Wear, I49 (1991) 55-71
55
On the particle size effect in slurry erosion*
Randall
Mechanical
Kien
S. Lynn
Engineering
Department,
University
of New Mexico, Albuquerque,
NM 87131
(U.S.A.)
K. Wong and Hector MCI. Clark
Mechanical
(Received
Engineering
February
Department,
University
of Kansas,
Lawrence,
KS 66045-2234
(U.U.)
23, 1991)
Abstract
The erosion rates of cylindrical steel specimens tested at a constant speed of 18.7 m s-’
in an erosion pot tester using 1.2 wt.% suspension
of SIC in oil for particle diameters
between 20 and 500 pm have been determined.
The rate of particle impact on unit area
of the surface at the stagnation
line of erosion specimens was established
as a function
of particle size by short-time erosion tests, allowing a calculation of the mean mass removed
for each particle impact as a function of particle size. These values were compared with
the kinetic energy of particles using impact velocity values derived from a model of suspension
flow. Results show that the decrease
in erosion rate with decreasing
particle size for
suspensions
of constant solids loading reflects the decrease in the proportion
of particles
impacting the target surface as well as the decrease in impact velocity. A value of about
24 kJ g-r is tentatively suggested for the energy of removal of PllO steel by erosion. It
is concluded
that for these dilute suspensions
with particle sizes greater than about 100
km the erosion rate is proportional
to the kinetic energy dissipated by particles during
impact, but for particle sizes less than 100 pm other metal removal mechanisms become
increasingly significant.
1. Introduction
The erosion process is essentially
the removal of material
from a surface by the
repeated
impact of gas-borne
or liquid-borne
particles.
Since the early investigations
of Finnie [l] there has been speculation
that a relationship
should exist between
the
amount of material
removed
in erosion
and the work done, or energy dissipated, by
impacting particles. The 1960 paper of Finnie [l] is worth quoting in part because
of its succinct exposition of the problem.
The erosion of a surface by abrasive particles in an inert fluid should depend on
the number of particles striking the surface, their velocity and their direction relative
to the surface. These quantities are largely determined by the flow conditions and
many practical examples may be found where a change in flow conditions has greatly
increased or decreased erosion.
Several investigations have been conducted of the effect of changing particle size
on the amount of material removed by erosion by liquid-borne particles [2-lo] and
*Paper presented
at the International
U.S.A., April 7-11, 1991.
0043-1648/91/$3.50
Conference
on Wear of Materials,
0 1991 -
Orlando,
FL,
Elsevier Sequoia, Lausanne
56
gas-borne particles [ll-171. While these investigations
generally agree that larger
particles give rise to more mass loss by erosion than the same mass of smaller particles,
there is no agreement
on the origin of this phenomenon
nor has any successful
quantitative explanation of the effect been offered. Some examinations of slurry erosion
[4,6] have been concerned with suspensions of relatively high solids loading (lo%-30%).
Under these circumstances
other wear mechanisms,
such as constrained
sliding of
particles, may contribute to mass loss from the test specimen surface. Work by Hojo
ef al [18] and Clark [lo] on slurry erosion has drawn attention to the importance of
flow conditions
as a dominating
factor influencing
the erosion process in slurries.
Earlier, the work of Ahmad and Goulas [6] for slurry pumps and Tabakoff et al. [19]
for gas-borne particle erosion in turbines has emphasized the usefulness of techniques
of particle trajectory prediction in the erosion process in machinery subject to this
type of damage.
Particularly useful in this regard is the concept of collision efficiency n (sometimes
called striking efficiency) discussed by Soo [20]. The collision efficiency may be defined
as the ratio of the number of particles striking unit area of the surface in unit time
and the number of particles contained within the volume of suspension swept by that
area in unit time. Vittal and Tabakoff [16] have calculated the collision efficiency for
a cylinder (diameter 3.175 mm) exposed to air-borne quartz particles (sizes between
25 and 140 pm) at a cylinder Reynolds number of 40. Their work showed that n
decreased sharply with decreasing particle size. The value of collision efficiency for
glass beads between 75 and 750 pm in water-glycerin
suspensions
and cylindrical
copper targets [lo] and for A1203 particles in oil suspensions
[21] under erosion
conditions has been assessed for a range of viscosities.
