See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/257013957

Analytical and Experimental Characterization of Erosion Effects According to

Pin-Fin Shape in Electronics Cooling Loops

Conference Paper · May 2012

CITATIONS READS

0 251

2 authors, including:

Ralph Remsburg
Magic Leap, Plantation, FL
47 PUBLICATIONS   126 CITATIONS   

SEE PROFILE

Some of the authors of this publication are also working on these related projects:

low temperature bonding of dissimilar metals View project

All content following this page was uploaded by Ralph Remsburg on 29 May 2014.

The user has requested enhancement of the downloaded file.

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

Analytical and Experimental Characterization of Erosion Effects

According to Pin-Fin Shape in Electronics Cooling Loops
Ralph Remsburg, Jackson Gilmore
Amulaire Thermal Technology, San Diego, CA, 92121
ralphr@amulaire.com, jacksong@amulaire.com

Abstract
A numerical and experimental study of erosion of nickel-plated copper heat sinks is present-
ed. High power automotive electronics are often cooled by liquids, and because of dissimilar
metal corrosion, copper heat sinks are usually plated with a thin nickel layer. Previous stud-
ies have shown that some pin-fin shapes have better heat transfer characteristics or lower
pressure drop, but the long-term endurance of these pin-fin shapes in an automotive cooling
loop environment has not been demonstrated. The current study shows that nickel-plated
copper pin-fins with sharp edges, i.e. square and diamond shapes are prone to particle ero-
sion and may not survive automotive lifetime requirements as well as rounded pin-fins. Using
similar fluid turbulence, CFD analysis shows that square pins eroded about 1.5X, and Dia-
mond pins about 2.1X, the rate of round pin-fins. The test sample experiments showed simi-
lar relative erosion rates.

1. Introduction
1.1. Pin-Fin Environment
Increasing waste heat from Hybrid and EV drives has caused automotive engineers to con-
centrate on increasing the heat transfer from IGBT heat sinks. There have been many stud-
ies of different pin-fin shapes from academia and commercial firms. Recent analysis tech-
niques have concentrated on an alternate form of the Reynolds Analogy [1] and Entropy Min-
imization [2]. However, the numerical techniques become quite complex when the additional
variables of an array of pin-fins is considered. Optimization of pin-fin arrays have used En-
tropy Minimization techniques [3-4] and Multi-objective genetic algorithms [5]. Most recently,
non-linear pin-fin arrays, in which the shape of each pin-fin is individually optimized for its lo-
cation in the pin-fin array have been discussed [6].
The majority of studies have concluded that there is no best fin shape. Every variable most
be considered and weighted to determine the optimum geometry for each particular applica-
tion. This was clearly shown in a study by Hall and Marthinuss [7] who compared 56 fin sur-
faces using data from Kays and London [8]. They found that straight fins are the most effi-
cient, but straight fins often lack the cooling power required for high power electronics; Pin
fins are the best shape for small volumes; and louvered fins are best for low mass applica-
tions. However, the results also depend on the Reynolds number. For example, at Reynolds
numbers below 1000 and above 3000 wavy fins are more efficient than offset fins, but be-
tween these values offset fins are more efficient than wavy fins.
In most automotive applications there are a variety of different metals in contact with the
cooling fluid. Some of these materials are widely separated on the galvanic scale, and there-
fore present a high risk of long-term corrosion. The copper heat sink and aluminum radiator
is one such combination. In order to minimize corrosion, the copper heat sink is generally
plated with nickel. Over a period of time, if erosion of the nickel plating occurs, it leads to cor-
rosion. The presence of corrosion particles increases the rate of erosion, which produces
more corrosion particles, and a destructive spiral begins. Automotive coolant systems are not
well maintained in the general population. A statistical study by Woodward and Gershun [9]

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 510

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

found that 37% of a vehicle’s coolant particulate matter was greater than 100 microns, and
80% of vehicles contained greater than 300PPM of particles.
The use of aggressive (sharp-edged) pin-fin shapes may increase the heat transfer
coefficient, but will also increase the fluid shear stress and the maximum angular fluid
velocity. Sharp edges are also known to produce more fragile plating. Combining the sharp-
edge pin-fin effects of high shear stress, higher fluid velocities, and fragile plating with solid
particle impingement can initiate the erosion/corrosion destructive cycle.

