A numerical investigation of a geometry independent integrated method to predict erosion rates in slurry erosion

Wear 271 (2011) 712–719

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A numerical investigation of a geometry independent integrated method to predict erosion rates in slurry erosion A. Gnanavelu ∗ , N. Kapur, A. Neville, J.F. Flores, N. Ghorbani Institute of Engineering Thermofluids, Surfaces and Interfaces, Mechanical Engineering Department, University of Leeds, Leeds, West Yorkshire LS2 9JT, United Kingdom

a r t i c l e

i n f o

Article history: Received 7 September 2010 Received in revised form 21 December 2010 Accepted 21 December 2010

Keywords: Slurry erosion wear Numerical erosion wear equation CFD particle tracking Jet impingement erosion

a b s t r a c t An erosion prediction method with the objective of determining wear profiles on various geometries due to slurry erosion, based on material wear data acquired from a minimum set of carefully selected laboratory tests and CFD (computational fluid dynamic) simulations has been developed. Data from a single standard laboratory test [Jet Impingement Test on a flat specimen oriented at 90◦ to an impinging solid suspension (water and sand)] is characterised using CFD to acquire wear data for a range of erosion parameters as a function of position. This data is used to build a wear map for that specific material–abrasive (316L steel-AFS50/70 sand) combination. The accuracy of this method is assessed by predicting wear from further jet impingement tests at 90◦ but under different flow velocities to that used to build the map and subsequently assessing against experiments. A good correlation between predicted and measured wear was observed. An assessment of two phenomenological wear models (which profess to capture wear characteristics as a function of material properties) and one wear model that captures the above wear map statistically through the use of appropriate fitting functions is made. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Surface erosion of materials by solid particle impacts during multiphase flow is a major problem in many types of industrial equipment. Severe degradation of materials can cause premature failure of equipment leading to increased environmental and personnel risks along with the added financial repercussions. Material is removed due to repeated particle impacts which can be severe at a particular location within any geometry (due to a particular combination of flow conditions and equipment design) leading to concentrated loss which can cause abrupt failure [1]. It is vital to precisely predict the location and the rate of loss in order to prevent equipment failure. Accurate predictions can also be used to aid material and plant design and allow areas of high wear rates to be excluded from equipment design. Erosion prediction is also critical in characterisation of materials and subsequent use of these in industrial applications. A wide range of particle impact conditions (angle and velocity) can exist within hydrotransport equipment [2]. Often certain materials may exhibit good wear characteristics for small particle impact angles but wear severely for larger impact angles (the case of brittle materials) or

∗ Corresponding author. Tel.: +353 (43) 3335629. E-mail address: [email protected] (A. Gnanavelu). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2010.12.040

vice versa [3], and hence accurate characterisation and prediction are required to make optimal material selection for a given plant design. Various models are used to predict erosive wear in engineering geometries which are characterised by a finite number of parameters. The erosion wear is reliant on several system parameters that include the properties of erodent-target materials, the macro and micro exposure conditions, local erodent impact kinetics and geometrical characteristics of the erodent. The effect of these factors are intertwined [4] and the actual wear mechanisms are intricate and can be due to micro-cutting, plastic deformation, fatigue, brittle fracture and melting or a combination of these [3,5–7]. For a phenomenological model to accurately predict erosion rates it should take into consideration the individual contribution of each of these mechanisms under the conditions in which each failure model prevails. No one model exists that covers all these parameters, however, models have been proposed for a sub-set of these conditions. Finnie [5] developed a theoretical equation based on metal cutting phenomenon under dry conditions (no fluid was present) to predict material wear. Since then, more than 200 reported models have been reported [8]. Meng and Ludema [4] found, among the numerous models available in literature, only 28 were of significance (using a criterion of historical value, good experimental data and validation, and not contravening the laws of physics); between these they contained a total number of 33 prominent parameters

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Table 1 Conditions at which CFD simulations of the jet impingement test geometry were performed to predict particle impact data as a function of position. Fluid

Temp. (◦ C)

Fluid density (kg/m3 )

Nominal impact angle

Fluid viscosity(Pa.s)

Nozzle-sample separation

Particle density (kg/m3 )

Particle shape

Particle size (␮m)

