A coherent approach to managing geometry, idealisation and meshing for simulation
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
A coherent approach to managing geometry, idealisation and meshing for simulation Emeritus Professor Cecil G Armstrong School of Mechanical and Aerospace Engineering Queen’s University, Belfast, N Ireland Email: c.armstrong@qub.ac.uk Publications: https://bit.ly/2MAsAdP Presentation to Siemens Lecture Series on Geometry and Mesh Generation 25th February 2021
Acknowledgements • Djinn • Cecil Armstrong, Adrian Bowyer, Stephen Cameron, Jonathan Corney, Graham Jared, Ralph Martin, Alan Middleditch, Malcolm Sabin, Jonathan Salmon https://bit.ly/3txpfgd • QUB Academic: • https://www.qub.ac.uk/contact/Staff-directory/ • Academic • Trevor Robinson, Declan Nolan • Recent Post Doctoral: • Chris Tierney, Flavien Boussuge flavien.boussuge@cea.fr, Liang Sun l.sun@ulster.ac.uk • Recent PhD: • Benoit Lecallard, Dimitrios Papadimitrakis, Sriharsha Sheshanarayana, Andrew Colligan, Adam Clugston • Siemens ex-QUB • Jonny Makem, Harry Fogg
Defining Simulation intent Goal • Capturing high level modelling & idealisation decisions in order to create a fit-for- purpose analysis model Equivalent geometries and meshes
Simulation Intent • Need • Move from separate structural and fluid models (structures, gas paths, external and internal air flows etc.) • To a subdivision of space into cells of simulation significance, some of which are structural, some which are fluid etc. • Maintaining a consistent, coherent description of the equivalent representations of a given region of space • Requires techniques for identifying the correspondence between different representations (geometry, mesh, surrogates, parameter sets, …) • Using geometric reasoning and relational learning to derive the equivalent representations
1. Cellular modelling Design volume divided into a non-manifold assembly of cells with simulation significance Multi-disciplinary Thin-sheet / long- slender Design geometry decomposition Structural and fluid cells Symmetry-based decomposition CRESCENDO Engine used with permission from Rolls-Royce
2. Virtual topology • No change in the underlying geometry • Abstract analysis topology: hints to mesh generator for vertices and edges to ignore • Avoids time-consuming geometric operations • Use partitioning and de-partitioning to identify analysis topology on the same geometry Detailed design Abstract geometry analysis Mesh topology Heal sliver face
Partitioning • Hard geometry e.g. to define Boundary Condition • Soft geometry e.g. to define partitions for structured meshing Partition
Partitioning for hex meshing Investigating singularities in hex meshing, Dimitrios Papadimitrakis et al., submitted for publication
3. Equivalencing • Specifying how different models represent the same region of space • Alternative geometric and analysis representations of the same cells or groups of cells • Equivalent models for different physics and fidelity Equivalent geometric and analysis models CRESCENDO Engine used with permission from Rolls-Royce
Lanyon building, Queen’s University Belfast Applications of Simulation Intent
Robust boundary condition application Boundary conditions applied Boundary conditions do not to specific faces in the model propagate to new faces Design update causes topology changes Current approach Cellular modelling approach Solid-fluid interface Interface = FLUIDA ∩ ENGINE
Re-use Simulation Intent Interfaces calculated Note: we can start with an abstract representation and add detail as the design evolves 1D beam + 0D mass Simulation Intent: • A fixed constraint at the interface of Cantilever example BEAM1 and ROW1 • BLOCK1 reduced Interfaces calculated to 0D point mass • BEAM1 3D tet meshed Different model same Simulation Intent
Lanyon building, Queen’s University Belfast Equivalent representations: decomposition into thin sheet / long slender / complex 3D regions
Geometric reasoning: Medial Axis Transform • Locus of centre of inscribed ball of maximal diameter • Provides: – Lower dimensional skeleton – Proximity and local thickness – Aspect ratios – Applications in – Dimensional reduction – Mesh generation – Detail finding and suppression
Multiple linked analysis models Tet elements Complex region Long, (yellow) Hex slender region (blue) elements 2D shell elements 1D beam elements Thin region (green) 3D Tet elements (or 0D mass and inertia + links) CRESCENDO Engine used with permission from Rolls-Royce J.E. Makem, C.G. Armstrong, T.T. Robinson, Automatic decomposition and efficient semi-structured meshing of complex solids, Eng. Comput. 30 (2012) 345–361. D.C. Nolan, C.M. Tierney, C.G. Armstrong, T.T. Robinson, Defining Simulation Intent, Comput. Des. 59 (2015) 50–63.