It was the objective of the present work to investigate the relationship
between
the rate of removal of material subject to erosion by a dilute suspension to the rate
of dissipation of kinetic energy of impacting particles as a function of particle size.
2. Experimental
details
Commercially available Sic powders were sieved into fractions, washed in distilled
water and dried at 90 “C in air to give a range of powders between 20 and 500 pm
of the size ranges listed in Table 1. Powders below 45 pm were prepared by air
classification but were not used in all tests. Scanning electron microscope images of
some of the powders are shown in Fig. 1. Typically, particles were jagged and irregular.
The largest particles were somewhat more rounded than the others and for this reason
particles in the size range 297-350 pm were taken as representative
to assess mean
particle mass and volume for powders below this size. The number of particles in a
mass of 0.0204 g of 297-350 Frn powder was counted (349), allowing the mass per
particle to be calculated. The corresponding
mean particle volume was derived using
the published density value for SIC of 3170 kg rnm3.
Taking the mean sieve size (m.s.s.) for these particles as 323.5 w, i.e. (297 + 350)/
2, a constant K,, relating particle volume to mean sieve size was derived:
particle volume = (m.s.s.)3 XK;
where K, has the value 0.545. This relationship was used to estimate the volume and
mass of all powder particles, except those in the 420-500 cwn range which were
evaluated by counting the number of particles in a known mass. The value of K, is
very close to the equivalent constant for spherical particles, namely ?r/6 (0.524). Final
Kinetic energy of impact
Mass loss per impactxlti
(g J-l)
1012(g)
39.1
Erosion rate X lo”, adjusted
for area (g mrne2 min-‘)
x
0.78
0.150
0.88
0.077
Collision efficiency q
Particle impact rate
(lo6 rnn~-~ min-*)
Mass loss per impact
5.14
13.3
Particle kinetic energy at
impact, &zV: (10m6 3)
218.5
42.4
508.5
38.3
32.5
32.0
38.8
Erosion rate X 106, I?,, from
Fig. 6 (g mm-* min-‘)
297-350
323.5
420-500
423
Particle size range (pm)
Mean sieve size (pm)
Particle sizes and processing of data
TABLE 1
44.3
89.3
25.6
0.69
0.29
2.02
25.0
121-250
250
40.9
17.3
13.6
0.53
0.79
0.423
13.0
147-180
163.5
45.6
4.24
7.49
0.42
1.77
0.0929
7.0
106-12s
115.5
77.8
0.852
3.4
0.26
4.0
0.011
3.0
75-88
75
133
0.355
1.93
0.16
5.4
0.00267
1.7
53-62
57.5
987
0.141
0.943
0.04
6.7
0.000236
0.8
40
40
22187
0.0213
0.172
0.01
8.1
0.96x 1O-6
0.134
20
20
Y
(b)
(4
Fig. 1. Typical Sic powders: (a) 297-350 pm, bar is 1 mm; (b) 147-180
75-88 pm, bar is 0.1 mm; (d) 40 pm, bar is 0.1 mm.
pm, bar is 1 mm; (c)
59
assessment of particle sizes was made photographically
by reference to the scanning
electron micrographs of the powders. Particle sizes used for calculation are listed as
mean sieve sizes in Table 1.
Suspensions used in this investigation were made up from commercially available
diesel fuel oil of density 856 kg me3 and viscosity 2.1 x 10e3 N s m-* at 40 “C.
Cylindrical erosion test specimens 46 mm long were made either from OFHC
copper rod (diameter 5.17 mm) for short-time erosion tests or from API PllO casing
steel (diameter 4.76 mm) for longer-time erosion rate tests. The copper specimens
were annealed at 300 “C for 1 h to give a hardness from 48-54 Rockwell F and were
electropolished
using concentrated
orthophosphoric
acid at a d.c. voltage of 1.75 V
for a minimum of 4 h to produce a highly reflecting, strain-free surface.
