.

Correlation Analysis of VLSTRACK

Model Results With Theoretical

and Experimental Data for Rigid

Sphere Terminal Velocities

by Josip 2. Soln

and Judith T. McCullen

ARL-TR-1938

,.. . . ,.

April 1999

Approved for public release; distribution is unlimited.

DTIC QUALITY INBPECTFJJ 4

L .
4

.

The findings in this report are not to be construed as an official

Department of the Army position unless so designated by other

authorized documents.

Citation of manufacturer’s or trade names does not constitute an

offkial endorsement or approval of the use thereof.

Destroy this report when it is no longer needed. Do not return

it to the originator.

‘ I
Abstract

In this report, we undertake the task of verifying the VLSTRACK model on the specific

example of raindrop terminal velocities, which were calculated directly from Fluid Dynamics.

In this example, the verification is in good agreement with experiments.

ii
Table of Contents

1.

2.

3.

4.

5.

6.

7.

ListofTables .....................................................

ExecutiveSummary ................................................

Introduction ......................................................

Theory: Overview of Fluid Dynamics Calculations of Raindrop Terminal

Velocities .........................................................

Implementation: Analysis Using VLSTRACK .........................

Example Application: Number Crunching of Terminal Velocity ..........

Conclusions and Results ............................................

Discussion of the Significant Results ..................................

References ........................................................

Distribution List ...................................................

Report Documentation Page .........................................

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iv
List of Tables

Table

1.

2.

3.

Comparison of VLSTRACK Calculated, Fluid Dynamics Calculated, and

Experimental Terminal Velocities of Water Droplets . . . . . . . . o . . . . . . . . . . * o . .

Example of the VLSTRACK.TRK Output File Containing the Properties of the

Droplets as They Propagate Through the Atmosphere . e . . . . a . . . . . . . . . . . . . e .

Example of the VLSTFUCKXEC Output File Containing the Properties of the

Droplets Impacting the Ground Surface n................................

Pane

4

10

19

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h’IENTIONALLY LEFT BLANK.

Vi
Executive Summary

In this research, we undertook a task to verify the validity of the Vapor, Liquid, and Solid

Tracking (VLSTRACK) Computer Model in calculating terminal velocity of raindrops. The findings

compare very well with Fluid Dynamics calculations and experiments.

The version VLSTRACK 1.6.2, used here, is developed and owned by the U.S. Naval Surface

Warfare Center (NSWC), Dahlgren Division, Dahlgren, VA 22448-5 100.

If the revision of VLSTRACK is contemplated, we recommend that more detailed documentation

of input parameters for explaining specific tasks be included.

.

vii
. . .

Vlll
1. Introduction

In this report, we are verifying whether the VLSTRACK [l] computer model is applicable for

a specific example-omparison of terminal velocities of falling water droplets under the influence

of gravity and drag forces (the drag forces contain ordinary drag forces and buoyancy forces).

Specifically, we are comparing the VLSTKACK calculated terminal velocities in the atmosphere

with those calculated interactively through fluid dynamics formalism [2].

Although one might think that this is a simple task, it turned out that before one could set

VLSTRACK to calculate the terminal velocities, a lot of preliminary manipulations were necessary

in the data input files in order to successfully accomplish this comparison.

Section 2 outlines the purpose of this analysis. Section 3 is devoted to recapitulation of fluid

dynamics calculations of raindrop terminal velocities and the experimentally determined values. The

analysis using VLSTRACK is discussed in section 4. Section 5 provides the velocities and

summarizes the results. The significant results are discussed in section 6.

The purpose of this report is to show that an accurate description of a particular situation by

VLSTFLACK requires significant manipulation of input VLSTRACK parameters. Our specific

example of VLSTlUCK calculated raindrop terminal velocities and their subsequent comparison

with fluid dynamics calculations [2] and experimental data [3] illustrates how comparisons for other

agents may be made.

2. Theory: Overview

Raindrop Terminal

of Fluid Dynamics

Velocities

Calculations of

Here we give a short review of fluid dynamics calculations of raindrop terminal velocities. A

full account may be found in Sohr [2].

1
When a raindrop is of a diameter that is smaller than 5 mm, one can treat a freely falling droplet

as a sphere; a fact that can be verified a posteriori by comparison with experiments.

