A laboratory investigation of ground erosion and dust generation by air cushion vehicles

Journal of Terramechanics, 1979, Vol 15, No 4, pp 185 to 206

0022-4898/78/1201-0185 $02.00/0

Pergamon Press Ltd. Printed in Great Britain International Society for Terrain Vehicle Systems

A LABORATORY INVESTIGATION OF GROUND EROSION AND DUST GENERATION BY AIR CUSHION VEHICLES R. J. KIND*,M. SEP* and J. Y. WONG* Summary--The erosion process which occurs when an air cushion vehicle (ACV) passes over certain types of surface material has been investigated. Experiments were conducted in laboratory apparatus which simulates conditions under the edge of an ACV skirt. Tests were carried out on three samples of dry erodible materials for a variety of cushion parameters. Representative photographs and data on time rates of erosion are presented. The results indicate that erosion rates are proportional to cushion pressure to the power 3/2 and that skirt angle, hoverheight and time since start of a run are of secondary importance. The results and analysis indicate that erosion rates are independent of particle size when this exceeds about 0.1 ram. 1. I N T R O D U C T I O N

AIR cushion vehicles (ACV's) are at times required to operate over surfaces consisting of loose or erodible granular material (e.g. dust, dry earth, sand, loose snow). The air escaping from the cushion at the skirt/ground interface tends to 'pick up' such material and throw it or carry it into the air surrounding the ACV. A cloud of particulate material is thus formed. The height to which particles rise and the length of time they remain in the air depend on particle size, density and shape and on the nature of the air flow under the skirt edge and around the ACV. Dust particles, for example, can reach heights well above the top of the ACV and can remain in suspension for periods of 10 min or longer [1]. This phenomenon is undesirable for a number of reasons. It necessitates provisions to prevent detrimental ingestion of particulate material by humans, engines, lift fans and other machinery. Large persistent dust clouds in the wake of an ACV seriously impair the visibility of other users of the right-of-way. In potential agricultural applications not only is the particle cloud undesirable, but erosion of soil cover from plant roots would also be a problem. Little information has been reported on the phenomenon outlined above. This paper describes a preliminary laboratory investigation into one aspect of the problem, namely the processes occurring near the skirt/ground interface where the particulate matter is picked up by the air escaping from the cushion. Experiments were conducted in an apparatus in which airflow like that under the edge of an ACV skirt can be produced. Samples of erodible material were placed in a horizontal layer in the apparatus and the erosion processes which occurred near the skirt edge were recorded *Department of Mechanical and Aeronautical Engineering, Carleton University, Ottawa, Canada KIS 5B6. 185

186

R.J. KIND, M. SEP and J. Y. WONG

photographically and subsequently analyzed. Tests were carried out on three samples, namely a coarse sand, a fine sand and a very fine powder. Cushion pressure, skirt angle and initial hovergap (the gap between the lower edge of the skirt and the erodible surface) were varied. Representative photographs and data on time rates of erosion are presented. Also reported are some preliminary observations on deflector devices intended to reduce the density and/or extent of the particle clouds produced by the escaping cushion air. The tested samples were homogeneous and cohesionless and thus relatively simple compared to many erodible surfaces that might be encountered in practice. It was felt advisable, however, to keep complexity to a minimum since the tests were a 'first look' at the phenomenon. The experimental results, together with observations of sample behaviour during the experiments, provided some insight into the phenomenon of erosion at the edge of ACV skirts. Certain parameters are shown to be of relatively minor importance and explanations for this are developed in the paper. 2. DESCRIPTION OF TEST PROGRAM AND METHODS 2.1

Generaldescription of apparatus

Figure l shows a schematic diagram of the apparatus and Fig. 2 is a photograph of it. A 6 in. (15.2cm) deep layer of the erodible material being used for the tests could be placed in a 6 in. (15.2cm) wide by 40 in. (101.6cm) long by 18 in. (45.7 cm) AIR INLET

ill

D,F USER

,~[HEIGHT 305 cm [ 12 in. ~

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111

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Am 101.6 cm 40 in.