Typical mechanical properties of the PllO quenched and tempered steel are:
hardness 290 BHN; yield strength 835 MPa; tensile strength 975 MPa; elongation on
SO mm, 17%; reduction in area at fracture, 60%. The steel erosion specimens were
either polished using 1 pm diamond paste or were tested with a previously eroded
surface. No difference was detected in the rate of mass loss for these two surface
treatments.
2.1. Erosion pot tester
The pot tester is shown schematically in Fig. 2. It consisted of a circular section
stainless steel vessel (capacity 5.0 1) with a central vertical stainless steel shaft supporting
two vertically positioned erosion test specimens. The shaft was driven by a 3.7 kW
electric motor through a toothed belt to give a nominal rotation speed of 18.7 m s-r
at the specimen. Temperature
control of the suspension to 40*1 “C was achieved
through the use of two water-cooled coils. Erosion specimens were supported by pin
ends located in nylon cups of the specimen diameter to avoid the generation
of
corrosion couples with the support frame and to maintain the cylindrical flow pattern
at the specimen ends. The progress of erosion was measured by mass loss after 10,
20, 35 and 60 min using an analytical balance weighing to 0.1 mg and was computed
as the average for the two specimens.
Lower Bearing
I of 2)
Copper Cooling
Coil (1of 2)
Baffle
Nylon Cup
Erosion Specimen
Stainless Steel
Pot
b-1
65
4
Fig. 2. Schematic diagram of slurry erosion pot. Dimensions are in millimeters.
60
2.2. Erosion test method
The pot was filled with oil and the machine operated with two dummy specimens
to heat the oil to a temperature
of 40 “C. The specimens were replaced, the requisite
amount of Sic powder added and the machine operated either for 120 s for shorttime impact rate tests or in intervals up to 60 min for erosion rate tests.
2.3. Short-time tests
Known quantities of SIC powder between 0.01 and 0.025 g were added to the
pot for these tests and were chosen so that the leading surface of the copper test
specimens would be covered with impact craters after about 10 min testing. Tests
were stopped after 120 s. The number of impact craters per unit area was counted
along the stagnation line of the specimen using an optical microscope. Typical specimen
surface areas close to the stagnation line are shown in Fig. 3. There is some uncertainty
associated with the number of impacts, since the shape of craters was irregular and
it was possible that a single impact event produced two separate craters as the particle
rotated or that craters were superimposed.
2.4. Erosion rate tests
For erosion rate tests a constant solids loading of 1.2 wt.% was used by adding
50 g of powder to the pot. This choice of solids loading represented
a compromise
between avoiding particle-particle
interactions
at higher solids loading and obtaining
measurable erosion rates at small particle sizes. Mass loss was measured after 10, 20,
35 and 60 min. It was found that the rate of mass loss decreased with time, a commonly
observed effect that has been ascribed to particle blunting and comminution
[3].
The erosion rate as a function of time R, was assessed as the slope of the mass
loss-time curve at zero time and was taken as representative
of the erosion rate of
the steel specimens by fresh SIC particles. For consistency
the initial slope was
determined
using a third-order
polynomial curve fit which corresponded
quite well
with the mass loss-time curve.
After 10 min testing, the angle subtended at the specimen center by the eroded
cylinder surface (called the circumferential
erosion angle 28) was recorded for most
suspensions. It was observed that a sharp boundary separated the eroded from the
uneroded surface, allowing evaluation of the angle with some confidence.
3. Results
Impact rate values in units of impacts per square millimeter per minute for the
suspensions used in the short-time tests were used to calculate the collision efficiency
77for the specimen as a function of powder particle size; that is, the number of impacts
per square millimeter per minute divided by the number of particles calculated to be
in the volume swept out by a 1 mm2 area of specimen moving at a speed of 18.7 m
s-l in 1 min, assuming a uniform distribution
of particles in the suspension. Values
of the collision efficiency lie between zero and unity <and are given in Fig. 4 as a
function of particle size. Each point is derived from between 20 and 55 determinations
of the number of impacts on unit area.
