Validated equivalent source model for an underexpanded hydrogen jet

1. Validated equivalent source model for an underexpanded hydrogen jet Ethan Hecht, Xuefang Li, Isaac Ekoto Sandia National Laboratories Tsinghua University

2. Typical hydrogen accident scenarios • The first two stages are critical to design hydrogen safety codes and standards • CFD simulations are too computationally expensive, so fast running engineering models are necessary • Systematic experiments of high pressure underexpanded hydrogen jets to validate the models Deflagration LFL Ignited/self-ignited dispersion & mixing Unintended release Detonation

3. Fast-running, first order models can be used to predict hydrogen trajectory • Assume Gaussian profiles for mean velocity and density profiles • Conserve mass, momentum, species along the centerline, with empirical model for entrainment • Physical plume/jet model coupled to probability of component failure and ignition models to quantify risk

4. Fueling stations and vehicles have 350 and 700 bar hydrogen • Flow is choked when a leak occurs • Expansion causes shock waves as atmospheric pressure is reached • First-order model assumes constant pressure • What are the boundary conditions to the first-order model?

5. Schlieren imaging is used to observe the shock structure • Quantitative spatial information about how expansion occurs

6. Mach disk size, location, and slip region size all scale linearly with the square root of the pressure ratio crooked • Can we scale boundary conditions to first-order model using the same parameter (square root of the pressure ratio)?

7. Planar laser Rayleigh scattering is used to measure concentration fields • Two-cameras used due to expected high-spreading rate • ICCD used to determine laser shot power and laser power distribution

8. Signal intensity corrections used to create quantitative concentration image R: Raw image BG: Background luminosity pF: Laser power fluctuation OR: Camera/lens optical response SB: Background scatter St: Laser sheet profile variation I: Corrected intensity

9. Nonlinear fit of the initial parameters to predict the entire mole fraction field (not just the centerline) • Fitted pixel by pixel for each set of data • Objective function: • Differential evolution, followed by basin hopping algorithm • 3 fit parameters: initial jet diameter (), starting point (), and mole fraction () • 12 data sets (5 diameters, up to 4 pressure ratios)

10. First-order model initial diameter and position scale linearly with the square root of the pressure ratio • and constrained to lie between 0 and 10

11. Comparisons of the calculated and measured concentration fields • The disagreement is due to several model parameters (density spreading ratio, air entrainment, etc.)

12. Summary • Mach disk size, location, and slip region size all scale linearly with respect to the square root of the pressure ratio, • Initial diameter and starting point for first order model scale linearly with respect to the square root of the pressure ratio • Initial centerline mole fraction varies smoothly from 0 to 1 as the pressure ratio increases • Empirical model can be used to generate initial conditions for a first-order model that can be used to rapidly predict mean concentration fields (that include the effects of buoyancy), for underexpanded jets

13. Future work • Investigate whether other first-order model parameters (relative velocity to concentration spreading ratio and entrainment sub-model) are valid for hydrogen • Validate model for cold hydrogen jets/plumes

14. Acknowledgements • United States Department of Energy Fuel Cell Technologies Office, Safety, Codes, and Standards subprogram managed by Will James • National Natural Science Foundation of China, Grant No. 51476091 • China Scholarship Council Thank you for your attention!