NISTIR 7252

Particle Image Velocimetry

Measurements of Buoyancy Induced

Flow Through a Doorway

Rodney A. Bryant

 
NISTIR 7252

Particle Image Velocimetry

Measurements of Buoyancy Induced

Flow Through a Doorway

Rodney A. Bryant

Building and Fire Research Laboratory

Fire Research Division

September 2005

U.S. DEPARTMENT OF COMMERCE

Carlos M. Gutierrez, Secretary

TECHNOLOGY ADMINISTRATION

Michelle O’Neill, Acting Under Secretary of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

William A. Jeffrey, Director

 
DISCLAIMER 

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. 

 
ABSTRACT 

Quantifying the ventilation available to an enclosure fire is an important step to 

understanding fire behavior. Accurate measurements of mass flow rate across an 

enclosure opening require a complete mapping of the velocity and density fields due to

the three dimensional nature of vent flows. Conventional flow measurement methods in 

fire research consist of vertical arrays of thermocouples and differential pressure probes 

at the vent plane which are physically obtrusive and offer limited spatial sampling. A 

reduced-scale analog of a full-scale fire experiment was studied for the purpose of 

studying the potential use of Stereoscopic Particle Image Velocimetry, a laser based nonintrusive imaging technique, to measure fire induced flows through vents. The

experiment was isothermal and modeled the convective transport by using a helium 

plume as the buoyant source. Stereoscopic PIV measurements were successfully 

demonstrated for a large-scale flow field with planar image regions of 0.71 m x 0.62 m (l 

x h). Measurements of the complete velocity vector, vx,vy,vz, were performed and a full

mapping of the velocity field in the region of the doorway was achieved. The vector field 

data displays the three dimensional structure of the flow through the doorway, revealing 

regions where the velocity component normal to the doorway plane may not completely 

dominate the velocity vector. A comparison of mass flow rate computations using the

velocity component normal to the opening, vx, and the velocity magnitude, demonstrated 

that mass flow rate will be over predicted by as much as 25 % if computed using the

velocity magnitude. Velocity magnitude is representative of bi-directional probe 

measurements and the over prediction is consistent with the use of doorway flow orifice 

coefficients to correct mass flow rates computed from bi-directional probe data. The 

intermediate scale of the flow field was sufficient to test the performance of a current PIV 

system and to identify the requirements for conducting successful PIV measurements in a 

full-scale fire experiment. 

iii
ACKNOWLEDGEMENTS 

The success of any experimental project is due to more than just the work of the author. 

Therefore the author wishes to thank the following NIST staff for their valuable 

contributions: Marco Fernandez and Michael Selepak, NIST Fire Research Technicians,

for fabrication of the reduced-scale enclosure and sampling probes, and Xiabo Yao, a 

University of Maryland graduate student in Fire Protection Engineering, for assisting 

with experimental setup. 

iv
TABLE OF CONTENTS 

page

ABSTRACT III

ACKNOWLEDGEMENTS IV

1 INTRODUCTION 1

2 FIRE INDUCED FLOW THROUGH VERTICAL VENTS 2

2.1 A SIMPLE ILLUSTRATION 2

2.2 METHODS OF MEASUREMENT 5

3 PARTICLE IMAGE VELOCIMETRY 7

3.1 TWO DIMENSIONAL PIV 8

3.2 STEREOSCOPIC PIV 10

3.3 LARGE-SCALE PIV 11

4 REDUCED-SCALE CONVECTIVE ANALOG EXPERIMENT 17

4.1 FIRE EXPERIMENT SCALING 17

4.2 EXPERIMENTAL SETUP 20

5 UNCERTAINTY ANALYSIS 30

5.1 TYPE A UNCERTAINTY 30

5.2 TYPE B UNCERTAINTY 31

5.3 UNCERTAINTY PROPAGATION 33

6 RESULTS OF REDUCED-SCALE EXPERIMENTS 35

6.1 VECTOR PROCESSING 35

6.2 FLOW VISUALIZATIONS 42

6.3 GAS DENSITY 49

6.4 MASS FLOW RATE 51

7 CONCLUDING REMARKS 56

REFERENCES 58

APPENDIX 60

.1 TABULATED VALUES OF THE VELOCITY AND DENSITY FIELD AT THE DOORWAY PLANE 60

.2 NUMERICAL INTEGRATION 64

v
1 Introduction 

Fires release large amounts of energy. This energy, mostly in the form of heat, raises the 

temperature of the surrounding gases, causing them to expand. In the case of a fire 

within an enclosure, the hot gas will fill the top of an enclosure and increase the pressure 

within the enclosure, therefore causing gas to move out of the enclosure through the 

available openings. At the same time, the buoyant hot gases that rise to the top of the

enclosure induce a low pressure region at the floor of an enclosure into which ambient 

gases will flow. The fire acts as a pump, pulling ambient air in while pushing 

combustion products mixed with air out. The openings which the gases flow through are 

referred to as vents and typically are doorways and windows. Quantifying the ventilation 

available to an enclosure fire is an important step to understanding fire behavior. The

fresh air that moves into an enclosure provides the necessary oxygen to “feed” the fire 

while also serving to moderate the temperature of the compartment, depending on the

stage of the fire growth. The hot fire gases that move out of an enclosure transfer heat 

and combustion products from the localized point of the fire to remote locations within a

built structure. Ventilation therefore can play two important roles in fire spread, 1) to 

reduce the hazard by moderating the enclosure temperature and 2) to increase the hazard

by transferring the heat, smoke and toxic gases to other locations of a built structure. 

Measuring the velocity field across an opening together with the density field is 

necessary to quantify the mass flow rate of gas into and out of a burning room. Ideally 

this requires a full mapping of the velocity and density fields due to the three dimensional 

nature of vent flows. Early treatments quantifying fire induced flow through vents relied 

on Bernoulli’s equation and a hydraulics-orifice approach [1,2,3], therefore only a few 

well placed pressure and temperature measurements were required. Later treatments 

were improved by adding vertical arrays of pressure and temperature measurements and

scanning them across the vents in order to address the three dimensional nature of the 

flows. [4,5] 

Ventilation measurements have typically consisted of vertically spaced differentialpressure and temperature measurements between the enclosure and the ambient or within

the vent plane itself. Emmons [6] presents a good review of the different levels of 

sophistication for these typical measurements. Velocity and gas density, both required to 

compute mass flow rate, are inferred from the pressure and temperature measurements.

Velocity is coupled to gas density through the gas temperature measurement. These 

measurements are performed with physical probes which inherently alter the flow and are 

subject to the extreme conditions of a fire. 

The typical instrument for velocity measurement in a fire test is the bi-directional probe, 

developed by McCaffrey and Heskestad. [7] The probe was designed to measure 

localized differential pressure in areas were the bulk flow direction can change. It is a 

robust device capable of withstanding the harsh conditions produced by fires. Some laser 

based techniques offer a non-intrusive and independent measurement of gas velocity. 

Single Point LDV (Laser Doppler Velocimetry) measurements of gas velocity in the 

1
doorway have been demonstrated in a fluid flow analog of an enclosure fire. [8] Single 

point measurements are insufficient for fire testing due to the need to map a vertical 

profile at minimum. A planar field laser based measurement such as Particle Image 

Velocimetry is a promising technique due to its potential ability to map the entire area of

a vent opening without the need to translate any probes. 

Basic PIV delivers a planar image of two components of the velocity vector, however 

more advanced systems offer all three components of the velocity vector. PIV has been 

employed with great success in small-scale flow fields. Applying the technique to flow 

fields typically encountered in fire systems presents a host of challenges, the minimum of

which includes meeting the illumination and seeding requirements to ensure the accuracy 

of the measured velocity vectors. PIV systems have evolved into turnkey measurement 

devices but experimental setup and interpretation of the results is not entirely routine. 

In order to create a better understanding of the challenges to be encountered when 

performing PIV measurements for full-scale fire tests, a reduced-scale model of a fire

experiment was constructed. The reduced-scale experiment employed a helium plume as 

the buoyant source to produce an isothermal fluid-flow analog of the fire experiment. 

The experiment is a model of experiments by Steckler, Quintiere, and Rinkinen [9] which 

are possibly the most comprehensive doorway flow measurements to date. PIV and gas 

concentration measurements were conducted to measure the mass flow rate into and out 

of the enclosure doorway. The scale of the flows and the size of the measurement

regions were intermediate, therefore they were not quite equivalent to what would be 

experienced for a full-scale fire test but large enough to push the performance envelope 

for current PIV systems. A major result of this study is the identification of the 

requirements for conducting successful PIV measurements in full-scale fire tests as well 

as laying the foundation for a measurement methodology. 

2 Fire Induced Flow Through Vertical Vents 

2.1 A Simple Illustration 

Consider an enclosure with a single vertical opening, such as a doorway, and a fire source 

located on the floor and well within the enclosure. The fire produces a plume of hot gas 

that rises upward into the top of the enclosure due to buoyancy. The plume consists of 

combustion products and air that has mixed with the plume due to the entrainment along 

the edges. The hot gas fills the top of the enclosure, developing a layer that grows in 

depth and ultimately spills out of the top of the doorway, creating an outward flow of gas

due to the increase in pressure within the enclosure. At the same time a flow of fresh air 

into the enclosure occurs in the bottom layer of the doorway. This flow of air is driven 

by a low pressure region which is induced by the lighter gas in the upper layer and the 

entrainment of air into the buoyant plume. An illustration of this model is shown in 

Figure 1. The fire acts as a pump by pulling ambient air in while simultaneously pushing

combustion products mixed with air out. 

2
y

hN

H

hT

1 2

Vin

Vout

Figure 1 Fire induced flow for an enclosure with a single vertical vent opening. 

Both the inflow and outflow occur within a single vent, creating a countercurrent flow. 

At the interface of the two flows the horizontal velocity component (parallel to the bulk

flow direction) is zero. This interface is defined as the neutral plane with height, hN, 

above the door sill. The local velocity in the doorway will depend upon the height above 

or below the neutral plane. 

Within the enclosure two layers of gas exist, an upper layer of hot combustion products 

and air and a lower layer of cold air. The interface of these two layers is defined by the 

maximum vertical temperature gradient and has height, hT. Similar to velocity there is a 

vertical distribution of temperature within the enclosure. 

Time averaged mass flow rates of gas entering and exiting a vent are the typical 

parameters used to quantify ventilation in an enclosure fire. Theoretically the mass flow 

rate can be determined by integrating the product of local gas density, ρ , and velocity 

normal to the vent plane, vx, across the inflow and outflow areas of the doorway. 

Equations 1 and 2 show that the gas density and velocity can vary with both vertical and 

horizontal location across the doorway. The height, H, and width, W, of the doorway 

along with the location of the neutral plane, hN, establish the limits of integration. The z

coordinate is the horizontal direction normal to the plane of Figure 1, or parallel to the 

width of the door. 

Theoretical mass flow rate in: 

∫ ∫

−

=

2

2

, ( , ) ( , )

W

W

h

y

in thrtcl x

N

o

m& ρ y z v y z dydz ( 1 ) 

Theoretical mass flow rate out: 

3
∫ ∫

−

=

2

2

, ( , ) ( , )

W

W

H

h

out thrtcl x

N

m& ρ y z v y z dydz ( 2 ) 

The general flow behavior indicated in Figure 1 can be derived from some visual 

observations of enclosure fires. However a more detailed description of the physical 

processes and their relationship to measurable quantities is required to define an ideal 

mass flow rate computation. Assuming a one-dimensional flow, this can be achieved 

with a hydrodynamics analysis. Kawagoe [10] developed such a hydrodynamic model to 

describe under-ventilated fires. The model was equally applicable to over-ventilated or 

developing fires and Rockett [2] presents the more generalized model for such 

applications. Emmons [6] has summarized the model and a similar summary is presented 

here to provide adequate background for the reader. 

The model assumes the following for an enclosure with a single vertical vent as 

illustrated in Figure 1: 

1) the entire system is at steady state 

2) the gas inside the enclosure is a stratified layer of hot gas in the upper region and 

a layer of cool ambient gas in the lower region 

3) a steep thermal gradient serves as the boundary between the two layers 

In order for flow to occur across the vent a pressure difference must exist. Due to 

gravity, ambient pressure decreases with increasing height. In addition, inside the room,

in the plane of the doorway, and just outside the room, the gas temperature and therefore 

the gas density varies with respect to height. Starting at the floor of the enclosure (y=0)

and assigning region 1 as inside the room and region 2 as outside the room the pressure 

difference is 

∆p f = p f 1 − p f 2 ( 3 ) 

where pf1 is the pressure at the floor inside the enclosure and pf2 is the ambient pressure at 

the floor level outside the enclosure. 

The pressure difference at any height y within the plane of the doorway can be 

determined from the following equations. 

Inside the enclosure: 

( 4 ) ∫ = −

y

p p f gdy

0

1 1 ρ1

Outside the enclosure: 

4
( 5 ) ∫ = −

y

p p f gdy

0

2 2 ρ 2

The resulting pressure difference across the vent at any height, h, is then: 

( 6 ) ∫ ∆ = − = ∆ − −

h

p p p p f gdy

0

1 2 2 1 (ρ ρ )

Flow will be out of the enclosure for a positive pressure difference and into the enclosure

for a negative pressure difference (relative to the sign convention applied in this study).

The above equations give evidence to the pressure differential and associated gas flow 

across the doorway. Flow velocity has traditionally been inferred from pressure 

differential measurements. A brief summary of how pressure probe measurements have 

been applied to quantify fire ventilation will be provided in sections to follow. 

2.2 Methods of Measurement 

If it is assumed that points 1 and 2 lie along a streamline where the flow is steady, 

without friction and mass is conserved, then Bernoulli’s equation describes the relation 

between the pressure difference and the flow velocity. 

( ) 2

2

1

2

p1 − p2 = V2 −V ρ ( 7 ) 

Consider the gas flowing from the hot upper layer, region 1 Figure 1, through the top of 

the doorway and out into the ambient. Region 2 for this outflow is defined as the hot 

plume just outside the doorway If the assumption is made that the fluid accelerates from 

rest inside the enclosure, then V1 = 0 and the flow out of the top of the doorway can be 

described by the familiar relation for flow velocity and pressure, Equation 8. The same

relation describes the flow into the bottom portion of the doorway with the assumption 

that the flow accelerates from rest in the ambient of region 2. 

2

2 V

p ρ ∆ = ( 8 ) 

Equation 8 demonstrates that it is possible to infer flow velocity across the doorway from

a differential pressure measurement. Pitot-static probes have long been used to measure

local differential pressure and therefore to infer local flow velocity. Because the probe is

a physical obstruction to the flow the right hand side of the relationship as described in 

the equation above must be multiplied by a correction constant, K. The constant K is a

function of Reynolds number, Re=VD/ν; where D is the diameter of the probe and ν is 

the gas kinematic viscosity. K is usually determined by calibration and will be close to

unity for a well designed probe. 

5
Pitot-static probes measure flow velocity in a single direction and are therefore excellent

instruments for experiments where the flow direction is known or the three dimensional

motion of the flow is not significant. Fire induced vent flows, as shown in Figure 1, are 

counter-current flows, therefore flowing in opposite directions. To properly quantify a

vent flow for a developing enclosure fire, measurements must be continuously performed 

at multiple locations along a vertical line. The location of the flow direction shift is only

moderately predictable in the case of a steady state fire and for a developing fire the 

location will vary. In addition, flow in the upper layer and near the boundary of the vent 

may be highly three dimensional. The application of pitot-static probes to measure fire 

induced vent flows therefore has limitations. McCafferry and Heskestad [7] developed a 

modified pitot-static probe to address these limitations, the bi-directional probe. 

Bi-directional probes were designed specifically to measure velocity in flow fields where 

the direction of the flow can change by 180 degrees. Their orientation within a flow is 

typically with the major axis of the probe parallel to the bulk flow direction. The angular 

sensitivity of bi-directional probes is 10 % or less in the range of (0 – 40) deg for off-axis 

flow. Bi-directional probes are less sensitive to flow direction compared to pitot-static 

probes due to the pressure taps being located within large flow capture wells. Sensitivity 

to flow direction is reduced as the size of the well is increased. However spatial 

resolution and velocity component selectivity is reduced due to the larger probe. A bidirectional probe essentially senses the flow speed without any off-axis directional 

information. Even though a bi-directional probe may be aligned with the bulk flow, the 

resulting measurement may not accurately represent the desired flow component if threedimensional motion is significant. 

It is apparent from Equation 6 that the pressure differential in the doorway is height 

dependent. Therefore a vertical array of pressure probes is required to measure the

velocity through the doorway. Each pressure probe requires a pressure transducer to 

detect the induced pressure differential. Because fire induced flows are very low speed 

O(10 m/s), each transducer must accurately resolve pressure differentials on the order of 

10 Pa. 

Equation 9 demonstrates that measurements of pressure and density are required to infer

the local velocity. Density is derived from a thermocouple measurement of temperature 

by applying the equation of state for an ideal gas and assuming a constant molecular 

weight. 

ρ

p V C ∆ = 2

( 9 ) 

It is possible to measure the local gas velocity through other methods such as Laser 

Doppler Velocimetry (LDV), Particle Tracking (PT) or Particle Image Velocimetry 

(PIV). Each of these methods requires that the flow is seeded with a tracer that follows

the flow, typically tiny particles such as smokes or fogs. Velocity information is inferred

from the measured Doppler frequency shift when LDV measurements are applied. These 

are typically single point measurements. Particle displacement is measured by particle 

6
tracking and PIV. These measurements are typically image measurements, therefore 

offering more spatial information. In addition, each of the three techniques is nonintrusive. It is acceptable to think of the seed particles as the probes; very tiny probes

that move and react to the flow. In the case that the flow reacts to the presence of the 

seed particles, the particles are considered intrusive, and the seed loading would be too 

great for either of the techniques to work. 

PIV, specifically stereoscopic PIV, is explored in this study to provide an independent 

measurement of local flow velocity in vent openings. Stereoscopic PIV measures all 

three components of the velocity vector therefore providing directional selectivity and 

information on the three dimensional flow dynamics. PIV measurements are inherently 

planar measurements with good spatial resolution, therefore field measurements are now 

possible. This offers orders of magnitude more measurements in a single acquisition than 

previously available and makes the calculation of mass flow rate described in Equations 1 

and 2 a closer reality. 

As beneficial as PIV is presented, it is not a trivial technique to apply. It requires 

specialty lasers, optics, digital cameras, and complex control and analysis software. 

These systems are not inexpensive, but market growth has lowered the cost while at the 

same time the performance has improved. PIV has been applied with great success in

small laboratory-scale experiments, but large-scale flows such as those encountered in 

fire systems push the performance limits of PIV. Fortunately, the laser and digital 

camera industry have improved dramatically over the current decade in order to make 

such measurements increasingly feasible. 

3 Particle Image Velocimetry 

PIV is an optical imaging technique for obtaining whole field velocities, therefore 

thousands of velocity vectors, instantaneously. The technique measures the motion of a 

fluid by observing the location of small tracers within the fluid at two distinct moments in

time. The fundamental definition of velocity is the foundation for the technique. 

t

d V

∆

∆ = ( 10 ) 

The distance traversed by the tracer, ∆d , is the quantity measured, while the time 

between observations, ∆t , is specified. The method is applicable in gas and liquid flows. 

Flow tracers, often referred to as seed particles, are typically solid particles suspended in

a gas or liquid or liquid droplets suspended in a gas. They may also include bubbles 

immersed in the fluid or solid particles with hollow cores. 

Compared to typical point measurement techniques such as pitot-probes or LDV, PIV 

offers an instantaneous mapping of a specified flow field, increased spatial resolution, 

instantaneous information on velocity derivatives such as vorticity and strain, quantitative

information about the spatial structure of the flow, and time averaged statistics of the 

velocity field. 

7
The standard PIV system will give two components of the velocity vector for a specified 

field. The method has further developed to offer all three components of the velocity 

vector for a specified field. The advanced feature technique, known as Stereoscopic PIV, 

has been applied in this study. PIV is a planar imaging technique that relies heavily on 

image post processing to infer the final results. Adrian [11] presents a good overview of 

the physical aspects of the technique, while Keane and Adrian [12] discuss the theory 

behind the image post processing1

. In the sections to follow, a general summary of 

standard PIV will be presented first, followed by a brief description of the additional 

components and procedures necessary for Stereoscopic PIV. 