Treating a droplet as a sphere with water density simplifies the calculation of the terminal

velocities.

For the sake of completeness, we write down the differential equation for the water sphere when

forces acting on it are all in the vertical direction. The velocity of the sphere in the horizontal

direction is assumed to be zero. Hence the differential equation for the vertical motion of the sphere

reads as follows:

-(l-P)g-zc, ulul 1, (1)

where u is the velocity of the sphere in the vertical direction, whose coordinate here is denoted as

y, looking upward.

The relevant parameters appearing in equation (1) are:

P

Pf

= 1000.0 kg/m3, pf = 1.22 kg/m3, p = - = 0.0012, g = 9.8 m/s2,

P

(2)

where p is the density of water, pf is the density of air, and c, is a drag coefficient that depends on

the dimensionless Reynolds number

cd = cd @e> * (3)

The Reynolds number has to be computed separately for each velocity, u, according to

$ = “d,

V

(4)

2
.

where d is the diameter of the sphere and v is the ordinary viscosity of air:

v = 0.0000149 m2/s .

For air as a medium, empirical relation (3) can be specified as [2,3]

24

‘d = -, 1 < R, I 400.

RY6

(6)

The terminal velocity u, follows when equation (l), acceleration, is equivalent to zero, i.e., when

the velocity in the downward direction becomes constant. Thus, equating (1) to zero and setting

u = -L+, where u, looks in the downward direction, we obtain:

(7)

The next thing one does is to “guess” on the initial value of terminal velocity u,for a droplet with

a given diameter d. For example, for d = 0.001 m, we guess the initial value for u, to be 3 m/s.

Rutting this into relation (4) for the velocity u, we obtain R, = 201.34. This now is used to calculate

cd according to relation (6), resulting in cd = 0.78. Now we have everything for calculating the

“improved” value for u, according to relation (7). The improved value is u, = 3.73 m/s. Now one

repeats the cycle with this new value for u, yielding even better approximation for u,. Eventually,

this repetition will yield t+‘s that do not differ from each other, which means that we found the most

accurate value for u,. In our case, u, = 4.1 m/s as a final value.

One can do this type of calculation of u, for every diameter d. The results are exhibited and

compared to equivalent values and VLSI’RACK calculations in Table 1.

3
Table 1. Comparison of VLSTRACK Calculated, Fluid Dynamics Calculated,

and Experimental Terminal Velocities of Water Droplets

Calculations of

Terminal Velocity of

Calculations of Measured Terminal

Terminal Velocity of

The measured terminal velocities of water droplets come from Blanchard [3]. The VLSTRACK

data will be discussed in the next section.

3. Implementation: Analysis Using VLSTRACK

Now that we have provided the rationale for calculated terminal velocity, we want to look at

VLSTRACK computer model [l] calculated terminal velocities compared to those we have

calculated interactively through the fluid dynamics equation sequence discussed in Section 2.

The sequence we used to set up the VLSTIUCK files is discussed in this section. We are going

to specify the process used to compute the VLSTRACK results in Table 1. Before starting to

4
interrogate VLSTRACK, we must determine the boundaries of what comparisons we want to make.

We want to compare VLSTRACK calculated values to the fluid dynamics calculated values, so we

need to duplicate the parameters used in the fluid dynamics terminal velocity calculations as closely

as possible. This means that we want to look at the water droplet as a rigid sphere. We therefore

set forth to define a VLSTIUCK “threat” scenario that will replicate the physical conditions and

properties of a rigid sphere of water and will mimic stabile atmospheric conditions.

The first step in this definition sequence was to establish an agent in the agent parameter file

named VLSAGN.PAR [l] to define the physical properties of the rigid sphere of water. The agent

file was modified to identify water as a biological type agent (type 5), meaning that the water would

be treated as particle beads rather than as a liquid.

