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A note on erosion by moving dust particles
Powder Technology. 0 Elsevier Sequoia
17 (19’77)
S.A.,
259 - 263
Lausanne -
259
Printed in the Netherlands
A Note on Erosion by Moving Dust Particles s. L. so0 Department of Mechanical 61801 (U.S.A.)
and Industrial Engineering.
(Received
revised form February
July 6, 1976;
in
of Illinois
at Dibana-Champaign.
Urbana.
IL
28, 197i)
SUMMARY
Ductile and brittle modes of erosion by dust or granular materials suspended in a gas at moderate speeds are discussed by estending the relations of Hen and Rayleigh. Conditions include directionai impact, random impact, and sliding bed motion. The actual condition at a pipe turn is often a combination of these effects. Relations are also applicable to dust erosion of turbine blades, control of sand blasting, and wear produced by fluidized beds and sliding beds. Wear of a solid surface by dust erosion has been a subject of many studies [l - 3). It may be produced by powdered or granular materials via directional impact such as on turbine blades or pipe turns when dust flow velocity is high and concentration is Low [4], random Impact such as in a fluidized bed 151, or sliding bed of solids ln a chute or at a pipe turn when dust concentration is high and flow velocity is low [3] _ An extensive survey was recently given by Milk and Mason [S] _ It appears feasible at this time to extend the treatment of beat transfer [S] and charge transfer [7] by impact to that of material removal for cases where deviation from elastic impact is small. Known experimental facts on the specific wear rate (volume removed per unit mass of dust impacted) are (1) proportional to (impact velocity)” with R < 3 Cl, 8,9]; (2) increase with increase of particle size for quartz on steel 191, no effect of particle size for silicon carbide on copper or aluminum
WI ; and
Unkersity
(3) at pipe bends, specific wear rate decreases with dust loading (mass flow ratio of
solid to gas) but is proportional to (gas velocity)” with n up to 4 [3] _ It is seen that the particle velocity for a given gas flow needs to be strictly defined. Among the data available, particle velocity was taken to approach the gas velocity in each case_ This is not true in reality because of inertia of particles and boundary layer effect of gas flow [6]. The local stress must esceed the yield stresses via ductile or brittle failure or their combination for producing wear_ The yield stress for ductile removal co must be greater than the onset yielding stress or one-half of the yield strength in simple tension [lo] _ Its value is nearly that of plastic flow stress of three times the flow stress in dynamic test or the yield strength [ 111. It is also greater or nearly equal to the pressure for plastic deformation. the dynamic flow stress for 8% permanent strain, or 0.35% of the modulus of elasticity [12] . The yield stress for brittle failure uB to normal impact is nearly equal to three times the yield stress [ 131 or the Brinell hardness 1143, or stress to cause fracture at static condition, or 0.43% of shear modulus. It is also equal to [ (1 - 2~)/3(0.62)] times of the yield strength in simple tension, Y being the Poisson ratio. The energies to remove a given volume of material are denoted as 1151 I en, ultimate yield stress for ductile wear and eB, ultimate impact resistance for brittle wear_ To relate the mechanisms of erosion to basic material properties, we need to identify the normal compressive force PB and the tangential machining force PO ~ area of contact A, the duration of contact t, and the ratio r* of the reflection speed to incoming speed V of a particle of mass m colliding with a surface at an angle of incidence 0 with the plane of
the surface, When the deviation from the elastic state of the surfaces of materials is smaII, the formulation of Herz and Rayleigh [lo] for contacting spheres consisting of spherical dust particIe of radius 3 and a plane of infinite radius [ 63 gives I
PBt = (2_94)(5/16)mV(l
+ r-)
(1)
