NIST Technical Note 1484 

A Computational Model of 

Dissipation of Oxygen from an 

Outward Leak of a 

Closed-Circuit Breathing Device 

Kathryn M. Butler 

 

 

 

 

NIST Technical Note 1484
 

A Computational Model of 

Dissipation of Oxygen from an 

Outward Leak of a 

Closed-Circuit Breathing Device 

Kathryn M. Butler 

Building and Fire Research Laboratory 

Fire Research Division 

June 2007 

U.S. Department of Health and Human Services U.S. Department of Commerce 

Mike Leavitt, Secretary Carlos M. Gutierrez, Secretary 

Centers for Disease Control and Prevention Technology Administration 

Julie Louise Gerberding, Director Robert Cresanti, Under Secretary for Technology 

National Institute for Occupational Safety and Health National Institute of Standards and Technology 

John Howard, Director William Jeffrey, Director 
 

Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1484 

Natl. Inst. Stand. Technol. Tech. Note 1484, 41 pages (June 2007) 

CODEN: NSPUE2 
ABSTRACT 

Closed-circuit breathing devices recycle exhaled air after scrubbing carbon dioxide and 

adding make-up oxygen from a tank of pure oxygen. Use of this equipment allows first 

responders to work for up to four hours without swapping out cylinders and scrubbing 

canisters. Firefighting situations in which these devices would be useful include tunnels, 

mines, ships, high-rise buildings, and environments contaminated with biological or 

chemical toxins. A risk perceived by firefighters entering environments containing open 

flame and high radiant heat is the possibility of fire ignition in the vicinity of the 

respirator caused by the outward leakage of oxygen around the facepiece. 

This paper presents the results of a computational fluid dynamics (CFD) study of oxygen 

dissipation into the environment surrounding a respirator facepiece. Actual heads and 

masks are scanned into a 3D data set for entry into the CFD software, providing a 

physical boundary for the problem to be solved. Leak geometries representing an 

imperfect seal are defined. Oxygen concentration fields and flow streamlines are 

presented for multiple combinations of fuel and air in the surrounding environment, for 

pure oxygen and air expelled from the leak, and for both normal and high stress breathing 

patterns. The flammability diagram for propane is used to estimate the flammable 

regions as a function of time during two breathing cycles for each case. 

i 
ACKNOWLEDGEMENTS 

The preparation of this report was supported by the Office of Law Enforcement 

Standards under Interagency Agreement # HSSCHQ-04-X-00641, and by the National 

Institute for Occupational Safety and Health (NIOSH) National Personal Protective 

Technology Laboratory (NPPTL) as part of the project entitled “Task for Computer 

Simulation of Face Piece Oxygen Leakage Under Positive Pressure”. The results 

published herein are solely the responsibility of the author. The author would like to 

thank John Kovac of NPPTL for his oversight on this project and many helpful 

discussions. Nicholas Kyriazi of NPPTL helped us understand the experimental 

evidence. Informative discussions on respirators with Ronald Shaffer, Ziqing Zhuang, 

and William Newcomb of NPPTL are also gratefully acknowledged. Daniel Crowl of 

Michigan Technological University provided valuable information on flammability 

diagrams. Dennis Viscusi of NIOSH provided the 3D scanned image of the headform 

used in NPPTL experments, and Dräger Safety provided technical drawings for a 

respirator. Technical discussions with Rodney Bryant and Nelson Bryner of NIST are 

gratefully acknowledged. 

ii 
ABSTRACT ...........................................................................................................I
 

ACKNOWLEDGEMENTS ....................................................................................II
 

1 INTRODUCTION ...........................................................................................1
 

2 MODEL CONDITIONS ..................................................................................3
 

2.1 Breathing Rates........................................................................................3
 

2.2 Leaks.........................................................................................................4
 

2.3 External Environment ..............................................................................5
 

3 MODEL GEOMETRY ....................................................................................7
 

3.1 Headform ..................................................................................................7
 

3.2 Respirator Geometry ...............................................................................8
 

3.3 Combining Headform and Respirator.....................................................9
 

4 COMPUTATIONAL FLUID DYNAMICS MODELING .................................12
 

4.1 Flow.........................................................................................................12
 

4.2 Chemistry................................................................................................13
 

4.3 Turbulence..............................................................................................14
 

4.4 Problem Geometry .................................................................................15
 

4.5 Boundary Conditions.............................................................................16
 

4.6 Initial Conditions ....................................................................................18
 

5 MESH STUDY .............................................................................................19
 

5.1 Leak resolution.......................................................................................19
 

5.2 Size of External Box...............................................................................21
 

5.3 Mesh Refinement in Direction of Jet ....................................................23
 

iii 
6 RESULTS FOR A SMALL LEAK DURING BREATHING AT REST ..........26
 

6.1 Leak of Pure Oxygen into Pure Propane Environment.......................26
 

6.2 Leak of Pure Oxygen into 10 % Propane Environment.......................30
 

6.3 Leak of Air into 10 % Propane Environment........................................32
 

6.4 Leak of Pure Oxygen into 5 % Propane Environment.........................33
 

7 RESULTS FOR A SMALL LEAK WHILE BREATHING UNDER STRESS 37
 

7.1 Leak of Pure Oxygen into 10 % Propane Environment.......................37
 

8 CONCLUDING REMARKS .........................................................................39
 

REFERENCES ...................................................................................................40
 

iv 
 

1 INTRODUCTION 

The respiratory system provides a major access route into the body for chemicals, 

particulates, and bioactive agents. Respirators protect the body by preventing hazardous 

gases, vapors, and particles from entering the respiratory system. 

Atmosphere-supplying respirators, which incorporate a self-contained air supply, are 

used in environments that are considered immediately dangerous to life or health (IDLH). 

These environments may contain highly toxic respiratory contaminants or too little 

oxygen to sustain life. While fighting a fire or overhauling a building, firefighters often 

work in environments where the respiratory hazards are unknown. Firefighters are 

therefore provided with self-contained breathing apparatus (SCBA) units, with a clean air 

supply cylinder that is carried on the wearer’s back. These respirators also provide the 

unrestricted mobility required during firefighting. 

Open-circuit SCBAs, which vent exhaled air to the atmosphere, are by far the most 

commonly used in firefighting. The standard compressed air cylinders used in these 

devices contain a limited air supply with a duration of 30 min to 60 min when breathing 

rates are normal. Under heavy workloads, a compressed air cylinder may last as little as 

10 min to 20 min. Although this may be adequate for fighting ordinary house fires, 

longer durations may be necessary in certain situations, including fires in tunnels, mines, 

ships, and high-rise buildings. A situation of particular concern after the events of 9/11 is 

that of a terrorist attack, in which a fire is accompanied by possible chemical, biological, 

radiological or nuclear (CBRN) contamination. 

An alternative to the open-circuit SCBA is the closed-circuit Self-Contained Breathing 

Apparatus (CC-SCBA), which recirculates exhaled air by absorbing carbon dioxide and 

adding fresh oxygen. Because oxygen needs are only around 5 % of air needs (oxygen 

consumption rate/ventilation rate),1 an oxygen cylinder of comparable weight to a 

compressed air cylinder can sustain the firefighter for a much longer period of time. 