3.1 Two Dimensional PIV 

A standard PIV system, as displayed in Figure 2, consists of a double-pulsed laser to 

deliver two consecutive laser pulses coincident in space and separated in time ( ), sheet 

forming optics to expand the collimated laser beams into a planar sheets, a double-framed 

CCD (Charge Coupled Device) camera synchronized with each laser pulse and oriented 

perpendicular to the laser sheet, a data acquisition and control unit and a signal 

processing unit (frame grabber, computer and software). 

∆t

Tiny seed particles which follow the flow are injected into the flow. The light sheet 

produced by the laser illuminates the region of interest in the flow with very short pulses 

of light, optically freezing the motion of the seed particles. The position of the seed 

particles is detected by the CCD camera which records two images, one for each pulse, of 

the scattered light from the seed particles. The particles appear in the images as white 

spots on a dark background (black and white images). The camera and the laser are

synchronized so that particle positions at laser pulse 1 appear on camera frame 1 and 

particle positions at laser pulse 2 appear on camera frame 2. Images of the particle 

positions are sent to the computer for storage and signal processing. 

 

1

 Details concerning the image analysis are omitted from the current discussion as it is a routine function of 

any PIV system and beyond the scope of this discussion. 

8
Laser

Data Acquisition and 

Signal Processing

CCD Camera

Optics

Seeding

Flow

Light Sheet

Figure 2 Basic PIV setup 

Each image is divided up into square regions called interrogation areas. For each

interrogation area, image 1 and image 2 are correlated to determine the average particle 

displacement over the interrogation area. This is repeated for all interrogation areas and a

displacement vector map is created for the image space. Dividing the displacement

vector map by the known between the laser pulses produces the velocity vector map.

Figure 3 demonstrates this process. 

∆t

Frame 1 Frame 2 Velocity Vectors

Figure 3 Mean particle displacement is computed in each interrogation region 

(dashed squares) and converted to a velocity vector. The white arrows in frames 1

and 2 indicate the initial position of the selected particles (centered black dots). 

9
3.2 Stereoscopic PIV 

In standard PIV the laser sheet is oriented so that the bulk motion of the flow runs 

parallel to the laser sheet and the optical axis of the CCD camera and collection optics is 

perpendicular to the laser sheet. In this configuration only the velocity vector in the plane 

of the laser sheet is measured; the out of plane component is unaccounted for. By 

introducing another camera to view the same area as the first camera but from a different 

angle, a setup is created which allows the out of plane velocity component to be 

determined. This configuration is called Stereoscopic PIV. Both cameras record

different information about the same object in two-dimensions. The information can be 

combined to infer three-dimensional information. 

Camera 1 Camera 2

Laser Sheet

Figure 4 Typical Stereoscopic PIV configuration 

A typical Stereoscopic PIV configuration, shown in Figure 4, places the cameras at 40 - 

50 degrees off the axis perpendicular to the laser sheet and aligned to see the same field

of view.2

 A calibration target which consist of equally spaced black dots or crosses on a 

white background (or vise versa) is placed in the field of view and the cameras are 

focused on the target and aligned to get the maximum overlap between the two images. 

A sample target is shown in Figure 5. 

 

2

 Other configurations are possible as described in the Stereoscopic PIV system manuals.

10
Figure 5 Target of black dots on white background used for Stereoscopic PIV 

calibration.

The calibration target is a well defined grid of markers used to create a set of transfer

equations for the object in real space to the image space on the CCD chip. The target is

aligned in the plane of the laser sheet, and as part of the calibration procedure it is 

traversed through the plane of the laser sheet at specified displacements in order to create 

the out of plane transfer equations. (Multilayered targets are also available to perform the 

same function without the need to traverse the target.) Additional analysis software,

which is an add-on to the standard PIV analysis software, is required to process the stereo

images and produce velocity vector fields with all three components of velocity. A stereo 

configuration adds complexity and effort, but it is an essential tool for measuring threedimensional flows. 

3.3 Large-Scale PIV 

PIV has been employed with great success in the laboratory for small to medium-scale 

flow fields that are well controlled. Flows inherent to full-scale fire experiments are on 

the scale of the size of the structure for enclosure fires. In addition the flow is buoyancy 

induced, and therefore is subject to the changing thermal conditions due to the fire. 

There is therefore limited knowledge about the flow structure of any given fire system

before it has been studied. It is possible to exert control over the fire source (the source 

of buoyancy) and to some extent the physical boundary conditions. The physical 

dimensions of full-scale fire experiments push the limits for illuminating the test area, 

image collection, and seed particles selection. Fortunately the challenges in illumination

and image collection are being met due to market forces which are credited with the great 

improvements in off-the-shelf laser and digital imaging technology. 

11
3.3.1 Illumination 

Expanding the laser beam into a sheet across a large region reduces the intensity of

incident light available for scattering by the seed particles. Therefore high pulse energy 

laser beams are recommended for large measurement areas. Typically (150 - 200)

mJ/pulse of laser energy for each beam is sufficient when illuminating a 1 m x 1 m area.

As a general rule of thumb, as much laser pulse energy as possible should be acquired 

within the fiscal, space, and supply power constraints of the experiment. It is possible to

try to optimize laser pulse energy, particle size, and CCD chip responsivity to increase 

the scattering signal. The best recommendation is to maximize laser power and CCD 

responsivity at the laser wavelength to allow room for selecting smaller particles which 

are better flow tracers. 

The laser for the current study is a Spectra Physics PIV-200. Laser pulse energy was 

measured at approximately 150 mJ/pulse for each laser beam. It is shown in Figure 6 

with a light arm designed to allow high pulse energy laser beams to be safely delivered to 

the desired location. 

Figure 6 Double head Nd:YAG laser with light arm. 

12
3.3.2 Seeding 

Seed particles are the simplest and perhaps the most important part of a PIV system.

Seeding is essentially thousands of tiny probes suspended in the fluid that ride along with 

it. Without seeding, a measurement cannot be conducted. Therefore it is apparent why 

uniform seeding within a flow region is desirable. Uniformly seeding low speed flows 

that originate from the ambient surroundings is a challenging task. 

Seeding Density 

The cross correlation technique used to compute the particle displacements will produce 

some random noise in its computation. In order to keep the noise from dominating the 

results, several particle pairs have to exist within an interrogation region. Too low a 

number of particle pairs biases the results toward zero. Therefore the recommended 

minimum number of particle pairs per interrogation region is 5 for the cross correlation 

technique. Too high a seeding density may result in images where individual particles 

are not discernable. Ideal images will have particles appearing as discernable white spots 

on a dark background. 

Particle Selection 

It is a requirement that the seed particles follow the flow field. Ideally the seed particles 

should be neutrally buoyant for the flow conditions. If not neutrally buoyant, their 

terminal velocity and flow response time should be small compared to the velocity 

magnitudes expected and the time scales of the flow. At the same time the particle must 

provide sufficient light scattering intensity to allow detection by the CCD camera. 

Financial limitations are often a constraining factor in experimental design. CCD 

cameras and lasers are the most expensive parts of a PIV system and both play a large 

part in seed particle selection. For large-scale PIV, image magnifications will be less 

than unity and the CCD cameras will be required to detect particles typically less than 1 

mm. Therefore determining if the CCD camera can detect candidate particles for a 

desired optical setup is a good place to start in selecting seed particles. 

When the image of an individual particle is projected onto the CCD chip, it should cover 

at least 2 pixels. The CCD pixel pitch for the cameras employed in this study is 9 μ m. 

Therefore the particle image should cover at least 18 μ m. This allows the PIV analysis 

software to interpolate the position of the particle to within 0.1 pixels; a feature

commonly referred to as sub-pixel interpolation. The predicted particle image diameter,

dimage, is computed by the following relation which is a convolution of geometric optics 

and diffraction limited optics. 

2

#

2 2 d d M (2.44(1 M ) f λ) image = p + + ( 11 ) 

The first term under the square root is the contribution from geometric optics where dp is 

the particle diameter and M is the image magnification. The diffraction limited 

contribution to the image is the second term where f# is the collection optics f-number

and λ is the wavelength of collected light. Figure 7 displays a few sets of curves 

13
generated from Equation 11, plotted with respect to image scale factor, SF, which is the 

inverse of the image magnification. The plot demonstrates that adjusting the collection 

optics f-number has a greater effect than choosing the particle size in meeting the 2 pixel 

coverage requirement. However, increasing the f-number reduces the lens aperture and

therefore reduces the amount of light to be collected. So there are tradeoffs to be made. 

10 20 30 40 50 60 70 80

6

8

10

12

14

16

18

20

22

24

26

Scale Factor

Particle Image Diameter, micro

meters

30

50

70

90

110, micrometer

f# = 5.6 

f# = 11

f# = 16

Figure 7 Particle image diameter plotted with respect to image scale factor, 1/M. 

Other important parameters are collection optics f-number and particle diameter. 

For example in this experiment the seed particle diameters range from (30 – 50) μ m, the 

effective magnification is 0.014 (SF = 70) and the wavelength of the scattered light is 

0.532 μ m. For an f-number of 5.6 the particle image diameter is 7.4 μ m. Increasing

the f-number to 16 reduces the collected scattering signal far too much. However, 

slightly defocusing the camera lens causes a blur which enlarges the particle image

diameter to meet the 2 pixel coverage requirement. Note that selecting a CCD camera 

with a smaller pixel pitch may be a very expensive method of reaching the 2 pixel 

coverage requirement 

In general, to reduce the cost associated with lasers and CCD cameras, larger particles are 

desired because they scatter more light and are more capable of being detected by the 

CCD camera. However, larger particles may not follow the flow as desired. If the seed 

particles are not neutrally buoyant they will either fall or rise in the flow. Depending on 

the magnitude of the flow velocity and the flow component of interest, particles that are

14
not neutrally buoyant may be acceptable. Typical seed particles are solid or liquid

aerosols and therefore when used in air are negatively buoyant, meaning that they are 

constantly falling in the flow. 

When a particle falls in a surrounding fluid, the viscous drag exerts a force in the upward 

direction which balances the downward force of gravity on the particle. Once these 

forces are balanced a condition of constant velocity is created called the terminal 

velocity. Terminal velocity is estimated from the following equation for particle 

diameters greater than 1 μ m and particles having Reynolds number less than 1.0. 

μ

ρ ρ

18

( ) 2 d g V p g p

T

− = ( 12 ) 

Estimates of terminal velocity were made for the (30 – 50) μ m particles used in this

study with a particle density, ρ p , of 42 kg/m3

, a surrounding gas density, ρ g , of 1.16 

kg/m3

, and a gas viscosity, μ , of 1.846 x 10-5 N s/m2, with 9.81 m/s

2

 for the gravitational

acceleration, g. Results range from (0.0011 - 0.0030) m/s for the (30 – 50) μ m particles

respectively. At the low range of the horizontal velocity component measured in this 

study, the particle terminal velocity amounts to 1 % or less of the horizontal component. 

A ratio of less than 1 % is acceptable as a good rule of thumb for characterizing the seed 

particles as not being too negatively buoyant. 

A particle must also sufficiently respond to abrupt changes in the flow to be considered a

good flow tracer. The particle response time is another measure of a particles ability to 

follow the flow. Consider a particle suspended in a gas at rest and at time zero a pressure 

wave propagates through the gas, suddenly forcing it to move at some constant velocity.

The particle must accelerate in order to catch up to the gas velocity. The time it takes for 

the particle velocity to reach 63 % of the gas velocity is called the particle response time

and is defined by the following equation. 

g

d p p

υρ

ρ

τ

18

2

= ( 13 ) 

For the case of a 50 μ m particle with a gas kinematic viscosity, υ , of 1.59 x 10-5 m2

/s,

and the same particle and gas densities defined above, the particle response time is 0.3 

ms. The time required for the particle velocity to equal 99 % of the gas velocity is 4.6

times greater, 1.4 ms. The characteristic time scales of the flows under consideration are 

on the order of seconds, therefore the particles are excellent candidates for following the 

flow. 

Materials typically used for seeding range from liquid droplets to solid particles. Some

of these materials are listed in Table 1. The particles selected for this study are dry 

expanded microspheres. The microspheres are filled with a gas, usually isopentane, and 

15
the shell is a copolymer of some monomers such as vinylidene chloride, acrylonitrile and 

methylmethacrylate. The particles are non-toxic and in bulk appear as a fluffy white dust.

Proper respiratory protection should be worn when handling them. They are 

manufactured by Expancel (551 DE 40 d42) with a weight averaged diameter of (30 – 

50) μ m, and a particle density of 42 ± 4 kg/m3

. 

Table 1 Typical seeding materials for PIV 

Material 

Size

Distribution,

μ m

Recommended 

Flow Medium

Comment

Al203 <8 Air High temperature

applications

Glycerin 0.1 - 5 Air Generated by atomization, 

water based, good light 

scattering properties

Silicone Oil 1 - 3 Air High temperature 

applications

SiO2 1 - 5 Air High temperature 

applications, spherical 

particles 

Water 1 - 2 Air Generated by atomization, 

very inexpensive 

Polymer 

Microspheres 

30 – 50 Air Low density particles, good

light scattering properties

Hollow Glass 

Microspheres 

2 - 20 Water Smooth spherical surface, 

good light scattering 

properties, high density 

Pine Pollen 30 - 50 Water Oval shaped, inexpensive 

and available in large 

volumes

3.3.3 Recommendations for Large-Scale PIV 

1) Use pulsed lasers with energy in excess of 150 mJ/pulse. 

2) Select large pixel format CCD cameras with small pixel pitch (e.g. 2 mega pixels 

or greater, with 9 μ m x 9 μ m pixels or less). 

3) Optimize signal collection with wide angle collection optics; large f# result in 

better image quality but reduced image intensity. Use aspheric optics to minimize 

the distortion for wide angle views. 

4) Balance seed particle size with flow response; the larger the particle the greater 

the resulting image intensity, but the less responsive it is to the flow. 

16
5) Employ uniform seeding whenever possible; it is possible to achieve uniform

seeding over time with a large sample of measurements. 

6) Optimize seeding density to capture at least 5 particle pairs per interrogation 

region. 

7) For large-scale fire measurements: 

A remotely controlled seeding system is recommended as manual seeding will be

unsafe. 

Remote or triggered automatic control is also recommended since seeding is only 

required at the moments when measurements are conducted. 

Mixing the seed particles into small air jets is an effective means of issuing

seeding into the almost quiescent flow that enters the enclosure. (Small vacuum

pumps that are driven by high pressure air are good candidates for mixing the 

solid particles and air.) 

4 Reduced-Scale Convective Analog Experiment 

The NIST Fire Research Division has established the goal of developing a methodology 

for PIV measurements in full-scale fire tests. This study serves as an important step in 

meeting this goal. PIV measurements of large-scale flows push the performance 

envelope of the typical off-the-shelf PIV system. Therefore, before going to full-scale 

fire experiments, attempting similar experiments at an intermediate scale under less harsh 

conditions was determined to be a necessary step. Steckler and his colleagues performed 

an extensive set of velocity measurements in the doorway of an enclosure with a 

constant-flow gas fire source which simulated the early stages of fire growth. [9,13] 

Applying Froude number scaling, one experimental condition performed by Steckler et 

al. was simulated in this study with a helium plume as the source of buoyancy. The

helium plume experiment was scaled to be 0.55 of the full-scale fire experiment. This 

reduced-scale convective analog only offered information on the flow and flow induced 

mixing of a similar real system. The performance of such a model is expected to be very 

good when heat transfer, chemical reactions, or boundary conditions are not important in

the real experiment. Because the goal of this study is to demonstrate a flow measurement

technique, a purely convective and isothermal analog is sufficient. 

4.1 Fire Experiment Scaling 

Fire scaling laws are typically derived from the non-dimensional Navier Stokes 

equations. The equations include non-dimensional coefficients such as Reynolds and 

Froude number which are ratios of relevant forces specific to the problem. If the nondimensional coefficients are kept invariant between the full-scale and reduced-scale 

experiments, both experiments are described by the same set of equations and hence their 

non-dimensional solutions are the same. Therefore proper scaling of geometrically 

similar fire experiments should have similar normalized spatial distributions of flow, 

temperature and composition. 

17
The helium plume is a low density gas relative to the ambient air. It is analogous to a

high temperature buoyant fire plume. Since plume flows are buoyant the nondimensional equations describing them are governed by the Froude number, Fr. 

gl

u Fr

ρ

ρ

∆ = ∞

2

( 14 ) 

The Froude number is the ratio of the inertia and buoyant forces, where ρ ∞ is the 

ambient gas density, ∆ρ is the density difference between the plume and ambient gas, u

is the plume gas velocity, l is the characteristic length scale (source diameter), and g is 

the gravitational acceleration constant, 9.81 m/s

2

. Therefore the Froude number must be 

preserved between the model and the real experiment. 

Quintiere [14] and Steckler et al. [15] present a scaling analysis starting with the nondimensional equations describing a fire plume and an isothermal buoyant plume. By 

preserving the Froude number between the model and real-scale experiments the source 

terms, heat release rate, Q , of the fire plume and the mass flow rate, , of the isothermal

buoyant plume are related. 

& m&

The Reynolds number of a turbulent fire plume is on the order of 105

. Steckler et al.

estimate that if the Reynolds number of the reduced scale plume is on the order of 104

 or 

greater, the terms in the non-dimensional equations proportional to 1/Re may be

neglected. The Reynolds number defined as ul υ , where u is the characteristic velocity 

of the Froude scaling and l is the height of the reduced-scale enclosure, was estimated to 

be on the order of 104

. Therefore the Reynolds number was ignored in the scaling 

analysis. 

The scaling analysis presented in this report is more of a phenomenological one that picks 

up from the formal scaling of the non-dimensional equations describing the two systems

and demonstrates how to apply the scaling to design the reduced-scale experiment. 

In order to preserve the Froude number, a relation for the characteristic velocity, u, in

terms of the experiment length scale, l, should be defined. Equation 14, implies that u ~ 

l

1/2 and the following analysis will make use of this requirement. 

The rate of heat released from a fire is equivalent to the advection of enthalpy away from

the source 

( 15 ) Q Cp Tmplume & & = ∆

where, Cp is the specific heat of the gas and ∆T is the temperature difference between

the hot plume gases and the ambient air , T −T∞ . For a highly ventilated fire plume the 

gases can be approximated as air, therefore Cp = Cp,air. For a perfect gas, the gas density, 

ρ , is inversely proportional to the gas temperature, T and the following relation holds. 

18
∞

∆ = ∆

T

T

ρ

ρ ( 16 ) 

This relation is significant because it illustrates the analogy of the temperature difference 

in the fire plume to the density difference in the isothermal helium plume. Recall that 

mass flow rate is defined as ρAu , where A is the cross sectional area and is proportional

to l

2

. A relation for the characteristic velocity can be defined from Equation 15 by 

substituting for the definition of mass flow rate and employing the temperature difference 

relation from Equation 16. 

2 C T l

Q

u

p ∆ρ =∞

& ( 17 ) 

The Froude number relation can now be written in terms of the heat release rate and the 

experiment length scale. 

5

2

2 2 2

3

1

l

Q

gC T

Fr

p

&

∞ ∞

∞

⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

∆ = ρ ρ

ρ ( 18 ) 

The density ratio was held constant for this experiment but it is a variable that may be

used to maintain a constant Froude number. The second term is a constant for ambient 

conditions. The final term, 5 / 2 Q l & , was the control variable for this experiment and 

Froude number was preserved by keeping this ratio constant between the real experiment 

and the model. The subscripts FS and RS in Equation 19 refer to Full-Scale and 

Reduced-Scale respectively. 

5 / 2 5 / 2

RS

RS

FS

FS

l

Q

l

Q& & = ( 19 ) 

The equivalence of heat release rate and enthalpy advection, Equation 15, holds true for

the reduced-scale plume as well. Since the reduced-scale system employs a helium 

plume as its source of buoyancy, it is a purely isothermal and convective analog of the 

full-scale system. Therefore the model should scale according to the convective heat 

release of the full-scale system, which is typically 0.7 .[16] For a given heat release

rate from a full-scale fire, the required mass flow rate for an analogous helium plume is 

computed using the following relation. 