Water

20

1000

90◦

1 × 10−3

5 mm

2650

Sphere

250

(for example, velocity, angle, particle hardness, shape, diameter, strength, material hardness, strength). These models, for example, Finnie [5], Bitter [7], Neilson and Gilchrist [9], McLaury et al. [10], Grant and Tabakoff [11] and Huang et al. [12] are either purely theoretical or empirical based. Models developed on purely conceptual foundations contain material coefficients whilst those on experimental data contain empirical constants not necessarily amenable to any interpretation. The adaptability of most of these numerical models for different conditions (other than those under which the model was developed) presents an obstacle for engineers in the form of obtaining values for these coefficients. A second issue is the robustness of these models in capturing material behaviour. Empirical equations generally only perform well within the conditions under which the equation was developed and if the failure modes of the material are different then the model can fail [4]. Conceptual based equations aim to predict erosion rates over a wider range of conditions, however since the range of possible conditions are enormous, it is hard to gauge the success of these equations over all the specified conditions (an enormous amount of testing on various materials should be carried out to do so). So, despite the progress made in improving prediction techniques and in understanding the local wear mechanisms, the need for an accurate numerical model still exists since not one method or model can yet confidently predict material wear rates over the entire spectrum of conditions within which erosion degradation due to impacts can be predominant [8]. Until this has been achieved, other methods are being pursued to predict material wear rates within plant equipment without having to execute an elaborate testing scheme. A novel methodology, using a combination of numerical and experimental methods, which aims to extract a wide range of erosion parameters for a specific material–erodent combination from a minimum set of laboratory tests and correlate these to field conditions in a way in which a computational model can be used to predict erosion wear on more complex geometries for the same material–erodent combination was previously reported by the authors [13]; the findings suggested good predictive power. This paper, after highlighting the key steps in this method, compares the approach to using a range of existing models. 2. Methodology The method is based on the concept that the local wear rate is influenced by local impact angles and velocities of an erodent at the time it impacts the surface. This involves two key stages to build a material–erodent specific wear map using a combination of standard experimentation and CFD (computational fluid dynamics). The objective is to generate a wear map that is universal for a specific material and erodent combination; once generated, actual wear in complex geometry of that particular material–erodent combination can be predicted using further CFD simulations. 2.1. Stage 1 – generating a material-specific wear map A minimal set of erosion tests are conducted on a flat specimen of the selected test material orientated at 90◦ to the flow

using a submerged jet impingement test. Post test surfaces are analysed to provide the quantitative local wear rate as a function of radial position from the centre of the wear scar. At each location from the centre of the jet a thickness loss is determined. CFD simulations of these standard tests are run under exact conditions to predict local particle impact data (velocity, angle and rate) as a function of radial position from the centre of the test surface. It is assumed that actual (experimental) local particle impact velocities and angle are accurately described by CFD simulations [14,15]. The final part of this stage is to generate a universal wear map for the material–erodent combination under test which gives wear/impact as a function of local particle impact velocity and angle. 2.2. Stage 2 – predicting wear rates in specific geometries A CFD simulation is run for the specific geometry of interest from plant operation. This gives impact velocity, angle and frequency at each position within the geometry; the wear map from stage 1 is then used to predict the local wear rate (i.e., thickness loss) at each point for that specific material–erodent combination. This allows the final wear scar depth and shape to be determined as a function of position, together with the overall wear on the component. Ultimately any geometry may be examined (for this particular sand–material combination), where hydrodynamic impact erosion is dominant. It is proposed that this method is generally applicable to various types of erodent and fluid medium; in this study commercially available AFS (American Foundry Society) 50/70 sand particles (properties in Table 2) and water were chosen as erodent and fluid medium. Before proceeding further, the impact parameters need to be clearly defined since confusion exists in the literature regarding impact angle and velocity [16] and a clear distinction should be drawn between local and nominal conditions. Local impact conditions are defined as those associated with an abrasive particle just prior to impact, whilst nominal conditions are those which are used to define mean flow parameters and can be distinguished as illustrated in Fig. 1, where V is the average flow velocity at the exit of the nozzle, ˛ is the nominal impingement angle (90◦ in this case), Vp and  are particle impact velocity and angle, respectively (and will be a function of position); also note h is the standoff or sample nozzle separation distance and sand concentrations are defined as the weight ratio of total number of particles contained within a fixed volume of fluid exiting the nozzle (measured using a filter-paper positioned beneath the nozzle for a known time). 3. CFD simulation of impingement erosion Numerical simulations of the fluid jet flow and particle impingement on a flat specimen were carried out using a commercially available CFD package, Fluent (Ansys Inc.). All simulations reported were conducted on the geometry defined in Fig. 2 and at conditions listed in Table 1, to provide impact data (local velocity, angle and impact frequency as a function of position, measured radially from the centre of the specimen). The entire CFD process involved two elements, which were to simulate the single phase flow sce-