2. Erosion
2.1. Development of Erosion Model Theory
Erosion is a very complex phenomenon and is due primarily to the following parameters:
1. Erodent velocity
2. Erodent shape
3. Angle of impact
4. Erodent size
5. Material properties of erodent and target
6. Temperature

Finnie [10] experimentally showed that the manner of material removal varies with the direc-
tion and the velocity of erodent particles and predicted the velocity exponent as n = 2. Finnie
derived an expression for material removal, as given by the equations below:
𝑀𝑉 𝑛
𝑞
= 𝑠𝑖𝑛2𝛼 − 3𝑠𝑖𝑛2 𝛼 𝛼 < 18.5𝑜
8𝑝
𝑀𝑉 𝑛
𝑞
= 𝑐𝑜𝑠 2 𝛼 𝛼 > 18.5𝑜
24𝑝
Where:
𝑞
= rate of material volume removal
M = mass of particles
V = particle velocity
p = plastic flow stress
α = impact angle

The two expressions worked well in finding the erosion rate for angles below 45°. However
for angles above 45°, the Finnie equations estimated a lower volume loss, and at 90o impact
angle the Finnie formulas result in no material loss.
The phenomenon of volume loss at angles above 45° was accounted for by Bitter [11,12].
Depending on the angle of impact he explained erosion as deformation wear:
2
0.5𝑀 𝑉 sin 𝛼 − 𝐾
𝑊𝐷 =
𝜀

Cutting wear when particle velocity is much greater than 0:

2 2
2𝑀𝐶 𝑉 sin 𝛼 − 𝐾 𝐶 𝑉 sin 𝛼 − 𝐾
𝑊𝐶1 = 𝑈 cos 𝛼 − 𝜚
𝑉 sin 𝛼 𝑉 sin 𝛼

And, cutting wear when particle velocity approaches 0:

0.5𝑀
𝑉 2 𝑐𝑜𝑠 2 𝛼 − 𝐾1 𝑉 𝑠𝑖𝑛 𝛼 − 𝐾 1.5
𝑊𝐶2 =
𝜚
Where:
K = maximum particle velocity where collision is purely elastic
ε = energy to remove a unit volume of material by deformation wear
ϱ = cutting wear factor
C = hardness of base material

