High-pressure release and dispersion of hydrogen in a partially enclosed compartment: Effect of natural and forced ventilation

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High-pressure release and dispersion of hydrogenin a partially enclosed compartment: Effect ofnatural and forced ventilation

Kuldeep Prasad*

National Institute of Standards and Technology, 100 Bureau Drive, Stop 8663, Gaithersburg, MD 20899, USA

a r t i c l e i n f o

Article history:

Received 23 October 2013

Received in revised form

23 January 2014

Accepted 27 January 2014

Available online 14 March 2014

Keywords:

High-pressure release

Dispersion

Hydrogen

* Tel.: þ1 301 975 3968.E-mail addresses: [email protected]

0360-3199/$ e see front matter Copyright ªhttp://dx.doi.org/10.1016/j.ijhydene.2014.01.1

a b s t r a c t

The study of compressed hydrogen releases from high-pressure storage systems has

practical application for hydrogen and fuel cell technologies. Such releases may occur

either due to accidental damage to a storage tank, connecting piping, or due to failure of a

pressure release device (PRD). Understanding hydrogen behavior during and after the

unintended release from a high-pressure storage device is important for development of

appropriate hydrogen safety codes and standards and for the evaluation of risk mitigation

requirements and technologies. In this paper, the natural and forced mixing and dispersion

of hydrogen released from a high-pressure tank into a partially enclosed compartment is

investigated using analytical models. Simple models are developed to estimate the volu-

metric flow rate through a choked nozzle of a high-pressure tank. The hydrogen released in

the compartment is vented through buoyancy induced flow or through forced ventilation.

The model is useful in understanding the important physical processes involved during the

release and dispersion of hydrogen from a high-pressure tank into a compartment with

vents at multiple levels. Parametric studies are presented to identify the relative impor-

tance of various parameters such as diameter of the release port and air changes per hour

(ACH) characteristic of the enclosure. Compartment overpressure as a function of the size

of the release port is predicted. Conditions that can lead to major damage of the

compartment due to overpressure are identified. Results of the analytical model indicate

that the fastest way to reduce flammable levels of hydrogen concentration in a compart-

ment is by blowing through the vents. Model predictions for forced ventilation are pre-

sented which show that it is feasible to effectively and rapidly reduce the flammable

concentration of hydrogen in the compartment following the release of hydrogen from a

high-pressure tank.

Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 6 5 1 8e6 5 3 2 6519

1. Introduction

The US Department of Energy [1] has estimated that a tran-

sition to hydrogen as the main automotive fuel could be

completed by the middle of the century. Hydrogen is clearly

regarded as an energy carrier for future vehicles and offers the

possibility of reducing pollution and securing the energy

supply, especially when produced with renewable energy

source. As a result, the safety of hydrogen systems has

become a key factor in ensuring a smooth transition towards a

hydrogen-fueled economy. Current technologies that are

capable of providing acceptable levels of vehicle driving range,

storage volume, and weight require high-pressure storage of

hydrogen up to 70MPa. It is therefore of paramount interest to

fully understand the risk associated with high-pressure

hydrogen storage systems in automotive applications. Un-

derstanding hydrogen behavior during and after an unin-

tended release from a high-pressure storage device is

important for development of appropriate hydrogen safety

codes and standards, as well as for effective mitigation tech-

niques and requirements [2].

The study of compressed hydrogen release from high-

pressure storage systems has practical application for

hydrogen and fuel cell technologies. High-pressure hydrogen

release may happen either due to accidental damage to a

storage tank, connecting piping, or direct PRD releases. In the

case where a storage tank is damaged resulting in a large

opening, the release rates can be very large and generally

catastrophic. On the other hand, if the opening is a crack or a

hole in the vessel wall, or failure of the PRD, the hydrogen flow

rates can be relatively small. PRD devices for most hydrogen

tanks currently on the market are thermally triggered with an

operating temperature range of �40�C to 85�C and usually

have a diameter of 6 mm [3]. When activated, these devices

open and release the pressurized gas into the external envi-

ronment in order to limit a potentially dangerous internal

pressure increase in the event of a fire. In this paper, we study

the risk associated with the release of hydrogen due to PRD

failure or other cracks or holes in the vessel wall (also referred

to as the release port) into a partially enclosed compartment.

The risk due to intentional or accidental hydrogen release

depends on the size of the compartment in which the

hydrogen is released. If the release occurs in an un-enclosed

space, the buoyant hydrogen gas will rise up and dissipate,

and the risk of hydrogen accumulation will be negligibly

small. If hydrogen gas is released accidentally in a fully

enclosed space, the risk due to chemical explosion will be

relatively small if the total volume of the hydrogen released is

smaller than 4% (lower flammability limit) or greater than 74%

(upper flammability limit) of the enclosure volume, under the

well mixed assumption [4,5]. Sudden release of hydrogen in

fully enclosed spaces can result in over-pressurization of the

compartment and compartment damage [6]. However, if

hydrogen gas is released into a partially enclosed space, then

obtaining flammable concentration of hydrogen will be

influenced by a number of factors including hydrogen release

rate, volume of released gases, vent location (openings in the

compartment walls), cross-sectional area of vents, wind

speed/direction and thermal effects. Time dependent and

spatially evolving concentration of hydrogen in a partially

enclosed compartment with leaks whose size and location

may be unknown is difficult to predict. The uncertainty in

predicting the concentrations can increase due to real gas

effects associated with high-pressure release of hydrogen.

