wear manuscript (3)

8/3/2019 Wear Manuscript (3)

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High Precision Suspension Erosion Modeling

D. R. Lester a L. A. Graham a J. Wu a

aCSIRO Materials Science and Engineering, PO Box 56, Highett, Vic. 3190,Australia

Abstract

To date, prediction of particulate erosion in suspension flows has been wildly inac-curate, with the state-of-the-art reporting errors upwards of 40% [Y. Zhang et al.,

Wear, 240:4051, 2000]. These errors stem chiefly from the underlying erosion mod-els, significantly hindering understanding of erosion dynamics in suspension flowsand design of plant equipment with improved erosion characteristics. Herein wepresent improved experimental methodologies and data analysis techniques basedon computational fluid dynamics (CFD) to solve the associated inverse problem andgenerate high precision models of suspension erosion. These methods are appliedto a test case of silica sand particles wearing an Aluminium surface, and the resul-tant data fitted to an erosion function. To test the predictive accuracy of the fittedmodel, CFD predictions are compared with an independent erosion experiment,and the peak erosion rate is found to agree to within 1%. These results suggest themethodologies presented provide a sound basis for high precision suspension erosion

modeling.

1 Introduction

Particulate suspensions are responsible for accelerated wear in piping infrastruc-

ture and plant equipment by way of particulate erosion. This wear significantly

shortens the service life of such equipment, incurring maintenance, shutdown andrepair costs many times the original capital cost of the worn equipment. To date,

quantitative models for prediction of such suspension erosion have been notoriously

inaccurate, with the state-of-the-art reporting errors upwards of 40% [12], despite

a significant research effort into improving quantitative models. These inaccuracies

have hindered insight into the dynamics of suspension erosion and retarded develop-

ment of equipment designs with improved wear characteristics. The purpose of this

Preprint submitted to Elsevier Science 14 September 2009


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paper is to address these short-comings in erosion prediction by developing novel

suspension erosion characterization methods capable of significantly increasing the

accuracy of erosion predictions. To illustrate implementation, these characterization

methods are applied to a test case and the accuracy of the resultant erosion model

predictions are ascertained against independent experiments.

An illustrative example of the utility of accurate, quantitative erosion models is that

of erosion localization. Erodent wear arising from suspension flows often manifests

as pitted regions which wear extremely rapidly, leading to premature and local func-

tional failure although the remainder of the material surface is relatively unworn.

This accelerated wear is due to a positive feedback between the evolving (eroding)

material surface, the fluid flow field and the advected solid particles. If pitting be-gins, local vortices in the fluid flow field can result, which due to centrifugal scouring

results in greatly accelerated wear, further pitting of the material surface and so on.

The result of this process is clearly illustrated in Fig. 1, which shows an example of

prematurely worn plant equipment due to localization and positive feedback of the

erosion process. This phenomenon is remarkably common. Of note is the severity of

the local pitting and scouring whilst the remaining erodent wear is relatively small.

Accurate erosion models are crucial to understanding and predicting this feedback

process, and the ultimate goal is the ability to design plant equipment which exhibits

neutral or even negative feedback such that small erodent wear do not increase the

local erosion rate. Moreover, inertia and energy arguments suggest that the scope

for reduction of total erodent wear in plant equipment such as pipe elbows is lim-

ited for a given material/suspension combination, however there is significant scope

for influencing the distribution and hence localization of wear. Again, accurate pre-

dictive methods are required to achieve this and understand the fundamentals oferosion dynamics. Erosion prediction is also important in the characterization of

materials and employ of these in erodent applications. Often certain materials may

exhibit good wear characteristics for small particle impact angles but wear rapidly

for larger impacts (brittle) or the reverse (ductile), and so accurate characteriza-

tion and prediction are required to make optimal material selections for a given

equipment design and vice-versa.

