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RD-R145 784 AN INVESTIGATION OF PARTICULATE IMPACTION ON SPHERICAL i/iAND CYLINDRICRL TAiRGETS(U) DEFENCE RESEARCHESTABLISHMENT SUFFIELD RALSTON (ALBERTA)
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.SUFFIELD MEMORANDUM=
00 NO. 1102
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AN INVESTIGATION OF PARTICULATE IMPACTION
I ON SPHERICAL AND CYLINDRICAL TARGETS (U)
by
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Jeffery L. Hall and Stanley B. Mellsen
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L*L~ PCN No. 13E10
SEP 18 1984ILAugust 1984E
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DEFENCE RESEARCH ESTABLISHMENT SUFFIELD
RALSTON ALBERTA
SUFFIELD MEMORANDUM NO. 1102
AN INVESTIGATION OF PARTICULATE IMPACTION
ON SPHERICAL AND CYLINDRICAL TARGETS (U)
by
Jeffery L. Hall and Stanley B. Mellsen
PCN 13E10
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UNCLASSIFIED
DEFENCE RESEARCH ESTABLISHMENT SUFFIELD
RALSTON ALBERTA
S
SUFFIELD MEMORANDUM NO. 1102
0
AN INVESTIGATION OF PARTICULATE IMPACTION ON
SPHERICAL AND CYLINDRICAL TARGETS (U)
by
Jeffrey L. Hall and Stanley B. Mellsen
ABSTRACT -
his project was a theoretical investigation of particulate
impaction on spheres and cylinders. The motion model developed was
implemented on a computer and yielded results focused on two main goals: pfirst, the net effect of gravity on particulate impaction was determined;
and second, a man simulation was conducted. This simulation calculated to
a first approximation the amount of chemical that would impact on a man
subjected to a chemical attack -
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TABLE OF CONTENTS
Page No.
Abstract
List of Symbols
INTRODUCTION ............................................. 1
BACKGROUND THEORY ............................................... 2
COMPUTER PROGRAMS........................................ .14
RESULTS........................................................ 17
DISCUSSION................................................ 19
CONCLUSIONS ............................................. 26
REFERENCES ..................................................... 27
TABLES
FIGURES
APPENDIX A: LISTING OF PROGRAM AEROSOL-B
APPENDIX B: LISTING OF PROGRAM AEROSOL-6
cc P,:s on For
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LIST OF SYMBOLS
b - constant
CD - drag coefficient
F - Froude number
Fd - drag force
F - gravity force
g - acceleration of gravity
g9 - non-dimensional gravity
G - ground fraction
K - inertia parameter
L - target radius
m - particle mass
r - distance from the origin
rp - particle radius
Re - local Reynold's number
Re0 - free stream Reynold's number (based on particle size)
t - time
u - local fluid velocity
u- non-dimensionalized local fluid velocity
U - free stream velocity (synonymous with windspeed)
v - particle velocity
vs - non-dimensionalized particle velocity
v - terminal velocityo - rotation angle of frame 1 re frame 0
y - rotation angle of frame 2 re frame 0
a - position angle in frame 0
Pa - air density
p p - particle density
P- air viscosity
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DEFENCE RESEARCH ESTABLISHMENT SUFFIELD
RALSTON ALBERTA
SUFFIELD MEMORANDUM NO. 1102
AN INVESTIGATION OF PARTICULATE IMPACTION ON
SPHERICAL AND CYLINDRICAL TARGETS (U)
by
Jeffrey L. Hall and Stanley B. Mellsen
INTRODUCTION
1. In assessing the hazard to troops from attacks with chemical
agents in aerosol form, it is important to be able to predict the motion of
the chemical agents as they disperse through the atmosphere and impact onvarious target objects (Figure 1). This project was conducted to
investigate the impaction aspect of the overall motion problem specifically
to provide an answer to the question, "How much chemical will hit a
target.
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2. Some theoretical studies have been performed in this area of
aerosol impaction1 . This project sought to upgrade the theoretical models
used through the inclusion of the gravity force into the problem; in fact,
the secondary purpose of the project was to quantify the error incurred
when gravitational effects are ignored. The primary purpose of the project
was to develop a model which would calculate the amount of chemical that a
man received in relation to how much the ground received.
3. The complex nature of this fluid mechanical problem required
a number of simplifying approximations in order to be tractable.
Consequently, the results obtained are first approximations only,
calculated on the basis of a theoretical model which required computer
programs for implementation. The project results are seen as a
foundation upon which to conduct experimental and/or improved theoretical
research.
4. The project evolved significantly durings its lifetime. The
initial phases were very much a learning phase during which the model was
continuously tested and changed. Spherical targets were used for these
initial tests, tests which also provided much data on the effect of gravity
on the problem. This initial phase ended with the study of cylindrical
targets during which the last gravity effect calculations were performed.The final phase of the project dealt with the man-target simulation.
BACKGROUND THEORY
Fundamentals of Particulate Motion
5. The derivation of the aerosol particle motion equation follows
directly from Newton's Second Law2 . There are two forces present, namely
gravity and aerodynamic drag:
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F d CD% (1r2) ( P4U 112)[1
F =m 2]
The particles are assumed to be spherical because of their small size(42000 jo radius). The resulting equation of motion is therefore:
m;v =%(irrp2)( ipa [1 - 12) + nM. [3]
Noting that;
4M r p3P [4]
2r pPa [
Re =- - I
we can re-arrange equation [31 to produce:
3uCDRe(U - V)
- 16r p2 P [6
6. Equation [61 can be non-dimensionalized by using the free stream* velocity U and the characteristic target length L:
V, U-Iv [7]=LU-
2 ; [8 1*U = U'1u [9] -
t tUL-1 [101
L' = 2Uj [11]
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If we define:
2P rpp
K [12]9 uL
U2 :F [13]
Lg
then equation [6] can be written in the following non-dimensional form:
CDRe(U'-v') 1V= +__ _ -1]..
24 K F
7. Clearly, the problem can be solved by either equation [6] or
equation [14]. Traditionally, these problems have been solved in non-
dimensional form resulting in graphs of collection efficiency vs. inertia
parameter for various Reynold's numbers (Collection efficiency is explained
in the next section). In this problem, however, the inclusion of gravity
adds another parameter, namely the Froude number. The graphical presenta-
tion of non-dimensional results now becomes quite complicated, and the
physical interpretation of such results becomes obscure. It was felt that
superior physical insight and applicability would result from analysis of
the restricted case of motion in air under representative experimental
situations. Equation [61 was therefore used in the model.