Closed-circuit SCBAs, also known as rebreathers or four-hour sets, can be used for up to 

4 h before swapping cylinders and CO2-absorbent canisters. This type of equipment is 

currently used as rescue breathing apparatus in mining operations.2,3 

The National Institute for Occupational Safety and Health (NIOSH) is developing 

standards for the use of closed-circuit SCBA by firefighters and other first responders 

after a terrorist attack.4,5

 In addition to the respiratory protection of first responders in 

environments containing CBRN agents identified as inhalation hazards, the equipment 

must be usable under conditions of high heat and open flames. Although a leak is 

unlikely for a respirator with good fit, the possibility of outward leakage of oxygen in a 

fire environment is a concern. If the oxygen remains concentrated around the face in the 

presence of fuel gases and heat, ignition may occur. If the oxygen diffuses rapidly away 

from the face, however, the possibility of ignition is negligible. The intent of this study is 

to consider the potential for danger under worst-case conditions. 

1 
Computational fluid dynamics (CFD) numerically simulates fluid flow by solving the 

equations of motion. The solutions can be obtained in detail that is impossible to achieve 

in experiments, and for variables that are difficult or impossible to measure in practice, 

especially in three-dimensional space. A variety of situations, including breathing 

pattern, leak geometries, and varying concentrations of gaseous components, may be 

tested. The visualization of the computational results as they vary with time and space 

enhances our understanding of the flow phenomena. Validation of CFD with 

experimental measurements is recommended to ensure that the results accurately reflect 

reality. 

2 
 

 

2 MODEL CONDITIONS 

In this report, respirator leakage effects on the environment exterior to the mask are 

investigated over a set of conditions that are within the range expected to be encountered 

by a firefighter. The variables of primary interest in this study are breathing rate, leak 

geometry, and external environment. 

2.1 Breathing Rates 

The pulmonary system is capable of supporting a variety of activity levels. Increased 

workloads require increased oxygen to the bloodstream, which is obtained by a 

combination of increased breathing rate and increased volume of air per breath. The 

respiratory minute volume or minute ventilation V&

E is defined as the volume of air that is 

moved out of a person’s lungs in one minute, and is given by the product of the tidal 

volume VT , the volume of air moved during the exhalation phase of each breath, and the 

respiratory frequency f, the number of breaths per minute. For an average adult, values of 

V&

E can range from about six liters per minute at rest to a maximum value of (70 to 90) 

L/min during strenuous exercise. For well-trained or elite athletes, maximum V&

E can 

easily exceed 100 L/min. In a study of firefighters, the median minute volume during 

heavy work rates was found to be about 60 L/min, with a capability of 100 L/min or more 

over short time periods. 6 So the minute ventilation under a heavy workload may be 12 to 

15 times that at rest or even more.7 

While at rest, an average adult breathes at a rate of (12 to 15) breaths per minute, with a 

tidal volume of about 0.5 L. (The maximum capacity of the lungs is about ten times this 

volume.) Inhalation requires the contraction of the diaphragm, and the flow rate rises and 

falls more or less symmetrically in time, with variability due to changes in the rate of 

contraction. During normal exhalation the diaphragm relaxes, and the flow rate quickly 

rises to a maximum value then decreases in time. Durations of inhalation and exhalation 

cycles may not be exactly the same. 

For the respirator leak model studied here, a simplified breathing cycle is assumed. For a 

normal resting breath, the respiratory frequency is taken to be 15 breaths per minute, with 

inhalation and exhalation cycles each lasting two seconds. The flow during exhalation is 

considered to be steady over time, with a tidal volume of 0.5 L released over the 2 s 

duration, a fraction of which is expelled steadily through the leak. During inhalation, the 

leak is assumed to close. This assumes that the low positive pressure that exists within 

the respirator facepiece during inhalation is insufficient to keep the leak open. 

This study also considers a breathing cycle at high breathing rate and tidal volume, 

representing breathing under high stress due to exertion. This cycle takes the same form 

as the breath at rest, with a breathing rate of 60 breaths per minute and tidal volume of 

3 L. This gives a minute ventilation of 180 L/min, which is very high. 

3 
2.2 Leaks 

Most CC-SCBAs are positive pressure respirators, which maintain positive pressure in 

the facepiece throughout the breathing cycle. An outward leak is therefore a possibility if 

a perfect seal between respirator and face is lost. 

In order to use a respirator with a tight-fitting facepiece, a firefighter must undergo fit 

testing using the same make, model, style, and size of respirator that will be worn on the 

job. Fit testing must be performed at least once a year, whenever there is a change in the 

respirator, and whenever there is a change in the physical condition of the face, such as 

dental changes and weight gain or loss. The fit can also be affected by facial hair and 

breathing demands caused by high work rates. A seal check performed by the user every 

time the respirator is put on helps to ensure a tight seal. 

The most likely position and size for an outward leak from a respirator facepiece is not 

known. In the absence of this information, a leak location near the temples was selected 

for this study. The size of the leak was arbitrarily chosen to be 1 mm wide by 43.6 mm 

long – larger than a pinhole leak but not catastrophic in extent. 

The mixture of gases expelled by a leak is determined by the gaseous content of the 

facepiece. In normal breathing without a respirator, an exhalation contains 

approximately 16 % O2 by volume and 4 % CO2 by volume. When using the CC-SCBA, 

the exhaled air passes through a canister that absorbs the CO2, then into a flexible 

breathing bag. For most types of apparatus, the O2 is supplied to the breathing bag at a 

steady rate from the oxygen source, which can be either compressed O2 gas, liquid O2, or 

solid potassium superoxide (KO2). With compressed-O2 apparatus, when O2 

consumption is greater than the O2 flow rate, a demand valve supplies more O2 as 

needed. When the breathing bag is full, a relief valve vents excess contents to the 

ambient environment. 

The concentration of oxygen within the respirator facepiece must therefore be somewhere 

between the 16 % of normal exhalation and the 100 % content of the oxygen source. 

(Note that below 19.5 % a gas mixture is considered to be oxygen deficient.) Tests 

performed by NIOSH on fourteen rescue breathing apparatus showed that, for all but two 

units, the average inhaled oxygen concentration was much higher than that of the exhaled 

breath.2

 In fact, average O2 concentrations were above 60 % for eleven units and above 

80 % for six. 

The danger posed by an outward leak into a mixture that contains flammable gases 

depends, among other things, on the concentration of oxygen in the facepiece. Since the 

intent of this study is to investigate a worst-case scenario, and since elevated levels of 

oxygen have been measured within the facepieces of several CC-SCBA units during 

operation, the model will assume that the content of the gas expelled through the leak is 

pure oxygen. 

4 
2.3 External Environment 

The incomplete combustion that takes place in an uncontrolled fire generates smoke and 

flammable fuel gases that may be transported a distance from the fire. One of the hazards 

faced by the firefighter, and a primary reason for using an atmosphere-supplying 

respirator, is a lack of knowledge about the contents of the surrounding atmosphere. 

Especially while fighting a fire in the same room, a firefighter may be subjected to high 

concentrations of flammable gases. It is important to understand what the possible 

consequences are if oxygen from a respirator mask leak is introduced into this 

environment. 

For this study, a way is needed to estimate the potential for fire to occur in the vicinity of 

a leak of oxygen into a fuel/air mixture. First, consider a mixture of a fuel gas with air. 