PDt = fPat _4t = A,t,(sin
(2) 0)-l’”
(3)
and _4&
= (2_94)(15;I~/s)2-““mV(k~8~)“2(l r*)J151v;htI~
f (4)
whereO
(5) which correlates the dynamic and the material properties of the impacting systems; F1 is the density of the material forming the dust particle- These basic relations are applied to the two different modes of erosion [ 15 - 17) : the “ductile” mode (subscript D) and the “brittle” mode (subscript B)_ Erosion via tangential machining tends to be more prominent for ductile materials (metals) than for brittle materials (ceramics). While the normal compressive force has a reverse influence, erosion of real mzterid is a result of the combined effect of these modes. Again, for smaIl deviation from the elastic states, a linear combination is seen to be valid. Ductile mode Experimental results show that the ductile mode which is typical of metal targets is characterized by a maximum erosion occurring at some intermediate incidence angle between 0 o and 90 O, usuaIIy at 20 - 30 o [23 _ The mechanism appears to be one of cutting or machining sustained by force Po of eqn. (2). The machining is produced by a Yriction” force and erosion occurs onIy when this force exceeds the yield strength (iD of the surface
being eroded_ The erosion per impact is given by WD
in volume
loss wn
=~)D[CD(PD/A)-U~~JJVC~SOA~/~D
(6)
where Co corrects the non-sphericity of the actual dust, stress concentration at sharp edges, roughness of the surface impacted, and non-specular reflection from an actual surface CD 5 1, usually for non-sphericaI particles. ho is a mechanical efficiency of impact, including the effects of gliding, scattering, lifting of the particles by the gas stream; rlD < 1 usuaIly_ In terms of 2 volumetric erosion rate per unit area WD produced by a dust stream of concentration pl, we can express this rate as a dimensionIess erosion energy parameter: f r’j(2.94)(5/16)sD
E;, = &,~,/&v3C,f(1 = cos O[l -
KG(sin
0)-1fs]
= F,(O,Kk) (‘I)
and the resistance
parameter
KL is given by
Since (1 + T~)“~ is _ nearly 1 in general, KL can be treated as a parametric constant and the function FD (O,&) characterizes the ductile wear at various angles 0. The maximum value of function FD occurs at an angle 0, given by KG = 5(sin 8m)1115(4 sin* 0,
i- 1)-l
(9)
Figure 1 gives the relation I;& uersus 0, and the function F, (O,,KL) E Fn, showing that the physically meaningful range is for 0 < K& < 1. Figure 2 shows the values FD/FD, at various angles 0 and KG. It is seen that even with the uncertainty of the param eters Co,
Fig. 1. Relation of ductile resistance parameter KL to
angle 8, function
for maximum
erosion and erosion energy
FD at various a,.
261 0,4
01 10
0.5
0,607
0 6
09
06 F, b
02
00
0
IO
20
30
40
50
IM?ACT
60
70
80
90
0
IO
It%ACT 40
20
60
50
ANGLE.
9
70
80
90
DEG.
Fig_ 2. Normalized ductile erosion energy function at various iFpact angles 0 and ductile resistance parameter KD _
Fig. 3. Brittle erosion energy function Fa at various impact angles 0 and brittle resistance function KG_
uD, f and eD, the above relation provides for the correlation of experimental results or to determine the design condition where erosion rate can be controlled. It is further noted that f is, in general, related to 8 and r*_
Fiuidized bed When applied to wear by random motion of particles in a fluidized bed, the random motion at intensity V2 is averaged over directions and magnitudes to give. for ductile wear.
Brittle mode The brittle mode which is typical of glass and ceramics is characterized by an erosion rate increasing with impingement angle up to, but below, 90 o [2] _ The mechanism is one of cracking of the target surface by fatigue and brittle failure for stress above an impact yield stress us [ 14]_ The erosion in terms of volume loss per impact wn is given by
E;, = WD+,/f-pr(v2)3/2(1
wa = qs[C,(P,/A)
-
oa]Vsin
@At/es
= sin f3[1 -Kk(sin
+ r*)(2.94)(5/16)oB 19)-r’~] z Fa(6,Kg)
= 1 -
(11)
where
(2.94)(5/16)(2/3 0.9586K;
E;
(13)
= WBeB/p1(V2)3’2Ca(1 (2-94)(5/16) =
(2/3
+I=*) 6)
n
1 - 0.8981K;
(14)
with the averages obtained in ductile wear.