8. In reference frame 1 (Figure 2), equation [6] can be resolved
into the following scalar equations:
;x bCDRe (N " vx) [15]
y bCoRe (Uy vy) [16]
;z =bCDRe (Uz - v z) g [17]
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where 3pb - [18]
16r 2 p
9. The drag coefficient for spheres is defined in terms of the
Reynold's number by the following equations 3:
For Re4, CDRe2
Re - 2.3363x10-4(CDRe2)+2.0154x10-6(CDRe2)3
24 - 6.9105xi0-9(CDRe2)4 [19]
For 34Re410 4, loglo Re = 1.29536 + 9.86 x 10- 1(logoCDRe2)- 4.6677x 10-2 (logl 0 CDRe 2) + 1.1235 x 10- 3 (log1 o CDRe 2)3 [20]
10. Two assumptions were made regarding the initial condition of the
aerosol particle. First, it was assumed that the particle was moving
horizontally at the free stream velocity and that a starting position
upstream would experience negligible flow perturbations caused by the
target. Second, the particle was defined to be falling at its terminal
velocity, because small aerosol particles quickly attain that speed.
Consequently, the particle initially possessed a velocity given by its
terminal velocity (vZ ) and the free stream velocity, with a direction
defined by the angle y eo the x-axis:
0 [21]y =tan- 1 :
The terminal velocity was calculated by setting ,-=0 and U, 0 in
equation [17], and solving for vo. The result was:
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.8r pg 1/2 [
VZ p [221
11. Therefore, simultaneous solution of [5], [221 and one of [19] or[20] yielded the terminal velocity.
12. The flow equations will be derived in paragraphs 15-24 for thevarious target geometries. All such equations were inviscid fluid
equations. These were deemed applicable to the problem because real fluidflow is virtually ideal on the leading face of an object, which was the
only face of interest in this particle impaction problem. It was also
assumed that the chemical particles themselves did not perturb the fluid
flow.
Collection Efficiency
13. The concept of a collection efficiency is the primary means of
quantifying the amount of chemical which impacts on a target (Figure 3).
The collection efficiency is a number ranging from zero to one, and is
defined by equation [23]: .
Collection = Cross-sectional area of the envelope [23]
Efficiency Cross-sectional area of the targetThe envelope is that region on the starting plane in which initial particle
placement results in a trajectory which hits the target. Clearly, the
absence of the fluid medium would result in a collection efficiency of one,
because the particles would travel in straight lines, and massless
particles would have a collection efficiency of zero, because the particles
would follow fluid streamlines around the target without impaction. .
14. The task at hand is to calculate the collection efficiency for
any given test situation. This is done using a half-interval method to
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find the boundaries of the envelope. A series of particles are considered, 5
each of which begins on the starting plane with the same initial velocity
(Figure 4). Two initial particle positions are required to start the
procedure: an 'inside' one that results in target impaction (P2) and an'outside' one that results in target miss (Pl). A third position (P3) iscalculated such that it lies halfway between the first two points; this
particle is then tracked to the target. If it misses, the (P3) becomes the
new 'outside' position and a new starting position is chosen at (P4). If
it hits, then (P3) becomes the new 'inside' position, and a new starting •
position is chosen at (P5). The distance between the inside and outsidepositions is successively reduced by half, and it asymptotes to the
envelope boundary. In this manner, the envelope boundary is defined,allowing its area to be calculated for use in equation [23]. Note that the
boundary is generally a two-dimensional curve on the starting plane whichrequires a large number of boundary points before an accurate estimation of
its shape and size can be made.
Target Geometry For Spheres
-.. . .... --
15. The fluid velocity field around a sphere is given in terms ofpolar coordinates 4 : o
Ur =U cos e [24] 0
U = -U sin 0 L + 1/2 [251
These equations are valid for any plane passing through the origin of the
sphere and parallel to the x-axis of Frame 1. Let us designate such aplane as Frame 0 with x, n, i axes; Frame 1 is related to Frame 0 by the
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rotation angle a about the x-axis (Figure 5). In terms of Frame 0 0
cartesian coordinates, equations [24] and [25] become:
Ux = Ucos2 e + Usin 2 I + 112 _ [26]
-3U /L\Un 2 crCos o sin e [27] 0
U -0 [28]
Equation [28] is obtained by inspection. These three equations can be used
to specify the velocity field at any point in space in Frame 1 via a
suitable rotation of Frame 0 to align it with the position of interest. In
matrix notation, the required velocity components are generated as PP
follows:
U 1100 UxU = 0 cosa - sino Un [29]
60 sin cosa U A.
Upon evaluation we get:
Ux = U cos 2 0 + U sin 2e + [30]
-3U /L 3 L _
UY= 2()3 cos 0 sin e cos 8 [31]
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• " - 2 . i . -. . .. . '-0
. . .. . . . . . . . .
S
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-3U(L,\3 Uz= cos o sine sin B [32]
By definition, we obtain these auxiliary equations:
r = (x2 + y2 + z2)1/2 [33]
rZ \
ycos 8 + z sinae tan- [35]
xp
16. Due to the wide range of initial particle velocities angles y, it
was decided that calculations would be simplified if done in a reference
frame aligned at y to Frame 1. Consequently, Frame 2 was defined for each
particle test such that the starting plane was perpendicular to the initial ji
particle direction (Figure 6). All transformed into this frame by means of
the following rotation matrix:
C2= cos y 0 -sin y S
0 1 0 [36]sin y 0 cos y
17. The collection envelope for this sphere geometry was necessarily S
two-dimensional. Essentially, the half-interval method was used to
calculate z' boundary values for a series of y coordinates; the y'boundaries themselves were also calculated by means of the half-interval
method. The set of boundary points (y', z') were then connected by cubic
splines and then the enclosed envelope area calculated.
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Target Geometry For Horizontal Cylinders
18. In reference Frame 1 (previously defined for spherical geometry)
the fluid velocity field is given by the following equations5 :
1 L2(X 2 - Z 2) ' ,'Ux = U [37] "
r4
Uy =0 [38]
-2UxzL2
uz =[39]r4
where r = (x2 + z2)1/2 [40]
It is readily deduced from these equations that the particle motion will be
confined to the x-z plane provided that the initial particle velocity in
the y direction is zero. That velocity was set to zero in accordance with
the previously stated initial conditions; therefore, this problem was two-
dimensional.
