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EFFECT OF VISCOSITY, PARTICLE SIZE AND SHAPE ON EROSION MEASUREMENTS AND PREDICTIONS

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XI. EFFECT OF VISCOSITY, PARTICLE SIZE AND SHAPE ON EROSION MEASUREMENTS AND PREDICTIONS

1. Introduction

Erosion is the progressive loss of material from solid surface due to mechanical interaction between that surface and a fluid or impinging fluid stream. This phenomenon is common in industries which deal with fluid flow containing impurities. Erosion is studied in slurry transport, aerospace, oil and gas production and many other industries. Oil and gas that are removed from reservoirs generally contain impurities like sand particles of varying sizes that are often sharp. These particles are responsible for material loss from the pipe wall. This loss of material from the pipe wall is termed as erosion. The material loss caused by particles in the fluid flow is a major concern for oil and gas industries due to heavy damage caused to the fluid carrying systems such as pipe fittings, pipe elbows, joints and thus reducing the life of these parts. Erosion due to solid particles at times can be very expensive as it requires repairs and change of piping components frequently. In the extreme case, erosion can cause a system to shut down thus worsening the situation. In order to counter the losses many oil and gas companies are banking on erosion models to predict the life time of fluid carrying systems thus increasing safety and production rates.

Erosion is a complex phenomenon and is effected by various factors like particle size, shape, density and hardness, material density and hardness, fluid density and viscosity, impact angle, flow rate of fluids, particle rate, geometry and others.

Research Goals and Approach

Normally erosion experiments are conducted in vacuum or air and the results of these tests are used to obtain the erosion ratio equations. These erosion ratio equations are then used in CFD simulation or SPPS 2-D to predict erosion of gases (at high pressures) and liquids. The validity of this assumption is being investigated in this work. Thus, the main goal of this work is to examine the effect of particle size and shape along with liquid viscosity on erosion ratio equations that is used in CFD and SPPS. This investigation is a follow-up of a couple of other studies that are briefly discussed below.

The Erosion/Corrosion Research Center (E/CRC) at The University of Tulsa has conducted research on erosion and corrosion occurring under a range of conditions and pipe geometries. One of the main goals of E/CRC is to develop, validate and expand the software

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called Sand Production Pipe Saver (SPPS) which can predict erosion for a certain geometry and set of operating conditions. This software can be used as a tool by the oil and gas industries to predict erosion damage and a threshold velocity. Threshold velocity is a flow velocity required to minimize the erosion damage.

Previously, Zhang et al. (2006) at E/CRC conducted a series of erosion measurements and calculations to show that erosion equations can be utilized in Computational Fluid Dynamics (CFD) code to predict erosion. Series of erosion tests were conducted by them to obtain erosion equation. Then they implemented the erosion equation into a commercially available CFD code and predicted erosion for various single-phase gas and liquid cases. However, these studies were limited to only one particle size and in single geometry i.e., direct impingement geometry and for one fluid viscosity. In order to extend the previous work and predict erosion for various viscous liquids and particle sizes, Okita et al. (2010) has measured velocities of particles and carrier fluid and erosion rate of the direct impact geometry by varying the viscosity of carrier fluid and particle sizes. They conducted series of erosion tests on Inconel, Aluminum and Stainless Steel and developed erosion models. CFD was utilized to predict erosion rates of the above three materials for 20, 150 and 300 µm sand particle sizes in a carrier fluid of viscosities 1, 6, 10 and 30 cP. It was observed that CFD tends to under predict erosion rate for 150 and 300 µm particles and for 20 µm particles it predicted a decrease in erosion rate from 1 to 6 cP, but an increase from 6 to 30 cP which was not in good agreement with the experimental data. In order to investigate the differences between measured erosion (through experiments) and CFD predictions, the present author used spherical particles (glass beads) of sizes 50 µm, 150 µm and 350 µm and measured velocities of these particles and carrier fluid (gas). Previously, Miska (2008) and Okita (2010) measured particle and fluid velocities in the direct impingement geometry utilizing Laser Doppler Velocimetry (LDV). The present author has repeated the same, but used glass beads, and measured erosion rate of the direct impact geometry varying the viscosity of carrier fluid and particle sizes and also performed erosion testing of a direct impingement geometry using material coupons.

Erosion model obtained from experiments is implemented in Computational Fluid Dynamics (CFD) and simulations are performed to predict erosion rate. Gambit 2.3 is used to create mesh and Fluent 6.3 is used to simulate the flow of the direct impingement geometry. Also Fluent 6.3 is used to calculate the trajectories of particles after the fluid flow solution is obtained. User Defined Functions (UDF) created by Zhang (2006) are utilized to perform the erosion calculations in CFD.


