Wear 273 (2011) 38–42
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A CFD model of particle concentration
effects on erosion–corrosion of Fe in aqueous conditions
M.M. Stack ? , S.M. Abdelrahman
University of Strathclyde, Department of Mechanical Engineering 75 Montrose Street, Glasgow G1 1XJ, UK
a r t i c l e
i n f o
a b s t r a c t
A CFD (computational ?uid dynamics) model has been developed to evaluate the effects of particle concentration on the erosion–corrosion of the inner surfaces of a circular pipe of 90? bend at room temperatures. The relative intensity of erosion and corrosion around the pipe geometry results in transitions between various erosion–corrosion regimes, for a given inlet particle concentration. The results indicate that the corrosion-dominated regime at the pipe bend is reduced with an increase in particle concentration. Typical results from the model are shown illustrating how this 3D mapping method can be used to model parameters such as particle concentration on the erosion–corrosion regimes over the surface. Crown Copyright ? 2011 Published by Elsevier B.V. All rights reserved.
Article history: Received 2 August 2010 Received in revised form 23 June 2011 Accepted 24 June 2011 Available online 1 July 2011 Keywords: Erosion–corrosion maps CFD modelling Fe Particle concentration effects
1. Introduction In studies of modelling erosion–corrosion, both ?nite element (FE)  and computational ?uid dynamics (CFD) [2–4] techniques have been used to investigate mass loss of materials and to evaluate the effect of various parameters controlling the erosion and corrosion process. However, the majority of these investigations do not introduce a full de?nition for erosion–corrosion regimes resulting from the interaction between erosion and corrosion, where various regimes of corrosion can occur . These regimes  are very useful in identifying the mechanism of erosion–corrosion, in addition to identifying the corrosion mechanism component of the interaction as identi?ed by Pourbaix diagrams . An approach to identify the transition regimes for the erosion–corrosion process and also to monitor the effects of various parameters has been developed by the current authors as an extension of earlier work on erosion–corrosion mapping [6–8]. Although 2D mapping is capable of capturing the in?uence of any particular parameter on erosion–corrosion regime boundaries, it does not give any indication of the combined effect of all the parameters on these boundaries, nor the metal degradation in a 3D space. A new methodology was introduced in previous work  to study the integrated effect of these parameters together (namely those related to the particle, ?uid ?ow, and environment), on the boundaries of the erosion–corrosion regime and wastage maps by
combining the concept of CFD with the erosion–corrosion mapping techniques. Such approach facilitates mapping the surfaces of any 3D component that is exposed to aqueous slurry ?ow. Furthermore, it provides a powerful predictive tool for estimating the predominance of various erosion–corrosion regimes. In this study, a 3D mapping technique is used to investigate the effect of the particle concentration and on the construction of erosion–corrosion mechanism and wastage maps for Fe. The effects of particle concentration are evaluated on the regime boundaries. The results are discussed in terms of the applications of this technique to erosion–corrosion in slurry ?ows in addition to addressing some current limitations. 2. Methodology A dilute slurry ?ow of water-alumina particles of size 10?3 m and four volume fractions i.e. 0.025, 0.05, 0.075, and 0.1 is ingested through a pipe bend inlet with bore diameter (D) equal to 0.078 m and (R D?1 ) ratio of 1.2 (ratio of pipe bend radius to diameter), where R is the pipe bend radius. The CFD simulation generated by FLUENT ver.6.3  uses a ?nite element based ?nite volume method to solve the ?ow governing equations. Table 1 summarises the equations used, operating and boundary conditions used in this study whilst Table 2 lists the mechanical and physical properties for the slurry and target material. Validation of the erosion results is carried out in  by comparison to previous experimental work as described elsewhere , and is summarised in Table 3. The simulation validation was car-
? Corresponding author. Tel.: +44 141 5483754; fax: +44 141 5525105. E-mail address: firstname.lastname@example.org (M.M. Stack).
