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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 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!