989

velocity in the direction of the ambient wind is literally the wind speed. Once this
approximation is made, the plume can be viewed as two-dimensional in the crosswind
direction with the downwind direction represented by time. The large scale structure of
the plume can then be computed in detail and the small scale “sub-grid” mixing and
dissipation is represented with a constant eddy viscosity. This permits the mathematical
structure of the Navier-Stokes equations to be retained. The effective Reynolds number,
defined by the buoyancy induced velocity, plume height and eddy viscosity, is chosen to
be above 10°. It is in this sense that ALOFT is a large eddy simulation.

Mathematical Model

The mathematical model assumes that the plume is described in terms of steady-state
convective transport by a uniform ambient wind of heated gases and particulate matter
introduced into the atmosphere by a continuously burning fire. A detailed description
of the equations used in the ALOFT model have been presented previously (Walton, er
al., 1993). The model does not predict features of the fire itself, but rather the plume of
smoke which emanates from it. Only the convective heat release rate and smoke
particulate release rate of the fire need be specified. The simulation begins several fire
diameters downwind of the fire, where the flow field is characterized by relatively small
temperature changes, minimal radiation effects, and a velocity field dominated by the
prevailing wind. The plume gases ascend to a point in the atmosphere of neutral
buoyancy, and then gradually disperse. The trajectory of the plume is governed by the
ambient wind, the atmospheric stratification and the level of turbulent motion. The wind
is taken as uniform, but the temperature may vary with height according to a prescribed
profile.

Given these assumptions, the mathematical model of a smoke plume consists of the
conservation equations of mass, momentum and energy which govern the absolute
temperature, pressure, density, and crosswind velocity components in a plane normal to
the direction of the uniform ambient wind. It is convenient to divide the temperature and
pressure fields into mean background values plus perturbations induced by the fire.
Similarly, the density is decomposed into an ambient density and a small thermally
induced perturbation, which is related to the temperature perturbation through the
equation of state taken in the small disturbance, low Mach number form appropriate to
this problem. The ambient density is-related to the background pressure through the
hydrostatic balance.

The uniform ambient wind speed is assumed to be constant and larger than the crosswind
velocity components. This assumption is quite realistic several flame lengths downwind
of the fire. Since the wind speed does not change, there is no need for a windward
component of the momentum equations. Since the details of the fire are not being
simulated. the only information about the fire required is the overall convective heat
release rate and the particulate mass release rate. The model does not take into account
the heat loss due to thermal radiation. The initial temperature distribution in the plume
cross section 1s assumed to be Gaussian, but the temperature downwind is not assumed
to be Gaussian and is computed from the conservation equations.


994

Table 2. Relationships between Pasquill-Gifford stability category
and the standard deviation of the wind direction

Pasquill-Gifford Standard deviation Standard deviation
stability category of the horizontal of the vertical
wind direction wind direction
i) (°)
A: Extremely unstable 25 16
B: Moderately unstable 20 12
C: Slightly unstable 1S 10
D: Neutral 10 6
E: Slightly stable 5 3
F: Moderately stable 2.5 2

Tables | and 2 have been combined and included in the input routine so the user can
select standard deviations of the wind based on observed conditions if measurements are
not available. The range for standard deviation of lateral wind speed is 10 25° and
for the vertical wind speed is 2 to 17°

Downwind Distance: This is the distance downwind of the fire that the plume is
tracked. in kilometers. Distances should me in the range from 0.5 to 20 km. Although
results are for distances less then | km the predictions may not be valid for areas close
to the fire since the details of the fire are not modeled. Beyond 20 km the assumption
that the wind and temperature conditions do not vary with downwind distance are less
likely to be valid.

Fire Heat Release Rate: This is the convective heat release rate of the fire in MW.
Radiative heat is not considered by the model. For very sooty fires, it is often assumed
that about 10% of the total heat release rate is lost to radiation so the convective heat
telease rate is 90% of the total heat release. The heat release rate per unit burning area
is a function of the fire size since the rate of fuel vaporization is a function of the thermal
radiation from the flames to the fuel. It is also a function of the type of fuel being
bumed. For fires of the size normally considered for in sirw burning, that is larger than
10 m in diameter, the rate of heat release per unit area is nearly constant. The heat
release rate per unit area for a particular fuel can be determined in the laboratory by
enhancing the thermal radiation to the fuel surface with an external source. The heat
release rate should be in the range of S50 MW to 2000 MW.