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 511

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

Total wear is the sum of WD + WC1 or WD + WC2. For ductile materials at low angles, the cut-
ting wear predominates, while at acute angles deformation wear predominates.
Unlike previous theories, Sheldon and Kanhere [13] in 1972 gave the velocity exponent as
3.0 to match with the experimental work. Indentation theory and an energy balance equation
was used to explain deformation and machining action.
Hutchings and Winters [14] in 1974 explained the material removal mechanism and showed
that material is more readily removed from work hardened copper than from annealed cop-
per. In 1981 Hutchings [15] proposed the erosion of metals by spheres at normal incidence
employing critical plastic strain as the failure criterion. He incorporated two material strength
properties: dynamic hardness and ductility, the high values of which are needed for good re-
sistance to erosion and also predicted a velocity exponent of 3.0, as did Sheldon [13].
In 1981 Bellman and Levy [16] observed the formation of three distinct types of craters; in-
dentation, ploughing and smear craters on the stress free surface, due to the impact of the
particles. The authors provided experimental evidence to show that the material removal dur-
ing erosion involves the deformation of surface material into platelets by repeated impacts,
that eventually detaches from the metal surface.
In 1983 Rao and Buckley [17] investigated the influence of exposure time on volume loss
rate and found a direct relation between erosion versus time curves and pit morphology for
glass erodents. Through analysis they showed four types of erosion rate versus time curves.
That same year Levy and Chik [18] studied the erosion mechanism of both brittle and ductile
materials and found their behavior to be completely different. They explained the ductile ero-
sion mechanism in the same manner as that of Bellman and Levy in 1981 [16].
In 1986, Hutchings and Levy [19] considered that during high velocity impact, the surface
temperature increases, which leads to the softening of the near surface region, and a work
hardened material beneath acts as an anvil against which the softer material is deformed. In
1995 Levy [20] combined all his experimental and theoretical results correlating with other
theories in a book. He explained the erosion mechanism in ductile metals as a series of op-
erations resulting in the formation of platelets and craters. Initial impacts produce platelets
without material loss. Adiabatic shear heating occurs on the impacted surface causing the
formation of a work hardened zone beneath its surface, which acts as an anvil, increasing
the efficiency of the hammer-like impacting particles. When the anvil is fully in place and the
platelets are fully formed, maximum steady-state material removal occurs.
In 2002, Wensink and Elwenspoek [21] used an “Erosion Classification Value” (Ecv), which is
the ratio of the 45o and 90o impact angle erosion rates combined with a particle kinetic ener-
gy exponent to explain the difference between ductile and brittle materials erosion.
The degree to which the particle motion is tied to the fluid motion can be determined through
evaluation of the Stokes number. This is defined as the ratio of the particle response time
due to viscous drag to a characteristic turbulent eddy time in the carrier fluid:
𝜌𝑝 𝐷𝑝2 𝑈𝑓
𝑆𝑡𝑘 =
18𝜇𝑓 𝐷𝐻
Where:
ρp = particle density
Dp = particle diameter
Uf = fluid velocity
μf = fluid viscosity
DH = hydraulic diameter

For large values, Stk>2.0, the particulate flow is highly inertial and, in a confined geometry,
would be dominated by particle-wall interactions, whereas for values less than 0.25 the effect
of particle-wall interactions on the particle flow is essentially negligible because the particles
are more tightly coupled to the fluid through viscous drag [22]. At Stokes numbers below 0.05
the particles and carrier fluid are strongly coupled and the particles would be expected to

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 512

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

closely follow the fluid flow. The overall Stokes flow in this model is roughly 1.7, so the parti-
cle flow is strongly affected by particle-wall interaction.

2.2. Numerical Simulation of Erosion

The numerical simulations were run using SolidWorks Flow Simulation software. This soft-
ware calculates both flow patterns and heat transfers for systems of various geometries,
combinations of materials, fluid flows, boundary conditions, and heat sources.
The code can be used for turbulent or laminar flow simulations. To predict turbulent flows, the
software uses the Favre-averaged Navier-Stokes equations, where time-averaged effects of
the flow turbulence on the flow parameters are considered. Other, i.e. large-scale, time-
dependent phenomena are taken into account directly [23].
SolidWorks Flow Simulation was set to calculate a two-phase flow as a motion of constant
mass, spherical solid particles in the steady-state flow field. The drag coefficient is calculated
with Henderson’s formula [24], derived for flow over particles, and the temperature difference
between the fluid and the particles. The particle/fluid heat transfer coefficient is calculated
with the formula proposed by Carlson and Hoglund [25]. The interaction of particles with the
model surfaces was account for by specifying ideal reflection. Ideal reflection denotes that in
the impinging plane the particle velocity component tangent to the surface is conserved,
whereas the particle velocity component normal to the surface changes sign.
As a result of particle impingement on the solid surfaces, the total erosion mass rate, RΣerosion,
was determined as follows:
𝑁

