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On the impact rate and impact energy of particles in a slurry pot erosion tester
Wear, I47 (1991)
165
165-183
On the impact rate and impact energy of particles slurry pot erosion tester*
in a
Hector MCI. Clark Department of Mechanical Engineering, (7JLT.A.)
Universi@
of Kansas, Lawrence, KS 66045-2234
(Received September 24, 1990; accepted November 21, 1990)
Abstract Short-time erosion tests were conducted with dilute water and water-glycerin suspensions of glass beads to determine the rate of particle impact and the dimensions of impact craters using annealed and electropolished OF’HC copper rod specimens. Particle diameters were 75-90, 212-250, 500-600 and 750 pm, nominal rotation speeds of the erosion targets in the pot were 9.35 and 18.7 m s-’ and the carrier liquid viscosity was in the range (0.66-60)x 10e3 N s m-‘, (0.66-60 cp). The work done in forming a crater of specified diameter was determined for each particle size by indentation using a single glass bead mounted on a microhardness tester. Using the assumption that all the kinetic energy of an impacting bead was dissipated in plastic work, the impact velocities of particles forming craters were calculated for most test conditions. The collision efficiency for the specimen was determined for most test conditions and was found to decrease with decreasing nominal velocity, increasing carrier liquid viscosity and decreasing particle size. The erosion rate, expressed as either material lost per unit area per unit mass of impacting particles or material lost per unit area per unit time, was estimated and shown to be strongly affected by the flow conditions for individual particles.
1. Introduction While the formation of significant erosion damage is the result of collisions of many particles with an eroding body, there has been continuing interest in the events associated with the impact of single particles and the consequent progress of damage [l-6] in an effort to elucidate the processes leading to material loss. Analysis of ~di~du~ impacts of gas-borne spheres has been undertaken by Hutchmgs [Z] who concluded that more than 90% of the energy of a sphere impacting on a soft copper target is consumed in plastic deformation to form a crater on the surface. Assuming the validity of this conclusion for slurry erosion, an examination of the frequency of impact and the size of impact craters produced in annealed copper by individual glass beads was undertaken using dilute suspensions of glass beads in water-glycerin carrier liquids at nominal erosion speeds of 9.35 and *Paper presented at the 4th Berkeley Conference on Corrosion-Erosion-Wear at Elevated Temperatures, Berkeley, CA, January 31-February 2, 1990.
0043-1648/91/$3.50
of Materials
0 Elsevier Sequoiafl?rinted in The Netherlands
166
18.7 m s- ’ in a slurry pot tester. From these data the proportion of particles impacting the specimen and values of mean particle impact velocity were derived.
2. Experimental
details
All testing was conducted in the slurry erosion pot shown in Fig. 1. This consisted of a circular section stainless steel vessel, 5000 ml volume, with a central stainfess steel shaft supporting two vertically positioned cyfindricd test specimens. Each specimen was supported by nylon spacers of the same diameter. These spacers prevent the generation of corrosion couples between the specimens and the stainless steel support frames. They also lessen the influence of the suspension flow pattern produced by the rotating frame. The shaft was driven by a 3.7 kW electric motor operating at a speed of 3515 rev min-’ through a toothed belt. Using pulleys of different sizes, the nominal rotation speed at the specimen support point 51 mm from the rotation axis could be set at either 9.35 or 18.7 m s-l. The vessel was equipped with four baffles extending 12 mm into the pot to disrupt liquid rotation during testing. The vessel was also vented to prevent pressure built-up. Temperature control of the Iiquid suspensions to 40 t- 1 “C was achieved through a heating tape around the body of the pot and two internal water-cooled copper coils. Erosion test specimens were produced from 5.17 mm diameter cold drawn high-conductivity copper rod. The hardness after annealing for 1 h at 300 “C was in the range Rockwell F 48-54, Shore scleroscope 4. Erosion test specimens were 46 mm long, each with 2 mm pin extensions to locate
Erosion Specimen
Stainless Steel
+.----165-4 Fig.
1. Schematic diagram of erosion pot tester, dimensions in milliicters.
167
the specimens in the nylon supports. Specimens were polished with 1 pm diamond paste followed by electropolishing for 2.5 h as the anode in concentrated orthophosphoric acid at 1.7 V d.c. This polishing process produces a highly reflecting and strain-free surface [ 71. Suspensions were made up from distilled water which had been freshly boiled to remove dissolved oxygen and minimize corrosion, with or without additions of glycerin. The liquid compositions were selected to give chosen values of viscosity for the carrier liquid at 40 “C, shown in Table 1, using published viscosity data [S]. Glass beads, of density 2420 kg me3, and diameters in the ranges 75-90, 212-250, 500-600 and 750 pm were used in these tests (Fig. 2). Tests at all viscosities and both rotation speeds were conducted using beads in the size ranges 212-250 and 500-600 km. In order to provide a calibration of impact crater size in the copper erosion test specimens, a Leitz direct-loading microhardness tester was used to provide data on the size of indentations produced at low strain rates by using indentors on which a single glass bead was mounted. Indentation diameter was plotted as a function of indentation mass for spheres of diameter 78, 213, 574 and 750 pm as shown in Fig. 3. The calculated depth of each TABLE 1 Composition, viscosity (at 40 “C), density and cylinder Reynolds number for carrier liquids used in this investigation Composition (wt.%) Water
Glycerin
100.0 46.5 20.5 10.0
0.0 53.5 79.5 90.0
Viscosity (N s m-‘X
0.66 3.63 20.0 60.0
103)
Density (kg me3)
Reynolds number Reu 18.7 m s-’
9.35 m s-l
998 1139 1208 1236
146000 30400 5850 1990
73000 15200 2925 995
Fig. 2. Three of the sizes of glass beads wed in this investigation, 75-90, 500-600 pm; the bar represents 1 mm.
212-250
and
168
1000
750 pm 550 pm
500-
10-e =
300E
200-
2 r" s .Z s fi -a t
loo-
504030 2510-e
5
6
10
Indentation Diameter (pm)
Fig. 3. Diameters of microhardness mass for indcntor bead diameters Fig. 4. Work done (energy) diameters shown.
~dentatio~s shown.
in indentation
in annealed
with respect
20 40 60 100 Crater Diameter (pm)
200
copper as a function of indentation to crater
diameter
for the indcntor
indentation was then used to produce plots of indentation load (w) against indentation depth, the area under this curve giving the energy expended in forming the indentation. These energy values were plotted as a function of indentation (crater) diameter for each sphere size, assuming a mean sphere diameter within the sphere size range. The relationships are shown in Fig. 4. After mixing, the carrier liquids were heated to 40 “C by conducting a dummy erosion test in the liquid alone. A polished specimen was then mounted on the specimen frame and a known mass of glass beads added. Quantities ranged from 0.002 to 0.1 g and were selected so that the polished surface of the specimen was essentially covered with impact craters after about 10 min testing. These low concentrations of solids ensured that particle-particle interactions could be neglected [9]. The testing time was 60 s, usually continued for a further 60 s for each test condition. After each test period, the specimen was removed and the diameters of impact craters on the surface close to the stagnation line of the cylinder were measured for a number of craters, every crater traversing a line beneath the microscope objective being measured. ‘&pica1 results are shown in Fig. 5. The number of impact craters on known areas containing the stagnation line was also recorded. A second 60 s test period typicahy showed a doubling
169
Impact Crater Diameter (pm) Fig. 5. Histograms of erosion impact crater diameters: (a) 212-250 pm beads in water, 18.7 m s-’ nominal test speed; (b) 500-600 pm beads in 46.5% water, 53.5% glycerine, 18.7 m 5-I nominal test speed.