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A promising technique for prediction of the magnitude and distribution of erodent

wear on material surfaces is the modeling of particle impact erosion via computa-

tional fluid dynamics (CFD). CFD erosion modeling involves calculation of sample

particle trajectories and their associated impact dynamics, which when coupled

with models of erosion dynamics, generates predictions of erodent wear rate dis-

tributions over the material surface of industrial process equipment. Advantages of

CFD erosion modeling include

quantitative insight into fundamental erosion dynamics

visualization of erosion dynamics inside process equipment

facilitation of rapid and inexpensive design and modification appraisal

And so, if accurate, CFD represents a powerful tool for suspension erosion predic-

tion. CFD simulation of slurry erosion typically consists of the following steps:

(1) Calculation of the fluid velocity field and subsequent advection of a large num-

ber of particle trajectories (in certain dynamical regimes it is necessary to

perform this simultaneously with the fluid field)

(2) Calculation of particle impact rate, angle and velocity distributions over rele-

vant material surfaces.

(3) Application of an appropriate erosion model derived from material data to

calculate the erosion rate distribution over relevant material surfaces.

The validity of CFD to accurately determine flow fields for particulate flows andthe calculation of associated particle paths has been well-established over decades

of research, so steps 1 and 2 are accepted as robust and accurate methodologies.

For more complex flows, experimental validation of CFD predictions is necessary,

however for simple flows approaches such as grid convergence studies can be used

to verify the predictions of the fluid velocity field. Conversely, the actual erosion

model (step 3) which quantifies the local erosion rate in terms of local particle

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impact dynamics is a major source of error, and so represents the stumbling block

to achieving high precision erosion predictions.

For example, Zhang et al [12] measured particle impact angles and velocities in a

suspension flow using Laser Doppler Velocimetry (LDV), and found these measure-

ments to agree very well with predictions made by CFD. Two erosion models (one

developed by the authors and another by Oka et al [10]) were applied to the exper-

imentally validated CFD results, and the resultant erosion rate predictions ranged

between 40% and 270% of the measured rates. These predictions were considered

to be good by the authors. As such, whilst both CFD and particle tracking are

well validated and can be performed to high accuracy, the current state-of-the-art

of erosion modeling is severely hindered by the lack of accurate erosion data and

appropriate models. It is precisely these errors which hinder improved design of

process equipment to minimize erodent wear and better understand the dynamics

of particle-fluid interactions and particulate erosion in suspension flows.

Errors in erosion predictions for slurry flows chiefly stem from the difficulties inher-

ent to experimental design and subsequent data analysis. Experiments are required

which must achieve an accurately measurable amount of wear, yet also are simple

enough to facilitate data analysis for formulation of quantitative erosion models.

In this paper we address these limitations by developing improved protocols for

conducting erosion experiments, coupled with CFD-based analytical methods to

elucidate the underlying erosion model to high precision from the experimental

data. These methodologies are applied to a test system of mono-disperse silica sand

particles suspended in water, which is used to wear test samples of aluminium, and

the precision of the erosion model generated is quantified by comparing erosion

predictions of the model with experimental observations for an independent test.

We begin by reviewing suspension erosion modeling techniques in Section 2, followed

by an overview of experimental design in Section 3 and CFD modeling in Section 4.

Experimental and CFD results are combined to generate erosion models in Section

5, and the accuracy of these models is explored in Section 6. Finally, conclusions

and future research directions are explored in Section 7.

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2 Suspension Erosion Modeling Techniques

There exist several modeling approaches for erodent wear prediction which facilitate

an experimental and analytic framework for erosion characterization. Many factorsinfluence erodent wear in suspension flows, and to date, attempts to develop gener-

alized models from first principles have proved unsuccessful [9], chiefly because of

the complexity of the erosion process at the microscale. Clark [1] lists the following

parameters as affecting the erosion process in a slurry flow:

(1) Suspending liquid density and viscosity

(2) Particle size, shape, density, hardness and friability

(3) Material properties: hardness, fracture toughness etc

(4) Concentration of particles

(5) Particle impact speed

(6) Particle impact angle

Of these factors, 1-3 are specific to a given suspension/impact material combination,

whereas 4-6 vary spatially and temporally in a given experiment and so evolve as

distributions over the impact material surface. Given the limitations of ab initio

models, a practical modeling philosophy is to consider models specific to a particular

impact particle/material combination (i.e. 2 & 3), such that the local average mass

erosion rate E [kg m2 s1] is dependant upon parameters 4-6:

E = mF(, v), (1)

where m is the local average particle impact rate [kg m2 s1], v the local aver-

age particle impact velocity [m s1], the local average particle impact angle []

(with respect to the material surface) and F is the dimensionless wear function. The

assumptions of this formulation is that the local erosion rate E is directly propor-

tional to the local particle impact rate m, with the unspecified dimensionless wear

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function F the ratio of proportionality, dependant upon v and only. These as-

sumptions are common to many suspension erosion models [12,11,3,7,8,4]. Note that

a particular model F is independent of the suspending fluid, regardless of rheology

or density, as these properties affect the particle impact dynamics ( m, v, ) alone,

but not the mechanics of the erosion process specific to the actual material/particle

combination.