A mixture of fuel and air is able to burn only when the concentration of the fuel gas is 

within a certain range of values, delineated by the lower flammable limit, or LFL, and the 

upper flammable limit, or UFL. Below the lower flammable limit, the mixture of fuel 

and air lacks sufficient fuel to burn. Above the upper flammable limit, the mixture is too 

fuel rich and lacks sufficient oxygen to burn. Flammable limits have been determined 

experimentally for many gases and vapors.8 The ignition of a mixture within the 

flammable range requires a small source of energy, which can be provided, for example, 

by a spark due to static electricity. 

In the problem described in this paper, pure oxygen is introduced to a fuel/air mixture. 

An estimate of the potential for fire to occur in the vicinity of a leak of oxygen into a 

fuel/air mixture requires a flammability diagram for the fuel.9,10 For this project, 

propane is chosen as a simple gaseous hydrocarbon fuel. 

Fig. 1 shows a flammability diagram for propane. In this diagram, concentrations of 

propane, oxygen, and nitrogen (fuel, oxidant, and inert gas respectively) are shown on 

three axes. Each point within the diagram describes a unique mixture of the three gases. 

Concentrations are given in percent by volume. Combinations of air with fuel are found 

along the air/fuel line, which connects pure propane at point D at the top, to pure air at 

point E at the bottom (79 % nitrogen, 21 % oxygen, and 0 % propane). The LFL and 

UFL for propane in air are located along this line at values of 2.1 % by volume and 9.5 % 

by volume.8

 These are plotted at points B and A respectively. The line from point D that 

is tangent to the flammable region, at point C, is known as the limit line. The mixtures 

along the limit line have a fixed ratio of oxygen to nitrogen below which flame 

propagation is not possible for any amount of propane. This line meets the lower axis at 

the limiting oxygen concentration, LOC, which is 11.5 % by volume for propane.10 

In pure oxygen, the LFL and UFL have been determined experimentally for several fuels. 

Values for propane were not found in the literature, but a reasonable estimate can be 

obtained using values for other simple hydrocarbon fuels. The UFL in oxygen is 61 %, 

66 %, 49 % and 52 % for methane, ethane, n-butane, and n-hexane respectively.11 These 

are simple linear hydrocarbons with one, two, four, and six carbon atoms respectively. 

5 
 

Figure 1. Flammability diagram for propane (in volume percent). UFL for oxygen 

(Point G) is estimated. 

According to the principles of the group contribution method,12 molecules are expected 

to behave according to the number and type of functional groups within them. Thus the 

UFL in oxygen of propane, with three carbon atoms, can be estimated as about 58 % by 

volume by plotting UFL versus number of carbons. For most fuels, the LFL in oxygen is 

not much different than the LFL in air. The LFL in oxygen of propane is therefore 

estimated as 2.1 % by volume, the same as that in air. The LFL and UFL in oxygen are 

plotted in Fig. 1 as points F and G respectively, along the axis with zero nitrogen 

concentration. 

The connection of points F, B, C, A, G in the flammability diagram provide an estimate 

of the flammable region for propane.13 All mixtures within this region can be ignited. 

Mixtures outside of this range cannot. 

The flammability diagram is a function of temperature and pressure. For the values 

presented here, the conditions are 25° C and atmospheric pressure. 

6 
 

 

3 MODEL GEOMETRY 

Experiments using mannequins have demonstrated that a simplified cylindrical geometry 

is not adequate to represent the flow field near a human face.14 The complex features of 

the human face combined with the features of a respirator mask are necessary for an 

accurate flow model. 

For this modeling effort, the complex geometry for a human head wearing a respirator 

facepiece has been obtained by assembling the shapes for a headform and a facepiece that 

were developed separately. 

3.1 Headform 

A headform used by the National Institute for Occupational Safety and Health (NIOSH) 

in respirator breathing experiments was digitized for use in this model. NIOSH used a 

3D head scanner to capture the three-dimensional external profile of the headform in the 

form of a point cloud, which is a large set of data points with values in x, y, and z 

directions. These points define the location of the surface. The scanner software 

arranged this set of points into an IGES file, a standard format for Computer Aided 

Design (CAD) systems, which was then provided by NIOSH to the National Institute of 

Standards and Technology (NIST). 

A software package called Raindrop Geomagic was used to convert the point cloud to a 

set of geometrical surfaces. Fig. 2 illustrates the development of the headform geometry. 

In Fig. 2(a), the point cloud is shown, with over 180 000 points. The object sticking out 

of the back of the headform is a holder used to keep it in place during scanning. Points 

representing the holder were removed first. Fig. 2(b) shows an early stage of model 

development after the point cloud was converted into a set of triangles. At this point 

there were some holes in the geometry; in particular at the mouth, where the physical 

headform has an opening, and on the top of the head, where the scanner was unable to see 

and therefore could not fix any points. The ridge that surrounds the face is clay that is 

molded onto full facepiece masks to provide a seal during experiments. The Geomagic 

software has a variety of tools for filling holes and smoothing surfaces. Fig. 2(c) shows 

the headform geometry after it was cleaned up. The final step in Geomagic was the 

conversion of the set of triangles to a few hundred patches, or 3D surface entities, that 

were then exported to another IGES file as NURBS surface data. 

The computational fluid dynamics (CFD) software package used for this project, CFDACE+, has a pre-processor, CFD-GEOM, for geometry development. The IGES file 

from Geomagic was read into CFD-GEOM, resulting in a set of surface entities that 

describe the 3D surface of the headform. The surfaces can be changed to develop the 

geometry further.15 In Fig. 2(d), the boundaries of surfaces around the face were 

smoothed to eliminate the clay ridge. The final step in preparing the headform geometry 

was to split it into two along a vertical plane of symmetry. As is discussed below, the use 

7 
 

Figure 2. Steps in preparing headform geometry: a) point cloud from 3-D scanner, 

b) conversion into triangles, c) holes filled in, d) clay removed. 

of symmetry allowed the problem size to be halved. To accomplish this final step, all 

surface entities that intersected the symmetry plane were re-defined such that one edge 

was along the plane. 

3.2 Respirator Geometry 

For a prototypical full facepiece respirator, mechanical drawings were obtained from the 

manufacturer. This allowed a geometry to be built in CFD-GEOM from the relative 

locations of points, curves, and surfaces shown in multiple views and cross-sections. 

Figs. 3(a) and (b) show front and side views of points, lines and curves that were used 

during construction. Figs. 3(c) and (d) show two views of the completed facepiece. In 

these latter two illustrations the visor and facepiece connector region below the visor 

have been left open to allow better viewing of the geometry. For final preparation of the 

model, both visor and facepiece connector are closed. Note that the inner mask, which 

covers the mouth and nose, is missing in this model. Since this project is concerned only 

with leaks to the outside environment, the inner mask is not needed. 

8 
 

Figure 3. Preparation of mask geometry: a) and b) are wire frame images of 3-D 

geometry derived from mechanical drawings, and c) and d) are perspective views. 

Only half of the facepiece was actually constructed from the mechanical drawings. The 

other half was obtained by mirroring the points and curves about the plane of symmetry. 

Halving the facepiece to take advantage of symmetry, therefore, was a trivial operation. 