in a similar way as
Sliding bed Wear by a sliding bed is seen to depend on the bed thickness, gravity (in the case of a chute), or centrifugal force (in the case of pipe turns) acting on the particles moving as a sliding bed. For skiing particles, the wearing force is given by, for a unit projected area, p10 rgh /(contact
Equation (11) shows that maximum wear occurs at 3 = 90 9 Experimentahy, at 8 = 90 3 interference of rebound partides with incoming particles is problematic (close to the condition of r* = 0 plus sliding), and maximum wear rate is more demonstrable at 6 < 90 o [2] _ Function Fs(8,KE) is shown in Fig. 3_
,/&,
where & is given by replacing V2 by V* in both K;, and Nr,_ For brittle wear. we get
(10)
where CB has an analogous meaning as Cn given before, although it may differ in magnitude even for similar particles and surfaces. The volumetric erosion rare per unit area WVB produced by a dust stream of concentration p1 can be expressed in the form of a dimensionless erosion energy parameter EG : E; = W,~a/p,V~Ca(l
C,
+T*)
area) = PD /A
(15)
assuming cubical piling for a moving bed, g is the gravity force per unit mass and g = V’/R for pipe turns of radius R. Here we get the dimensionless erosion energy for sliding as E; = WDED/4C,, fFI@,ghVqD where Qr is the volume moving bed
= 1-
fraction
K,*
(16)
solid of the
363 Ei; = ~r~~~3*/~o~(k~k~)~‘*/4f~:
(1’7)
and -~1*,
= d,&gh(k,k,)l*Z
(\m+
dm,-’ (13)
For a pipe turn of radius R, part of the wear will be due to a sliding bed motion along the larger radius side according to E,’ = WDE,-,/4CD fp1V3qD
(19)
E: decreases with increase in p 1 or large mass ratio of solid to gas [ 3 ] _
pacted [S] . The angle of incidence also spread over a range for each jet setting. The situation still holds in the case of a fluidized bed - the wear of 316 stainless steel by dolomite particles (700 m) for 1 - Kg = IO-*, en = 1O’O n/m*, nnCn = lo-‘. The magnitude of Co is often greater or near to one and tends to be small for a large particle because of small contact area for a given mass of particle; it tends to be small also for a very small particle because of the large effect of air friction n is, in general, small for gas-conveyed particles. A desirable reference test condition will be that of electrically accelerated particles in a vacuum_
DISCUSSION LIST
The above delineation of ductile and brittle modes, directional impacts, random motion of particles, and sliding bed motion constitute idealized components of wear of surfaces by dust particles. In reality, most cases consist of combinations of the above items. For instance, wear at pipe turns in general includes impact over a range of directions of particles and sliding bed motion as particles are accumulated by centrifugal forces along one side of the pipe. Equations (7 j and (11) have esplained the observed fact of velocity effect, showing additional effect of velocity on the sliding bed function of eqn. (II)_ The particle motion produced by a given direction of gas jet is subject to inertia effect of particles which may give a larger angle of impact. The lift force of the boundary layer motion of the gas may produce a gliding (barely touching) or lift motion (non-touching) of particles which reduces q n and n s _ For a small angle of gas jet, the deflective motion of the gas may produce a centrifugal force on the particles, thus increasing the compressive stress_ Comparison of trend [4] shows that the friction coefficient is best represented by [(l - r’)/(l + r’)] cot 0 = f ‘j3, thus giving maximum wear below 30 o of impact angle in all cases. This will also change the coefficient R& in eqn_ (13) to O-6841_ For the cases of impaction of tempered steel by silica for en = 10’ n/m2, es = 1Oro n/m*, f = 0.1, VnCn = 10-s showing the significance of lift action by the gas [lS] or the velocity lag of particles, or small fraction im-