Agent parameter file specifications also include the bulk density, dissemination efficiency,

median lethal or effective dosage, probit slope, and freezing temperature. Dissemination efficiency

was set at lOO%, and median lethal or effective dosage was set at only 0.001 mg-mum3 to assure the

water would exhibit deposition (in the case of deposition runs) and that effects would be detected

(in the case of dosage effects runs). The bulk density, probit slope, and freezing temperature were

set equivalent to that of water. In addition to the overall agent identification, each type 5 agent

includes particle MMD [ 11, geometric droplet/particle distribution sigma, particle density, daytime

biological decay rate, nighttime biological decay rate, biological agent purity, and biological agent

dissemination efficiency for exploding munitions. The particle MMD was varied from 500 p to

6,000 p in increments of 500 p. The fluid dynamics calculations are valid up to a water droplet

diameter of 5,000 p . We included up to 6,000 p diameters in order to exhibit explicitly the departure

from experimental values. The geometric droplet/particle distribution sigma was set at 1, signifying

that all droplets are the same size; the particle density was set at that of water (at 21’ C) equal to 1

g/cm3; and the biological agent dissemination efficiency is not pertinent since it is not used when

useridefmed (i.e., puff-type, localized concentration of a gaseous or liquid substance [ 11) munitions

are utilized. Daytime and nighttime biological decay rates were set at zero, and the biological agent

purity was set at 100% to maximize capacity of the water “hazard.”

5
The second sequential step was to define a munition in the parameter file named VLSMUN.PAR

[1], which is the location where munition descriptions are built or modified. It was decided to

disseminate water ih puffs as a line source to view the water from each puff as it was deposited via

the graphics output file, to track and compare terminal velocities of each puff by reviewing the

output files named VLSI’RACK.TRK and VLSTRACK.REC, respectively [l]. The munition was

categorized as a user defined munition and then further defined in a separate puff property file named

VIXI’RACK.POS [l]. This file was configured to contain five records for each munition puff,

including the mass, dowmange and crossrange distance, height, and detonation time. After making

several successful VLSI’RACK runs, in terms of measuring terminal velocity, a standard scenario

was established and then the puff property file parameters were varied many times. Keeping in mind

that it was desired to make the puff release height higher than the distance the droplet would travel

in 1 min, the puff parameter values were varied to substantiate uniformity of terminal velocity from

run to run and to determine terminal velocity for each different MMD.

The third step was to develop a meteorology file in a file named VLSTRACK.MET. We know

that meteorological conditions have a significant impact on how agents transport and disperse on the

battlefield. The object of our VLSTRACK.RIET file is to define atmospheric conditions that parallel

the constant conditions used for the fluid dynamics calculations [2] for the droplets under the

influence of only gravity and drag. Preliminary V’ISTRACK runs were performed using a time

series meteorology file in which meteorology data was input for specific time periods at one

measured height. The model computes meteorological data for all other pertinent heights based on

the meteorological input data and on the atmospheric stability category known as the Pasquill

category [l]. VLSTRACK is programmed to either allow the program to specify the Pasquill

stability category based on the meteorological conditions, time of day, and terrain information or to

allow the operator to select a particular stability category. There are seven categories available,

ranging from very unstable to very stable. In this case, the option was selected for the program to

determine the Pasquill category.

A height-time variable meteorology file was used for all MMD comparative analysis runs in

order to fix the wind at a constant 0 km/hr and the temperature at a constant 21 o C at all elevations

6
to parallel the conditions of the fluid dynamics calculations 121. It was necessary to use the O.OOlkm/hr wind speed because an anomaly of the model did not allow a constant 0 lcm/lrr wind speed.

The height-time variable meteorology file includes ground surface type, Pasquill stability category,

cloud cover, terrain elevation above sea level, threat measurement height above sea level, wind

bearing, wind speed, air temperature, and atmospheric pressure. The lreiglMime variable

meteorology file that was used consisted of two identical time steps. Including the constant

temperature and wind, the additional parameters were brush-type ground surface, neutral Pasquill

stability category, clear-no cloud cover, and O-m terrain elevation above sea level for location to

100% at the deposition. Four records were included for each time period. They were as follows:

l O.OOl-km measurement height above sea level, 90” true north @TN) [l] wind bearing,

0.001~km/hr wind speed, 21 O C air temperature at l,OOO-mbar atmospheric pressure.

l 0.5~lun measurement height above sea level, 90 DTN wind bearing, 0.001 -lcm/hr wind speed,

21’ C air temperature at 950-mbar atmosplieric pressure.

l 1 .O-km measurement height above sea level, 90 DTN wind bearing, 0.001 -km/hr wind speed,

21’ C air temperature at 900-mbar atmospheric pressure.

l 2.0~km measurement height above sea level, 90 DTN wind bearing, 0.001~km/hr wind speed,

21’ C air temperature at 800-mbar atmosplieric pressure.