Fig. 6. Typical impact craters produced by 212-250 and 500-600 in water, tested at 18.7 m s-l; the bar represents 100 pm.
pm glass beads suspended
in the number of craters per unit area. Test times at 9.35 m s-l nodal rotation speed were 120 and 240 s to produce a comparable number of craters with testing at 18.7 m s-’ nominal speed. The exact number of glass beads was unknown, except in some tests with larger diameter beads where it was possible to count the number added to the pot. Otherwise the range of the number of beads in a given test was estimated from the mass, density and values of nominal maximum and minimum bead diameter.
3. Results Typical erosion impact craters are shown in Fig. 6 and the distribution of craters about the frontal surface of a specimen is shown in Fig. 7. In this specimen craters were found on the surface described by an arc of about 70” on either side of the front centerline. Almost exclusively, impact craters were well defined circles. The occasional elliptical craters observed were ignored in the assessment of crater size. Mean values of crater diameter, produced at various conditions of nominal testing speed, bead size and carrier liquid viscosity are given in Table 2. For beads in the 75-90 pm range,
,+
Stagnation Line
i
Fig. 7. Composite photograph of impact crater distribution firem I stagnation line (top) to glancing impact for X2-250 and 500 at 18.7 m s-‘; the bar represents 500 pm.
lal
bc
kacl: (90”) at the in water, te: ;ted
171 TABLE 2 Values of mean impact crater diameter for the test speeds, glass bead diameters and viscosities indicated Glass bead diameter (pm)
Mean impact crater diameter (pm) Carrier liquid viscosity at 40 “C (N s m-‘X
Nominal speed 18.7 m s-’ 750 500-600 212-250 Nominal speed 9.35 m s-l 750 500-600 212-250
0.66
3.63
102.3 36.4
146.0 102.6 33.3
133.1 88.4 21.6
-
105.6 71.0 20.8
77.2 51.2 =ll
78.6 27.6
20.0
103) 60.0
62.5 none 30.4 none
crater diameters were too small to be measured reliably and these data have not been included. However, it was possible to count the number of craters formed by beads of this size range. The flow pattern within the pot under the test conditions used is turbulent; the volume of the pot is swept out by the frontal area of the specimen at 18.7 m s- ’ in approximately 1.1 s. In analyzing the results it is assumed that the suspension is homogeneous, that complete mixing is achieved in a negligibly short time after start-up and that the specimen moves in a uniform environment. The impact frequency Ni on the projected normal surface of the specimen (number of impacts millimetres squared per minute) for each test condition was divided by the number of particles N, calculated to be in the volume swept by 1 mm2 of projected surface area each minute, to give values of the collision efficiency 7. That is, 77=NiINv
(1)
The value of Ni was determined from the average number of impact centers observed on a 0.4 mm wide strip along the front centerline (stagnation line) of the specimen. The value of N, was calculated from N, = 6ONIA, t,
(2)
where N is the number of beads added to the pot, A, (238.0 mm2) the projected frontal area of the specimen and t, the time in seconds for the specimen frontal area to sweep out the volume of the pot, i.e. the time for all beads to impact the specimen once, on average (at a collision efficiency of unity). This gave a value for N, of 0.224 N for a nominal rotation speed of 18.7 m s-’ and 0.112 N for 9.35 m s-l. Values of collision efficiency for each nominal velocity and bead size range are plotted with respect to
172
carrier liquid viscosity in Figs. 8 and 9. The extremities of the error range bars correspond with the nominal maximum and minimum bead sizes in the range. At larger bead sizes the exact number of beads used in the test was
1 0.6
1
21 Z-250 pm
6 10 2 Viscosity (103 NsfmZ)
\
20
60
100
Fig. 8. The variation of collision efficiency with viscosity for the test conditions indicated. Error bars reflect the range of particle numbers corresponding with the nominal diameter range, nominal test speed-18.7 & s-‘.
L
-\ \\ \\ \ \ \ :
i \ \
\ t t
\,212-250
1 I :
urn
h
75-90pm
Nominal Speed 9.35 m/s 10-3
'
“I
0.6
I”1
I
I
t /111/l
2 6 10 Viscosity(1O3 Nsim’)
,
20
,lIf
60 100
Fig. 9. The variation of colliision efficiency with viscosity for a nominal test speed of 9.35 m s-1.
173
0.5 t_
,.*,,,.,,
0.6
1
2
6
10
20
60
1 IO
Viscosity (lo3 Ns/m*)
Fig. 10. The variation of calculated impact velocity with viscosity 18.7 m s-’ for the bead sizes shown.
at a nominal
test speed of
10
5
0.6
1
2
6
10
20
60
100
Viscosity (1 O3 Ntim*)
Fig. 11. The variation of calculated impact velocity with viscosity 9.35 m s-’ for the bead sizes shown.
at a nominai test speed of
known and the error bars have been omitted. These data are represented by filled points. Measured crater diameters were compared with those produced by hardness test indentation of the surface. Values of the impact velocity were derived assuming that all the kinetic energy of the impacting bead under erosion conditions was expended in pfastie deformation of the copper specimen
174
that the of crater depended only the diameter kinetic energy the impacting and was of strain The kinetic was equated the indentation value corresponding the mean impact crater from Fig. Impact velocity were plotted respect to liquid viscosity each nominal speed and size in 10 and
4. Discussion 4.1. Collision eficiency The collision efficiency 17shows a strong dependence on viscosity, particle size and nominal rotation speed (Figs. 8 and 9). At lower viscosities and larger particle sizes the calculated values approach unity. This signifies that almost all the particles lying in the path of the erosion specimen under these circumstances collide with it. The velocity used to calculate NV, the number of particles lying in the path of the specimen, was the nominal rotation speed, either 18.7 or 9.35 m s-l, and must be close to the free-stream velocity, i.e. the speed of the erosion specimen relative to a particle in its path but distant from it. If this were not so and lower velocities were used, unacceptable values of collision efficiency greater than unity would result. Since the collision efficiency represents the proportion of particles which strikes the specimen, it is to be expected that under erosion conditions low values of collision efficiency will be associated with low values of erosion mass loss. Qualitatively, the origin of the observed drop in collision efficiency with increasing viscosity is straightforward. A liquid of high viscosity will exert a greater drag force on a particle than a liquid of low viscosity, so that as an element of high viscosity liquid starts to flow around the approaching cylindrical erosion specimen, it will be more effective in moving particles laterally than would liquid of low viscosity. As a consequence, at high viscosities, relatively few particles will be able to collide with the specimen, as is shown schematically in Fig. 12. Similarly, a small particle with a large ratio of surface area to volume is more easily swept aside by the flowing liquid than a large particle with its greater inertia. Indeed, under some conditions no impact craters were detected at all on the specimen surface (eg. 212-250 pm beads in 60 X lop3 N s m-’ liquid or 75-90 Frn beads in 20x 10e3 N s rnd2 liquid), giving a collision efficiency of zero. The concept of collision (striking) efficiency, already familiar in a number of problems in multi-phase fluid flow [ lo], has been applied to erosion by liquid suspensions [ 11, 121. Hojo et al. [ 1 l] incorporated the collision efficiency in an investigation of the rate of material loss from cylindrical specimens of polymethylmethacrylate eroded by dilute sand suspensions in water and found good correlation with experimental measurements of material loss. Clark [ 121 showed a strong correlation between measured rate of mass loss in the erosion of steel by liquid suspensions of alumina particles and
175 Particles
Non-l~acting
Low Viscosity
0
0
0
0 0 .