Since convective heat release rates per unit burning area are not normally available for
crude oils a typical value for crude oil has been provided in the input routine. The user
has the option of entering either the convective heat release rate of having the input



991

like the temperature distribution is uniform within an elliptical area in the crosswind
plane. All particles move at the same downwind speed equal to that of the wind. The
average of the velocity at the start and at the end of a time step is used to update the
particle position. Particles that reach the ground level cells are considered to have been
deposited on the ground and are not carried forward in the calculation.

The viscosity and thermal conductivity terms included do not account for larger scale
atmospheric motions, which may be thought of as variations of the prevailing wind over
a time scale of minutes to hours. These deviations can be measured, and are introduced
into the model through random perturbations to the trajectories of the particles. In a
smoke plume the path of particles originating from a given area on the fuel surface
changes over time with fluctuations in the wind. Thus, the motion of each particle is
governed by the fire-induced velocity field, found by solving the conservation equations,
plus a perturbation velocity field which represents the random temporal and spatial
variations of the ambient wind. The perturbation velocities are determined from the
input standard deviations of the prevailing wind direction in the horizontal and vertical
directions.

The present version of the model decouples the random spatial and temporal motion of
the advected particles and the governing hydrodynamic equations. The reason for this
is that the hydrodynamic equations describe the steady-state plume structure and cannot
readily accommodate temporal fluctuations. As a result use of this model for high wind
fluctuation values (>25°) is not recommended.

ALOFT-PC

ALOFT-PC includes an interactive input/output routine which 1) allows the user to select
the input units. 2) performs error and range checks on the data. 3) provides methods to
estimate input values based on observed conditions, 4) allows convenient input and
output file selection, 5) provides explanations for inputs, and 6) provides a simple
graphical display of the results.

In addition to the outputs displayed by the program, ALOFT generates a number of
output files. These files provide the particulate concentration profiles and information
on the computational grid. These files allow the user to display the output in other
formats or use the output as input to another program. A complete description of the
output files is included with the program.

The ALOFT-PC is written for the Windows95° environment and is presently undergoing
testing and refinement. Typical run times are on the order of LO minutes with a Pentium?

3 Certain trade names and company products are mentioned in the text in order
to adequately specify the procedure used. In not case does such identification imply
recommendation or endorsement by the National Institute of Standards and. Technology,
nor does it imply that the products are necessarily the best available for the purpose.


990

The equations of motion are made non-dimensional with the windward spatial coordinate
replaced by a temporal coordinate where the plume height is given in terms of the
potential temperature of the undisturbed atmosphere. Following this scaling, the
three-dimensional. steady state system of equations can be considered as a
two-dimensional, time-dependent system. This is an initial value problem in which the
initial conditions are prescribed in a plane perpendicular to the direction of the prevailing
wind a few fire diameters downwind of the fire.

Initially, the crosswind velocity components are assumed to be zero. No-flux, free-slip
boundary conditions are prescribed at the ground, consistent with the assumed uniformity
of the prevailing wind and the resolution limits of the calculation. At the outer and upper
edges of the computational domain, the perturbation temperature. perturbation pressure,
and windward component of vorticity are set to zero.

Atmospheric turbulence effects mixing on a wide range of scales, extending to scales
which are smaller than the resolution of the calculations performed here. There are two
mechanisms by which turbulent atmospheric motions are introduced into the simulation.
First, the small scale mixing is represented by a constant eddy viscosity, which is taken
to be three orders of magnitude greater than the viscosity of air. The choice is governed
by the desire for resolution limits in the five to fifteen meter range which are needed to
capture the large scale fire induced eddy motions.

Numerical Method

The uniform wind assumption and the subsequent scaling of the equations transforms the
three dimensional, steady state problem into a two dimensional. time dependent problem.
sometimes referred to as an initial value problem. The equations constitute a mixed
system of partial differential equations: i-e., the equations for the temperature and
velocity components are parabolic and the equation for the pressure (which is derived
from the incompressibility condition) is elliptic. The equations and the associated
boundary conditions are solved using a relatively simple finite difference technique. The
computational domain spanning the crosswind plane is one unit in the vertical direction
and four units in the horizontal direction and is divided into uniformly sized rectangular
cells. The size of the cells is computed by the model so that the plume will fit within the
computational space. The horizontal velocity is assigned on the left and right boundaries
of each cell, the vertical velocity is assigned at the top and bottom, and the perturbation
temperature and pressure are taken at cell centers. This placement of the flow variables
leads to a natural and efficient differencing scheme for the equations. Cenwal differences
are used for all spatial derivatives, and the solution is advanced in time (i.e. follow the
evolution of the plume downwind) with a second order Runge-Kutta scheme. The model
automatically adjusts the time steps to assure stability

Particle Tracking
A fixed number of particles are used to represent the particulate matter carried aloft and

downwind by the plume. The particles are introduced into the flow at the start of the
calculation and convected with the induced flow. The initial distribution of particles,



993

provided as guidance for the user has not been incorporated into the input routine. [tis
recommended that the user obtain specific information for the location of interest.