Accidental release of hydrogen in real-world environments

has been documented in the literature. The 1983 Stockholm

accident [7] involved hydrogen leak from a rack of hydrogen

cylinders located on a truck. The subsequent explosion

resulted in injury to several people and damage to the facade

of several buildings. The H2 Incident Reporting and Lessons

Learned database [8] has many documented cases involving

hydrogen release from high-pressure systems (including

piping, fixtures and valves) that resulted in injury and

damage.

The general topic area of hydrogen release, dispersion and

safety has been studied through experiments, theoretical

methods, and through the use of computational fluid dy-

namics (CFD) tools. The proceedings of the International

Conference on Hydrogen Safety [9,10], covers various aspects

of hydrogen as a fuel for automobiles, including hydrogen

safety, codes and standards. Experimental data on low speed

release and dispersion of buoyant gases (release of 5 kg of

Hydrogen or Helium over a 4 h or 24 h period) in partially

enclosed compartments has been reported in a number of

papers, including Refs. [11e18]. This experimental data has

been very useful in validating numerical models and for

improving our understanding of the physical phenomena.

CFD software [9,10,19e26] has also been used to simulate

hydrogen release and dispersion calculations with clearly

defined geometries and boundary conditions. Theoretical

models have been developed for ventilation flows in a room

with a buoyant gas or a heated floor [27e36]. These models

typically look at the effect of point heating (pure buoyant

flows) or distributed heating of the entire floor instead of the

release of a buoyant gas. CFD simulation have been used to

study hydrogen burning and combustion/explosions from

high-pressure releases [10,22,37e40], since experiments

involving hydrogen release in real-scale are very expensive.

Research clearly indicates that vertical stratification can

occur when buoyancy forces dominate during the release of

hydrogen [29,34]. On the other hand, whenmomentum forces

dominate, the hydrogen can get well mixed with the sur-

rounding air [15,14,30]. Much of the experimental, theoretical,

and numerical work [9e36] has been limited to low speed flow

of hydrogen or helium in reduced scale or full scale geometries

with clearly defined vents. The current work builds upon

previous research by considering the release of hydrogen from

a high-pressure tank, which can result in sonic velocities at

the nozzle exit, and the subsequent dispersion of the high

speed jet in a ventilated compartment.

In this paper, simple theoretical models are developed for

studying the release of hydrogen from a high-pressure tank

and its dispersion into a partially enclosed compartment. Real

gas equation of state is employed to model the volumetric

flow rate of hydrogen from the high-pressure tank. The

hydrogen gas is assumed to mix quickly with the surrounding

air. Natural ventilation due to buoyancy induced flow from the

compartment is modeled through two idealized openings

(vents) located at the top and bottom of the side walls of the




compartment. The diameter of the release port throughwhich

hydrogen is released into the compartment and the cross-

sectional area of the vents were varied as parameters. The

effects of these parameters on compartment overpressure

and flammable concentration of hydrogen in the compart-

ment are discussed. Finally, the effect of changing the natural

ventilation (increasing vent areas) as well as increasing the

rate of forced ventilation on reducing the flammable volume

of hydrogen in the compartment is predicted.

2. Hydrogen release and dispersion inventilated compartments

The release of hydrogen from a high-pressure tank is usually

in the form of a high speed jet. The duration of the release and

the jet exit conditions influence the concentration of

hydrogen in a ventilated compartment. It is therefore neces-

sary to accurately predict the volumetric release rate of

hydrogen from a high-pressure tank. As the hydrogen is

released from the tank, the pressure, density and mass of the

gas inside the tank will reduce. The volumetric flow rate of

hydrogen released from a high-pressure tank will reduce as

the stagnation pressure and the hydrogen density in the tank

decreaseswith time. For jets involving a high-pressure storage

device, the tank pressure is often sufficient to result in flow

that is choked at the jet exit, and the exit pressure is consid-

erably greater than atmospheric pressure. In such cases, the

flow rapidly expands to atmospheric pressure through a series

of expansion shocks.

2.1. Abel-Nobel equation of state

Ideal-gas behavior is valid for tank pressures less than

17.4 MPa [41,42]. For such conditions, isentropic flow relations

have been developed for tank blow-down [42]. However, at

higher pressures the gas behavior increasingly departs from

that of an ideal-gas, and the relations must be modified to

account for gas compressibility. Sudden expansion from a

high-pressure tank can be adequately described through an

Abel-Nobel equation of state of the form

P ¼ rRH2T

ð1� brÞ ¼ ZrRH2T; (1)

where, Z ¼ 1/(1 � br) is the compressibility factor, b is the co-

volume constant (b¼ 7.691E�3m3/kg for hydrogen), and RH2is

the gas constant ðRH2¼ 4120 Nm=kg KÞ. Eq. (1) can be used to

relate the pressure and the density of the gas in the tank, for a

known tank temperature [42].