A commonly used erosion model similar to (1) is that of Finnie [4],

E = mvnf(), (2)

where f() = f0

1

3cos()2 if tan() > 1

3,

sin(2) 3sin() if tan() 13

,

(3)

where n is an empirical coefficient, i.e. n=1.8-2.3 for ductile materials and n=2.0-

4.0 for brittle materials, and f is the material/particle specific dimensionless wear

function, where f0 scales the erosion rate. As noted by Meng and Ludema [9], the

experimental evidence justifying the functional form in (2) is limited, and errors

in prediction have been reported. The popularity of the Finnie model (and others

such as Grant and Tabakoff [6] model) stems chiefly from the scarcity of reliable

suspension erosion data for any material/particle combination; although known to

be unsuitable for particular combinations, it is used in the absence of a better

alternative. In this work we utilize the general framework of (1) as a basis for

quantification of erosion, deferring specification of detailed functional forms such

as (2) until data is available. As such, the methodology herein is applicable to any

erodent system, so long as the assumptions supporting (1) are valid.

3 Experimental Techniques and Results

Application of such erosion models represents a regular forward problem; for a par-

ticular geometry, given the wear function F, and calculated particle impact rate m,

velocity v, and angle distributions of the material surface, what erosion distribu-

tion E results? Conversely, determination of the wear function F from experimental

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data represents an inverse problem: for a particular experiment given the calculated

particle impact rate m, velocity, v, and angle distributions, what function F (or

possible set of functions) generates the observed erosion distribution E?

Directly or indirectly, analysis of erosion data involves solution of this inverse prob-

lem, and the challenge for accurate erosion modeling (F) is to design experimental

devices for which measurable amounts of wear (E) occur, and a range of particle

impact angles () and velocities (v) are expressed, yet the particle dynamics are

simple enough for the inverse problem to be tractable and robust. Given valida-

tion of a model of the form (1), ideally an erosion test would exhibit a significant

distribution of particle impact angle and velocity combinations {v, } relevant to

industrial applications. Furthermore, to render the inverse problem tractable, thesevariables need to be steady and unique at any particular location on the sample ma-

terial surface. Although strongly turbulent flows achieve rapid particulate erosion

for testing, strong turbulent dispersion generates random fluctuations in particle

trajectories, resulting in strongly varying particle impact angles and velocities at a

fixed point on the material surface. Conversely, particles in weakly turbulent and

laminar flows are dispersed less, and so in such flows we assume m, v and to be

unique local quantities which in practice have very narrow stochastic distributions.

Again, non-uniqueness is not problematic for forward problems such as erosion pre-

diction, but does represent a significant complication for inverse problems such as

data analysis.

The primary difficulty with design and analysis of erosion experiments for suspen-

sion flows as opposed to pneumatic flows is the different regime of Stokes number,

St; a dimensionless quantity which measures the ratio of particle relaxation time

to the approach time of an obstacle. For pneumatic flows St 1, and particlesapproaching an obstacle continue on their upstream paths and deviate little as the

gas streamlines bend around the object. As such, particle impact angles and veloc-

ities can be inferred from the upstream dynamics with reasonable accuracy, greatly

simplifying experimental analysis. Conversely, as the viscosity of the carrier fluid

for slurry flows is several orders of magnitude higher, the particle relaxation time

is much shorter, St 1. In this regime, particles tend to follow the fluid stream-

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lines much more closely, and so the particle impact dynamics are a manifestation of

non-local interactions between the particle and fluid velocity fields, and so cannot

be prescribed a priori.