19. As with the spherical geometry, Frame 2 was defined and used as
the main frame in which all motion and envelope calculations were made.
Due to the planar motion, the envelope was only one-dimensional, requiring
only an 'upper' and a 'lower' boundary to be calculated (Figure 7). This
case is consequently very much simpler than that of the spheres.
Target Geometry For Vertical Cylinders
20. The theory here is essentially the same as in the horizontal
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cylinder case. The only change involves the flow field which was changed
to the x-y plane from the x-z plane in Frame 1 (Figure 8). The flow
equations are:
mU"L2 (X2 - 2)
-u u - • [40]
-2UxyL2
Uy= - [41]y r4
Uz :0 [42]
where r = (x2 + y2)1/2 [43]
21. The combination of an infinite vertical cylinder with the
required five target radii starting position from the cylinder, removed the
usefulness of Reference Frame 2. Therefore, Frame 1 was chosen as the
frame for motion and envelope calculations. Due to the motion symmetry
about the x-axis and the z-axis, only a y-boundary needed to be calculated
for the envelope; clearly, any z-coordinate starting position will result --
in a similar trajectory that differs only by a fixed z-direction
displacement.
Target Geometry For Man Simulation
22. This simulation was rather crude, and it comprised many
simplifying approximations (Figure 9). First, a vertical cylinder of
approximate man dimensions was used since the determination of the flow
field around a man was much too complicated a proposition for this project.
Second, the flow field of an infinitely long cylinder was used because a
calculation of end flow conditions around a finite cylinder was deemed too
complicated for a first approximation model like this one. Third, theparticles which impacted on the top of the cylinder were ignored.
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23. A major component of this model was the inclusion of a wind
gradient to mimic the Earth's own boundary layer. Essentially, the
horizontal windspeed is a function of height above the ground. The
equation used was:
UI(Z) = U1 (zl' [44]
The base point (Z, UI) scales the curve; for this application, the basis
used was:
Z, = 5.0 m [45]
U' = 1.0, 1.5, 2.5, 5.0 and 7.5 m/s [46]
Therefore, five tests were conducted at five different reference
windspeeds.
24. The flow equations for vertical cylinders, equations [40] to [42]
were modified for this simulation by replacing the factor U with U(Z) as
defined in equation [44]. The resulting flow equations were: --
1 / 7 L2(x2 y2jUx U 5 )' r1 4 [47]
UY 1 , .2L2 [48]
Uz =0 [49]
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25. As for the vertical cylinders, Reference Frame 1 is used for all
motion and envelope calculations. The presence of the wind gradient
destroys the problem symmetry in the z-direction; therefore, the envelope
on the starting plane was necessarily two-dimensional. Its calculation was
quite similar to that of the spherical targets. Specifically, the bounds
in the z-direction were found by the half interval method, then the y-
bounds were calculated for eleven equally spaced z-coordinates over this
interval. The resulting boundary points (z,y) were then integrated to
yield the enclosed envelope area.
26. In order to relate the chemical concentration on a man to that
which falls on the ground, an extra number was introduced, termed the
ground fraction (G). It was defined by equation [50]:
Man Concentration = Ground Concentration x G [50]
(This man concentration is based on frontal cross-sectional area, not
surface area.)
Calculation of G combined the factors of collection efficiency with the
relative areas of impact regarding the target and the corresponding ground;
the equation was:
Collection Efficiency
tan
In this equation, a is a representative trajectory angle of all particles
in the envelope; note that the trajectories are not straight lines because
of the wind gradient. The angle a is that between the horizontal and the
line connecting the top of the 'man' to the top of the envelope.
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Computer Programs
27. During the course of the project, several computer programs were
written. Four collection efficiency programs were written; one for each
geometrical case. Two programs were written to tabulate and plot chemical
particle trajectories for the sphere and horizontal cylinder cases; these
programs were used primarily for verification of the motion model. Final-
ly, a number of utility programs were written to tabulate and graph
results. All programs were written in the Honeywell FORTRAN-77 language
and executed on the Honeywell CP-6 computer at DRES.
28. The collection efficiency and trajectory plotting programs shared
many features, most importantly, the initial condition and motion
calculations. This redundancy, coupled with space limitations, has limited
the program listing in this report to just two representative programs:
AEROSOL-8 which performed the man simulation (Appendix A), and AEROSOL-6,
which performed the trajectory plotting for horizontal cylinders (Appendix
B). The only real difference between these programs and their sister
programs was in geometry; different target geometries required different
envelope calculations and sometimes different reference frames, as has been
illustrated in the previous section. Implementation of the background
theory on the computer was quite similar for the different geometries, and
will now be explained in detail for programs AEROSOL-8 and AEROSOL-6.
29. AEROSOL-8 was designed to accommodate five sets of test
conditions (the '700 loop', commencing line 50). The test conditions,
namely windspeed, target radius and chemical particle density, were
obtained from the data file AEROINFO. The program then proceeded to
calculate collection efficiencies for a range of particle sizes which were
stored in the array SIZE(1O). This loop (the '650 loop', commencing line
63) comprised four main sections: calculation of initial conditions (lines
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68-83), calculation of the z-direction envelope boundaries (lines 86-138),
calculation of the y-direction envelope boundaries (lines 141-161) and
calculation of resulting collection efficiency (lines 164-172). The
implementation of the background theory in these sections was relatively
straightforward except for the following points. First, in order to 0
implement the half-interval method, a starting position which results in
particle impact must be found; in the z-direction, it was searched for
(the '200 loop', commencing line 95), but in the y-direction it was assumed
that y=O resulted in impact since it lay on the target centerline and would
experience no sideways drag force. Secondly, preliminary calculations
showed that the y-bounds increased monotonically with increasing z-
coordinate, therefore the previous y-boundary value (variable YMEM, line
143) was used as the 'inside' position for the ensuing half-interval B
calculation. Finally, note that the problem was symmetrical about the y-
axis, requiring that only positive y-boundaries be calculated for the
envelope.