2.2. High-pressure release and exit conditions

Let P1, r1 and T1 represent the instantaneous pressure, density

and temperature in the tank, while P2, r2, and T2 are the cor-

responding state of the gas at the exit. For a given constant

downstream pressure, namely, standard atmospheric pres-

sure P0, the decrease of the upstream stagnation pressure P1will eventually reduce the mass flux from the sonic (choked)

release to a sub-sonic release. The choked sonic release lasts

until the ratio of the pressure in the tank over the ambient

pressure satisfies the relationship [42]

P1=P0 ��gþ 12

�ð ggþ1Þ

(2)

where, g is the ratio of specific heats at constant pressure (cp)

and constant volume (cy), and is defined as g ¼ cp/cy [33].

2.2.1. Choked flow conditionsIsentropic flow relationship for an Abel-Noble gas [42] from a

high-pressure stagnation state (sub-script 1) to the jet exit

state (sub-script 2) relate the gas densities in the two states as

follows (assuming choked flow),

�r1

1� br1

�g

¼�

r2

1� br2

�g�1þ

�g� 1

2ð1� br2Þ2��g=ðg�1Þ

(3)

Furthermore, the ratio of temperature in the stagnation

tank to the jet exit temperature is given by

T1

T2¼ 1þ

g� 1

2ð1� br2Þ2!

(4)

The jet exit density and temperature can be combined

along with Eq. (1) to obtain the jet exit pressure P2. Finally the

sonic velocity V2 at the jet exit can be determined as follows

V2 ¼ 1ð1� br2Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigRH2

T2

p(5)

2.2.2. Sub-sonic flow conditionsWhen the flow exiting from the tank is sub-sonic, then the exit

conditions can be related to the tank conditions using isen-

tropic relationships for an ideal gas. Since the pressure at the

exit is equal to atmospheric pressure P0, the Mach number M

of the flow exiting the tank, can be computed by inverting the

relationship

P1

P0¼�1þ g� 1

2M2

� gg�1

(6)

The temperature and density are related to the Mach

number using the following relationships

T1

T2¼ 1þ g� 1

2M2 (7)

r1

r2¼�1þ g� 1

2M2

� 1g�1

(8)

Finally, the velocity V2 at the exit is computed as

V2 ¼ MffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigRH2

T2

p(9)

Furthermore, if the area of the jet at the tank exit is denoted

as A2, corresponding to a diameter d2, then the instantaneous

density of the gases in the tank can be obtained by solving a

first-order differential equation for density with time

VTdr1dt

¼ �r2V2A2 (10)

where, VT is the volume of the tank. The instantaneous den-

sity can be related to the instantaneous tank pressure through

the equation of state (Eq. (1)).



Fig. 1 e Schematic diagram of a compartment with vents at the top and bottom. The pressure distribution inside and outside

the compartment at the height of the lower and upper vents is also indicated. The variation of pressure as a function of

height within the compartment (dashed line) and outside of the compartment (solid line) are also indicated.


2.3. Under-expanded jets

Jets involving a high-pressure storage device usually result in

a choked flow at the jet exit, where the exit pressure is

considerably greater than atmospheric pressure. The flowwill

then rapidly expand to atmospheric pressure through a series

of expansion waves. Birch et al. [43,44], related the jet exit

conditions (sub-script 2) to fully expanded conditions (sub-

script 3). If d3 is the diameter of the fully expanded jet, then it

can be related to the jet exit diameter d2 through conservation

of mass and momentum as follows

r2V2A2 ¼ r3V3A3 (11)

r2A2V22 � r3A3V

23 ¼ A2ðP3 � P2Þ (12)

Rearranging the equations for conservation of mass (Eq.

(11)) and momentum (Eq. (12)) yield the exit velocity and

diameter of the fully expanded jet as follows

V3 ¼ V2 � ðP3 � P2Þr2V2

(13)

d3 ¼ d2

ffiffiffiffiffiffiffiffiffiffir2V2

r3V3

s(14)

2.4. Justification of the well mixed assumption

The accidental release of hydrogen in a confined environment

can be significantly more dangerous than that in open atmo-

spheres. When hydrogen is released in a partially enclosed

compartment, a buoyant layer of hydrogencandevelop close to

the ceiling or the hydrogen can mix with the compartment

gases. In either case, the concentration of hydrogen can build

up in the compartment. Hydrogen will also disperse through

openings in the compartmentwalls, or forced ventilation of the

compartment. If the hydrogen is released as a low-momentum

jet, then buoyancy will drive themotion of the hydrogen gas to

theceiling.This results instratificationofhydrogenandair, and

the formation of stable layers of fluid which do not mix with

each other [34,35,16]. However, if the hydrogen is released as a

high-momentum jet typical of high-pressure systems,

buoyancy effects are less significant. The inertia of the jet will

drive the mixing of hydrogen with the surrounding air, result-

ing in awellmixed system [15,16,25]. The jet will gradually lose

its inertia as it mixes with the surrounding gases. The two

different states of the compartment flowfield (stratified vswell

mixed) obtained during the release of hydrogen, can be char-

acterizedbytheratioof inertia tobuoyancy forces,expressedby

the densimetric Froude number Fr,

Fr ¼ r3V23

ðr0 � r3Þgd3(15)

where, r0 is the density of the ambient fluid, and g is the ac-

celeration due to gravity. Peterson [45] proposed that for round

jets, stratification will occur when

�Hd3

�Fr�1=6

�1þ d3

0:2ffiffiffi2

pH

�2=3

[1 (16)

where, H is the height of the compartment. This relationship

was consistent with experiments performed by Lee [46] and

Jain [47].

