Validated equivalent source model for an underexpanded hydrogen jet Ethan Hecht, Xuefang Li, Isaac Ekoto Sandia National Laboratories Tsinghua University Travel to US to work at Combustion Research Facility of Sandia National Labs for 8 months

Typical hydrogen accident scenarios Ignited/self-ignited LFL Deflagration Detonation Unintended release 　dispersion & mixing 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

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 Model runs on a PC in a few seconds Video shows series of plume model runs for a 45 degree release Initially momentum driven Towards the end becomes buoyancy dominated Model captures both regimes White line is 4% mole fraction boundary Use this model coupled with probability 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? Model requires starting conditions Need to find these starting conditions from known parameters (leak diameter, pressure ratio) CFD impractical for all scenarios generated by risk models

Schlieren imaging is used to observe the shock structure Discuss setup Schlieren line-of-sight measurement, not quantitative for density (averaged over line-of-sight) Spatially calibrated Mean of 80 5us images Algorithm developed to quantify location of Mach disk, width of Mach disk, and width of slip region All characteristics grow as pressure increases Limited to 60 bar with this setup 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 0.5 and 0.75 mm orifices crooked (throw off slip-region measurements) The results are further used in Li and Christopher’s work to build a two-layer model. 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 We use dynamic feedback control to keep the pressure inside the tank stable.

𝜒𝐻2 𝜒 𝐻2 𝑅= 𝑂 𝑅 ∙ 𝐼∙ 𝑆 𝑡 + 𝑆 𝐵 ∙ 𝑝 𝐹 + 𝐵 𝐺 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 𝑅= 𝑂 𝑅 ∙ 𝐼∙ 𝑆 𝑡 + 𝑆 𝐵 ∙ 𝑝 𝐹 + 𝐵 𝐺 Mole Fraction 𝜒𝐻2 ∝𝐼 The mean mole fraction is averaged from 800 instantaneous images taken over 400 s. 𝜒𝐻2 𝜒 𝐻2

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: 𝜖= 𝑥,𝑦 𝜒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑥,𝑦)− 𝜒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 (𝑥,𝑦) 2 𝑥,𝑦 𝜒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑥,𝑦)− 𝜒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 (𝑥,𝑦) 2 Differential evolution, followed by basin hopping algorithm 3 fit parameters: initial jet diameter ( 𝐷 𝑒𝑓𝑓 ), starting point ( 𝑦 𝑒𝑓𝑓 ), and mole fraction ( 𝑌 𝐶𝐿, 𝑒𝑓𝑓 ) 12 data sets (5 diameters, up to 4 pressure ratios) pixel by pixel.

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 Disagreement due to several model parameters (density spreading ratio, air entrainment, etc.) that may not be appropriate for hydrogen Without measurements of the velocity fields for these hydrogen jets, it is unclear whether this value, taken from historical work on water jets is appropriate. Yuceil and Otugen found that the velocity to temperature spreading ratio for dry air was significantly higher (1.42) than the concentration spreading ratio used in this work. The entrainment sub-model may also not be appropriate for these hydrogen jets. 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 Further measurements, especially of the velocity fields, could justify these (or assist in calculating more appropriate) model parameters. We have submitted a paper on the model parameters to IJHE, in which the calculated fields agree with the experimental results very well. We already have some positive comments from the reviewers and have submitted the final version.

Thank you for your attention! 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!