QFS

&

ρ

ρ

∆ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

∞

5 / 2

0.7

FS

RS

p

FS

He l

l

C T

Q

m & & ( 20 ) 

19
Since the goal of this study is to measure the flow through the doorway, the doorway 

height is used as the characteristic length scale (l = H) of the experiments. The ratio of 

the doorway heights is the geometric scale factor (lRS/lFS = HRS/HFS). All geometric 

dimensions are scaled according to this factor and its influence on the dynamic scaling 

appears in Equation 20. A doorway height of 1 meter was chosen for the reduced-scale

experiment which is 0.55 times the full-scale height. This dimension is on the order of 

the measurement area limits of PIV and therefore exposes the challenges of applying PIV 

with a dynamically similar experiment. The relevant parameters for both the full-scale 

and reduced-scale experiments are shown in Table 2 for the conditions listed. 

Table 2 Full-scale to reduced-scale parameter values. 

Parameter Full-Scale Reduced-Scale

Doorway Height, H (m) 1.8 1.0 

Doorway Width, W (m) 1.0 0.6 

Room Height, h (m) 2.1 1.2 

Room Width, w (m) 2.8 1.5 

Room Length, l (m) 2.8 1.5 

Burner Diameter, d (m) 0.31 0.17 

Heat Release Rate, Q (kW) & 32 7.0

Target Helium Mass Flow Rate, 

(kg/s) 

mHe & - 0.0026

 =300 K, = 103 kPa, T∞ Pamb ρ air = 1.1614 kg/m3, ρ He = 0.1625 kg/m3, Cp=1.007 kJ/kgK 

4.2 Experimental Setup 

Conducting the experiments for this investigation required many steps. In addition many 

preliminary experiments such as flow meter confirmations, experiments to determine the 

best particle seeding, experiments to select the best optical configurations for the 

cameras, and experiments to estimate the optimum timing between laser pulses had to be 

performed. Once an optimum set of steps and conditions had been defined, the required 

measurements were conducted at the selected measurement planes. 

The first step was to set up the stereoscopic PIV system. This required aligning the 

cameras so that each camera was focused on the same region. The calibration target was 

placed in the field of view of each camera and they were aligned so that the full target 

was in focus. The cameras were oriented to view the forward scatter from the particles as 

shown in Figure 8. The center of the target was imaged in almost the same position on 

each camera. This ensured that the overlap of the two images was nearly maximized. 

Next the calibration was performed to map the 3 dimensional object space to image 

space. The calibration was performed by traversing the target in the out-of-plane 

direction (z direction) relative to the laser sheet and recording images of the target at 5 to

9 z positions. The target was returned to the center of the traversed distance and the laser 

sheet was aligned to vertically coincide with the center of the target (this was for a twosided target with both cameras viewing forward scatter, in the case that both cameras 

were viewing the same side of the target then the center of the laser sheet would be 

20
aligned to coincide with the front plane of the target). The laser sheet was spread over 

the imaged region with sufficient energy for scattering measurements. 

As long as the cameras and laser sheet were not bumped or moved the calibration was

valid. Any movement of the optical system required a new calibration to be performed.

The enclosure was capable of being traversed around the optical setup. It was traversed 

in the z direction to measure velocity vectors at 11 positions across the doorway. 

Because the entire height of the doorway could not be imaged, the enclosure was also

traversed in the y direction to completely map the velocity vectors in the full vertical

height of the doorway. 

CCD cameras

y 

x z

Laser sheet

Doorway

Figure 8 Optical configuration for the analog fire-enclosure experiments. 

Starting at the z = 0 cm position, the helium flow was turned on to give a typical volume

flow rate of 1133 SLM (0.003 kg/s). Two high pressure helium bottles were run in 

parallel with separate regulators and flow meters. The helium flow was run for a 

maximum of 4 minutes and 1 minute was allowed to pass before any measurements were 

recorded (FDS results showed the flow at the doorway to be at steady state after about 40

seconds).3

 At 40 seconds after the helium flow was started, seed particles were 

 

3

 At this flow rate the experiment could ideally run continuously for approximately 10 minutes. However 

release of the high pressure gases causes the bottle temperature to decrease and therefore could influence 

the exit conditions at the helium plume. For this reason the helium flow was typically run for a maximum

of 4 minutes which allowed two experiments to be conducted per pair of helium bottles. 

21
introduced to fill the region that supplied the inflow gas at the doorway. When the 

seeding was determined to be sufficient and the 1 minute duration had completed, the 

system was triggered to record images for velocity vectors. Three bursts of 20 

measurements were recorded for a total of 60 velocity vector maps at each location. The 

three burst all occurred within the 4 minute helium flow duration. The image acquisition 

rate was set at 2 Hz. Upon completion of the measurement the helium flow was shut 

down and the room was traversed to the next z location. 

4.2.1 Reduced-Scale Enclosure 

Visible light was required to pass through the walls of the enclosure in order to produce a

laser sheet in the required measurement location and in order to observe the resulting

scattering from the seed particles. Therefore the enclosure walls were constructed of 

clear Plexiglas of thickness 0.3 cm, and the frame was constructed of aluminum angle 

(3.7 cm width on one side, 0.5 cm thickness). All vertical walls were formed from a

single piece of Plexiglas, therefore no seams were present. The ceiling and the floor were 

constructed from two separate pieces with a single seam. The aluminum angle frame was 

located at all corners; a flat aluminum bar supported the ceiling and floor seams. The 

Plexiglas was attached to the frame using screws and two sided adhesive stripping (3M 

Scotch Brand Tape, 1.3 cm wide). At initial construction, the adhesive stripping 

provided a good seal for the enclosure, but as time passed the seals began to fail at 

locations away from the screw fasteners. These locations were fortified with duct tape. 

The outside dimensions of the enclosure were 1.53 m x 1.16 m x 1.53 m (w x h x l). The 

doorway was located in the horizontal center of one end of the enclosure and 4 cm above 

the floor of the enclosure. The doorway dimensions were 0.54 m x 1.0 m (w x h). A hole 

was cut in the center of the floor of the enclosure and the helium plume inlet protruded 

through the hole to stand above the floor by 8.0 cm. The outside diameter of the helium 

plume inlet was 19.0 cm. A schematic of the enclosure with dimensions is shown in 

Figure 9 and a photograph of the enclosure is displayed in Figure 10. 

22
1.53 m

1.53 m

1.16 m

1.0 m

0.54 m

0.77 m 0.77 m

Doorway

Helium Nozzle

0.12 m

0.04 m

0.19 m

0.08 m

Figure 9 Schematic of reduced-scale enclosure with the helium plume inlet at the

floor. 

Figure 10 Photograph of reduced-scale enclosure. 

Experiments with complicated optical setups are typically designed to keep the optical 

setup stationary and move the experiment relative to the optics. This was true for most of

the experiments described in this report, however physical space limitations required the 

optics to be translated for a few experiments. A translating support mechanism was

23
fabricated from extruded aluminum bar (80 / 20 Inc.) for moving the enclosure, Figure 

11. The enclosure was placed on top of the support and securely attached. The support 

mechanism was moved horizontally by a hand crank attached to a threaded rod, which 

pushed and pulled the sliding supports. Vertical translation was accomplished by placing

heavy duty laboratory jacks on both sides of the support mechanism to lower and raise 

the assembly. The sliding supports were locked in place once the desired vertical height 

was achieved. Because the enclosure was raised above the laboratory floor, a temporary

floor was placed in front of the doorway to simulate the enclosure sitting on the floor. 

3.8 cm x 3.8 cm

(1.5 x 1.5)

3.8 cm x 7.6 cm

(1.5 x 3.0)

3.8 cm x 7.6 cm

(1.5 x 3.0)

76 c

m

167 cm

Top bar translates horizontally

Sliding support with lockVertical translation

3.8 cm x 3.8 cm

(1.5 x 1.5)

3.8 cm x 7.6 cm

(1.5 x 3.0)

3.8 cm x 7.6 cm

(1.5 x 3.0)

76 c

m

167 cm

Top bar translates horizontally

Sliding support with lockVertical translation

Hand crank Threaded rod

165 c

m

Hand crank Threaded rod Hand crank Threaded rod

165 c

Top View m

Side View

Sliding supports

Figure 11 Schematic of translating support mechanism for the enclosure. 

4.2.2 Helium Flow System

A flow system was fabricated to deliver helium from standard high pressure bottles (5.66 

m3

, at 13,790 kPa) to a circular exit near the floor of the enclosure. The flow was

controlled by regulating the supply pressure from the bottles and next setting the volume 

flow rate by adjusting the variable area flow meters (Dwyer Rate Master, RMC-122-SSV,

566 SLM maximum flow rate (20 SCFM)). Pressure gauges (Ashcroft, (0 – 207) kPa ((0 

– 30) psig)) were installed near the exit of the flow meters to provide pressure readings 

24
for correcting the flow meter readings. The tubing employed was 3/8” plastic tubing. A 

schematic of the flow system is shown in Figure 12. 

Helium

bottles

Pressure

gauges

Flow meters

Shut-off

valves

Plume

exit

All 3/8” plastic tubing

Figure 12 Helium plume flow system. 

The helium plume exit assembly is shown in Figure 13. A Plexiglas tube (19 cm o.d., 0.6 

cm wall thickness) served as the outer shell of the plume assembly. A section of 

aluminum honeycomb (0.35 cm cells) located above the entry plenum provided flow

straightening and 4 steel screens (200 mesh) served to provide flow uniformity. Smaller 

inner Plexiglas tubes (16.7 cm i.d., 0.6 cm wall thickness) served as spacers to support 

the honeycomb and screens. Helium entered the flow plenum from two entry ports (total 

of 4 entry ports, the remaining two ports were closed). High frequency acoustic energy 

was produced by the helium issuing into the plume assembly. A layer of cotton balls was 

placed in the empty space above the honeycomb to absorb some of this acoustic energy 

and also to contribute to the flow uniformity. The helium plume exit assembly stands 25 

cm high. It protruded by 8 cm through a hole cut in the enclosure floor. An adjustable 

platform below the enclosure and attached to the enclosure supported the plume exit 

assembly. A steel screen covered the exit of the plume assembly. The inner diameter at 

the exit was 16.7 cm due to the spacers for the screens. 

25
Screen

(200 mesh)

Tube

Spacer

Honeycomb 

Flow 

Straightener

Plenum

1.0 cm

Screen

(200 mesh)

16.7 cm

25 cm

5 cm

5 cm

12 cm

Tube

Spacer

Inlet,

1⁄4 NPT,

Male

Inlet,

1⁄4 NPT,

19.0 cm Male

Figure 13 Helium plume exit assembly. 

The variable area flow meters were calibrated for air by the manufacturer. Correction 

factors were applied to the scale reading, , for the pressure within the flow meter,

P

Vscale

&

flowmeter, and for specific gravity, S.G., of the gas of interest. The actual volume flow rate 

of helium was determined using the following equation. 

. .

1

P S G

P

V V

amb

flowmeter

He scale & = & ( 21 ) 

The accuracy of the variable area flow meters was quoted as ±2 % of the full-scale 

reading. A dry test meter (Singer American Meter Division, DTM-200) was used to 

confirm the output from the flow meters. Figure 14 demonstrates the very good 

agreement between the measured output and the flow rate settings, therefore ensuring

confidence in the operation of the flow meters. The flow meters regulate the flow for 

standard conditions, which are defined as 101325 Pa and 294 K by the manufacturer.

The mass flow rate of helium was determined by computing the product of volume flow 

rate and helium gas density, ρ He,STP , at this condition. 

26
400

500

600

700

800

900

1000

1100

1200

400 500 600 700 800 900 1000 1100 1200

flow meter 1

flow meter 2

flow meter 1&2

M

e

a

s

u

r

e

d

F

l

o

w

R

a

t

e

,

S

L

P

M

Flowmeter Setting, SLPM

Figure 14 Helium flow confirmation. 

4.2.3 Stereoscopic PIV System 

A general description of a PIV system was presented in Section 3. A detailed description 

of the PIV system employed in this study shall follow. The Stereoscopic PIV system

described here was supplied by Dantec Dynamics. 

The laser was a pulsed Nd:YAG with two lasing heads (Spectra Physics PIV-200). The 

two lasing heads delivered two 532 nm beams that were coincident in space but separated

in time. Each beam had an average pulse energy of 150 mJ/pulse at 532 nm (enough 

energy to rate the laser as a Class IV radiation hazard, i.e. eye protection was required at

all times). The two lasing heads made possible the combining of two lasers in one

package. Each laser beam pulsed at a rate of 15 Hz and the time between the two laser

beam pulses was controllable from 5 μ s to 66 ms. A light arm for high power lasers 

27
delivered the laser pulses from the laser exit port to the rear of the enclosure. Sheet 

forming optics were attached at the end of the light arm to spread the laser beams into a

diverging set of light sheets which passed through the Plexiglas wall of the enclosure and 

illuminated the particles in the measurement region of the doorway. The laser sheets, like 

the laser beams, were coincident in space but separated in time. 

The seed particles were dry expanded microspheres (Expancel 551 DE 40 d42). The 

microspheres were hollow plastic shells which enclosed a gas. They had a weight

averaged diameter of (30 – 50) μ m and a density of 42 kg/m3

. The seed particles were 

manually introduced into the flow using a shaker. The shaker was essentially a paint can

with a fine mesh metal screen covering the opening. The experimenter stood about 1 m 

outside of the enclosure and was removed from the measurement location. The particles

were introduced in a broad region so as to cover the incoming air with particles. The

particles that entered the enclosure with the incoming air were entrained by the helium 

plume and transported to the upper layer to provide the outflow with seed particles. 

Therefore seeding from a single location provided ample seed particles for both the 

inflow and outflow. 

Two cross-correlation CCD cameras (Kodak Megaplus ES1.0, Type 16) were employed 

in this PIV system. The term cross-correlation is used because the cameras were capable 

of recording two images, one for each laser pulse, and therefore offering a velocity 

measurement free of directional ambiguity. The minimum time between the two image 

frames was 1 μ s. The CCD chip pixel dimensions were 1008 pixels x 1016 pixels. 

Each pixel had a pixel pitch of 9 μ m x 9 μ m, therefore resulting in CCD physical 

dimensions of 9.07 mm x 9.14 mm. The cameras were capable of frame rates up to 30 

Hz in single frame mode and 15 Hz in double frame mode. The bit depth per pixel was 8 

bits. This resulted in 256 grey levels. Attached to each camera was a 20 mm focal length

Nikon AF Nikkor lens with f# of 5.6. The short focal length lens allowed for wide angle 

image views. 

Stereoscopic PIV requires the cameras to be mounted at off-axis angles to the object 

plane as opposed to traditional PIV which has a single camera mounted on the axis of the 

object plane. In order to achieve the best plane of focus for this configuration, the camera

image plane (CCD chip) must be rotated to simultaneously intersect with the lens plane

and the object plane. This condition is known as the Scheimpflug condition and requires 

some distance between the lens and camera housing to allow for rotation. Special camera

mounts were supplied which allowed the CCD chip plane to be rotated relative to the lens 

plane. The mounts also allowed the entire camera and lens to be rotated about the CCD 

chip vertical axis. 

A calibration target was required to determine the object space to image space coordinate 

mapping. The calibration target was a grid of black dots on a white background. The 

dots were spaced 21.5 mm apart and had a diameter of 4.5 mm. The center of the target

was defined by a 6 mm dot surrounded by four 3 mm dots that defined the vertical and 

horizontal axis. The target was constructed of 90 cm x 100 cm x 0.6 cm (height x width x 

thickness) Plexiglas sheet. Two identical dot patterns were adhered to both sides of the 

28
sheet to create a two sided target. The dot patterns covered an area of 77 cm x 77 cm.

The sheet was held rigid by placing it in a square frame of 2.54 cm x 2.54 cm extruded 

aluminum. This assembly was attached to a three axis traverse. 

The data acquisition and control unit used to acquire the images from the CCD cameras 

and control timing between the experiment, lasers, and cameras was essentially a 

personal computer equipped with frame grabbers, an analog-to-digital converter, signal 

processing hardware, pulse synchronization hardware, and communications link to the

user interface computer. The unit read images from the cameras to an input buffer. From

this input buffer the images were temporarily stored in memory from which they could be 

sent directly to the computer hard disks for later processing or sent to the correlator unit 

which produced vector maps from the images in real time. The images were sent to the 

personal computer via an Ethernet communications board. The software (Flow Manager 

version 3.7) then stored the images and vector maps in a database, keeping track of all 

corresponding data acquisition and analysis parameters. The software was used for 

subsequent analysis of the vector maps, such as adaptive correlations and vector statistics. 

The full detail of the Stereoscopic PIV system is presented in the “FlowMap Particle 

Image Velocimetry Instrumentation Installation and Users Guide” (Publication #: 

9040U3624, Date: 15 August 2000) and the “FlowMap 3D-PIV System Installation and 

User’s Guide” (Publication no.: 9040U4112. Date: 16 August 2000) published by Dantec 

Dynamics. The reader is encouraged to review these documents for a complete 

description of the PIV system. 

4.2.4 Gas Sampling System

Flow density was inferred from measurements of oxygen volume fraction in the flow 

stream. A gas sampling system, shown in Figure 15, was assembled for the oxygen 

volume fraction measurements. The system consisted of a stainless steel sampling probe 

(6.35 mm o.d., 4.57 mm i.d.) that was placed in the doorway plane at several different

sampling locations. A volume displacement flow meter (Dry-Cal-Lite, DCLT 20k

Rev1.08) was installed in the system to measure the sampling volume flow rate. The 

pressure at the exit of the flow meter relative to ambient pressure was monitored with a

differential pressure gauge (Magnehellic, (0 – 981) Pa, ((0 – 10) cm H2O)). A pump

provided the pressure differential to pull a sample of gas from the flow and push it 

through the oxygen analyzer. The volume flow rate was controlled by a manual valve

that was installed in the line. 

29
Sample probe

Flow meter

Differential pressure

gauge

Flow control 

valve

Pump

Particle filter

Oxygen analyzer

Vent

Figure 15 Gas sampling system to measure oxygen concentration. 

The portable oxygen analyzer (Servomex 570A/712) was a paramagnetic device. Its 

voltage output ranged from 0.0 to 1.0 V. Having a linear response to the oxygen volume

fraction, an output of 1 V represented an oxygen volume fraction of 1.0. The output of 

the oxygen analyzer was monitored on a digital voltmeter and simultaneously recorded 

by a data acquisition system (Omega PDAQ56, OMB-DAQ-56) and stored on a personal 

computer. The sampling rate of the voltage signal by the data acquisition system was 1 

Hz. 

5 Uncertainty Analysis 

Measurement uncertainty is presented and follows the methodology described in the ISO 

guidelines and adopted by NIST. [17,18] Each component of uncertainty is presented as 

a standard uncertainty. So named Type A uncertainties are those that can be computed 

based on statistics, such as the standard deviation about the mean. Uncertainties that are 

determined from scientific judgment and other available information are designated as 

Type B uncertainties. 

5.1 Type A Uncertainty 

Mean Velocity Measurement

The velocity data presented are the mean values of at least 60 samples. The standard

deviation about the mean is listed in Table 3. It is used to compute the standard 

uncertainty of the mean measurement, u = σ / N . This value is the estimated standard 

uncertainty of the velocity measurement. The uncertainty estimates are divided among 

the two flow regions, inflow and outflow. These estimates are representative of 21 

locations selected from the inflow region and 9 locations selected from the outflow 

region. 

30
Table 3 Mean velocity uncertainty estimates. 

Velocity Inflow Outflow

Component σ , m/s ( ) i,sample u v , m/s σ , m/s ( ) i,sample u v , m/s

 vx 0.057 0.007 0.152 0.020

 vy 0.051 0.007 0.090 0.012

 vz 0.060 0.008 0.151 0.020

Oxygen Concentration

The standard uncertainty is estimated using the sample standard deviation of repeat 

measurements. Measurements conducted near the neutral plane have a larger standard 

deviation due to the changing flow direction. Repeat measurements were conducted at

this location in order to determine an upper bound on the standard deviation, Table 4. 

The standard deviation defines the standard uncertainty for a single measurement. This

sample of measurements is used to estimate the uncertainty of all the measurements on

centerline of the doorway. The estimate is conservative since the upper bound of the 

standard deviation of measurements is being applied. 

Table 4 Sample oxygen concentration data near the neutral plane. 

 x, mm y, mm Z, mm X O ,SS 2

-14 690 0 0.1969

-14 690 0 0.1919

-14 690 0 0.2016

-14 690 0 0.2010

-14 690 0 0.1942

-14 690 0 0.1959

-14 690 0 0.1999

Mean 0.1973

Standard Deviation 0.0036 

5.2 Type B Uncertainty 

Temperature

A stationary mercury thermometer with graduations of 1 o

C was employed for the 

ambient temperature measurements, Tamb. It is assumed that the temperature reading is 

described by a symmetric triangular probability distribution with upper bound (Tamb + 1) o

C and lower bound (Tamb - 1) oC. The standard uncertainty is then u(Tamb) = 1 6 = 

0.48 o

C. 