Wind direction is not an input since the wind direction is assumed to be constant with
altitude and the plume always travels in the direction of the wind. It is not uncommon,
particularly in the marine environment. for the wind direction to change with altitude.
The model cannot at this time accommodate changes in wind direction with altitude and
user should be aware that the predictions can be misleading when that condition exists.

Standard Deviation of lateral and vertical wind speed: These represent
time-averaged deviations of the wind from the prevailing direction in degrees. These are
normally obtained with special anemometers with readings taken over time periods of
the order of the burn time. Typically these values cannot be obtained directly and are
obtained from correlations. Table | gives relationships between Pasquill-Gifford
stability category and the standard deviation of the wind direction (Randerson, 1984).
Table 2 provides the relationship between observed weather conditions and Pasquill-
Gifford stability category (Randerson, 1984, Slade, 1968).

Table |. Pasquill-Gifford stability category for observed weather conditions

Nighttime conditions

Surface Daytime insolation Thin overcast %

wind speed or 2% cloudiness
(m/s) Strong Moderate Slight cloudiness
2 AB B c E F
+ B B-C Cc D E
6 Cc Cc-D D D D
>6 Cc D D D D

” Use D for heavy overcast day or night

The degree of cloudiness is defined as that fraction of the sky above the horizon which
is covered by clouds.


ALOFT-PC A SMOKE PLUME TRAJECTORY MODEL
FOR PERSONAL COMPUTERS

by

William D. Walton, Kevin B. McGrattan
Building and Fire Research Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899
and
Joseph V. Mullin
Technology Assessment and Research Branch
Minerals Management Service
U.S. Department of Interior
Herndon, VA 22070

Reprinted from Arctic and Marine Oilspill Program (AMOP) Technical Seminar, June 12-
14, 1996, Calgary, Alberta, Canada. 19th, Volume 2. Proceedings. Sponsored by the
Environmental Protection Service, Environmental Technology Advancement Directorate,
Environment Canada. 1996,

Notes: This paper is a contrbution of the National Institute of Standards and
Technology and is not subject to copyright.



996

Table 3. Relationships between Pasquill-Gifford stability category
and the temperature lapse rate

Pasquill-Gifford Temperature lapse rate
stability category (?C/km)

A: Extremely unstable 9

B: Moderately unstable 6

C: Slightly unstable 3

D: Neutral 0

E: Slightly stable 0

F: Moderately stable 0

ALOFT-PC STATUS

The Beta test version of ALOFT-PC with draft user guide is presently available for
evaluation and comment. The authors anticipate that the program and user guide will be
published in the fall of 1996.

ACKNOWLEDGMENTS

This work was funded by the Technology Assessment and Research Branch, Minerals
Management Service, U.S. Department of Interior.

The authors wish to acknowledge contributions of Howard R. Baum and Ronald G.
Rehm of the National Institute of Standards and Technology in the development of the
LES model.

REFERENCES

Brode, R.W., “Screening Procedures for Estimating the Air Quality Impact of Stationary
Sources,” U.S. Environmental Protection Agency, EPA-450/4-88-010, 1988, p.3-1

Buist, I.A., Ross, S.L., Trudel, B.K., Taylor, E., Campbell, T.G., Westphal, P.A., Myers.
MLR.. Ronzio, G.S., Allen, A.A, and Nordvick, A.B., “The Science, Technology and
Effects of Controlled Burning of Oils Spills at Sea,” Marine Spill Response Corporation.
Wash. DC, MSRC Tech. Report 94-013, 1994, 382p.

McGrattan, K.B., Baum. H.R. and Rehm. R.G., “Smoke Plume Trajectory from In Situ
Burning of Crude Oil in Alaska,” Proceedings of the Seventeenth Arctic and Manne
Spill Program (AMOP) Technical Seminar, Vancouver, BC. June 8-10. 1994.
pp.725-734


995

routine determine it ftom the rate of heat release per unit area and a specified buming
area.

Fire Smoke Particulate Mass Release Rate: This is the mass rate of particulate being
generated by the fire in units of kg/s. The smoke particulate mass release rate is normally
calculated from measurements of the surface regression rate, smoke yield. and fuel
properties in a large scale fire experiment. The user may select a typical smoke
particulate mass release rate per unit area in the input routine which is multiplied by the
burning area to provide an estimate of the mass release rate. [f the downwind
concentration of particles in a particular size range is desired then in input release rate
should be the fraction of the total mass in the desired size range. Although the input is
identified as smoke particulate, the model can calculate the downwind concentration of
any non-reacting product of combustion.