-I

N 15.2 cm

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SECTION A-A

FIG. 1. Schematicdiagram of apparatus. deep box, one side-wall of which was transparent. A moveable 6 in. (15.2 cm) wide divider plate was installed across the box, about 12 in. (30.5 cm) from its left hand end; this divider plate represented the skirt of an ACV. Its angle was adjustable between 0 ° (vertical) and 45°; it could also be raised and lowered to adjust the gap (i.e. the hovergap) between its lower edge and the surface of the erodible material. The two edges where the divider plate met the side-walls of the box were sealed with felt to prevent air leakage. The space between the left end-wall of the box and the divider plate was supplied

GROUND EROSION AND DUST GENERATION

187

FIG. 2. Photograph of apparatus. with air from a blower. This air entered from a wide-angle diffuser which was fitted with several screens to ensure uniform flow from the diffuser exit. The air left the space via the hovergap under the divider plate. The cross-sectional area of the space to the left of the divider plate was much greater than the area of the hovergap; this space was thus effectively a plenum (negligible air velocity) and the flow under the divider plate was thus similar to that under the edge of the skirt of a plenum-chamber cushion system. The static pressure in the plenum region to the left of the divider plate was equivalent to the cushion pressure under an ACV. Atmospheric pressure prevailed on the right-hand side of the divider plate (or skirt). The cushion pressure could be varied between about 0.1 to 1 psi (0.690-6.90kPa) by suitably adjusting a butterfly valve and by-pass valve in the duct between the blower and the aforementioned wide-angle diffuser. Pressures below 0.1 psi (0.690 kPa) could be achieved by installing a porous cloth diaphragm in the duct. The duct was also fitted with a shut-off valve. The cushion pressure was monitored using both a U-tube manometer and a 0-1 psi (0.690-6.90 kPa) pressure transducer whose output was led to a strip-chart recorder.

188

R.J. KIND, M. SEP and J. Y. WONG

2.2 Scope of tests The test p r o g r a m m e consisted o f the following parts: Visualization, using smoke filaments, o f the flow under the edge of the skirt. This w o r k was intended to confirm that the flow under the skirt did not exhibit any unexpected behaviour. Measurement o f the m i n i m u m cushion pressure required to initiate erosion for each o f the three samples o f erodible material used in the tests. Detailed observations o f erosion using three samples o f erodible material and a variety o f cushion parameters. The main effort was devoted to this part o f the test p r o g r a m m e . The test conditions are summarized in Table 1. Figure 3 shows the particle-size analysis and other properties o f the three samples o f erodible material.

100

SPECIFIC

BULK

GRAVITY

DENSITY

1 COARSE SAND

2,7

1.8g/cm z

2 FINE S A N D

2.7

1.7

3 FINE POWDER

2.3

1,0

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SIZE

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FIG. 3. Particle size analysis of samples. TABLE 1,

Sample coarse sand (18 runs) fine sand (18 runs) fine powder

SUMMARY OF CONDITIONS USED IN EROSION TESTS

Cushion pressure range (psi) high med. low high med. low low

(0.8--0.4) (0.4-0.15) (0.2-0.1) (0.8-0.4) (0.4--0.15) (0.2-0.1) (0.2-0.07)

Initial hovergap (in.) t, ½ t, ½ t, ½ t, ½ ¼, ½ ¼, ½ ¼, ½

Skirt angle (from vertical) 0°, 22½, 45° 0,22½, 45~ 0,22½, 45 ~' 0,22½, 45° 0,22½, 45° 0,22½, 45~ 0 ~, 45°

Preliminary tests to assess the potential effectiveness o f deflectors. Two deflectors were tested; they are shown in Fig. 4. The conditions used in these tests are summarized in Table 2.

GROUND EROSION AND DUST GENERATION

189

SKIRT

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3.375 in.

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2.9cm,1.125 in.

b, LABYRINTH DEFLECTOR RG. 4b. Diagram of deflectors.

TAn[,~ 2. SUMMARYOVCONDITIONUSEDIN DEFLECTORTESTS (the fine sand sample was used for all these tests)

Deflector Simple (2 runs) Simple (2 runs) Labyrinth (2 runs)

2.3

Cushion pressure range (psi) reed. (0.4-0.1) low (0.15-0.03) med. (0.35-0.05)

Initial hoversap (in.) ½ ½ ½

Skirt ansle (from Vertical) 45° 0 45°

Initial gap at deflector edge (in.) 1½, 3 1½, 3 ½, 1

Test methods and data reduction

The flow under the skirt was visualized by supplying smoke to a rake of tubes in the diffuser which supplied the cushion air. Before introducing the smoke, the apparatus was run for a short period to produce an erosion trough under the skirt edge (see Fig. 5). Smoke was then introduced with the cushion pressure set at a very low value, to give low air escape velocity; this prevented both further erosion and break-up o f the smoke filaments. The minimum pressures required to initiate erosion were determined by gradually increasing the cushion pressure until erosion was visually observed to begin. F o r both sand samples this condition was quite distinct, repeatable and easily detectable;

