1. CCMT Validation of Shock Tube Simulation Chanyoung Park, Raphael (Rafi) T. Haftka and Nam-Ho Kim Department of Mechanical & Aerospace Engineering, University of Florida

2. CCMT | 2 Motivation  Explosive solid particle dispersal -Explosive processes influence dynamics of densely packed particles -Predicting particle dynamics with a simulation

3. CCMT | 3 Outline  Validation using shock tube experiments  Multi-fidelity surrogates  Measuring volume fraction with X-ray

4. CCMT | 4 Simulation  Rocflu developed by the Center for Simulation of Advanced Rockets (CSAR)  Modeling the interaction of a planar shock wave with a dense particle curtain is a key element of simulation  2-way interaction between shock and particles becomes dominant at the volume fraction of 20%  1-D simulation (Rocflu Lite)

5. CCMT | 5 Validation of Shock Tube Simulation  Validation of the models for shock-particle interactions Experimental Data Shock Tube Simulation Validation

6. CCMT | 6 Prediction Metric Prediction Metric: The locations of the particle curtain edges at upstream and downstream  Normalized (by initial curtain thickness L) location vs. time Curtain thickness after impact Before impact After impact

7. CCMT | 7 High-speed Schlieren Interaction at shock Mach number = 1.67 Curtain thickness Upstream edge Downstream edge

8. CCMT | 8 Experimental Uncertainty Examination Inputs Uncertainties in Inputs Measured Metrics Uncertainties in Measured Metrics 1.Identifying inputs and their uncertainties and determining prediction metrics 2.Variable screening by influence and uncertainty 3.Quantifying and modeling uncertainties Experimental Data Shock Tube Simulation Validation

9. CCMT | 9 Key Uncertainties and Prediction Metrics #InputsUncertainties in Inputs 1Volume fractionMeasurement error (21%±2%) Local variation in particle curtain 2Diameter of particle Errors in distribution type / parameters 3Particle curtain thickness Variation in particle curtain thickness 4Pressure at driver section P Very small measurement noise …… # Prediction Metrics Uncertainties in Prediction Metrics 1Particle curtain location Large measurement noise 2Pressure curveVery small measurement noise …… Experimental Data Shock Tube Simulation Validation Inputs Uncertainties in Inputs Measured Metrics Uncertainties in Measured Metrics

10. CCMT | 10 Simulation Process Examination Inputs Uncertainties in Inputs Measured Metrics Experimental Data Shock Tube Simulation Validation Prediction Metrics Numerical Uncertainty Model Uncertainty Uncertainties in Prediction Metric Propagated Uncertainties from Inputs 1 2 Uncertainties in Measured Metrics

11. CCMT | 11 Propagated Uncertainties Propagated uncertainty in upstream curtain edge location Propagated uncertainty in downstream curtain edge location

12. CCMT | 12 Quantifying Propagated Uncertainties  Propagated uncertainties in predicted curtain boundary locations  Quantified effects of errors in inputs  1-D simulation (Rocflu lite) Particle diameterVolume fraction

13. CCMT | 13 Estimating Model Uncertainty  Only model uncertainty is not quantified  Assuming the measurement uncertainty is independent  Little numerical uncertainty in the 1-D simulation y meas + e meas = y calc + e model + e num + e prop e model ≈ (y meas + e meas ) – (y calc + e prop ) Prediction Metric (y obs + e meas ) y meas y calc Uncert ainty e model y obs - y calc (y calc + e prop )

14. CCMT | 14 Key Model Uncertainties #Model UncertaintiesComment 1Coupling modelCome from Micro scale 2Particle force modelCome from Micro scale 3Particle curtain model 1D/2D/3D Boundary layer effect ……  Gas and particles coupling model  Inviscid force term of the particle force model is critical  Low/High fidelity models (1D/2D/3D) 21±2% 26±2% 15±2% Slit opening

15. CCMT | 15 Multi-fidelity Models 1-D Simulation2-D Simulation3-D Simulation Particle curtain model Assuming constant curtain thickness Modeling volume fraction variation in the vertical direction Modeling general volume fraction variation Consideration of the boundary layer effect no yes  Multi-fidelity models with different fidelities for the same physical problem (1D/2D/3D)  Particle curtain model / Consideration of the boundary layer effect

16. CCMT | 16 Computational Challenge in UQ  Simplest approach for propagating uncertainty is Monte Carlo technique often requiring thousands of simulations  To avoid this large number of simulation runs we use three tools –Fit surrogates for the UQ process –Adaptive sampling for efficient surrogate improvements Simulation Output Input

17. CCMT | 17 Multi-Fidelity Surrogate  Multi-fidelity model  36 samples and 6 samples from the low and high fidelity models (i.e. 1D, 2D and 3D models)

18. CCMT | 18 Multi-Fidelity Surrogates  Gaussian process to combine spatial correlation  Characterizing uncertainties in a surrogate based on their processes

19. CCMT | 19 Measuring Volume Fraction with X-ray 136cm8cm x X-ray intensity

20. CCMT | 20 Measuring Volume Fraction φ p : volume fraction A: mass x-ray attenuation coefficient (should be calculated) ρ: density of medium w 0 : thickness of medium Beer-Lambert law X-ray intensity I I0I0 x

21. CCMT | 21 Calibration Error bars from 4 sets of ratios A for wρ

22. CCMT | 22 Volume Fraction Profiles  Uncertainty in calibration process (75%)  Uncertainty in measured intensity ratio

23. CCMT | 23 Summary  Validation of a simulation for predicting particle dynamics can be carried out with shock tube experiments  X-ray is used to measure volume fractions of particle curtains  Computational intensity of UQ needs the use of a multi fidelity surrogate model