A C
E E’ F f % h K’ k
Ll n pB PD
R r* t V v* W W u E
4 0 V
OF SYMBOLS
area of contact correction factor for non-sphericity, stress concentration, surface roughness, and non-specular reflection modulus of elasticity dimensionless erosion energy parameter as defined geometric erosion function coefficient of friction gravitational acceleration thickness of bed dimensionless erosion resistance parameter elastic param eter of material as defined mass of dust particle impact number a numerical exponent normal compressive force tangential machining force radius of bend ratio of reflecting speed to incoming speed duration of contact incoming speed of impact intensity of random motion volumetric erosion rate per unit area volume loss per impact yield stress for removal of material energy to remove a given volume of material mechanical efficiency of impact angle of impact Poisson ratio of material
263
Pl P 0
density density volume
of dust stream of material fraction solid 6
su&scripts 1 2 B
D F S
(-)
dust partkles surface impacted brittle wear ductile wear masimum wear reference value sliding mean value as defined
7 8
9
(superscript)
10
11 REFERENCES I. Finnie, J_ Wolak and Y. H. Kabil. Erosion of metals by solid particles, ASP&I J. Mater., 2 (196i) 6S2 - 700_ C. E_ Smeltzer, M. E. Gulden and W. A_ Compton, hIechanisms ofmetalremovalby impacting dust particIes,Trans. ASME,J. Basic Eng_,93D (19'70) 639-654. D. Mills and J. S. Mason, The interaction of particle concentration and conveying velocity on the erosive wear of pipe bends in pneumatic conveying lines. Paper presented at the International Powder and Bulk Solids Handling and Processing Conference. IITRI and Powder -4dvisory Center. Rosemont, Ill.. May 13. 1976. A_ P. Fraas. Survey of turbine bucket erosion deposits and corrosion, ASLME Paper No_ 75 GTlz?3(1975)_ National Research Development Corp. (London),
I2
13 11
15
16 17 18
Pressurized fluidized bed combustion research and development, Report No. 85, Interim No. I, prepared for the Office of Coal Research, Department of interior (1971). NTIS, PB-210073. S. L. Soo, Fluid Dynamics of Multiphase Systems, Blaisdell, W&barn. MS, 1967. p_ 208_ L. Cheng and S. L. Soo, Charging of dust particles by impact, J. Appl. Phys., 41 (1970) 585 - 591. G. I. Sheldon, Similarities and differences in the erosion behavior of materials, ASlIE Paper No_ 69-WAlMet-7 (1969). J_ E. Goodwin, WV.Sage and G. P_ Tilly, Study of erosion by solid particles. Proc. Inst. Mech. Eng.* 181 (Pt. 1) (1969/70) 279 - 292. S. Timoshenko and J. N. Goodier, The Theory of Elasticity, McGraw-Hill, New York, 2nd edn., 1951. R. M. Davies, The determination of static and dynamic yield stresses using a steel ball, Proc. Roy. Sot. (London), A197 (1949) -l16 - -l32. WV.Goldsmith and P. T_ Lyman, The penetration of bard steel sphere into plane metal surfaces, J_ Xppl. Mech., Trans. ASME, (1960) 717 - 725. D_ Tabor. The Hardness of Metals, Oxford Univ_ Press, Oxford, 1951. J. J. Gilman, Relationship between impact yield stress and indentation hardness. Preliminary Reports, Memoranda, and Technical Notes of the Materials Research Council Summer Conference, LaJolla, Cal., July 19’74, vol. 1, FP_ 364 - 374_ J. H. Neilson and A. Gilchrist, Erosion by a stream of solid particles. Wear, 11 (1968) 111 122. L Finnie, Erosion of surfaces by solid particles, Wear. 3 (1960) 87 - 103. J. G. A_ Bitter, A study of erosion phenomena, Parts I and II, Wear, 6 (1963) 5 - 21,169 - 190_ S. L. Soo and S. K. Tung, Deposition and entrainment in pipe flow of a suspension, Powder Technol., 6 (1972) 283 - 29-1.