Ambient Pressure

The ambient pressure was read from a digital pressure indicator (Druck DPI 145). The

expanded uncertainty of the instrument listed by the manufacturer is ±0.014 kPa over the 

range of 79.979 kPa to 115.142 kPa. Assuming a coverage factor of 2, the standard 

uncertainty is estimated at 0.007 kPa. 

31
Helium Volume Flow Rate

The volume flow rate of helium, , was controlled by variable area flow meters. The 

scale was divided into graduations of 0.5 SCFM (14.2 SLPM). The manufacturers

reported accuracy is ± 2 % of the full-scale reading, which results in an absolute accuracy 

of 0.4 SCFM (11.3 SLPM) for all readings. It is assumed that each volume flow rate 

reading is described by a symmetric rectangular probability distribution with upper bound 

( + 0.4) SCFM and lower bound ( - 0.4) SCFM. The standard uncertainty is then 

 = 

VHe

&

VHe

& VHe&

( ) VHe u & 0.4 3 = 0.24 SCFM (6.8 SLPM). 

Dimensions

The dimensions of the enclosure and measurement locations were measured using a 

flexible tape measure. The minimum graduation was 1 mm. Considering the flexibility

of the device and the skill of the operator, the standard uncertainty of all dimensions and 

measurement locations are estimated to be 1 mm unless otherwise stated.

PIV

The uncertainty of a single PIV vector has contribution from a variety of sources such as 

the algorithm to compute the particle displacement, the particle response, particle seeding 

density, particle size distribution, and collection optics to name a few. Two contributions 

were estimated for this study, the uncertainty of the measured particle displacement and 

the particle response to the flow. 

The quoted accuracy of the pixel displacement measurement was 1/10 of a pixel. This 

resulted in a particle displacement uncertainty of 68 μ m for the CCD pixel pitch and 

image scale factor employed in this study, 9 μ m and 75.24, respectfully. The average 

time separation between PIV images was 7500 μ s, which produces an estimated velocity 

uncertainty of u(algorithm) = 0.009 m/s. 

The particles were estimated to respond almost instantaneously to the bulk flow relative 

to the characteristic time scales of the bulk flow. Therefore the uncertainty due to the

temporal response of the particle is considered to be negligible. However the particles 

have a small terminal velocity in the vertical direction of -0.003 m/s. This should add a 

bias to the measured vertical velocity component, but its contribution to the other 

components is unknown. Therefore the terminal velocity was considered as the 

uncertainty contribution for the particle response, u(PartResp) = 0.003 m/s. 

Oxygen Concentration Field Assumption

Measurements of oxygen concentration were also conducted off centerline (z ≠ 0 mm) to

estimate the dependence on horizontal location across the doorway, Table 5. The 

standard deviation from this sample of measurements serves as an estimate of the 

standard uncertainty in the assumption that the measured value on centerline at a specific 

elevation is representative of the value at any horizontal location across the doorway. 

32
Table 5 Sample oxygen concentration data at centerline (z = 0 mm) and off 

centerline. 

 x, mm y, mm z, mm X O ,SS 2

-14 80 0 0.1735

-14 80 0 0.1730

-14 80 0 0.1759

-14 80 10 0.1746

-14 80 20 0.1708

-14 80 20 0.1728

-14 80 25 0.1779

Mean 0.1741

Standard Deviation 0.0023 

Neutral Plane Height

The average position of the neutral plane was determined from a set of y locations

meeting the criteria for the neutral plane. The standard deviation for this set of positions 

was 20 mm and serves as an estimate for the standard uncertainty of the neutral plane 

height. 

5.3 Uncertainty Propagation 

Suppose a general equation can be applied to describe a measurement process which has 

an output y and the output y is based on a number of input quantities, xi. 

( , , ,..., ) 1 2 3 N y = y x x x x ( 22 ) 

In the case that all input quantities are uncorrelated, the combined relative expanded 

uncertainty is given by 

∑= ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = =

N

i i

i

i

e c

x

u x k s

y

u y k

y

U y

1

2

2 ( ) ( ) ( ) ( 23 ) 

In Eq. (23), u(xi) is the standard uncertainty for each input, uc(y) is the combined 

uncertainty, k is the coverage factor, and si is the associated dimensionless sensitivity 

coefficient given by 

y

x

x

y s i

i

i ∂

∂ = ( 24 ) 

5.3.1 Helium Mass Flow

Two variable area flow meters were used to set the helium volume flow rate. The mass

flow rate of helium was determined by the following relation. 

33
( ) mHe VHe,1 VHe,2 ρ He,STP & & & = + ( 25 ) 

Volume flow rate and helium density, ρ He,STP , were both referenced to the standard

conditions of 101325 Pa and 294 K as defined by the flow meter manufacturer. Applying 

the standard uncertainty estimates for each volume flow rate measurement to the general 

equation for uncertainty propagation, the relative combined uncertainty of the helium

mass flow rate is u mHe mHe ( & ) & = 0.01. A coverage factor of 2.0 is applied, resulting in an 

expanded relative uncertainty of ±0.02. 

5.3.2 Mean Velocity Field 

Since there is not one simple equation to describe the velocity measured with 

Stereoscopic PIV, each of the uncertainty components described previously were added 

in quadrature to estimate the uncertainty of the mean velocity field, 

2

,

2 2 ( ) ( lg ) ( Re ) ( ) i i sample u v = u a orithm + u Part sp + u v . 

Table 6 Mean velocity field uncertainty estimates. 

( )i

Velocity u v , m/s Component Inflow Outflow

 vx 0.012 0.022

 vy 0.012 0.015

 vz 0.012 0.022

5.3.3 Mean Gas Density Field 

The mean gas density field is inferred from the oxygen concentration measurements as 

defined by Equation 31. Uncertainty estimates for the mean oxygen concentration 

measurements are derived from data in Table 4 and Table 5. The relative uncertainty of

the mean computed from Table 4 is 0.007 and represents the relative standard uncertainty 

for the mean vertical profile for the center of the doorway, . The entire 

oxygen concentration field was approximated by the centerline profile 

( ); a valid assumption as demonstrated by the relatively low 

standard deviation of the measurements in Table 5. The relative uncertainty of the mean 

was computed from this sample, 0.005, to estimate the relative standard uncertainty of 

this assumption. Both relative standard uncertainties were added in quadrature and the

relative combined uncertainty of the oxygen concentration field was estimated to be 

0.009. Applying the general equation for uncertainty propagation, the relative combined 

uncertainty of the density field is estimated to be 0.009. A coverage factor of 2.0 is

applied, resulting in an expanded relative uncertainty of ±0.018. 

( , 0) 2 X O y z =

( , ) ( , 0) 2 2 X O y z ≈ X O y z =

34
5.3.4 Doorway Mass Flow Rate 

The mass flow rate of fluid into and out of the enclosure was computed using a numerical 

integration technique, the Trapezoid Rule (See Appendix). The technique is essentially 

the product of the length of the integration interval and the mean value of the integrand 

over the integration interval. A double integration estimated by the Trapezoid Rule is

therefore the product of the area defined by the integration intervals and the mean value 

of the integrand over the defined area. For the purpose of estimating the uncertainty, the 

numerical integrals to compute mass flow rate were approximated by the following 

relations. 

in avg in x avg inWhN m v ,exp , , & ≈ ρ ( 26 ) 

( ) out,exp avg,out x avg,out N m& ≈ ρ v W H − h ( 27 ) 

The mean gas density and gas velocity were computed from the spatial field of 

measurements. The relative standard uncertainty of the gas density field was defined in 

Section 5.3.3. The standard uncertainty of the mean velocity of the region was computed 

by normalizing the standard uncertainty defined in Table 6 by the square root of the 

number of measurement locations within the region. Nominal values of the parameters 

for Equations 26 and 27 are listed in Table 7 along with estimates of their relative

standard uncertainty. The general equation for propagation of uncertainty was applied to 

estimate the relative standard uncertainty of doorway mass flow rate. A coverage factor 

of 2 is applied to compute the relative expanded uncertainty. 

Table 7 Doorway mass flow rate relative standard uncertainty estimates. 

Parameter 

Nominal 

Value 

inflow

 u(xi)/xi

inflow

Nominal

Value 

outflow

u(xi)/xi

outflow

ρ avg , kg/m3 1.165 0.009 0.991 0.009

x avg

v , m/s 0.187 0.002

(N=693) 

-0.342 0.004

(N=330)

W, m

 h

0.54 0.002 0.54 0.002 

N, m 0.69 0.029 -

(H – hN), m - - 0.31 0.065

exp exp uc (m& ) m& 0.030 0.066 

6 Results of Reduced-Scale Experiments 

6.1 Vector Processing 

6.1.1 Instantaneous Measurements 

The steps involved in running the experiment were described in Section 4.2. Generating 

vector maps from the CCD image maps involved another set of steps that made use of the

35
software provided by the PIV manufacturer. Figure 16 is an example of typical images of 

the seed particles recorded during an experiment. Both cameras recorded two images 

separated by a specified t. Approximately 60 acquisitions of such image pairs were 

recorded at each measurement location. The cameras viewed the same field but from

different sides of the laser sheet. In the images below, the inflow (solid arrow) is more 

heavily seeded with particles since they are introduced outside of the enclosure. The 

particle laden air flowing into the enclosure mixed with the helium plume to provide 

seeding for the outflow. Note that even though the outflow seeding density was less than 

the inflow, it was still sufficient to produce good quality velocity vectors. The lower

seeding density was due some dilution of incoming particle stream by the unseeded 

helium plume but it is mostly due to particles falling out of the flow before being 

entrained into the upper layer. Regions where the laser sheet passed through the walls 

and caused strong reflections appeared as bright saturated pixels within the images.

Computation of 

∆

true velocity vectors from these regions was not possible. Use of 

advanced computation techniques could, however, produce substituted velocity vectors. 

Camera A image Camera B image 

 Laser sheet hitting top of doorway

I i 1008 1016 (0 0) 8 bit (f 1)

Reflections of laser sheet

I i 1008 1016 (0 0) 8 bit (f 1)

Figure 16 Particle images from cameras A and B. Solid arrow represents inflow 

dotted arrow represents outflow. 

The PIV system was capable of displaying in real time the displacement vectors as the 

images were acquired. Figure 17 is an example of what the experimenter saw during a 

measurement. The displacement vectors were computed using the standard cross

correlation of the image maps with a 50 % overlap of the interrogation regions. The 

vector field was 64 x 64 vectors due to the 50 % overlap; however only 32 x 32 vectors 

are shown in the figures below for the sake of clarity. Blue vectors met the validation

criteria while the red vectors did not and were therefore rejected. Rejected vectors

occurred in areas of the image map where the seeding density was too low or the pixels 

36
were saturated. The vector maps in Figure 17 were produced with a basic level of post 

processing in order to provide the experimenter some immediate feedback on the quality 

of the measurements. 

Camera A Camera B 

Figure 17 Displacement vectors computed from Figure 16 images A and B using the 

standard cross correlation technique. 

An advanced method of post processing called adaptive cross correlation was performed 

on the image maps in order to achieve a higher quality of data. The adaptive cross 

correlation method began with an interrogation region three times the size of the final 

interrogation region. This helped to reduce the number of rejected vectors due to low 

seeding density and particles leaving the interrogation region due to long laser pulse 

separations. Multiple iterations of the cross correlation were applied and the average

displacement vector computed. On the next iteration of cross correlations, the 

interrogation region was shifted by an amount determined from the displacement results 

of the previous cross correlation. Therefore, the shift in interrogation regions was not

constant but adaptive to the magnitude and direction of displacements measured on a 

previous pass. This process of multiple passes and shifting the interrogation regions was 

repeated for a specified number of iterations, and in addition, the size of the interrogation 

regions was reduced and the steps were performed again. This continued until the final 

specified interrogation region was achieved. Figure 18 is an example of the displacement

vectors computed with the adaptive cross correlation technique. Like with the standard

cross correlation technique the blue vectors represent valid vectors. The green vectors 

represent vectors that have been computed by interpolation of the information from the

valid vectors surrounding them. 

37
Camera A Camera B 

Figure 18 Displacement vectors computed from Figure 16 images A and B using the 

adaptive cross correlation technique. 

The displacement maps, d, in Figure 18, which will from now on be referred to as 

adaptive correlations, were further processed by applying the stereoscopic calibration

function to map the displacements recorded in two dimensions to represent displacement 

vectors in the three dimensional object space. The result of applying the stereoscopic 

calibration is shown in Figure 19. The displacements were simply divided by the time 

between the laser pulses to compute the velocity components. This t is stored in the 

header information with each set of images. The vectors in Figure 19 represent the v

∆

∆

x and

vy velocity components while the color map represents the velocity component normal to 

the plane, vz. 

Validation and substitution information was retained with each vector. Adaptive 

correlations, Figure 18, did not contain rejected vectors, only substituted vectors. The 

vector results in Figure 19 retain the status of the vectors from the adaptive correlations

as either valid or valid and substituted. Retaining this status flag is important for 

computing vector statistics. 

38
Figure 19 Velocity vector field computed from displacements. Vectors represent vx

and vy components, color map represents vz component. 

All of the vector processing tasks previously described were standard functions of the 

Dantec Dynamics PIV software. Computation time for standard cross correlations and 

stereoscopic transformations were on the order of one second or less. The time to 

compute a single adaptive correlation was about 6-10 seconds for the recipe applied in 

this study. Therefore for a single experiment which included a set of 60 measurements, 

requiring 120 adaptive correlations, the computation time could range from 12 minutes to 

20 minutes. 

6.1.2 Mean Vector Maps 

At least 60 instantaneous vector maps were recorded at each measurement location. The 

stack of 60 vector maps represents a time ensemble of measurements for a single steady

state experiment. The mean vector map is therefore a time average computed at each (x, 

y) coordinate. However, at each time t and each coordinate position (x, y) a valid vector 

was not necessarily computed. For example, at the z = 0 cm location and for coordinate 

position (3.7 mm, 617.5 mm) only 18 valid vectors were computed from the 60

measurements. Therefore the average vector is for a set of 18 vectors and not 60. In this

case the statistics were computed for valid vectors only. Statistics were also computed 

for valid and substituted vectors, which meant that a set of 60 vectors were available 

because the substituted vectors were being included. The statistics were computed with 

the PIV software which also included other statistical values such as standard deviation, 

and co-variance of the velocity components. 

39
Valid vectors Valid and substituted vectors

Figure 20 Example of mean vector maps for two cases of vector statistics. 

Examples of mean vector maps are displayed in Figure 20. The example of the vector 

statistics computed with only valid vectors is on the left. There were regions without

valid vectors and these regions are displayed with dots overlaying the color map (note 

that the color map is displayed for the vz component in this region but this is an artifact of 

the graphics program). These regions correspond to saturated pixel areas in the image 

maps, usually due to reflections from the laser sheet on the enclosure walls. Therefore it

is recommended to avoid reflections in the camera field of view which will cause a 

constant degradation to the available information. 

The vector map on the right in Figure 20 is an example of the vector statistics computed

for both valid and substituted vectors. Vectors were interpolated from surrounding valid 

vectors and substituted into the regions with saturated pixels in each instantaneous vector 

map. The result is a smooth and continuous mean vector field. The field of mean valid 

only vectors is spotty or lacks data in some very important regions. In order to make

quantitative computations such as mass flow rate the data would need to be interpolated 

through these regions. The valid and substituted vector field is essentially a two 

dimensional interpolation therefore the mean vector field computed from valid and

substituted vectors is used for both the qualitative display of information and quantitative 

computations. 

6.1.3 Vector Map Vertical Overlap 

The camera orientation for this set of experiments resulted in a vector field covering 0.71 

m x 0.62 m (l x h). The dimensions of the enclosure doorway opening were 0.54 m x 1.0 

m (w x h). Due to space restrictions and the need for optimum scattering signals, the 

laser sheet passed through the doorway propagating perpendicular to the doorway plane 

while the cameras were oriented to record the forward scattering from the seed particles. 

Therefore the resulting vector field is a planar slice of the flow inside and outside the 

enclosure. The height of the vector field is 0.61 m and therefore the enclosure had to be 

40
translated in the vertical direction to map the entire vertical vector field. This was 

performed in three stages. As indicated in Figure 21, experiments were conducted in 

overlapping lower, middle, and upper regions of the doorway. While in a region, all z

location (normal to vector field plane) measurements were conducted. The enclosure was 

translated vertically and the experiments at the z locations repeated. The vector maps in 

Figure 21 are mean vector maps at a z = 0 cm. The vector maps statistics were computed 

for valid and substituted vectors. 

-400 -200 0 200

0

200

400

600

800

1000

x, mm

y

,

m

m

lower region

-400 -200 0 200

x, mm

middle region

-400 -200 0 200

x, mm

upper region

-400 -200 0 200

x, mm

combined

Figure 21 Overlapping vertical measurement regions. 

There was intentional overlap in the vertical measurement regions in order to account for 

camera perspective and to provide some repeatability information. A composite mean 

vector map was created by layering the three mean vector maps and computing a second 

mean within the overlapping regions. The mean was weighted with respect to the 

number of valid vectors included in the statistics of the time averaged mean (set of 60

measurements). For example if two mean values, 10 and 20, were computed from sets of 

50 and 10 measurements, respectively, the mean of 10 and 20 will be weighted more

towards 10 because of the larger number of measurements. The vector map on the far 

right of Figure 21 is the resulting composite mean vector map for the entire vertical

distance of the doorway. For clarity, every other vector is displayed. The doorway plane 

is located at x = -14 mm and the vertical distance of the doorway ranges from y = 40 mm 

to 1040 mm. 

41
Vertical slice measurements were taken at 5 cm intervals across the doorway plane, with 

z = 0 cm representing the center of the doorway. The result was 11 composite vector 

maps similar to the one in Figure 21. The 11 vertical z-slice locations are shown as 

dotted lines in Figure 22. The extent of the vector field measurement is shown as the 

dotted box in Figure 22. The resulting measurement field is a volume of 0.67 m x 1.0 m 

x 0.5 m (l x h x w). 

y

z x

1.0 m

-0.25 m 0.0 0.25 m -0.42 m 0.01 0.25 m

Figure 22 Doorway (solid line), measurement slice planes (dotted line). 

6.2 Flow Visualizations 

6.2.1 Velocity Scalar Field

Imaging measurements taken at sequential locations generate a volumetric field of 

information. By mapping an entire measurement volume, the uncertainty associated with 

assuming that a specific measurement profile applies across a region is reduced. In

addition, volume mapping offers visualization and qualitative information of the flow

field that is difficult to achieve with limited point measurements. Thirty three

measurement slices were conducted in this study and a sample of the resulting volumetric 

visualization information is shown in Figure 23. The figure offers a visual representation 

of the velocity magnitude within the vicinity of the doorway. That vicinity includes the 

doorway plane and a finite amount of space on both sides of the plane. The upper and 

lower layer flows are clearly distinguishable; the upper layer flow having a negative sign 

convention for flow exiting the enclosure. It is apparent that the lower layer flow moves 

at a much slower velocity compared to the fastest upper layer flow which moves as fast 

as 1.5 m/s. 

42
Figure 23 Velocity magnitude volume map. 

A vertical profile of velocity measurements through the center of the doorway has often 

been used to graphically convey the concept of a fire induced doorway flow. In a 

likewise manner, Figure 24 displays a planar field of the velocity measurements through 

the center of the doorway. The image displays flow in the ambient, just outside of the 

doorway (located at x = -14 mm), and the flow immediately inside the enclosure. 

Velocity magnitude is a positive quantity, however a sign convention is necessary to 

properly display the counter current flows. The direction of the flow is determined by the 

vx component of the velocity vector. Therefore the vx velocity field was normalized by its 

absolute value and the product of this ratio and the velocity magnitude field results in a 

velocity magnitude field with directional information, Equation 28. This sign 

convention is with respect to the bulk flow only, vx, which is into and out of the 

enclosure. 

( ) x

x

abs v

v V = V ± ( 28 ) 

43
-400 -300 -200 -100 0 100 200

100

200

300

400

500

600

700

800

900

1000

x, mm

y

,

m

m

|V|, m/s

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

Figure 24 Vertical slice of velocity magnitude and streamlines at z = 0 mm. 