After the water agent, puff munitions, and meteorological data were detailed in the appropriate

parameter files, the next step was to complete an attack scenario using the six available VLSlR4CK

editor windows. Included is the time of day for onset of the attaclc-in this case, release of the first

puff. All of the modeling scenarios were performed using 0400 (military denoted) local onset time

since night time and early morning conditions provide the calmest atmospheric conditions 141.

Cumulative deposition intervals of 1 min were used for run output. Level of detail of deposition

contour levels was set as low as possible-O.01 mg/m2 in order to detect any deposition.

7
4. Example Application: Number Crunching

Velocity

of Terminal

Model scenarios were built and run one at a time, with each subsequent run description

contingent on the preceding run results. Output graphics of hazard footprints were viewed at each

interval during each model run to monitor the time at which water deposited on the ground. Model

scenario inputs were modified until run output graphics exhibited deposition. A uniform base

scenario was then defined and run sequentially varying only sphere MMDs from 500 p to 6,000 p.

Terminal velocity numbers were calculated by looking at each individual munition puff and by

analyzing all resulting output files. In particular, after viewing deposition contours in the graphics

output display file, the corresponding VL,STRACK.TRK output file was saved for each file. This

VLSlXACK.TRK file shows tracking for each droplet (discharged in the munition puff), including

such data as the x and y distance traveled and the height of the droplet at that record. The terminal

velocity was approximated by looking at the time it took for deposition to start and the height the

droplets were released as recorded in the output file VLSTRACK.OUT file [l]. The

VLSTRACK.TRK file was also used to calculate an exact terminal velocity by calculating the

difference in the height of the droplet from one time snapshot to the next.

5. Conclusions and Results

The VLSTRACKTRK, Table 2, and the VLSTFLACK.REC, Table 3, output files track and

record the cloud properties of all airborne vapor, droplet, or particle clouds for each individual puff

released. These files were used to calculate and compare the terminal velocities of water beads from

each puff. The resulting terminal velocity calculations from tracked puffs were all consistent for

each individual MAD.

The results of the VLSTRACK calculated terminal velocities were within expected tolerance of

the fluid dynamics calculations up to a MMD of 2,500 p . Table 1 shows the VLSTRACK and fluid

8
dynamics [2] calculated

velocity of rain droplets.

terminal velocity of a rigid sphere of water and the measured terminal

The fluid dynamics calculations are consistent with the measured terminal velocities of up to

5,000 p MMD, while VLST’RACK calculations are consistent to water droplets of up to 2,500 p

MMD. In fact this conclusion can also be obtained through statistical analysis which compares

calculated values with each other and with experiments [S].

6. Discussion of the Significant Results

The final results of this study showed that VLSTRACK models terminal velocity accurately for

rigid spheres of water with MMDs from 500 to 2,500 p as indicated by the heavy line in Table 1.

The larger the MMD, >2,500 p , the more discrepancy in the results. These results are reassuring

and could be expected since chemical agents that VLSTRACK is intended to model would not have

such large MMDs anyway. For example, typical Mh4Ds for most dusty and bio agents are only 5 p ,

for glass beads are 250 p , for neat agent droplets are 500 p, and for thickened agent droplets are

2,500 p maximum. VLSI’RACK terminal velocity calculations also remained uniform for each

different MMD even when altering mass or release position. The discrepancy of the fluid dynamics

calculations to the measured terminal velocities beyond 5,000 p MMD would indicate a breakup of

droplets.

This comparison study clearly indicates the validity of VLSI’RACK for evaluating terminal

velocities in the range for which it is intended.