17 (19’77)
S.A.,
259 - 263
Lausanne -
259
Printed in the Netherlands
A Note on Erosion by Moving Dust Particles s. L. so0 Department of Mechanical 61801 (U.S.A.)
and Industrial Engineering.
(Received
revised form February
July 6, 1976;
in
of Illinois
at Dibana-Champaign.
Urbana.
IL
28, 197i)
SUMMARY
Ductile and brittle modes of erosion by dust or granular materials suspended in a gas at moderate speeds are discussed by estending the relations of Hen and Rayleigh. Conditions include directionai impact, random impact, and sliding bed motion. The actual condition at a pipe turn is often a combination of these effects. Relations are also applicable to dust erosion of turbine blades, control of sand blasting, and wear produced by fluidized beds and sliding beds. Wear of a solid surface by dust erosion has been a subject of many studies [l - 3). It may be produced by powdered or granular materials via directional impact such as on turbine blades or pipe turns when dust flow velocity is high and concentration is Low [4], random Impact such as in a fluidized bed 151, or sliding bed of solids ln a chute or at a pipe turn when dust concentration is high and flow velocity is low [3] _ An extensive survey was recently given by Milk and Mason [S] _ It appears feasible at this time to extend the treatment of beat transfer [S] and charge transfer [7] by impact to that of material removal for cases where deviation from elastic impact is small. Known experimental facts on the specific wear rate (volume removed per unit mass of dust impacted) are (1) proportional to (impact velocity)” with R < 3 Cl, 8,9]; (2) increase with increase of particle size for quartz on steel 191, no effect of particle size for silicon carbide on copper or aluminum
WI ; and
Unkersity
(3) at pipe bends, specific wear rate decreases with dust loading (mass flow ratio of
solid to gas) but is proportional to (gas velocity)” with n up to 4 [3] _ It is seen that the particle velocity for a given gas flow needs to be strictly defined. Among the data available, particle velocity was taken to approach the gas velocity in each case_ This is not true in reality because of inertia of particles and boundary layer effect of gas flow [6]. The local stress must esceed the yield stresses via ductile or brittle failure or their combination for producing wear_ The yield stress for ductile removal co must be greater than the onset yielding stress or one-half of the yield strength in simple tension [lo] _ Its value is nearly that of plastic flow stress of three times the flow stress in dynamic test or the yield strength [ 111. It is also greater or nearly equal to the pressure for plastic deformation. the dynamic flow stress for 8% permanent strain, or 0.35% of the modulus of elasticity [12] . The yield stress for brittle failure uB to normal impact is nearly equal to three times the yield stress [ 131 or the Brinell hardness 1143, or stress to cause fracture at static condition, or 0.43% of shear modulus. It is also equal to [ (1 - 2~)/3(0.62)] times of the yield strength in simple tension, Y being the Poisson ratio. The energies to remove a given volume of material are denoted as 1151 I en, ultimate yield stress for ductile wear and eB, ultimate impact resistance for brittle wear_ To relate the mechanisms of erosion to basic material properties, we need to identify the normal compressive force PB and the tangential machining force PO ~ area of contact A, the duration of contact t, and the ratio r* of the reflection speed to incoming speed V of a particle of mass m colliding with a surface at an angle of incidence 0 with the plane of
the surface, When the deviation from the elastic state of the surfaces of materials is smaII, the formulation of Herz and Rayleigh [lo] for contacting spheres consisting of spherical dust particIe of radius 3 and a plane of infinite radius [ 63 gives I
PBt = (2_94)(5/16)mV(l
+ r-)
(1)
PDt = fPat _4t = A,t,(sin
(2) 0)-l’”
(3)
and _4&
= (2_94)(15;I~/s)2-““mV(k~8~)“2(l r*)J151v;htI~