Fire Area: This is the area of burning fuel in m’. The fire area is not directly used in
model however it may be used in several places by the input routine in conjunction with
user specified alternative input methods. In order to avoid conflicts between parts of the
input routine a fire area is required. The fire area should be in the range of 25 m’ to
1000 m*

Initial Plume Height, Width, and Centerline Elevation: The model prediction begins
with the source of heat and smoke distributed ov an ellipse shaped area in a vertical
orientation, located at a specified elevation above ground level. Normally the starting
size and elevation would correspond to the plume conditions several fire diameters
downwind of the fire. Downwind concentrations however, are not sensitive to smail
changes in these inputs. Since the actual shape of the fire area is often unknown, the
normally the user selects the option for a circle with an area equal to the specified fire
area and a centerline elevation equal to the diameter of the circle. The units for the initial
plume height, width. and centerline elevation are meters.

Temperature Profile: Starting at ground level. the elevation and temperature of the
atmosphere. The units for the elevation are meters and the temperature degrees C, and
the maximum number of points is 200. The user may either enter specific points
defining a temperature profile or a lapse rate for a linear profile. The limitation for a user
specified profile is the slope using any two of the points must be greater than -9 *C km.
The profile should be specified to the elevation to which the plume is expected to mses
which is typically 1 km. If the plume nses to an elevation greater than the highest point
in the specified profile, the profile will be linearly extrapolated using the highest Wo
specified points. If a lapse rate is used the rate must be greater than -9 °C’km. Since a
temperature profile is often difficult to obtain, the input routine contains the estimates
made by the authors shown in table 3 based on the Pasquill-Gifford stability category
determined from table |


992

based computer. The user should refer to material provided with the program for the
latest information.

ALOFT-PC INPUTS

The input parameters for ALOFT-PC are the same as those for the ALOFT version 2
workstation program however the parameters related to grid size are fixed by the input
routine at optimum values and the user is not given the opportunity to change them.
Many of the required inputs are values that would difficult to obtainable by the user.
ALOFT-PC offers the user the choice of either directly entering the parameters used by
the model or utilizing estimates based on more readily available observations and
measurements.

Many of the inputs have units associated with them. ALOFT-PC provides the user with
the choice of a number of common units for the input parameters. The input file and
output files generated are all in SI units regardless of the input units selected by the user.

The following is a description of the inputs required for the model, methods used by
ALOFT-PC to obtain estimates if selected by the user, and the range of acceptable
values. The units associated with the values in the input file are also given.

Title: This is a title to identify the data set to the user. The maximum length is 80
characters.

Wind Speed: The model assumes the wind speed to be constant with height and
downwind distance. The user should estimate the average speed of the wind at the height
to which the plume will eventually rise over the distance to be calculated. The units for
wind speed are m/s. The model predictions should not be used for wind speeds below
2 m/s or above 15 m/s. Usually wind speeds are measured near ground level and the
corresponding wind speed at the height to which the plume will rise is generally greater.
Correlations can be found in the literature which relate the wind speed near the surface
with the wind speed at elevations up to.a few hundred meters (Brode. 1988). These
correlations are usually of the form:

where:

u = the wind speed at elevation h
u, = the measured wind speed at elevation h,
p = function of the stability and terrain

Based on this correlation using a typical value of p. the wind speed 200 meters above the
ground would equal approximately twice the wind speed measured 2 meters above the
ground. Since the wind speed can be a function of many factors, this information is



988

INTRODUCTION

dn situ burning has grown in acceptance as an oil spill mitigation tool as the capabilities
and limitations are better understood (Buist er a/., 1994). Although in situ burning has
been included in a number of regional response plans, limiting the exposure of
downwind populations to smoke particulate remains a concem. The downwind
distribution of smoke particulate is a complex function of the fire parameters,
meteorological conditions. and topographic features. Simple smoke plume models
designed for smoke stack emissions do not adequately capture the observed features of
plumes from large in situ oil spill burns. Under the sponsorship of the Minerals
Management Service, U.S. Department of Interior, the National Institute of Standards
and Technology has developed a computer based model, ALOFT. to prediction the
smoke plume trajectory from in situ oi) spill burns.