9
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere

y-dist. 1 height sigma-x

0.0 1200.0 0.0

0.0 1200.0 0.0

-5.2 967.2 0.2

-5.6 971.1 0.2

-6.1 974.9 0.2

-6.5 978.8 0.2

sigma_y 1 sigma-z shavg 1 shght

0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0

0.2 0.2 0.0 0.0

0.2 0.2 0.0 0.0

0.2 0.2 0.0 0.0

0.2 0.2 0.0 0.0

mix. ht. I Cld. rot. radius

800.0 0.0 500.0

800.0 0.0 500.0

800.0 0.0 500.0

800.0 0.0 500.0

800.0 0.0 500.0

800.0 0.0 500.0

cont.

6.3494E+ll

6.3494E+ll

7.6418E+O7

7.6418E+07

7.6418E+O7

7.6418E+O7

7.6418E+O7

7.6418E+O7

7.6418E+O7

mass II

Note: The columns are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma iu meters, average terrain elevation in meters, local terrain elevation iu meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.

.

L
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (continued)

Note: The columns are for time in seconds, droplet sire group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (continued)

time 1 idrop in 1 x-dist. y-dist. 1 height 1 sigma-x I sigma_y I sigma-z I shavg shght I mix. ht. I Cld. rot. I radius

120 1

*

120 1

120 1

-0.6 738.2

*

-1.0 742.1

-1.5 746.0

1201 1 5 1 42.8 - 1.9 I 749.9

120 1

f

6 52.6

120 1 7 62.4

120 1 8 72.2

120 1

120 1

120 1 f

9 82.0

10 91.8

11 101.5

120 1 -I- 120 112 111.4

t13 121.2

-4.1 777.0 0.6 0.6 0.5 0.0 i 0.0 800.0 0.0 500.0

-3.7 780.9 0.3 0.3 0.3 0.0 0.0 800.0 0.0 500.0

-3.2 784.8 0.3 0.3 0.3 0.0 0.0 800.0 0.0 500.0

-2.7 788.7 0.3 0.3 0.3 0.0 0.0 800.0 0.0 500.0

120 1

+

120 1

14 131.0

t

15 140.9

120 1 d=120 1

120 1

16 1 150.7 -2.3 1 792.6 1 0.3 1 0.3 1 0.3 1 0.0 / 0.0 1 800.0 1 0.0 1 500.0 3.0836E+O7 11 .OOOOE+O7~~

17 160.5

t,18 170.3

- 1.8 796.4 0.3 0.3 0.3 0.0

-1.4 800.3 0.3 0.3 0.3 0.0

Note: ‘lhe columns are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (continued)

Note: The cohmms are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (continued)

time 1 idrop 1 in 1 x-dist. y-dist. height 1 sigma-x I sigma_y I sigma-z I shavg I shght

~ -6.8

-7.2

i -7.7

-8.1 532.6 1.9 1.9 1.5 0.0 0.0

’ -8.5 536.5 1.9 1.9 1.5 0.0 0.0

-9.0

-8.5

-8.1

-7.6 552.0 1.8 1.8 1.4 0.0 0.0

555.9 1.8 1.8 1.4 0.0 0.0

800.0 0.0 500.0 1.4239E+O5 1 .OOOOE+O7

-7.2 800.0 0.0 500.0 1.4485E+O5 1 .OOOOE+O7

-6.7 559.7 1.8 1.8 1.4 0.0 0.0

563.6 1.8 1.8 1.4 0.0 0.0

567.5 1.8 1.8 1.4 0.0 0.0

571.4 1.7 1.7 1.3 0.0 0.0

800.0 0.0 500.0 1.4738E+O5 1 .OOOOE+O7

800.0 0.0 500.0 1.4998E+O5 1 .OOOOE+O7

800.0 0.0 500.0 1.5264E+O5 1 .OOOOE+O7

800.0 0.0 500.0 1.6029E+O5 1 .OOOOE+O7

-6.2

-5.8

Note: The columns are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.
. .

. .