f (4)
whereO
(5) which correlates the dynamic and the material properties of the impacting systems; F1 is the density of the material forming the dust particle- These basic relations are applied to the two different modes of erosion [ 15 - 17) : the “ductile” mode (subscript D) and the “brittle” mode (subscript B)_ Erosion via tangential machining tends to be more prominent for ductile materials (metals) than for brittle materials (ceramics). While the normal compressive force has a reverse influence, erosion of real mzterid is a result of the combined effect of these modes. Again, for smaIl deviation from the elastic states, a linear combination is seen to be valid. Ductile mode Experimental results show that the ductile mode which is typical of metal targets is characterized by a maximum erosion occurring at some intermediate incidence angle between 0 o and 90 O, usuaIIy at 20 - 30 o [23 _ The mechanism appears to be one of cutting or machining sustained by force Po of eqn. (2). The machining is produced by a Yriction” force and erosion occurs onIy when this force exceeds the yield strength (iD of the surface
being eroded_ The erosion per impact is given by WD
in volume
loss wn
=~)D[CD(PD/A)-U~~JJVC~SOA~/~D
(6)
where Co corrects the non-sphericity of the actual dust, stress concentration at sharp edges, roughness of the surface impacted, and non-specular reflection from an actual surface CD 5 1, usually for non-sphericaI particles. ho is a mechanical efficiency of impact, including the effects of gliding, scattering, lifting of the particles by the gas stream; rlD < 1 usuaIly_ In terms of 2 volumetric erosion rate per unit area WD produced by a dust stream of concentration pl, we can express this rate as a dimensionIess erosion energy parameter: f r’j(2.94)(5/16)sD
E;, = &,~,/&v3C,f(1 = cos O[l -
KG(sin
0)-1fs]
= F,(O,Kk) (‘I)
and the resistance
parameter
KL is given by
Since (1 + T~)“~ is _ nearly 1 in general, KL can be treated as a parametric constant and the function FD (O,&) characterizes the ductile wear at various angles 0. The maximum value of function FD occurs at an angle 0, given by KG = 5(sin 8m)1115(4 sin* 0,
i- 1)-l
(9)
Figure 1 gives the relation I;& uersus 0, and the function F, (O,,KL) E Fn, showing that the physically meaningful range is for 0 < K& < 1. Figure 2 shows the values FD/FD, at various angles 0 and KG. It is seen that even with the uncertainty of the param eters Co,
Fig. 1. Relation of ductile resistance parameter KL to
angle 8, function
for maximum
erosion and erosion energy
FD at various a,.
261 0,4
01 10
0.5
0,607
0 6
09
06 F, b
02
00
0
IO
20
30
40
50
IM?ACT
60
70
80
90
0
IO
It%ACT 40
20
60
50
ANGLE.
9
70
80
90
DEG.
Fig_ 2. Normalized ductile erosion energy function at various iFpact angles 0 and ductile resistance parameter KD _
Fig. 3. Brittle erosion energy function Fa at various impact angles 0 and brittle resistance function KG_
uD, f and eD, the above relation provides for the correlation of experimental results or to determine the design condition where erosion rate can be controlled. It is further noted that f is, in general, related to 8 and r*_
Fiuidized bed When applied to wear by random motion of particles in a fluidized bed, the random motion at intensity V2 is averaged over directions and magnitudes to give. for ductile wear.
Brittle mode The brittle mode which is typical of glass and ceramics is characterized by an erosion rate increasing with impingement angle up to, but below, 90 o [2] _ The mechanism is one of cracking of the target surface by fatigue and brittle failure for stress above an impact yield stress us [ 14]_ The erosion in terms of volume loss per impact wn is given by
E;, = WD+,/f-pr(v2)3/2(1
wa = qs[C,(P,/A)
-
oa]Vsin
@At/es
= sin f3[1 -Kk(sin
+ r*)(2.94)(5/16)oB 19)-r’~] z Fa(6,Kg)
= 1 -
(11)
where
(2.94)(5/16)(2/3 0.9586K;
E;
(13)
= WBeB/p1(V2)3’2Ca(1 (2-94)(5/16) =
(2/3
+I=*) 6)
n
1 - 0.8981K;
(14)
with the averages obtained in ductile wear.