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At first, velocity of particles and fluid are determined using Laser Doppler Velocimetry (LDV). Flow parameters such as fluid velocity and pressure are calculated using flow simulations in Fluent 6.3. Secondly, particle tracking is performed in Fluent 6.3 which gives particle parameters such as particle velocity, particle trajectories, number of particles impacting the wall and number of particles that missed the target wall. Finally, the flow simulation and calculations are obtained using Fluent 6.3. The CFD results of particle and fluid velocities need to be validated by LDV measurements for selected cases. Now, using the velocities from LDV, erosion experiments are performed and erosion equations are generated. These equations are implemented in Fluent 6.3 to calculate erosion rates. Finally, erosion rates calculated from Fluent 6.3 are compared to actual experimental results and validated for selected cases.

Figure 1-1 summarizes various steps followed in the present work. By comparing CFD results to various experimental data, validation of fluid, particle velocities and erosion predictions are performed. Improvements to the erosion modeling and calculations are examined and the results are compared to data for various fluid viscosities and particle sizes.


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Fig 1-1: Flow Chart of Erosion Prediction Using CFD

No No

Measure Particle Velocity with LDV

Erosion Testing in Gas

Erosion Equations CFD Predictions in Liquid with Different Viscosities

Compare CFD Results with Exp. Data

Erosion Exp. in Liquids

Agree

Improved CFD and SPPS

Yes

Improve Particle Tracking


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2. Literature Review

Erosion is a type of wear mechanism where in damage to a solid surface usually involves progressive loss of material due to relative motion between that surface and a contacting substance or substances. Impact of erosion in the oil and gas industry is a great concern as a result of which interest in researching about it has increased considerably. This section provides a detailed background of erosion researches carried out by various researchers as well as erosion equations used in this work.

Background of Erosion Mechanisms and Modeling

Erosion is a complex phenomenon and is effected by various factors like particle size, shape, density and hardness, material density and hardness, fluid density and viscosity, impact angle, flow rate of fluids, particle rate, geometry and others. All these parameters need to be studied individually. Meng and Ludema (1985), after a detailed study on many previous researches related to erosion modeling during that time, concluded that there is no universal erosion model that can predict erosion for all materials and flow conditions. As a result of this there are many publications in literature which focus on various parameters that effect erosion. Finnie (1960) concluded that ductile and brittle materials exhibit different erosion mechanisms. Ductile erosion is described as resulting from cutting or displacing process.

Levy (1986) proposed that erosion takes place due to shear deformation that occurs at the point of impact of abrasive particles and metals. Due to this shear deformation at the impacting surface, the material gets heated near to its annealing temperature. Small distressed platelets are formed in this softened layer. Underneath this soft layer, there is a hard metal layer which is cold worked by plastic deformation. There is an increase in erosion efficiency due to this hard layer. After formation of platelets, successive onslaught of numerous particles at the target surface knock off these platelets formed by initial impacts.

As already mentioned, in the factors effecting erosion, particle velocity is a major factor. The effect of particle velocity can easily dominate the erosion model in predicting the erosion rates. Lindsley and Marda (1999) studied the effect of particle velocity on erosion rates through experiments with 70-30 brass and Fe-C martensite and derived a relation for erosion rate which varies exponentially with particle velocity as shown in Equation 2-1.


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n (2-1)

where ER is the erosion rate, V is the particle velocity and n is an empirical constant. They reported that the empirical constant n is independent of target material and erosion mechanism; however, it is governed by the test conditions. They showed that the value of the exponent n was 2.9 for both brittle cracking and plastic deformation erosion mechanisms.

After particle velocity, another major factor effecting erosion rate is the impact angle of the particles. From the equation of motion for rigid abrasive particles impacting a ductile surface Finnie (1972) derived an angle function. This model is in good agreement with experimental data except for higher impact angles as the model shows that maximum erosion for aluminum alloys occurs at 13 degrees and becomes null at zero and at ninety degrees. He accounts for this discrepancy between measurements and model stating that at high angles erosion is mostly due to surface roughening and low cycle fatigue fracture whereas at low angles erosion is mostly due to the cutting mechanism.

Particle properties like shape of the particle can affect the erosion of ductile materials. Winter and Hutchings (1974) focused on this aspect affecting the erosion rate. Erosion experiments were performed on mild steel and lead using flat-faced particles. Here, they studied the rake angle of the particles when they impacted the surface. Rake angle is the angle between the perpendicular to the surface and the leading edge of particle. It is found that rake angle makes a difference in the mechanism of erosion. When the rake angle had positive or small negative values the erosion took place because of cutting mechanism. Whereas at large negative rake angle values erosion was due to ploughing mechanism.