Clark [1] suggests that a slurry jet test (the suspension equivalent of the ASTM-

G76 gas jet test) is not a suitable option because the particle impact velocities and

angles are not well defined, and instead advocates both a slurry pot test as well as a

pipe loop test. Both of these tests involve cylindrical samples which express a wide

range (virtually 0-90) of impact angles in a single experiment, and also cylindrical

samples can be accurately measured using standard metrology equipment. These

tests are briefly described here, for further details see Clark [1].

The slurry pot test consists of a cylindrical pot containing a coaxial rotating spindle

with arms which hold cylindrical material samples. The pot is filled with sample

suspension for testing, and rotation of the spindle drives a relative flow over these

arms, resulting in particle impacts and erosion. This test appears to be advantageous

as it can generate much faster wear than the pipe loop test, however extensive testing

found the slurry pot device to be unsuitable for erosion characterization because at

high rotation velocities particles would tend to be centrifuged to the outside of the

pot, and moreover the pot baffles generated an unsteady flow (and hence particle

impacts) local to the samples, rendering the inverse problem intractable. Removal of

the baffles would result in a steady flow, however a narrow boundary layer would also

develop near the pot walls, significantly reducing the relative fluid velocity local to

the material samples and hence the erosion rate. The small suspension volume in the

slurry pot relative to the sample size also meant erodent particles were significantly

degraded before accurately measurable levels of wear were produced.

The pipe loop test consists of a closed circuit pipe loop connected to a large suspen-

sion reservoir, with the cylindrical material samples inserted across the pipe normal

to the flow direction. So long as straight uninterrupted sections of pipe occur sev-

eral diameters upstream of each sample, the flow is well-characterized over each

sample and generates particle impacts and erosion. The pipe loop test is considered

advantageous as large volumes of suspension could be maintained with minimal

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degradation, and particle impact rates, velocities and angles at the sample material

surface are steady and can be well characterized in the laminar regime.

As such, a pipe loop test was chosen as an experimental technique to erode cylindri-

cal specimens under well defined flow conditions. The pipe loop rig used consisted of

a 3000L agitated tank filled with a working suspension of water with 7% by volume

of Garfield sand with d50 200 m diameter particles. The full sand particle size

distribution (PSD) shown in Fig. 3 is fairly narrow, although a monodisperse PSD

is ideal. This suspension was driven by a Warman 2x1.5 slurry pump through 53mm

ID pipework, with the flow rate monitored by a magnetic flowmeter. Three mean

suspension pipe velocities V0 were used for erosion testing in the pipe rig; 2.5, 3.6,

and 4.5 [m s1

], denoted as low, medium, and high flow velocities respectively. A

special insert was made for the pipework with matching flanges to allow a 10 mm

diameter cylindrical samples to be installed as shown in Fig. 2, with Aluminium

used as the sample material in this study. A schematic of the incident particle paths

(black arrows) and relevant erosion (E) and particle impact variables ( m, v, ) is

shown in Fig. 4, including the material sample reference angle .

A novel device was constructed to enable accurate measurements of the erosion of

cylindrical samples. The device is similar to that described by Clark and Wong [2],

and consists of a collet chuck for holding cylindrical samples, a 200 step stepper

motor drive and a Schaevitz gauge head (precise Linear Variable Differential Trans-

ducer (LVDT)). Further details of this device and the pipe loop rig are given in

Graham et al [5]. The erosion depth h [m] measured by the LVDT is related to the

local erosion rate E as

E = h

t, (4)

where [kg m3] is the sample material density and t [s] the run time of the ex-

periment. The device is computer controlled via a LabView program which outputs

sample reference angle vs LVDT data E in 0.45 increments to file. This mea-

sured distribution of erosion rate E as a function of sample reference angle is the

primary data generated by the experiment, which must be analyzed to determine

the underlying erosion model.

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4 CFD Techniques for Experimental Data Analysis

To determine the wear function F from the measured erosion rate E, distributions

of the particle impact rate m, angle and velocity v distributions over the sample

material are required. For simple flows such as the pipe loop flow, these distri-

butions can be calculated reliably via CFD, given the fluid and particle properties

(viscosity, densities etc) and inflow data. Calculations were performed over the three

mean suspension velocities (low, medium and high) used in the experiments. As the

particle volume fraction was low (7%) and Reynolds number moderate, one-way

fluid-particle coupling can be employed, meaning the fluid velocity field may be cal-

culated a priori and particle advection is calculated as a post-processing step. Thispresents several computational advantages as for given fluid conditions, the velocity

field need only be determined once, and so very high accuracy can be achieved.