3.3 Combining Headform and Respirator 

To combine the head with the facepiece, the headform was translated and rotated into the 

proper position relative to the mask within CFD-GEOM, with planes of symmetry 

oriented in the same direction. The first attempt, simply merging the two geometries, did 

not provide a good fit. With the chin in good position, the top of the facepiece was not in 

contact with the forehead, as shown in Fig. 4(a), and the sides extended inside of the 

headform by more than a centimeter. In the real world this geometrical mismatch is 

eliminated by the flexibility of the facepiece, which allows it to fit the shape of the head 

as it is put on. A good fit was achieved in the virtual world through adjustment of the 

facepiece geometry by moving the top toward the forehead, pulling out the sides, and 

defining the inner and outer seals to follow the contours of the face, as shown in 

Fig. 4(b). In the real world, surface areas of sections of the respirator remain constant 

while the angles between them adjust to fit the head. Maintaining these physical 

9 
 

Figure 4. Side view showing fitting of respirator mask to headform: a) original 3-D 

geometries of mask (yellow) and headform (blue) brought together, b) after 

adjustment of mask geometry. 

relationships was not attempted, although an effort was made to prevent gross deformities 

in the shape of the facepiece. 

The final step in making a single model out of two geometries was to redefine surface 

entities in contact with each other such that adjacent surfaces share a common boundary. 

Fig. 5 shows the combined headform and facepiece after processing, as they appear in 

CFD-GEOM. 

In this study, the geometry for a leak is defined by the modeler. A representative leak 

was selected along the outer seal of the facepiece just above the temple region, where 

straps are attached. The leak is shown in Fig. 5 as a thin red line in front of the ears. It 

represents a thin breach of the outer seal about 1 mm thick and 43.6 mm long. 

10 
Figure 5. Model geometry for headform combined with respirator facepiece. Red 

mark indicates the location selected for a representative leak to be studied with this 

model. 

11 
4 COMPUTATIONAL FLUID DYNAMICS MODELING 

The flow of gases and liquids can be determined using mathematical equations that 

describe the conservation of mass, momentum, and energy within the space occupied by 

the fluid. The equations are derived by balancing the time rate of change of the quantity 

of interest in a small volume with its flux in and out, transport due to diffusion, and any 

sources or sinks within the volume. The momentum conservation equation for fluids is 

also known as the Navier-Stokes equation. The terms that are required in the equations 

depend on the physics and chemistry of the particular problem to be solved. The 

equations provide only an approximation to reality – the challenge is to make sure that 

the most important factors are included. In addition to the fluid dynamics equations, the 

mathematical description of a problem requires the definition of boundary conditions on 

all boundaries defining the problem space. For a time-dependent problem, initial 

conditions must be specified. 

The subfield of computational fluid dynamics (CFD) develops numerical methods and 

algorithms for the accurate and efficient solution of the equations for fluid flow. Many 

computational fluid dynamics codes have been written to solve various types of 

problems. The needs of a model of oxygen leaking from a respirator facepiece were 

found to be met by a commercial CFD software package called CFD-ACE+. CFD-ACE+ 

is a multiphysics code that is capable of solving a wide variety of problems, including 

fluids, heat transfer, chemistry, biochemistry, structural dynamics, electricity, and 

electromagnetism. In this application, flow, chemistry, and turbulence modules have 

been used.16 The version of CFD-ACE+ used to develop and run this model was V2004. 

4.1 Flow 

The CFD-ACE+ software is based on the finite volume method. With this approach, the 

solution space is divided into a large number of cells, also known as control volumes. 

The cells are arbitrarily shaped triangles or quadrilaterals in two dimensions, and 

arbitrary 4- to 6-sided volumes in three dimensions. This allows the discretization of 

complex solution spaces, such as the geometry for the combined headform and facepiece 

in this model. 

The governing equations to be solved are integrated numerically over each computational 

cell. The average cell value of all dependent variables (such as velocity, pressure, and 

oxygen concentration) and all material properties (such as density and viscosity) are 

stored at the cell center. Boundary conditions of fixed value or zero flux are assigned 

through the use of fictitious boundary nodes for computational cells adjacent to the 

boundary. A variety of solution schemes are available. First-order upwind differencing 

in space and the Euler method in time were found to give good results for this problem. 

At each timestep, the solution procedure is repeated until either a specified convergence 

property is obtained or until a maximum number of iterations is reached. The iterative 

12 
method used for this problem was the Conjugate Gradient Squared (CGS) + 

Preconditioning equation solver. 

The material properties of the gases used in this model were taken from the standard 

tables of gaseous species. The viscosity for the mixture of gases was calculated using 

Sutherland’s Law and the mix kinetic theory of gases. The ideal gas law was used to 

relate density, pressure, and temperature. This model did not take heat transfer into 

account. So although in reality the mix of fuel and air in the exterior environment will be 

at elevated temperatures, the material properties used in the analysis are room 

temperature values. Note that, in practice, the temperatures of the gases cannot be so 

high that they prohibit the presence of the firefighter. 

Gravity was neglected in this problem. 

4.2 Chemistry 

The Chemistry Module in CFD-ACE+ enables the solution of mixing and reacting flow 

problems. In this model, oxygen from the leak in the respirator facepiece mixes with the 

fuel-air mixture in the surrounding environment. So the concentrations of each chemical 

species must be determined as they vary in time and space. To follow each of four 

chemical species (C3H8-propane, O2-oxygen, N2-nitrogen, and Ar-argon) separately, the 

Species Mass Fractions option was selected. (Although argon was included in the 

problem, it makes up a small fraction of air and could have been neglected.) 

CFD-ACE+ contains a chemistry database that holds basic data for many elements, 

species, and mixtures.17 A new mixture may be added to this database by specifying the 

mass fraction or concentration of each species in the mixture and assigning a unique 

name. The new mixture is then available by name for use for setting boundary and/or 

initial conditions. 

Because oxygen is present in this problem both as an individual gas and as a component 

of the fuel-air mixture, the Species Mass Fraction option is chosen. In this approach, a 

transport equation is solved for every species in the problem. The mixing of oxygen from 

the leak with the fuel-air mixture requires a model for mass diffusion. A constant 

Schmidt number model is assumed, in which the mass diffusivity is assumed to be equal 

to the viscosity divided by a constant, the Schmidt number. The Schmidt number is 

assumed to equal 0.7 for this model. 

Some care needs to be taken in interpreting the gas concentration values in the analysis 

results, since the variables in the CFD-ACE+ calculations are mass fractions and the 

lower and upper flammable limits (LFL and UFL) are volume fractions. To plot the 

contours of LFL and UFL, therefore, the mass fraction of propane under these conditions 

needs to be calculated. This is accomplished by using the molecular weights of each 

species in the mixture. For example, the UFL of propane in air at standard temperature 

and pressure (STP) is 9.5 % by volume. Pure air is 78.1 % N2, 20.9 % O2, and 0.9 % Ar 

by volume. (Note that in the flammability diagram, argon may be added to nitrogen as an 

13 
 

 

inert gas.) The concentrations by volume of the components of air in a UFL propane-air 

mixture are obtained by multiplying the values in pure air by (1.00-0.095) = 0.905 to get 

9.5 % C3H8, 70.7 % N2, 19.9 % O2, and 0.8 % Ar. The molecular weights for each 

species are: 

C3H8: MW = 3 (12.01) + 8 (1.01) = 44.1 g/mol 

N2: MW = 2 (14.01) = 28.0 g/mol 

O2: MW = 2 (16.00) = 32.0 g/mol 

Ar: MW = 1 (39.95) = 40.0 g/mol 

The conversion from volume fraction Ci to mass fraction Yi for species i with molecular 

weight Mi is given by: 

Y =

∑

CiM i
 

i CiM i
 

Therefore, the value of mass fraction of propane that corresponds to the UHL in air is 

(0.095)(44.1) YUHLair = = 0.138 (0.095 ) (44.1) ( + 0.707) (28.0 ) ( + 0.199 32.0 ) ( ) ( + 0.008) (40.0)

Similarly, the mass fraction of propane at the LFL in air of 2.1 % by volume is 0.032. 