Further advancement in the study of particle properties was done by Bahadur and Badruddin (1990). They characterized particles based on width to length ratio (W/L) and also perimeter squared to area ratio (P2/A) and used them as particle shape indicators. They characterized SiC, Al2O3 and SO2 particles in above terms. It was found that the terms P2/A and W/L were affecting erosion. With increasing P2/A erosion also increased and erosion decreased with decreasing W/L for all the particles. Also it was noted that sharp particles engaged in cutting and ploughing mechanisms whereas spherical particles were engaged only in ploughing mechanism. Later, an angularity parameter, An was proposed by Palasamudram and Bahadur (1997). This parameter is calculated based on geometrical parameters of abrasives. The effect of this parameter was studied by measuring erosion rates


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of 1020 steel. It was found that when the particle size was maintained constant, erosion rate increased with an increase in An and when An was kept constant and particle size was increased erosion also increased. Many literatures support the idea that particle size influences erosion rates for smaller sizes. Finnie (1972), Tilly and Sage (1970) showed that effect on erosion is negligible after a critical size which is reported to be 100 µm.

E/CRC Erosion Model Background

As already mentioned, there is no universal erosion equation for all materials to predict erosion rate as erosion is dependent on many factors. At E/CRC (Erosion/Corrosion Research Center) Ahlert (1994) developed an erosion equation for carbon steel materials and McLaury (1996) for aluminum. Equations 2-2 and 2-3 are called the E/CRC equation. Even though this equation developed was for a particular material (carbon steels), it can be used for other materials if the constants C, n and angle function are adjusted.

. . . . . (2-2)

..

(2-3)

where ER is the erosion ratio which is the ratio of mass loss of material to mass of impacting particles, C and n are empirical constants, V is the particle velocity, Fs is the particle shape factor (sharpness factor). Fs is 0.2 for spherical particles, 0.5 for semi-rounded particles and 1 for sharp particles. BH is the Brinnel hardness of the target material that is calculated on the basis of Vicker’s hardness, Hv of that material. F(θ) is the angle function. It should be noted that E/CRC investigators removed BH factor from equation (2-2) when dealing with other materials than carbon steels.

Ahlert (1994) and McLaury (1996) proposed F(θ) for carbon steel and aluminum as shown in Equation 2-4.

0 (2-4)

cos2 sin sin 2 0

Zhang et al. (2006) obtained angle function for Inconel 625 as shown in Equation (2-5).


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1.4234 6.3283 10.9327 5.3983 (2-5)

Equation 2-5 is a polynomial equation and each coefficient is deduced based on erosion experiments conducted on Inconel 625. θ is the impact angle in radians.

Torabzadeh (2009) and Okita (2009) developed another angle function (Equation 2-6) for aluminum and stainless steel based on experiments.

sin . 1 1 sin (2-6)

Table 2-1: Inconel 625 Erosion Equation Coefficients.

Oka et al. (2005) used a sand blast type test rig to study erosion by various types solid particles on various materials. Based on the results, Oka et al. (2005) developed an erosion equation (Equation 2-7) and an angle function (Equation 2-8) that work for any type of material and at any impact angles.

. . ′ . ′ . . (2-7)

sin . 1 1 sin (2-8)

Constants K, k1, k2 and k3 are found based on particle properties and hardness of the target material. ρ is the density of the target material, V and D are the velocity and diameter of the impacting particles and ′, ′ are reference values based on experiments (104 m/s and

Equation Component Al 6061 SS 316 Inconel 625

Hv (GPa) 1.12 1.5 3.43

N 2.41 2.41 2.41

F 5.27 1.716 N/A

n1 0.59 1.4 N/A

n 3.6 1.64 N/A

n3 2.5 2.6 N/A

C 1.5E-07 1.42E-07 2.17E-07


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326 µm respectively). Values of the constants in Equations 2-7 and 2-8 are shown in Table 2-2.

Table 2-2: Empirical Constants in Oka’s Equation

Equation Components Values

Hv (GPa) 3.43

K 65

k1 -0.12

k2 2.3 (Hv 0.038

k3 0.19

n1 0.71 (Hv 0.14

n2 2.4 (Hv ‐0.94

The main difference between E/CRC equation and Oka’s equation is that Oka’s equation includes a term that takes into account the effects of particle size while the E/CRC equation does not. However, the particle size exponent, k3, is 0.19 and has a small effect on calculated erosion rates.

Both Oka’s equation and E/CRC’s equation are developed based on air testing. Using the particle information such as particle speed and angle for each impingement from CFD, total erosion rates of the target material are calculated. The reason for this is, previous investigators have assumed that the equations developed through gas testing can be used to predict erosion in liquids.