With respect to erosion prediction, simulations with particle size distributions can

be handled by simulating each particle bin separately and subsequently scaling and

superimposing results to build up that for a given distribution. This has advantages

both with respect to rapidly simulating multiple distributions, and also with respect

to particle statistics for distributions with narrow tails (the upper one of which can

be very important as large particles dominate erosion), as the total number of par-

ticles required is significantly reduced.

To determine the fluid velocity field, the commercial CFD code ANSYS CFX-11.0

was employed in steady-state mode with an unstructured 3D mesh. This mesh used

is illustrated in Fig. 5, where the pipe, inlet, outlet and sample are clearly depicted.

A k turbulence model was employed with non-buoyant incompressible flow, and

the pipe inlet velocity and particle distribution were both assumed to be uniform5 pipe diameters downstream of the sample. Calculations were performed for inlet

velocities of V0 = 2.5, 3.6 and 4.5 m s1, and in all cases convergence was very

rapid, with the RMS of all residuals less than 108 in 1000 iterations. In all cases,

solution change under a two-fold mesh refinement was negligible, and so there is a

high degree of confidence of the calculated fluid velocity field for this simple flow.

Alternate turbulence models (Reynolds stress, SST) were also used and found to

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have negligible effect on both the fluid and particle dynamics. Resultant velocity

distributions and streamlines for the pipe flow at V0 = 4.5 [m s1] are depicted in

Fig. 6, where local acceleration of the fluid around the sample is clearly illustrated.

Lagrangian particle tracking was performed as a subsequent run in CFX with solu-

tion of the fluid equations switched off. 2106 particles of diameter dp=200 micron

were released randomly over a small disc of the same radius as the material sample,

centered at the pipe inlet, so particle impacts were localised about the centre of

the material sample. An extremely fine scale mesh (depicted in Fig. 7) was used on

the sample surface in this region to generate high resolution results, and about 74%of the particles released impacted with the cylinder. This high number of impacts

ensures generation of high resolution data for the particle impact angle and velocity

over the sample. The impact angle and velocity distributions for 200 micron parti-

cles at inlet velocity V0=3.6 m s1 are depicted in Fig.s8. Fig. 9 summarizes these

results in chart form, plotted against the sample reference angle . In this case the

particle impacts extend only +/- 80 from the mid-plane of the pipe, and further-

more these impacts are distributed nonlinearly. These effects are more pronounced

as both particle size and inlet velocity are reduced.

To determine the particle impact rate distribution m, a separate particle tracking

simulation was necessary as the localized release in the previous simulation skews

the particle impact distribution. As such, the second simulation was performed with

5 105

particles of diameter 200 micron uniformly distributed over the pipe inlet,and the particle trajectories recorded. The particle impact distribution was inferred

from the discrete particle trajectory data rather than over the sample surface mesh

(Fig. 7) as the very fine mesh means many face elements did not experience a particle

impact, let alone a significant enough number to yield statistically reliable results.

From the particle tra jectory data, the particle impact rate distribution is very close

to Gaussian (see Fig. 10) for all particle sizes and inlet velocities.

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5 Data Analysis and Model Extraction

The sets of data ( m, v, as function of) obtained from CFD can now be analyzed

with the experimental erosion data (E as a function of ) to determine the dimen-sionless wear function F in Eq. (1). As both particle impact angle and velocity vary

over the material sample, the data obtained for any given experiment represents a

curve of erosion E in (v, ) space, where the trajectory in {v, } space is governed

by the distributions of v and over . By dividing the experimental erosion distri-

bution E by the particle impact rate m obtained from CFD, we can obtain a curve

of F in {v, } space

F(v(), ()) =E()

m()

, (5)

as depicted schematically in Fig.11. Hence the surface F can be resolved by per-

forming a set ofN experiments at different inlet velocities V0, generating N different

trajectories in {v, } space.