Doorway plane located at x = -14 mm. 

Figure 24 is a quantitative representation of what has been conveyed in words and 

sketches in the past. The ambient air outside the enclosure is sucked (left to right) into

the enclosure. The flow induced in the ambient is slow and gradual along the flow 

direction and the vertical change in flow speed is very gradual. The helium-air mixture 

(low density) flow out of the enclosure (right to left) is faster and far less gradual. 

Distinct flow gradients are evidenced by the acceleration of the flow out of the enclosure 

and by the deceleration of the flow at the layer interface. This image also shows the 

complete shape and location of the layer interface in the vicinity of the doorway. The

location of the neutral plane, defined by zero velocity, is accurately determined from data 

fields such as this and will be discussed later. 

It should be noted that the fast and accelerating flow at the top left of the image is mostly 

due to the buoyancy of the low density helium-air mixture. However, an exhaust hood 

was placed above the enclosure and over the exit to exhaust the large amounts of helium 

being released in order to prevent asphyxiation. Therefore some fraction of the upward 

velocity outside the room may be due to the exhaust system. 

44
-250 -200 -150 -100 -50 0 50 100 150 200 250

100

200

300

400

500

600

700

800

900

1000

z, mm

y

,

m

m

|V|, m/s

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

Figure 25 Velocity magnitude vertical slice across the doorway plane, x = -14 mm. 

A cross section of the velocity data at the doorway plane is presented in Figure 25 from 

the point of view of the observer standing outside the enclosure looking into it. Recall 

that measurements were conducted at every 5 cm in the z direction. The measurement

spacing in the y direction was 1.1 cm. The color contour plot shown interpolates the

color map between measurement locations. Therefore the velocity information in the z

direction is largely estimates (except for the 11 z locations) and should be viewed as such, 

especially in regions of high gradients. 

The neutral plane height slightly increases from left to right across the doorway. The 

increase is less than 2 cm. A possible reason for the increase is that the flow into the 

enclosure was not symmetric due to flow currents within the laboratory. Another 

possible reason could have been unbalanced suction from the exhaust hood above. The 

neutral plane occurs at an average height of 730 mm across the doorway. This was

computed by determining the two locations along a vertical line where the vx velocity is

very low and changes sign; one location will be for positive vx and the other will be for 

negative vx. This resulted in 22 y locations, two for each z position. The geometric mean 

of these values was then computed. The image shows that flow into the enclosure occurs

over 72 % of the doorway area while flow out of the enclosure occurs over the remainder. 

45
There is a relatively uniform velocity distribution in the lower layer of the doorway 

(inward flow), with greater uniformity in the z direction. The upper layer velocity 

(outward flow) is not uniform in the y direction but for the portion just above the layer 

interface it appears to be quite uniform in the z direction. 

-250 -200 -150 -100 -50 0 50 100 150 200 250

-400

-300

-200

-100

0

100

200

z, mm

x

,

m

m

|V|, m/s

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Figure 26 Horizontal slice of velocity magnitude at y = 730 mm. 

A bird’s eye view of the velocity magnitude field is displayed in Figure 26. The image is

a horizontal slice at the mean height of the neutral plane, y = 730 mm. The doorway 

plane was located at x = -14 mm, therefore flow both inside and outside the enclosure is 

displayed. Identical to Figure 25, the color map is interpolated between measurement 

locations. Measurement spacing in the x direction is 1.8 cm and 5 cm in the z direction. 

Recall that positive velocity is flow into the enclosure while negative velocity is flow 

exiting the enclosure. Similar to Figure 25, this view shows the increase in flow 

gradients in the vicinity of the layer interface. 

6.2.2 Velocity Vector Field 

It is often easier to display visual information of a scalar quantity, therefore the velocity

magnitude was displayed in the previous figures, Figure 23 through Figure 26. However, 

a wealth of information within the scalar quantity remains to be explored. It is possible 

46
to display the information for each velocity component as demonstrated in Figure 27. 

Each velocity component is displayed for a vertical slice through the doorway. The color 

map represents the vz velocity component which is normal to the plane of the page and 

the vectors represent the vx and vy velocity components. The doorway plane is located at 

x = -14 mm, so this image is an example of the full velocity vector field for a region 

inside and outside the enclosure. 

-400 -300 -200 -100 0 100 200

0

100

200

300

400

500

600

700

800

900

1000

x, mm

y

,

m

m

w, m/s

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.5 m/s

Figure 27 Vertical velocity slice through doorway centerline, z = 0 mm. Color map

represents vz velocity component, vectors represent vx and vy velocity components. 

The doorway plane is located at x = -14 mm. 

47
-250 -200 -150 -100 -50 0 50 100 150 200 250 

100

200

300

400

500

600

700

800

900

1000

z, mm

y

,

m

m

v

x

, m/s

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.15 m/s

Figure 28 Vertical velocity slice across doorway plane, x = -14 mm. Color map 

represents vx velocity component, vectors represent vy and vz velocity components. 

The neutral plane lies within the green contour which ranges from (-0.05 to 0.05) 

m/s. 

Figure 28 is a vertical slice of the velocity vector field across the doorway plane. The 

color map represents the vx velocity component which is now normal to the plane of the 

page. The vectors represent the vy and vz velocity components parallel to the plane of the 

page. Figure 25 and Figure 28 have very similar color maps, therefore indicating that 

displaying the scalar quantity was effective in conveying much of the qualitative 

information for this specific slice view. Figure 28 demonstrates that, at the doorway 

plane, there can be portions of the flow field where the vx velocity component does not 

dominate or where it is on the same order as the vz velocity component. This observation 

is generally accepted but has not been adequately quantified for fire induced doorway 

flows due to the difficulty of conducting multi-component velocity measurements over 

large regions of interest. The availability of stereoscopic PIV measurements now 

increases the capability to better understand the structure and dynamics of such flows. 

48
6.3 Gas Density 

In order to compute the mass flow rate through the doorway the gas density field in the 

doorway plane was also determined, as required by Equations 1 and 2. Since the fluid 

flow was non-reacting, the three gas species (oxygen, nitrogen, and helium) were 

conserved, and the ratio of oxygen volume fraction to nitrogen volume fraction is 

constant in ambient air, it was necessary to measure the volume fraction of only one gas 

constituent to infer the gas density field. Oxygen volume fraction, , was measured at 

a variety of elevations at the center of the doorway plane, z = 0 mm. The experiment was

allowed to run long enough to establish steady state conditions, therefore average oxygen 

volume fraction was computed from the time history results. 

O2 X

Selected time history plots of oxygen volume fraction are shown in Figure 29. Gas 

sampling was continuous and the helium flow was turned on 60 seconds after data 

acquisition began. The helium flow was maintained for 180 seconds and then shut off. 

Data acquisition was continued until the oxygen volume fraction returned to the ambient 

value. Figure 29 demonstrates the growth of the layer of helium mixed with air. At the 

lower elevations it takes longer for the helium-air mixture to descend. 

0.16

0.17

0.18

0.19

0.20

0.21

0.22

0 100 200 300 400 500

O

x

y

g

e

n

V

o

l

u

m

e

F

r

a

c

t

i

o

n

Time, s

y = 690 mm

y = 730 mm

y = 800 mm

y = 950 mm

Figure 29 Time history plot of oxygen volume fraction measured at selected

elevations at the centerline of the doorway plane. 

49
Average oxygen volume fraction is determined by integrating the time history results

over the period of assumed steady state conditions. This period is defined by the full 

width at half the deflection height of the curve and the average oxygen volume fraction is 

given by the following relation. 

2 1

,

2

1

2

2

( )

t t

X t dt

X

t

t

O

O avg − =

∫

( 29 ) 

The mean volume fractions of nitrogen and helium are defined in terms of the mean 

oxygen volume fraction using the following relations, X N2 ,avg 773X O2 ,avg = 3. and 

. The gas mixture is assumed to be an ideal gas mixture with 

invariant temperature throughout and the variation in pressure negligible with respect to 

its effect on gas density. Therefore the molecular weight, MW

X He,avg 773X O2 ,avg = 1− 4.

mix, is the only variable in 

the equation of state and is given in terms of the mean oxygen volume fraction. 

MWmix = X O avg MWO + MWN − MWHe + MWHe ( 3.773 4.773 ) 2 2 2 , ( 30 ) 

Following the assumptions that the gas mixture behaves as an ideal gas and temperature 

and pressure are invariant, the gas density is defined with respect to the gas density of air

at standard temperature and pressure (300 K and 101.325 kPa). 

air

mix

mix air STP MW

MW

ρ = ρ , ( 31 ) 

The vertical profile of gas density is shown in Figure 30. Measurements were conducted 

in the full vertical extent of the outflow region and for a portion of the inflow region 

where . Measurements therefore extended from 550 mm to 950 mm in 

the y direction. Multiple measurements were conducted at a few locations and an 

interpolation of the mean values was computed as shown Figure 30. Below 550 mm, the 

gas flowing into the enclosure is purely air. The gas density field is approximated from

the interpolated vertical profile, 

X O2 ,avg ≤ X O2 ,amb

( y,z) ( y,0) ρ ≈ ρ mix . This approximation is valid since 

measurements of gas density in the outflow region and along a line at constant elevation 

varied by 1 % or less. 

50
0.950 1.00 1.05 1.10 1.15 1.

0

200

400

600

800

1000

20

experiment

interpolated

Gas Density, kg/m3

y

m,

m

neutral plane

Figure 30 Vertical profile of gas density measured at z = 0 mm. 

Note that the mean neutral plane height is 730 mm and there is a measurable oxygen 

deficit for the gas flowing into the enclosure between 550 mm and 730 mm. The neutral

plane location varies throughout the experiment and therefore it is expected that there 

will be a mean oxygen deficit below the neutral plane. However other causes of the 

oxygen deficit must be given consideration such as the flow mixing that occurs at the 

interface. Simultaneous measurements of concentration and velocity with comparable 

time response would offer more information to interpret these mean results. 

6.4 Mass Flow Rate 

Typical measurements of fire-induced flow in a doorway are bi-directional probe 

measurements. The assumption is made that the measurement is dominated by the vx

velocity component, the component normal to the doorway plane. This component of 

velocity is used to compute the net mass flow rate of gas through the doorway. A goal of 

this work is to determine how much of a discrepancy exists between mass flow rate 

computations based on velocity magnitude (flow speed) and computations based on the vx

component of the velocity vector. Figure 31 is a vertical slice of the ratio of the square of 

the vx velocity component and the square of the velocity magnitude at the doorway plane, 

51
vx

2

 / |V|2. The three levels of red represent ratios of 0.7, 0.8, and 0.9 with 0.9 being the 

darkest shade of red. The figure demonstrates that for most of the flow region the 

contribution to the velocity magnitude by vx is 70 % or better. However, a 90 % 

contribution by vx occurs in less than 1/3 of the flow region. This study estimates the 

discrepancy between mass flow rate computations based on the directly measured vx

velocity component and the velocity magnitude. 

-250 -200 -150 -100 -50 0 50 100 150 200 250 

100

200

300

400

500

600

700

800

900

1000

z, mm

y

,

m

m

v

x

2 / |V|

2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 31 Vertical slice at doorway plane, x = -14 mm, of vx

2

 normalized by |V|

2

. 

A vertical slice of the mean velocity field in the entire doorway plane is shown in Figure 

28. Flow normal to the doorway plane, vx, is displayed as a color field. The locations

where the flow changes direction lie within the green contour. The neutral plane is 

relatively uniform across the doorway, with an average height of 730 mm. Along with 

the physical boundaries of the doorway, the neutral plane location defines the limits of 

integration for computing gas mass flow rate into the enclosure. 

Ideal mass flow rate entering and exiting the enclosure was described by Equations 1 and 

2. The gas density field is approximated from a single vertical profile of gas density 

measured at the center of the doorway, ( y,z) ( y,0) ρ ≈ ρ mix , as described in Section 6.3. 

Since the full density field cannot be measured at present, the experimental mass flow 

rates entering and exiting the enclosure are described by the following relations, where W

52
is the width of the doorway, hN is the height of the neutral plane, and H is the height of 

the doorway. 

Experimental mass flow rate in: 

∫ ∫

−

=

2

2

,exp ( ) ( , )

W

W

h

y

in x

N

o

m& ρ y v y z dydz ( 32 ) 

 

Experimental mass flow rate out: 

∫ ∫

−

=

2

2

,exp ( ) ( , )

W

W

H

h

out x

N

m& ρ y v y z dydz ( 33 ) 

A numerical integration using the trapezoid rule was applied to estimate the integrals

described in Equations 1 and 2. The integration was performed in two parts. First the

mass flux along a vertical line, ∫ y v y z dy x i ρ( ) ( , ) , was computed at each of the eleven

measurement locations across the doorway, zi. Zero velocity was prescribed at each

horizontal solid boundary. At the neutral plane, the velocity in either direction was

approximately zero. The vertical spacing of the numerical integration, dy, was 10.7 mm.

Therefore the measured velocity value on the respective side of the interface was used in

the integration and hN at each z location, not the average hN, was used to define the 

vertical integration limits. The horizontal spacing for the integration, dz, was prescribed 

as 10 mm in order to include the boundaries in the numerical integration. This required 

the array of line mass fluxes previously computed to be interpolated for a 10 mm spacing. 

Again, zero velocity was prescribed at the vertical boundaries and the numerical

integration was performed horizontally across the doorway on the line mass fluxes to 

compute the mass flow rate. An example computation of mass flow rate into the 

enclosure is presented in the Appendix. 

For a steady-state system the flow of mass into the system equals the flow of mass out of 

the system. Considering the enclosure as a complete system and assuming that the 

experiments were allowed to reach steady state, the following relation applies. 

123 & 14 24 4 34 & &

& & in mout

out

m

min,exp + mHe = m ,exp ( 34 ) 

The average mass flow rate of helium injected into the plume, , was measured to be

0.0030 kg/s for all of the experiments. The mass flow rates entering and exiting the 

doorway were computed by numerical integration as described above, and they are listed 

under the columns labeled “Doorway” in the table below along with their expanded 

uncertainty.

mHe &

53
Table 8 Experimental mass flow rates. 

Mass Flow Rate In, kg/s Mass Flow Rate Out, kg/s

Helium Injection Doorway Doorway

0.0030 ± 0.0001 0.079 ± 0.005 0.061 ± 0.008

Relative Discrepancy: = 0.256 −

in

in out

m

m m

&

& &

There is a relative discrepancy of 26 % between the in and out mass flow rates. In an 

attempt to understand the source of this discrepancy, a comparison was made between the 

mass flow rates of helium out of the doorway and helium injected into the enclosure. 

Using the gas sampling data to determine XHe(y) (See Section 6.3), the helium mass flow 

rate out of the enclosure was computed by performing a numerical integration for the

following relation. 

∫ ∫

−

2

2

( ) ( , )

W

W

H

h

He He x

N

ρ X y v y z dydz ( 35 ) 

Employing a constant helium density in Equation 35, ρ He = 0.1625 kg/m3

 (300 K and

101.325 kPa), the mass flow rate of helium out of the enclosure was computed to be 

0.0019 kg/s. This was 37 % less than the amount of helium being injected into the 

enclosure. Since the measured helium flow out of the enclosure was less than what was 

measured to flow into the enclosure, and the total out-flow was less than the total in-flow, 

it seems logical that the out-flow measurement may be flawed. A plausible explanation 

is the zero biasing of the velocity results due to laser sheet reflections causing large 

regions of invalid vectors. Vectors were interpolated through these regions in order to 

estimate the data necessary to compute the mass flow rate and to produce a smooth vector 

field for display purposes. Another plausible explanation is the influence of the exhaust 

hood when vertically translating the enclosure in order to measure the entire flow field.

A check to build confidence in this hypothesis has not been performed, but the likelihood 

has not been dismissed. It is recommended that the entire doorway flow be measured in a 

single experiment. If this cannot be accomplished it is recommended to translate the 

optics. The latter option will require a more sophisticated setup and possibly more setup

time, but the reward should be better repeatability of the experiments. Since the lower

layer velocity measurements did not require the same degree of interpolation as the upper 

layer measurements, greater confidence is placed in the lower layer velocity

measurements and they will be used in the remaining discussion. 

6.4.1 Example Comparison 

Stereoscopic PIV measures the complete velocity vector and therefore allows for a

comparison of flow speed, |V|, and the desired velocity component, vx. This comparison 

54
has significance because the response of a bi-directional probe may be more 

characteristic of the flow speed instead of the on-axis velocity component. The angular 

sensitivity of bi-directional probes is 10 % or less in the range of 0 to 40 deg for off-axis 

flow. [7] This suggests that the probe response is not very selective with respect to flow 

direction and therefore exhibits an averaged response to the flow which is characteristic 

of the flow speed. The assumption that accompanies any bi-directional probe 

measurement is that the major contribution of the probe response comes from the on-axis

velocity component. Figure 28 and Figure 31 are good illustrations of how velocity 

magnitude may have significant contribution from velocity components other than the vx

component. In areas of the flow such as near the solid boundaries, near the neutral plane

and the outflow, other velocity components, especially vz, are competitive contributors to 

the flow speed measurement. 

Bi-directional probe measurements were not conducted in this set of experiments. 

However, since the flow speed information was available from the Stereoscopic PIV 

results, an example comparison of the methods of determining the velocity fields could 

be conducted. Assuming that a single vertical array of bi-directional probes were 

horizontally scanned across the doorway the resulting velocity field would be |V(y,z)|, 

following the ideal introduced here that a bi-directional probe responds to flow speed. 

An alternate assumption is that a single vertical array of bi-directional probes were placed 

on the horizontal centerline, z = 0, of the doorway and the resulting profile estimates the

entire flow field. This assumes that the velocity variation with respect to z is negligible 

and therefore the resulting velocity field would be, |V(y,z)| ≈ |V(y)|. The latter assumption

is typical of doorway flow measurements and the former is characteristic of a historical 

series of steady state experiments. [5,19] 

The best mass flow rate estimate is computed using the velocity component normal to the 

doorway plane, vx. Mass flow rate estimates computed using the velocity magnitude are

normalized by the best mass flow rate estimate and displayed in Table 9. These estimates

are for the flow into the room. The results show that if mass flow rate were computed 

from velocity magnitude measurements scanning the doorway or on centerline of the

doorway, the computation would over-predict the best estimate. These example results

are consistent with the need for a mass flow coefficient to correct mass flow rates

computed from bi-directional probe measurements. 

Table 9 Comparison of mass flow rate estimates. 

Velocity Field Normalized Mass Flow Rate 

vx(y,z) 1.00 

|V(y,z)| 1.11 

|V(y,z)|=|V(y,0)| 1.25 

These results demonstrate the need to perform a direct comparison of bi-directional probe 

measurements and PIV measurements for fire-induced flows. Such a comparison can add 

to the body of data of flow coefficients for doorway flows and improve the confidence in 

these empirically determined constants. 

55
7 Concluding Remarks 

A reduced-scale analog of a full-scale fire experiment was studied for the purpose of 

studying the potential use of Stereoscopic Particle Image Velocimetry to measure fire 

induced flows through vents. The size of the experiment was such that it was physically 

manageable yet large enough to challenge the performance of an off-the-shelf PIV system 

and therefore serve as a practice scenario prior to conducting experiments in full-scale 

enclosure fires. 

Successful measurements of the complete velocity vector, vx,vy,vz, were achieved and a 

mapping of the velocity field in the region of the doorway was performed to produce a 

volumetric field of the velocity. The vector field data shows that the buoyancy induced 

flow through the doorway can be highly three dimensional. Regions of the flow may 

exist where the velocity component normal to the doorway, vx, may not dominate the 

velocity vector but may be in competition with other components such as the vz

component. This was observed near the solid vertical boundaries of the doorway. 

Therefore conventional fire measurement tools such as bi-directional probes may not be 

reliable when used in these regions of the flow. 

Since the vx component of the velocity vector field was directly measured, it could be 

combined with a vertical profile of gas density measurements that were conducted on 

centerline of the doorway to estimate the mass flow rate through the doorway. The 

experiments were assumed to be at steady state; therefore the mass flow into the 

enclosure should equal the mass flow out of the enclosure. The relative discrepancy 

between the in and out mass flow rates was 26 %. The cause of the discrepancy is not

clear but possible reasons include a zero bias of the outflow velocity measurements due

to laser sheet reflections saturating regions of the particle images or a change in

experiment conditions due to the influence of the exhaust hood during the vertical

translation of the enclosure. Considering the complexity of the experiment and that a

large but limited number of experiments were conducted to achieve a single mass flow 

rate value, the discrepancy between the in and out flow is very reasonable and quantifies

the success of such first ever measurements. 