For the UHL and LFL of propane in pure oxygen, there are only two species present. For 

the UHL in oxygen of 58 %, the volume fraction of oxygen is 42 %. The mass fraction 

of propane at this level is 

(0.58)(44.1) YUHL O2 = = 0.656 (0.58) (44.1 ) ( + 0.42) (32.0)

Similarly, the mass fraction of propane at the LFL in pure oxygen of 2.1 % by volume is 

0.029. 

4.3 Turbulence 

For fluid flow problems, the presence of turbulence may strongly affect the transport of 

mass, momentum, and energy. Generally speaking, turbulence should be taken into 

account if the Reynolds number Re in the problem exceeds 1000, where Re = ρUL/μ, ρ is 

density, U is a typical velocity in the problem, L is a length scale, and μ is viscosity. 

Turbulence may be a factor if the Reynolds number is above 100. In this problem, the 

largest velocity and smallest length scale are both found at the leak. For a normal breath, 

the velocity at the leak is about 1 m/s, as will be shown in section 4.5. The width of the 

leak gives a length scale of 1 mm. For oxygen at STP, the density is 1.3 kg/m3

 and the 

viscosity is 2.0 × 10-5 kg/m-s. The resulting value of Re is about 50, low enough that 

turbulence is not necessary for calculations under conditions of normal breathing. If the 

first responder is breathing more heavily under stress, the velocity at the leak will be 

14 
significantly higher, and a turbulence model may be advised (although turbulence will 

still be a factor only close to the leak). 

When the turbulence module is employed, the standard k-epsilon model is chosen.16 This 

model assumes the eddy viscosity approximation, in which the Reynolds stress tensor is 

proportional to the rate of mean strain, and solves transport equations for the turbulent 

kinetic energy k and the rate of dissipation ε. 

4.4 Problem Geometry 

The solution space for the outward leak problem is a volume exterior to the combined 

headform and respirator facepiece. Because of the symmetry along the centerline of the 

face and mask, the size of the computational problem to be solved can be cut in half. It 

should be understood, however, that the assumption of geometrical symmetry also 

requires that the outward leak is mirrored on the opposite side. As discussed in the 

section on Model Geometry above, the headform and respirator facepiece were developed 

with symmetry in mind. For ease of creation, a rectangular box was chosen, with the 

headform / facepiece roughly centered along one side. Fig. 6 shows the geometry of the 

computational problem, using only the exterior surfaces of the combined headform and 

facepiece from Fig. 5. The face inside of the facepiece has been removed and the visor 

and facepiece connector region below the visor have been filled in. 

The rectangular box must encompass a sufficient volume of the surroundings such that 

the locations of the walls of the box have a negligible effect on the results in the 

immediate vicinity of the leak. A study of sensitivity to the size of the box is discussed in 

section 5.1. 

For solution of the flow field and gas species concentrations by the finite volume analysis 

of CFD-ACE+, the region enclosed by the exterior surfaces of head and facepiece plus 

the walls of the box is divided into a tetrahedral finite element mesh to be used for 

computing the solution. This is accomplished using CFD-GEOM to first divide the 

surface entities of the geometry into a 2D triangular surface grid, then to use the surface 

grid to divide the volume into a 3D tetrahedral mesh. The 2D mesh generation 

automatically concentrates the mesh in any area with fine features defined by the surface 

entities, including the region around the thin leak. Much larger cells are defined near the 

walls where fine detail is not necessary. Setting a transition factor to a reasonable value 

such as 1.1 limits the maximum percentage change in cell size from one cell to the next. 

Further control over mesh size is obtained by defining a maximum or minimum cell size, 

by defining a source point to concentrate small cells, and by using the edge entity to 

define surfaces. The edge entity can be split into a one-dimensional grid that specifies 

the locations for the points of the 2D triangular mesh, and is used to make the mesh finer 

in regions of interest. This approach was used both to improve the resolution of velocity 

across the thin leak, described below in section 5.1, and to refine the mesh in the 

direction of the jet, described in section 5.3. 

15 
Figure 6. Model geometry for solving flow in the environment external to facepiece. 

4.5 Boundary Conditions 

To fully define the model, boundary conditions must be applied to all surfaces. There are 

four basic types of boundaries for this model: input, output, symmetric, and wall 

boundaries. Fig. 7 indicates where these boundary conditions are applied to the model. 

As the critical element in this problem, the boundary conditions for the leak are of 

greatest interest. Because the flow is into the computational volume, this is an inlet 

boundary condition. Of the inlet flow boundary condition options available in CFDACE+, fixed normal velocity was selected as the most appropriate for this problem. The 

chemistry boundary condition is pure oxygen. Thus, at the leak oxygen flows into the 

volume with an assigned velocity profile. As a simplification of the breathing cycle, two 

sets of boundary conditions are used to represent exhalation and inhalation. During the 

exhalation half of the cycle, the leak is assumed to have a steady velocity. During 

inhalation, the leak is assumed to be cut off, with zero flow entering the computational 

space. In reality, an SCBA respirator is under positive pressure throughout the entire 

breathing cycle. The assumption made here is that the positive pressure is high enough to 

break the seal and cause a leak only during the exhalation part of the cycle. 

As discussed in section 2.1, under normal rest conditions, a cycle of 15 breaths per 

minute with a tidal volume of 0.5 L is a reasonable assumption. Thus, over the twosecond exhalation part of the cycle 0.5 L = 0.5 × 10-3 m3

 is released. Assume that a large 

fraction equaling 20 % of that breath is lost through the leak (and another 20 % is lost 

16 
Figure 7. Model geometry illustrating boundary conditions 

through the symmetric leak on the opposite side of the facepiece). Since the area of the 

leak is about 44 mm by 1 mm = 4.4 × 10-5 m

2

, the velocity through the leak is 

approximately 

−3 3 (0.5×10 m ) v = 0.20 × = 1.1 m / s leak −5 2 (4.4 ×10 m )(2 s)

The velocity through the leak for a normal resting breath is therefore taken as 1 m/s over 

a two second time period. For the following two seconds, the leak is closed. Then the 

leak of 1 m/s is open again for two seconds, followed by another two second closure, for 

a total of two breathing cycles. 

To look at the effect of stress on the characteristics of flow from a leak, a case was run 

with an elevated breathing rate of 60 breaths per minute and tidal volume of 3 L. This 

corresponds to 0.5 s for each exhalation and inhalation half of the breathing cycle and a 

leak velocity of 6 m/s. Since the Reynolds number at the leak location is around 300, 

according to the discussion in section 4.3, turbulence is included in running this problem. 

For the inlet boundary condition, a standard guess of 

2 2 2 k = 1.5(U ×TI ) m / s 

for turbulent kinetic energy and 

17 
k 1.5 

0.75 2 3 ε = Cμ m / s 

0.07 L 

for turbulence dissipation rate are assigned, with TI = 0.1 the turbulence intensity, Cμ = 

0.09 a constant, L = 1 mm the characteristic dimension of leak width, and U = 6 m/s the 

reference velocity. 