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Nozzle Particles in flow Fluid jet directon V

Vp

h

Sample Fig. 1. Diagram of particle impacts as generated by a JIT (jet impingement test) illustrating the difference between nominal and local impact data.

nario and then solve particle motion equations on the obtained flow solution to predict particle impact data, a procedure similar to those adopted at low abrasive concentrations [16,17]. For the configuration of 90◦ nominal impingement angle, axisymmetric conditions were used to generate a half model for the optimum use of computational resources. The flow problem was treated as steady, incompressible and Newtonian. The Renormalised group (RNG) version of the K–ε equation [18] was used to model the effects of turbulence on flow solutions and all numerical simulations were solved using the second order differential scheme in order to reduce computational errors. Coupling between velocity and pressure fields were achieved using the SIMPLE scheme and all simulations were terminated when the residuals of all monitored flow parameters were below 1 × 10−4 . Flow solutions obtained were insensitive to further increases in number of computational grid elements used. Particle tracking

Fig. 2. Geometry of the jet impingement test with the appropriate boundary conditions for the computational domain.

equations were then solved discretely over the obtained flow simulations using the Lagrangian approach to calculate particle motion and impact data [19]. The average size of the particle was taken to be 250 ␮m in diameter (the mean of the actual sand used within this study) and the shape assumed to be spherical. In reality the non-sphericity would have two effects; (i) the drag (which couples the particle motion to the fluid motion) may differ. The Newton shape factor for sand (or scruple) is 1.2–1.8 and a typical particle Reynolds number in this case is around 500. Consequently the drag is estimate to be within 5% of a sphere, based on the data with [20]. (ii) the angular nature of the particle will cause different wear behaviour on the surface. Since the correlation is developed for a particular erodent the wear data will inherently represent the average behaviour of particle impacting as different angles. Impact data as a function of position for nozzle exit flow velocities of 5, 7.5 and 10 m/s for conditions (Table 1) were determined from CFD data and are illustrated in Fig. 3 (for the case of 5 and 10 m/s only) and the data corresponded qualitatively with the observations of Benchaita et al. [21]. 4. Experimental wear data It has been demonstrated, numerically and experimentally (using particle image velocimetry [14,15]) that a standard submerged jet impingement test rig can reproduce a wide range of local impact angle and velocities along the surface of a flat specimen oriented at 90◦ to the oncoming fluid suspension [21] and these angles and velocities can be determined using CFD simulations. Hence testing was carried out using a standard submerged jet impingement test facility, the functioning of which is reported elsewhere [22,23]. Specimens fabricated out of stainless steel 316L (UNS316L) were chosen for testing since they are used extensively as piping material in oil industries and more importantly for this erosion study, the potential for complications due to corrosion interactions on erosion process is minimised. AFS 50/70 (American Foundry Society) sand was used as the erodent (properties given in Table 2). The surface of every test sample prior to testing was ground and polished using an automatic polishing machine and sand papers up to 1000 grit size. The tests were then conducted on steel specimens oriented at 90◦ to the oncoming solid suspension at three nozzle exit velocities of 5, 7.5 and 10 m/s at conditions listed in Table 2. Post test surfaces were characterised using a contact profilometer to analyse the wear scar. The profilometer used was the Talysurf 1200 model with an ultimate resolution of 0.8 nm, however, a typical resolution of 0.1 ␮m was easily achieved. This enabled local wear depths to be measured as a function of radial distance from the stagnation point (centre of the wear scar) as illustrated in Fig. 4. CFD simulations were used to characterise the wear scar region in terms of impact angles and velocities, which enabled direct correlation of material wear data (normalised by impact frequency) for various sets of impact angles and velocities. This array of data was used to develop a material–abrasive specific map which can associate a local wear rate for any impact angle or velocity within the envelope of the map. A detailed description of the develop-