30. The TRAJECTORY subroutine comprised all of the motion calcula-
tions from initial conditions to a determination of particle impact or
miss. Upon receipt of the initial conditions, the subroutine sets up an
iterative loop (the '10 loop', commencing on line 244) to 'move' the . -
particle towards the target. The iteration involved five main steps:
calculation of local flow velocity (lines 248-252), calculation of
Reynold's number and Drag Coefficient (lines 254-279), solution of the
differential equations of motion over a predetermined time interval (lines
284-291), testing for impact or miss (lines 291-297) and adjustment of the
differential equation step-size if the iteration is to continue (lines 303-
305). Note that the step-size is governed by the choice of the variable
DT, not the IMSL routine OVERK, because the positional dependence of the A-
flow velocity requires frequent updating. DVERK could not accommodate non-
constant coefficients, and in practice performed only one step per call due
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to the choice of DT which determined the end condition TEND. This alsomeant that the OVERK accuracy parameter TOL was of no practical importance;
its assigned value of 0.01 was arbitrary.
31. The remaining two program subroutines require no detailed
explanation above the internal documentation notes. Note that a partial
output is included with the program listing in Appendix A.
32. AEROSOL-6 was designed to plot particle 'streamlines' near a
horizontal cylindrical target. It was restricted to one size of particle,
which can be arbitrarily set, and one set of test conditions. The
calculation of initial conditions (lines 64-84) was identical to that ofAEROSOL-8, with the exception of the ability to perform in a no gravity
environment; hence, this program could recognize and plot streamlines for ahypothetical no gravity situation. The motion analysis section (the '60
loop', commencing on line 105) was the same as that of AEROSOL-8.
33. The one aspect of AEROSOL-6 that differs from AEROSOL-8 was the
trajectory plotting. To fully understand the details of this plotting, one
must study the CALCOMP Electromechanical Plotters User's Manual (From
California Computer Products, Inc.). As far as this project was concerned,
CALCOMP provided a list of subroutines which could be called upon to drawgraphs; separate subroutines could draw axes, plot lines, print titles and
draw other graph elements. In AEROSOL-6, the arrays XVAL(500) andZVAL(500) were used to store the x and z coordinates of each successive
particle location. This data was then sent to the CALCOMP System and
plotted (lines 211-241). Examples of these trajectory plots as given in
Figures 10 and 11, and a sample output is included in Appendix B with theprogram listing.
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RESULTS
34. The computer generated collection efficiency results for all four
geometrical cases are listed in Tables l-VIII. Figures 10 and 11 show
trajectory pictures generated by AEROSOL-6. Figures 12-15 show
representative and comparative graphs based on the data contained in Tables
I-VIII. Although a detailed analysis of these results will be conducted in
the next section, the acquisition and content of these results require some
explanations. Note that all results are in W4S units unless otherwise
stated.
35. Sphere runs S1 to SlO, and horizontal cylinder results C1 to C10
were all performed under gravity and no gravity conditions to calculate the
effect of gravity on the problem. These results are listed side by side in
Tables I, II, IV and V. At the bottom of each double column are two sets
of numbers labelled 'maximum positive change', and 'maximum negative
change'. These are simply the greatest divergence values between the two
sets of data, recorded as either a positive or a negative divergence
relative to the gravity values. The numbers in brackets are the particle
sizes corresponding to those divergences.
36. Because spheres were the first geometrical case to be studied, a
few extra runs were conducted in order to evaluate the validity and the
accuracy of the motion model. The accuracy test, run S11, used half the
step-size as run S2 in order to check the numerical accuracy of the method.
In actuality, several accuracy checks were conducted, resulting in many
step-size modifications until the final accuracy level was achieved. The
similarity test, runs S12 and S13, was conducted in an attempt to validate
the motion model. According to the principles of fluid mechanics, tests
with the same set of non-dimensional numbers must yield identical results.
Here, there are three non-dimensional numbers which describe the problem:
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CD, Reo, F. These were kept constant for runs S2, S12, and S13, but the
constitutive parameters (U, L, F, P, g) were varied to learn whether or not
the results would change. A change in the results would indicate that the
motion model was flawed.
37. The computer time required for solution of test runs varied
considerably with the problem geometry. The one-dimensional nature of the
horizontal and vertical cylinder envelopes resulted in very little computer -
execution time, typically ten minutes or less per test. (By way of
clarification, a 'test' refers to the calculation of collection
efficiencies for all ten particle sizes under a given set of windspeed,
target size and particle density values. Each column in Tables I-VIIIk represents one test.) The two-dimensional envelopes for the sphere cases
typically required one and a half hours per test. The man simulation was
somewhat peculiar. Because the particles travelled almost horizontally in
test M1, it required only twenty minutes; but the more vertical
trajectories of test M4 and M5 resulted in much longer trajectories (note
that the horizontal distance travelled remained constant so as to minimize
the cylinder flow perturbation at start) and execution times of up to six
hours per test. Actually, the collection efficiencies for the 2000 on
particle were not calculated for tests M4 and M5, and the 1000 pm particle
collection efficiency was not calculated for MS. The reason was that hours
of execution time would have been required for each particle, a cost which
was not thought to be worthwhile. The absence of these three values is
indicated in Tables VII and VIII by a negative value.
38. Finally, note that the graphs plotted in Figures 12-15 were done
using small plotting programs written during the project. These programs
are not listed in this report.
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~ ~ ~~~~~~~~~~~~~ -. -''-" -. -' - -. -" -, -.. -. - -... . .... , . . -,. -
o
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DISCUSSION
39. The computed similarity and accuracy test results (Table III)
verified the motion model and provided an indication of its accuracy. The
accuracy test clearly showed that numerical accuracy improved with
increasing particle size. This was because larger particles were less
affected by drag forces, and it was the drag force which exhibited non-
linear behaviour with position, making it the most difficult aspect to
numerically approximate. This also accounted for the observation that all
errors were positive, because the total influence of the drag force (and
hence the greatest particle deflection) will only be attained in the limit
as the number of steps approaches infinity. Hence, the drag force was
underestimated by this model. Since the overall collection efficiency was Apo.
the chief result sought, the relative error was of less importance here;
that is to say, the large relative error of the smallest particles was made
insignificant by the very small collection efficiencies involved. Based on
the absolute errors tabulated, the maximum error present in the
calculations was on the order of + 0.003 for the collection efficiency (+
0.3% for the values in Tables I-VII). It should be noted that the computer
model worked to four significant digits in distance values (0.1 mm or 100
pm). Since the targets were generally 0.1 m in radius, 0.1 mm represents .
an accuracy to 0.1%.