in a similar way as
Sliding bed Wear by a sliding bed is seen to depend on the bed thickness, gravity (in the case of a chute), or centrifugal force (in the case of pipe turns) acting on the particles moving as a sliding bed. For skiing particles, the wearing force is given by, for a unit projected area, p10 rgh /(contact
Equation (11) shows that maximum wear occurs at 3 = 90 9 Experimentahy, at 8 = 90 3 interference of rebound partides with incoming particles is problematic (close to the condition of r* = 0 plus sliding), and maximum wear rate is more demonstrable at 6 < 90 o [2] _ Function Fs(8,KE) is shown in Fig. 3_
,/&,
where & is given by replacing V2 by V* in both K;, and Nr,_ For brittle wear. we get
(10)
where CB has an analogous meaning as Cn given before, although it may differ in magnitude even for similar particles and surfaces. The volumetric erosion rare per unit area WVB produced by a dust stream of concentration p1 can be expressed in the form of a dimensionless erosion energy parameter EG : E; = W,~a/p,V~Ca(l
C,
+T*)
area) = PD /A
(15)
assuming cubical piling for a moving bed, g is the gravity force per unit mass and g = V’/R for pipe turns of radius R. Here we get the dimensionless erosion energy for sliding as E; = WDED/4C,, fFI@,ghVqD where Qr is the volume moving bed
= 1-
fraction
K,*
(16)
solid of the
363 Ei; = ~r~~~3*/~o~(k~k~)~‘*/4f~:
(1’7)
and -~1*,
= d,&gh(k,k,)l*Z
(\m+
dm,-’ (13)
For a pipe turn of radius R, part of the wear will be due to a sliding bed motion along the larger radius side according to E,’ = WDE,-,/4CD fp1V3qD
(19)
E: decreases with increase in p 1 or large mass ratio of solid to gas [ 3 ] _
pacted [S] . The angle of incidence also spread over a range for each jet setting. The situation still holds in the case of a fluidized bed - the wear of 316 stainless steel by dolomite particles (700 m) for 1 - Kg = IO-*, en = 1O’O n/m*, nnCn = lo-‘. The magnitude of Co is often greater or near to one and tends to be small for a large particle because of small contact area for a given mass of particle; it tends to be small also for a very small particle because of the large effect of air friction n is, in general, small for gas-conveyed particles. A desirable reference test condition will be that of electrically accelerated particles in a vacuum_
DISCUSSION LIST
The above delineation of ductile and brittle modes, directional impacts, random motion of particles, and sliding bed motion constitute idealized components of wear of surfaces by dust particles. In reality, most cases consist of combinations of the above items. For instance, wear at pipe turns in general includes impact over a range of directions of particles and sliding bed motion as particles are accumulated by centrifugal forces along one side of the pipe. Equations (7 j and (11) have esplained the observed fact of velocity effect, showing additional effect of velocity on the sliding bed function of eqn. (II)_ The particle motion produced by a given direction of gas jet is subject to inertia effect of particles which may give a larger angle of impact. The lift force of the boundary layer motion of the gas may produce a gliding (barely touching) or lift motion (non-touching) of particles which reduces q n and n s _ For a small angle of gas jet, the deflective motion of the gas may produce a centrifugal force on the particles, thus increasing the compressive stress_ Comparison of trend [4] shows that the friction coefficient is best represented by [(l - r’)/(l + r’)] cot 0 = f ‘j3, thus giving maximum wear below 30 o of impact angle in all cases. This will also change the coefficient R& in eqn_ (13) to O-6841_ For the cases of impaction of tempered steel by silica for en = 10’ n/m2, es = 1Oro n/m*, f = 0.1, VnCn = 10-s showing the significance of lift action by the gas [lS] or the velocity lag of particles, or small fraction im-