0043-1648/$ – see front matter. Crown Copyright ? 2011 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.06.024
M.M. Stack, S.M. Abdelrahman / Wear 273 (2011) 38–42 Table 2 Physical and mechanical properties for the slurry and target material. Fluid (water) Density [kg m ] Particle size [m] Flow rate [kg s?1 ] k2 
Nomenclature Latin letters pipe inlet area [m2 ] Ain C particle concentration [g cm?3 ] Cp speci?c heat capacity [J kg?1 K?1 ] D diameter of the pipe [m] applied potential [V] (SCE) E en normal coef?cient of restitution F Faraday constant (96,485) [C mol?1 ] numerical constant (0.025) ft Hs hardness of the substrate [Pa] H thickness of the oxide layer [m] ho initial thickness of the oxide [m] Ip impact frequency [imp cm?2 s?1 ] net anodic current density [A m?2 ] ianet io exchange current density [A m?2 ] Kc pure corrosion rate [g m?2 s?1 ] total wastage rate [g m?2 s?1 ] Kec pure erosion rate [g m?2 s?1 ] Ke material constant (0.699) K k2 material constant (1.398) Mt amount of mass removal per impacting particle [g impact?1 ] mass of impacting particle [kg] mp nc strain hardening coef?cient (0.3) RAM relative atomic mass of Fe (55.8) [g mol?1 ] Tm melting point of the Fe (1808) [K] Vp particle velocity [m s?1 ] vf. volume fraction of particles WC erosion by cutting [kg kg?1 ] WD erosion by deformation [kg kg?1 ] number of electrons (2) zm Greek letters ?p impact angle [? ] particle shape factor (0.0) frictional coef?cient (0.1) critical friction coef?cient (Sundararajan) f ? Pi ratio (3.142) density of the oxide layer (5240) [kg m?3 ] f density of the particle (2650) [kg m?3 ] p Subscripts Ap applied potential Rev reversible equilibrium potential passivation Pas
Particles (alumina) 2670 10?3 Variable
Target (mild steel) 7850
2.1. Erosion modelling The second model of Sundararajan is divided into two expressions; one accounts for the localised deformation at the impact point, whilst the other addresses the ductile cutting mechanism during the impact. The total erosion rate is the summation of these two mechanisms. The formulation is as follows : ˙ D= W 5.5 × 10?2 (Tm ? 436)
?t V 2 sin2 ? (1 ? e2 ) 2nc f n nc Cp × (nc + 1) ( /
f ) (2 ? ( / f ))V (1 + )22?nc nc Cp 2
(1) cos2 ?
˙ C= W where
5.5 × 10?2 (Tm ? 436)
1 (1 + ) (1 + e) tan ?
and en is the normal restitution ratio : en = 0.988 ? 0.78? + 0.19?2 ? 0.024?3 + 0.027?4 (4)
For unit consistency, erosion rates should be converted to [kg m?2 s?1 ] in line with the calculated corrosion rates below. V is the impact velocity as de?ned in Sundararajan’s model above. 2.2. Corrosion rates 2.2.1. Active corrosion model In the active region, it is assumed that the total corrosion is estimated from knowledge of the dissolution current density from the Butler–Volmer equation: ianet = io exp ˇzm Fr E Ro T ? exp ?(1 ? ˇ)zm Fr E Ro T (5)
where the over-potential E = Eap ? Erev
E is de?ned as: (6)
ried out for a SS304L stainless steel alloy using Forder’s erosion model  as in the case study, and the results were simulated for mild steel using Sundararajan’s second model .