The problem with dimensionally-reduced models • At joints, the solution to the FE problem is of full dimension • ∴ Mixed-dimensional models, coupled using MPCs • Error estimates from implied stress jumps (adaptive model refinement) • Abstracted as equivalent joint stiffness Rel Energy Error based on Stress Ju Stepped end loaded mixed dimensl mod 0.0015 Relative energy error 0.001 0.0005 0 0.25 0.5 0.75 1 1.25 Distance per unit width to end of step Error energy/Total energy ratio R. W. McCune, C. G. Armstrong, and D. J. Robinson, “Mixed-dimensional coupling in finite element models,” Int. J. Numer. Methods Eng., vol. 49, no. 6, pp. 725–750, 2000. R. J. Donaghy, C. G. Armstrong, and M. A. Price, “Dimensional Reduction of Surface Models for Analysis,” Eng. Comput., vol. 16, no. 1, pp. 24–35, 2000.
Thick-thin decomposition • Original bodies - 6503 • Thin-sheet = 7278 bodies (~65 % of volume) • Thick = 6032 bodies • (~33 % of volume) • Number of unprocessed bodies = 3595 • (~2% of volume) • (55% of number of bodies) VESTA Engine used with permission from Rolls-Royce VESTA Engine used with permission from Rolls-Royce
Lanyon building, Queen’s University Belfast Equivalent representations: exploiting axial symmetry
Quasi-axisymmetric models – dimensional reduction • Gas turbine engines that have a lot of symmetry about the rotational axis! • Starting from facetted model project all facets of 3D model to r-z plane • Identify facets • With zero area (F1-F5) • With non-zero area (F6-F9) • Silhouette edges • Adjacent facets change area sign • Build axisymmetric profile • Correct material properties
Quasi-axisymmetric models • Automatically reduce to an axisymmetric model • Calculate shape properties • Update material properties accordingly 3D VS 2D-axisymmetric at sample points 550 3D temperatures (C) 11 8 9 14 7 10 450 5 12 13 6 350 3 1 4 15 2 250 250 350 450 550 2D temperatures (C)
Features of interest for quasi-axisymmetric models • Axisymmetric • For analytical surfaces, easy to identify those with symmetry about a given axis: cylinders, cones, spheres, tori, planes perpendicular to the axis etc • Cyclic features • If there a rotational transform to bring a given geometry to = 0? Are there similar features at multiples of ? Face classification Virtual decomposition Cyclic grouping
Minimal meshable representation • Using geometric reasoning to partition a model up into regions for which meshing strategies are known • Minimal meshable representation is the minimum CRESCENDO assembly number of cells we need to Symmetry based mesh, to mesh the entire decomposition assembly • Each different region type can be meshed using different strategies 60% - axisymmetric 28% - cyclic 5% - transition • Transition cells can be used to 2% - sweepable create meshes to join different 1% - block topology Minimal meshable meshes together 4% - residual representation CRESCENDO Engine used with permission from Rolls-Royce 10.14733/cadaps.2019.478-495
Non-planar cuts for cyclic repeats 1- Delaunay Triangulation of 2- Approximate medial edge from opposite edge features triangulation 3- Generate cut surfaces and partition Benoit Lecallard (for Jonny Makem)
28th IMR, Buffalo, NY, USA Marie Curie Individual Fellowship: MUMPS APPLICATION OF TENSOR FACTORISATION Next Generation TO ANALYSE SIMILARITIES IN CAD ASSEMBLY Digital Mock-Ups MODELS* for Multi-Physics Simulation Flavien Boussuge, Christopher M. Tierney, Trevor T. Robinson, Cecil G. Armstrong https://www.qub.ac.uk/research- centres/FiniteElementModellingGroup/Projects/ mumps/ *Best paper award, submitted to CAD
Statistical Relational Learning All relationships between entities are stored in one large tensor • 0 : “is bounded by”, e.g. face 1 is bounded by edge 24 • 1 : “is type”, e.g. face 1 is planar • 2 : “is interfacing with”, e.g. solid 1 is interfacing with solid 5 • 3 : interface “is type” (contact, can be factorized as interference, gap) e.g. solid 1 is in ≈ , ∈ 1. . contact with solid 5 The returned matrix contained the “latent variables” for all entities Adjacency matrix is the same for all slices of defines the number of common factors in Nickel, A. “A Three-Way Model for Collective Learning on Multi-Relational Data”
Retrieval of Similar Entities Entities can be compared looking at their common factors in A. Selection of an entity: solid 78 Solids k 373 559 481 78 1.0 Input78 373 1.0 481 1.0 623 559 1.0 179 0.0 788 295 0.0 194 388 889 295 889 0.0 403 724 953 968 724 0.0 179 788 0.0 = 1e-5 623 0.0 Similar entities to solid 78 953 0.0 194 0.0 388 0.0 403 0.0 968 0.0
Clustering of similar parts 111111111111111111 39 111222 222 4 4 5 5 5 36 5 5 5 5 5 5 33 10 10 10 25 10 10 Clustering of solid 10 25 entities 10 10 10 10 10 10 10 Number of entities per cluster Cluster distance threshold: 0.005 generating 56 clusters