An example comparison of mass flow rate computed using the vx velocity component 

field and the velocity magnitude field was performed. The velocity magnitude is

representative of a bi-directional probe measurement since the probe measurement lacks

velocity component selectivity. The comparison demonstrates that mass flow rate will be

over predicted if computed using the velocity magnitude data by as much as 25 %. This 

is consistent with mass flow rate orifice coefficients for doorway flows which suggest 

that mass flow rate computed from bi-directional probe measurements will be 30 %

greater than the actual mass flow rate. 

Stereoscopic PIV measurements were successfully demonstrated for a large-scale flow 

field with image regions of 0.71 m x 0.62 m (l x h). Seed particles were selected which 

effectively follow the flow and produce enough scattered light to produce quality images 

56
for vector processing. Achieving quality PIV results for such large-scale flow fields is 

not entirely trivial due to the need to balance the requirements for image resolution,

scattering signal, and flow tracking. Conducting measurements in full-scale fire 

experiments will require image regions of 1 m x 1 m to be imaged. Achieving the 

necessary requirements for quality PIV results is possible with the current and steady 

improvements of technology in digital imaging and solid state lasers. However, 

consistent seeding of such large and quiescent flow fields remains a challenge to be 

overcome. 

PIV provides the velocity field measurement necessary for the doorway mass flow rate 

computation. However, the gas density field is also required. A vertical profile of gas

density on centerline proved to be sufficient for the fluid analog experiment. The

shortcomings of this method when applied in real fires should be quantified, especially in 

the high temperature outflow where the flow will be thermally stratified. 

57
Reference List 

[1] J. Prahl and H. W. Emmons, Fire Induced Flow Through An Opening, Combustion 

and Flame 25 (3), 369-385 (1975). 

[2] J. A. Rockett, Fire Induced Gas-Flow in An Enclosure, Combustion Science and 

Technology 12 (4-6), 165-175 (1976). 

[3] B. J. McCaffrey and J. A. Rockett, Static Pressure Measurements of Enclosure 

Fires, Journal of Research of the National Bureau of Standards 82 (2), 107-117 

(1977). 

[4] K. Steckler, J. G. Quintiere, and W. J. Rinkinen, Flow Induced by Fire in a 

Compartment, Proceedings of the Combustion Institute 19 913-920 (1982). 

[5] I. Nakaya, T. Tanaka, M. Yoshida, and K. Steckler, Doorway Flow Induced by A 

Propane Fire, Fire Safety Journal 10 (3), 185-195 (1986). 

[6] H. W. Emmons, Vent Flows, The SFPE Handbook of Fire Protection Engineering, 

3rd Edition (Section 2, Chap 3), National Fire Protection Association and The 

Society of Fire Protection Engineers, Quincy, MA, P. J. DiNenno, D. Drysdale, C. 

L. Beyler, and W. D. Walton, eds., 32-41 (2002). 

[7] B. J. McCaffrey and G. Heskestad, Robust Bidirectional Low-Velocity Probe for 

Flame and Fire Application, Combustion and Flame 26 (1), 125-127 (1976). 

[8] A. C. M. Braga, A Helium-Air Model for the Simulation of Fire Induced Flows, 

Worcester Polytechnic Institute, Worcester, MA, (1989). 

[9] K. Steckler, J. G. Quintiere, and W. J. Rinkinen, Flow Induced by Fire in a 

Compartment, NBSIR 82-2520 National Bureau of Standards, Gaithersburg, MD, 

(1982). 

[10] K. Kawagoe, Fire Behavior in Rooms, BRI Report 27 Building Research 

Institute, Ibaraki-Ken, Japan, (1958). 

[11] R. J. Adrian, Particle-Imaging Techniques for Experimental Fluid-Mechanics, 

Annual Review of Fluid Mechanics 23 261-304 (1991). 

[12] R. D. Keane and R. J. Adrian, Theory of Cross-Correlation Analysis of Piv Images, 

Applied Scientific Research 49 (3), 191-215 (1992). 

[13] K. Steckler, J. G. Quintiere, and H. R. Baum, Fire Induced Flows Through Room

Openings: Flow Coefficients, NBSIR 83-2801 National Bureau of Standards, 

Gaithersburg, MD, (1984). 

58
[14] J. G. Quintiere, Scaling Applications in Fire Research, Fire Safety Journal 15 (1), 

3-29 (1989). 

[15] K. Steckler, H. R. Baum, and J. G. Quintiere, Salt Water Modeling of Fire Induced 

Flows in Multicompartment Enclosures, Proceedings of the Combustion Institute 21 

143-149 (1986). 

[16] A. Hamins, K. Konishi, P. Borthwick, and T. Kashiwagi, Global Properties of

Gaseous Pool Fires, Proceedings of the Combustion Institute 26 (1), 1429-1436 

(1996). 

[17] Guide to the Expression of Uncertainty in Measurement, International Organization 

for Standardization, Switzerland, (1995). 

[18] C. E. Kuyatt and B. N. Taylor, Guidelines for Evaluating and Expressing the 

Uncertainty of NIST Measurement Results, NIST/TN-1297 NIST, Gaithersburg, 

MD, (1994). 

[19] K. Steckler, J. G. Quintiere, and H. R. Baum, Fire Induced Flows Through Room

Openings: Flow Coefficients, Proceedings of the Combustion Institute 20 1591-

1600 (1984). 

59
Appendix 

.1 Tabulated values of the velocity and density field at the doorway 

plane 

Table 1 Tabulated values of vx velocity component (m/s) and density (kg/m3) at 

doorway plane, x= -14 mm. 

z, mm y, mm -250.0 -200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0 150.0 200.0 250.0 ρ, kg/m3

39.7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.172 

50.4 0.122 0.192 0.143 0.194 0.176 0.205 0.186 0.200 0.201 0.175 0.155 1.172

61.1 0.159 0.214 0.212 0.234 0.209 0.240 0.217 0.222 0.245 0.200 0.171 1.172 

71.8 0.169 0.232 0.229 0.247 0.230 0.255 0.236 0.240 0.266 0.216 0.170 1.172

82.5 0.183 0.239 0.240 0.255 0.243 0.266 0.251 0.249 0.271 0.225 0.166 1.172 

93.2 0.183 0.241 0.254 0.257 0.247 0.273 0.258 0.251 0.268 0.230 0.167 1.172

103.9 0.179 0.239 0.251 0.256 0.245 0.274 0.261 0.250 0.268 0.227 0.171 1.172 

114.6 0.179 0.245 0.233 0.254 0.243 0.275 0.265 0.250 0.265 0.224 0.166 1.172

125.3 0.175 0.251 0.243 0.251 0.246 0.279 0.267 0.250 0.263 0.224 0.163 1.172 

136.0 0.170 0.247 0.266 0.247 0.251 0.279 0.267 0.248 0.254 0.220 0.161 1.172

146.7 0.172 0.242 0.292 0.244 0.249 0.274 0.267 0.243 0.244 0.215 0.154 1.172 

157.4 0.168 0.242 0.305 0.242 0.246 0.272 0.268 0.237 0.241 0.215 0.147 1.172

168.1 0.164 0.235 0.300 0.236 0.249 0.271 0.268 0.237 0.239 0.214 0.143 1.172 

178.8 0.157 0.235 0.286 0.235 0.248 0.269 0.263 0.239 0.245 0.211 0.141 1.172

189.5 0.154 0.234 0.255 0.235 0.246 0.265 0.258 0.240 0.261 0.208 0.144 1.172 

200.2 0.156 0.229 0.217 0.236 0.241 0.262 0.253 0.241 0.270 0.203 0.148 1.172

210.9 0.149 0.228 0.200 0.234 0.239 0.258 0.249 0.240 0.261 0.196 0.143 1.172 

221.6 0.146 0.227 0.190 0.234 0.236 0.253 0.244 0.239 0.242 0.192 0.135 1.172

232.3 0.143 0.221 0.192 0.235 0.236 0.252 0.241 0.239 0.242 0.192 0.126 1.172 

243.0 0.138 0.217 0.181 0.229 0.230 0.253 0.236 0.240 0.237 0.186 0.128 1.172

253.7 0.132 0.239 0.164 0.223 0.228 0.249 0.230 0.238 0.231 0.180 0.127 1.172 

264.4 0.126 0.230 0.152 0.215 0.223 0.248 0.225 0.232 0.233 0.175 0.117 1.172

275.1 0.114 0.207 0.147 0.207 0.220 0.248 0.224 0.218 0.225 0.172 0.116 1.172 

285.8 0.107 0.188 0.123 0.213 0.215 0.239 0.223 0.211 0.213 0.172 0.107 1.172

296.5 0.117 0.182 0.102 0.211 0.213 0.234 0.217 0.215 0.210 0.173 0.094 1.172 

307.2 0.120 0.172 0.121 0.211 0.203 0.230 0.210 0.208 0.209 0.173 0.088 1.172

317.9 0.144 0.202 0.189 0.213 0.220 0.256 0.214 0.222 0.205 0.174 0.100 1.172 

328.6 0.133 0.200 0.195 0.215 0.216 0.248 0.206 0.212 0.205 0.172 0.093 1.172

339.3 0.133 0.203 0.208 0.227 0.214 0.245 0.204 0.212 0.211 0.170 0.100 1.172 

350.0 0.133 0.199 0.213 0.227 0.200 0.239 0.207 0.203 0.204 0.163 0.110 1.172

360.7 0.135 0.196 0.210 0.228 0.200 0.231 0.210 0.198 0.201 0.161 0.121 1.172 

371.4 0.130 0.190 0.203 0.225 0.205 0.228 0.207 0.211 0.204 0.161 0.122 1.172

382.1 0.117 0.192 0.199 0.221 0.210 0.227 0.206 0.210 0.207 0.159 0.128 1.172 

392.8 0.119 0.194 0.202 0.225 0.210 0.217 0.206 0.215 0.210 0.162 0.129 1.172

403.5 0.117 0.198 0.208 0.226 0.208 0.211 0.207 0.216 0.210 0.161 0.125 1.172 

414.2 0.111 0.196 0.213 0.226 0.209 0.210 0.208 0.213 0.210 0.159 0.126 1.172

424.9 0.114 0.191 0.210 0.221 0.207 0.214 0.211 0.211 0.210 0.157 0.125 1.172 

435.6 0.117 0.188 0.207 0.220 0.205 0.216 0.210 0.212 0.211 0.155 0.126 1.172

446.3 0.118 0.187 0.205 0.219 0.201 0.214 0.209 0.211 0.214 0.152 0.132 1.172 

457.0 0.107 0.190 0.204 0.215 0.200 0.212 0.206 0.211 0.211 0.152 0.134 1.172

467.7 0.095 0.197 0.206 0.216 0.198 0.212 0.204 0.210 0.205 0.152 0.132 1.172 

478.4 0.101 0.196 0.207 0.222 0.194 0.210 0.203 0.210 0.199 0.150 0.128 1.172

489.1 0.108 0.196 0.204 0.218 0.194 0.207 0.201 0.206 0.195 0.149 0.127 1.172 

499.8 0.101 0.193 0.201 0.210 0.192 0.204 0.200 0.199 0.192 0.149 0.128 1.172

510.5 0.096 0.198 0.208 0.213 0.199 0.212 0.206 0.205 0.197 0.156 0.138 1.172 

521.2 0.081 0.166 0.176 0.183 0.172 0.183 0.174 0.171 0.169 0.132 0.117 1.172

531.9 0.091 0.199 0.212 0.234 0.217 0.220 0.205 0.223 0.212 0.149 0.126 1.171 

542.6 0.086 0.197 0.210 0.225 0.212 0.219 0.204 0.213 0.207 0.149 0.112 1.171

553.3 0.085 0.205 0.211 0.218 0.204 0.219 0.204 0.200 0.202 0.149 0.105 1.171 

564.0 0.086 0.210 0.209 0.213 0.201 0.217 0.197 0.189 0.199 0.147 0.106 1.171

574.7 0.082 0.197 0.200 0.204 0.198 0.214 0.190 0.181 0.199 0.145 0.103 1.171 

585.4 0.071 0.173 0.193 0.200 0.194 0.213 0.187 0.177 0.199 0.143 0.105 1.171

596.1 0.061 0.168 0.189 0.201 0.192 0.213 0.185 0.172 0.195 0.140 0.115 1.170 

606.8 0.080 0.167 0.169 0.181 0.175 0.200 0.160 0.148 0.161 0.139 0.095 1.170

617.5 0.101 0.197 0.194 0.205 0.200 0.229 0.188 0.171 0.182 0.163 0.107 1.169 

628.2 0.095 0.187 0.184 0.195 0.191 0.215 0.188 0.166 0.176 0.159 0.099 1.168

638.9 0.095 0.176 0.177 0.191 0.190 0.211 0.186 0.174 0.177 0.156 0.088 1.160 

649.6 0.098 0.147 0.164 0.182 0.188 0.208 0.176 0.171 0.174 0.156 0.085 1.145

660.3 0.098 0.119 0.147 0.170 0.183 0.203 0.169 0.156 0.169 0.156 0.087 1.135 

671.0 0.092 0.097 0.127 0.150 0.172 0.186 0.165 0.134 0.163 0.149 0.082 1.125

681.7 0.089 0.073 0.102 0.127 0.156 0.162 0.152 0.108 0.155 0.138 0.075 1.119 

692.4 0.083 0.047 0.077 0.102 0.136 0.137 0.131 0.068 0.144 0.129 0.069 1.110

703.1 0.076 0.019 0.043 0.070 0.101 0.097 0.106 0.026 0.132 0.119 0.065 1.080 

713.8 0.063 -0.027 -0.001 0.030 0.052 0.043 0.078 -0.017 0.115 0.106 0.058 1.059

724.5 0.039 -0.076 -0.052 -0.024 0.002 -0.013 0.034 -0.066 0.087 0.080 0.044 1.047 

735.2 0.019 -0.123 -0.107 -0.076 -0.055 -0.075 -0.011 -0.123 0.051 0.049 0.032 1.034

745.9 0.006 -0.171 -0.160 -0.127 -0.127 -0.137 -0.064 -0.181 0.005 0.017 0.023 1.019 

756.6 -0.016 -0.217 -0.205 -0.187 -0.201 -0.199 -0.126 -0.235 -0.045 -0.024 0.008 1.013

767.3 -0.045 -0.265 -0.247 -0.253 -0.271 -0.261 -0.186 -0.282 -0.104 -0.074 -0.011 1.009 

778.0 -0.057 -0.325 -0.295 -0.305 -0.330 -0.319 -0.252 -0.324 -0.164 -0.130 -0.034 1.006

788.7 -0.050 -0.373 -0.338 -0.341 -0.376 -0.374 -0.312 -0.365 -0.219 -0.195 -0.074 1.004 

799.4 -0.041 -0.392 -0.384 -0.374 -0.408 -0.419 -0.361 -0.396 -0.269 -0.256 -0.116 1.001

810.1 -0.034 -0.395 -0.420 -0.411 -0.437 -0.455 -0.409 -0.423 -0.314 -0.316 -0.147 0.998 

820.8 -0.009 -0.367 -0.434 -0.437 -0.454 -0.483 -0.438 -0.442 -0.349 -0.366 -0.158 0.994

831.5 0.019 -0.351 -0.470 -0.475 -0.495 -0.524 -0.490 -0.457 -0.395 -0.427 -0.183 0.991 

842.2 0.015 -0.282 -0.417 -0.421 -0.434 -0.456 -0.425 -0.399 -0.344 -0.388 -0.132 0.988

852.9 -0.024 -0.279 -0.575 -0.577 -0.565 -0.515 -0.522 -0.470 -0.445 -0.521 -0.018 0.987 

863.6 -0.049 -0.251 -0.590 -0.595 -0.587 -0.420 -0.547 -0.487 -0.470 -0.554 -0.023 0.986

874.3 -0.036 -0.239 -0.582 -0.610 -0.603 -0.369 -0.558 -0.517 -0.486 -0.569 -0.031 0.985 

885.0 0.018 -0.213 -0.595 -0.630 -0.623 -0.383 -0.572 -0.544 -0.504 -0.587 -0.032 0.984

895.7 0.034 -0.218 -0.613 -0.656 -0.646 -0.435 -0.598 -0.544 -0.526 -0.605 -0.029 0.984 

906.4 0.022 -0.265 -0.609 -0.675 -0.667 -0.469 -0.623 -0.524 -0.560 -0.616 -0.023 0.983

917.1 0.017 -0.297 -0.613 -0.694 -0.691 -0.469 -0.639 -0.518 -0.598 -0.639 -0.031 0.981 

927.8 -0.001 -0.326 -0.610 -0.704 -0.712 -0.384 -0.663 -0.563 -0.614 -0.670 -0.050 0.979

938.5 -0.044 -0.375 -0.622 -0.692 -0.716 -0.348 -0.681 -0.631 -0.641 -0.700 -0.078 0.977 

949.2 -0.094 -0.460 -0.643 -0.690 -0.713 -0.552 -0.692 -0.645 -0.707 -0.739 -0.099 0.977

959.9 -0.113 -0.534 -0.645 -0.688 -0.713 -0.739 -0.682 -0.622 -0.781 -0.788 -0.103 0.977 

970.6 -0.089 -0.469 -0.610 -0.647 -0.689 -0.727 -0.579 -0.614 -0.812 -0.843 -0.106 0.977

981.3 -0.079 -0.384 -0.545 -0.578 -0.632 -0.603 -0.392 -0.557 -0.783 -0.882 -0.124 0.977 

992.0 -0.113 -0.447 -0.506 -0.549 -0.592 -0.412 -0.229 -0.486 -0.713 -0.917 -0.154 0.977

60
1002.7 -0.148 -0.498 -0.526 -0.522 -0.559 -0.306 -0.126 -0.471 -0.653 -0.950 -0.167 0.977 

1013.4 -0.130 -0.482 -0.558 -0.469 -0.427 -0.283 -0.082 -0.477 -0.534 -0.906 -0.147 0.977

1024.1 -0.069 -0.308 -0.424 -0.287 -0.207 -0.173 -0.063 -0.394 -0.306 -0.596 -0.093 0.977 

1034.8 -0.028 -0.100 -0.151 -0.015 -0.092 -0.063 -0.040 -0.191 -0.134 -0.198 -0.047 0.977

1045.5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.977 

Table 2 Tabulated values of vy velocity component (m/s) at doorway plane, x = -14 

mm. 

z, mm y, mm -250.0 -200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0 150.0 200.0 250.0

39.7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

50.4 0.022 0.036 0.025 0.032 0.015 0.026 0.047 0.044 0.017 0.002 0.007

61.1 0.026 0.053 0.045 0.053 0.023 0.037 0.055 0.056 0.010 0.001 0.005 

71.8 0.024 0.053 0.036 0.041 0.009 0.026 0.049 0.043 -0.011 -0.001 0.001

82.5 0.016 0.048 0.027 0.028 0.002 0.018 0.034 0.031 -0.019 -0.006 0.002 

93.2 0.014 0.037 0.016 0.020 0.000 0.010 0.021 0.020 -0.023 -0.007 0.004

103.9 0.017 0.036 0.011 0.017 0.001 -0.001 0.010 0.012 -0.027 -0.007 0.010 

114.6 0.015 0.027 0.016 0.010 -0.003 -0.011 -0.002 -0.001 -0.026 -0.006 0.014

125.3 0.013 0.018 0.023 0.004 -0.008 -0.015 -0.014 -0.011 -0.022 -0.003 0.021 

136.0 0.009 0.012 0.008 -0.001 -0.011 -0.021 -0.023 -0.017 -0.025 0.000 0.020

146.7 0.006 0.007 -0.028 -0.003 -0.016 -0.025 -0.029 -0.023 -0.029 0.001 0.020 

157.4 0.006 0.005 -0.016 -0.004 -0.017 -0.028 -0.034 -0.024 -0.027 0.001 0.023

168.1 0.007 0.004 -0.010 -0.006 -0.019 -0.035 -0.038 -0.024 -0.028 0.001 0.021 

178.8 0.008 0.002 0.010 -0.009 -0.022 -0.041 -0.044 -0.026 -0.025 -0.002 0.020

189.5 0.009 0.002 -0.006 -0.013 -0.022 -0.044 -0.055 -0.026 -0.015 -0.005 0.023 

200.2 0.008 0.005 -0.031 -0.014 -0.026 -0.047 -0.060 -0.026 -0.013 -0.005 0.022

210.9 0.005 0.008 -0.035 -0.018 -0.026 -0.050 -0.063 -0.027 -0.022 -0.004 0.027 

221.6 0.001 0.004 -0.029 -0.018 -0.024 -0.052 -0.063 -0.026 -0.030 -0.003 0.036

232.3 0.002 0.001 -0.024 -0.019 -0.024 -0.053 -0.064 -0.025 -0.033 -0.009 0.038 

243.0 0.007 -0.002 -0.010 -0.021 -0.022 -0.051 -0.065 -0.024 -0.033 -0.012 0.039

253.7 0.011 -0.004 -0.012 -0.025 -0.024 -0.052 -0.062 -0.025 -0.032 -0.013 0.042 

264.4 0.005 -0.004 -0.014 -0.027 -0.026 -0.055 -0.060 -0.023 -0.032 -0.007 0.042

275.1 0.000 0.000 -0.013 -0.025 -0.025 -0.050 -0.060 -0.026 -0.028 0.001 0.045 

285.8 -0.004 -0.002 -0.010 -0.024 -0.023 -0.048 -0.062 -0.029 -0.024 0.004 0.043

296.5 -0.005 -0.003 -0.016 -0.025 -0.024 -0.045 -0.063 -0.032 -0.026 0.004 0.043 

307.2 -0.012 -0.002 -0.028 -0.023 -0.025 -0.042 -0.062 -0.034 -0.027 0.006 0.041

317.9 -0.017 -0.040 -0.056 -0.036 -0.047 -0.062 -0.067 -0.070 -0.053 -0.001 0.028 