Outlet boundary conditions of fixed atmospheric pressure are assigned to the open sides, 

top, and bottom of the box defining the computational volume. This allows for flow both 

into and out of the model. The chemical content of any gaseous material flowing back 

into the volume from outside is assumed to be the fuel-air mixture of the surroundings. 

Symmetric boundary conditions are assigned to the side of the box along the center plane 

of the combined headform and respirator. The conditions along this plane of symmetry 

are zero flux for all variables: velocity, species concentration, and pressure. This ensures 

that a mirror image of the computational volume about the plane of symmetry would 

yield a mirror image of the results. 

The exterior surfaces of the combined headform and respirator, with the exception of the 

leak, are assigned a wall boundary condition. No flow is permitted through these 

surfaces. 

4.6 Initial Conditions 

At time t = 0, just before the leak due to exhalation begins, the computational volume is 

filled with the fuel-air mixture of the surrounding environment, and the flow is zero. Still 

air represents a worst case for oxygen buildup near the respirator, since any flow around 

the mask will act to mix the oxygen with the fuel-air mixture. 

18 
5 MESH STUDY 

To make sure that the results are accurate and not dependent on the mesh, studies were 

carried out on the necessary resolution of the 1 mm wide leak, the mesh refinement in the 

direction of the jet, and the effects of the size of the computational box on the results. 

Since the time to solve the 3D problem is strongly dependent on the total number of grid 

cells, the goal is to keep the number of cells in the model as small as possible without 

introducing grid dependence. 

A steady state problem was used to study mesh resolution and its effects on gas 

concentrations and velocities. The inlet boundary condition for this problem was a steady 

flow of oxygen through the leak at a velocity of 1 m/s. Initially the solution space was 

filled with propane. The calculation proceeded until a steady state condition of oxygen 

and propane concentrations in the region was reached. 

5.1 Leak resolution 

The leak region of this model is both the most challenging to resolve and the most 

important for the accuracy of the solution. The specified leak represents a thin breaking 

of the seal between the head and facepiece above the temple region during the exhalation 

part of the breathing cycle. The leak is 1 mm wide and 43.6 mm long and follows the 

curve of the facepiece seal along the headform. To properly set the boundary conditions 

here, the leak needs to be adequately resolved along the width. 

One way to force a specific mesh resolution in a certain region using CFD-GEOM is to 

introduce edge entities, which are assigned a specified number of gridpoints along their 

length. The edges are then used to define the boundaries of surface entities. When the 

surfaces are meshed, the nodes of the mesh are forced to coincide with the gridpoints 

along the edges. The meshing algorithm tries to keep all sides of each triangle roughly 

the same, so the number of gridpoints along the length of the edge determines the average 

area of the 2D triangular elements in that region. A similar algorithm keeps the triangular 

sides of the 3D tetrahedral mesh in proportion, so the number of gridpoints also sets the 

average volume of the 3D tetrahedral cells adjacent to this boundary. 

Fig. 8 shows the two-dimensional surface mesh along the leak resulting from three values 

of the number of gridpoints along each side of the leak. Above the plot of the 2D mesh 

for the entire leak is a close-up of the mesh near the upper endpoint of the leak. The 

purple dots are the gridpoints. The mesh in Fig. 8(a), with the edges along the sides of 

the leak divided into 87 gridpoints, provides a resolution across the leak width of only 

two triangles, as can be seen in the close-up. The resolution obtained by dividing each 

edge into 130 gridpoints in Fig. 8(b) is roughly three triangles across the leak width, and 

for 174 gridpoints in Fig. 8(c) is roughly four triangles. 

19 
Figure 8. 2D mesh for three leak resolutions: a) 87 gridpoints along curve, b) 130 

gridpoints, and c) 174 gridpoints. 

Fig. 9 shows the profile of mass fractions across the leak for each of the three leak 

resolutions. These plots were obtained using the post-processing software CFD-VIEW, 

which provides tools for visualizing the results of CFD-ACE+ calculations.18 To the 

right of each plot is a set of curves that delineates the surfaces in the region near the leak. 

The short line bounded by an x in each case lies on the model surface across the width of 

the leak. The plot shows the value of propane mass fraction along this line. Because 

oxygen and propane are the only gases in this model, the mass fraction of oxygen is equal 

to one minus the propane mass fraction. It is clear from Fig. 9(a) that the case using 87 

gridpoints does not adequately resolve the mass fraction across the leak. However, both 

Figs. 9(b) and (c) show a smooth profile. 

To make sure that the mass flow was correct, CFD-VIEW was asked to provide a 

boundary-by-boundary mass flow summary showing the inflow and outflow for each 

inlet and outlet boundary. These values were compared to the mass flux of oxygen 

flowing with a velocity of 1 m/s through a rectangle 1 mm wide by 43.6 mm long. The 

leak is a curved area rather than a rectangle, but no method was found for calculating the 

exact 2D area of the leak. The mass flow calculated by CFD-VIEW was within 2 % of 

the estimate for flow through a rectangle in each case. 

20 
Figure 9. Comparison of propane concentration profiles for three leak resolutions 

As the largest resolution (smallest number of gridpoints) of the three tested that gave 

good results, the number of gridpoints along the leak length was set equal to 130 for the 

final mesh. Fig. 10 demonstrates the location of the leak by drawing velocity vectors on 

a set of planes from just below to just above the leak. 

5.2 Size of External Box 

As discussed in section 4.4 and illustrated in Fig. 6, the computational space for this 

model was defined by a rectangular box into which the combined headform and 

respirator facepiece were embedded. For the first set of runs to test the model, the size of 

the box was chosen to be 600 mm wide in the direction to the right of the head, 900 mm 

long in the direction from front to back, and 600 mm high. A top view of this box is 

shown in Fig. 11(a). The shaded contour in this plot delineates the surface along which 

the mass fraction of propane is equal to 0.97 for the steady state problem described 

above. It was clear from the solutions of early problems that the size of this box resulted 

in a considerable amount of dead space over which gas concentrations and velocities 

varied little. A reduction of the size of the computational space to 600 mm wide by 600 

mm long by 500 mm high reduced the number of grid cells and thus the analysis time 

without significantly affecting the results, as demonstrated by comparing 11(a) to 11(b). 

21 
Figure 10. Velocity vectors on a set of planes across leak. 

Figure 11 Comparison of propane mass fraction = 0.97 contour for two sets of 

dimensions for the computational space: a) 600 mm wide × 900 mm long × 600 mm 

high, and b) 600 mm wide × 600 mm long × 500 mm high. 

22 
5.3 Mesh Refinement in Direction of Jet 

The oxygen from the leak flows into the solution space as a jet in the direction normal to 

the leak boundary. As shown in Fig. 11, this results in a region that extends in a more or 

less straight line from the leak to the side wall. The solution values within this region are 

of greatest interest. The previous section discussed how taking account of this region 

reduced the size of the computational space. It would be also advantageous to 

concentrate the mesh within this region in preference to the surrounding volumes. This 

can be accomplished using CFD-GEOM. 

The first step is to locate the region of interest. Fig. 12 shows a view of the 0.97 contour 

surface from the side away from the head and mask, along with the same top view shown 

in Figure 11(a) (rotated by 90°). The post-processor CFD-VIEW is used to obtain plots 

of the mixture fraction of propane in the vertical z-direction (top plot) and horizontal ydirection (bottom plot), with the axes centered where the contour surface meets the side 

wall. This locates the centerpoint for generating a denser mesh. 