190

R.J. KIND, M. SEP and J. Y. WONG

I

(a) h o = T

ho--

l1

;

8s=O

; 0s--45"

FIG. 5. Typicalflow visualization results.

for the fine powder the condition was not very distinct and repeatability was relatively poor. The sample surface was flat and level for these tests. The erosion test results were recorded on black-and-white film using a 35 mm motor-driven framing camera set to take exposures every 1/5 sec. The time interval between exposures was subject to an error of 10 ~ . A shutter speed of 1/500 sec was used. The duration of each run was three to four sec. Runs were initiated by opening the shut-off valve after the blower had reached its steady operating speed. The cushion pressure decreased progressively during each run as the hovergap increased due to erosion of material from the region under the skirt. The pressure transducer/recorder system was statically calibrated against a U-tube manometer; its frequency response was such that it was easily able to follow the variation of the cushion pressure with time. The method used in the erosion tests with the fine sand

GROUND EROSION AND DUST GENERATION

l

j

&X

191

=

ORIGINAL

SKIRT

-" -z2 I 2 J . F : 0

ACTUAL EROSION TROUGH PARABOLIC APPROXIMATION y=kx 2 k 4Ay = AX'~-~

FxG. 6. Parabo]ic approximation to erosion trough cross section.

sample were slightly different from the other tests in that a U-tube manometer was used instead of a pressure transducer to monitor the cushion pressure; these were the first runs to be conducted and a suitable pressure transducer was not available. Unfortunately the manometer was unable to follow the pressure varitaion early in the runs (~ < 1.5 sec). It was subsequently established however, that for given settings of the butterfly valve, by-pass valve and skirt angle the cushion pressure for a given instantaneous hovergap was virtually the same for both the fine sand and the coarse sand samples. This fact was used to deduce the cushion pressure existing at any given time during the fine-sand erosion test runs. After development, the film from the framing camera was projected, at life size, onto a grid using a standard slide projector. The depth and width of the erosion trough under the skirt were measured for each frame and the cross-sectional area of the trough was then calculated using the assumption that the cross-section was parabolic in shape (see Fig. 6). This area multiplied by the length of the trough gives the volume of material eroded by the air escaping under the skirt. A maximum error of about 15 % is involved in the assumption that the cross-sectional shape is parabolic; in most cases the error is only about 7 %. The methods and procedures used for the preliminary tests with the two deflectors were essentially the same as those used for the erosion tests as outlined above. Only qualitative results are presented for the deflector tests. 3. RESULTS AND DISCUSSION

3.1 Applicability of the results As discussed earlier, the flow in the apparatus should be similar to that under the edge of an ACV skirt. The experiments approximately simulated conditions under the skirt edge of a stationary hovering ACV or at a fixed point under the side skirt of a forward-moving ACV. One shortcoming of the simulation was that the hovergap under a real ACV tends to remain constant while that in the erosion tests increased with time because the skirt was unable to settle into the erosion trough as it became deeper. Another shortcoming which stems from the first was that the air flow rate and cushion pressure varied with time during the erosion test runs. Figure 7 shows a

192

R.J. KIND, M. SEP and J. Y. WONG COARSE S A N D : ho= 1.3cm. 0.5 in Os= 45:

sec

L

3

I

I

~

2

1

psi 04

kPa

03

li'

0.2 01 ()

0

TIME

FIG. 7.

Typical cushion pressure-tzme trace.

typical trace of cushion pressure vs time. Fortunately the results indicate that their usefulness is not seriously affected by either shortcoming. 3.2 Flow visualization Two photographs typical of the flow visualization results are shown in Fig. 5. These photographs showed that the flow under the skirt behaves as one would expect. That is, the cushion air accelerates rapidly near the hovergap and leaves the cushion as a jet sheet which remains attached to the ground surface until the flow reaches the berm of the erosion trough. As is typical of flow through orifices, the flow contracts somewhat after passing under the edge of the skirt so that the thickness of the jet sheet is some fraction of the hovergap height. The maximum air velocity near the ground surface thus occurs slightly downstream of the skirt edge, at the so-called vena contracta where the jet sheet is at its thinnest. Downstream of the vena contracta the jet sheet slowly thickens and its mean velocity decreases, due to mixing with ambient air and shear stress at the ground surface. 3.3

M i n i m u m cushion pressures to initiate erosion

The measured cushion pressures which were just sufficient to cause erosion are given in Table 3. Unfortunately these pressures are very much lower than those typically used in practice. TABLE 3.