Plots of erosive mass loss as a function of test time are shown for pre-eroded
PllO steel specimens in Fig. 5. For these tests no damage nucleation delay was expected
or observed, the curves passing smoothly through the origin. Experimentally
determined
values of erosion rate for each Sic particle size are shown in Fig. 6. Values of erosion
61
(4
-
Fig. 3. Impact craters close to the stagnation line on copper short-time erosion test specimens:
(a) 297-350 pm Sic particles; (b) 147-180 pm; (c) 75-88 Km; (d) 40 pm. Each bar represents
0.1 mm.
62
1.0
0.8
0.6
100
PARTICLE
SIZE ( pm)
Fig. 4. Variation of collision efficiency TJ with particle size based on impact crater numbers in
short-time erosion tests. Particle size refers to the mean sieve size of the powder. Values are
the mean for between 20 and 55 determinations
of numbers of impacts at each particle size.
1.5
1.o
0.5
0.0
0
20
TEST
40
TIME
60
80
(min )
Fig. 5. Mass loss per square millimeter of frontal area (diameter~length)
of erosian specimen
with testing time for PI10 steel specimens tested in diesel oil at 40 “C, nominal test speed 18.7
m s-* for 1.2 wt.% suspensions of SIC of the mean sieve size shown (microns).
rate corresponding to each mean sieve size were taken from this line and are listed
in Table 1. The corresponding values of circumferential erosion angle 28 are shown
in Fig. 7.
63
100
(0
0
r
X
m-
10
1
,
“1 0
100
PARTICLE
SIZE ( p m)
Fig. 6. Erosion rate R, of PllO steel in 1.2 wt.% suspensions of SC powders of indicated particle
sizes in diesel oil at 18.7 m 5-I nominal test speed.
180I-
160/ *-
140/
-
120/
-
10
100
PARTICLE
1000
SIZE (fl m)
Fig. 7. Variation of circumferential erosion angle 28 (see text) with particle size for test conditions
used in this investigation.
Using a potential flow model for a suspension
Wang and Ctark [22], values of the impact velocity
about a cylinder developed by
at the stagnation line, VI, were
calculated for the conditions used in these tests, with the assumption that the suspended
particles were spherical rather than angular and irregular. These values are plotted
64
p
Nominal Tesf Speed 18.7 m/s
100
PARTICLE
1000
10000
SIZE ( pm)
Fig. 8. Calculated
impact velocity VI as a function of particle size for spherical particles of the
same density as Sic impacting the erosion test cylinder along the stagnation line [ZZ].
in Fig. 8. It is acknowledged
that irregular
particles
will show a range of impact
velocities.
The usefulness
of Fig. 8 lies in indicating how the mean velocity of impact
would vary with particle
size.
4. Discussion
Calculated values of the impact velocity of particles on the cylinder surface show
a dramatic decrease with decreasing particle size, reflecting decreasing particle inertia
with decreasing size. Thus smaller particles in the path of the advancing erosion
specimen are more easily constrained by the liquid flowing about the cylinder to follow
liquid streamlines rather than follow an undiverted cohision course with the cylinder
surface. This is shown schematically in Fig. 9. Further, small particles impacting the
cylinder do so with a much reduced velocity compared to larger particles.
Bperimental
evidence for such particle retardation
under conditions of erosion
has been given for suspensions of glass beads in the size range 75-750 Frn in water
or water-glycerin
suspension
[lo, 181. Clark [lo] found that glass beads may be
decelerated
to as httle as 10% of the nominal test speed and that consequently
assumptions
concerning
the impact velocity of particles based on the nominal test
speed in a slurry erosion test may be seriously in error. Similarly, Hojo et al. [34]
have pointed out that even in a slurry jet, particle impact velocities and impact angles
with the target vary strongly across the jet diameter.
From the data on mean particle mass m for each size range and calculated impact
velocity, values of mean particle kinetic energy at impact &mfr:, were calculated
(Table 1).