𝑅
𝑒𝑟𝑜𝑠𝑖𝑜𝑛 = 𝐾𝑖 ∙ 𝑈𝑝𝑏 𝑖 ∙ 𝑓1 𝑖 𝛼𝑝 𝑖 ∙ 𝑓2 𝑖 𝑑𝑝 𝑖 𝑑𝑚
𝑝 𝑖

𝑖=1 𝑀𝑝 𝑖
Where:
N is the number of fractions of particles specified,
i is the fraction number,
Mp i is the mass impinging on the coldplate walls in unit time for the i-th particle fraction
Ki is the impingement erosion coefficient specified for the i-th particle fraction
Up i is the impingement velocity for the i-th particle fraction
b is the velocity exponent (3.0 recommended [13,15])
f1 i (αp i) is the dimensionless function of particle impingement angle αp i
f2 i (dp i) is the dimensionless function of particle diameter dp i

2.3. Particle Size and Concentration

While there are no standards for particle size and concentration in automotive cooling loops,
the comprehensive study by Woodward and Gershun [9] was used for this study. These re-
searchers analyzed roughly 25.6m3 (6757 gal) of used engine coolant. Figure 1 shows the
particle size distribution. The distribution is evenly split between particles >50 microns and
particles <50 microns. Figure 2 shows the gravimetric analysis results for that study. The
largest group of coolant samples had a concentration of 300PPM.

Fig 1 - Particle size distribution (micron) [9] Fig 2 – Particle Concentration (PPM) [9]

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 513

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

In the following figures, Figure 3 shows the relationship between the erosion function, C(dp),
and particle diameter. Larger particles cause more erosion. Figure 4 shows the function of
the impact angle, f(). This function diagram relates specifically to thin coatings in heat trans-
fer equipment.

Fig 3 - Function of Particle Diameter, C(dp) [26] Fig 4 - Function of Impact Angle, f() [27]

3. Analytical Erosion Models

3.1. CFD Modelling
Three pin-fin shapes were evaluated to draw conclusions regarding potential for erosion as
shown in Figure 5:
1) Round pin-fins similar to the copper coldplate used for the Infineon HybridPack 2,
2) Square pin-fins with similar pin size and pin spacing to the Infineon HybridPack 2,
3) Diamond pin-fins with similar pin size and pin spacing to the Infineon HybridPack 2.

In order to compare dissimilar pin-fin shapes, the coldplates were designed to produce near-
identical turbulence (Re). This was accomplished by varying the pin characteristic dimension
and pin spacing so that the hydraulic diameter (DH) was identical for each coldplate.

𝜌𝑈𝐷
𝑅𝑒 =
𝜇
Where:
ρ = fluid density (kg/m3)
U = Fluid inlet velocity (m/s)
DH = Hydraulic diameter (m)
μ = fluid viscosity (Pa)

Fig 5 – Round, Square, and Diamond Pin-Fin Shapes

Figure 6 shows the pin side of the round copper coldplate. Each coldplate was roughly
220mm x 100mm x 4mm thick base with 2.36mm diameter pins, 8mm tall. Figure 7 shows
the results of the CFD analysis for the statistical coolant properties found by Woodward and
Gershun [9]: square pin-fins erode about 1.5X faster than round pin-fins, and diamond pin-
fins erode about 2.1X faster than round pin-fins.

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 514

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

Fig 6 – Copper coldplate with round pin-fins Fig 7 – CFD Solution Relative Erosion Rates

3.2. CFD Fluid Shear Stress and Particle Impingement

Shear stress and particle impingement angle are important factors in evaluating total erosion.
Figure 8 shows the fluid shear stress on the three pin shapes evaluated under identical
Reynolds numbers. The maximum fluid shear stress for Round pins was 226Pa, for Square
pins 343Pa, and 546Pa for Diamond pins. The Diamond pins and Square pins had 90o an-
gles to simulate common CNC machining or skiving practice. Figure 8 also depicts impinge-
ment of 100µm diameter particles. The round pin has a thicker boundary layer which allows
the particles to travel around the pin without greatly impacting the surface. The diamond pin
exhibits a much thinner boundary layer and also has a large area at a 45o angle to the parti-
cle flow. Particles impact the large frontal surface of the diamond pin, rebound, and then im-
pact again at the sharp-edge corners. The square pin shows a very large frontal face. Parti-
cles impact once, and then slide across the frontal surface at a lower velocity. Erosion is pri-
marily on the front face, and leading edge corners.