l a
k
a
L
-*
Center Line fC T
l
I
Collision
efficient,
q
II
18.7 m/s
rc
-_
Il
-.-
----------
0
0
O
3 3
0
High Viscosity
0
0
0
0
Fig. 12. Schematic diagram of flow of suspended liquid viscosity is low (above) and high (below).
particles
about a cylinder when the carrier
collision efficiency (calculated from the number of impacts per unit area of specimen) as a function of carrier liquid viscosity. 4.2. Impact velocity The assumption that all the kinetic energy of an impacting glass bead is dissipated in plastic deformation of the specimen is only valid if the particle does not rebound from the specimen surface, but in view of the low hardness of annealed copper, rebound energy is expected to be small and was neglected. The question of whether annealed copper shows a strain rate dependence of yield stress or work hardening rate remains unresolved. A simple calculation indicates that the strain rate for a 500 pm diameter glass sphere impacting on copper at 20 m s-’ is about 5 X 10” s-‘. Hutchings [ 131 has postulated an increase in yield stress with strain rate as a contributing factor to the observed decrease in erosion rate with particle size. However, more recently Hereil [ 14) reported no effect of strain rate on the yield stress of copper in the range lo3 to 5 x lo5 s- ’ and suggested that those increases reported may reflect changing test specimen geometry. Indeed, softening of copper under dynamic hardness test conditions has been reported f 151. For the purpose of this work impact crater size was assumed to be independent of strain rate. The plots of calculated impact velocity with respect to viscosity shown in Figs. IO and 11 appear to show a limiting impact velocity with decreasing carrier liquid viscosity for each particle size, and a sharp reduction in impact velocity at higher viscosities, especially for smaller particle sizes. Further, the limiting velocity is less than 50% of the nominal rotation speed of the specimen in the suspension for both test speeds.
176
The free-stream velocity is not revealed by the present data, except indirectly, through the calculation of the collision efficiency, which cannot exceed a value of unity. The calculated impact velocity, less than 50% of the nominal rotation speed, must be regarded as the result of interactions between particle, liquid and the specimen and the prevailing flow regime. Hojo et al. [ 111 have measured trajectories in a 1% glass-bead-water suspension at a velocity of 6 m s-i in channel flow about a 6 mm diameter polymer erosion specimen and found that 2 mm before the stagnation line there was already a deceleration of particles by as much as 50% of the freestream velocity. At the same time, particles passing around the specimen were found to undergo an increase in velocity in the flow direction of as much as 50%. In the current work little variation in crater size with angle of impact except for very low angles was found, as shown in Fig. 7. However, the crater size is presumably a function of the radial component of particle velocity and not of the particle speed. It is to be expected [ 161 that as the stagnation line on the cylindrical erosion specimen is approached, the component of velocity of the liquid in the free-stream direction will be reduced to zero and that this reduction will be detectable well before the cylinder surface, as indicated by the flow rate measurements of Hojo et al. [ 111. It is suggested that it is this effect that causes the impact velocities calculated from impact crater diameters to be less than 50% of the nominal rotation velocity even at low viscosity and large particle sizes. Because of relative inertia effects, the deceleration for small particles will be more marked than for large particles. In addition to this relatively large-scale effect, it is suggested that the boundary layer may also play an important role in determining particle impact speed. In order to impact the specimen a particle must penetrate the boundary layer of liquid on the specimen surface. The thickness 6 of the boundary layer at the stagnation point of a cylinder, diameter D, is given by 8=(1.2)0/G
(3)
where Re, is the Reynolds number for the cylinder (Re,=pV,D/p), p is the liquid density, V, the free-stream velocity and p the liquid viscosity. Plots of boundary layer thickness as a function of free-stream velocity for viscosities in the present investigation are given in Fig. 13. The boundary layer thickness increases rapidly with increasing viscosity and becomes similar in magnitude to the diameter of the impacting particles (which will themselves be associated with a boundary layer). Particles impacting the specimen must penetrate the boundary layers and will experience deceleration as they do so. The reduction in velocity will be greater with increasing liquid viscosity and decreasing particle size. It is suggested that this phenomenon contributes to the sharp decrease in impact velocity at higher viscosities, especially for smaller particle sizes as shown in Figs. 10 and 11. However a quantitative assessment of the effect of boundary layers on impact in erosion remains to be carried out.
177
\ 20
50
100
200
500
1000
Boundary Layer Thickness S (pm) Fig. 13. Variation of boundary layer thickness at the stagnation line with free stream velocity
for flow about a cylinder (after White [ 161).
For gas-borne powders flowing normal to an eroding surface Laitone [ 171 has predicted that the impact speed varies with high powers of the
free stream velocity. It is not clear whether this analysis is also applicable to slurry flow in which viscosity effects will be much more pronounced than in gas flow, although some experimental work has been conducted on velocity distribution and particle impact angles in normal impingement slurry flow using a slung jet [ 181. This work emphasizes the importance of establishing particle trajectories if the effect of experimental variables on the erosion rate is to be understood. 4.3. Erosion rate The erosion rate is used as a measure of the progress of damage but has been defined according to differing criteria in the literature. It may be defined as mass loss per unit area per unit impacting mass R, or as mass loss per unit area per unit time Rt. The former is useful for assessing the importance of individual impact events, whereas the latter is more appropriate for engineering parts in service. Unfortunately, calculations of erosion rate R, in the literature appear to be based on the assumption that all particles directed at the erosion specimen do impact it, i.e. a collision efficiency of unity. It is clear from the present work and that of Hojo et al. [ 11, 181 that this assumption is not necessarily valid. If the rate of material loss from the eroding surface is a function of the rate at which the kinetic energy of impacting particles is dissipated, as suggested by Finnie [ 11, the relative magnitudes of R, and Rt can be compared from the present data. If the average energy per impact is E,, for particles
178
of any chosen size, the value of R, expressed as R,
for a unit mass of particles may be (4)
a EiNm
where N, is the relative number of particles of that size in unit mass. Values of Ei (for particles impacting close to the stagnation line), N, and relative values of R, (normalized to the value for 750 wrn glass beads at nominal velocity of 18.7 m s- ’ in water) are given in Table 3. Normalized values of R, are plotted in Fig. 14 as a function of viscosity. Were erosive mass loss directly proportional to the total kinetic energy of impact dissipated (mr”l2) and were there no flow effects tending to reduce impact velocity, the plots of R, with respect to viscosity would be horizontal lines, with the rate for all particle sizes at 18.7 m s- ’ four times that for 9.35 m s- ’ . The reduction in R, with decreasing particle size and at higher viscosities results from the smaller values of IS’, produced by the decrease in impact velocity for smaller particles and carrier liquids of higher viscosity. This reduction in impact velocity has been ascribed here to particle TABLE 3 Calculated conditions
impact energies,
collision
efficiencies
Test conditions Nominal speed (m s-l) particle diameter (pm)
Viscosity (N s mm2X 103)
18.7, 750 N,=N,,,= 1
0.66 3.63 20.0
18.7, 550 N,=N,,,=2.28
0.66 3.63 20.0 60.0
18.7, 230 N,=N,,,=34.7
0.66 3.63 20.0
9.35, 750 N,=O.5, N,=
1
0.66 3.63 20.0
and derived relative erosion
Impact energy,
rates for all test
Collision efficiency mean
Relative erosion rate R,
Relative erosion rate R,
(0.9) 0.825 0.567
1.0 1.0 0.67
1.0 0.92 0.42
6.2 6.2 3.3 0.65
0.61 0.59 0.34 0.28
0.83 0.83 0.44 0.09
0.56 0.54 0.17 0.03
0.21 0.15 0.021
0.46 0.325 0.12
0.43 0.31 0.04
0.22 0.11 0.006
0.35 0.23 0.06
0.11 0.07 0.01
E, (JX 10e6)
(17) 17 11.3
(6.0) 3.9 0.98
(0.55) 0.52 0.42
9.35, 550 Nt= 1.14, N,,,=2.28
0.66 3.63 20.0 60.0
1.9 1.2 0.27 0.027
0.41 0.365 0.25 0.068
0.25 0.16 0.04 0.0035
0.06 0.03 0.005 0.00014
9.35, 230 Nt= 17.3, N,,,=34.7
0.66 3.63 20.0
0.06 0.02 0.0013
0.34 0.145 0.035
0.12 0.04 0.0026
0.02 0.0033 0.00005
Figures
in parentheses
are extrapolated.
