DESIGN ATTRIBUTES OF A VARIABLE APERTURE PRESSURE RELIEF DEVICE FOR ON-BOARD HYDROGEN STORAGE David Yates, Dr. Dmitriy Makarov, Prof Vladimir Molkov HySAFEr, University of Ulster at Jordanstown Hydrogen and Fuel Cell Researcher Conference, 2014

Overview

Accident scenario: PRD cascade Design goals Proposed design of TPRD Design calculations Valve performance

Accident Scenario: PRD cascade

Hydrogen vehicles in transport packed closely together (10 cm end-to-end)

PRD diameter of 4.2 mm causes 1200 K temperature rise under car floor

Car fire that results in PRD release could activate PRDs of adjacent cars

Tamura, et al. IJHE, 2014

Design Goals

For given nozzle diameter (1mm), confine flame length to 1m (3.8 g/s mass / 10 MPa nozzle inlet [Molkov, 2012])

Passively minimise blow-down time by achieving consistent mass flow rate

Hydrogen jet fire

Automobile H2 Storage Tank

Tamura, et al. IJHE, 2014

Telegraph, 2011

Design Attributes: Variable Aperture PRD

Valve / throttle radii r1, r2

Valve seat angle θ Spring coefficient k(x)

h = min([cos(θ)*(r2-{∆x tan(θ)+r1})],r2-r1)

A = 2π*h*[r1+h/2*cos(θ)]

m α A√ ∆P

F = k(x) ∆x

H2 in

Spring force

Proposed Valve Design

1 mm nozzle diameter θ = 0.2º r1= 1.9 mm, r2 = 2.0 mm Spring sits on throttle end

Constant inlet (tank) pressure

Narrow gap between throttle and valve seat Throttled pressure

in chamber

CFD Calculation Domain

6 2D axisymmetric domains Valve displacements: 12.5,

16.5, 18.5, 20.5, 24.5, 25 mm Inlet pressures 17.5-70 MPa x: -4.7 – 11.55 cm y: 0 – 5.2 cm 36332 CVs

Domain

Throttle

Nozzle

Near throttle

CFD simulations: governing equations

Standard continuity, momentum, energy, species conservation equations

Spalart-Allmaras turbulence model

Peng-Robinson equation of state

FLUENT theory guide, 2009

Real gas model

Real gas model used at high pressures because ideal gas over-predicts density up to 37%

Ideal vs. real gas mass flow rate closer, <10% difference

m α A√ (∆P /ρ)

0

10

20

30

40

50

60

70

0 20 40 60 80

Cal

cula

ted

dens

ity (

kg/m

^3)

Pressure (MPa)

Densities, various EoS

Ideal gas (kg/m^3)

P-R (kg/m^3)

Abel-Noble (kg/m^3)

0 0.0005

0.001 0.0015

0.002 0.0025

0.003 0.0035

0.004 0.0045

0 20 40 60 80

mas

s fl

ow r

ate

(kg/

s)

Inlet pressure (MPa)

Mass Flow Rate vs. Pressure

Ideal Gas m (kg/s)

Peng-Robinson m (kg/s)

Linear (Ideal Gas m (kg/s))

CFD results: throttle position vs pressure

Fixed throttle: P-m curve is linear, through origin

Single point can be used to predict desired pressure for given flow and valve position

Throttle position vs pressure to maintain 1m jet flame

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70 80 90

m, k

g/s

Pressure, MPa

12.5

16.5

18.5

20.5

24.5

25

Simulation results: nozzle flow

Nozzle (choked) velocity ~2700 m/s

Canonical barrel shock outside nozzle

Some circulation in chamber before nozzle

Chamber velocity less than 100 m/s except at throttle exit and near nozzle entrance

Nozzle exit velocity contours

Nozzle chamber velocity vectors

Simulation results: throttled pressure gradient

Narrow gap between throttle and valve seat drops pressure from inlet value to ~10 MPa

Velocity across throttle gap accelerates to supersonic (>2600 m/s)

For a fixed mass flow rate inlet pressure proportional to 1/ht (1/√A)

Pressure contours across throttle, assorted inlet P

y = 0.9453x + 0.0034 R² = 0.9692

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

0 0.01 0.02 0.03 0.04 0.05 0.06 valv

e op

enin

g ht

(m

m)

1/(inlet P) (1/MPa)

1/(inlet P) vs. h

Simulation results: valve force calculations

Valve displacement 12.5-25 mm

Valve forces up to 700N for pressures up to 70 MPa

Spring stiffness coefficient k ≈ 57.8N/mm (to 1st order)

y = 57.828x - 734.95 R² = 0.9278

0

100

200

300

400

500

600

700

800

900

10 15 20 25 30

forc

e on

val

ve a

ssem

bly

(N)

valve displacement (mm)

Force vs. throttle displacement

y = 11.27x - 109.64 R² = 1

0 100 200 300 400 500 600 700 800 900

0 20 40 60 80 100

valv

e F,

N

inlet P, MPa

Force vs. pressure

Conclusions

Proposed design of pressure relief device to limit jet flame length to 1 m (constant mass flow rate 3.8 g/s) at various pressures during whole blowdown process

CFD simulations were conducted targeting constant mass flow rate at different hydrogen inlet pressures by varying throttle displacement

Force on the throttle appear to be a linear function of the storage pressure

Spring characteristics are constant and predictable Pressure drop across throttle can reliably be used to

keep nozzle mass flow rate constant

Future Work

Dynamic mesh simulation showing actual throttle motion / transient closing of valve (if necessary; effect of initial release is minor in literature)

Feasibility study of particular spring characteristics (60 N/mm is very stiff! Spring is tiny, and pressures are enormous! Also, would nonlinear k work better?)

Examination of nozzle chamber design features and effects of circulation; how can Lf be further reduced?

Particular effects of valve seat boundary condition on pressure gradient and throttle action (do very narrow gaps behave differently? Why did force jump between dx = 24.5 and 25 mm?)