Performing many erosion tests at different inlet velocities is very time consuming,

especially at low V0, where small wear rates require very long experiment run times

to achieve accurately measurable amounts of wear. So the question arises as how

much can be done with a limited data set in {v, } space? If we employ a simplified

functional form for F similar to the Finnie (1960) model (2), with the distinct

difference that the function f() is unspecified, the problem is simplified markedly.

Using two sets of data as per Fig. 11, the velocity index n may be treated as a

fitting parameter to match the curves

fi(i()) =Ei()

mi() vi()n, i = 1, 2, (6)

where Ei(), mi(), vi() and i() are the F, m, v and distributions over where i = 1 and i = 2 correspond to the low and medium inlet speed cases re-

spectively. By optimizing n to minimize the RMS error between the resultant f1()

and f2() curves over = [0, 90], an estimate of n is generated and some indica-

tion of the suitability of the erosion model form (2) is given. The advantage of this

approach is that no specific function form needs to be specified for f(). The resul-

tant fi() curves are significantly different, as shown in Fig. 12, and so it is argued

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the functional form (2) is unsuitable for erosion modeling of the sand/Aluminium

combination studied herein. Therefore, not only is the specific Finnie model (2) and

(3) unsuitable, but even the general form of (2) alone is too simple to capture the

erosion behavior of the materials under consideration here. It is likely that this is

also the case for other particle/impact material combinations.

As the Finnie formulation (2) is found to be unsuitable in this case, we introduce

the more general formulation

F(v, ) = f()g(v) (7)

to fit the erosion data. This formulation is a formalization of the assumption that the

angular and velocity dependencies of erosion are independent processes such thatthe angular dependance is constant for all velocities and vice-versa. This approach

is similar to that of Finnie, except the velocity dependence vn is generalized to

the arbitrary function g(v). Using the NonlinearFit package in Mathematica 7.0,

we consider several different functional forms and the following forms for g and f

respectively give the best fit whilst minimizing the number of fitting parameters gi,

fi to avoid spurious regression

g(v) = g0v + g1v2

+ g2 [eg3v

1] , , (8)

f() = (90 )f0 + f1 + f2

2

f3 + f4 + f5f6, (9)

As zero wear is expected for zero particle impact velocity, Eq. (8) is constrained such

that g(0) = 0. Likewise, from experimental evidence here and elsewhere, erodent

wear for ductile materials is zero for normal and tangential particle impacts, hence

Eq. (9) is constrained such that f(0) = 0 and f(90) = 0. The fits of these functions

against the experimental data parameterized as a function of are quite good, as

shown in Fig.s 14 (a) and (b) respectively for the high and low speed data.

However, when the actual functions g(v) and f() are plotted (Fig.s 15 (a) and (b)

respectively), some non-physical behavior is observed. No mechanism exists which

can explain a decrease in wear rate with velocity as depicted by the g(v) curve. As

such, this curve is not physically plausible, however the combinations of functions

g and f give a good fit to the observed data. Likewise, the angular dependence

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f() is contaminated by these effects and so physical interpretation of this curve

is limited. Attempts to use fitting functions which involve strictly monotonic in-

creasing functions for the velocity dependence g(v) were found to be unsuitable for

the experimental data, and so the non-physical behavior of the angle and velocity

functions is considered to be of secondary importance at this juncture. With more

experimental data, it may be possible resolve the of non-physical behavior of g(v)

and deduce improved functional forms. Despite these problems, the wear function

F(v, ) looks quite plausible over the range of experimental measurement, as per

Fig. 16. As such, the fitted wear curve appears suitable for interpolation between

the high speed data trajectory (red) and the zero velocity axis (as we know wear is

zero here), however extrapolation outside (i.e. greater v and/or ) the high speed

data trajectory (red) is extremely dangerous, as evidenced by the non-physical be-

havior of g(v) at high v. Errors between the fitted wear function F(v, ) and the

experimental data are shown in Fig. 17, which correspond to a maximum error of

10% in both data sets. This error is due to both experimental noise and limitations

of the functional forms of f() and g(v) in equations (4) and (5) respectively.