179
Viscosity
(lo3
Ns/m2)
Fig. 14. Variation of relative erosion rate per unit mass of impacting particles of viscosity for test speeds of 18.7 m S-I (-) and 9.35 m s-’ (---).
R, as a function
inertia and drag effects as well as boundary layer deceleration of impacting beads. An assumption of unit collision efficiency is not valid for the present data. The erosion rate R, may be expressed as J4 a &%I
(5)
where Nt is the relative number of particles in the path of unit area of the specimen surface per unit time and 77 the prevailing collision efficiency. These values are given in Table 3. It should be noted that in a pot tester at a nominal speed of V/Z the number of particles in the path of the specimen in unit time is one half of the number at test speed V. Relative values of Rt have been normalized to the value of 750 ,um beads in water at a nominal test speed of 18.7 m s-’ and are shown in Fig. 15. There are some difficulties, however, to this approach of estimating relative erosion rates. These include the following. (1) It is difficult to estimate, much less predict, the impact velocity of particles without direct measurement of the type used here or a proven computer model of the erosion process. It is clear, however, that estimates of impact velocity as essentially corresponding with the free stream velocity will generally not be correct. (2) The impact velocity of particles will vary with the location on the cylinder circumference so that the assumption of a mean value of energy dissipation per impact Ei may be too simple. However, the specimen surface in Fig. 7 shows that impact crater diameters are similar, except for those formed by glancing angle impact. (3) The collision efficiency is difllcult to determine and, especially for small particle sizes and higher viscosities, may be much less than unity.
180
0.4
0.6
1
2
4
6
10
20
40
60
100
Viscosity (IO3 Ns/m2) 15. Variation of relative erosion rate per unit time I& as a function of viscosity for test speeds of 18.7 m SC’ f-) and 9.35 m s-j (---).
Fig.
Nevertheless, if the relationship between particle impact energy and the rate of mass loss in erosion is to be clarified, knowledge of the proportion of particles impacting the eroding surface must be incorporated. 4.4. Effect of testing speed As noted earlier, the free-stream velocity for these tests is not precisely known. However, it is not unreasonable to assume that for tests at 9.35 m s-’ it will be one half of the value of the free-stream velocity at 18.7 m s - ’ . Many investigations of velocity effects in erosion in slurries have determined the velocity exponent for erosion to be greater than 2, the value derived from the erosion rate dependent on the dissipation of kinetic energy alone 119-251. The relative erosion rates R, and Rt for the 550 @rn glass beads over the viscosity range are shown in Fig. 16 as a function of nominal test speed. The velocity exponents for each viscosity condition are given. Values of R, drop at the lower test speed, owing to the decrease in impact velocity, the effect increasing with increasing viscosity. The values of R, are more dramatically affected because of the influence of flow conditions (collision efficiency) in reducing the number of particles impacting the specimen. That velocity exponents greater than 2 should be found may not be surprising if the increase in velocity is also accompanied by an increase in collision efficiency. In view of the variability of the velocity exponent revealed by these results its usefulness as an inherent characteristic of the erosion process is dubious.
181
, l_
2_
60.0
3_
4_
1
1
9.35
18.7 Nominal RotationSpeed
9.35
10.7
(.nIs)
Fig. 16. Variation of relative erosion rates R, and R, for 550 pm glass beads as a function of test speed at viscosities indicated (units N s m -2~ 10e3); velocity exponents are marked for each viscosity condition.
5. Conclusions
(1) The impact velocity of particles close to the stagnation point on a cylindrical erosion specimen was found to be less than 50% of the nominal specimen rotation speed owing to the change in flow conditions as a particle approaches the stagnation line of .the specimen. (2) The calculated impact speed of particles decreased at an increasing rate with increasing carrier liquid viscosity for a given test speed. (3) The decrease in impact speed with increasing carrier liquid viscosity occurs at lower viscosities for smaller particle sizes because of their lower inertia compared with larger particles. (4) The rate of collision of particles with the erosion specimen, expressed as the collision efficiency 77,falls rapidly with increasing viscosity, decreasing particle size and decreasing test speed. (5) The fall in erosion rates often observed with increasing viscosity, decreasing particle size and decreasing test speed, reflects the changes in flow interaction of liquid, particles and eroding surface and emphasizes the
182
need for knowledge of particle trajectories by liquid suspensions.
in the ~d~rst~djng
of erosion
Acknowledgments The author wishes to thank Lawrence Technology, Lawrence, KS for providing the copper rod used in this work which was supported in part by the Center for Research, Inc. of the Universi~ of Kansas.
References
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6 7 8 9 10 11 12
13 14
15 16 17 18 19 20 21
I. Fiinic, Erosion of surfaces by solid particles, Wear, 3 (1960) 87. I. M. Hutchings, A model for the erosion of metals by spherical particles at normal lncidcnce, Wear, 70 (1981) 269. G. Sundered, An analysis of the localization of deformation and weight loss during single-particle normal impact, Wear, 84 (1983) 217. M. Naim and S. Bahadur, Work hardening in erosion due to single particic impacts, Proc. Int. CmJ on Wear of Materials, American Society of Mechanical Engineers, New York, 1983, p. 340. J. R. Keiser, The relationship of an alloy’s mechanical properties to its response to individual erosive particle impacts, Proc. Co@ on CorrosimGErosion-Wear of Materials at Elevated Temperatures, National Association of Corrosion Engineers, Houston, TX, 1986, p. 345. A. V. Levy, The platelet mechanism of erosion in ductile metals, Wear, 108 (1986) 1. H. MCI. Clark, Met~lo~phic aspects of fatigue defo~ation in some ordering solid solutions, Ph.D. Thesis, University of London, 1966. J. B. Segur and H. E. Oberstar, Viscosity of glycerol and its aqueous solutions, Ind. Erzg. Chern., 43 (1951) 2117. H. H. Steinour, Rate of sedimentation, In&. Eng. Chem., 36 (1944) 618; 840; 901. S. L. Soo, FYuid Dl/namics of Multiphase S?&ems, Blaisdell, Waltham, MA, 1967. H. Hojo, K. Tsuda and T. Yabu, Erosion damage of polymeric material by slurry, Wear, 112 (1986) 17. H. MCI. Clark, The effect of carrier liquid viscosity on the erosion rate of steel by solid/ liquid suspensions and the nature of the wear debris produced, Proc. 5th Int. Congress on ~&o~g~, Fin&h Society for Tribology, Helsinki, 1989. I. M. Hutchings, Strain rate effects in microparticle impact, J. Phys. D, 10 (1977) L179. P. L. Here& On the strain rate dependence of yield stresses of copper at high strain rates, Proc. Irit. Cor+& on Impact Loading and Dynamic Behaviour of Materials (IMPACT ‘871, Vol. 1, DGM Informationsgesellschaft, Oberursel, 1988. T. H. Kosel, Center for Materials Science and Engineering, Notre Dame University, private communication, 1990. F. M. White, Yticous Fluti Flow, McGraw-Hill, New York, 1974. J. A. Laitone, Aerodynamic effects in the erosion process, Wear, 56 (1979) 239. H. Hojo, K. Tsuda, K. Shirato and T. Yabu, Erosion behavior of plastics by slurry jet method, Kagaku Kogaku R~bu~hu, 14 (1988) 161. A. V. Levy and G. Hickey, Liquid-solid particle slurry erosion of steels, Wear, 117 (1987) 129. A. V. Levy, N. Jee and P. Yau, Erosion of steels in coal-solvent slurries, Wear, 117 (1987) 115. C. Lhymn and P. Wapner, Slurry erosion of polyphenylene sulfide-glass fiber composites, Weur, 119 (1987) 1.