and Eap and Erev are the applied and reversible potentials, respectively. It should be noted that further details of the corrosion models are given in earlier work . The Faraday constant above in the Butler–Volmer equation is given by Fr and ˇ is the transfer coef?cient of ions in the reaction. The corrosion rate is therefore given by: Kc = Kco = RAMianet zm F (7)
Table 1 CFD modelling equations, operating and boundary conditions. Model parameter Solver equations Turbulence model Wall treatment Coupling Operating cond. Inlet velocity [m s?1 ] Water Navier–Stokes Standard k-ε Standard wall function-no slip Ambient 3.0 Sand particles DPM
Table 3 Comparison between the current study and Experimental and simulation work of Wood et al. . Experimental  Erosion rates [mm3 imp?1 ] (volume per impacting particle) 2.2–5.5 Simulation  5.5 Current study 5.45
One way 3.0
M.M. Stack, S.M. Abdelrahman / Wear 273 (2011) 38–42
2.2.2. Repassivation model For the passivation mechanism, we assume that pure corrosion (Kco ) rate is suf?ciently low as to be negligible and the corrosion rate is the additive effect of corrosion enhanced by erosion ( Kc ) . An expression for the corrosion rate in passivation conditions has been introduced  and is currently modi?ed to include the effect of the oblique impact [9,15]. Mt = kh
2 dp 2 p (1 ? en ) 0.5
(Vp sin ?1 )
The constant k is de?ned as the mass ratio between the metal and the oxide created during the corrosion reaction, multiplied by the number of moles of metal involved in the reaction and is related to k2 in  by de?nition as (k = k2 /2). The thickness of the passive layer h can be assumed to vary with the potential difference and may be given from  assuming a linear relationship between the over-potential and passive layer thickness: h = ho + 3 × 10?9 (Eap ? Epas ) = 1 × 10?9 (9)
and ho m. The unit given by Eq. (8) is [kg impact?1 ]. To convert to [kg m?2 s?1 ], it is multiplied by particle impact ?ux as outlined in . This can be varied according to the application under investigation. For example, if the ?ow is homogeneous then particle impact frequency may be used and is given as : Kc = Kc = Mt cVp sin ? mp (10)
Fig. 1. Simpli?ed Pourbaix diagram for Fe at T = 298 K in aqueous media . The parallel lines indicate the reduction and oxidation of water respectively.
2.2.3. Erosion–corrosion boundaries The regime boundaries are determined in terms of the ratio Kc /Ke as Kc < 0.1 (Erosion dominated) Ke 0.1 ≤ 1≤ Kc < 1 (Erosion–corrosion dominated) Ke (11) (12) (13) (14)
Kc < 10 (Corrosion–erosion dominated) Ke
Kc ≥ 10 (Corrosion-dominated) Ke
The transition boundaries for the wastage maps are given as follows: Kec < 1 mm year?1 (Low wastage) (Medium wastage) (15) (16) (17)
The simulation was thus run at various particle mass ?ow rates; namely 0.957, 1.9169, 2.87 and 3.8276 kg s?1 which are equivalent to particle inlet volume fractions of 0.025, 0.05, 0.075 and 0.0909, respectively. Fig. 2 shows the regime maps at the inner surfaces of the pipe bend at pH = 7 (pure water) and applied potential E = ?0.6 V (SCE), illustrating the changes in erosion–corrosion regimes with increasing the particle volume fraction. As the particle volume fraction increases, as the particles are introduced to the pipe on the left hand side of the ?gure, Fig. 2(a), the erosion rates increases linearly and as a result, the erosion–dissolution and erosion dominated regimes are enlarged. In addition, the dissolution dominated regime reduces with increasing particle volume fraction. This indicates the importance of the volume fraction (or particle concentration) as a factor affecting the erosion–corrosion regimes. Fig. 3 illustrates the wastage maps for pH = 7 and at applied potential E = ?0.6 V (SCE) for the same particle mass ?ow rates listed above as in Fig. 2. Again the high wastage regime area (red colour region) is increased as the particle mass ?ow rate increases.