40. The results of the similarity test were within numerical error
for all three runs, provided that one qualification to the collection
efficiency error value of + 0.003 be accepted; specifically, that the
absolute collection error was a function of the target size in addition to
step-size. It seems plausible that the relative magnitude of the step size
to the target size would influence numerical accuracy, since an increase in
the target size would attenuate the rate of change of the drag force over
distance, allowing a greater accuracy for the same step size. As proof,
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note that the S12 and S13 results are within .003 of each other, with the
S13 values uniformly lower; this suggests that its larger target radius
(L=0.15) improved numerical accuracy, since the step sizes were equal.
Conversely, the small target size of test S12 seemed to have degraded
numerical accuracy; the S12 values were up to .008 higher than the S2
values. In summary, the results of tests S2, S12 and S13 were deemed
sufficiently close as to be judged the same to within numerical error.
41. Figures 10 and 11 qualitatively demonstrate many of the aspects
of this motion problem. The smaller particle (Figure 10) showed a mostly
horizontal trajectory which indicated low terminal velocity. Close to the
cylinder, all trajectories were substantially deflected to the extent that
I. only one particle impacted on the cylinder. This was an indication that
the collection efficiency would be low for this small (50 sin) particle.
Figure 11 demonstrated the aspects of large particle motion. The trajec-
tory was much steeper due to a higher terminal velocity. There was almost
no particle deflection; consequently, one would expect a high collection
efficiency for this large (250 pm) particle. Reference to run C4 which hadthe same test conditions as in Figures 10 and 11, yielded the expected
magnitude of collection efficiencies: a low 14.11% for 50 pm, and a high
93.70% for 250 Pm. The qualitative model verification by these and many
other trajectory pictures supported the similarity tests and led us to
conclude that the motion model was valid.
42. The collection efficiency test results for spheres and cylinders
yielded many noteworthy features, most of which will be discussed in the
next few pages. We will start with the effect of gravity on the motion
results.
43. All of the sphere and horizontal cylinder tests (Si - SlO and C1
-C1O) produced results similar to that shown in Figure 12. The sigmoidal
UNCLASSIFIED
o
UNCLASSIFIED /21
shape of the curve agreed with the previous theoretical work. 7 The most S
notable feature of the double curve plot in Figure 12 was the crossing of
the two curves between 100 im and 250 tim particle sizes; this was thoughtto be due to the following reasons. For larger particles, gravity caused
the particles to fall with a terminal velocity close to or greater than the
horizontal free stream velocity. Hence, the particle's inertia was
significantly greater, rendering the particle much less susceptible to
deflection by the diverging fluid streamlines around the target. This
resulted in a collection efficiency with gravity, as evidenced by the .
larger particles in Figure 12.
44. The gravity-decrease effect on the smaller particles was much .
more difficult to explain. First, the terminal velocity was low, virtually
insignificant compared to the free stream velocity; therefore, the
particle's inertia was not noticeably higher. This allowed a second factor
to make a discernible impact on the motion; this factor was a motion
asymmetry around the target due to gravitational effects. The envelope
results for test C3 (Table 9) illustrate this asymmetry. It can be seen
that gravitational effects decrease the upper bound more than they increase
the lower bound for particles of 50 - 100 tim, which was the range of the
gravity decrease effect in Figure 12. The explanation of this asymmetry
was as follows. Near the upper boundary, the fluid streamlines are
deflected upwards by the target, in effect flowing crossways to the
particle motion vector, thereby increasing the local Reynold's numbers and
hence the drag force, resulting in a smaller boundary. At the lower .
boundary, however, the fluid streamlines are deflected in the direction of
the particle motion vector (that is, diagonally downwards) thereby reducing
the local Reynold's number and the drag force, resulting in a larger
boundary. The non-linear nature of the problem was such that the former
effect was greater than the latter effect, resulting in lower collection
efficiencies for particles in this motion regime when gravity was included.
UNCLASSIFIED
UNCLASSIFIED /22
45. Generally, gravitational effects altered collection efficiencies
in these tests by less than ±3% (Tables I, II, IV, V). The exceptions were
tests involving low windspeeds, speeds of 1.5 m/s or less. The greatest
difference was found in test S5; there, gravity added 21.2% to the
collection efficiency of 100 wm particles. Note that the crossover point
between the gravity and no gravity curves in this test was not present; all
differences were positive. Generally, the crossover point decreased in
particle size with decreased windspeed.
46. In summary, the gravity effect on collection efficiencies was
negligible except in cases of low windspeed. Other facets of the sphere
and cylinder studies will now be explored.
47. Figure 13 compared the collection efficiencies of the vertical
cylinder, the horizontal cylinder and cylinder no gravity cases, under the
same test conditions. (Note that in the absence of gravity, the vertical
and horizontal cylinders were geometrically equivalent.) The crossover of
the no gravity and horizontal cylinder curves occurred at 500 Am; the
gravity effect was minimal here as would be expected from the high
windspeed. The vertical cylinder curve was lower than either of the other
curves, except for a brief particle range around 100 pm. The reduced
collection efficiency was easily explained: as particles approached the
cylinder, they initially deccelerated, thereby increasing the trajectory
angle relative to the horizontal (the terminal velocity remains almost
constant) and provided more time for the diverging fluid streamlines to
deflect the particle. The exception at 100 om was probably a result of the
asymmetrical particle flow around the horizontal cylinder, postulated
before as the explanation for the gravity-decrease effect. The vertical
cylinder possessed symmetrical flow conditions and was therefore not
affected. However, the steepening trajectory effect with vertical
cylinders still lowered the collection efficiency relative to the no
gravity case; the reduction was just marginally less than that of the
horizontal cylinders.
UNCLASSIFIED
. . . . . .. .. .. .. mill d I3
UNCLASSIF IED /23
48. Figure 14 compared the two cylinder geometries to spheres, under
slightly different test conditions than in Figure 13. Spheres clearly
possessed higher collection efficiencies than cylinders for all particle
sizes. This can be understood in light of the fact that cylinders perturb
the flow more than spheres, in the sense that cylinders represented a
greater obstacle to the flow and thus cause faster fluid motion around the
periphery. This larger fluid velocity represented a greater drag force
which tended to deflect the particles away from the target; hence, the
collection efficiencies were lower. The relationship between the vertical
and horizontal cylinder curves was the same as in Figure 13 except that the
difference here was smaller because of the smaller target size. It should
be noted that Figures 13 and 14 were representative of all of the test
results listed in Tables I to VI, and were not just the product of those
specific test conditions.