Release of hydrogen from a high-pressure tank will result

in a high-momentum jet (large Froude numbers). However if

the height of the compartmentH is significantlymore than the

diameter of the fully expanded jet d3, then the left hand side of

Eq. (16) can still be much greater than one. However, if

hydrogen is released under an automobile, the height of the

free jet is not equal to the height of the compartment, but

instead is equal to the clearance between the floor and the

body of the automobile. For such a scenario, the hydrogen jet

would hit the under-carriage of the automobile and break up

into multiple jets. Rapid mixing will occur under the auto-

mobile. Most of the hydrogen will escape from under the

vehicle through the wheel wells and the perimeter of the

vehicle as multiple plumes rising towards the ceiling. This

mixing of hydrogen and air under the vehicle, and its subse-

quent release in the form of multiple independent plumes,

results in a well mixed hydrogen air mixture in the compart-

ment. Turbulent mixing under an obstruction resulting in a

well mixed hydrogen air mixture in the compartment has

been observed in full scale experiments [14,15], as well as

through CFD simulations [19,20].



Fig. 2 e Time dependent profiles of pressure, density, temperature, jet diameter, velocity and volumetric flow rate during

the emptying of a 40 MPa tank containing 5 kg of hydrogen. The diameter of the release port was 1 mm.


3. Dispersion in partially enclosedcompartments

Consider the case of a compartment of heightHwith a volume

V, in which hydrogen is leaking accidentally from a high-

pressure tank. The compartment is assumed to be ventilated

through two vents; “Vent 1” is located at the base of the

compartment close to the floor and is also referred to as the

“lower” vent, while “Vent 3” is located at the top of the

compartment, also referred to as the “upper” vent. The two

vents have cross-sectional areas a1 and a3, respectively. Here

the suffixes 1 and 3 correspond to the lower and upper vents.

Note that sub-script 2 will be used to denote intermediate

level vents, consistent with prior work on this subject [25].

Fig. 1 shows a schematic diagram of the compartment of

height H, with vents located close to the floor and close to the

ceiling. The formulation presented here is based on the

concept of compartment overpressure, and is more general

than that discussed in Ref. [25], which was based on height of

the neutral plane.

3.1. Mathematical formulation

Let _MH2 be the mass flow rate of pure hydrogen gas acciden-

tally leaking into the compartment from a pressurized tank.

The mass flow rate varies as a function of time and was dis-

cussed in Section 2.2. As the release of hydrogen from the

high-pressure tank commences, there will be an outflow from

both the upper and lower vents. This is due to compartment

overpressure in response to the sudden introduction of

hydrogen into the compartment. As some of the gases are

allowed to escape from the enclosure, the compartment

overpressure reduces. We assume that the hydrogen within

the compartment is well mixed with the compartment air,

and that the concentration of hydrogen is uniform every-

where (discussed in Section 2.4).

The pressure within and outside the compartment varies

hydrostatically with depth (see Fig. 1). Owing to the lower

density of the gas mixture inside the compartment, the ver-

tical pressure gradient is lower than the vertical pressure

gradient outside the compartment. These gradients are



Fig. 3 e Time dependent profiles of hydrogen volume fraction, compartment overpressure, location of the interface and

volumetric flow rates through the lower and upper vents of a compartment during the emptying of a 40 MPa tank containing

5 kg of hydrogen. The diameter of the release port was 1 mm.


primarily due to the weight of the fluid. The difference be-

tween these pressure gradients leads to a buoyancy-driven

flow through the vents [25,27e30,33]. We denote the velocity

of the fluid through the lower and upper vents as y1 and y3,

respectively (consistent with the formulation in Ref. [25]). It is

assumed that the flow through each opening is unidirectional

at any given instant in time. In general, the velocity yj of a gas

mixture through a vent j is related to the pressure drop DPjusing Bernoulli’s theorem,

yj ¼ffiffiffiffiffiffiffiffiffiffi2DPj

r

s; (17)

where, r corresponds to the density of the gas mixture. The

volumetric flow rate Qj through vent j of area aj is then related

to the velocity yj according to

Qj ¼ aj � yj � cj; (18)

where, cj is the discharge coefficient that accounts for the

reduction in the area of the streamlines through the vent. The

discharge coefficient is a constant lying between 0.5 for a

sharp expansion at the inlet and 1.0 for a perfectly smooth

expansion.

Fig. 1 includes the pressure variations with height, both

inside and outside the compartment. The ambient pressure at

the height of the upper vent outside the compartment is

represented by P0. The pressure inside and outside the

compartment varies hydrostatically with height. As a conse-

quence, the pressure at the height of the lower vent outside

the compartment will be higher due to the weight of the fluid

and will equal to P0 þ r0gH, where r0 is the density of the

ambient fluid and g is the gravitational acceleration. If we let

DPc be the instantaneous compartment overpressure, then the

pressure inside the compartment at the height of the upper

vent is represented as P0 þ DPc, while that at the height of the

lower vent is represented as P0 þ DPc þ rgH, as shown in Fig. 1.