MINIMUM CUSHION PRESSURES REQUIRED TO INITIATE EROSION

Cushion pressures (psi) Sample

Observed

Coarse sand

0.01

Fine sand

0.006

Fine powder

0.05

Calculated 0.005 (C: = 0.0055) 0.0015 ~c: = 0.O055) 0.008

((7: = 0.0025)

It is interesting that the cushion pressure required to initiate erosion of the fine powder exceeds that for the fine and coarse sands. This result is consistent with the established fact that the wind speed required to cause blowing of sand or soil is a minimum for a particle size of about 0.1 m m (particle specific gravity 2.7) and is higher for both smaller and larger particle sizes [2, 3]. The conditions at which the

G R O U N D EROSION A N D D U S T G E N E R A T I O N

193

fine and coarse sand samples started to erode were fairly distinct and easily identifiable and erosion proceeded in an orderly and uniform fashion under the skirt edge. This was not the case for the fine powder sample. Erosion of the powder started with small chunks, not individual particles, of powder being blown away at a few scattered points and then no further activity until the cushion pressure was increased. This process was repeated with increasing intensity after each increment in cushion pressure, the erosion process finally becoming sustained, though still relatively erratic. Bagnold [2] has developed a correlation for predicting wind speeds required to cause blowing of cohesionless sands and soils. His work can be adapted to the present problem. By considering the balance between aerodynamic and gravity forces acting on an exposed particle one can arrive at the relation, (1)

%h = AS~gd

where %h is the threshold shear stress, that is the shear stress that the air flow must exert on the particle bed in order to cause particles to move. A is an empirical factor is the mass density of the particles g is the gravitational acceleration d is the nominal particle dla as determined by sieve analysis Figure 8 shows results for the factor A ~ as determined by testing long beds of particles in uniform airflow [2, 3]. The steep slope at the left end of the curve corresponds to the rise in threshold wind speed as particle size decreases below about 0.1 mm. 1.0

B

I

I 0.1

\

m

0.001 0.01

I

I

I

0.1

1.0

10

I 100 "

I 1000

d~' J I J a01 0.05 a l

FIG. 8.

g d

J 05

IFor S.G 2.7 I~fficlI {es in 20"(; otrno~1.0 rnmjpl~ri c oironiy

The empirical factor A ' for cohesionless materials (from Rzfercnces 2 and 3).

To use equation (1) a correlation between air velocity and shear stress ~"is required; this normally takes the form of a skin friction coefficient Cf defined by

e f = ¢/½ pg,

(2)

194

R.J. K1ND, M. SEP and J. Y. WONG

where p is the air density and V is the air velocity. A suitable value for C I in the present application is a matter of conjecture. Some work in [4] suggests that a value of 0.0055 is appropriate where a thin 'fresh' shear layer is just starting to develop, as under the edge of an ACV skirt, over a bed of particles whose nominal diameter exceeds 0.1 ram. For particles smaller than 0.1 mm the results of Fig. 8 indicate the surface is aerodynamically smooth and a value of 0.0025 is then more appropriate for C I. These values are adopted here for C I. Equations (1) and (2) and Fig. 8 can then be used to estimate the air velocity and cushion pressure (equal to ½ pV ~) required to initiate erosion under the skirt edge. These estimates are included in Table 3 where they can be compared with the measured values. The estimates are seen to be low by a factor of about 2-6. The most probable explanation of the discrepancy is that the values of A 2 given by Fig. 8 are inappropriate for the present application where the air travels only a very short distance over the particle bed. It would appear that minimum cushion pressures required to initiate erosion can be estimated by using equations (1) and (2) with values of A s about 4 times larger than those given by Fig. 8; if ~ differs from 2.7 the correlation used in Fig. 8 necessitates an iterative procedure to obtain these estimates. In cases where the erodible material consists of a mixture of particle sizes, the work of Chepil [3] suggests that the particles most susceptible to erosion will determine the minimum cushion pressure required to initiate erosion. Chepil's work also suggests that if the ACV remains stationary, erosion will only continue until all particles susceptible to erosion at the prevailing cushion pressure have been removed from the region under the skirt edge. This is in fact confirmed by experience. 3.4 Erosion tests As mentioned earlier, the main effort in this study was devoted to examining the erosion process under the skirt edge for a variety of conditions; these are summarized in Table 1. The results of the erosion tests are presented and discussed in this section of the paper; the discussion includes a dimensional analysis and a simple theoretical model, both of which were found to be helpful in interpreting and explaining the results. 3.4.1 Erosion test results Figure 9 shows sequences of photographs taken by the framing camera for seven of the erosion test runs. These seven sets of photographs are representative of all those taken during the erosion rest runs. Comparison of Figs. 9(a), (b) and (c) shows clearly that erosion proceeds more rapidly at the higher cushion pressures, as one would expect. Comparison of Figs. 9(b) and (d) indicates that the effects of initial hovergap height are relatively minor, although some differences are noticeable. The influence of skirt angle is also minor, as seen by comparing Figs. 9 (b), (b) and (f). Figure 9 (g) illustrates that the erosion process with the fine powder sample was essentially the same as with the sand samples even though it was somewhat less orderly and was rapidly obscured by clouds of suspended powder. Only a few runs were conducted with the fine powder because of the problem due to dust clouds. The photographs in Fig, 9 show that the majority of the moving particles are carried along in a thin sheet. Within the erosion trough this sheet is immediately