1 ≤ Kec < 10 mm year?1 Kec ≥ 10 mm year
4. Discussion The results indicate that particle volume fraction effects play a signi?cant role in changing the erosion–corrosion regime in 3D, Figs. 2 and 3. In the 3D case, various regimes are observed over the surface, Fig. 2. With increasing volume fraction, the erosiondominated regime is enhanced. This is due to the increase in erosion rate with increasing particle concentration, shifting the corrosion affected regimes towards those dominated by erosion. It should be noted that in Fig. 2(a), for the lowest concentration modeled, no erosion-dominated behaviour was observed. However, as the particle concentration was increased, the time interval between impacts was reduced, thereby increasing the overall erosion to corrosion contribution on the surface. As a result, the erosion-dominated regime is more prevalent at the higher volume fractions, Fig. 2(c and d), with the erosion–dissolution area reduced, and marginally spreading out to areas which previously had been dominated by dissolution on the pipe elbow. This indicates that
(Further details of the erosion–corrosion model are given in a recent paper by the authors .) 3. Results Fig. 1 illustrates the Pourbaix diagram for Fe at T = 298 K with respect to the standard hydrogen electrode and identi?es the possible corrosion mechanisms (i.e. immunity, dissolution and passivation mechanisms) for various values of temperature, pH and applied potential. To investigate the particle concentration effect, a homogeneous particle distribution in the pipe inlet is assumed and the particle concentration is thus related to the particle mass ?ow rate according to the relation: ˙ p = ?p m
p Vp Ain
M.M. Stack, S.M. Abdelrahman / Wear 273 (2011) 38–42
Fig. 2. Regime maps on the outer surface of Fe pipe bend at pH = 7 and E = ?0.6 V (SCE) for total particle mass per second: (a) 0.957, (b) 1.9169, (c) 2.87, (d) 3.8276 kg s?1 .
Fig. 3. Wastage maps on the outer surface of Fe pipe bend at pH = 7 and E = ?0.6 V (SCE) for total particle mass per second: (a) 0.957, (b) 1.9169, (c) 2.87, (d) 3.8276 kg s?1 .
particle concentration enhances erosion and reduces corrosion in such conditions. The above trends in the variation of erosion–corrosion regimes on the pipe bend are also observed in earlier work by the current authors . In this work, the signi?cant changes in particle concentration and velocity for the component are identi?ed, resulting in a variation of erosion intensity on the surface. In addition, the local impact angle also changes. Hence, the erosion–corrosion regime variation on the component can be attributed to these factors. Nonetheless, it should be noted that the variation of the erosion–corrosion regimes only occurs at the pipe bend only and the remaining parts (i.e. entrance and exit) exhibit no erosion–corrosion regime change (results not shown). This indicates that the erosion rates at these regions remain unaffected during the simulation. For the wastage maps, the pipe exit exhibits a minor variation from the medium to the high wastage regime as the particle concentration increases. Hence, the erosion–corrosion mapping technique is a potentially sensitive method of detecting any change in the erosion–corrosion behaviour in such environments where changes in component geometry are anticipated. For the present study, additive erosion–corrosion behaviour is assumed i.e. erosion enhanced corrosion and the effect of corrosion on erosion is negligible. (It is acknowledged that at higher pH values where passivation takes place, this would not be the case.) For the effect of corrosion on erosion, the so-called “syn-
ergistic/antagonistic” interaction has been attributed to a number of possible mechanisms relating to the material microstructure [18,19] and it is acknowledged that this is a simplistic assumption. Hence, initial work on mapping the component for the materials above has made such assumptions but future work will address such issues in more detail by assessing materials with composite structures. The erosion and corrosion rates are assumed, in this study, to be constant with time, i.e. both processes are independent of time. The time interval between impacts is a very important factor in the erosion–corrosion process, as in the passive region, it determines the ?lm thickness and growth kinetics. However, for this study as the thickness of the passive ?lm is assumed to be in the order of nanometers, signi?cant increase in ?lm thickness is not considered for long intervals between impacts, as de?ned for low concentrations of particles. It is acknowledged that this may be a simplistic assumption and will be considered in further work. It should be noted that for the 2D mapping approaches presented in earlier work, qualitative agreement has been found between the results from these studies and experimental studies . For the 3D mapping approach above, it was not possible to verify experimentally the regimes on the simulated pipe. Further work, will address the issue of quantifying experimentally the regimes from post exposure pipe bends exposed to such conditions. Hence, 3D erosion–corrosion maps provide a useful tool for prediction and identi?cation of the erosion–corrosion regimes and wastage regions when parameters such as in-let particle concentration are varied. The results have indicated signi?cant changes in