The aim is to develop a 2D triangular mesh along the side wall that concentrates cells 

around the centerpoint. From this, the generation of the 3D mesh will fill in smaller grid 

cells through the entire region between the head and the opposite side wall, providing the 

desired improvement in resolution where it is needed. Two methods available in CFDGEOM were used to produce a localized concentration of 2D grid cells: a point source 

and a set of edge elements in a circle. With the source method, the location of the 

centerpoint was identified along with a radius value that gives the length of cells 

emanating from this point. With the edge elements, a grid along each edge specified the 

desired resolution, in the same way as described for the leak mesh in section 5.1. 

Fig. 13 shows the 2D mesh along the boundaries of the computational domain in the 

absence of mesh refinement along the side wall to the right of the head and facepiece. 

The grid along this wall, appearing in the lower left corner of the figure, is uniform and 

coarse. In Fig. 14, the source method has been used to obtain a higher density of cells in 

the region around the centerpoint of the jet. Fig. 15 shows the 2D mesh obtained from 

the use of edge elements arranged in a circle around the centerpoint. This grid was the 

finest and best controlled, and was selected to generate the final 3D mesh for the 

problem. 

The number of grid cells in the final model was slightly under 500 000. Problems were 

run on a desktop workstation, with run times of less than 24 h for each exhalation or 

inhalation cycle. 

23 
Figure 12. Finding the point of minimum propane mass fraction along the side wall 

of the computational space. The 0.97 contour is shown for both top and side views. 

Figure 13. Mesh generation along boundaries of model space. 

24 
Figure 14. Mesh generated with source at side wall. 

Figure 15. Mesh generated with circular edge element at side wall. 

25 
 

 

6 RESULTS FOR A SMALL LEAK DURING BREATHING AT REST 

The effects of a respirator mask leak on the flammability of the nearby gas mixture 

depend on the oxygen content in the respirator and the fuel and oxygen content in the 

surrounding environment. Analyses were performed on three fuel-air mixtures, two 

levels of oxygen concentrations within the respirator, and two breathing patterns. Fig. 16 

sketches the breathing patterns used in this study. Fig. 16(a) shows the breathing pattern 

for a person at rest, with tidal volume of 0.5 L and breathing rate of 15 breaths per 

minute. The results for this breathing pattern are discussed in this section. Fig. 16(b) 

shows the breathing pattern under high stress, which will be discussed in section 7. Both 

patterns assume a steady velocity from the leak during exhalation and zero leakage 

during inhalation. 

CFD-VIEW provides several tools to visualize the three-dimensional flow field and gas 

concentration as functions of space and time. Results are displayed here on a horizontal 

plane located at the approximate midpoint of the leak, as indicated by the red line in 

Fig. 17. The view used for the display plane is from the top. 

The flammability of the gases in the immediate vicinity of the head and facepiece is 

assessed by comparing the gas mixture at every point to the flammability diagram. If the 

mixture falls within the flammability region on the diagram, it is considered flammable. 

6.1 Leak of Pure Oxygen into Pure Propane Environment 

The first problem to be considered is pure oxygen leaking into a pure propane 

environment. In this case, the concentration of nitrogen is zero everywhere. Referring to 

the flammability diagram in Fig. 18, the mixtures in this problem all lie along the gold 

line on the left boundary, with values from pure oxygen at the lower left corner to pure 

propane at the top. 

The flammable mixtures along this line lie between the LFL of 2.1 % by volume for 

propane in pure oxygen and the UFL of 58 % by volume. A conversion to mass fractions 

was performed as described in section 4.2 in order to correctly define the volume 

containing flammable gases in the results from CFD-ACE+. Fig. 19 shows a closeup of 

the area near the head at the end of the exhalation part of the breathing cycle. The red 

contour that extends outward from the leak by approximately a centimeter is the UFL 

contour. The LFL contour is very close to the leak. The area between these two contours 

is the flammable region in this problem. 

The gray shading in Fig. 19 indicates the oxygen concentration. The values range from 

0 % oxygen (100 % propane) in white to 100 % oxygen (0 % propane) in black. 

Note that with both pure oxygen and pure propane in the problem, it is necessary to have 

a flammable region somewhere. This would also be true if the respirator was leaking 

26 
Figure 16. Breathing cycles for a) person at rest, and b) person under high stress. 

Figure 17. Vertical location of display plane. 

27 
Figure 18. Flammability diagram showing range of mixtures for a pure oxygen leak 

into pure propane. 

Figure 19. Top view of head and respirator showing oxygen expelled during 

exhalation. Red contours mark the UFL and LFL of propane in pure oxygen. 

28 
 

Figure 20. Time sequence of oxygen concentration from pure oxygen leak into pure 

propane environment. 

either air or the 16 % by volume oxygen content of an exhaled breath. In the case of air, 

the gas mixtures in the problem follow the air/fuel line in the flammability diagram, and 

the flammable region is between the UFL and LFL in air. In the case of exhaled breath, 

the mixtures follow a line drawn between pure propane at the top and 16 % O2 / 84 % N2 

along the bottom axis, which still crosses into and out of the flammability region in the 

diagram. 

In this case, the flammable region near the head of the person wearing the respirator is 

small during exhalation and disappears completely during inhalation. Fig. 20 shows a 

time sequence of gas concentrations for these two breathing cycles. The evolution of the 

oxygen concentration is due to convection and diffusion. 

Fig. 21 shows the flow field over time. During exhalation, between 0 s and 2 s and again 

between 4 s and 6 s, the flow at the leak itself has a value of 1 m/s, colored in red at the 

top of the scale. However, within a very short distance from the leak the velocity has 

decreased to a small fraction of that magnitude, less than 0.2 m/s. The jet from the leak 

creates a pair of rotating vortices, one on each side of the leak. 

29 
Figure 21. Time sequence of velocity vectors from pure oxygen leak into pure 

propane environment. 

6.2 Leak of Pure Oxygen into 10 % Propane Environment 

A much more challenging condition is the leak of pure oxygen into an environment in 

which the fuel level is very close to the UFL already, but just slightly too fuel rich for 

flammability. Since the UFL of propane in air is 9.5 % by volume, the value of 10 % by 

volume is assumed for the fuel/air mixture for this test. The introduction of oxygen into 

this environment will certainly result in a flammable region – the only question is what 

the size will be. 

The flammability diagram is again used to determine the concentrations that bound the 

flammable region. In this case, all mixtures in the problem must lie along a line drawn 

from the 100 % oxygen content expelled from the leak to the 10 % propane point along 

the air/fuel line. This line is shown in gold in Fig. 22. The line crosses the lower curve 

bounding the flammable mixtures at 2.1 % propane, about 13 % N2, and about 85 % O2. 

At the upper curve, the mixture must be between the 9.5 % UFL value and the 10 % 

value of the surrounding mixture. It is important to get a good estimate for this mixture 

in order to get a good approximation for the size of the flammable region caused by the 

respirator leak. The mixture content is calculated as the intersection point between the 

30 
 

Figure 22. Flammability diagram showing range of mixtures for a pure oxygen leak 

into a 10 % propane environment. 

line describing possible mixtures for this problem and the line between point A, the UFL 

in air, and point G, the UFL in oxygen. The propane concentration at this intersection 

point is found to be 9.96 % by volume. 