Table 2, Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (continued)

Note: ‘fhe columns are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (continued)

time 1 idrop 1 in x-dist. 1 y-dist. height sigma-x I sigma-y I sigma-z shavg I shght I mix. ht. I Cld. rot. radius i cont. mass II

240 t 1 1101 94.6 -11.9 303.6 1 3.1 1 3.1 1 2.3 1 0.0 1 0.0 1 800.0 1 0.0 1 500.0 ~2.87OlE+O4

2401 1 1111 104.4 ~ -12.3 307.5 1 3.1 1 3.1 1 2.3 1 0.0 1 0.0 1 800.0 1 0.0 1 500.0 2.9131E+O4

-11.9 ‘2.9529E+O4 1 .OOOOE+O7

--i 1 .OOOOE+O7

311.4 3.1 3.1 2.3 0.0 0.0 800.0 0.0 500.0

l-11.4 315.3 3.0 3.0 2.2 0.0 0.0 800.0 0.0 500.0

-11.0 319.2 3.0 3.0 2.2 0.0 0.0 800.0 0.0 500.0 3.1927E+O4

-10.5 323.0 3.0 3.0 2.2 0.0 0.0 800.0 0.0 500.0 ~3.2359E+O4

- 10.0 3.28OOE+O4

-9.6 3.325OE+O4

-9.1 ,303709E+O4

-8.7 3.4566E+O4

-8.2 i3.5048E+O4

-7.7

-7.3 13.6517E+O4

-6.8 ’3.7477E+04

-6.3

-5.8

240 1 1 1261 252.7 -5.3 2.8 500.0 j 1 .OOOOE+O7]~

Note: The columns are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (continued)

time 1 idrop

240 1

*

240 1

240 1

240 1

300 1

~

300 1

300 1

3001 1

3001 1

300 1

+

300 1

300 1

300 1

300 1

%

300 1

300 1

300 1

in xdist. y-dist. height sigma-x sigmay sigma-z shavg shght mix. ht. Cld. rot. radius cont. mass

27 262.7 -4.8 369.6 2.8 2.8 2.1 0.0 0.0 800.0 0.0 500.0 4.0661E+04 1 .OOOOE+O7

28 272.7 -4.3 373.5 2.7 2.7 2.0 0.0 0.0 800.0 0.0 500.0 4.1246E+04 1 .OOOOE+O7

29 282.7 -3.8 377.4 2.7 2.7 2.0 0.0 0.0 800.0 0.0 500.0 4.2389E+O4 1 .OOOOE+O7

7 71.0 -8.3 59.2 4.4 4.4 3.1 0.0 0.0 800.0 0.0 500.0 l.O842E+O4 1 .OOtlOE+O7

8 80.8 -8.8 63.1 4.3 4.3 3.1 0.0 0.0 800.0 0.0 500.0 l.O957E+O4 1 .OOOOE+O7

9 90.6 -9.2 66.9 4.3 4.3 3.1 S 0.0 0.0 800.0 0.0 500.0 l.l075E+O4 1 .OOOOE+O7

;lO 100.4 -9.7 70.8 4.3 4.3 3.1 0.0 0.0 800.0 0.0 500.0 l.l194E+O4 1 .OOOOE+O7

~11 110.2 -10.1 74.7 4.3 4.3 3.1 0.0 0.0 800.0 0.0 500.0 l.l324E+O4 1 .OOOOE+O7

L

12 120.0 -9.6 78.6 4.3 4.3 3.0 0.0 0.0 800.0 0.0 500.0 l.l447E+O4 1 .OOOOE+O7

13 129.8 -9.2 82.5 4.2 4.2 3.0 0.0 0.0 800.0 0.0 500.0 l.l889E+O4 1 .OOOOE+O7

Note: The columns are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter, and cloud mass in milligrams, respectively.
Table 2. Example of the VLSTRACK.TRK Output File Containing the Properties of the Droplets as They Propagate Through

the Atmosphere (co Itinued)

300

1 23 228.5 -4.5

1 24 238.5 -4.0

1 25 248.5 -3.5

1 26 258.5 -3.1

1 27 268.5 -2.6

Note: ‘Ihe columns are for time in seconds, droplet size group number, puff number, downwind distance in meters, crosswind distance in meters, height above sea level in meters,

downwind cloud sigma in meters, crosswind cloud sigma in meters, vertical cloud sigma in meters, average terrain elevation in meters, local terrain elevation in meters, mixing layer

height in meters, downwind cloud rotation angle in degrees, droplet radius in microns, cloud concentration in milligrams per cubic meter. and cloud mass in milligrams, respectively.

