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Validated equivalent source model for an underexpanded hydrogen jet. Ethan Hecht, Xuefang Li , Isaac Ekoto Sandia National Laboratories Tsinghua University. Typical hydrogen accident scenarios. The first two stages are critical to design hydrogen safety codes and standards

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## Validated equivalent source model for an underexpanded hydrogen jet

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**Validated equivalent source model for an underexpanded**hydrogen jet Ethan Hecht, Xuefang Li, Isaac Ekoto Sandia National Laboratories Tsinghua University**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**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**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?**Schlieren imaging is used to observe the shock structure**• Quantitative spatial information about how expansion occurs**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)?**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**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**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)**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**Comparisons of the calculated and measured concentration**fields • The disagreement is due to several model parameters (density spreading ratio, air entrainment, etc.)**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**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**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!

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