183 22 H. MCI. Clark, A comparison of the erosion rate of casing steels by sand/oil suspensions, Wear, in the press. 23 J. J. Tuzson, Laboratory slurry erosion tests and pump wear rate calculations, J. Fluids Eng., 106 (1984) 135. 24 A. V. Levy, J. Yan and V. D. Arora, Sand-water slurry erosion of carburized AISI 8620 steel, Wear, 101 (1985) 117. 25 H. MCI. Clark, Shury erosion, Proc. Cc@ 072 Corrosion-Erosio+Wear of Materials at Elevated Temperatures, National Association of Corrosion Engineers, Houston, TX, in the press.
165
165-183
On the impact rate and impact energy of particles slurry pot erosion tester*
in a
Hector MCI. Clark Department of Mechanical Engineering, (7JLT.A.)
Universi@
of Kansas, Lawrence, KS 66045-2234
(Received September 24, 1990; accepted November 21, 1990)
Abstract Short-time erosion tests were conducted with dilute water and water-glycerin suspensions of glass beads to determine the rate of particle impact and the dimensions of impact craters using annealed and electropolished OF’HC copper rod specimens. Particle diameters were 75-90, 212-250, 500-600 and 750 pm, nominal rotation speeds of the erosion targets in the pot were 9.35 and 18.7 m s-’ and the carrier liquid viscosity was in the range (0.66-60)x 10e3 N s m-‘, (0.66-60 cp). The work done in forming a crater of specified diameter was determined for each particle size by indentation using a single glass bead mounted on a microhardness tester. Using the assumption that all the kinetic energy of an impacting bead was dissipated in plastic work, the impact velocities of particles forming craters were calculated for most test conditions. The collision efficiency for the specimen was determined for most test conditions and was found to decrease with decreasing nominal velocity, increasing carrier liquid viscosity and decreasing particle size. The erosion rate, expressed as either material lost per unit area per unit mass of impacting particles or material lost per unit area per unit time, was estimated and shown to be strongly affected by the flow conditions for individual particles.
1. Introduction While the formation of significant erosion damage is the result of collisions of many particles with an eroding body, there has been continuing interest in the events associated with the impact of single particles and the consequent progress of damage [l-6] in an effort to elucidate the processes leading to material loss. Analysis of ~di~du~ impacts of gas-borne spheres has been undertaken by Hutchmgs [Z] who concluded that more than 90% of the energy of a sphere impacting on a soft copper target is consumed in plastic deformation to form a crater on the surface. Assuming the validity of this conclusion for slurry erosion, an examination of the frequency of impact and the size of impact craters produced in annealed copper by individual glass beads was undertaken using dilute suspensions of glass beads in water-glycerin carrier liquids at nominal erosion speeds of 9.35 and *Paper presented at the 4th Berkeley Conference on Corrosion-Erosion-Wear at Elevated Temperatures, Berkeley, CA, January 31-February 2, 1990.
0043-1648/91/$3.50
of Materials
0 Elsevier Sequoiafl?rinted in The Netherlands
166
18.7 m s- ’ in a slurry pot tester. From these data the proportion of particles impacting the specimen and values of mean particle impact velocity were derived.
2. Experimental
details
All testing was conducted in the slurry erosion pot shown in Fig. 1. This consisted of a circular section stainless steel vessel, 5000 ml volume, with a central stainfess steel shaft supporting two vertically positioned cyfindricd test specimens. Each specimen was supported by nylon spacers of the same diameter. These spacers prevent the generation of corrosion couples between the specimens and the stainless steel support frames. They also lessen the influence of the suspension flow pattern produced by the rotating frame. The shaft was driven by a 3.7 kW electric motor operating at a speed of 3515 rev min-’ through a toothed belt. Using pulleys of different sizes, the nominal rotation speed at the specimen support point 51 mm from the rotation axis could be set at either 9.35 or 18.7 m s-l. The vessel was equipped with four baffles extending 12 mm into the pot to disrupt liquid rotation during testing. The vessel was also vented to prevent pressure built-up. Temperature control of the Iiquid suspensions to 40 t- 1 “C was achieved through a heating tape around the body of the pot and two internal water-cooled copper coils. Erosion test specimens were produced from 5.17 mm diameter cold drawn high-conductivity copper rod. The hardness after annealing for 1 h at 300 “C was in the range Rockwell F 48-54, Shore scleroscope 4. Erosion test specimens were 46 mm long, each with 2 mm pin extensions to locate
Erosion Specimen
Stainless Steel
+.----165-4 Fig.
1. Schematic diagram of erosion pot tester, dimensions in milliicters.
167
the specimens in the nylon supports. Specimens were polished with 1 pm diamond paste followed by electropolishing for 2.5 h as the anode in concentrated orthophosphoric acid at 1.7 V d.c. This polishing process produces a highly reflecting and strain-free surface [ 71. Suspensions were made up from distilled water which had been freshly boiled to remove dissolved oxygen and minimize corrosion, with or without additions of glycerin. The liquid compositions were selected to give chosen values of viscosity for the carrier liquid at 40 “C, shown in Table 1, using published viscosity data [S]. Glass beads, of density 2420 kg me3, and diameters in the ranges 75-90, 212-250, 500-600 and 750 pm were used in these tests (Fig. 2). Tests at all viscosities and both rotation speeds were conducted using beads in the size ranges 212-250 and 500-600 km. In order to provide a calibration of impact crater size in the copper erosion test specimens, a Leitz direct-loading microhardness tester was used to provide data on the size of indentations produced at low strain rates by using indentors on which a single glass bead was mounted. Indentation diameter was plotted as a function of indentation mass for spheres of diameter 78, 213, 574 and 750 pm as shown in Fig. 3. The calculated depth of each TABLE 1 Composition, viscosity (at 40 “C), density and cylinder Reynolds number for carrier liquids used in this investigation Composition (wt.%) Water
Glycerin
100.0 46.5 20.5 10.0
0.0 53.5 79.5 90.0
Viscosity (N s m-‘X
0.66 3.63 20.0 60.0
103)
Density (kg me3)
Reynolds number Reu 18.7 m s-’
9.35 m s-l
998 1139 1208 1236
146000 30400 5850 1990
73000 15200 2925 995
Fig. 2. Three of the sizes of glass beads wed in this investigation, 75-90, 500-600 pm; the bar represents 1 mm.