Identifying inconsistencies in CAD parts (a) (c) Inconsistent filleting Interference between solids (b) Misaligned components (different distance from center) Inconsistent edges’ convexity
Lanyon building, Queen’s University Belfast Thermomechanical design in Rolls-Royce
Gas turbine thermomechanical design • Thermal expansion of the mechanical parts of the engine changes seal clearances • Seal clearances affects thermal cooling flows and thus part temperatures • Non-optimal seal clearances affect engine performance and life • This requires a multi-physics model where • Cooling flows are modelled as an ‘air system diagram’, a network of 0D-1D chambers and flow resistances • The air system model provides thermal boundary conditions to a 3D thermomechanical FE analysis • The ‘air system’ and ‘structural’ models are developed independently • A change in one model is not automatically reflected in the other • Both require highly-skilled engineers, and a great deal of manual work
Automating the process using Simulation Intent ~3hrs in Parasolid ~10 mins ~3hrs Cellular Model Seal/Hole Fluid Domain extraction Identification Segmentation Cellular Model Fluid cavities Partition surfaces Cell_Solid Cell_Interference Cell_Fluid Main_Cavity Cavities VESTA Engine used with permission from Rolls-Royce
Identification of Seal Inlet/Outlet 1 2 3 • User selects 2 edges Tensor factorisation Generate partition of a seal inlet and 2 surfaces edges of the outlet. • automatic for seal • Same operation for Top and hole) any seal edge • Added manually configuration three partitions (instantiation of seal (gaps) is automatic) Similar entities Pair similar entities by distance Bottom edge VESTA Engine used with permission from Rolls-Royce
Fluid segmentation 4 Main Cavity Main Gas Path C5 C6 R2 C1 Cavity R1 C4 + Segmentation surfaces S4 C1 S1 Seal R1 C2 R1 Restrictor S3 S2 C3 VESTA Engine used with permission from Rolls-Royce
Lanyon building, Queen’s University Belfast Cellular models as a carrier for simulation data
Trivial example – a tube carrying a fluid • Domain captured with cellular model • Cell hasManifoldDimension 0 .. 3 Thermal and Structural Model • IsBoundedBy (relations between cells) of hollow tube with internal flow (next slide) • Simulation attributes can be attached to 0, 1, 2, 3D cells • ‘I am standing on the internal wall of the tube watching the flow go by at xx m/s. The temperature here is yyoC.’ • Physics captured by hasGoverningEquations relation • ‘Ground truth’ is the equations to be solved • Idealisations captured by hasEquivalentRepresentation relations • Conventional material substance hasA • Modulus E • Conductivity • … Hyunmin Cheong & Adrian Butscher (2019): Physics-based simulation ontology: an ontology to support modelling and reuse of data for physics-based simulation, DOI: 10.1080/09544828.2019.1644301 Flavien Boussuge, Christopher M. Tierney, Harold Vilmart, Trevor T. Robinson, Cecil G. Armstrong, Declan C. Nolan, Jean-Claude Léon & Federico Ulliana (2019) Capturing simulation intent in an ontology: CAD and CAE integration application, DOI: 10.1080/09544828.2019.1630806
Structural and flow models for a hollow tube Flow Structural 4 hasGoverningEqns = 8 Transfer of pressure and ( ) temperature BCs through common boundary Flow domain hasGoverningEqns (Navier Stokes) 4 hasGoverningEqns EI = − = − 4 Tube hasGoverningEqns . = − ; = hasEquivalentRepresentation
Lanyon building, Queen’s University Belfast Finishing up
Conclusions • Simulation intent can be defined independent of model geometry and topology • Makes simulation workflows much more robust • Cellular modelling, virtual topology and equivalencing for: • Linking analysis attributes between different representations • Interface management within components and assemblies • Managing models of different fidelity and physics • Streamline CAE workflows by: • Using analysis topology and virtual topology operations to ease geometry operations • Using Simulation Intent to automate time-consuming pre-processing activities • Utilising geometric reasoning and relational learning to facilitate the pre-processing of large, complex multi-physics models • A next generation digital mock-up should incorporate these ideas
Grand Philosophical Musings • Trevor Robinson, Acknowledgements, “Automated creation of mixed dimensional finite element models”, PhD thesis, 2007. • To Professor Cecil G Armstrong … “It has been his refusal to accept that some things are just not possible which led to many of the topics of work making it this far.” … • A fanatic: • One who redoubles his effort when failure is certain
Acknowledgements • We wish to acknowledge the financial support provided by Innovate UK through projects: • GEMinIDS (ref 113088): Slides: 16, 21, 31-33 • Colibri (ref 113296): Slides 22 • We also thank Rolls-Royce for permission to publish this material
You can also read