The pressure differences at the levels of the lower vent DP1and upper vent DP3 can be written as

DP1 ¼ DrgH� DPc (19)

DP3 ¼ DPc (20)






where, Dr ¼ r0 � r, and r0 is the density of the ambient air,

while r is the instantaneous density of the compartment.

Substituting equations for pressure difference across the

vents (Eqs. (19) and (20)) in (17), the velocities through vent 1

and vent 3 can be expressed as

y1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2DrgH� DPc

r0

s(21)

y3 ¼ffiffiffiffiffiffiffiffiffiffiffiffi2DPc

r

s(22)

For any hydrogen accidental release scenario, it is critical

to develop a capability to predict the hydrogen volume frac-

tion inside the compartment as a function of time. Since the

velocity and volumetric flow rates through the vents are

related to the instantaneous compartment overpressure, the

hydrogen concentration in the compartment is dependent on

the instantaneous overpressure. The rate of accumulation of

hydrogen in the compartment is dependent on the rate at

which hydrogen gas is released in the compartment and the

outflow of hydrogen through the upper vent.

Vd�rYH2

�dt

¼ _MH2� YH2

� r � ða3y3c3Þ (23)

where, YH2is the instantaneous mass fraction of hydrogen.

The ordinary differential Eq. (23) can be solved to obtain the

gas density within the compartment, and this in turn can be

used to compute the mass fraction or volume fraction of

hydrogen in the compartment as a function of time. Since the

velocity (and volumetric flow rates) through the vents are

related to the instantaneous compartment overpressure, an

additional equation is needed to predict the instantaneous

overpressure of the compartment DPc, needed to obtain the

velocity y3 in Eq. (23). Since the volume of the compartment is

fixed, the volumetric flow rate into the compartment must

equal the volume of gases leaving the compartment through

the upper vent, or

_VH2þ a1y1c1 ¼ a3y3c3 (24)

where, _VH2is the volumetric flow rate of pure hydrogen gas

released into the compartment and can be obtained by

dividing the mass flow rate _MH2by the density of pure

hydrogen gas rH2.







Eqs. (24) and (23) form a system of equations that were

solved to obtain the density r of the compartment and the

compartment overpressure DPc as a function of time. Eq. (23) is

an ordinary differential equation that was advanced in time

using a second order RungeeKutta (RK) method (midpoint

method), followed by a NewtoneRaphson iteration to solve

the volume conservation Eq. (24) to obtain the compartment

overpressure and compartment density (hydrogen volume

fraction). The volumetric flow rates through the lower and

upper vent can be subsequently obtained using Eq. (18) along

with Eqs. (21) and (22).

3.2. Design of idealized vents

Leak rates for garages are typically described in terms of the

number of air changes per hour (ACH) for an enclosure of

volume, Venc, which corresponds to a volume flow exchange

rate across the enclosure boundary, Qenc, given by

Qenc ¼ Venc � ACH/3600. ACH can vary substantially with time

and depends not only on the areas of openings connecting

across the enclosure boundary, but also on such factors as

weather conditions and forced ventilation. Values of Qenc can

be related to an effective leak area, ELA by use of the Bernoulli

equation,

ELA ¼ ðQencÞ �ffiffiffiffiffiffiffiffiffir

2DP

r; (25)

where, DP is the pressure difference across the vent usually

set at 4 Pa, and r is the density of the gas. In the current work,

the vents were designed using an ACH ¼ 3, along with Eq. (25).

Although the values of ACH and ELA varywidely for garages in

the United States [48,49], an ACH ¼ 3 is consistent with the

recommendation of American Society of Heating, Refriger-

ating, and Air-Conditioning Engineers (ASHRAE) as well as

current ICC standards [50].

3.3. Time required to empty a compartment

Once the hydrogen tank is empty, the mass flow rate of

hydrogen into the compartment becomes zero. Beyond this






point (referred to as the dispersion phase), the hydrogen

concentration in the compartment will gradually decrease as

the hydrogen is dissipated through the vents in the

compartmentwalls. An important problem in hydrogen safety

is to predict the time required to empty a compartment that is

initially filled with a hydrogen/air mixture.

During the dispersion phase, fresh air flows into the

compartment through the lower vent while hydrogeneair

mixture leaves through the upper vent, resulting in a stratified

compartment. The upper layer of the compartment consists of

the hydrogeneair mixture, while the lower layer of the

compartment contains fresh air. It is assumed that the

incoming air does not mix with the fluid in the compartment,

but instead forms a layer of increasing depth in the

compartment. The hydrogeneairmixture in the compartment

is vented through a buoyancy-driven flow out of the

compartment. The location of this interface between the fresh

incoming fluid and hydrogeneair mixture is referred to by a

height hi, which is a function of time. A complete discussion of

the mathematical formulation for predicting the time

required to empty a compartment was presented in Ref. [25].

The equations developed in that reference were also used in

the current work, to obtain the instantaneous location of the

interface during the emptying process and to predict the time

required to empty the compartment.

3.4. Forced ventilation

In Section 3, a mathematical model for natural ventilation of a

compartment and its effect on hydrogen concentration in the

compartment was discussed. The analysis can be extended

readily to the case of forced ventilation of the compartment. In

the case of forced ventilation through the upper or lower vent,

the volumetric flow rate at those vents were set to fixed (con-

stant)values,and thesevalueswereused inEqs. (23)and (24). For

the case of forced ventilation, the volumetric flow rate through

the upper or lower vent is fixed and does not vary with time.