Collision efficiency decreases with decreasing particle size. The appropriate form
of the relationship is unclear, however, and for the sake of simplicity a straight line
65
Non-Impacting Particles
Center tine
t
= Collision Efficiency, q
1
18.7 mfs
Fig. 9. Schematic diagram of suspension flow about an erosion test specimen to show the changes
of collision efficiency q with particle size. The circumferential erosion angle 2B is indicated for
each case.
has been chosen on the semiiog plot (Fig. 4). The results of Vittal and Tabakoff [16]
for collision efficiency of quartz particles in air also yield a straight line on a semilog
plot, although the relationship
must be asymptotic with collision efficiency values of
zero and unity.
The numbers of particles impacting 1 mm2 of the steel erosion specimens each
minute were calculated from the numbers of particles in the path of that area of
surface each minute and the collision efficiency for those flow conditions taken from
Fig. 4. These are given in Table 1 as the particle impact rate.
The plot of circumferential
erosion angle 28 with respect to particle size appears
to be linear in a semifog plot (Fig. 7). This result suggests that a relationship
also
links the collision efhciency and the circumferential
erosion angle, which might yield
values of collision eil’iciency indirectly but simply, thus obviating the tedious process
of counting impact craters. This relationship requires further investigation but will be
useful only when closely sized particle samples are used, since a wide range of particle
sizes in the suspension will lead to an ill-defined boundary at the edge of the eroded
area. A plot of collision efficiency with respect to circumferential
erosion angle using
data taken from the best-fit lines in Figs. 4 and 7 is given in Fig. 10.
Values of the erosion rate given in Fig. 6 and Table 1 are based on the projected
frontal area of the erosion specimen. Since the actual area subjected to erosion changes
with particle size as the circumferential
erosion angle decreases, values of the erosion
rate have been adjusted to reflect the concentration
of damage over a smaller area
as the particle size decreases by dividing erosion rate values by the corresponding
value of sin e (Fig. 7). Adjusted values of erosion rate are given in Table 1.
The mean mass loss for each particle may then be calculated from the ratio of
erosion rate and particle impact rate for each particle size. It is recognized that
66
CIRCUMFERENTIAL
EROSION
ANGLE,
28 (Deg.)
Fig. 10. Variation of collision efficiency with circumferential erosion angle for the erosion test
conditions.
intermediate
impact angles are generally more effective in removing material from a
ductile target, but it is assumed that the distribution
of particles over the eroding
surface is independent
of particle size. Values of mass loss per impact are given in
Table 1 and compare closely with previous calculations of the mean mass loss per
impact for erosion of this steel using suspensions of 75-106 pm AlaOs in water or
oil [21]. Values of the ratio of mean mass loss per impact and kinetic energy of impact
are given in Table 1. Between 500 pm and about 100 pm the ratio is essentially
constant, but rises with decreasing particle size below 100 pm.
A constant value of mass loss per impact divided by impact energy indicates that
mass loss is proportional
to impact energy, as predicted by Finnie [l], over a range
of particle sizes. The value of the ratio is about 42X 10m6 g J-l. It is interesting to
compare this result with the energy requirements
for machining. For steels these are
given as 0.35-1.225 kJ g-i for cutting and 2.1-10.5 kJ g-’ for grinding [24]. Taking
the reciprocal of the mass-energy
ratio yields an energy requirement
of 24.0 kJ g-i
(about 70 hp min ind3) for removal of PllO steel by erosion. It appears that for the
conf-lguration used in the present test erosion is not a very efficient method of material
removal. This value should be regarded as an upper limit. The value of kinetic energy
is very sensitive to the value of impact velocity used. Those given in Fig. 8 do not
incorporate consideration
of boundary layer effects which may give rise to additional
particle retardation.
A cylindrical test specimen in an erosive flow normal to its axis is impacted by
particles at all angles between normal (90”) and glancing (W) impact. The importance
of impact angle in determining
the rate of metal removal is well established and the
progressive change of shape of cylindrical erosion specimens has been noted by Levy
[3], intermediate
impact angles being most effective in metal removal from a ductile
target. At normal impact much work will be done on the target material but, at least
67
for ductile metals, the rate of material removal is low. Nevertheless, the calculated
energy necessary to remove unit mass of metal by erosion is high.