49. Some general observations on the sphere and cylinder studies will
now be made. In all three cases, a decrease in windspeed resulted in
reduced collection efficiency for any given particle size. Evidently, the
reduced drag force was more than compensated for by the decrease in
particle inertia. Increased particle density appeared to merely shift
collection efficiency values from larger to smaller particles;
equivalently, plots of collection efficiency vs log (particle radius) were
translated left. The reason for this was that particle terminal velocity
and inertia were increased, rendering the particles more difficult to
deflect. A reduction in target size had the same effect as increased
particle density. The explanation in this case, however, was that larger
targets create more far-reaching flow perturbations, the net effect of
which was subject to incoming particles to greater deflecting drag forces;
conversely, smaller targets resulted in less deflecting drag forces.
50. The remaining discussion will focus on the man simulation
results. Although the ground fraction values are of most importance here,
UNCLASSIFIED
UNCLASSIFIED /24
a brief comparison of the collection efficiency results in Tables VI and
VII needs to be done. The only difference between the two tests was that
the 'M' tests (Table VII) incorporated a velocity gradient from the ground
up. This velocity gradient significantly lowered the collection efficiency
for all particle sizes. The reason was that as the particles fell, the S
windspeed decreased which in turn decreased the particle's horizontal
speed. As in all previous cases of reduced windspeed, this must result in
reduced collection efficiency.
51. The ground fraction results demonstrated several noteworthy
features. Most striking were the greater than unity ground fractions for
some of the particles in high windspeed tests. This was due to almost
horizontal particle trajectories for these cases; near horizontal
trajectories will result in low ground concentration since the particles
will be distributed over a large area. Clearly, objects standing
vertically in such a situation could receive greater concentrations than -
the ground. 0
52. Figure 15 showed three curves corresponding to tests M1, M2 and
M3. The central peak in each curve resulted from the interaction of two
effects. For small particles, the collection efficiency was so small that
the ground fraction was zero; for large particles, their near vertical
trajectories meant that relatively few could impact on the vertical sides
of the cylinder, so that the ground fraction was again near zero. Both
ground fraction reducing effects decreased toward the opposite end of
the particle size spectrum; therefore, the largest ground fractions
occurred in the middle region, in which neither effect dominated. This
peak migrated from 50 lim in the upper curve to 100 wm in the lower curve.
53. The tremendous effect of windspeed was well illustrated by Figure
15. The lower windspeeds possessed very low ground fractions; note that a
maximum ground fraction of 0.17 was calculated for the 1.0 m/s windspeed
UNCLASSIFIED
_o
UNCLASSIFIED /25
case. The reason for this was that particle trajectories were near S
vertical for such low windspeeds; hence, little particle impaction could
occur on the vertical cylinder sides.
54. The man simulation model in this project was undoubtedly crude. 0
Nevertheless, the essential aspects of this kind of man simulation problem
were believed to have been demonstrated, even though the flow geometry was
drastically simplified. Some speculative conclusions will now be drawn
from the ground fraction data. S
55. The curves of Figure 15 indicate that the largest aerosol
particles are not suitable for impacting on a standing man; in fact, the
best particle size is around 100 pm. This must be viewed in light of two ,
important qualifiers: first, the smaller particles will travel further from
the dissemination point, resulting in lower ground concentrations to begin
with; and second, aerosols from materials with some volatility will tend to
evaporate as they move downwind, so that the smaller particles might •
disappear altogether. Note that the evaporative characteristics will also
influence ground persistence of the chemical, which is another vital
consideration. Nonetheless, these ground fraction results suggest that an
upper limit for ideal particle size for impaction on a man may exist. P
56. The subject of man motion under this kind of chemical particle
bombardment was not considered in the project. Although authoritative
comments will have to wait until detailed work is done, there is one S
speculation that needs to be recorded here. Specifically, if the man were
walking in the direction of the wind, the particle trajectories would
assume a more vertical shape in the man's frame of reference. This would
be equivalent to a man-stationary, reduced windspeed problem such as was
studied in this project; and according to those results, the ground
fraction, and hence the man contamination, would be reduced. Incorporation
UNCLASSIFIED
-S
UNCLASSIFIED /26
of a moving target into this simulation model is a logical next step for
research, one that would help to resolve the speculation suggested above.
CONCLUSIONS
57. The numerical tests conducted with spherical cylindrical targets
indicated that gravitational effects altered the collection efficiencies
insignificantly, on the order of t 3% (absolute), provided that the free
stream velocity was 2.5 m/s or higher. Lower free stream velocities A
resulted in much greater gravitational effects, up to 21.2% (absolute) for
100 im particles impacting on a spherical target. Changes in the particle
density and target size were found to have a negligible effect on the
importance of gravity in the problem. D
58. The man simulation tests indicated that a man would receive the
most chemical relative to the ground concentration for particles on the
order of 100 im radius. In fact, he could receive up to 6.9 times the A
ground concentration. Although there were mitigating factors, the analysis
suggested that an upper limit may exist for the ideal particle size in
considering impaction on a standing man.
ULS-
UNCLASSIFIlED
0
UNCLASSIFIED /27
REFERENCES
1. Mellsen, S.B., "The Impaction Force of Airborne Particles on
Spheres and Cylinders", Suffield Technical Paper No. 486, 1978,
UNCLASSIFIED.
2. Saucier, Richard, "A Mathematical Model For Liquid Impaction On A
Moving Vehicle", Technical Report ARCSL-TR-82046, Chemical
Systems Laboratory, Aberdeen Proving Ground, Maryland, 1983
UNCLASSIFIED
4. Prandtl, L. and Tietjens, O.G., Fundamentals Of Hydro- and
Aeromechanics, Dover Publications, Inc., New York, N.Y. (1957)
pp 149-151
6. Wark, Kenneth and Warner, Cecil F., Air Pollution: Its Origin and
Control, Harper and Row Publishers, New York, N.Y. (1981) p 84
7. Friedlander, S.K., Smoke, Dust and Haze: Fundamentals of Aerosol
Behaviour, John Wiley & Sons, Inc., Toronto (1977) pp 104-109
UNCLASSIFIED
-1
UNCLASSIFIED SM 1102
'' F) ') CY. C)(' N -4 " .10
s . tip 0* r-. a:
L"j. L Is~ -I (o U 0 0 co, 0) C
+
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vl i r- r 0' 4) P-If (A) 0-
C'. C' .f) -4.. IN 0- 4.) LP, Ar%
U) ~ ~ t L-) C)C-4-it .'0i .~ 00 L.) (JC
(l t)0 ' 0 ') JU0 0 a i
U, C
C/)AJl C t 0 LI) U-1 p,0'C) L3 C)-s r-It" rJ- 0-C-1 N-
C)L 0. . . . . . l
C)) (-4 *- 10 0) -l EN
EN) 00-0-03 0
I LA. . . I.)