6 Erosion Model Testing

To test the accuracy of the fitted wear function F(v, ), this function is used to

predict the erosion for a test case in the same geometry at the intermediate velocity

V0=3.6 m s1, and the results compared with the experiment performed under the

same conditions. As for the high and low velocity cases, CFD is used to determine

the particle impact flux rate, velocity and angle distributions in a similar manner

to the high and low velocity cases. In this case the forward problem is solved;

erosion is calculated via Eq. (1) using F(v, ) over the surface of the sample. The

results are summarized in Fig. 18, illustrating very good agreement ( 5%) between

the predicted and measured wear. Scatter in the experimental and predicted data

reflects measurement and CFD errors respectively.

Whilst there is some discrepancy in the predicted erosion away from the maxi-

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mum, most importantly the maximum erosion is predicted to a very high degree

of accuracy ( 1%), and the location of the maximum erosion point is also quite

accurate ( 5%). These results show better agreement between predicted and mea-

sured erosion than any other known erosion prediction, and so impart a high level of

confidence in the methodology employed. Clearly the true test of the methodology

is to predict erosion in a different geometry such as a pipe elbow, however accurate

measurement of wear over the surface of such geometries is not trivial although novel

methods are promising [5]. The experimental results for the intermediate speed case

can also be projected onto the wear function F(v, ), and the data is shown to fol-

low a similar trend to that of the high and low speed results. As expected, the error

between the fitted curve F(v, ) and the experimental data is much higher for the

intermediate case (Fig. 18) as this data was not used in the fitting process.

7 Conclusions

In this paper we have presented improved experimental methodologies and data

analysis techniques to generate high precision models of suspension erosion. These

methods are based upon judicious experimental design coupled with CFD analysis,

so to facilitate straightforward solution of the inverse problem associated with model

generation. Upon application of these methods to a model system of silica sand

particles impacting an Aluminium surface, we find the traditional functional forms

for erosion models used by Finnie [4] are not suitable, and it is likely this behavior

extends to other particle/material combinations.

Good fits of the observed erosion data are found when a general fitting functionis used for the velocity dependance, however the fitted functions do exhibit non-

physical behavior when extrapolated to higher velocities outside the envelope of

experimental data. This behavior suggests extrapolation of such models is a dan-

gerous practice in general, and the issue of generating precise erosion models lies

no so much with fitting functions but rather with the attainment of high accuracy

erosion data over regions of {v, } space relevant to application. It is anticipated

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that the fitting functions (8) and (9) are not universal for all particle/material com-

binations, however so long as good quality experimental data and accurate CFD

predictions are available, there exist a variety of fitting methods to achieve interpo-

lation of the F(v, ) function.

To test accuracy of the fitted erosion model, erosion predictions are made via CFD

and compared to an independent erosion experiment. Excellent agreement between

prediction and experiment, with relative errors in the maximum erosion rate of

approximately 1%. This is a significant improvement on the current state-of-the-

art for suspension erosion modeling, suggesting the experimental and analytical

protocols presented are sound methods to achieve high precision suspension erosion

modeling. A more robust test of these methods would be an experimental validation

of erosion predictions in a different geometry to that of the cylindrical sample used

herein the pipe loop test, such at the pin-in-pipe geometry of Graham et al [5] which

still involves a wide range of particle impact angles and velocities.

The success of the erosion predictions herein generates confidence as to the modeling

of more complex erosion scenarios, such as plant equipment and piping infrastruc-

ture. This work also represents a basis for address of more complex erosion issues

such as localization and geometric stability, where evolution of the eroding material

surface (and hence local fluid dynamics) must be accounted for during the model-

ing process. Such developments pave the way for new equipment designs which have

improved erosion characteristics and much improved operation life.

Acknowledgements

The authors wish to thank AMIRA International and the sponsors of the AMIRA

P931 project for their support of this work.

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erosion by dilute slurries. Wear, 186187:454464, 1995.

[3] I. Finnie. Some Reflections on the Past and Future of Erosion. In 8th

International Conference on Erosion by Liquid and Solid Impact (ELSI VIII),

Cambridge, England. Elsevier Science Sa Lausanne.

[4] I. Finnie. Erosion of surface by solid particles. Wear, 3:87103, 1960.

[5] L.J.W. Graham, D.R. Lester, and J Wu. Quantification of Erosion Distributions

in Complex Geometries. Wear, pages 121, 2009. in press.