Fig 8 – CFD Shear Stress and Particle Streams for Round, Diamond, and Square Pin Arrays

3.3. Edge Radius Sensitivity

The sharp-edge diamond and sharp-edge square pin-fin shapes showed much worse re-
sistance to erosion than did round pin-fins in the CFD simulation. To determine if the shear
stress and erosion could be reduced by replacing the machined sharp edges with rounded
edges, an additional CFD simulation was run. Figure 9 depicts the reduction in erosion rate
made by increasing the edge radius for diamond and square pins. The graph shows that as
the edge radius increases the erosion rate decreases. There was no erosion rate decrease
for radiuses larger than 0.60mm.
Figure 10 shows the effect when pressure drop is equalized for each coldplate. The tempera-
ture rise is very slightly less for the diamond pin array (about 0.00123oC/W), but the erosion
rate increases by 1.92X, which is consistent with Figure 6. The temperature rise for the
square pin array is greater than for the round pin (about 0.006oC/W), but the erosion rate de-
creases to about 90% of the round pin erosion rate. This may indicate that with further opti-
mization a square pin array with rounded corners may have less temperature rise and less

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 515

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

erosion for the same pressure drop. However, it should be noted that cost associated with
manufacturing such an optimized pin shape would be prohibitive for CNC or skiving-based
technologies, but is possible with molded shape techniques (MIM).

Fig 9 – Edge radius sensitivity Fig 10 – T and Erosion normalized to P

4. Experimental Results of Coolant Loop Erosion

4.1. Test Setup and Fluid
Figure 11 shows a schematic of the erosion experiment. The setup contained a Dayton ¼ HP
3GRV7 coolant pump, two Omega PX209-030G5V pressure transducers, an Omega FTB
4805 Flowmeter, and a Staco Energy 3PN1010B variable transformer to control the flowrate.

Fig 11 - Erosion experiment setup Fig 12 - Particle size distribution for experiment

The round-pin, diamond-pin, and square-pin copper coldplates described in section 3.1 were
used for the experiment. Each coldplate received a 1.0 micron thick, medium phosphorus,
electroless nickel coating per MIL-C-26074E. During testing, each coldplate was attached to
an aluminum manifold per Infineon drawing ATV-PD-3040, except ¾” ID hose barbs were
used instead of the oblong ports shown on the Infineon drawing.

A corrosive water test solution was prepared per ASTM D1176, by dissolving anhydrous so-
dium salts (148mg of sodium sulfate, 165mg of sodium chloride, and 138mg of sodium bicar-
bonate) per liter of distilled water. The corrosive water solution was then combined with
ehylene glycol (Zerex Original Formula ZX001) to form a 44% by volume coolant solution. A
1% by weight mixture of water atomized copper particles was mixed with the coolant solution
to form the erosion test fluid. The erosion test was run with a flow rate of 20LPM with a cool-
ant temperature of 50oC. Figure 12 shows the experiment particle size distribution compared
to the Woodward and Gershun [9] statistical coolant survey.

The experiment was run for 25 hour periods. At the end of each 25 hour period the coldplate
was separated from the manifold, cleaned, and inspected for wear. The diamond pin-fin
coldplate began to show some scuffing wear after 300 hours of operation. At 500 hours,
some of the diamond pin fins showed slight copper exposure along the sharp edges. At 700
hours, rounding of some of the diamond pin transverse edges and copper exposure was

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 516

PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

clearly evident. The square pin coldplate showed more resistance to erosion than the dia-
mond pin shapes. After 650 hours some scuffing and exposed copper was evident on the
sides of some pins. This wear was unexpected because this pin-fin side wall is parallel to the
fluid flow. But because the sides are adjacent to the manifold wall, it is possible that the high-
er velocity and turbulence created by the manifold wall produced an opportunity for acceler-
ated erosion. Finally, the round pin fin design, which is found in the Infineon Hybrid Pack 2
showed no signs of wear at the test limit of 2000 hours. 2000 hours of accelerated testing in
corrosive, particle-laden coolant represents much more than 2000 of actual use, but the mul-
tiple is unknown.