212-250
and
168
1000
750 pm 550 pm
500-
10-e =
300E
200-
2 r" s .Z s fi -a t
loo-
504030 2510-e
5
6
10
Indentation Diameter (pm)
Fig. 3. Diameters of microhardness mass for indcntor bead diameters Fig. 4. Work done (energy) diameters shown.
~dentatio~s shown.
in indentation
in annealed
with respect
20 40 60 100 Crater Diameter (pm)
200
copper as a function of indentation to crater
diameter
for the indcntor
indentation was then used to produce plots of indentation load (w) against indentation depth, the area under this curve giving the energy expended in forming the indentation. These energy values were plotted as a function of indentation (crater) diameter for each sphere size, assuming a mean sphere diameter within the sphere size range. The relationships are shown in Fig. 4. After mixing, the carrier liquids were heated to 40 “C by conducting a dummy erosion test in the liquid alone. A polished specimen was then mounted on the specimen frame and a known mass of glass beads added. Quantities ranged from 0.002 to 0.1 g and were selected so that the polished surface of the specimen was essentially covered with impact craters after about 10 min testing. These low concentrations of solids ensured that particle-particle interactions could be neglected [9]. The testing time was 60 s, usually continued for a further 60 s for each test condition. After each test period, the specimen was removed and the diameters of impact craters on the surface close to the stagnation line of the cylinder were measured for a number of craters, every crater traversing a line beneath the microscope objective being measured. ‘&pica1 results are shown in Fig. 5. The number of impact craters on known areas containing the stagnation line was also recorded. A second 60 s test period typicahy showed a doubling
169
Impact Crater Diameter (pm) Fig. 5. Histograms of erosion impact crater diameters: (a) 212-250 pm beads in water, 18.7 m s-’ nominal test speed; (b) 500-600 pm beads in 46.5% water, 53.5% glycerine, 18.7 m 5-I nominal test speed.
Fig. 6. Typical impact craters produced by 212-250 and 500-600 in water, tested at 18.7 m s-l; the bar represents 100 pm.
pm glass beads suspended
in the number of craters per unit area. Test times at 9.35 m s-l nodal rotation speed were 120 and 240 s to produce a comparable number of craters with testing at 18.7 m s-’ nominal speed. The exact number of glass beads was unknown, except in some tests with larger diameter beads where it was possible to count the number added to the pot. Otherwise the range of the number of beads in a given test was estimated from the mass, density and values of nominal maximum and minimum bead diameter.
3. Results Typical erosion impact craters are shown in Fig. 6 and the distribution of craters about the frontal surface of a specimen is shown in Fig. 7. In this specimen craters were found on the surface described by an arc of about 70” on either side of the front centerline. Almost exclusively, impact craters were well defined circles. The occasional elliptical craters observed were ignored in the assessment of crater size. Mean values of crater diameter, produced at various conditions of nominal testing speed, bead size and carrier liquid viscosity are given in Table 2. For beads in the 75-90 pm range,
,+
Stagnation Line
i
Fig. 7. Composite photograph of impact crater distribution firem I stagnation line (top) to glancing impact for X2-250 and 500 at 18.7 m s-‘; the bar represents 500 pm.
lal
bc
kacl: (90”) at the in water, te: ;ted
171 TABLE 2 Values of mean impact crater diameter for the test speeds, glass bead diameters and viscosities indicated Glass bead diameter (pm)
Mean impact crater diameter (pm) Carrier liquid viscosity at 40 “C (N s m-‘X
Nominal speed 18.7 m s-’ 750 500-600 212-250 Nominal speed 9.35 m s-l 750 500-600 212-250
0.66
3.63
102.3 36.4
146.0 102.6 33.3
133.1 88.4 21.6
-
105.6 71.0 20.8
77.2 51.2 =ll
78.6 27.6
20.0
103) 60.0
62.5 none 30.4 none
crater diameters were too small to be measured reliably and these data have not been included. However, it was possible to count the number of craters formed by beads of this size range. The flow pattern within the pot under the test conditions used is turbulent; the volume of the pot is swept out by the frontal area of the specimen at 18.7 m s- ’ in approximately 1.1 s. In analyzing the results it is assumed that the suspension is homogeneous, that complete mixing is achieved in a negligibly short time after start-up and that the specimen moves in a uniform environment. The impact frequency Ni on the projected normal surface of the specimen (number of impacts millimetres squared per minute) for each test condition was divided by the number of particles N, calculated to be in the volume swept by 1 mm2 of projected surface area each minute, to give values of the collision efficiency 7. That is, 77=NiINv
(1)
The value of Ni was determined from the average number of impact centers observed on a 0.4 mm wide strip along the front centerline (stagnation line) of the specimen. The value of N, was calculated from N, = 6ONIA, t,
(2)
where N is the number of beads added to the pot, A, (238.0 mm2) the projected frontal area of the specimen and t, the time in seconds for the specimen frontal area to sweep out the volume of the pot, i.e. the time for all beads to impact the specimen once, on average (at a collision efficiency of unity). This gave a value for N, of 0.224 N for a nominal rotation speed of 18.7 m s-’ and 0.112 N for 9.35 m s-l. Values of collision efficiency for each nominal velocity and bead size range are plotted with respect to
172
carrier liquid viscosity in Figs. 8 and 9. The extremities of the error range bars correspond with the nominal maximum and minimum bead sizes in the range. At larger bead sizes the exact number of beads used in the test was
1 0.6
1
21 Z-250 pm
6 10 2 Viscosity (103 NsfmZ)
\
20
60
100
Fig. 8. The variation of collision efficiency with viscosity for the test conditions indicated. Error bars reflect the range of particle numbers corresponding with the nominal diameter range, nominal test speed-18.7 & s-‘.
L
-\ \\ \\ \ \ \ :
i \ \
\ t t
\,212-250
1 I :
urn
h
75-90pm
Nominal Speed 9.35 m/s 10-3
'
“I
0.6
I”1
I
I
t /111/l
2 6 10 Viscosity(1O3 Nsim’)
,
20
,lIf
60 100
Fig. 9. The variation of colliision efficiency with viscosity for a nominal test speed of 9.35 m s-1.
173
0.5 t_
,.*,,,.,,
0.6
1
2
6
10
20
60
1 IO
Viscosity (lo3 Ns/m*)
Fig. 10. The variation of calculated impact velocity with viscosity 18.7 m s-’ for the bead sizes shown.
at a nominal
test speed of
10
5
0.6
1
2
6
10
20
60
100
Viscosity (1 O3 Ntim*)
Fig. 11. The variation of calculated impact velocity with viscosity 9.35 m s-’ for the bead sizes shown.