M.M. Stack, S.M. Abdelrahman / Wear 273 (2011) 38–42  C. Davis, P. Frawley, Modelling of erosion–corrosion in practical geometries, Corrosion Science 51 (4) (2009) 769–775.  Y. Ferng, Y. Ma, N. Chung, Application of local ?ow models in predicting distributions of erosion–corrosion locations, Corrosion 56 (2) (2000) 116–126.  M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, Nace, Houston, 1977.  M. Stack, N. Corlett, S. Zhou, A methodology for the construction of the erosion–corrosion map in aqueous environments, Wear 203 (1997) 474–488.  M. Stack, N. Pungwiwat, Erosion–corrosion mapping of Fe in aqueous slurries: some views on a new rationale for de?ning the erosion–corrosion interaction, Wear 256 (5) (2004) 565–576.  M. Stack, T. Abd El Badia, On the construction of erosion–corrosion maps for WC/Co–Cr-based coatings in aqueous conditions, Wear 261 (11–12) (2006) 1181–1190.  M. Stack, S. Abdelrahman, B. Jana, A new methodology for modelling erosion–corrosion regimes on real surfaces: gliding down the galvanic series for a range of metal-corrosion systems, Wear 268 (3–4) (2010) 533–542.  FLUENT Inc., “FLUENT User’s Guide, Version 6.3,” US.  R.J.K. Wood, T. Jones, J. Ganeshalingam, N. Miles, Comparison of predicted and experimental erosion estimates in slurry ducts, Wear 256 (9–10) (2004) 937–947.  A. Forder, M. Thew, D. Harrison, A numerical investigation of solid particle erosion experienced within oil?eld control valves, Wear 216 (2) (1998) 184–193.  G. Sundararajan, A comprehensive model for the solid particle erosion of ductile materials, Wear 149 (1–2) (1991) 111–127.  M. Stack, B. Jana, Modelling particulate erosion–corrosion in aqueous slurries: some views on the construction of erosion–corrosion maps for a range of pure metals, Wear 256 (9–10) (2004) 986–1004.  S. Abdelrahman, M. Stack, Some re?ictions on a model to predict the erosion rate of the passive ?lm on pure materials, in: 13th Int. Conf. on Aerospace Science and Aviation Technology, ASAT-2009, Cairo, Egypt, 2009.  M. Graham, J. Bardwell, G. Sproule, D. Mitchell, B. Macdougall, The growth and stability of passive ?lms, Corrosion Science 35 (1–4) (1993) 13–18.  B. Lu, J. Lue, Correlation between repassivation kinetics and corrosion rate over a passive surface in ?owing slurry, Electrochimica Acta 53 (23) (2008) 7022–7031.  M. Stack, N. Corlett, S. Turgoose, Some thoughts on modelling the effects of oxygen and particle concentration on the erosion–corrosion of steels in aqueous slurries, Wear 255 (2003) 225–236.  M. Stack, M. Antonov, I. Hussainova, Some views on the erosion–corrosion response of bulk chromium carbide based cermets, Journal of Physics D: Applied Physics 39 (15) (2006) 3165–3174.
regimes along the geometry of the component and as a function of increasing particle volume concentration in the pipe. Further work will be to model the effects of other parameters such as oxygen concentration and temperature in addition to extending the range of materials in the model and the synergism/antagonism between the processes. 5. Conclusions CFD methods, involving ?uid dynamics and multiphase ?ow parameters, have been used to model the erosion–corrosion behaviour of Fe at range of particle concentration values for a 3D space and thus represents the ?rst study of the effect of particle concentration on a 3D erosion–corrosion map. The technique enables both erosion–corrosion regimes and wastage rates to be predicted over a simulated pipe component. Changes in erosion–corrosion regimes over the component geometry were observed with increases in particle concentration. In particular, at the pipe bend, at the highest concentration evaluated, the erosion-dominated regime increased and the erosion-dissolution regime reduced, compared to that observed at the lowest particle concentrations. The boundaries of the erosion–corrosion regimes were also observed to vary at the pipe inlet and exit following simulation of increases in particle concentration, with the dissolution affected regimes being reduced in favour of dissolution–erosion and erosion–dissolution. References
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