4. Results and discussion

The formulation developed in the Sections 2 and 3was used to

study the release of hydrogen from a high-pressure tank, and

its dispersion in a partially enclosed compartment. The inte-

rior dimensions of the compartment used for this study were

6.0 m � 6.0 m � 3.0 m, with a total volume of 108 m3. The







compartment was vented through two square vents (leaks)

located at the top and bottom of one side wall. The vent cross-

sectional area was varied as a parameter to understand the

effect of leaks on flammable hydrogen concentrations in a

compartment. For the base case, each vent had a cross-

sectional area of 0.01 m2, selected to give an ACH value of 3

(See Section 3.2). Hydrogen contained in a high-pressure tank

was released through a release port (representative of a failed

PRD, or a crack in the vessel wall), located under an automo-

bile parked in the center of the compartment. For all of the

cases discussed in the paper, the initial tank pressure was

40 MPa and contained 5 kg of hydrogen at room temperature.

The diameter of the release port was varied from 1 mm to

6 mm as a parameter during this study. The diameter of the

release port for the base case was chosen as 1 mm. In this

section, we study the effect of changing the diameter of the

release port and its effect on compartment overpressure and

flammable concentration of hydrogen. The effect of changing

the compartment ventilation (air changes per hour) as well as

forced ventilation to reduce the hazard associated with

flammable volume of hydrogen will also be discussed.

4.1. Base case

Fig. 2 shows the time dependent profiles of the jet exit

conditions, including pressure, density, velocity, volumetric

flow rate and jet diameter, during the release of hydrogen

from a high-pressure tank. The tank has an initial pressure

of 40 MPa, and contains 5 kg of hydrogen at room tempera-

ture. The diameter of the release port was set at 1 mm. The

top left sub-figure shows the tank pressure, pressure in the

under-expanded jet as well as that of the fully expanded jet.

The tank blow-down time for a 1 mm diameter release port

was predicted at 1950 s. Results indicate that the tank

pressure reduced rapidly as hydrogen was released as a

choked flow. The pressure at the under-expanded jet was

lower than the tank pressure and reduced with time. The

pressure in the fully expanded jet was equal to the

compartment pressure. The top right sub-figure shows the

density of the hydrogen gas in the tank, in the under-

expanded jet as well as in the fully expanded jet. The den-

sity of hydrogen in the tank reduces, as the gas expands and

flows through the release port.



Fig. 8 e Compartment overpressure plotted as a function of

diameter of the release port, for various ACH values.


The bottom left sub-figure (Fig. 2) shows the velocity of the

under-expanded jet as well as the fully expanded jet on the y-

axis, plotted as a function of time. The volumetric flow rate as

a function of time through the release port is shown on the

2nd y-axis. The velocity of the under-expanded jet is equal to

the sonic jet velocity and is constant for the first 1700 s.

Beyond this point, the jet transitions from a sonic to sub-sonic

flow. The velocity of the fully expanded jet is highest at time

t ¼ 0 and gradually reduces with time. Once the jet becomes

sub-sonic, the two velocities are identical, as expected. The

volumetric flow rate is extremely high initially, but drops

rapidly as the pressure in the tank reduces. The jet diameter of

the under-expanded jet (bottom right sub-figure) was equal to

the diameter of the release port and did not change with time.

The jet diameter of the fully expanded jet was approximately

10 times larger than that of the under-expanded jet. As the

tank pressure reduces, the jet diameter of the fully expanded

jet becomes smaller, until it is equal to the diameter of the

under-expanded jet.

Fig. 3 summarizes the state of the compartment during the

high-pressure release of hydrogen as well as the dispersion

phase that follows the release phase. This figure shows plots

for the hydrogen volume fraction in the compartment, the

instantaneous overpressure in the compartment, height of

the interface (valid only during the emptying phase) and the

volumetric flow rates through the vents plotted as a function

of time. As discussed earlier, the release phase lasts for 1950 s,

and is followed by a dispersion (emptying) phase. The

dispersion phase is assumed to end when hydrogeneair

interface is located at height greater than 99% of the

compartment height, and lasts for a period of 4770 s. The

hydrogen volume fraction (top left sub-figure) is initially zero

inside the compartment. Following the initiation of hydrogen,

the volume fraction increases rapidly to reach a maximum

value of 0.36, and then reduces to 0.25 at the end of the release

phase. The hydrogen volume fraction increases because

hydrogen is released at high-pressure into the compartment

at a rate higher than the rate at which it can dissipate through

the openings (leaks) in the compartmentwall. However, as the

volumetric flow rate of hydrogen through the release port in

the high-pressure tank reduces rapidly, the hydrogen volume

fraction reaches a peak value and subsequently starts to

decrease. The compartment overpressure (top right sub-

figure) exhibits high-pressure in the compartment immedi-

ately following the release of hydrogen, followed by a rapid

decrease in the overpressure.