Table 2 Operating conditions under which erosion tests were conducted on flat 316l samples to provide material wear data for correlation with CFD predictions. Fluid

Temp. (◦ C)

Water 20

Fluid density (kg/m3 )

Fluid viscosity (Pa.s)

Nominal impact angle

Test duration (min)

Nozzle exit velocity (m/s)

Sand density (kg/m3 )

Sand content at nozzle exit (by weight %)

Sand size distribution (␮m)

1000

1 × 10−3

90◦

120

5, 7.5, 10

2650

1%

212–300

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715

Fig. 3. (a) Particle impact velocity and (b) angle data as a function of radial position along the test surface as predicted by CFD simulations performed under conditions listed in Table 1 for only the nozzle exit flow velocities of 5 and 10 m/s.

ment of this map is provided in Gnanavelu et al. [13]. This map is developed on the assumption that all the particles that do impact (assuming no inter-particle collisions) contribute to wear loss and the wear rate for a particular impact angle and velocity is constant with time (i.e., no work hardening effects). An inherent assumption in the CFD model is that each particle only makes one impact and is re-circulated into the bulk flow. 5. Numerical treatment of material wear and local particle impact data Data obtained from testing and simulations were numerically treated in order to obtain a numerical equation which can predict erosion ratio (ER) for the range of conditions enveloped by the wear-map (this range is the conditions recreated on the surface of the specimens for conditions defined in Table 2). The erosion ratio is defined as the ratio of the total mass loss to the mass of the particles causing that damage. Parslow et al. [24] reported that erosion wear is a function of particle impact kinetics and material properties of target-abrasive and can be expressed as, ER = A × Vpn × f (),

(1)

where A is generally taken as a constant depending on the properties of target material, abrasive material, shape factor and other factors. It can be either only one or a combination of those factors related to material–abrasive properties and geometrical features, Vp and  are local impact velocity and angle, n is the velocity exponent. It has been well established from several experimental studies that the exponent, n, tends to lie between 2 and 3. The angular dependence of erosion wear has been described by various authors in the form of multi-parameter equations. Wang and Shirazi [1] used an erosion model which had a dual function for angular dependence in which the trigonometric functions of impact angle were of the third order. In the model developed by Bitter [7], the function

Fig. 4. Schematic representation of a cross section of the wear scar measured by a contact profilometer. X here represents the radial distance from the stagnation point located beneath the centre line of the jet (also the centre of the overall wear region) and Y is local wear depth as function of radial position.

f() was taken as K(sin ␪)2 , where K is a constant. In the wear formulation proposed by Grant and Tabakoff [11] the trigonometric function of impact angle was of the fourth degree. Thus the angular dependence function generally contains a trigonometric function of the impact angle (impact energy is resolved into horizontal and vertical components to account for wear by cutting and deformation mechanisms) and the order was demonstrated to vary between 2 and 4 [25]. To develop an erosion equation within the framework of Eq. (1); values for n, A and the angle dependency function are required. Using wear data from a single jet velocity (the motive of the study is to use data from a single test), it is very difficult to obtain these values for n, A and angle dependency. Given the significant literature quoting 2 < n < 3, a value of 2 was chosen. Based on wear data from experiments and local impact data from CFD, for a jet velocity of 7.5 m/s and 90◦ nominal impingement angle, a numerical model for erosion rate (Eq. (2)) was developed. This Eq. (2) is within the general frame work of (1) and consisted of several constants. Using a mathematical software Minitab 15, values for these constants which provided the best fit between local experimental data (at 90◦ and 7.5 m/s) and corresponding impact conditions in Eq. (2) were determined. 4