Okita (2010) conducted experiments with sand particles in a direct impingement geometry both with liquid in liquid jet and gas. The erosion equations obtained from gas testing were implemented in CFD to calculated erosion in liquids. When CFD predictions were compared to experimental results it was observed that CFD was under predicting for 150 µm and 300 µm sand particles and were over predicting for 20 µm sand particles as shown in Figures 2-1, 2-2 and 2-3. The reason for these differences is being investigated in this study. One reason for the differences may be due to the shape of particles because in CFD we assume particles are spherical and use models for tracking spherical particles. So,


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in the present work, experiments are conducted with spherical particles in gas and liquids and results will be compared with CFD calculations.

Fig 2-1: Comparison of Experimental Results with CFD predictions (300 µm Sand) (Okita, 2010)


1.00E-07

1.00E-06

1.00E-05

0 5 10 15 20 25 30 35

Ero

sion

Rat

io (k

g/kg

)

Viscosity (cP)

300 micron SandCFD (E/CRC) - 300 micron Sand

1.00E-08

1.00E-07

1.00E-06

1.00E-05

0 5 10 15 20 25 30 35

Ero

sion

Rat

io (k

g/kg

)

Viscosity (cP)

150 micron SandCFD (E/CRC) - 150 microns


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1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

0 5 10 15 20 25 30 35

Ero

sion

Rat

io (k

g/kg

)

Viscosity (cP)

20 micron SandCFD (E/CRC) - 20 micron Sand


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3. Experimental Facilities and Test Procedures

In order to examine effects of viscosity and particle size on erosion rates, two types of experiments were performed. These are direct impact material loss experiments and submerged liquid testing. In this section details of the above experimental facilities and test procedures followed are explained. Also a detail of Laser Doppler Velocimetry (LDV) that has been used to determine the particle and gas velocities for calculating erosion rates of Aluminum material is explained and Scanning Electron Microscope (SEM) images of glass beads are shown.

Experimental Facility for Direct Impact Material Loss

Figure 3-1 shows a schematic of the test apparatus. Nozzle draws air through the compressor. The amount of air (gas) flowing can be controlled with the help of the valve located above the flow meter in Figure 3-1. Glass beads are drawn into the nozzle with the help of a sand feeder and a feeding tube. The main aim of the sand feeder is to maintain a constant flow of particles. Glass beads coming out of the nozzle impact the target thus creating material loss of coupon. The actual test setup is shown in photographs in Figures 3-2 and 3-3.

Fig 3-1: Schematic of Experimental Test Facility


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Fig 3-2: Photograph of Actual Test Setup

Fig 3-3: Photograph of Specimen Holder and Sand and Floe Injection Nozzle


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The velocity of different particle sizes exiting the nozzle was measured using the same test rig with Laser Doppler Velocimetry (LDV) technique by the present author with the help of Okita (2010). Photograph of the nozzle and LDV beams are shown in Figure 3-4 and the results are summarized in Figure 3-5. A Pitot tube is used to measure the gas velocity and this information will be used to set the gas velocity in North Campus where erosion testing is done.

Fig 3-4: Photograph of Nozzle and LDV Beams

Fig 3-5: Measurements of Particle Velocity (from LDV) Versus Gas Velocity (from Pitot Tube)

y = 0.4534xR² = 0.9779

y = 0.3468xR² = 0.9878

y = 0.7022xR² = 0.9872

y = xR² = 1

0

20

40

60

80

100

120

140

0 50 100 150ParticleVe

locity

(LDV)(m/s)

Gas Velocity (Pitot Tube) (m/s)

Particle Velocity vs. Gas Velocity

150 micron GB

350 micron GB

50 micron GB

Vp = Vg

Linear (150 micron GB )

Linear (350 micron GB )

Linear (50 micron GB)

Linear (Vp = Vg)


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After particle velocities were measured from LDV, erosion measurements were conducted for aluminum material with glass beads entrained in air. Particle velocities of 24 m/s and 42 m/s were used. At each velocity, measurements were taken for impact angles of 90°, 60°, 45°, 30° and 15°. At each particle velocity and angle, the measurements were taken at least three times with 900 g of 50 µm, 150 µm and 350 µm glass beads each time. Figure 3-1 shows a schematic of the experimental facility. The test section was contained in a hood during the measurements. Erosion rates are calculated by mass loss of target coupon divided by the total mass of sand through put. Erosion results for each particle size are summarized in the results section.

SEM pictures of glass beads of sizes 50, 150 and 350 µm are shown in Figures 3-6, 3-7 and 3-8. Most particles showed to be spherical in shape under SEM.