ALOFT (A Large Open Fire plume Trajectory model) is a model to prediction the
downwind concenrration of smoke particulate from a large outdoor fire. The model was
previously known as the NIST LES model based on the large eddy simulation technique
used (Walton, ef al., 1993). ALOFT-PC? is a public domain. personal computer
implementation of version 2 of the ALOFT model for level terrain. The development
of the ALOFT-PC program is a continuing process and the future addition of new
features will change the model inputs and outputs. Detailed instructions for using the
model are included with the program.

ALOFT-PC is envisioned as a prototype tool for developing in situ burn plans. [t also
has the potential for use as a training tool and perhaps an operational tool. At the present
time the model has not been officially certified. ALOFT has. however. been used to
examine the expected downwind particulate deposition under meteorological conditions
common to Alaska (McGrattan, er al. 1994).

It is difficult to verify models such as ALOFT. The model has the ability to predict the
downwind concentration of smoke particulate from a fire over a large area. Large oil
spill fire experiments occur infrequently and it is difficult to accurately measure smoke
concentrations as well as the input parameters required for the model. To date there has
only been limited verification testing of model although the comparisons of the model
predictions with measurements from large experiments have been favorable (McGrattan,
eral. 1994).

PLUME TRAJECTORY MODEL

The mathematical model consists of the Navier-Stokes equations simplified for the
problem at hand. This is accomplished in part by assuming the component of the plume

* This software was produced by the National Institute of Standards and
Technology (NIST), an agency of the U.S. government. and by statute is not subject to
copyright in the United States. Recipients of this software assume all responsibility
associated with its operation, modification, maintenance, and subsequent re-distnbution.


987

ALOFT-PC A Smoke Plume Trajectory Model for Personal Computers'

William D. Walton
Kevin B. McGrattan
National Institute of Standards and Technology
U.S. Department of Commerce
Gaithersburg, MD 20899

and

Joseph V. Mullin
Technology Assessment and Research Branch
Minerals Management Service
U.S. Department of Interior
Herndon, VA 22070

ABSTRACT

As the understanding of the capabilities and limitations of in situ burning of oil spills
increases, in situ buming continues to gain acceptance as an oil spill mitigation tool.
One widely imposed criteria for the use of in situ burning is limiting the exposure of
downwind populations to smoke particulate. Since the downwind distribution of smoke
particulate is a complex function of the fire parameters, meteorological conditions, and
topographic features, a computer based model is required to predict the smoke plume
trajectory. Measurements and observations at experimental burns have shown that the
downwind distribution of smoke is not Gaussian and simple smoke plume models do not
capture the observed plume features. To resolve these problems, NIST has developed
a smoke plume trajectory model that solves the fundamental Navier-Stokes equations
using an eddy viscosity over a uniform grid which spans the smoke plume and its
surroundings. This large eddy simulation smoke plume model has been refined over a
period of years using a computer workstation and the results have compared favorably
with the limited data available from experimental bums. ALOFT-PC (A Large Open
Fire plume Trajectory model) is the public domain version of the model for windows
based personal computers. The model inputs include wind speed and variability.
atmospheric temperature profile. and fire parameters and the output is the average
concentration of smoke in each of the computational cells from ground level to the top
of the plume. ALOFT-PC is designed to aid in the in situ bun planning process. For
this purpose a “foot print” of the ground level smoke concentration is the most
commonly used model output.

* Official contribution of the National Institute of Standards and Technology. not
subject to copyright in the United States.




997

McGranan, K.B., Walton, W.D., Putorti, A.D., Twilley, W.H., McElroy, J., and Evans,
D.D., “Smoke Plume Trajectory From In Situ Burning of Crude Oil in Alaska - Field
Experiments.” Proceedings of the Eighteenth Arctic and Marine Spill Program (AMOP)
Technical Seminar, Edmonton, Alberta, June 14-16, 1995, pp.901-913

Randerson. D., ed.. Atmospheric Science and Power Production, U.S. Department of
Energy, DE84005177 (DOE/TIC-27601), 1984, p.591.

Slade, D.H., ed., “Meteorology and Atomic Energy,” U.S. Atomic Energy Commission,
TID 24190, 1968, p.52-53

Walton, W.D., Evans, D.D.. McGrattan, K.B., Baum, H.R, Twilley, W.H.,
Madrzykowski, D., Putorti, A.D., Rehm, R.G.. Koseki, H.. and Tennyson, E.J., "“/n Situ
Burning of Oil Spills: Mesoscale Experiments and Analysis.” Proceedings of the
Sixteenth Arctic and Marine Spill Program (AMOP) Technical Seminar, Calgary,
Alberta, June 7-9, 1993, pp.679-734.