3

2

ER = Vp2 [(A(sin ) + (B(sin ) + (C(sin ) + (D(sin ) + E]F,

(2)

where A, B, C, D, E and F are all correlation coefficients and are presented in Table 3. These constants will be dependent on the physical properties of both the target and abrasive material. It is also stressed that Eq. (2) can work only for this particular 316L-AFS50/70 combination and under conditions were erosion by impact is established. In Eq. (2), the angular dependence was chosen to be a fourth order polynomial since this provided the best numerical fit between local experimental wear data (for a test conditions of 7.5 m/s flow velocity at 90◦ nominal impingement angle) and impact conditions (local angle and velocity, with the velocity exponent set at 2); a comparison with angle dependent function of different orders showed this gave a numerical fit of 6% better than other forms). Using a different velocity exponent (e.g. n = 2.5 or 3, would result in a different set of parameters, but the goodness of fit is similar).

Table 3 Correlations for ER Eq. (2) obtained using material data obtained at 90◦ nominal impingement angle and 7.5 m/s nozzle exit flow velocity with impact conditions provided for by CFD simulations at same conditions. A

B

C

D

E

F

−0.396

8.38

−16.92

10.747

−1.765

0.434

716

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(maximum depth of 60 ␮m, 6 mm from the centre of the specimen translates to surface slope of 0.6◦ ) were incorporated. Predictions suggested that differences in local particle impact conditions for both the cases (flat and fully eroded) were negligible (a maximum of 3% at some positions and an average of less than 1%). Thus for these conditions, evolution of the surface with time should have minimal errors on wear predictions. This assumption can be considered to be valid for low testing times for which changes in the surface profile are low, however, testing for longer durations can drastically modify inner wall contours affecting erosion wear rates significantly which, necessitates the development of unsteady state predictive models accounting for changes in geometry. Fig. 5. A schematic of ER prediction using data obtained from CFD simulations and a numerical wear equation.

On the basis of the coefficients listed in Table 3, developed from one laboratory test, Eq. (2) was used to predict ERs for different flow conditions (note these constants are for a particular material–erodent combination so only the flow variables were changed). To do this the flow field and subsequent local impact parameters were calculated using CFD; this was done for two further jet impingement tests with a 90◦ nominal impingement angle and flow velocities of 5 and 10 m/s. The local impact conditions (angle and velocity) obtained from the CFD simulations were input in Eq. (2) which gave the erosion rate at each point on the surface, as illustrated in Fig. 5. This was then compared with ERs obtained from experimental tests conducted at these conditions and observations are graphically represented in Fig. 6. A good correlation can be observed, and this suggests that data from a single test can be used to predict erosion rates over a wide range of conditions using the wear-map method. Some scatter in predicted data were observed but overall the performance is generally satisfactory and it can be confidently said that this method can be used to predict wear for specific material–abrasive combinations where erosion is prevalent by conducting a minimum set of laboratory tests which are characterised by CFD simulations. Due to constant material wear, the surface profile changes with time and this could have an effect on local flow dynamics and hence local wear rates. To study the effect of evolution of the surface with time, CFD simulations on a surface with the fully eroded profile

Fig. 6. ER predicted by wear map model (Eq. (2)) developed from the wear-map correlations (based on CFD characterised impact data and wear data) and actual material wear data as characterised by experimental conditions for 5 and 10 m/s.

6. Comparisons with existing numerical models In Section 5 it has been shown data obtained from one well defined test characterised by CFD simulations can provide a range of erosion parameters which are able to map erosion wear. To evaluate the performance of the wear-map method in relation to the prediction capabilities of several other existing models, the local erosion rate for the combination of 316L-AFS 50/70 for conditions defined in Table 2 are predicted using a range of different erosion models and impact data obtained from CFD simulations. These are shown in the following sub sections with discussions in Section 7. 6.1. Huang et al. model correlations [12] Huang et al. [12] stated that several existing models are unable to accurately predict slurry erosion behaviour since these models were developed under air borne impact conditions and do not consider the impact angle dependency on flow field and the resulting variation of impact angles over the length of surface. A new phenomenological model was theoretically derived for erosion of materials in jet flow and was implemented in conjunction with CFD by Wang et al. [26]. Wear rates were determined using the erosion ratio described by Eq. (3), 2