GROUND EROSION AND DUST GENERATION

t~ 0

(O)

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t~l~

t ,,~ I i

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FIG. 9.

Typical photographs of erosion test runs (a-f--Coarse sand sample; g - Fine powder sample).

196

R . J . KIND, M. SEP and J. Y. W O N G

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GROUND EROSION AND DUST GENERATION

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197

t = 2Se¢

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adjacent to the boundary of the trough and it extends some distance above the trough where it makes an angle of about 50° with the horizontal• The erosive ability of the escaping air is maximum near the vena contracta (see Section 3.2) where its velocity is highest. The erosion trough accordingly forms with its bottom at this position. As the air erodes material from the bottom of the trough, its sides tend to become steeper but this is counteracted by the tendency for material to slump down. Thus the slope of the upstream side of the erosion trough remains about equal to the angle of repose of the particulate material (see Fig. 5). This is about 33° for the sand samples. At the downstream side of the erosion trough the tendency for the material to slump towards the bottom tends to be counteracted by the outflowing air stream; the slope of this side thus exceeds the angle of repose by a considerable margin when the cushion is pressurized. This slope sets the angle of the sheet of particles leaving the erosion trough. For each run, the cross-sectional area of the erosion trough was plotted against time from the start of the run. The slope of the smooth curves drawn through these data points was taken for four time intervals, 0.2-0.4 sec, 1-1.2 sec, 2-2.2 sec and 3-3.2 sec. These slopes gave the erosion rate prevailing during the time interval. These erosion rates are plotted against cushion pressure in Figs. I0, 11 and 12. The scatter in Figs. 10, 11 and 12 is large but this is not surprising since the points were obtained by differentiation of the basic data which was subject to about ± 15 % lack of repeatability and also to an inaccuracy of about 15 % associated with the method of data reduction as outlined earlier. The only strong trend apparent in Figs. 10 and 11 is that the erosion rate is approximately proportional to cushion pressure to the power 3/2. The power 3/2 is suggested by dimensional analysis and a simple theory which appear later in the paper. Skirt angle, hoverheight and time since start of the run do not appear to have an important influence on the erosion rate. This implies that the experimental shortcomings mentioned in Section 3.1 are unimportant. There is a weak, but definite indication in Figs. 10 and 11 that erosion rates are relatively high near the start of a run (t < 0.4 sec). Presumably this is because the erosion trough is then not yet well established and particulate material is more easily removed since it need not be carried up out of a

198

R.J. KIND, M. SEP and J. Y. WONG kg/m.s 20 It

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1

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Q2 0.4 0.6 CUSHION PRESSURE

Erosion rate

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cushion pressure for coarse sand.

trough. Comparison of Figs. 10 and 11 indicates that erosion rates for the coarse and fine sands are roughly equal, although the scatter o f the results for the fine sand is a good deal greater. The reasons for the greater scatter are not understood, although some of it may stem from the fact that cushion pressures were not directly measured in most of the fine-sand runs, as mentioned earlier. Figure 12 shows that erosion rates for the fine powder are substantially greater than those for the sand samples; insufficient data are available to draw conclusions regarding the effects of skirt angle, hoverheight or time, for this case. In the light of previous work [2] it is not surprising that the erosion rates of the sand samples depend strongly only on cushion pressure. The ability of the natural wind to transport sand has been found [2] to depend almost entirely on the shear stress which the wind exerts on the sand surface. The photographs of Fig. 9 show that the material being eroded under the edge o f an ACV skirt is confined to a thin layer or sheet and one would therefore expect that here too the erosive ability of the air stream must depend mainly on the shear stress which it can exert on the erodible surface. This shear stress depends mainly on the velocity of the escaping air and this