Fig 3-6: SEM picture of 50 µm Glass Beads



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Experimental Facility for Submerged Liquid Testing

An experimental facility for measuring erosion rate in carrier fluids with various viscosities and different particle sizes was constructed. Figure 3-9 shows the schematic of this experimental facility.

Fig 3-9: Schematic of Submerged Liquid Testing

Test matrix comprises of three viscosities and one velocity. Viscosities being 1, 10 and 30 cP, flow velocity inside nozzle was about 10 m/s. Erosion rates are calculated for aluminum specimen using glass beads of sizes 50, 150 and 350 µm. Viscous liquid is prepared in the tank prior to experiments by mixing CMC (Carboxymethyl Cellulose) and

Slurry Mixer

Pump

Valve

Testing Tank

Nozzle

Target Al 6061 T6


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water. Viscosities were tested with the help of a viscometer. Viscosities of the fluid were measured before and after experiments to monitor change in viscosity. If the difference in viscosity is not more than 5 cP then original viscosity was reported. CMC is known to be a non-Newtonian fluid. However for the current testing conditions, CMC behaves as a Newtonian fluid.

Glass beads are mixed with liquid in the testing tank. The volume ratio of glass beads and liquid is 0.1% for 150 and 350 µm particles and 2% for 50 µm particles to get measurable erosion rates in a reasonable period of time. The slurry mixer is turned on throughout the test duration in order to maintain homogeneity of mixture. Mixture of glass beads and liquid flow from testing tank to the pump. The velocity of the jet can be controlled by using the valve present between the line of pump and nozzle. Nozzle and target wall are completely submerged in the mixture. The mixture jet exits the nozzle at a velocity of 10 m/s, impinges the target wall and drains into the testing tank. This mixture again flows to the pump and drains into the testing tank. In this way the mixture is circulated. Distance from nozzle exit to the target wall is 12.7 mm. Nozzle diameter is 8 mm. Results are summarized in the results section.


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4. Erosion Results

Erosion Results in Air

Erosion rates for aluminum 6061 are measured in air. 50 µm, 150 µm and 350 µm glass beads are used as abrasive particles. A total of 4500 g of glass beads for particle velocity of 42 m/s and 9000 g of glass beads for 24 m/s was injected at the nozzle for each of the erosion tests that are presented in this section. After injecting 900 g of glass beads, the weight of the coupon was measured and recorded. A sample cumulative mass loss of material is shown with amount of particle through put in Figure 4-1. This figure is for the particle impact velocity of 24 m/s using 50 µm glass beads. As shown in the figure, the mass loss of material has a linear relationship with the weight of particles injected after a short incubation sand impact period. For example, at impact angle of 90 degrees it requires about 4 kg of glass beads to impact the specimen before steady state erosion is observed. The incubation period was longer at 15 and 90 degree impact angles. After the incubation period, a steady state erosion, where cumulative mass loss increase with particle throughput is observed. All the air test results behave in this manner. So, in order to calculate the erosion ratios, points that were considered to be no mass loss during the incubation period were ignored and a linear fit is obtained for each case for the remaining data points and the slope of these lines represent erosion ratio for that particular test condition. This is shown in Figure 4-2. However, the data points during the incubation period i.e., data points representing zero mass loss, are ignored while taking the slope of the line for each case. In this manner erosion rates for all the particle sizes at different angles for different velocities are measured. Each test was repeated at least two times.


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Figure 4-1: Cumulative mass loss vs. Particle throughput at Vp =24 m/s (50µm Glass Beads)

Figure 4-2: Cumulative mass loss vs. Particle throughput at Vp =24 m/s (50µm Glass Beads)

00.0020.0040.0060.0080.01

0.0120.0140.0160.0180.02

0 2000 4000 6000 8000 10000

Cum

ulat

ive

Mas

s Los

s (g)

Particle Throughput (g)

45° 60°

30°

15° 90°

y = 6.5370E-07x - 1.1744E-03R² = 9.9549E-01

y = 1.0833E-06x - 1.1714E-03R² = 9.7094E-01

y = 4.4556E-06x - 2.9900E-03R² = 9.9155E-01

y = 3.6349E-06x - 2.0667E-03R² = 9.9990E-01

y = 6.3492E-07x - 2.0714E-03R² = 9.9657E-01

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 2000 4000 6000 8000 10000

Cum

ulat

ive

Mas

s Los

s (g)

Particle Throughput (g)

45° 60°

30°15°

90°

Erosion Ratio


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Erosion rates thus obtained for all three particle sizes are shown in Table 4-1. Figures 4-3, 4-4 and 4-5 show effect of impact angle on erosion rates for aluminum 6061 for different particle sizes. From these figures, it is evident that maximum measured erosion is observed at 45° for all particle sizes.