at a nominai test speed of
known and the error bars have been omitted. These data are represented by filled points. Measured crater diameters were compared with those produced by hardness test indentation of the surface. Values of the impact velocity were derived assuming that all the kinetic energy of the impacting bead under erosion conditions was expended in pfastie deformation of the copper specimen
174
that the of crater depended only the diameter kinetic energy the impacting and was of strain The kinetic was equated the indentation value corresponding the mean impact crater from Fig. Impact velocity were plotted respect to liquid viscosity each nominal speed and size in 10 and
4. Discussion 4.1. Collision eficiency The collision efficiency 17shows a strong dependence on viscosity, particle size and nominal rotation speed (Figs. 8 and 9). At lower viscosities and larger particle sizes the calculated values approach unity. This signifies that almost all the particles lying in the path of the erosion specimen under these circumstances collide with it. The velocity used to calculate NV, the number of particles lying in the path of the specimen, was the nominal rotation speed, either 18.7 or 9.35 m s-l, and must be close to the free-stream velocity, i.e. the speed of the erosion specimen relative to a particle in its path but distant from it. If this were not so and lower velocities were used, unacceptable values of collision efficiency greater than unity would result. Since the collision efficiency represents the proportion of particles which strikes the specimen, it is to be expected that under erosion conditions low values of collision efficiency will be associated with low values of erosion mass loss. Qualitatively, the origin of the observed drop in collision efficiency with increasing viscosity is straightforward. A liquid of high viscosity will exert a greater drag force on a particle than a liquid of low viscosity, so that as an element of high viscosity liquid starts to flow around the approaching cylindrical erosion specimen, it will be more effective in moving particles laterally than would liquid of low viscosity. As a consequence, at high viscosities, relatively few particles will be able to collide with the specimen, as is shown schematically in Fig. 12. Similarly, a small particle with a large ratio of surface area to volume is more easily swept aside by the flowing liquid than a large particle with its greater inertia. Indeed, under some conditions no impact craters were detected at all on the specimen surface (eg. 212-250 pm beads in 60 X lop3 N s m-’ liquid or 75-90 Frn beads in 20x 10e3 N s rnd2 liquid), giving a collision efficiency of zero. The concept of collision (striking) efficiency, already familiar in a number of problems in multi-phase fluid flow [ lo], has been applied to erosion by liquid suspensions [ 11, 121. Hojo et al. [ 1 l] incorporated the collision efficiency in an investigation of the rate of material loss from cylindrical specimens of polymethylmethacrylate eroded by dilute sand suspensions in water and found good correlation with experimental measurements of material loss. Clark [ 121 showed a strong correlation between measured rate of mass loss in the erosion of steel by liquid suspensions of alumina particles and
175 Particles
Non-l~acting
Low Viscosity
0
0
0
0 0 .
l a
k
a
L
-*
Center Line fC T
l
I
Collision
efficient,
q
II
18.7 m/s
rc
-_
Il
-.-
----------
0
0
O
3 3
0
High Viscosity
0
0
0
0
Fig. 12. Schematic diagram of flow of suspended liquid viscosity is low (above) and high (below).
particles
about a cylinder when the carrier
collision efficiency (calculated from the number of impacts per unit area of specimen) as a function of carrier liquid viscosity. 4.2. Impact velocity The assumption that all the kinetic energy of an impacting glass bead is dissipated in plastic deformation of the specimen is only valid if the particle does not rebound from the specimen surface, but in view of the low hardness of annealed copper, rebound energy is expected to be small and was neglected. The question of whether annealed copper shows a strain rate dependence of yield stress or work hardening rate remains unresolved. A simple calculation indicates that the strain rate for a 500 pm diameter glass sphere impacting on copper at 20 m s-’ is about 5 X 10” s-‘. Hutchings [ 131 has postulated an increase in yield stress with strain rate as a contributing factor to the observed decrease in erosion rate with particle size. However, more recently Hereil [ 14) reported no effect of strain rate on the yield stress of copper in the range lo3 to 5 x lo5 s- ’ and suggested that those increases reported may reflect changing test specimen geometry. Indeed, softening of copper under dynamic hardness test conditions has been reported f 151. For the purpose of this work impact crater size was assumed to be independent of strain rate. The plots of calculated impact velocity with respect to viscosity shown in Figs. IO and 11 appear to show a limiting impact velocity with decreasing carrier liquid viscosity for each particle size, and a sharp reduction in impact velocity at higher viscosities, especially for smaller particle sizes. Further, the limiting velocity is less than 50% of the nominal rotation speed of the specimen in the suspension for both test speeds.
176
The free-stream velocity is not revealed by the present data, except indirectly, through the calculation of the collision efficiency, which cannot exceed a value of unity. The calculated impact velocity, less than 50% of the nominal rotation speed, must be regarded as the result of interactions between particle, liquid and the specimen and the prevailing flow regime. Hojo et al. [ 111 have measured trajectories in a 1% glass-bead-water suspension at a velocity of 6 m s-i in channel flow about a 6 mm diameter polymer erosion specimen and found that 2 mm before the stagnation line there was already a deceleration of particles by as much as 50% of the freestream velocity. At the same time, particles passing around the specimen were found to undergo an increase in velocity in the flow direction of as much as 50%. In the current work little variation in crater size with angle of impact except for very low angles was found, as shown in Fig. 7. However, the crater size is presumably a function of the radial component of particle velocity and not of the particle speed. It is to be expected [ 161 that as the stagnation line on the cylindrical erosion specimen is approached, the component of velocity of the liquid in the free-stream direction will be reduced to zero and that this reduction will be detectable well before the cylinder surface, as indicated by the flow rate measurements of Hojo et al. [ 111. It is suggested that it is this effect that causes the impact velocities calculated from impact crater diameters to be less than 50% of the nominal rotation velocity even at low viscosity and large particle sizes. Because of relative inertia effects, the deceleration for small particles will be more marked than for large particles. In addition to this relatively large-scale effect, it is suggested that the boundary layer may also play an important role in determining particle impact speed. In order to impact the specimen a particle must penetrate the boundary layer of liquid on the specimen surface. The thickness 6 of the boundary layer at the stagnation point of a cylinder, diameter D, is given by 8=(1.2)0/G
(3)
where Re, is the Reynolds number for the cylinder (Re,=pV,D/p), p is the liquid density, V, the free-stream velocity and p the liquid viscosity. Plots of boundary layer thickness as a function of free-stream velocity for viscosities in the present investigation are given in Fig. 13. The boundary layer thickness increases rapidly with increasing viscosity and becomes similar in magnitude to the diameter of the impacting particles (which will themselves be associated with a boundary layer). Particles impacting the specimen must penetrate the boundary layers and will experience deceleration as they do so. The reduction in velocity will be greater with increasing liquid viscosity and decreasing particle size. It is suggested that this phenomenon contributes to the sharp decrease in impact velocity at higher viscosities, especially for smaller particle sizes as shown in Figs. 10 and 11. However a quantitative assessment of the effect of boundary layers on impact in erosion remains to be carried out.
177
\ 20
50
100
200
500
1000
Boundary Layer Thickness S (pm) Fig. 13. Variation of boundary layer thickness at the stagnation line with free stream velocity
for flow about a cylinder (after White [ 161).
