international conference on hydrogen safety, sep. 8-10, pisa, italy numerical study of a highly...

International Conference on Hydrogen Safety, Sep. 8-10, Pisa, Italy

NUMERICAL STUDY OF A HIGHLY UNDER-EXPANDED HYDROGEN JET

B P Xu, J P Zhang, J X WEN, S Dembele

and J Karwatzki

Faculty of Engineering, Kingston UniversityFriars venue, Roehampton Vale, London, SW15 3DW, UK

Summary of Hydrogen accidents (1916-2005)

Category Number of Accidents

Percentage of Total Accidents

Undetected leaks, accidentally generated H2

178 28

System malfunction, components failure, material failure

125 20

Human error, inadequate procedure, design flaws

84 13

Piping and pressure vessel ruptures

39 6

Road, rail and aviation incidents

25 4

Inadequate inert gas purging

12 2

Others 168 27 Total: 631 100


Analysis of Hydrogen accidents (1916-2005)

Category Number

of Accidents

Percentage of Total

Accidents

Utilisation 408 65 Production 120 19 Transport 62 10 Others 35 6 Unknown 6 1 Total: 631 100


Very High Pressure Hydrogen Storage

• The Fuel cell vehicles (FCV) currently in trial use are mounted with hydrogen containers pressurized up to 400 bar and yield a driving range of 300-350 km per filling - roughly half of the gasoline vehicle’s driving range.

• Industry is developing containers for up to 700 bar pressurization.

• Need to gain insight of such release and its potential for ignition


Schematic diagram of free jet flow shock structure

Two Modelling Approaches

• Pseudo-source approach (Ewan and Modie 1985)– Leak modelled from

downstream as a sonic jet with the same mass flow rate

• Numerically solving the under-expanded shock structure

• Results used as inflow for the subsequent large eddy simulation of the jet

0.5(0.536 )oeq j Da

PD D C

P

/ 12( )

1e oP P

/ 12

( )1e o

1/ 2 1/ 24.99( )gs

o Da

DY C

z


Simulation of the Under-expanded Shock Structure

• Commercial code CFX– Total energy model take into the kinetic energy

of high speed flows– The k-ω based shear stress turbulence (SST)

model– A TVD type high resolution discretisation

scheme to represent sharp gradients without numerical oscillations

– A global 2nd accuracy, which switches to a 1st order upwind scheme locally to prevent non-physical oscillations

– The 2nd order backward Euler scheme to define the discretisation algorithm for the transient term.

Validation of the code for supersonic application is available through CFX Vendor, now part ANSYS Europe


Simulation of the free hydrogen jet

• KIVA-LES (modified for LES from KIVA-3V)– Finite volume based ALE (Arbitrary Lagrangian-

Eulerian) method

– the 2nd order Crank-Nicolson scheme for the diffusion terms and the terms associated with pressure wave propagation;

– The 2nd order MacCormack method for the convective terms in the rezone phase;

– A 2nd order centred scheme for the convection term in the momentum equation.

17. B B P Xu, J X Wen, S Dembele, Large eddy simulation of

plane impinging jets, submitted to Physics of Fluids.

18. B P Xu and J X Wen, Validation of a new droplet collision model in LES of non-evaporating diesel fuel sprays, submitted to Int. J of Multiphase Flow.


Real Gas Property

• Abel-Noble EOS (Equation of State)

bPRTP (1)

For hydrogen, b=1.55×10-5 (m3/mole), valid for P<1600atm and 200<T< 350K

• Van der Waals EOS

0abavvRTPbPv 23 (3)

RTbvv

aP

2

(2)

This EoS has been reported to reproduce a large part of the experiment thermodynamic data on hydrogen within 0.1% and practically all data within 0.5%.


Comparison of density as a function of pressure for constant temperatures

Temperature=250K

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0 20 40 60 80 100 120

Pressure (bar)

Den

sity

(kg

/m3)

Temperature=350K

0.00

2.00

4.00

6.00

8.00

0 20 40 60 80 100 120

Pressure (bar)

Den

sity

(kg

/m3)

Temperature=50K

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 20 40 60 80 100 120

Pressure (bar)

Den

sity

(kg

/m3)

VAW

Abel-noble

Ideal

Temperature=150K

0.00

3.00

6.00

9.00

12.00

15.00

18.00

0 20 40 60 80 100 120

Pressure (bar)

Den

sity

(kg

/m3)


Choked Flow Nozzle Dynamics

• Assuming isentropic flow

• T* from Van der Waals EoS

• Table 1. Initial data in the high-pressure jet simulation

1*

1

1*

2

1)

2

1)

o

o

P P

Vessel pressure (MPa) 20

Release temperature (K) 267

Vessel temperature (K) 300

Release velocity (m/s) 1020

Orifice diameter (m) 0.01

Discharge coefficient 0.85

Release pressure (MPa) 10.6

Density in the vessel (Kg/m3)

14.1

Density at nozzle exit (kg/m3)

8.93


Exit tempeature VS vessel pressure for a vessel temperature of 300K

200

250

300

350

400

0 200 400 600 800 1000

Pressure (Bar)

Tem

per

atu

re (

K)

530

K Mohamed and M Paraschivoiu, Real gas simulation of hydrogen release from a high-pressure chamber, Int J of Hydrogen Energy, 30 (2005).


• Release pressure: 200 Bar


• Release pressure: 20 bar

• At very high pressure ratios (such as the previous one), only one Mach disk

• Several Mach disks at relatively lower pressure ratios

Predicted pressure, velocity, temperature and hydrogen mass concentrations at the centreline


The free hydrogen jet (with KIVA-LES)

Instantaneous density Mean velocity

Normalized values of main axial velocity, axial turbulent intensity and hydrogen mass fraction on the centreline

Normalized values of main axial velocity and hydrogen mass density versus distance to the centreline at different Z positions.


Conclusion

• The predicted flow pattern and Mach number distribution within the shock structure are in line with previous experimental observation and theoretical analysis.

• Apparent air entrainment is found after these shock structures, implying that the widely used pseudo-source approach may incur some errors for such jet simulations.

• The hydrogen release temperature is lower than the vessel temperature when the container pressure is below a certain value (e.g. 530 bar in the current configuration). The situation is different for higher vessel pressures.

• A combustible cloud could be formed above the leak source within a very short period of time (about 0.1s).


ACKNOWLEDGEMENT

• We gratefully acknowledge the helpful discussion with Vincent Tam, Peter Cumber and Marius Paraschvoiu.

• Jet flame simulation is already ongoing

• Work will continue jointly with BP and HSL through the EC funded HYFIRE project in several areas concerning fire and explosion safety of hydrogen.

FUTURE WORK

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