UNDERBODY BLAST (project 1b)

Transcription

1 UNDERBODY BLAST (project 1b) PI: Mingjun Wei, New Mexico State University (overall project lead: Charbel Farhat, Stanford University) Graduate Students: HaoQan Gao, Mehdi Tabandeh Khorshid Post- Doctoral Researcher: Tao Yang Undergraduate Student: Shaw Houlihan, CurQs Tade, Fazzel Gurrola

2 PROJECT OVERVIEW ScienQfic problem - construct a low- dimensional mathema/cal representa/on of the Under Body Blast problem to enable real- /me reliable parametric studies and decisions Army relevance - leading cause of casual/es in current Army opera/ons; limited Army capability to accurately and efficiently assess its effects on both personnel and vehicle - faster & cheaper tes/ng for survivability Technical challenges - nonlinearity, high speed - moving boundary, coupled fluid- solid system - non- symmetric formula/on for weak solu/on

3 PROJECT OVERVIEW (continue) Research objecqves - To develop a predic/ve High Performance Computa/onal (HPC) model for under body blast and its effects on personnel and vehicles - To develop a nonlinear Model Order Reduc/on (MOR) methodology that is applicable to this and other HPC models in order to enable parametric studies in a reasonable amount of /me Technical approach - High- Fidelity Model: Immersed Boundary + WENO - Low- Dimensional Model: Global POD- Galerkin projec/on, modified inner product Related work - C. Farhat (Stanford), B. Noack (Poi/er), M. Barone (Sandia)

4 PROJECT COMPONENTS Core components - To develop a high- fidelity computa/onal model combining immersed boundary technique and high- resolu/on shock- capture scheme for HPC programs involving complex/moving geometry and fluid- solid interac/on - To develop a global model reduc/on approach for moving boundary/object in a uniform Eulerian framework ThemaQc components - Computa/onal Blast Theme: using both high- fidelity HPC code and reduced- order model for the parametric study and understanding of under body blast wave interac/ng with armored vehicles

5 PROJECT DELIVERA LES Deliverable #1 (methodology, code, documentaqon) - High- fidelity numerical simula/on using high- order Weighted Essen/al Non- Oscillatory (WENO) scheme and Immersed Boundary (IB) method for underbody blast Deliverable #2 (methodology, code, documentaqon) - Global model order reduc/on using POD- Galerkin projec/on for complex flow with moving boundary and objects

6 Schedule and milestones PROJECT ROADMAP

7 Research Progress High-Fidelity Simulation Reduced-Order Model

8 High-Fidelity Simulation High-Fidelity Model Using Immersed Boundary Technique and High-Resolution WENO/ENO Scheme Euler equation Shock capture: WENO/ENO Moving/complex boundary: Immersed Boundary Method o Fluid-Structure Interaction

9 High-Fidelity Simulation Immersed Boundary Method

10 Simulation Results Stationary Boundary Supersonic flow passing backfacing step: steady flow, benchmark Supersonic flow passing stationary cylinder: unsteady, benchmark

11 Simulation Results Moving Boundary, Multiple Objects Supersonic flow passing counter-rotating plates

12 Research Progress High-Fidelity Simulation Reduced-Order Model

13 Model Reduction Two Kinds of Reduced-Order Models Bottom-up approach Top-down approach Projec/on Subspace Not today s topic Model Reduction more like this!

14 Model Reduction More Mathematic Illustration of Model Reduction

15 Galerkin Projection Original system equation (High-Fidelity Model) Expansion on (orthogonal) base functions Projection Approximation to lower dimension Order is reduced for:

16 Proper Orthogonal Decomposition Proper Orthogonal Decomposition (POD): - Optimal subspace by to represent Hilbert space defined by inner product Properties - Optimality: - Homogeneity: translation invariant - Orthogonality:

17 Method of Snapshots POD kernel in discrete form: then solve,, an eigenvalue problem for mesh Method of snapshots: use M snapshots from simulation, normally M << N, have a new kernel: an then, problem:

18 POD-Galerkin Projection Traditional POD-Galerkin Projection for Model Reduction - Navier-Stokes equation (HFM) - ROM from POD-Galerkin Projection - Inner product

19 POD-Galerkin Projection Application on flow passing stationary cylinder with 8 POD modes (Noack et al. 2003) What about a moving cylinder (or a deforming steel plate)?