G R O U N D EROSION A N D DUST G E N E R A T I O N

199

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t

,o

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2

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Erosion rate

vs

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kPa

0.8 1.0 psi

c u s h i o n pressure for fine sand.

velocity is fixed by the cushion pressure and is largely independent of skirt angle, hoverheight and time. The data of Figs. 10 and 11 are expected to be applicable to any cohesionless material composed primarily of erodible particles of diameter 0.1 mm or larger. This point is discussed in Sections 3.4.2 and 3.4.2. Erosion rates for particle sizes smaller than about 0.1 mm apear to be strongly influenced by particle size and no general statement can be made about such materials at this time. Such small particles can enter into suspension in the air stream and viscous effects may be important as suggested by Fig. 8. Abeels [5] gives some erosion data for a "'light sandy clay". His results cannot be directly compared with the present results since the soil characteristics are not defined in any detail; they do however show a substantial effect of skirt angle. Abeels includes some results on the effects of soil moisture content and soil compaction. Arnold [6] tested a natural dry sandy soil sample in the present apparatus (mean particle diameter 0.2 mm; from the Mer Bleu Forest near Ottawa); where the comparison was possible his results agreed well with those of Fig. 11.

200

R.J. KIND, M. SEP and J. Y. WONG

3.4.2 A dimensional analysis o f the erosion process The discussion now continues with a dimensional analysis which is helpful in further interpreting some features of the erosion test results. The erosion r a t e / n for a skirt of the type tested may depend on the following independent physical parameters: Pc cushion pressure P air density ~z air viscosity g gravitational acceleration 0s skirt angle ho initial hoverheight t time since start of run V~R terminal falling velocity of the particles in air zth threshold shear stress required to initiate erosion of the particulate material ~tR angle of repose of the particulate material kg / m s 4

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p

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0.6

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PRESSURE

Erosion rate vs cushion pressure for fine powder.

The last three parameters of the list characterize the particulate material and are used instead of particle size, shape and mass density. Standard techniques of dimensional analysis then yield the following functional relation:

I'RgVp- f [VTERTth 3/2 , o , , '

hog.__~tTth] t' '

x/PJp

x/PJP

(3)

GROUND EROSION AND DUST GENERATION

201

All the ratios in Equations (3) are non-dimensional. The test results indicate that the last four ratios on the right hand side of Equation (3) are unimportant. The reason why 0~, the hoverheight ratio and the time ratio seem to be unimportant has already been given, namely that these parameters have little influence on the shear stress ~" which the flow exerts on the erodible surface. The ratio (Zth/Pc) should usually be unimportant because practical cushion pressures are usually such that the shear stress exerted on the erodible material greatly exceeds the threshold value %h. The ratio involving [~ is a form of Reynolds number; when the erodible particles are small this Reynolds number is relatively low and viscous effects may influence the relation between shear stress z and air velocity and this would in turn affect the erosion rate. When the ratio (VTER/X/P,/P) is small as occurs when the particles are small, the particles will readily become suspended in the air flow and this too would influence the erosion rate. Thus, when the particle size is sufficiently small that the values of the VTERratio and the Reynolds number fall below some lower limits, the erosion rate will be affected. When the values are above these lower limits the values of these ratios do not influence the erosion rate. For such reasons the erosion rates for the two sand samples are the same while that for the fine powder sample is substantially higher. Figure 8 and the erosion test results, together suggest that particles which are 'small' in the present context have nominal diameter less than about 0.1 or 0.2 mm. Of course the height to which particles rise and the time they remain aloft will depend strongly on (VTER/X/Pc/P) even when the erosion rate is independent of this ratio. In the light of the preceding discussion, equation (3) predicts that the erosion rate m is proportional to cushion pressure to the 3/2 power, at least when particle size is greater than about 0.1 mm. This is because the left hand side of equation (3) is then a constant for any given value o f ~ R. The slopes of the data in Figs. 10, 11 and 12 are consistent with this prediction. Figs. 10 and 11 give a value of about 2.3 x 10-s for the non-dimensional ratio thg x/p/Pc al~. 3.4.3 A simple theoretical model of the erosion process An interpretation of how the erosion process under the skirt edge proceeds has already been given in Section 3.4.1. Figure 13 illustrates this interpretation, which will now be used as the basis of a simple theoretical model of the erosion process. To begin, it is useful to define three shear stresses as follows: z •~ zB Following

is the is the is the Owen

total shear stress exerted by the fluid flow shear stress exerted on the layer of moving solid particles shear stress exerted on the particle bed (non-moving particles). [7], it is assumed that

~=~+~

(4)

everywhere along the flow. This assumption was found by Owen and others to lead to good predictions of particle transport rates in situations involving erosion by wind blowing over long stretches of cohesionless particulate material. In the erosion region at the bottom of the erosion trough solid particles are picked

202

R . J . K I N D , M. SEP a n d J. Y, W O N G CONTROL VOLUME FOR DERIVATION---7 OF EQ. 5

Pc

//

.