Fig. 23 shows the time sequence for oxygen flowing into the 10 % propane/air mixture. 

In this case, the LFL contour is still very close to the leak, but the UFL contour has 

expanded considerably, indicating that there is a large region near the head that contains a 

flammable mixture. This contour is connected to the head throughout the breathing 

cycle. 

Note that the growth in size of the flammable region over these two breaths is due to the 

zero leakage before time t = 0, a necessary assumption for starting this transient problem. 

The flammable region should eventually arrive at an equilibrium size (with some 

fluctuation over the breathing cycle) in which inflow from the leak is balanced by 

diffusion. 

31 
Figure 23. Time sequence of oxygen concentration from pure oxygen leak into 10 % 

propane environment, showing flammable region. 

6.3 Leak of Air into 10 % Propane Environment 

To appreciate the meaning of the result in the previous section for the use of closedcircuit SCBAs, it is useful to compare the leak from a respirator containing pure oxygen 

to a leak from a respirator containing air. The latter is a reasonable assumption for a 

standard open-circuit SCBA using a compressed air tank. 

The gold line on the flammability diagram of Fig. 24 represents the range of mixtures in 

this problem, from pure air at point E to the 10 % propane point along the air/fuel line. 

Since this line lies along the air/fuel line, the points that bound the flammable region are 

already known to be the LFL and UFL of propane in air, 2.1 % and 9.5 % respectively. 

Fig. 25 shows the time sequence of gas volume fractions for air leaking into a 10 % 

propane environment. Comparing this figure to Fig. 23 for a pure oxygen leak, it is clear 

that the flammable regions here are smaller. They detach from the head during inhalation 

and move away from the head and respirator. It is also clear that this environment is 

indeed one into which the introduction of oxygen from any source results in a flammable 

mixture. 

32 
 

Figure 24. Flammability diagram showing range of mixtures for a leak of air into a 

10 % propane environment. 

6.4 Leak of Pure Oxygen into 5 % Propane Environment 

The final problem studied for a resting breath is that of a pure oxygen leak into a 5 % 

propane environment. This is an environment that is flammable even without the 

addition of more oxygen. 

The range of mixtures for this problem is plotted as a gold line on the flammability 

diagram in Fig. 26. In this case, the possible mixtures lie along a line from 100 % 

oxygen to 5 % propane along the fuel/air line. The point at which the line of possible 

mixtures crosses into the flammable region is at 2.1 % propane, about 24 % N2, and about 

74 % O2. This LFL point corresponds to a mass fraction for propane of 0.296. 

Fig. 27 shows a closeup of the area near the head at the end of the exhalation part of the 

first breathing cycle. The only contour in this plot is the LFL contour in red that extends 

outward from the leak by a few millimeters. The space within this contour is the only 

region in this case that is not flammable. 

33 
Figure 25. Time sequence of oxygen concentration from leak of air into 10 % 

propane environment, showing flammable region. 

Fig. 28 shows the time sequence of oxygen concentration for oxygen flowing into the 

5 % propane environment. The entire space is flammable, except for a small region next 

to the leak. 

34 
Figure 26. Flammability diagram showing range of mixtures for a pure oxygen leak 

into a 5 % propane environment. 

Figure 27. Pure oxygen expelled during exhalation into 5 % propane environment. 

Red contour marks the LFL of propane in this set of mixtures. 

35 
Figure 28. Time sequence of oxygen concentration from leak of pure oxygen into 

5 % propane environment. (Note that the region outside of the red line is 

flammable.) 

36 
 

7 RESULTS FOR A SMALL LEAK WHILE BREATHING UNDER STRESS 

For this final problem, the breathing pattern is changed to reflect the higher tidal volume 

and breathing rate for a person under stress from exertion. The breathing pattern is 

illustrated in Fig. 16(b), and represents a tidal volume of 3 L and breathing rate of 

60 breaths per minute. The velocity boundary condition at the leak has been increased to 

6 m/s, and a turbulence model has been added to the problem as described in section 4.3. 

7.1 Leak of Pure Oxygen into 10 % Propane Environment 

The most challenging environment is studied here, with pure oxygen leaking into a 10 % 

propane environment. These are the same conditions as in section 6.2, except for the 

higher leak velocity and breathing rate and the addition of the turbulence model. The set 

of possible mixtures is indicated on the flammability diagram of Fig. 22. 

Fig. 29 shows the time sequence of oxygen concentration and UFL contours over the first 

two breaths. Comparing these results with Fig. 23 for breathing at rest, the spatial extent 

of the oxygen jet from the leak into the surroundings is longer. The oxygen disperses 

more quickly into the fuel/air mixture, and increases the size of the flammable region. 

37 
Figure 29. Time sequence of oxygen concentration from leak of pure oxygen into 

10 % propane environment for breathing under stress, showing flammable region. 

38 
8 CONCLUDING REMARKS 

This study has used computational fluid dynamics to investigate a respirator leak in a 

firefighting environment. The geometries of an experimental headform and a respirator 

mask were digitized and combined for an accurate model of the space surrounding the 

leak. Visualization tools allow the interpretation of scalar and vector data over time and 

space. This study demonstrates the capabilities of CFD to enhance our understanding of 

flow phenomena and communicate the results. 

The focus of this study is on the potential dangers of a leak from the respirator of a closed 

circuit SCBA. Closed circuit SCBAs add pure oxygen to the breathing gases, which are 

scrubbed to eliminate carbon dioxide buildup. This compares to the open circuit SCBAs 

in widespread use, which supply air from compressed air tanks to firefighter respirators. 

The worst-case scenario for a leak from either respirator is that of a slightly fuel-rich 

mixture in the surrounding environment, such that the introduction of oxygen at even low 

levels may result in flammability. The flammable region generated by a leak of pure 

oxygen is larger than that generated by a leak of air. Heavier and more rapid breathing, 

such as that caused by exertion, increases the flammable region further. 

Under conditions of pure oxygen flowing into pure fuel, the flammable region is very 

small and disappears when the leak is closed off. When oxygen leaks into a flammable 

environment, a small non-flammable region is created very close to the leak. 

In this study, the leak is assumed to be pure oxygen, rather than a lower concentration 

expected in the respirator by the combination of oxygen from the oxygen tank and 

breathing gases. The mixture of fuel gas and air in the worst-case environment is just 

above the upper flammable limit, a severe environment for a firefighter to be in. The 

surroundings are assumed to be still air, neglecting the flows normally associated with a 

fire and firefighter movement that will tend to mix the leak gases with the surroundings 

more rapidly. These flows will lessen the size of the flammable zone. 

Validation of CFD with experimental measurements will ensure that these results 

accurately reflect reality. Of equal or greater importance is a better understanding of the 

actual conditions that may be encountered in the field, including the potential leak size 

and location, flow rates, and external environment. 

39 
 

REFERENCES 

1 Kyriazi, N. “Proposal for Certification Tests and Standards for Closed-Circuit Breathing 

Apparatus,” Information Circular 9449, U.S. Department of Health and Human Services 

(NIOSH), Pittsburgh, PA (1999). 

2 Kyriazi, N. “Performance Comparison of Rescue Breathing Apparatus,” Report of 

Investigations 9650, U.S. Department of Health and Human Services (NIOSH), 

Pittsburgh, PA, Oct 1999. 

3 De Vries, H., “Mining for Answers,” Fire Chief, 1 Jan 2002. 

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