Figures 13 and 14 show samples of actual plated pins. Figure 13 is a section of the diamond-
pin array showing erosion and copper exposure at 700 hours of accelerated testing. Figure
14 is an illustrative example of what is believed to be a first step in the failure mode, separa-
tion and cracking of the nickel plate from the underlying copper coldplate pin. Once the softer
copper is exposed, erosion is accelerated. This type of failure is described by several re-
searchers, particularly [19,28] who noted the effects of a hard coating on a softer base metal.

Fig 13 – Planar view of Diamond pin Coldplate Fig 14 – Illustrative failure mode of Ni/Cu pin-fin

5. Conclusion
5.1. CFD Analysis
A good approximation of erosion patterns was achieved by visualizing fluid shear stress in
the pin-fin arrays. Although the magnitude of shear stress does not always indicate the se-
verity of erosion, shear stress patterns did indicate regions of erosion. The discrepancy is
most likely due to the influence of the Stokes number. Whereby the flow path of larger parti-
cles becomes increasingly different from the fluid flow path due to particle inertia and mo-
mentum. The erosion formula of section 2.2 along with the particle diameter function C(dp) of
Figure 2 [26], and the impact angle function f() of Figure 3 [27], combined with the velocity
component b of 3.0 [13,15], coincided with the relative erosion rates found by experimenta-
tion. In relative terms the CFD analysis showed that square pins erode at 1.5 times the rate
of round pins and diamond pins erode about 2.1 times the rate of round pins.

5.2. Experimental Erosion

The erosion results of the CFD analysis seem to correlate with the erosion experiments. This
experiment was not designed to calculate an actual rate of wear or recommend a plating
thickness. However, some conclusions can be drawn from the CFD and experimental data.
Sharp corners on pin-fins show an increase in the rate of erosion. Diamond and square pins
with 90o sharp corners showed lower resistance to erosion than round pin-fins. Although cur-
rent electronics power cooling loops in hybrid vehicles usually consist of a separate system

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 517

 PCIM Europe 2012, 8 – 10 May 2012, Nuremberg Paper 65

from the internal combustion engine cooling loop, future systems will likely use shared cool-
ant. Thin plated pin-fin shapes with sharp edges may not survive the particulate levels that
are expected to be found in the general population of shared cooling loop hybrid vehicles.