328.6 -0.019 -0.040 -0.059 -0.040 -0.050 -0.063 -0.062 -0.068 -0.050 -0.001 0.031

339.3 -0.016 -0.043 -0.066 -0.043 -0.052 -0.063 -0.062 -0.068 -0.047 0.003 0.032 

350.0 -0.019 -0.039 -0.071 -0.043 -0.054 -0.064 -0.065 -0.071 -0.046 0.005 0.026

360.7 -0.023 -0.039 -0.070 -0.044 -0.058 -0.064 -0.069 -0.072 -0.045 0.006 0.023 

371.4 -0.025 -0.039 -0.063 -0.042 -0.060 -0.059 -0.068 -0.070 -0.044 0.004 0.028

382.1 -0.024 -0.038 -0.061 -0.041 -0.060 -0.055 -0.064 -0.069 -0.045 0.001 0.027 

392.8 -0.022 -0.035 -0.064 -0.045 -0.060 -0.056 -0.062 -0.067 -0.047 0.000 0.026

403.5 -0.021 -0.030 -0.067 -0.047 -0.061 -0.057 -0.063 -0.068 -0.046 -0.002 0.027 

414.2 -0.024 -0.032 -0.067 -0.046 -0.061 -0.057 -0.062 -0.067 -0.041 -0.002 0.023

424.9 -0.025 -0.032 -0.068 -0.044 -0.061 -0.057 -0.059 -0.066 -0.039 0.000 0.024 

435.6 -0.027 -0.033 -0.069 -0.045 -0.062 -0.056 -0.060 -0.067 -0.038 0.001 0.028

446.3 -0.026 -0.036 -0.065 -0.049 -0.063 -0.055 -0.062 -0.067 -0.038 0.002 0.027 

457.0 -0.026 -0.039 -0.066 -0.053 -0.062 -0.055 -0.061 -0.065 -0.038 0.002 0.025

467.7 -0.026 -0.038 -0.069 -0.055 -0.064 -0.054 -0.058 -0.065 -0.038 0.002 0.025 

478.4 -0.025 -0.040 -0.068 -0.053 -0.067 -0.052 -0.055 -0.064 -0.039 0.004 0.025

489.1 -0.021 -0.041 -0.069 -0.052 -0.065 -0.051 -0.054 -0.063 -0.039 0.005 0.024 

499.8 -0.013 -0.042 -0.067 -0.051 -0.062 -0.051 -0.055 -0.061 -0.041 0.004 0.023

510.5 -0.015 -0.042 -0.070 -0.051 -0.065 -0.051 -0.054 -0.061 -0.045 0.001 0.025 

521.2 -0.017 -0.037 -0.062 -0.045 -0.058 -0.042 -0.042 -0.051 -0.039 -0.003 0.020

531.9 -0.022 -0.059 -0.075 -0.058 -0.075 -0.060 -0.047 -0.073 -0.057 -0.013 0.022 

542.6 -0.025 -0.059 -0.081 -0.057 -0.069 -0.063 -0.046 -0.075 -0.058 -0.014 0.019

553.3 -0.029 -0.060 -0.086 -0.059 -0.064 -0.062 -0.046 -0.078 -0.059 -0.017 0.013 

564.0 -0.033 -0.064 -0.091 -0.061 -0.064 -0.058 -0.046 -0.079 -0.059 -0.018 0.012

574.7 -0.037 -0.064 -0.086 -0.062 -0.065 -0.058 -0.047 -0.079 -0.060 -0.020 0.011 

585.4 -0.038 -0.064 -0.079 -0.064 -0.066 -0.062 -0.050 -0.080 -0.059 -0.023 0.009

596.1 -0.034 -0.064 -0.079 -0.066 -0.067 -0.064 -0.050 -0.081 -0.058 -0.027 0.009 

606.8 -0.035 -0.076 -0.072 -0.063 -0.067 -0.077 -0.075 -0.083 -0.078 -0.072 -0.037

617.5 -0.044 -0.090 -0.083 -0.077 -0.079 -0.092 -0.091 -0.100 -0.094 -0.096 -0.055 

628.2 -0.048 -0.084 -0.081 -0.077 -0.077 -0.089 -0.088 -0.094 -0.087 -0.098 -0.050

638.9 -0.054 -0.081 -0.082 -0.078 -0.078 -0.093 -0.085 -0.092 -0.088 -0.102 -0.046 

649.6 -0.060 -0.081 -0.081 -0.079 -0.076 -0.093 -0.081 -0.084 -0.087 -0.101 -0.045

660.3 -0.061 -0.076 -0.076 -0.076 -0.076 -0.091 -0.077 -0.076 -0.087 -0.099 -0.044 

671.0 -0.056 -0.065 -0.067 -0.070 -0.074 -0.087 -0.073 -0.069 -0.086 -0.094 -0.045

681.7 -0.056 -0.049 -0.057 -0.060 -0.068 -0.080 -0.065 -0.059 -0.083 -0.087 -0.048 

692.4 -0.048 -0.031 -0.044 -0.048 -0.061 -0.069 -0.057 -0.043 -0.080 -0.082 -0.046

703.1 -0.031 -0.014 -0.025 -0.036 -0.051 -0.057 -0.049 -0.024 -0.075 -0.075 -0.041 

713.8 -0.010 0.021 -0.006 -0.018 -0.035 -0.040 -0.039 -0.001 -0.065 -0.064 -0.032

724.5 0.014 0.057 0.019 0.004 -0.016 -0.018 -0.022 0.023 -0.048 -0.051 -0.023 

735.2 0.042 0.082 0.046 0.029 0.003 0.005 -0.005 0.045 -0.027 -0.031 -0.015

745.9 0.063 0.106 0.068 0.060 0.030 0.028 0.015 0.067 -0.002 -0.013 -0.002 

756.6 0.079 0.124 0.089 0.092 0.057 0.053 0.036 0.089 0.021 0.009 0.014

767.3 0.096 0.135 0.110 0.122 0.081 0.077 0.057 0.108 0.046 0.040 0.034 

778.0 0.106 0.147 0.130 0.138 0.103 0.101 0.079 0.123 0.073 0.074 0.058

788.7 0.106 0.159 0.148 0.145 0.118 0.121 0.100 0.135 0.098 0.109 0.084 

799.4 0.106 0.173 0.160 0.154 0.128 0.136 0.119 0.145 0.119 0.136 0.108

810.1 0.112 0.186 0.173 0.162 0.133 0.143 0.134 0.156 0.138 0.162 0.130 

820.8 0.113 0.192 0.178 0.162 0.132 0.145 0.140 0.158 0.152 0.182 0.144

831.5 0.119 0.189 0.178 0.163 0.132 0.149 0.149 0.154 0.169 0.209 0.163 

842.2 0.109 0.149 0.144 0.123 0.103 0.114 0.120 0.130 0.150 0.175 0.127

852.9 0.143 0.160 0.150 0.110 0.102 0.099 0.115 0.151 0.195 0.181 0.094 

863.6 0.131 0.136 0.151 0.109 0.089 0.091 0.114 0.149 0.196 0.183 0.097

874.3 0.101 0.118 0.150 0.105 0.082 0.077 0.111 0.152 0.190 0.170 0.102 

885.0 0.066 0.098 0.167 0.096 0.081 0.057 0.111 0.156 0.182 0.149 0.107

895.7 0.040 0.063 0.187 0.090 0.075 0.043 0.113 0.154 0.178 0.122 0.116 

906.4 0.015 0.019 0.199 0.087 0.070 0.032 0.102 0.139 0.170 0.091 0.116

917.1 0.020 -0.018 0.209 0.081 0.068 0.018 0.088 0.122 0.151 0.062 0.118 

927.8 0.041 -0.038 0.203 0.084 0.070 0.011 0.088 0.137 0.136 0.043 0.115

938.5 0.019 -0.069 0.204 0.089 0.064 0.007 0.090 0.168 0.123 0.025 0.098 

949.2 -0.001 -0.077 0.193 0.081 0.051 -0.004 0.077 0.166 0.090 -0.004 0.093

959.9 -0.001 -0.058 0.166 0.060 0.040 -0.013 0.044 0.135 0.053 -0.029 0.092 

970.6 -0.004 -0.022 0.146 0.030 0.036 -0.024 -0.003 0.114 0.016 -0.046 0.083

981.3 -0.011 -0.008 0.106 0.010 0.040 -0.035 -0.028 0.069 -0.008 -0.067 0.086 

992.0 -0.029 -0.053 0.079 -0.002 0.046 -0.034 -0.021 0.014 -0.033 -0.098 0.103

1002.7 -0.038 -0.085 0.056 -0.030 0.040 -0.050 -0.014 -0.019 -0.073 -0.125 0.119 

1013.4 -0.026 -0.081 0.017 -0.069 0.034 -0.056 -0.002 -0.042 -0.088 -0.121 0.119

1024.1 0.001 -0.040 -0.003 -0.053 0.019 -0.019 0.012 -0.031 -0.045 -0.055 0.114 

1034.8 0.006 0.002 -0.004 -0.001 0.002 0.007 0.025 -0.006 0.007 0.007 0.102

1045.5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

61
Table 3 Tabulated values of vz velocity component (m/s) at doorway plane, x = -14 

mm. 

z, mm y, mm -250.0 -200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0 150.0 200.0 250.0

39.7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

50.4 -0.051 -0.007 -0.084 -0.045 -0.115 -0.119 -0.142 -0.109 -0.127 -0.151 -0.143

61.1 -0.013 0.002 -0.049 -0.024 -0.106 -0.112 -0.141 -0.098 -0.122 -0.145 -0.160 

71.8 -0.001 0.003 -0.042 -0.014 -0.092 -0.100 -0.133 -0.087 -0.107 -0.143 -0.162

82.5 0.013 0.016 -0.036 -0.009 -0.080 -0.089 -0.115 -0.079 -0.105 -0.138 -0.162 

93.2 0.023 0.021 -0.023 -0.005 -0.075 -0.083 -0.093 -0.070 -0.100 -0.133 -0.166

103.9 0.024 0.024 -0.013 -0.003 -0.065 -0.078 -0.080 -0.065 -0.096 -0.134 -0.172 

114.6 0.025 0.023 -0.016 -0.004 -0.066 -0.071 -0.079 -0.069 -0.101 -0.141 -0.172

125.3 0.023 0.024 -0.023 -0.002 -0.064 -0.065 -0.081 -0.067 -0.103 -0.139 -0.175 

136.0 0.022 0.024 -0.011 0.003 -0.060 -0.060 -0.080 -0.068 -0.100 -0.137 -0.177

146.7 0.023 0.030 -0.021 0.003 -0.054 -0.058 -0.080 -0.071 -0.099 -0.141 -0.173 

157.4 0.029 0.037 -0.031 0.003 -0.049 -0.056 -0.075 -0.071 -0.104 -0.142 -0.169

168.1 0.037 0.047 0.021 0.008 -0.045 -0.050 -0.075 -0.072 -0.112 -0.141 -0.171 

178.8 0.038 0.054 0.011 0.010 -0.040 -0.047 -0.073 -0.073 -0.118 -0.142 -0.175

189.5 0.038 0.053 0.008 0.011 -0.041 -0.044 -0.075 -0.075 -0.102 -0.145 -0.179 

200.2 0.035 0.060 0.001 0.009 -0.044 -0.038 -0.076 -0.074 -0.092 -0.148 -0.182

210.9 0.034 0.063 0.016 0.014 -0.044 -0.032 -0.075 -0.077 -0.105 -0.149 -0.179 

221.6 0.036 0.058 0.024 0.020 -0.040 -0.034 -0.072 -0.076 -0.116 -0.150 -0.178

232.3 0.038 0.061 0.023 0.022 -0.037 -0.033 -0.066 -0.077 -0.114 -0.148 -0.174 

243.0 0.034 0.071 0.030 0.029 -0.039 -0.031 -0.063 -0.078 -0.111 -0.146 -0.175

253.7 0.034 0.052 0.036 0.033 -0.036 -0.029 -0.063 -0.082 -0.109 -0.150 -0.178 

264.4 0.033 0.053 0.035 0.036 -0.033 -0.026 -0.064 -0.081 -0.109 -0.152 -0.176

275.1 0.038 0.061 0.031 0.040 -0.031 -0.025 -0.065 -0.069 -0.107 -0.152 -0.180 

285.8 0.037 0.073 0.049 0.042 -0.035 -0.026 -0.060 -0.072 -0.101 -0.149 -0.178

296.5 0.037 0.078 0.050 0.043 -0.037 -0.025 -0.054 -0.082 -0.098 -0.147 -0.172 

307.2 0.036 0.083 0.040 0.037 -0.044 -0.026 -0.050 -0.075 -0.093 -0.145 -0.167

317.9 0.081 0.080 0.053 0.031 -0.018 -0.064 -0.071 -0.063 -0.088 -0.131 -0.151 

328.6 0.081 0.074 0.038 0.022 -0.028 -0.066 -0.072 -0.063 -0.094 -0.130 -0.156

339.3 0.081 0.070 0.028 0.019 -0.034 -0.066 -0.068 -0.062 -0.104 -0.130 -0.158 

350.0 0.078 0.069 0.026 0.016 -0.043 -0.066 -0.064 -0.050 -0.104 -0.131 -0.166

360.7 0.075 0.065 0.028 0.010 -0.043 -0.065 -0.062 -0.045 -0.103 -0.132 -0.166 

371.4 0.082 0.072 0.033 0.013 -0.040 -0.067 -0.055 -0.055 -0.102 -0.132 -0.161

382.1 0.090 0.076 0.040 0.014 -0.038 -0.066 -0.048 -0.055 -0.099 -0.129 -0.164 

392.8 0.090 0.075 0.037 0.015 -0.037 -0.066 -0.045 -0.059 -0.096 -0.128 -0.160

403.5 0.093 0.075 0.036 0.019 -0.037 -0.068 -0.043 -0.059 -0.095 -0.128 -0.155 

414.2 0.087 0.076 0.036 0.021 -0.040 -0.064 -0.040 -0.054 -0.091 -0.128 -0.146

424.9 0.085 0.078 0.035 0.026 -0.040 -0.059 -0.038 -0.053 -0.085 -0.129 -0.139 

435.6 0.080 0.082 0.038 0.024 -0.038 -0.058 -0.037 -0.054 -0.084 -0.128 -0.139

446.3 0.077 0.082 0.038 0.027 -0.037 -0.056 -0.034 -0.055 -0.084 -0.127 -0.144 

457.0 0.070 0.076 0.040 0.031 -0.034 -0.055 -0.033 -0.058 -0.084 -0.126 -0.144

467.7 0.066 0.071 0.042 0.026 -0.034 -0.056 -0.032 -0.058 -0.082 -0.123 -0.143 

478.4 0.069 0.073 0.040 0.018 -0.032 -0.057 -0.031 -0.057 -0.079 -0.122 -0.143

489.1 0.073 0.069 0.040 0.021 -0.029 -0.057 -0.030 -0.055 -0.078 -0.121 -0.139 

499.8 0.077 0.067 0.036 0.024 -0.029 -0.058 -0.028 -0.052 -0.075 -0.115 -0.135

510.5 0.078 0.067 0.032 0.027 -0.029 -0.060 -0.029 -0.054 -0.077 -0.115 -0.141 

521.2 0.062 0.057 0.028 0.012 -0.031 -0.054 -0.027 -0.041 -0.060 -0.095 -0.116

531.9 0.073 0.066 0.040 -0.027 -0.082 -0.081 -0.046 -0.033 -0.051 -0.103 -0.117 

542.6 0.070 0.064 0.039 -0.027 -0.084 -0.078 -0.046 -0.026 -0.045 -0.102 -0.106

553.3 0.071 0.054 0.034 -0.025 -0.087 -0.077 -0.046 -0.020 -0.041 -0.100 -0.098 

564.0 0.075 0.044 0.030 -0.020 -0.092 -0.077 -0.047 -0.019 -0.039 -0.098 -0.097

574.7 0.075 0.048 0.031 -0.019 -0.095 -0.079 -0.047 -0.018 -0.036 -0.097 -0.089 

585.4 0.075 0.062 0.031 -0.025 -0.094 -0.083 -0.047 -0.024 -0.034 -0.096 -0.084

596.1 0.075 0.061 0.030 -0.031 -0.089 -0.083 -0.050 -0.028 -0.031 -0.094 -0.087 

606.8 0.041 0.044 -0.007 -0.027 -0.060 -0.034 -0.024 -0.020 -0.038 -0.083 -0.066

617.5 0.036 0.043 -0.019 -0.027 -0.064 -0.032 -0.026 -0.020 -0.047 -0.096 -0.072 

628.2 0.030 0.036 -0.023 -0.024 -0.058 -0.034 -0.032 -0.025 -0.048 -0.092 -0.073

638.9 0.020 0.025 -0.027 -0.026 -0.057 -0.034 -0.037 -0.043 -0.051 -0.089 -0.063 

649.6 0.011 0.019 -0.029 -0.029 -0.058 -0.032 -0.039 -0.051 -0.050 -0.086 -0.055

660.3 0.008 0.018 -0.035 -0.033 -0.057 -0.028 -0.041 -0.053 -0.050 -0.084 -0.056 

671.0 0.003 0.016 -0.037 -0.037 -0.056 -0.025 -0.046 -0.065 -0.053 -0.080 -0.056

681.7 -0.005 0.017 -0.038 -0.037 -0.055 -0.034 -0.057 -0.076 -0.058 -0.078 -0.057 

692.4 -0.003 0.016 -0.043 -0.040 -0.058 -0.050 -0.064 -0.084 -0.061 -0.080 -0.058

703.1 -0.001 0.008 -0.040 -0.048 -0.065 -0.067 -0.069 -0.099 -0.064 -0.083 -0.057 

713.8 -0.001 0.013 -0.028 -0.057 -0.070 -0.084 -0.076 -0.117 -0.075 -0.088 -0.058

724.5 -0.001 0.023 -0.011 -0.056 -0.080 -0.107 -0.086 -0.130 -0.091 -0.097 -0.056 