W - ") J) rxj %,k) u- U, 0-F' )
_jCC.L Li (I - )O-NU 7 o* * 0)1.w
u- (f) ZAS. ' ) C ) L -
Iii U. - 4 (10. c . r t.If\ - +=- (-.Q ( '( j l r\ - In -0 ) 1"I ~
c- it: u, V LiiP . .
>-4 :
fl ~ 4 (.7C') - O'* (Y) 0'
L.3 N C-) LiC 0) 4jYlr)Y0,L
I In* 1 l A
(\A C)) I'l C 1: C) 1- 0; C)- < - .-'LII ' N- r C- C i'LY (3, fr ;P
i ClIL) LJJ-
-'X -ZC~ * C) Q7i ILI 4 ClJi
t.) 9x I- In * r L* * L. C. t* * -* j * Zi z3 zi 1 LI;L-C n 4 z (NJ In P, ( C3E-)C) <1. < 1-1
frL n. <-s- .. rc
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Q -s4. uf' C) 'fl ) 0'% P l 01 ,
1 Ir-1u r L C') 01 01 U, (.1
(,j r-1 r- CD co) IV L) In Lo-
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C- 4-3 Q w ky 0* (Y * p 9
Cl) (0J I) 'Q T'4 V1 0 -0. )' + -0 '
(.J -4)c- ~u' ' r '- po tiY icp - s- I -
iii II (- . n 4 C I M.*
U) CID L ) I' '4. Q,* 001 01 0 1C
"1.1 Li ) Lill o) - ' "1C'C-.-
I-I .xr-c v r. .
Li I C) *j 0 M p0 Ir
_( 4v zr.,If 0 .) a) 01" 0' - ' ILI
II
uj~~~~A (A) 0 r p 0
c 4' * .) L I') "- V A 01 C' (' 17' C)-.). t. L) ftLL.A> 2 .w C.0 0 a 0C) 01 01 'C3 CD'. W~
In -'q:3 -4 uN-C-A- Lt I-"-'
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QLi
w L-J
UNCLASSIFIED
TABLE III
MISCELLANEOUS SPHERE RUNS
ACCURACY TEST SIMILARITY TEST
S2 Si ABS. REL. S2 S12 S13
ERROR ERROR
U 5.0 5.0 U 5.0 5.0 5.0
L 0.1 0.1 L 0.1 0.05 0.15
F 25.5 25.5 F 25.5 25.5 25.5
P 1000 1000 P 1000 500 1500
9 9.81 9.81 g 9.81 19.62 6.54
PARTICLE PARTICLE
RADIUS RADIUS
10 .00044 .00032 .00012 37.5% 10 .00044 .00156 .00020
15 .00640 .00515 .00125 24.3% 15 .00640 .01010 .00493
25 .11263 .11008 .00255 2.3% 25 .11263 .12058 .10988
50 .44986 .44751 .00235 0.5% 50 .44986 .45592 .44775
75 .63808 .63635 .00173 0.3% 75 .63808 .64261 .63666
100 .74054 .73904 .00150 0.2% 100 .74054 .74426 .73934
250 .92237 .92182 .00060 0.06% 250 .92237 .92443 .92158
500 .97778 .97771 .00007 0.007% 500 .97778 .97978 .97725
1000 .99656 .99656 - - 1000 .99656 .99792 .99603
2000 1.00032 1.00032 _ _ 2000 1.00032 1.00217 1.00001
L
UNCLASSIFIED
. . . . . . . mm . . . . . . . . . . . . . . . . . . nl . . . . . . . . .
UNCLASSIFIED SM 1102
4J 1- 4 '" '-' Zrrroo( )J LI U ) u"'- In C:
I- Y ' -4 - -.1u
f T I 1 r . (1 0 .V. V
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In If' I) C C )
Ini . . C .~i-~ 1 CD PI) cl 0 0
r- r f 11 .0. . 0.O
U- I . I' S ~~c * * * * * I
4-P ".cj (3 SU, I~ I-*(n
1-~' c) c. CCD..IAf ('j2~ O . '
-. j W~ z(I u,- fl.J u-, (7Oy(
CN 4I ) .) ~x C 0 i
c) 01C)0 N UJ'4W )' 14
v)~~i If 0' 0-tC.U?-4_> -
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01 . . . .7 S * * * l ,
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51UNCLASSIFIE-,
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UNCLASSIFIED
-7S
UNCLASSIFIED
TABLE IX
ENVELOPE RESULTS FOR TEST C3
PARTICLE UPPER LOWER NO GRAVITY
RADIUS BOUND BOUND BOUND
(microns) (Mn) (Mn) (Mn)
10 -.0003 -.0005 t.0001
15 -.0008 -.0010 .0001
2E -.0006 -.0039 .0016
50 +.0162 -.0299 .0236
75 +.0314 -.0523 .0439
100 +.0435 -.0668 .0579
250 +.0827 -.0967 .0873500 +.0971 -.1004 .0959
1000 +.1004 -.1009 .0994
2000 +.1019 -.1019 .1014
The boundary values listed here are z' co-ordinates (Frame 2). The target _
was 0.1 mn in radius.
UNCLASSIFIED
UNCLASSIFIED SM 1102 S
EXPLOSIVE DISSEMINATIONOF CHEMICAL AGENT
PARTICLE MOTION0- 'AND EVAPORATION
6 0'
lao.-
Figure 1
OVERVIEW OF CHEMICAL MOTION PROBLEM
TARGET CENTERED
U
x
GROUND LEVEL
Figure 2
REFERENCE FRAME 1
UNCLASSIFIED -
UNCLASSIFIED SM 1102 S
I
xTARGET
STARTINGPLANE .