Palm

/,

.,-~

~

/ ,,¢

:a==

ZONE(, =T, -.£1 lIMP / 7ONF S L' ' ~ l I ~Ui i n n /M iP~ P ZONE ~ " ~ i ~ ~

~

EROSION ZONE

(AIRFLOW SATURATED W i t h PARTICLES)

( LARGE 1" : TB > 0 ) --

~ PARTICLE~

. . . .

PARTICLES

FIG. 13.

SLUMPING DOWNHILL BEING MOVED BY AIRFLOW

Interpretative sketch of erosion process.

up and accelerated by the air flow. As more and more particles are picked up increases and zn decreases. Eventually rn falls to zero and the air flow is 'saturated" with particles; that is the flow is unable to pick up and accelerate more particles. It is postulated that the flow and particle velocities, the shear stress z and the mass flux rh of particles remain approximately constant up the side of the trough, and that rn is approximately zero along here. Then, by applying the momentum equation to the control volume shown in Fig. 13, assuming one-dimensional conditions, one obtains, As =- p=TAs g sin ~=

(5)

where p= is the mass of moving solid particles per unit volume, T is the thickness of the layer of moving particles, and 0¢s is the angle at which the layer of moving particles leaves the erosion trough (as already discussed, ~= is found to be substantially larger than the static angle of repose, ~R, of the material). Now,

Ps --

rh

rv=

(6)

where Vs is the average velocity of the moving particles. Using equations (6) and (5) and re-arranging gives, m-

~ V, g sin

(7)

GROUND EROSION AND DUST GENERATION

203

It is reasonable to assume that Vs and T are proportional to the air velocity and to the air velocity squared, respectively, Since the air velocity is equal to V'2Pc/p equation (7) then implies that/n, which is the erosion rate, is proportional to cushion pressure to the power 3/2. As already noted, the experimental results are consistent with this prediction. Equation (7) could give quantitative estimates for the erosion rate m if values of 3, Vs and =~ were available. The photographs (Fig. 9) suggest values near 50° for ~. The shear stress • can be related to the air velocity and cushion pressure by assuming a value for the skin friction coefficient (see equation (2)); data reported in [8] suggest that the value 0.0055 may be appropriate for the present condition if the particles are not too small (say d > 0.1 ram). Using these values, one can then deduce that,

V, = 0.23 ~ 2P¢/p

(8)

from the data of Figs. 10 and 11. The foregoing theoretical model assumes that the moving solid particles are confined to a thin layer; therefore it may not be applicable to very fine particulate materials since large numbers of such particles may become suspended in the airflow. The model implies that the erosion rate is independent of particle size; this is consistent with the earlier discussion and with the results for particle size exceeding about 0.1 ram. The model is of course rather crude and tentative. 3.5

Deflector tests

Figure 4 shows the two deflector devices which were tested. Figures 14 and 15 show some photographic results for the simple and labyrinth deflectors, respectively. It is noteworthy that with the deflectors the total crosssectional area of the erosion troughs is much smaller than that at corresponding times without deflectors (compare with Fig. 9). Presumably this is because with the deflectors the drop from cushion to ambient pressure occurs in two or more stages so that the maximum velocity of the escaping cushion air and thus its erosive ability are reduced. Another noteworthy feature is that the final spray of particles is almost horizontal for run time less than 4 sec or so. This contrasts with an angle of about 50° to the horizontal without deflectors and may in itself considerably alleviate dirt ingestion and visibility problems. It is apparent from the tests that the downstream edges of deflectors must not be placed too close to the ground surface otherwise the majority of the erosion takes place at this edge and the deflector is ineffective. Of course the deflector must also not be placed excessively high; clearly then there is some optimum height for any particular deflector design. 4. CONCLUSIONS A preliminary investigation has been conducted into erosion of particulate ground surfaces by air cushion vehicles.