ER =

Vp2·25 (cos ) (Sin ) K 1 m1·125 p

0·25

(1 + B)0·125 EB0·125 B0·7 ε 1·2 B



+

2 d0 · 05 mp Vp2 Sin  K2 E 1·1 B p

ε 0·98 ε 1·44 B B

1+ˇ

1.15 ,

(3)

where K1 and K2 are material coefficients and values of which must be experimentally determined for each material (for 44 W carbon steel, experimentally determined values were K1 = 7.48 × 10−4 and K2 = 0.283 × 10−6 ). EB ,  B and εB are the stiffness, hardness and elongation of the target material, respectively. B = EB /EP is defined as the stiffness ratio describing relative strength of eroded material to that of the particle. εB is the ductility (in 2 in. of specimen) of eroded material; mp is the particle mass; Vp and  are the local impact velocity and angle respectively. Eq. (3) is a combination of two physical erosion degradation mechanisms, the first part representing cutting wear and the second part representing deformation wear components. Wang et al. [26] used Eq. (3) in conjunction with CFD to predict wear due to impingement for flow exit velocities of 9 m/s and nominal impingement angle of 90◦ . On comparison with experimental results, good qualitative correlations were observed although quantitatively the size (wear scar region) and the maximum wear depth were both under predicted by nearly a margin of 50%. Predictions error were attributed to a combination of factors, namely, misalignments between test surface and nozzle end, particle size distributions and the turbulence effects on the particles which were neglected. Comparisons between predictions made by the model of Huang et al. [12] and several other models has shown good correla-

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tions [12]. It was suggested that this model can be used in a wider spectrum of erosion conditions, particularly on different target–abrasive combinations and for which K1 and K2 values were to be determined. To test this, Eq. (3) was simplified to the form of Eq. (4) to enable its application in our study, where A and B are material constants for 316L–AFS 50/70 combination. 2

ER = AVp2·25 (cos ) (sin )

0.25

+ BVp2.3 (sin )

2.3

.

6.2. Combined Finnie and Bitter model [27]

(2)(cos2 ER =

mp Vp2 2

 sin(n) +

mp (Vp sin )2 2ε

,

(5)

2

cos2  +

mp (Vp sin ) , 2ε

a

b

x

y

z

1.46

5.73

−5.28

−2.1

6.56

6.3. Alhert model correlations [29] Wang and Shirazi [1] predicted erosion rates on pipe bends using a CFD based approach and an erosion model developed by Alhert [29] for sand particle impacts in water which is given by Eq. (7); ER = AFs V 1.73 f ()B−0.59 ,

(6)

where mp is the mass of a single abrasive particle, Vp and  are the local impact velocity and angle, respectively, n = 4.85; a numerical constant, Ø and ε are the energy needed to remove a unit volume of material from a body due to deformation and cutting wear respectively and to be estimated from experimental data.Values for mp /Ø (the experimental constant in the cutting term; first part on the right hand side) and mp /ε (experimental constant in the deformation term; second part on the right hand side) in Eqs. (5) and (6), which provided the best correlation between experimental data obtained at 90◦ and 7.5 m/s and corresponding local impact conditions defined by CFD were determined using Minitab 15. Using the values mp /Ø = 0.1483 and mp /ε = 0.1382 in Eqs. (5) and (6), erosion ratios were predicted for the tests conducted at an impingement angle of 90◦ and nozzle exit flow velocities of 5 and 10 m/s. Predictions are graphically represented in Fig. 8a and b, alongside ERs predicted by the wear-map method and measured experimental results.

(7)

where Fs is the particle shape coefficient (Fs = 1.0 for sharp particle, 0.53 for semi-rounded or 0.2 for fully rounded sand particles; particles used in testing had sharp geometrical features), V is the local impact velocity; A is an empirical constant and the value is 1.2246 and B is the Brinell’s Hardness number of the test material. Alhert [29] used two functional forms of the angle dependence, with matching conditions applied at 15◦ . The dependence on impingement angle, f() is given by Eqs. (8) and (9). f () = a 2 + b