Table 4-1: Aluminum 6061 Erosion Results in Air

Angle (degrees)

Erosion Rate (g/g)

Impact Velocity = 24 m/s Impact Velocity = 42 m/s

50 µm 150 µm 350 µm 50 µm 150 µm 350 µm

90 7.79E-07 1.57E-06 1.63E-06 7.16E-06 1.21E-05 8.24E-06

60 4.03E-06 4.16E-06 3.63E-06 1.65E-05 1.91E-05 1.95E-05

45 4.25E-06 1.04E-05 6.89E-06 2.68E-05 4.21E-05 2.82E-05

30 2.75E-06 9.38E-06 4.66E-06 1.96E-05 3.87E-05 2.10E-05

15 7.82E-07 7.72E-06 3.39E-06 7.99E-06 3.42E-05 1.81E-05

Figure 4-3: Erosion Rate vs. Impact Angle for Aluminum 6061 in Air (50 µm Glass Beads)

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

0 20 40 60 80 100

Ero

sion

Rat

e (g

/g)

Impact Angle θ (degrees)Vp=42 m/s, Vg=71 m/s Trial 1 (exp) Vp=42 m/s, Vg=71 m/s Trial 2 (exp)Vp=24 m/s, Vg=41 m/s Trial 1 (exp) Vp=24 m/s, Vg=41 m/s Trial 2 (exp)


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0.00E+006.00E-061.20E-051.80E-052.40E-053.00E-053.60E-054.20E-054.80E-05

0 20 40 60 80 100

Ero

sion

Rat

e (g

/g)

Impact Angle θ (degrees)Trial1 Vg=104 m/s, Vp=42 m/s (exp.) Trial2 Vg=104 m/s, Vp=42 m/s (exp.)Trial1 Vg=64 m/s, Vp=24 m/s (exp.) Trial2 Vg=64 m/s, Vp=24 m/s (exp.)

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

0 20 40 60 80 100

Ero

sion

Rat

e (g

/g)

Impact Angle θ (degrees)Vp=42 m/s, Vp=136 m/s Trial 1 (exp) Vp=42 m/s, Vp=136 m/s Trial 2 (exp)Vp=24 m/s, Vg=77 m/s Trial 1 (exp) Vp=24 m/s, Vg=77 m/s Trial 2 (exp)


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Erosion Results in Liquids

A schematic of experimental facility for measuring erosion rate in carrier fluids with various viscosities and different particle sizes was shown in Figure 3-9. Also test procedure for this was explained earlier in detail in experimental facility section. Erosion results are summarized in Table 4-2. Figure 4-6 shows effect of viscosity on erosion rates of aluminum 6061 for different glass beads sizes. From Figure 4-6 it can be observed that viscosity has less effect on erosion rates of 350 µm at 1 cP and 30 cP, whereas at 10 cP erosion rate decreases. On the other hand, for 150 µm and 50 µm particle sizes it has a significant effect. As viscosity increases from 1 cP to 30 cP erosion rates for 150 µm and 50 µm particles decreases. A 90 % confidence interval has been build for each case based on experiments and are shown in Figure 4-6. Figure 4-7 shows comparison of sand and glass beads results. It is observed that the erosion results for sand is higher than the glass beads but the trend of results are similar for sand and glass beads. For the 350 um particles, the erosion ratio results for sand are higher than glass beads by a factor of approximately 5. This is due to the sharpness of sand versus glass beads. In the E/CRC erosion model we normally use Fs=1.0 for sharp sand and Fs=0.2 for glass beads. This may explain why the erosion test results are different by a factor of 5. For smaller glass beads and sand of 150 um (semi rounded Fs=0.5), the sand sharpness effects may be observed at viscosity of about 1, but the effects is not very large at viscosity of about 30 cP perhaps due to experimental uncertainty. These results for sand of 25 um in diameter (sharp sand) and spherical glass beads at 50 um are also shown. These results show similar trends but the magnitudes cannot be compared directly because they have different sizes and sharpness.

Table 4-2: Erosion Results for Al 6061 (Submerged Liquid Tests)

Viscosity (cP) Erosion Rate (m3/kg)

50µm 150µm 350µm

1 1.92E-11 1.86E-10 2.58E-10

10 7.11E-12 1.48E-10 2.00E-10

30 5.52E-12 1.34E-10 2.53E-10


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Figure 4-6: Erosion Rate vs. Viscosity for Al 6061 with Glass Beads of different particle sizes (90% Confidence Interval)

Figure 4-7: Erosion Ratio vs. Viscosity for Al 6061 with Glass Beads and Sand (Okita, 2010) of different particle sizes