735.2 -0.002 0.027 0.009 -0.047 -0.090 -0.129 -0.107 -0.139 -0.108 -0.111 -0.056

745.9 0.003 0.037 0.021 -0.038 -0.095 -0.142 -0.123 -0.147 -0.129 -0.121 -0.059 

756.6 0.015 0.044 0.018 -0.031 -0.096 -0.155 -0.132 -0.148 -0.147 -0.132 -0.067

767.3 0.029 0.050 0.011 -0.019 -0.091 -0.157 -0.140 -0.144 -0.163 -0.150 -0.076 

778.0 0.040 0.074 0.012 -0.012 -0.083 -0.145 -0.143 -0.140 -0.174 -0.173 -0.090

788.7 0.046 0.095 0.013 -0.014 -0.071 -0.125 -0.141 -0.132 -0.181 -0.198 -0.109 

799.4 0.050 0.094 0.014 -0.019 -0.061 -0.100 -0.125 -0.115 -0.185 -0.224 -0.124

810.1 0.054 0.090 0.005 -0.025 -0.050 -0.081 -0.100 -0.096 -0.188 -0.239 -0.138 

820.8 0.047 0.073 -0.004 -0.035 -0.046 -0.066 -0.075 -0.088 -0.192 -0.240 -0.149

831.5 0.047 0.056 0.009 -0.036 -0.054 -0.054 -0.065 -0.093 -0.208 -0.261 -0.168 

842.2 0.049 0.049 0.008 -0.041 -0.055 -0.040 -0.049 -0.107 -0.183 -0.233 -0.135

852.9 0.119 0.062 -0.009 -0.120 -0.094 0.004 -0.041 -0.186 -0.244 -0.300 -0.103 

863.6 0.155 0.084 -0.017 -0.120 -0.112 0.101 -0.028 -0.193 -0.263 -0.310 -0.099

874.3 0.158 0.108 -0.031 -0.124 -0.118 0.158 -0.024 -0.184 -0.282 -0.334 -0.098 

885.0 0.130 0.112 0.011 -0.110 -0.131 0.149 -0.031 -0.189 -0.310 -0.358 -0.092

895.7 0.103 0.128 0.074 -0.071 -0.143 0.111 -0.063 -0.218 -0.336 -0.386 -0.080 

906.4 0.093 0.164 0.103 -0.037 -0.137 0.086 -0.100 -0.254 -0.348 -0.407 -0.073

917.1 0.079 0.151 0.136 -0.002 -0.128 0.092 -0.134 -0.279 -0.349 -0.407 -0.080 

927.8 0.072 0.108 0.156 0.042 -0.116 0.178 -0.154 -0.260 -0.348 -0.394 -0.092

938.5 0.065 0.087 0.168 0.085 -0.096 0.226 -0.165 -0.220 -0.328 -0.365 -0.099 

949.2 0.069 0.083 0.189 0.116 -0.075 0.080 -0.172 -0.235 -0.280 -0.317 -0.099

959.9 0.063 0.100 0.206 0.138 -0.056 -0.036 -0.188 -0.285 -0.228 -0.260 -0.099 

970.6 0.045 0.114 0.206 0.120 -0.065 -0.012 -0.242 -0.298 -0.183 -0.224 -0.100

981.3 0.030 0.111 0.133 0.054 -0.112 0.067 -0.229 -0.322 -0.171 -0.200 -0.109 

992.0 0.013 0.058 -0.007 0.012 -0.150 0.183 -0.129 -0.360 -0.203 -0.173 -0.131

1002.7 -0.022 -0.018 -0.058 -0.009 -0.176 0.227 -0.075 -0.366 -0.215 -0.142 -0.136 

1013.4 -0.044 -0.027 -0.070 -0.041 -0.181 0.203 -0.068 -0.366 -0.280 -0.149 -0.113

1024.1 -0.047 0.008 -0.051 -0.020 -0.126 0.077 -0.085 -0.300 -0.296 -0.228 -0.084 

1034.8 -0.032 0.038 -0.009 -0.009 -0.070 -0.041 -0.093 -0.164 -0.149 -0.235 -0.074

1045.5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

62
Table 4 Tabulated values of |V| (m/s) at doorway plane, x = -14 mm. 

z, mm y, mm -250.0 -200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0 150.0 200.0 250.0

39.7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

50.4 0.134 0.196 0.168 0.202 0.211 0.238 0.239 0.232 0.238 0.232 0.211

61.1 0.162 0.220 0.222 0.241 0.236 0.267 0.265 0.249 0.274 0.247 0.235 

71.8 0.171 0.238 0.236 0.251 0.248 0.275 0.275 0.259 0.287 0.259 0.234

82.5 0.184 0.244 0.244 0.257 0.256 0.281 0.278 0.263 0.291 0.264 0.232 

93.2 0.185 0.245 0.255 0.258 0.258 0.285 0.276 0.261 0.287 0.266 0.236

103.9 0.181 0.243 0.251 0.257 0.254 0.284 0.273 0.259 0.286 0.263 0.243 

114.6 0.181 0.248 0.234 0.254 0.251 0.284 0.276 0.259 0.285 0.264 0.239

125.3 0.177 0.253 0.245 0.251 0.254 0.287 0.279 0.259 0.284 0.263 0.239 

136.0 0.172 0.249 0.266 0.247 0.258 0.286 0.279 0.258 0.274 0.260 0.240

146.7 0.173 0.244 0.294 0.244 0.255 0.281 0.280 0.254 0.265 0.257 0.233 

157.4 0.171 0.245 0.307 0.242 0.251 0.279 0.281 0.249 0.264 0.257 0.225

168.1 0.168 0.240 0.301 0.237 0.253 0.278 0.281 0.249 0.265 0.256 0.224 

178.8 0.161 0.242 0.286 0.236 0.252 0.276 0.276 0.251 0.274 0.255 0.225

189.5 0.159 0.240 0.255 0.236 0.250 0.272 0.274 0.253 0.280 0.254 0.231 

200.2 0.160 0.237 0.220 0.237 0.247 0.269 0.271 0.253 0.286 0.251 0.236

210.9 0.153 0.236 0.204 0.236 0.244 0.265 0.268 0.254 0.282 0.246 0.231 

221.6 0.150 0.234 0.194 0.236 0.240 0.261 0.262 0.252 0.270 0.243 0.226

232.3 0.148 0.229 0.195 0.237 0.240 0.260 0.258 0.252 0.269 0.243 0.219 

243.0 0.142 0.228 0.184 0.232 0.235 0.260 0.253 0.253 0.264 0.237 0.220

253.7 0.137 0.244 0.168 0.227 0.232 0.256 0.246 0.253 0.258 0.235 0.223 

264.4 0.130 0.236 0.157 0.220 0.226 0.255 0.241 0.247 0.259 0.232 0.215

275.1 0.121 0.216 0.151 0.213 0.223 0.254 0.240 0.230 0.251 0.229 0.219 

285.8 0.113 0.202 0.132 0.218 0.219 0.246 0.240 0.225 0.237 0.228 0.212

296.5 0.122 0.198 0.115 0.217 0.217 0.239 0.232 0.232 0.234 0.227 0.201 

307.2 0.126 0.191 0.130 0.215 0.209 0.235 0.224 0.224 0.231 0.225 0.194

317.9 0.166 0.221 0.204 0.218 0.226 0.271 0.236 0.241 0.230 0.218 0.183 

328.6 0.156 0.217 0.207 0.220 0.224 0.265 0.227 0.231 0.231 0.216 0.184

339.3 0.157 0.219 0.220 0.231 0.223 0.262 0.224 0.231 0.240 0.214 0.190 

350.0 0.156 0.214 0.226 0.232 0.212 0.256 0.226 0.220 0.234 0.209 0.201

360.7 0.156 0.210 0.223 0.232 0.213 0.249 0.229 0.215 0.230 0.209 0.207 

371.4 0.156 0.207 0.215 0.229 0.217 0.245 0.225 0.229 0.233 0.208 0.204

382.1 0.149 0.210 0.212 0.226 0.222 0.243 0.221 0.228 0.234 0.205 0.210 

392.8 0.151 0.211 0.215 0.230 0.222 0.233 0.220 0.233 0.236 0.206 0.207

403.5 0.151 0.214 0.221 0.232 0.220 0.229 0.221 0.234 0.235 0.206 0.201 

414.2 0.143 0.213 0.226 0.232 0.221 0.227 0.221 0.230 0.232 0.204 0.194

424.9 0.144 0.209 0.223 0.227 0.220 0.230 0.222 0.228 0.230 0.203 0.188 

435.6 0.144 0.208 0.221 0.226 0.218 0.230 0.222 0.228 0.231 0.201 0.189

446.3 0.143 0.207 0.218 0.226 0.214 0.228 0.221 0.228 0.232 0.198 0.197 

457.0 0.131 0.209 0.218 0.224 0.212 0.226 0.217 0.228 0.230 0.197 0.198

467.7 0.119 0.212 0.221 0.225 0.211 0.226 0.215 0.227 0.224 0.195 0.196 

478.4 0.125 0.213 0.222 0.229 0.208 0.223 0.212 0.227 0.218 0.193 0.194

489.1 0.132 0.211 0.219 0.225 0.207 0.221 0.210 0.223 0.214 0.193 0.190 

499.8 0.128 0.208 0.215 0.217 0.204 0.218 0.209 0.215 0.210 0.188 0.187

510.5 0.125 0.213 0.222 0.221 0.212 0.226 0.215 0.221 0.216 0.194 0.199 

521.2 0.103 0.179 0.189 0.189 0.184 0.195 0.181 0.183 0.184 0.162 0.166

531.9 0.118 0.217 0.228 0.243 0.244 0.242 0.215 0.237 0.225 0.182 0.173 

542.6 0.114 0.215 0.229 0.234 0.238 0.241 0.214 0.227 0.220 0.181 0.155

553.3 0.114 0.221 0.231 0.227 0.231 0.240 0.214 0.215 0.214 0.180 0.144 

564.0 0.119 0.224 0.230 0.223 0.230 0.237 0.208 0.205 0.212 0.178 0.144

574.7 0.117 0.213 0.220 0.214 0.229 0.235 0.201 0.198 0.211 0.176 0.137 

585.4 0.110 0.194 0.210 0.212 0.226 0.237 0.199 0.196 0.210 0.173 0.135

596.1 0.103 0.189 0.207 0.214 0.222 0.237 0.198 0.192 0.206 0.171 0.145 

606.8 0.097 0.189 0.184 0.194 0.197 0.217 0.178 0.171 0.183 0.177 0.122

617.5 0.116 0.221 0.212 0.221 0.225 0.248 0.210 0.199 0.210 0.212 0.140 

628.2 0.111 0.208 0.202 0.211 0.214 0.235 0.210 0.192 0.203 0.209 0.133

638.9 0.111 0.195 0.197 0.208 0.213 0.233 0.207 0.202 0.204 0.207 0.117 

649.6 0.116 0.169 0.185 0.200 0.211 0.230 0.198 0.197 0.201 0.204 0.111

660.3 0.116 0.142 0.169 0.189 0.206 0.224 0.190 0.181 0.196 0.203 0.112 

671.0 0.108 0.117 0.148 0.170 0.195 0.207 0.186 0.164 0.192 0.193 0.109

681.7 0.106 0.089 0.123 0.146 0.179 0.184 0.175 0.144 0.185 0.181 0.106 

692.4 0.096 0.059 0.098 0.120 0.160 0.161 0.157 0.117 0.176 0.173 0.101

703.1 0.082 0.025 0.064 0.092 0.131 0.131 0.136 0.105 0.165 0.163 0.096 

713.8 0.063 -0.037 -0.029 0.067 0.094 0.103 0.116 -0.119 0.152 0.152 0.088

724.5 0.042 -0.098 -0.057 -0.061 0.082 -0.109 0.095 -0.147 0.135 0.136 0.075 

735.2 0.046 -0.150 -0.117 -0.094 -0.105 -0.149 -0.107 -0.191 0.122 0.125 0.066

745.9 0.064 -0.205 -0.175 -0.146 -0.162 -0.199 -0.140 -0.243 0.129 0.123 0.064 

756.6 -0.082 -0.253 -0.225 -0.211 -0.229 -0.258 -0.186 -0.292 -0.155 -0.134 0.069

767.3 -0.110 -0.301 -0.271 -0.281 -0.297 -0.314 -0.240 -0.335 -0.199 -0.172 -0.084 

778.0 -0.126 -0.364 -0.323 -0.335 -0.356 -0.364 -0.301 -0.374 -0.249 -0.229 -0.112

788.7 -0.126 -0.416 -0.369 -0.371 -0.401 -0.413 -0.356 -0.411 -0.300 -0.299 -0.156 

799.4 -0.124 -0.438 -0.416 -0.405 -0.432 -0.452 -0.401 -0.437 -0.348 -0.366 -0.201

810.1 -0.129 -0.446 -0.454 -0.443 -0.459 -0.484 -0.442 -0.461 -0.391 -0.429 -0.240 

820.8 -0.123 -0.421 -0.469 -0.467 -0.475 -0.509 -0.466 -0.477 -0.427 -0.474 -0.261

831.5 0.130 -0.403 -0.503 -0.503 -0.515 -0.548 -0.516 -0.491 -0.478 -0.543 -0.297 

842.2 0.120 -0.323 -0.441 -0.440 -0.449 -0.472 -0.445 -0.433 -0.417 -0.485 -0.228

852.9 -0.187 -0.327 -0.595 -0.600 -0.581 -0.525 -0.536 -0.528 -0.543 -0.628 -0.141 

863.6 -0.209 -0.298 -0.610 -0.617 -0.604 -0.442 -0.559 -0.544 -0.573 -0.661 -0.140

874.3 -0.190 -0.288 -0.602 -0.631 -0.620 -0.408 -0.569 -0.569 -0.594 -0.681 -0.145 

885.0 0.147 -0.260 -0.618 -0.646 -0.642 -0.415 -0.583 -0.597 -0.619 -0.704 -0.145

895.7 0.116 -0.260 -0.646 -0.666 -0.666 -0.451 -0.612 -0.606 -0.649 -0.728 -0.144 

906.4 0.096 -0.312 -0.649 -0.681 -0.684 -0.478 -0.639 -0.598 -0.681 -0.744 -0.139

917.1 0.083 -0.333 -0.662 -0.699 -0.706 -0.479 -0.659 -0.601 -0.709 -0.760 -0.146 

927.8 -0.083 -0.345 -0.661 -0.710 -0.724 -0.423 -0.687 -0.635 -0.718 -0.778 -0.156

938.5 -0.081 -0.391 -0.676 -0.703 -0.726 -0.415 -0.707 -0.689 -0.730 -0.790 -0.160 

949.2 -0.116 -0.473 -0.698 -0.705 -0.719 -0.558 -0.717 -0.706 -0.766 -0.804 -0.168

959.9 -0.129 -0.546 -0.697 -0.704 -0.716 -0.740 -0.709 -0.698 -0.815 -0.831 -0.169 

970.6 -0.100 -0.483 -0.660 -0.659 -0.693 -0.728 -0.627 -0.692 -0.833 -0.873 -0.168

981.3 -0.085 -0.400 -0.571 -0.581 -0.644 -0.608 -0.454 -0.647 -0.801 -0.907 -0.186 

992.0 -0.117 -0.453 -0.512 -0.549 -0.612 -0.452 -0.264 -0.605 -0.742 -0.938 -0.227

1002.7 -0.154 -0.506 -0.532 -0.523 -0.587 -0.385 -0.148 -0.597 -0.691 -0.968 -0.246 

1013.4 -0.140 -0.490 -0.562 -0.475 -0.465 -0.353 -0.107 -0.603 -0.609 -0.926 -0.220

1024.1 -0.083 -0.311 -0.428 -0.292 -0.243 -0.191 -0.106 -0.496 -0.429 -0.640 -0.169 

1034.8 -0.043 -0.107 -0.152 -0.018 -0.115 -0.075 -0.104 -0.252 -0.201 -0.308 -0.135

1045.5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

63
.2 Numerical Integration 

A numerical integration of the mass flow rate at the doorway was computed using the 

Trapezoid Rule. 

) 2

1 .... 21 ( ) ( 0 1 2 n 1 n

b

a

f x dx = c f + f + f + + f + f ∫ − , where n

b a

c ( − ) =

Mass flow rate was computed for the inflow and outflow separately and in each case the 

computation was performed with two steps worth describing. First a numerical 

integration was performed along a vertical line to compute a line mass flux at each z 

measurement location. For the inflow, the lower limit of the vertical integration, a, was 

39.7 mm. This is the location of the door sill and here velocity was forced to zero. The

upper limit of integration, b, was defined by the local neutral plane. The vertical 

measurement spacing was 10.7 mm, which was less than the spatial resolution of the 

measurement (21.4 mm) due to the 50 % overlap in the cross correlation of vectors. 

Therefore assigning the location of the final positive vx velocity as the neutral plane 

location is sufficient. The velocity values are approximately zero, therefore interpolating 

to find the exact zero location would be of negligible benefit. For example, at z = 0.0 

mm, the last positive value is 0.043 m/s and occurs at 713.8 mm. This location is

selected as the upper limit of integration, b, instead of some location between 713.8 mm 

and 724.5 mm. This first step of the mass flow rate computation is demonstrated in Table 

5, where the line mass flux of the flow into the enclosure (shaded regions) is computed. 

Table 5 Step 1 of the numerical integration to compute mass flow rate into the 

enclosure (shaded regions): Mass flux along a vertical line. 

z, mm y, mm -250.0 -200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0 150.0 200.0 250.0

ρ, 

kg/m3

vx, m/s

39.7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.172 

50.4 0.122 0.192 0.143 0.194 0.176 0.205 0.186 0.200 0.201 0.175 0.155 1.172 

61.1 0.159 0.214 0.212 0.234 0.209 0.240 0.217 0.222 0.245 0.200 0.171 1.172 

71.8 0.169 0.232 0.229 0.247 0.230 0.255 0.236 0.240 0.266 0.216 0.170 1.172 

82.5 0.183 0.239 0.240 0.255 0.243 0.266 0.251 0.249 0.271 0.225 0.166 1.172 

93.2 0.183 0.241 0.254 0.257 0.247 0.273 0.258 0.251 0.268 0.230 0.167 1.172 

103.9 0.179 0.239 0.251 0.256 0.245 0.274 0.261 0.250 0.268 0.227 0.171 1.172 

.. .. .. .. .. .. .. .. .. .. .. .. .. 

.. .. .. .. .. .. .. .. .. .. .. .. .. 

.. .. .. .. .. .. .. .. .. .. .. .. .. 

692.4 0.083 0.047 0.077 0.102 0.136 0.137 0.131 0.068 0.144 0.129 0.069 1.110 

703.1 0.076 0.019 0.043 0.070 0.101 0.097 0.106 0.026 0.132 0.119 0.065 1.080 

713.8 0.063 -0.027 -0.001 0.030 0.052 0.043 0.078 -0.017 0.115 0.106 0.058 1.059 

724.5 0.039 -0.076 -0.052 -0.024 0.002 -0.013 0.034 -0.066 0.087 0.080 0.044 1.047 

735.2 0.019 -0.123 -0.107 -0.076 -0.055 -0.075 -0.011 -0.123 0.051 0.049 0.032 1.034 

745.9 0.006 -0.171 -0.160 -0.127 -0.127 -0.137 -0.064 -0.181 0.005 0.017 0.023 1.019 

756.6 -0.016 -0.217 -0.205 -0.187 -0.201 -0.199 -0.126 -0.235 -0.045 -0.024 0.008 1.013 

767.3 -0.045 -0.265 -0.247 -0.253 -0.271 -0.261 -0.186 -0.282 -0.104 -0.074 -0.011 1.009

778.0 -0.057 -0.325 -0.295 -0.305 -0.330 -0.319 -0.252 -0.324 -0.164 -0.130 -0.034 1.006

∫

hN

y

vxdy

0

ρ 0.096 0.151 0.152 0.166 0.163 0.178 0.166 0.159 0.168 0.136 0.097

64
The second step of the mass flow rate computation was a numerical integration across the 

width of the doorway, therefore integrating the line mass fluxes. The numerical 

integration routine required a constant spacing (dx), therefore in order to include the solid

boundaries which occurred at -270 mm and 270 mm the line mass fluxes computed at 50 

mm intervals were used to interpolate values at 10 mm intervals. The numerical 

integration across the width of the doorway to complete the mass flow rate computation

is demonstrated in Table 6. 

Table 6 Step 2 of the numerical integration to compute mass flow rate into the 

enclosure: Integration across the width of the doorway of the interpolated line mass 

fluxes. 

 z, mm -270.0 -260.0 -250.0 .. .. 250.0 260.0 270.0

Interpolated

h

y

x

N

v dy

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

∫

0

ρ 0.000 0.048 0.096 .. .. 0.097 0.049 0.000

∫ ∫

−

=

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ =

2

2

,exp 0.079 /

0

W

W Interpolated

h

y

in x m v dy dz kg s

N

& ρ

The same process is followed to compute mass flow rate out of the enclosure. In this 

case the lower limit of integration, a, is variable and is defined by the location of the first 

negative velocity value. The upper limit, b, is the door soffit, located at 1045.5 mm. 

Velocity at this boundary is forced to zero. 

65