20 Global POD Typical inner product for fluid flow Global POD for both fluid and structure Global POD for fluid and structure weighted by density

21 Global Galerkin Projection Global Galerkin Projection on a uniform equation for both fluid and solid: Direct forcing: solid is represented by a body-force term Global ROM with fluid and moving solid

22 Results for Oscillatory Cylinder Case 1: small amplitude, 8 modes (Re=185) DNS (HFM) ROM: without forcing ROM: with forcing

23 Results for Oscillatory Cylinder Case 2: large amplitude, 8 modes (Re=100) DNS (HFM) ROM: without forcing ROM: with forcing

24 Results for 3D Case 3: Moving 3D Sphere (Re=300) DNS (HFM) mode 1 mode 2 mode 3 mode 4

25 Results for Oscillatory Cylinder Case 3: Moving 3D Sphere DNS (HFM) ROM: without forcing ROM: with forcing

26 Comparison of Time Cost Computational time by CFD (high-fidelity model) and different ROMs CFD ROM Off- line On- line Total Sta/onary 2D Cylinder ~ 1.5 hr ~ 15 min ~ 2 sec ~ 15 min Moving 2D Cylinder (1*) ~ 1.5 hr ~ 15 min ~ 1 hr ~ 1.25 hr Moving 2D Cylinder (2*) ~ 1.5 hr ~ 1 hr ~ 2 sec ~ 1 hr Moving 3D Sphere Parallel: ~ 1 hr Serial: ~ 1 day ~ 2 hr ~ 2 sec ~ 2 hr *: two different model reduction approaches Critical!

27 Implementation in Android Compute Lift and Drag Coefficient for 2D Cylinder, Re=185 (undergraduate research project) Input: All the model coefficients Using tablet to Compute Galerkin model (small ODEs) Forces calculated directly from model variables:

28 Results for Shock Waves Using traditional POD modes on supersonic flow with shock waves DNS (HFM) DNS onto 8 modes It is hard to achieve a stable ROM at very low dimension! POD modes: 1-4

29 Symmetrization for Stablization (new direction, just started) Using the idea of symmetrization to define better inner product and more stable reduced-order models Gustafsson et. al. (1978) introduced the idea of symmetrization for stablization of incompletely parabolic problems (e.g NS equation) Their symmetrizer is non-unique and based on eigenvectors of the system. They have applied their idea for linearized equations Dafermos (2003) showed that the second law of thermodynamics is essentially a statement of stability. For the weak solutions of hyperbolic conservation laws, satisfying the Entropy (ClausiusDuhem) Inequality stablizes the solver Using Entropy Inequalities, Hughes et. al. (1986) and Harten (1983) introduced the symmetrized matrices for nonlinear Navier-Stokes and Euler equations respectively. Barone et. al. (2009) use the above ideas for Galerkin projection Symmetric inner product Linearized Euler equations Galerkin project for nonlinear Euler equations?

30 Summary and Future Plane High-Fidelity Model Using Immersed Boundary method and high-resolution high-order WENO/ENO scheme to simulate shock/blast wave interaction with moving structures (year 1, 2, 3) o Consider fluid-structure interaction (FSI) including structure induced shock wave (year 3, 4, 5) Reduced-Order Model Global model reduction for complex fluid-solid system with shock wave, blast wave, moving 2D and 3D structures (year 1, 2, 3) o Symmetrized matrix defining new inner product for better stability of Galerkin models (year 2, 3, 4) o Global model reduction with FSI (year 4, 5) o (Model adaptation to ``off-design parameters, year 5?)

31 APP Follow- up research in Q2FY14: Improvement on high-fidelity in-house code for efficiency and stability Q4FY14: Adding rigid-body dynamics to the in-house code to give this test bed the capability to handle shock-structure interaction and structure-induced shock waves Q1FY14: Symmetrization of full Euler equation and design of the corresponding inner product Q3FY14: Implement and test the new inner product and its performance in a comparison to other inner product in the POD- Galerkin model Q4FY14: Constructing new global ROM model for Euler equations

32 PROJECT PUBLICATIONS FY 2013 Refereed publicaqons and reports 1. B. R. Qawasmeh and M. Wei, Low- dimensional models for compressible temporally developing shear layers, Journal of Fluid Mechanics, Vol. 731, pp , H. Gao and M. Wei, Global model reduc/on for flows with moving boundary, accepted and will be presented at AIAA SCITECH 2014, January, 2014, Na/onal Harbor, Maryland