204

R.J. KIND, M. SEP and J. Y. WONG

t = 40sec

f=14sec !

=

( 0 ) P c : M e d ;ho= T

t =14sec

i'

• •

. (b)Pc:Med

~-~4-~ sec |

; ho= T

.

i

8s=45";

ho=3"

FIG. 14. Typical photographs of simple deflector tests for fine sand sample

M i n i m u m cushion pressures to initiate erosion have been m e a s u r e d and a scheme for e s t i m a t i n g these pressures is suggested. T h e e r o s i o n process u n d e r the skirt edge has been e x a m i n e d a n d erosion rates have been m e a s u r e d . T h e e x p e r i m e n t a l results, d i m e n s i o n a l analysis and a simple t h e o r y all indicate t h a t erosion rate is p r o p o r t i o n a l to cushion pressure to the p o w e r o f 3/2. Skirt angle, h o v e r h e i g h t and time a p p e a r to be o f s e c o n d a r y i m p o r t a n c e . E r o s i o n r a t e s a p p e a r to be i n d e p e n d e n t o f particle size if this exceeds a b o u t 0.1 mm. Deflector devices were briefly examined. This a p p r o a c h to alleviating e r o s i o n a n d d u s t g e n e r a t i o n showed some promise.

Acknowledgements---The apparatus was designed and constructed under the supervision of Dr. J. Y. Wong, with funding from National Research Council of Canada (NRC) Operating Grant A-5590 and Defence Research Board Grant 2201-03 awarded to Dr. Wong. The experiments and analysis were supported by funding from NRC contract 033-650/4785, NRC operating grant A-5173 and a Carleton University GR-5 grant awarded to Dr. R. J. Kind. The authors are grateful for the support from these sources.

GROUND EROSION AND DUST GENERATION

t = 8 sec

205

t=64sec

(o) P¢:Mod ; h 6 " T

; 8s = 4 5 . ;

t =8 tec

"D

t

t=OO~ec !

(b) Pc:Med;ho"'F

m

; 8s= 4~#to,,l--~-"

.

FIG. 15. Typical photographs of labyrinth deflector tests for fine sand sample

LIST OF SYMBOLS Empirical factor in equation (it Skin friction coefficient (see equation (2)) Nominal particle diameter as determined by sieve analysis (50% by weight is larger than this size and 50% by weight is smaller) g Gravitational acceleration h~ Initial hovergap hD Initial gap at deflector edge m Erosion rate, rate of mass removal per unit of skirt periphery P~ Cushion pressure t Time from start of a run T Thickness of layer of particles (see Fig. 13) V Velocity of air escaping from cushion V, Average velocity of moving solid particles (see equation (6)) VT,~R Terminal falling velocity of particles in air ct R Angle of repose of particulate material u, Angle of shtet of particles leaving erosion trough (see Fig. 13) As See Fig. 13 A C/ d

206 0s"

¢/ T "rB Ts

Ttk

R.J. KIND, M. SEP and J. Y. WONG Skirt angle Viscosity of air Air density Mass density of particles Total shear stress exerted by the airflow on the particulate material Shear stress exerted by the airflow on the particle bed (non-moving particles) Shear stress exerted by the airflow on the moving solid particles Threshold shear stress; that is, the minimum shear stress required to initiate particle motion

REFERENCES [l] R. N. YONO, Characteristics of Dust Susl~nsion in ACV Operation, Report No. SM-DS-3, Geotechnical Research Centre, McGill University 0977). [2] R. A. BAGNOLD, The Physics of Blown Sand and Desert Dunes. Methuen, London (1941). [3] W. S. CHEPIL, Dynamics of wind erosion: II. Initiation of soil movement, Soil Science 60, 397-411 (1945). [4] R. J. KIND, Estimation of Critical Wind Speeds for Scouring of Gravel or Crushed Stone on Rooftops. National Research Council of Canada, LTR-LA-142 (1974). [5] P. F. J. ABEELS,Air cushion vehicles and soil erosion, J. Terramechanics 13, 201-210 (1967). [6] R. ARNOt.D, An Investigation of Dust Generation by Air Cushion Vehicles, unpublished report, Dept. of Mechanical and Aeronautical Engineering, Carleton University (1977). [7] P. R. OWEN, Saltation of uniform grains in air. J. Fluid Mech. 20, 225-242 (1964). [8] R. J. KIND, Calculation of boundary layer development and particle transport rates for gas flows over saltating particle beds. Proc. of Fifth Canadian Congress of Applied Mechanics. Fredericton, 475-6 (1975).