The higher measured values of the ratio of mass loss per impact and kinetic
energy of impact for the smallest particle sizes is not understood but is believed to
be due in part to changes in the mechanisms of material removal. Figure 11 shows
a plot of mass loss per impact with respect to particle size for the sizes studied. The
dashed line corresponds to a constant value of the ratio of mass loss per impact and
particle impact energy. A number of experimental factors, discussed below, may contribute
to the high values calculated for the smallest particle sizes.
The results as a whole demonstrate the necessity of obtaining very carefully sized
powder samples for particle size work to be successful. A few particles significantly
greater than the mean size in the sample will contribute disproportionately
to erosive
mass loss through a greater collision efficiency and a greater impact velocity than the
mean, leading to a larger erosion rate. Values of the collision efficiency and numbers
of particles are derived from relationships
which are, necessarily, approximate. Suspensions containing 1.2 wt.% solids are rather dilute and the erosion rate produced
by small particle sizes yields a mass loss in the order of a few milligrams per hour.
Thus values of erosion rate for suspensions of small particles are inherently less precise
than those for larger particle sizes, particularly since erosion rate is calculated as the
initial slope of the mass loss-time curve.
A further complicating factor in slurry erosion that has received little attention
is the trajectory of particles after impact. For example, the present results for 45-53
pm particles suggest that about 5.5 million particles impact each square millimeter
of frontal area each minute or, in more understandable
terms, 220 particles impact
each 49 brn square of surface area each second. The coefficient of restitution
for
PARTICLE
SIZE f y m)
Fig. 11. Variation of mass Ioss per particle impact with particle size for erosion of PllO steel.
Full line shows experimental results; dashed line is calculated from constant value of the ratio
of mass loss per impact and kinetic energy of impact.
68
these particles is unknown, but it is doubtful whether they are able to rebound far
from the steel surface, particularly when their impact speed is in the order of 3 m
S -’ only. It is suggested
that the concentration
of particles close to the specimen
surface is higher than in the suspension
as a whole because of particle retardation
on impact and that these particles may produce multiple impacts on the surface by
collision with incoming particles and so enhance the erosion rate. There is some
evidence for this phenomenon
in that particle impacts could be detected over a
circumferential
erosion angle of about 175” for a diamond-polished
steel specimen
after testing in the 40 hrn suspension,
although damage was concentrated
within a
narrower band about 60” on either side of the specimen stagnation line. Some particles
may leave their impact point by sliding over the specimen surface and in so doing
would certainly remove more material than through a single impact. It is clear that
the difficulty of removing particles after impact on the specimen surface will increase
as the particle size decreases, since available rebound energy will decrease and the
mean distance between particles in the homogeneous
suspension wili be smaller.
The relationship between mass loss in erosion and particle size for larger particle
sizes (above about 200 pm for gas-borne erosion) shows an approximately
constant
value of mass loss. That is, above this value the erosion rate is independent
of particle
size. The results of Sage and Tilly [12] for gas-borne particles are typical. Below this
value the erosion rate decreases and becomes vanishingly small at some small particle
size, typically about 10 pm for gas-borne particles (the value will be greater for sIurries).
The present analysis allows this form to be understood.
Large particles suffer little retardation before impact because of their high inertia
and are also associated with values of collision efficiency close to unity. Thus the
kinetic energy of impact per unit time will be essentially constant, irrespective of
particle size, and the erosion rate, whether measured as a function of time, R,, or
unit impacting mass, R,, will also be essentially constant [25].
For particles of smaller size, particle retardation
prior to impact will become
increasingly significant. At the same time the collision efficiency of the particles on
the eroding surface will decrease, resulting in lower and lower dissipation of kinetic
energy by impact, and the erosion rate will fall to vanishingly small values. It is believed
that these considerations
are applicable both to erosion by slurries as well as gasborne particies. Certainly the work of Laitone [26, 271 in examining particle velocities
and trajectories for normal impingement
for gas-borne particles on a flat plate would
support this view. The usefulness of measuring erosion rate as a mass ratio (mass of
material eroded and mass of erodent employed) is questionable
unless the coliision
efficiency is known and constant. Generally the co&ion efficiency is implicitly assumed
to be unity.