The bottom right sub-figure shows the volumetric flow rate

through the upper and lower vent during the release and

dispersion phase. The volumetric flow rate of hydrogen

through the high-pressure tank has also been indicated. Pos-

itive volumetric flow rates indicate flow into the compart-

ment, while negative flow rates indicate flow out of the

compartment. During the release phase, the flow rate through

the upper and lower vents are initially negative. This implies

that the flow leaves the compartment through both the upper

and lower vent. This is primarily due to the higher compart-

ment overpressure. As the compartment overpressure re-

duces, the flow direction through the lower vent reverses and

air starts to flow into the compartment through the lower

vent. The magnitude of the volumetric flow rates through the

upper and lower vents gradually reduces as the air displaces

the hydrogen during the dispersion phase. As hydrogen flows

out of the upper vent, and fresh air enters the compartment

through the lower vent, hydrogen is displaced upwards,

resulting in a density interface. The bottom left sub-figure

shows the location of the interface during the dispersion

phase. When the density interface reaches the ceiling, there is

no hydrogen left inside the compartment. Results indicate

that the compartment is completely empty at 6723 s after the

initial release of hydrogen into the compartment.

4.2. Parametric study

Fig. 4 shows a set of predicted results (similar to those in Fig. 2)

for tank outlet conditions with a 3 mm release port. The cor-

responding compartment conditions plotted as a function of

time are shown in various sub-figures of Fig. 5. Similarly, Figs.

6 and 7 show the tank outlet conditions and the corresponding

compartment conditions during the high-pressure hydrogen

release from a 6 mm release port. For all these cases, release

occurs from a tank with an initial pressure of 40 MPa, and

containing 5 kg of hydrogen at room temperature. The tank

blow-down time for a 3 mm release port was predicted at

210 s, while the blow-down time for a 6 mm release port was

computed to be 50 s. Results confirm that as the size (diam-

eter) of the release port increases, the blow-down time de-

creases. The results are consistent with previously published

results in this subject [40]. The tank pressure reduces at a

faster rate from 40MPa to ambient pressures, as the size of the

release port increases. The jet diameter of the fully expanded

jet was larger as the diameter of the release port increases.

The maximum jet diameters of the fully expanded jet were

predicted at 1.1 cm, 3.0 cm, and 5.8 cm, for release port di-

ameters of 1.0 mm, 3.0 mm, and 6.0 mm, respectively. As the

jet diameter increased, the volumetric flow rate through the

release port also increased. The maximum volumetric flow




rate was computed at 0.17 m3/s, 1.7 m3/s, and 6.0 m3/s for

release port diameter of 1.0 mm, 3.0 mm, and 6.0 mm,

respectively.

Higher volumetric flow rates through the release port re-

sults in larger compartment overpressure as seen in the sub-

plots in Figs. 5 and 7. The compartment overpressure was

computed at 14 Pa, 500 Pa, and 10,000 Pa for release port di-

ameters of 1.0 mm, 3.0 mm, and 6.0 mm, respectively. Model

results indicate that the peak value of H2 volume fraction

during the release phase increases as the size of the release

port increases. Peak values of H2 volume fraction were

computed at 0.36, 0.47 and 0.49 for release port diameters of

1.0 mm, 3.0 mm, and 6.0 mm, respectively. The rate of in-

crease of the peak hydrogen volume fraction reduces as the

size of the release port increases. The H2 volume fraction in

the compartment at the end of the release phase increases

with the diameter of the release port. This result is directly

related to the reduction in the blow-down time associated

with the increase in the diameter of the release port. The H2

volume fractions at the end of the release phase were

computed at 0.22, 0.44, and 0.49 for release port diameter of

Fig. 9 e Time dependent profiles of hydrogen volume fraction,

volumetric flow rates through the lower and upper vents of a com

5 kg of hydrogen. The diameter of the release port was 1 mm a

0.1 m3/s.

1.0 mm, 3.0 mm, and 6.0 mm, respectively. Again, the rate of

increase in volume fraction (measured at the end of the

release phase) reduced as the diameter increases.

Even though the hydrogen volume fraction in the compart-

ment is higher at the end of the release phase, dispersion of

hydrogen through openings in the compartment wall was

predicted to take less time. This is primarily because of the

buoyancy associated with the hydrogen in the compartment

that drives the flow through the lower and upper vents. The

buoyancy induced flow was predicted to be larger at higher H2

volume fractions as seen in the volumetric flow rate plots.

4.3. Compartment damage

Fig. 8 shows themaximum compartment overpressure plotted

as a function of thediameter of the release port for variousACH

values. The figure also indicates the overpressure limits that

can result in catastrophic damage, major damage, minor

damage and cosmetic damage to the compartment [51]. Vent

sizes were designed using air changes per hour that vary from

1e5. Results indicate that compartmentoverpressure increases

compartment overpressure, location of the interface and

partment during the emptying of a 40 MPa tank containing

nd the forced ventilation through upper vent was set at




with diameter of the release port for all ACH values. However,

the rate of increase in compartment overpressure is smaller as

the diameter increases. For a given diameter, the overpressure

is larger for smaller values of ACH. This result is significant

because most pressure release devices for vehicle application,

currently in the market have diameters of 6 mm [3,6]. Results

indicate that if the diameter was reduced to 1 mm, the

compartment would be safe for all ACH values used in this

study. However the reduction in diameter will result in longer

blow-down times, and the risk associated with longer blow-

down time in a fire scenario must be weighed against damage

to the compartment due to compartment overpressure.