1.80E-15

5.00E-11

1.00E-10

1.50E-10

2.00E-10

2.50E-10

3.00E-10

3.50E-10

0 10 20 30 40

Ero

sion

Rat

io (m

3 /kg)

Viscosity (cP)350 microns 150 microns 50 microns

1.00E-08

1.00E-07

1.00E-06

1.00E-05

0 10 20 30 40

Ero

sion

Rat

io (k

g/kg

)

Viscosity (cP)

50 micron GB20 micron Sand150 micron GB150 micron Sand350 micron GB300 micron Sand

Okita (2010)

Okita (2010)

Okita (2010)


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5. Generation of Erosion Models for Aluminum 6061

Using 50 µm Glass Beads

Utilizing the information obtained from the erosion measurements in air, the erosion ratio equation for aluminum is generated. Average erosion test results for 50 µm glass beads are normalized and plotted together as shown in Figure 5-1.

The angle function shown in Equation 5-1 is a modified version of the angle function suggested by Oka et al, (2005) and was used with parameters n1, n2 and n3 which are chosen to fit the experimental data.

. sin . 1 1 sin (5-1)

Hv is the Vicker’s hardness of the target material i.e. aluminum 6061. It was found out to be approximately 1.089 GPa. θ varies from 0° to 90°, constants n1, n2 and n3 are found based on experimental data. Since the experimental data are normalized, the angle function must be normalized as well by dividing the function by A, which is the maximum value of the function. These values are shown in Table 5-1. The sample angle function is plotted together with the experimental data as shown in Figure 5-1.

Table 5-1: Constants Used in Angle Function and Erosion Equation (50 µm Glass Beads)

A 0.3070

n1 1.9

n2 0.96

n3 35

C 2.55E-07

BH 110.3

Fs 0.2

Hv (Gpa) 1.089

K 1.59E-08


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Figure 5-1: Erosion Rate vs. Impact Angle in Air for Al 6061 at Vp = 42 m/s (50 µm Glass Beads)

After the angle function is defined, the entire modified erosion equation can be defined based on the earlier work at the E/CRC. Equation 5-2 is the erosion equation developed by Zhang et al. (2006) at the E/CRC.

. -0.59. . . (5-2)

The above equation is modified by replacing the constant C and Brinnel hardness (BH) with another constant K. This is shown in Equation 5-3.

. . . (5-3)

where k is an empirical constant accounting for the effects of material Value of exponent n is taken as 2.41 as defined by Zhang et al. (2006). Since sharpness factor (Fs = 0.2), impact velocity (Vp in m/s) and angle function are known, an empirical constant C is found by trial and error method. This is done by plotting the erosion equation without C, together with experimental data for both particle velocities and then adjusting the value of C

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100

Nor

mal

ized

ER

(-)

Impact Angle θ (degrees)

Vp=42 m/s, Vg=71 m/s (exp. Data) Vp=24 m/s, Vg=41m/s (exp. data) F(theta)


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such that it helps the curve to match with the experimental data. This is shown in Figure 5-2. The values of C and K are shown in Table 5-1.

Figure 5-2: Erosion Rate vs. Impact angle – Exp. Data and Models – 50 µm Glass Beads

Using 150 µm and 350 µm Glass Beads

Erosion ratio equations for 150 µm and 350 µm glass beads were developed in the same manner as done for 50 µm glass beads. Tables 5-2 and 5-3 show the empirical constants used to generate the erosion ratio equations and Figures 5-3 and 5-4 show erosion ratio data versus impact angle together with the equations developed for 150 µm and 350 µm glass bead particles respectively.

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

0 20 40 60 80 100

Ero

sion

Rat

e (g

/g)

Impact Angle θ (degrees)Vp=42 m/s, Vg=71 m/s Trial 1 (exp) Vp=42 m/s, Vg=71 m/s Trial 2 (exp)Vp=42 m/s, E/CRC Eq. Vp=24 m/s, Vg=41 m/s Trial 1 (exp)Vp=24 m/s, Vg=41 m/s Trial 2 (exp) Vp=24 m/s, E/CRC Eq.