One of the earliest erosion models were developed by Finnie [5]. The proposed model was for the erosion of ductile metals based on an analysis of the mechanisms of kinetic energy exchange during the impact of a single solid particle where the cutting was the predominant mechanism in dry conditions. This simplified erosion model was able to accurately predict ductile material wear at low impact angles. However, at high impact angles predictions deviated significantly from experimental values. Finnie attributed this to the change of mechanism at high impact angles suggesting that material ‘cutting’ action ceases to exist and ‘deformation’ wear predominates. This model was later modified by Bitter [7] who incorporated the effect of deformation wear acting in conjunction with cutting wear. The resulting combined equation predicts single particle impact wear but has been used in by Sato et al. [28] to numerically predict erosion wear rates in a gas–solid suspension with glass spheres used as solid particles. A modified version of the combined Finnie–Bitter model equation is in the form of Eqs. (5) and (6). mp Vp2

Table 4 Empirical constants for the Erosion Ratio Model (Eqs. (8) and (9)) obtained from 316L stainless steel–silica sand combination erosion experimental data obtained at nozzle exit flow velocity of 7.5 m/s and nominal impingement angle of 90◦ .

(4)

Local erosion ratios from experimental data at 90◦ and 7.5 m/s nozzle exit flow velocity and local impact data obtained from CFD simulations at these conditions were input into Eq. (4) and, using Minitab 15, a value for A and B which provided the best fit of experimental erosion ratios to local impact conditions (data obtained from 90◦ and 7.5 m/s conditions) was determined as A = 0.102 and B = 0.00947. Impact data obtained from CFD simulations at 90◦ nominal impingement angle and for flow velocities of 5 and 10 m/s were then entered in Eq. (4) using the best fit values of A and B and the local erosion ratios were predicted along the length of the flat specimen for 316L–AFS50/70 combination. Predictions are graphically portrayed in Fig. 7a and, alongside erosion ratio predicted by the wear-map method (Eq. (2)) and the experimental results.

ER =

717

2

for  ≤ 15◦

(8) 2

f () = x cos  sin  + y sin  + z

◦

◦

for 90 >  > 15

(9)

It is stated that specific values for a, b, x, y and z were to be determined using experimental data obtained at any one condition. The equation is very similar to the model suggested by McLaury et al. [10] and was built on experimental observations of high silica sand impacts on carbon steels. Wear predictions using this equation demands new values for a, b, x, y and z, which for a combination of 316L stainless steel and silica sand (AFS 50/70) are obtained using the experimental ER data (90◦ and 7.5 m/s) and these values are provided in Table 4. Predictions on flat 316L–AFS50/70 specimens for nozzle exit flow velocities of 5 and 10 m/s and for nominal impingement angle of 90◦ is made using impact data obtained from CFD simulations and Eqs. (7)–(9). Predictions are graphically represented in Fig. 9a and b, alongside ERs predicted by the wear-map method and experimental results. 7. Discussion To demonstrate the robustness of the wear-map method a comparative study was carried out against three alternative wear models as described earlier. The model of Huang et al. [12] was developed from theoretical groundwork and the constants were obtained for wet erosion conditions. The combined Finnie and Bitter model [27] was developed for a single particle impact under airborne conditions. The primary difference between air-borne and wet conditions is the variation of particle impact data along the length of a specimen (in an impingement erosion system). In the Finnie and Bitter model, particle impact angles and velocities are assumed to be of the same numerical value as the nominal impingement angle and velocity, which can be considered valid provided the effect of the carrier fluid medium on modifying particle trajectories are minimal, whereas the Huang et al. [12] takes this into consideration. Thus adaption of combined Finnie and Bitter model for the liquid-particle systems here is perhaps not appropriate, however, it has been reported to have been successfully adopted in air suspension erosion system [28]. The final wear equation under study was developed by Alhert [29] on empirical basis and the equation coefficients were obtained from experiments conducted at wet impact erosion conditions. The three models all consisted of a number of constants and the values for which were suggested to be obtained from experimen-

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Fig. 7. A comparison between the erosion ratios for the (i) wear map method (ii) model of Huang et al. [12] (iii) experimental data for nozzle exit flow velocities of (a) 5 m/s and (b) 10 m/s. Other conditions are as defined in Table 2.