Figure 3
COLLECTION ENVELOPES
P1
P 5-P3
P2(
TARGET
STARTINGPLANE
Figure 4
HALF-INTERVAL METHOD
UNCLASSIFIEDboa
UNCLASSIFIED SM 1102
FRAME 0O- (x, 1, W)FRAME 1 -~ (x, ,z) 1
THE X-AXIS IS OUT OFTHE PAGE
Figure 5
SPHERE REFERENCE FRAMES 0 AND 1
aLS f
FRAME 2 Wx, y', z')
THE Y' (AND Y) AXIS/ IS OUT OF THE PAGE
*STARTING TRE
/ PPANE: X 9
Figure 6 x
SPHERE REFERENCE FRAME 2
UNCLASSIFIED
...- .....UNCLASSIFIED SM 1102 -
zAS" UPPER
.- BOUNDARY
LOWER 0BOUNDARY p
S.-!
•STARTING' " X
- PLANE ..
Figure 7 X
HORIZONTAL CYLINDER GEOMETRY
STARTINGLINE
Y-BOUNDARY
wx
V I
oo INFINITEI JCYLINDER
TYPICALSTARTING TRAJECTORY
LINE w X
(INTO PAGE)
Figure 8
VERTICAL CYLINDER GEOMETRY
UNCLASSIFIED
UNCLASSIFIED SM 1102
STARTING IPLANE
I INFINITE CYLINDER(TRUNCATED TO
II MAN HEIGHT)WIND
GRADIENTI
Y ~ 1.8 m
0.9 m
0.36 m
Figure 9
MAN SIMULATION GEOMETRY
UNCLASSIFIED
UNCLASSIFIED SM 1102
0;
(A
F 0 UE
PATCESZ= 0 MCOS WNDPE=J5/
UNLSSFE
.... - r r r r.rr" .-
S
UNCLASSIFIED SM 1102
;. AX I ...
o p
\ p0.4 -•S -J - --.~ -. 5 00 -0 .3 009 0 n o
\ --I
F GURE IPARTICLE SIZE= 250MICRONS WINDSPEED= 1 .5m/S
U S
UNLSSFE
o "/!-
\2
UNCLASSIFIED SM 1102
A0
0 0
0
LLJ
C)
0;o 0 ' ;0 0 ;C io 0 o0J~~j3NI310
0NLSSFE
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cr0
iu-c 0
0c 0
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UNCASSFIE
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w 0
a_ 0w
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0; o o o 0',o 0; c 0 0a. o cio 0AJN~l~ljU3 NC 310
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~U- <i
- [L
r-C)
0
:)
0~
06 ~ ~ ~ ~ ~ ~ ~ ~ .. Di ,-Q c 0 0 ' 0 oo
N~ll3Vb LjnO?-
UNCLASIFIE
UNCLASSIFIED
APPENDIX A
LISTING OF PROGRAM AEROSOL-8 (MAN SIMULATION)
SAMPLE OUTPUT FOR
FIRST SET OF TEST CONDITIONS (RUN 1)
UNCLASSIFIED
UNCLASSIFIED Im10
(I I j L 1V I n k>
a- t- - - (.rj k
.- - eU~ ISILA - . :) I C
y 4/) s,.4 1341 u -x
n Q L.) ti Z I -3 -. 1 - >- .cs Lj: LN C) i LAI
% l 0, J 1i -.1 LIJ % (I s-. (D-
El Il ) _ LX I I i :>) UJ Z t4 I~I. nL -. 1 1 -1 -LI J U n-> 1l (1 LIt C) Lz I->-Lfy I %- AI(j .
- L- I ~ *i t. 4. 1-- -) :i 1,- i- .1( .1- V. C') .1. '-4 c) 5-):31. L x~ I- ILLJ ~LII 0I Ill X- tit 4< -. U12 %/ IS n ;
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APPENDIX B
LISTING OF PROGRAM AEROSOL-6
(TRAJECTORY PLOTS AROUND HORIZONTAL CYLINDERS)
SAMPLE OUTPUT OF MINIMUM TABULATION RUN
SAMPLE OUTPUT OF FULL TABULATION RUN (FIRST PAGE ONLY)
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I UNCLASSIFIED
B 4 __UNCLASSIFIEDThis Shoet Security Classification
DOCUMENT CONTROL DATA- R &DlSecu, .ly clesss*,cation of title. bodv of ablstract end Indesting annotation must be entered when the overall document is Woess'd)
I ORIGINATING ACTIVITY 2a. DONtJ~~?T CLASSIFICATION
DEFENCE RESEARCH ESTABLISHMENT SUFFIELD 2b GROUP
3DOCUMENT TITLE
AN INVESTIGATION OF PARTICULATE IMPACTION ON SPHERICAL AND CYLINDRICAL TARGETS (U)
4 DESCRIPTIVE NOTES IType of report and inclusive dates)
SUEEIELMMDRANAUTHORIS) fLeet name. first namse. middle initil)
JEFFREY L. HALL AND STANLEY B. MELLSEN
6. DOCUMENT DATE Augus 1984L 78 O PAGES b NO. OF REFSAuus 1984 78 7
b.PROJEiCT OR GRANT NO. go. ORIGINATORS DOCUMENT NUMIERISI
13E10 SUFFIELD MEMORANDUM NO.
lb CONTRACT NO. 9b. OTHER DOCUMENT NO.tSI lAny other numbers that may beassigned this documentl
10. DISTRIBUJTION STATEMENT
UNL IMI TED
11. SUPPLEMENTARY NOTES t2. SPONSORING ACTIVITY
13. ABSTRACT'
(U) This project was a theoretical investigation of particulate impaction onspheres and cylinders. The motion model developed was implemented on a computerand yielded results focused on two main goals: first, the net effect of gravityon particulate impaction was determined; and second, a man simulation was con-ducted. This simulation calculated to a first approximation the amount of chem-ical that would impact on a man subjected to a chemical attack.
Due-
UNCLASSIFIED __
FI is .;he-et Sectrity Classifilcatio n
KEY WORDS
AerosolChemical DefenceParticulate Impaction
INSTRUCTIONS
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lied. Ech paiagraph of the abstract shell end with anbi D)LLIME N I DAIt E ~ithe (t0re irionth. year)I of iiidication of the seiuuity classification of the information
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10-84
DTIC