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A 0.2722

n1 0.85

n2 0.6

n3 44

C 4.65E-07

BH 110.3

Fs 0.2

Hv (Gpa) 1.089

K 2.89E-08


0.00E+00

6.00E-06

1.20E-05

1.80E-05

2.40E-05

3.00E-05

3.60E-05

4.20E-05

4.80E-05

5.40E-05

0 20 40 60 80 100

Ero

sion

Rat

e (g

/g)

Impact Angle θ (degrees)Trial1 Vg=104 m/s, Vp=42 m/s (exp.) Trial2 Vg=104 m/s, Vp=42 m/s (exp.)E/CRC Eq. (Vp=42 m/s) Trial1 Vg=64 m/s, Vp=24 m/s (exp.)Trial2 Vg=64 m/s, Vp=24 m/s (exp.) E/CRC Eq. (Vp=24 m/s)


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A 0.2747

n1 1.38

n2 0.68

n3 44

C 2.80E-07

BH 110.3

Fs 0.2

Hv (Gpa) 1.089

K 1.74E-08


0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

0 20 40 60 80 100

Ero

sion

Rat

e (g

/g)

Impact Angle θ (degrees)

Vp=42 m/s, Vp=136 m/s Trial 1 (exp) Vp=42 m/s, Vp=136 m/s Trial 2 (exp)E/CRC Eq. (Vp=42 m/s) Vp=24 m/s, Vg=77 m/s Trial 1 (exp)Vp=24 m/s, Vg=77 m/s Trial 2 (exp) E/CRC Eq. (Vp=24 m/s)


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Table 5-4 summarizes constants for all the particles. The erosion ratio equations developed will be used to calculate erosion of glass beads in liquid that were presented in Figure 4.6.

Table 5-4: Summarized Constants for all Particles

Constants Particle Size

50 microns 150 microns 350 microns

A 0.3070 0.2722 0.2747 n1 1.9 0.85 1.38 n2 0.96 0.6 0.68 n3 35 44 44 C 2.55E-07 4.65E-07 2.80E-07

BH 110.3 110.3 110.3 Fs 0.2 0.2 0.2

Hv (GPa) 1.089 1.089 1.089 K 1.59009E-08 2.89957E-08 1.74598E-08


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REFERENCES

Bahadur, S., and Badruding, R., "Erodent Particle Characterization and the Effect of Particle Size and Shape on Erosion", Wear, Vol. 138, pp. 189-208, 1990.

Bellman, R., and Levy, A., "Erosion Mechanism in Ductile Metals", Wear, Vol. 70, pp. 1-28, 1981.

Finnie, I., "Some observations on the erosion of ductile materials", Wear, 19, 1972.

Finnie, I., and McFadden, D., "On the velocity dependence of the erosion of ductile metals by solid particles at low angles of incidence", Wear, Vol. 48, pp. 181-190, 1978.

Levy, A., "The Platelet Mechanism of Erosion of Ductile Metals", Wear, Vol. 108, pp. 1-21, 1986.

Lindsley, B.A., Marder, A.R., "The Effect of Velocity on the Solid Particle Erosion Rate of Alloys", Wear, 225-229, 1999.

Meng, H.S., Ludema, K.C., "Wear models and predictive equations: their form and content", Wear 181-183 (1995) 443-457.

Miska, S., "Particle and Fluid Velocity Measurements for Viscous Liquids in a Direct Impingement Flow Resulting in Material Erosion", Masters of Science Thesis, The University of Tulsa, 2008.

McLaury, B., "A Model to Predict Solid Particle Erosion in Oilfield Geometries", Masters of Science Thesis, The University of Tulsa, 1993.

Oka, Y.I., Matsumura, M., and Kawabata, T., "Relationship between Surface Hardness and Erosion Damage caused by Solid Particle Impact", Wear, 162, 1993.

Oka, Y.I., Ohnogi, H., Hosokawa, T., and Matsumura, M., "The Impact Angle Dependence of Erosion Damage caused by Solid Particle Impact", Wear, 203, 1997.

Okita, R., "Effect of Viscosity and Particle Size on Erosion Measurements and Predictions", Masters of Science Thesis, The University of Tulsa, 2010.


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Palasamudram, S.L., and Bahadur, S., "Particle Characterization for Angularity and the Effects of Particle Size and Angularity on Erosion in a Fluidized Bed Environment", Wear, Vo;. 203-204, pp. 455-463, 1997.

Tilly, G., and Sage, W., 1970, "The Interaction of Particle and Material Behavior in Erosion Process", Wear, Vol. 16, pp. 447-465.

Torabzadehkhorasani, S., "Erosion Experiments and Calculations in Gas and Liquid Impacts Varying Particle Size and Viscosity", Masters of Science Thesis, The University of Tulsa, 2009.

Zhang, Y., Okita, R., Miska, S., McLaury, B.S., Shirazi, S.A., and Rybicki, E.F., "CFD prediction and LDV validation of liquid and particle velocities in a submerged jet impinging a flat surface for different viscosities and particle sizes", Proceedings of ASME 2009 Fluids Engineering Division, Vail, Colorado, August 2009.

Zhang, Y., Reuterfors, E.P., McLaury, B.S., Shirazi, S.A., Rybicki, E.F., "Comparison of Computed and Measured Particle Velocities and Erosion in Water and Air Flows", Wear, 263, 2007.


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