6. Literature
[1] Mälhammar, Å., “A Method for Comparing Heat Sinks based on Reynolds Analogy,” 10th Interna-
tional Workshop on Thermal Investigations of ICs and Systems, Côte d'Azur, France, 9/2004
[2] Khan, W.A., Culham, J.R., Yovanovich, M.M., “The Role of Fin Geometry in Heat Sink Perfor-
mance”, Transactions of the ASME, Vol. 128, pp 324-330, 12/2006
[3] Khan, W.A., “Modeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks, PhD
Thesis, University of Waterloo, Ontario Canada, 2004
[4] Abdel-Rehim, Z.S., “Optimization and Thermal Performance Assessment of Pin-fin Heat Sinks,”
Journal of Applied Sciences Research, 3(3), pp 227-235, 2007
[5] Ndao, S., Peles, Y., Jensen, M.K., “Multi-Objective Thermal Design Optimization and Comparative
Analysis of Electronics Cooling Technologies”, International Journal of Heat and Mass Transfer, 52, pp
4317-4326, 5/2009
[6] Remsburg, R., “Non-Linear Fin Patterns in Cold Plates for Liquid Cooling”, Power Electronics
Technology Conference, Long Beach, California, USA, 10/2006
[7] Marthinuss, J. and Hall, G., “Air Cooled Compact Heat Exchanger Design For Electronics Cooling”,
Electronics Cooling, Volume 10, Number 1, 2/2004.
[8] Kays, W.M. and London, A.L., “Compact Heat Exchangers”, Krieger Publishing, 1998.
[9] Woodward, S.M., Gershun, A.V., “Characterization of Used Engine Coolant by Statistical Analysis”,
Engine Coolant Testing: Third Volume, ASTM STP 1192, pp 234-247, 1993
[10] Finnie, I., “Erosion of Surfaces by Solid Particles”, Wear, 3, pp 87-103, 1960
[11] Bitter, J.G.A., “A Study of Erosion Phenomena”, Part I, Wear, 6, 5, 1963
[12] Bitter, J.G.A., “A Study of Erosion Phenomena”, Part II, Wear, 8, 161, 1963
[13] Sheldon, G.L. and Kanhere, A., “An Investigation of Impingement Erosion Using Single Particles”,
Wear, 21, 195, 1972
[14] Hutchings, I.M. and Winters, R.E., “Particle Erosion of Ductile Metals: A Mechanism of Material
Removal”, Wear, Vol. 27, No. 1, pp 121-128, 1/1974
[15] Hutchings, I.M., "A Model for the Erosion of Metals by Spherical Particles at Normal Incidence"
Wear, 70, pp 269-281, 1981
[16] Bellman, R. and Levy, A., “Erosion Mechanism in Ductile Metals”, Wear, 70, 1, pp 1-27, 9/1981
[17] Rao, P.V. and Buckley, D.H., “Time Effect of Erosion by Solid Particle Impingement on Ductile Ma-
terials”, Lewis Research Center, 1983
[18] Levy, A.V. and Chik, P., “The Effects of Erodent Composition and Shape on the Erosion of Steel”
Wear, 89, pp 151-162, 1983
[19] Hutchings, I and Levy, A.V., “Thermal Effects in the Erosion of Ductile Metals”, Wear, 131, pp 105-
121, 1989
[20] Levy, A.V., “Solid Particle Erosion and Erosion Corrosion of Materials”, ASM International, 1995
[21] Wensink, H. and Elwenspoek, M.C., “A Closer Look at the Ductile-Brittle Transition in Solid Parti-
cle Erosion”, Wear, Vol. 253, 2002
[22] Tu, J.Y. and Fletcher, C.A.J., “Eulerian Modelling of Dilute Particle-Laden Gas Flow Past Tubes”,
Computational Fluid Dynamics Journal, 5, pp 1-25, 1996
[23] Fundamentals of COSMOSM Floworks, Structural Research and Analysis Corporation, 2002,
pp.182 - 208.
[24] Henderson, C.B., “Drag Coefficient of Spheres in Continuum and Rarefied Flows”, AIAA Journal,
v14, pp. 707–708, 1976
[25] Carlson, D.J. and Hoglund, R.F., “Particle Drag and Heat Transfer in Rocket Nozzles”,
AIAA Journal, v. 2, No. 11, 1964
[26] Kleis, I. and Uuemois, H., “Wear Resistance of Grinding Equipment Operating on Impact”, Mashi-
nostroenie Publishers, Moscow, 1986
[27] Tadolder, J., “The Rules of Wear of Technically Pure Metals”, Proceedings of the Technical Uni-
versity of Tallinn, Vol. 237, pp 3-13, 1966
[28] Lepikson, H., Kleis, I., “Erosion of Enameled Boilers”, Proceedings of the Technical University of
Tallinn, Vol. 192, pp 3-19, 1962

ISBN 978-3-8007-3431-3 © VDE VERLAG GMBH · Berlin · Offenbach 518

View publication stats