A C
E E’ F f % h K’ k
Ll n pB PD
R r* t V v* W W u E
4 0 V
OF SYMBOLS
area of contact correction factor for non-sphericity, stress concentration, surface roughness, and non-specular reflection modulus of elasticity dimensionless erosion energy parameter as defined geometric erosion function coefficient of friction gravitational acceleration thickness of bed dimensionless erosion resistance parameter elastic param eter of material as defined mass of dust particle impact number a numerical exponent normal compressive force tangential machining force radius of bend ratio of reflecting speed to incoming speed duration of contact incoming speed of impact intensity of random motion volumetric erosion rate per unit area volume loss per impact yield stress for removal of material energy to remove a given volume of material mechanical efficiency of impact angle of impact Poisson ratio of material
263
Pl P 0
density density volume
of dust stream of material fraction solid 6
su&scripts 1 2 B
D F S
(-)
dust partkles surface impacted brittle wear ductile wear masimum wear reference value sliding mean value as defined
7 8
9
(superscript)
10
11 REFERENCES I. Finnie, J_ Wolak and Y. H. Kabil. Erosion of metals by solid particles, ASP&I J. Mater., 2 (196i) 6S2 - 700_ C. E_ Smeltzer, M. E. Gulden and W. A_ Compton, hIechanisms ofmetalremovalby impacting dust particIes,Trans. ASME,J. Basic Eng_,93D (19'70) 639-654. D. Mills and J. S. Mason, The interaction of particle concentration and conveying velocity on the erosive wear of pipe bends in pneumatic conveying lines. Paper presented at the International Powder and Bulk Solids Handling and Processing Conference. IITRI and Powder -4dvisory Center. Rosemont, Ill.. May 13. 1976. A_ P. Fraas. Survey of turbine bucket erosion deposits and corrosion, ASLME Paper No_ 75 GTlz?3(1975)_ National Research Development Corp. (London),
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15
16 17 18
Pressurized fluidized bed combustion research and development, Report No. 85, Interim No. I, prepared for the Office of Coal Research, Department of interior (1971). NTIS, PB-210073. S. L. Soo, Fluid Dynamics of Multiphase Systems, Blaisdell, W&barn. MS, 1967. p_ 208_ L. Cheng and S. L. Soo, Charging of dust particles by impact, J. Appl. Phys., 41 (1970) 585 - 591. G. I. Sheldon, Similarities and differences in the erosion behavior of materials, ASlIE Paper No_ 69-WAlMet-7 (1969). J_ E. Goodwin, WV.Sage and G. P_ Tilly, Study of erosion by solid particles. Proc. Inst. Mech. Eng.* 181 (Pt. 1) (1969/70) 279 - 292. S. Timoshenko and J. N. Goodier, The Theory of Elasticity, McGraw-Hill, New York, 2nd edn., 1951. R. M. Davies, The determination of static and dynamic yield stresses using a steel ball, Proc. Roy. Sot. (London), A197 (1949) -l16 - -l32. WV.Goldsmith and P. T_ Lyman, The penetration of bard steel sphere into plane metal surfaces, J_ Xppl. Mech., Trans. ASME, (1960) 717 - 725. D_ Tabor. The Hardness of Metals, Oxford Univ_ Press, Oxford, 1951. J. J. Gilman, Relationship between impact yield stress and indentation hardness. Preliminary Reports, Memoranda, and Technical Notes of the Materials Research Council Summer Conference, LaJolla, Cal., July 19’74, vol. 1, FP_ 364 - 374_ J. H. Neilson and A. Gilchrist, Erosion by a stream of solid particles. Wear, 11 (1968) 111 122. L Finnie, Erosion of surfaces by solid particles, Wear. 3 (1960) 87 - 103. J. G. A_ Bitter, A study of erosion phenomena, Parts I and II, Wear, 6 (1963) 5 - 21,169 - 190_ S. L. Soo and S. K. Tung, Deposition and entrainment in pipe flow of a suspension, Powder Technol., 6 (1972) 283 - 29-1.