For gas-borne powders flowing normal to an eroding surface Laitone [ 171 has predicted that the impact speed varies with high powers of the
free stream velocity. It is not clear whether this analysis is also applicable to slurry flow in which viscosity effects will be much more pronounced than in gas flow, although some experimental work has been conducted on velocity distribution and particle impact angles in normal impingement slurry flow using a slung jet [ 181. This work emphasizes the importance of establishing particle trajectories if the effect of experimental variables on the erosion rate is to be understood. 4.3. Erosion rate The erosion rate is used as a measure of the progress of damage but has been defined according to differing criteria in the literature. It may be defined as mass loss per unit area per unit impacting mass R, or as mass loss per unit area per unit time Rt. The former is useful for assessing the importance of individual impact events, whereas the latter is more appropriate for engineering parts in service. Unfortunately, calculations of erosion rate R, in the literature appear to be based on the assumption that all particles directed at the erosion specimen do impact it, i.e. a collision efficiency of unity. It is clear from the present work and that of Hojo et al. [ 11, 181 that this assumption is not necessarily valid. If the rate of material loss from the eroding surface is a function of the rate at which the kinetic energy of impacting particles is dissipated, as suggested by Finnie [ 11, the relative magnitudes of R, and Rt can be compared from the present data. If the average energy per impact is E,, for particles
178
of any chosen size, the value of R, expressed as R,
for a unit mass of particles may be (4)
a EiNm
where N, is the relative number of particles of that size in unit mass. Values of Ei (for particles impacting close to the stagnation line), N, and relative values of R, (normalized to the value for 750 wrn glass beads at nominal velocity of 18.7 m s- ’ in water) are given in Table 3. Normalized values of R, are plotted in Fig. 14 as a function of viscosity. Were erosive mass loss directly proportional to the total kinetic energy of impact dissipated (mr”l2) and were there no flow effects tending to reduce impact velocity, the plots of R, with respect to viscosity would be horizontal lines, with the rate for all particle sizes at 18.7 m s- ’ four times that for 9.35 m s- ’ . The reduction in R, with decreasing particle size and at higher viscosities results from the smaller values of IS’, produced by the decrease in impact velocity for smaller particles and carrier liquids of higher viscosity. This reduction in impact velocity has been ascribed here to particle TABLE 3 Calculated conditions
impact energies,
collision
efficiencies
Test conditions Nominal speed (m s-l) particle diameter (pm)
Viscosity (N s mm2X 103)
18.7, 750 N,=N,,,= 1
0.66 3.63 20.0
18.7, 550 N,=N,,,=2.28
0.66 3.63 20.0 60.0
18.7, 230 N,=N,,,=34.7
0.66 3.63 20.0
9.35, 750 N,=O.5, N,=
1
0.66 3.63 20.0
and derived relative erosion
Impact energy,
rates for all test
Collision efficiency mean
Relative erosion rate R,
Relative erosion rate R,
(0.9) 0.825 0.567
1.0 1.0 0.67
1.0 0.92 0.42
6.2 6.2 3.3 0.65
0.61 0.59 0.34 0.28
0.83 0.83 0.44 0.09
0.56 0.54 0.17 0.03
0.21 0.15 0.021
0.46 0.325 0.12
0.43 0.31 0.04
0.22 0.11 0.006
0.35 0.23 0.06
0.11 0.07 0.01
E, (JX 10e6)
(17) 17 11.3
(6.0) 3.9 0.98
(0.55) 0.52 0.42
9.35, 550 Nt= 1.14, N,,,=2.28
0.66 3.63 20.0 60.0
1.9 1.2 0.27 0.027
0.41 0.365 0.25 0.068
0.25 0.16 0.04 0.0035
0.06 0.03 0.005 0.00014
9.35, 230 Nt= 17.3, N,,,=34.7
0.66 3.63 20.0
0.06 0.02 0.0013
0.34 0.145 0.035
0.12 0.04 0.0026
0.02 0.0033 0.00005
Figures
in parentheses
are extrapolated.
179
Viscosity
(lo3
Ns/m2)
Fig. 14. Variation of relative erosion rate per unit mass of impacting particles of viscosity for test speeds of 18.7 m S-I (-) and 9.35 m s-’ (---).
R, as a function
inertia and drag effects as well as boundary layer deceleration of impacting beads. An assumption of unit collision efficiency is not valid for the present data. The erosion rate R, may be expressed as J4 a &%I
(5)
where Nt is the relative number of particles in the path of unit area of the specimen surface per unit time and 77 the prevailing collision efficiency. These values are given in Table 3. It should be noted that in a pot tester at a nominal speed of V/Z the number of particles in the path of the specimen in unit time is one half of the number at test speed V. Relative values of Rt have been normalized to the value of 750 ,um beads in water at a nominal test speed of 18.7 m s-’ and are shown in Fig. 15. There are some difficulties, however, to this approach of estimating relative erosion rates. These include the following. (1) It is difficult to estimate, much less predict, the impact velocity of particles without direct measurement of the type used here or a proven computer model of the erosion process. It is clear, however, that estimates of impact velocity as essentially corresponding with the free stream velocity will generally not be correct. (2) The impact velocity of particles will vary with the location on the cylinder circumference so that the assumption of a mean value of energy dissipation per impact Ei may be too simple. However, the specimen surface in Fig. 7 shows that impact crater diameters are similar, except for those formed by glancing angle impact. (3) The collision efficiency is difllcult to determine and, especially for small particle sizes and higher viscosities, may be much less than unity.
180
0.4
0.6
1
2
4
6
10
20
40
60
100
Viscosity (IO3 Ns/m2) 15. Variation of relative erosion rate per unit time I& as a function of viscosity for test speeds of 18.7 m SC’ f-) and 9.35 m s-j (---).
Fig.
Nevertheless, if the relationship between particle impact energy and the rate of mass loss in erosion is to be clarified, knowledge of the proportion of particles impacting the eroding surface must be incorporated. 4.4. Effect of testing speed As noted earlier, the free-stream velocity for these tests is not precisely known. However, it is not unreasonable to assume that for tests at 9.35 m s-’ it will be one half of the value of the free-stream velocity at 18.7 m s - ’ . Many investigations of velocity effects in erosion in slurries have determined the velocity exponent for erosion to be greater than 2, the value derived from the erosion rate dependent on the dissipation of kinetic energy alone 119-251. The relative erosion rates R, and Rt for the 550 @rn glass beads over the viscosity range are shown in Fig. 16 as a function of nominal test speed. The velocity exponents for each viscosity condition are given. Values of R, drop at the lower test speed, owing to the decrease in impact velocity, the effect increasing with increasing viscosity. The values of R, are more dramatically affected because of the influence of flow conditions (collision efficiency) in reducing the number of particles impacting the specimen. That velocity exponents greater than 2 should be found may not be surprising if the increase in velocity is also accompanied by an increase in collision efficiency. In view of the variability of the velocity exponent revealed by these results its usefulness as an inherent characteristic of the erosion process is dubious.
181
, l_
2_
60.0
3_
4_
1
1
9.35
18.7 Nominal RotationSpeed
9.35
10.7
(.nIs)
Fig. 16. Variation of relative erosion rates R, and R, for 550 pm glass beads as a function of test speed at viscosities indicated (units N s m -2~ 10e3); velocity exponents are marked for each viscosity condition.
5. Conclusions
(1) The impact velocity of particles close to the stagnation point on a cylindrical erosion specimen was found to be less than 50% of the nominal specimen rotation speed owing to the change in flow conditions as a particle approaches the stagnation line of .the specimen. (2) The calculated impact speed of particles decreased at an increasing rate with increasing carrier liquid viscosity for a given test speed. (3) The decrease in impact speed with increasing carrier liquid viscosity occurs at lower viscosities for smaller particle sizes because of their lower inertia compared with larger particles. (4) The rate of collision of particles with the erosion specimen, expressed as the collision efficiency 77,falls rapidly with increasing viscosity, decreasing particle size and decreasing test speed. (5) The fall in erosion rates often observed with increasing viscosity, decreasing particle size and decreasing test speed, reflects the changes in flow interaction of liquid, particles and eroding surface and emphasizes the
182
need for knowledge of particle trajectories by liquid suspensions.
in the ~d~rst~djng
of erosion
Acknowledgments The author wishes to thank Lawrence Technology, Lawrence, KS for providing the copper rod used in this work which was supported in part by the Center for Research, Inc. of the Universi~ of Kansas.
References
5
6 7 8 9 10 11 12
13 14
15 16 17 18 19 20 21
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