[6] G. Grant and W. Tabakoff. Erosion Prediction in Turbomachinery Resulting

from Environmental Solid Particles. Journal of Aircraft, 12:471478, 1975.

[7] J. A. C. Humphrey. Fundamentals of fluid motion in erosion by solid particle

impact. International Journal of Heat and Fluid Flow, 11:170195, 1990.

[8] J. A. Laitone. Erosion prediction near a stagnation point resulting from

aerodynamically entrained solid particles. Journal of Aircraft, 16:809814, 1979.

[9] H. C. Meng and K. Ludema.

[10] Y.I. Oka, K. Okamura, and T. Yoshida. Practical estimation of erosion damage

caused by solid particle impact. Part 1: effects of impact parameters on a

predictive equation. Wear, 259:95101, 2005.

[11] T. Omote, H. Morita, and A. Hirose. Some Reflections on the Past and Future

of Erosion. In 8th International Conference on Erosion by Liquid and Solid

Impact (ELSI VIII), Cambridge, England. Elsevier Science Sa Lausanne.

[12] Y. Zhang, Y.B. Cheng, and S. Lathabai. Erosion of alumina ceramics by air-

and water-suspended garnet particles. Wear, 240:4051, 2000.

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Fig. 1. Example of erosion localization and pitting in suspension flow equipment

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Fig. 2. Photograph of 10mm cylindrical material sample and holder for erosion

testing.

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Fig. 3. Particle size distribution of Garfield sand.

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Fig. 4. Schematic of incident particle paths (black) onto material sample cylinder

and reference sample angle .

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Fig. 5. Global mesh used for fluid velocity field CFD calculations in ANSYS

CFX-11.0

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(a) (b)

(c) (d)

Fig. 6. (a),(b) Streamlines and (c),(d) velocity magnitude contour plots for inlet

velocity V0 = 4.5 [m s1]

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Fig. 7. Fine-scale material sample mesh used for particle trajectory CFD calculations

in ANSYS CFX-11.0

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(a) (b)

Fig. 8. Distributions of (a) sand impact velocity v and (b) sand impact angle

across cylindrical material sample for 200 micron sand particles injected at inlet

velocity V0 = 4.5 m s1

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(a) (b)

Fig. 9. Distributions of (a) sand impact velocity v and (b) sand impact angle across

sample reference angle for 200 micron sand particles injected at inlet velocity V0

= 4.5 m s1.

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Fig. 10. Distribution of sand impact mass rate m across sample reference angle

for 200 micron sand particles injected at inlet velocity V0 = 4.5 m s1.

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Fig. 11. Schematic of the dimensionless wear surface F(v, ) in {v, } space from

multiple experiments performed at different inlet velocities V0.

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Fig. 12. Comparison of fitted dimensionless wear curves f() for two inlet superficial

velocities V0=2.5 m s1 and V0=3.6 m s

1 from the Finnie model (2) using velocity

index n=2.6.

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Fig. 13. Curves over the wear surface F(v, ) from experimental and CFD data for

two inlet superficial velocities V0=2.5 m s1 (blue) and V0=4.5 m s

1 (red) based

on Eq. (1) for aluminium.

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(a) (b)

Fig. 14. Fit ofF(v, ) to (a) high speed (superficial inlet velocity V0=4.5 m s1) and

(b) low speed (superficial inlet velocity V0=2.5 m s1) erosion data using equations

(6)-(8).

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(a) (b)

Fig. 15. (a) Fitted function f() in Eq. (6) and (b) fitted function g(v) in Eq. (6).

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Fig. 16. Surface of fitted wear function F(v, ) and incidental trajectories for high

speed (superficial velocity V0=4.5 m s1) and low speed (superficial velocity V0=2.5

m s1) experiments.

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Fig. 17. Errors between experimental data and fitted wear function F(v, ) for high

(red, superficial velocity V0=4.5 m s1) and low (blue, superficial velocity V0=2.5

m s1) speed experiments.

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Fig. 18. Comparison between experimentally measured and predicted wear via CFD

using the fitted wear function F(v, ) for the intermediate speed case superficial

velocity V0=3.6 m s1 over 42 hours.

35

wear manuscript (3)

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