Fig. 8. A comparison between the erosion ratios for the (i) wear map method (ii) combined model of Finnie and Bitter (iii) experimental data for nozzle exit flow velocities of (a) 5 m/s and (b) 10 m/s. Other conditions are as defined in Table 2.

tal results. Model constants were calculated based data obtained from JIT conducted at 90◦ nominal impingement angle and for nozzle exit flow velocity of 7.5 m/s. The equations were then modified and incorporated with CFD to enable ER predictions for nozzle exit flow velocities of 5 and 10 m/s, with the same impingement angle for the combination of 316L–AFS50/70. The combined Finnie–Bitter model significantly under predicted ERs at all locations (Fig. 8) and this can be accounted to the fact that the angle dependency functions does not really capture the effects of significant variation of impact angles which can also influence the local wear modes; this

finding is similar to that reported by Dobrowolski and Wydrych [30]. The model of Huang et al. [12] performed comparatively better than the combined Finnie and Bitter equation. ERs were fairly close to experimental ER (Fig. 7), but beyond 3–4 mm from the centre of the specimen, predictions began to deviate away from experimental results. It was observed that ERs for both the case (5 and 10 m/s) as predicted by the model of Huang et al. [12] increased steadily with radial distance from the centre of the specimen. The ER profile predicted by the model of Huang et al. [12] can be divided into

Fig. 9. A comparison between the erosion ratios for the (i) wear map method (ii) Alhert model [29] and (iii) experimental data for nozzle exit flow velocities of (a) 5 m/s and (b) 10 m/s. Other conditions are as defined in Table 2.

A. Gnanavelu et al. / Wear 271 (2011) 712–719

two parts. The first part is between 0 and 3.5 mm from the centre of the wear scar and the remaining region towards the edge of the scar comprises the second part. Based on impact data obtained from CFD predictions, particle impact angles within the first zone can be grouped as high to medium angles (80◦ –30◦ ; Fig. 3) and the prominent wear mechanisms for this range of impact angles is by deformation, even though cutting mechanism does contribute to wear. The second part comprises of medium to low angles of impact (≤30◦ ) where cutting mechanisms are generally dominant [25]. It has reported that both these mechanisms can contribute to material removal at both these conditions, but the majority is from either one of these mechanisms [31]. The model of Huang et al. [12] significantly deviates from the predictions at positions beyond 3.5 mm (Fig. 7) suggesting the wear function does not accurately capture the effects of cutting mechanism. However, good correlations were reported by Wang et al. [26] who implemented this model under conditions similar to those under which the model was developed (similar material–erodent combination, impact conditions, geometrical features, etc.). ER predictions obtained using the model of Alhert [29] are portrayed in Fig. 9, illustrating good qualitative correlations with experiments especially with the positioning of the maximum ERs for both the cases (5 and 10 m/s) were similar to those on the test sample. Numerical comparisons suggested that predictions at 5 m/s were over-predicted and for the case of 10 m/s, ER at majority of the locations were under-predicted. Overall the prediction accuracy of this model was within 70% of experimental results at almost all the locations and thus suggesting good performance of this model in our case. Good correlations by the model of Ahlert [29] can be accounted to the fact that the conditions under which this model was developed and validated was very similar to the one where the wear map model was built (similar material–abrasive property and geometries, impact kinetics, etc.). In common with the wear map model used here (Eq. (2)), this model does not try to associate any system parameter to the coefficients obtained. 8. Conclusions • It was shown that a single slurry jet impingement erosion test can provide a wide range of erosion parameters which can be characterised by CFD simulations. This data can then be correlated to local impact conditions as predicted by CFD simulations and can subsequently predict wear for the same material and abrasive combination at different flow conditions. • Good correlation between predicted and experimental wear can be achieved even though errors are inherent due to assumptions such as, particle shape and size, material hardening, numerical approximations, change in geometry with time, differences between CFD and experimental geometry. • The ability of the wear model to correlate a wide range of experimental data depends very much on the form of the model. Work shown here suggests that those models that represent the wear as a high order polynomial capture the data well, whilst more traditional models (which interpret the parameters to have a physical meaning) does not capture the nuances of the data. • Consequently, the proposed wear-map method [13] is a useful tool for capturing the behaviour of material under erosion conditions, and when linked with CFD a useful component of material specification and plant design.

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