1. 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

2. 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

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
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

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?
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

5. 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

6. 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)?

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
We use dynamic feedback control to keep the pressure inside the tank stable.

8. 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

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: 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.

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
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.)

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
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.

14. 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
China Scholarship Council
Thank you for your attention!