently a very active research area. Generic projectile- target collision 11 th September 2001.
Projectile-Target Collision Objective Modelling of high speed impact - collision Traditional FE contact-pair - definition problem dependant Lagrangian approach efficient for small strain. Difficulties Penetration mesh distortion - problematic Re-meshing automatic mesh tools CPU Complex cases need to be run in parallel but re-meshing affects the ability to parallelise
Computational Modelling of Collision University of Greenwich Spatial Discretisation Approach Lagrangian Finite element, most commonly used approach for structural deformation Fits mesh to projectile and target Mesh deformed in line with projectile and target deformation. Large distortion - necessary to remesh Computationally expensive and difficult to parallelise efficiently Eulerian Commonly used for CFD applications Fixed mesh through which projectile flows Requires accurate free surface algorithm to track deformation.
Governing Equations Coupled CFD - Heat Transfer - CSM Non-Newtonian viscosity model Plastic Norton Hoff law Heat Transfer - Friction between projectile and target. Free Surface - Scalar Equation Method Donor Acceptor scheme. Linear Elastic Structure
Generalise Newtonian fluid Momentum Conservation Continuity Equation Governing Equations - CFD t ( ρ ui ) + ρuui = p + [ F( & γ ) ui ] + Sui Viscosity model For Newtonian fluid i.e. Navier Stokes flow Viscosity model for non-newtonian fluid ρ + ρu t = 0 F( & γ ) = µ
Constitutive Equation - Viscosity Power Law - simplest viscosity model. F ( ) ( m 1) & γ = nγ& University of Greenwich where n is consistency of material and m is strain rate sensitivity index, m < 1.0, pseudo plastic fluid. The rate of strain tensor D, defined as 1 D= 2 ( u + u T ) The shear rate is given by Norton Hoff Law γ& = 2trD where tr is trace operator and D is rate of strain tensor 2
Governing Equations Heat Transfer Significant factor in deformation process. Energy entered into thermal equation as: t ( ρc T ) + ( ρc ut ) = ( k T ) + r& p p Temperature development dependant on energy dissipation at rate: r& = βσ & ε ij β is proportion of plastic deformation energy dissipated as heat in solid material. ij ij
Governing Equations Free Surface Scalar Equation Method marker f used to track free surface in fluid. FV discretisation: φ + t Advection Schemes Van Leer Donor acceptor smearing Gala Algorithm density gradients? face Aface ( u φ ) = 0 ( u n) φ face face
Van Leer Method The value of f at the face calculated as: φ face 1 φ = φu + ud face 2 n ( d ( u n) t) φ/ ν dependant on value of φ for upwind-upwind element Stable but susceptible to smearing
Donor Acceptor Method Upwind donor, downwind acceptor The value of φ at the face calculated using: where cr = u n t and face Less stable than van Leer BUT less smearing φ d Cφ = max 0.0, dφ = max 0.0, min,1. 0 cr = min crφ + Cφ φ φ AD, d A A V ( 1.0 -φ ) ( ) AD cr - 1.0 -φd VD D
Illustration of Advection Schemes Water-filled Hollow Square Dimensions width 1.6m, height 1.5m Mesh 2160 hexahedral elements Data Density fluid 1.0kgm -3 projectile and target 1000.0kgm -3 Gravity 10ms -2 Time step 0.001 seconds
Free Surface Donor Acceptor, t=0.59secs Van Leer, t=0.59secs
Target Problem - 3D projectile Entire domain (lwd) 15m x 10.2m x 10.2m Mesh 611,712 Hexahedral elements 634,151 Nodes Projectile geometry defined by location 2.0 x 0.2m, square cross section Constant cross section length1.6m Nose tapered along length from 1.6 2.0m Target positioned at 12m of entire length Dimension 3m width depth length University of Greenwich
Velocity Air and Target Static Projectile 100ms -1 Initial Conditions Temperature Air and Target ambient Projectile 200 o C above ambient
Specific Heat, c p kj(kgk) -1 1000.0 792.6 792.6 University of Greenwich Material Data Air Projectile Target Density, ρ, kgm -3 1.0 2000.0 3000.0 Thermal Conductivity, k W(mK) -1 0.003 180.0 180.0 Viscosity, µ kg m -1 s -1 1x10-6 m=0.6 Norton Hoff n = 20KPas -m Norton Hoff m = 0.6 30KPas -m
Free Surface iso-surface t = 0.015 to 0.075
Temperature t=0.015 to 0.075
Pressure t = 0.015 to 0.075
t = 0.05625 to 0.09375 seconds Effective Strain Rate University of Greenwich
Effective Stress in Target University of Greenwich 1. T = 0.06 secs 2. T = 0.0675 secs 3. T = 0.11625 secs
Parallel Simulation Itanium IA 64 cluster running Linux OS Eight nodes with two 733MHz processors per node Each with 2Gb memory & 2Gb swap University of Greenwich No of Simulation Time Total Run Time Processors Hours Speed up Hours Speed up 1 338.791 1.0 339.012 1.0 2 134.444 2.52 134.932 2.52 4 64.256 5.27 64.946 5.22 8 35.356 9.58 36.212 9.36 10 32.455 10.44 33.383 10.02 12 29.622 11.43 30.562 11.09
Parallel Simulation Timings University of Greenwich
Parallel Partitions University of Greenwich 2 4 8 16
Future Work University of Greenwich Distinguish between regions of high and relatively low stress in the target. High stress plastic fluid approach Low stress - conventional FE Lagrangian structural dynamics approach. Identification of material behaviour identified by its effective stress level - indicated by a marker. Parallelisation of the more complicated procedure involves multi-phase partitioning, exploited through the JOSTLE partitioning tool. Compare our predictions with the more conventional Lagrangian approaches. Reflecting the numerical performance, computational effort and relative scalability. Modelling of melting and re-solidification. Impact upon the integrity of the target structure.