UNCERTAINTIES IN RISK ASSESSMENT OF HYDROGEN …

UNCERTAINTIES IN RISK ASSESSMENT OF HYDROGEN DISCHARGES FROM PRESSURIZED STORAGE VESSELS AT LOW TEMPERATURES

1 Department of Management Engineering, Technical University of Denmark, Produktionstorvet 424, KongensLyngby, 2800, Denmark, [email protected]

2 Institute for Energy and Transport, Joint Research Centre European Commission, Westerduingweg 3, Post box 2, Petten, 1755 ZG, Netherlands, [email protected] , [email protected]

Markert, F.1, Melideo, D.2 and Baraldi, D.2

2013-09-09ICHS 2013 - Markert et al. paper 2192 DTU Management Engineering, Technical University of Denmark

Introduction

• Present hydrogen storing technologies apply, e.g.:

– The liquid state at about 20K under a low pressure < 1MPa

– The gaseous state at ambient temperatures under very high pressures up to 80 – 100 MPa.

– The cryo-compressed state at temperatures between 33K - 338K under pressures up to 35 MPa.

Real gas isotherms (continuous line) compared to ideal gas behaviour (dotted lines).

Wide ranges of temperature and pressures need real gas EOS for prediction as assuming ideal gas behaviour is not adequate in many situations


Introduction

1,3

1,4

1,5

1,6

1,7

1,8

1,9

0 20 40 60 80

Cp/

Cv

P [MPa]

Isothermal 100 K Isothermal 150 K Isothermal 200 K Isothermal 298 K Isothermal 500 K

10

15

20

0 20 40 60 80

Cv

[J/m

ol/K

]

Pressure [MPa]

10

15

20

25

30

35

40

50 150 250 350 450C

p &

Cv

[J

mo

l-1

K-1

]

Temperature K

Cv,Cp 21.3 mol/L

Cv, Cp 20.4 mol/L

Cv, Cp 11.6 mol/L

Cv Cp 2 mol/L

Cp

Cv

T K Cv ideal

500 20.953

298 20.47

200 19.023

150 17.165

100 14.525

• Specific heat capacity of hydrogen:• diatomic linear molecule (> 200 K): 5 degrees of freedom: Cv (theor.)= 2.5R= 20.785 J mol-1K-1

• monatomic gas (< 160 K): 3 degrees of freedom: Cv (theor.)= 1.5R= 12.471 J mol-1K-1.


Introduction

Isochoric temperature –pressure plots for 11.5 mol/L (equal to about 35MPa at ambient temperature)

• This is a first theoretical analysis using CFD and analytical models. • What is the potential uncertainty in the predictions of hydrogen

releases at low temperatures? • How does this affect the outcome of consequence assessments?


Definition of 3 release scenarious

Tank volume (L)

Orifice radius (mm)

Initial pressure (MPa)

Initial temperature (K)

case 1 (Validation) 27 3.18 34.5 300

case 2 27 3.18 30 200

case 3 197 5.7 30 200


CFD set-up

Mesh Number of nodes27 L coarse 2984

27 L fine 13380197 L 7328

• ANSYS CFX14.0 fully compressible solver • Hybrid axy-symmetric meshes were generated with Pointwise 17.0

• The mesh is a pseudo 2-dimensional mesh (one cell in the y direction representing 1/360 of the whole 3D geometry.

• The main domain in the tank is built with an unstructured tetrahedral mesh. • A structured mesh was generated for the leak region (having a preferential flow direction)• Validation case 27 L tank at room temperature: 2 computational grids were built in order to

investigate the grid independence.• Solving: high resolution advection scheme and the second order backward Euler time scheme • The free slip boundary condition applied to the walls • The exit surface modeled as a supersonic outlet boundary condition, (following the

modeling strategy by Mohamed and Paraschivoiu )


Analytical model

based on the Yellow book model for vessel dynamics

�� = 0�� = �� × �

�� = �� ∙ � � ∙ �� ∙ �� ∙2

� + 1

��

�� =��

�∙ ��

�� =��

�� ∙ � ��

∙ ��

�� = �� + �� = �� + ��

�� = ! �� , �� ∙ # ∙�� ∙ ��

$$��%&'())��

= ��%&'())�+ �� ∙ ��

*�+%,�� ≤ 2 ∙ 10.�%

ti – time; δt – time stepqi – mass flow rate CD – discharge coefficient A – hole area; γ- Cp/Cv ρi – density; Pi – vessel pressure; V – vessel volume; δTi – temperature difference; Ti – vessel temperature; Cv –isochoric specific heat capacity; Z(P,T) – compressibility factor; Rgas –gas constant; MM – molecular weight


Case 1: Validation of modelsT=300K, 27L, 34.5 MPa, r=3.18mm, 27L

Comparison:Ideal gas – excellentReal gas – good

-PR and L slight deviations(1 to 3s of the release)

-BB underpredicts the releaserate(0 to 3s of the release)


Case 1: Validation of models

Comparison:Ideal gas – excellentReal gas – good

-PR and L very slight deviations

-BB underpredicts the vesselpressure(0 to 3s of the release)


Case 1: Validation of models

Comparison:Ideal gas – excellent

Real gas – good up to 1 sIncreasing deviations from 1 s(<150K) for L, PR and BB very good agreement.


Case 2: release at low temperatureT=200K, 30 MPa, r=3.18mm, 27L


Case 2: release at low temperatureT=200K, 30 MPa, r=3.18mm, 27L


Case 3 T=200 K; 30MPa; 0.197 m3; D=0.0114 m


The time dependent specific heat capacities & ratio

gamma=Cp/Cv


Flame length predictions

sonic conditions , ambient temperature 288K (dry air), D=6.36 mm & 11.4 mm

07.0C

Ufor

C

U805

D

L3

N

N

S

N

47.03

N

N

S

NF >

=

ρρ

ρρ

Case 3: Peng Robinson

Saffers and Molkov:


Conclusion

• The paper describes a modeling approach comparing the use of an engineering numerical model and a CFD outflow model to characterize the hydrogen outflow from a pressurized vessel at ambient and cryogenic temperatures.

• The models have been compared to former findings in the literature and excellent agreements are found at ambient conditions using the ideal gas EOS.

• Different real gas EOS (PR, BB, L) are compared:

– mass release rate & vessel pressure (PR/L (compare well)->BB (deviates))

– vessel temperature (PR/BB (compare well) ->L (deviates increasingly towards low temperature)

• The uncertainty of the predicted vessel temperature depending on different strategies to estimate the specific heat Cv

• Flame length is dominated by the density at the nozzle:

– Application of the ideal gas law overestimates the flame length compared to the estimate with the real gas equation.

PR=Peng-Robinson; BB=Beattie-Bridgeman; L=Leachman (NIST stand.)


Thank you for yourattention.

[email protected]

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UNCERTAINTIES IN RISK ASSESSMENT OF HYDROGEN …