CCMT Validation of Shock Tube Simulation Chanyoung Park

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

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

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

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) CCMT |4

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

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

High-speed Schlieren Interaction at shock Mach number = 1. 67 Downstream edge Upstream edge CCMT Curtain thickness |7

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

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

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

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

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

Estimating Model Uncertainty ymeas + emeas = ycalc + emodel + enum + eprop § Only model uncertainty is not quantified § Assuming the measurement uncertainty is independent § Little numerical uncertainty in the 1 -D simulation emodel ≈ (ymeas + emeas) – (ycalc + eprop) (yobs + emeas) (ycalc + eprop) emodel ymeas ycalc CCMT Prediction Metric yobs - ycalc Uncert ainty | 13

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

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

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

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

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

Measuring Volume Fraction with X-ray 136 cm X-ray intensity 8 cm CCMT x | 19

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

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

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

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 CCMT | 23