Fig. 11 e Effect of forced flow rate on the duration of

flammable mixture in a compartment. Results for three

different hydrogen release port diameters are plotted.

4.4. Comparison of forced ventilation and naturalventilation

All the results that have been discussed so far utilize buoyancy

induced natural ventilation to disperse hydrogen. We next

compare the results of natural ventilation with those of forced

ventilation through the compartment on hydrogen volume

fraction and dispersion time of hydrogen gas from the

compartment. Fig. 9 shows the time dependent profiles of

hydrogenvolumefraction, compartmentoverpressure, location

of the interfaceandvolumetricflowrates through the lowerand

upper vents of a compartment during the emptying of a 40MPa

tank containing 5 kg ofH2 gas subjected to forced ventilation. In

this calculation the upper vent was forced ventilated and

the volumetric flow rate out of the compartment through the

upper vent was set at 0.1 m3/s. This forced ventilation corre-

sponds to an ACH value of 33.33. It is assumed that the forced

ventilation is continuous for the duration of the release and

dispersion phase. Forced ventilation during the release phase

has no effect on the jet exit conditions, as these are primarily

driven by the pressure in the tank. The diameter of the release

port was set at 1mm for comparisonwith base case conditions.

Comparison of the results shown in Fig. 9 with Fig. 3 indi-

cate that the peak hydrogen volume fraction was smaller for

Fig. 10 e Peak hydrogen volume fraction in the

compartment plotted as a function of forced ventilation

flow rates for leak diameter of 1 mm, 3 mm and 6 mm.

the case of forced ventilation, and the hydrogen volume

fraction at the end of the release phase was also significantly

lower. The compartment overpressure for the case of forced

ventilation was negative, due to the fact that gas was being

sucked out of the compartment resulting in negative over-

pressure. Results also indicate that the duration of the

dispersion phase was extremely small (30 s). These results

indicate that forced ventilation can be a viable technique for

reducing hydrogen volume fraction in the compartment, and

for reducing the time interval during which dangerous levels

of H2 concentration may exist in the compartment. Results of

this study indicate that forced ventilation is an effective

approach for reducing the risk associated with accidental

release of H2 in partially enclosed compartments.

Fig. 10 shows the peak hydrogen volume fraction in the

compartment plotted as a function of the forced flow rate (y-

axis). The corresponding ACH value is shown on the 2nd y-

axis. The peak volume fraction reduces as the forced flow rate

increases for all release diameters. This result indicates that

the methodology proposed in this paper can be used to design

forced ventilation requirements for a compartment such that

hydrogen concentration (during an accidental release), stays

below the flammability limits. Fig. 11 shows the time interval

duringwhich a flammablemixtures exist in the compartment.

Again, as the rate of forced ventilation increases, the time

interval during which a flammable mixture exists inside the

compartment reduces. This implies that the hazard due to

flammable hydrogen concentrations inside a compartment,

can be mitigated effectively using forced ventilation.

5. Conclusions

A simple analytical model was developed to predict the risk

associated with accidental release of hydrogen from a high-




pressure system into a partially ventilated compartment. The

model employs real gas equation of state and isentropic re-

lationships to determine the blow-down time of hydrogen

from a high-pressure tank and the volumetric flow rate of

hydrogen that is released into the compartment. Tank blow-

down studies were found to be consistent with published

data. The hydrogen released into the compartment as a high

speed jet was assumed to mix rapidly with the surrounding

air, andwas dispersed through two idealized openings located

in the top and bottom of one side wall of the compartment

(partially enclosed system). The analytical model was

designed to predict the concentration of hydrogen in the

compartment during the release phase, as well as to model

the effect of natural and forced mixing and dispersion on

hydrogen concentration. The transient analysis involves the

determination of the instantaneous compartment over-

pressure and the buoyancy induced flow or forced ventilation

through each vent.

The model was used to predict the maximum compart-

ment overpressure during the release of hydrogen from a

high-pressure system. Conditions that can lead to major

damage of the compartment due to overpressure were iden-

tified. The effect of changing the diameter of the release port

and ACH on maximum compartment overpressure was

determined. Results indicate that the instantaneous

compartment overpressure obtained with a 6 mm diameter

release port (diameter of PRD devices currently in themarket),

would result in significant damage to the compartment walls

for ACH values ranging from 1 to 5. On the other hand, a

release port diameter of 1.0 mm resulted in compartment

overpressures that were significantly below the limits for

cosmetic damage to the compartment walls, for ACH values

ranging from 1 to 5.

Themodel developed in this paper can be used to study the

consequences of natural and forced ventilation in a

compartment during the release of hydrogen from a high-

pressure system. Results indicate that forced ventilation is a

viable technique for reducing hydrogen volume fraction in the

compartment, and for reducing the time interval during

which dangerous levels of hydrogen concentrationmay exists

in the compartment. The models proposed in this paper can

be used to provide design guidelines for forced ventilation

requirements in a compartment to ensure that hydrogen

concentration following an accidental release never goes

above the lower flammability limit.

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High-pressure release and dispersion of hydrogen in a partially enclosed compartment: Effect of natural and forced ventilation