The present results ahow estimation of erosion rates for any particle size. Using
a constant value of the ratio of mass loss per impact and particle kinetic energy at
impact of 42~ 1O-6 g J-‘, the erosion rate Rt may be calculated as a function of
particle size. For larger particle sizes a collision efficiency of unity was assumed and
impact velocities were calculated using the method of ref. 22 (Fig. 8). Smaller particle
sizes required an assumption about the number of impacts on unit area in unit time.
Figure 12 shows the variation of particle impact rate with particle size for the range
2&5ooO pm. Values from 49 to 420 Km are derived from experimental
data for
collision efficiency using the straight line frt of Fig. 4. Above 500 pm a collision
efficiency of unity is assumed, while the trend towards a limiting value of impact rate
at smaller particle sizes reflects the very low values of collision efficiency for particle
sizes in this range.
59
107
106
105
104
103
102
10'
10
I
I
100
1000
PARTICLE
SIZE
10000
(wW
Fig. 12. Variation of SIC particle impact rate under erosion conditions (1.2 wt.% suspension)
as a function of particle size. Values from 20 to 423 pm are derived from n. Above 500 grn
values are calculated from an assumed co&ion efficiencyof unity.
bl Experimental
l
Calculated
t
100
PARTICLE
1000
SIZE
(pm}
Fig. 13. Plot of erosion rate R, for PllO steel in l.‘hvt.%SiC-oil
suspension
particle size. Full hne shows experimental results; dashed line is calculated.
as a function
of
70
The calculated erosion curve is shown in Fig. 13 together with the experimental
data. The relationship
shows the general form revealed by experiments on gas-solid
erosion [12] and liquid-solid erosion [4] in that above 500 pm the erosion rate changes
little with particle size, while at small particle sizes the rate falls sharply. At particle
sizes between 100 and 500 pm the erosion rate falls as shown also by the present
experimental results. The fit is exact in this portion because of the use of experimental
data to derive the calculated curve. The discrepancy between predicted and experimental
rates at low particle size, as noted above, is believed to be the result of a change in
the mechanism of metal removal, in which direct particle impact plays a decreasingly
important role as particle size decreases.
5. Conclusions
(1) Through short-time erosion tests using very dilute suspensions of Sic in oi1
and electropolished specimens it is possible to estimate the impact frequency of particles
on the specimen surface and the collision efficiency of particles in the flow regime.
(2) Both the collision efficiency and the impact velocity of particles decrease with
decreasing particle size under conditions of erosion testing.
(3) The mass loss rate in erosion is proportional
to the rate of dissipation of
kinetic energy of the impacting particles above about 100 pm in these tests.
(4) The frequently reported decrease in erosion rate with particle size is the result
of the combined effect of decreasing collision efficiency of particles and decreasing
impact velocity with decreasing particle size.
(5) A limiting value of erosion rate above some intermediate
particle size reflects
a condition in which the collision efficiency approaches unity and particle retardation
prior to impact is small.
(6) For cylindrical erosion specimens, measurement
of the circumferential
erosion
angle may provide a method of estimating the collision efficiency of particles in the
suspension if particles are of uniform size.
(7) Analysis of erosion rates for suspensions of small particles (less than 100 pm)
in terms of the rate of dissipation of kinetic energy of impact may be complicated
by an accumulation
of particles at the specimen surface caused by their retardation
on impact, with a consequent
change in the mechanism of material removal.
(8) Details of particle trajectories and velocities as well as an understanding
of
the flow regime are essential if comparisons of erosion rates are to be well founded.
Acknowledgments
The authors wish to thank Lawrence Technology,
of copper rod, and Barry Smith, Metallurgy Department,
for providing the air classification of powders.
Lawrence, KS for the supply
RMIT, Melbourne, Australia
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