.
. I

Table 3. Example of the VLSTRACK.REC Output File Containing the Properties of the Droplets Impacting the Ground Surface

ismth idrop in time diameter x-distance y-distance sigma-x sigma-y cloud rot. cont.

0 1 1 309.3 1000.0 12.3 -4.5 4.7 4.7 0.0 7.2476E+O4

0 1 2 310.3 1000.0 21.7 -4.8 4.8 4.8 0.0 6.9953E+O4

0 1 3 311.3 1000.0 31.6 -4.7 4.7 4.7 0.0 7.141OE+O4

0 1 16 324.3 1000.0 157.5 -3.2 4.7 4.7 0.0 7.2905E+O4

0 1 17 325.3 1000.0 167.0 -2.9 4.8 4.8 0.0 7.0344E+O4

Note: The columns are for cloud smoothing index, droplet size group number, puff number, time in seconds, droplet diameter in microns, downwind distance in

meters, crosswind distance in meters, downwind cloud sigma in meters, crosswind cloud sigma in meters, downwind cloud rotation angle in degrees, and concentration

in milligrams per cubic meter, respectively.
Table 3. Example of the VLSTRACKXEC Output Pile Containing the Properties of the Droplets Impacting the Ground

Surface (continued)

ismth idrop in

0 1 18

0 1 19

0 1 20

0 1 21

time

326.3

327.3

328.3

329.3

diameter

1000.0

1000.0

1000.0

1000.0

x-distance y-distance sigma-x sigma2 cloud rot. cont.

176.7 -2.0 4.7 4.7 0.0 7.0843E+O4

186.4 -1.0 4.7 4.7 0.0 7.1547E+04

196.1 -0.1 4.7 4.7 0.0 7.2058E+O4

205.8 0.8 4.7 4.7 0.0 7.2804E+O4

0 1 1 1 22 1 330.3 1 1000.0 1 215.7 1.8 4.9 4.9 0.0 1 6.7337E+O4

0 1 1 1 23 1 331.3 1 1000.0 1 225.6 2.8 4.8 4.8 0.0 1 6.7987E+04

0 1 1 1 24 1 332.3 1 1000.0 I 235.6 3.7 4.8 4.8 0.0 6.8464E+O4

0 1 1 1 25 1 333.3 1 1000.0 I 245.5 4.7 4.8 4.8 0.0 6.9132E+O4

0 1 1 30 1 338.3 1000.0 I 295.3 I 9.6 I 4.7 I 4.7 I 0.0 l 7.2019E+O4

Note: The columns are for cloud smoothing index, droplet size group number, puff number, time in seconds, droplet diameter in microns, downwind distance in

meters, crosswind distance in meters, downwind cloud sigma in meters, crosswind cloud sigma in meters, downwind cloud rotation angle in degrees, and concentration

in milligrams per cubic meter, respectively.
7. References

1. Batter, T., and R. Gibbs. “Software User’s Manual for the Chemical/Biological Agent Vapor,

Liquid, and Solid Tracking (VL-STRACK) Computer Model.” Version 1.6.2, NSWCDD/MP96031, June 1996.

2. Sohr, Josip Z. “Fluid-Dynamics Assessments of Deposition and Infiltration Models.”

ARLTR-1525, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, October

1997.

3. Blanchard, D. C. “From Raindrops to Volcanoes.99 Doubleday, Garden City, NY, 1967.

4. Smith, B. G., and J. T. McCullen. “Chemical Agent Challenge Analysis for the RAEI-66

Comanche: Blood Agents, AC and CK.” ARL-TR-1595, U.S. Army Research Laboratory,

Aberdeen Proving Ground, MD, January 1998.

5. Baker, William (Statistician). private communication. U.S. Army Research Laboratory,

Aberdeen Proving Ground, MD, December 1998.

21
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13. ABSTRACT(Maximum200 wo&)

In this report, we undertake the task of verifying the VLSTRACK model on the specific example of raindrop terminal

relocities, which were calculated directly from Fluid Dynamics. In this example, the verification is in good agreement

vith experiments.

14. SUBJECTTERMS

VLSTRACK, fluid dynamics, texminal velocity

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