Powder Technology 275 (2015) 182–187

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Powder Technology

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Erosion prediction of liquid-particle two-phase flow in pipeline elbowsvia CFD–DEM coupling method

Jukai Chen a, Yueshe Wang a,⁎, Xiufeng Li b, Renyang He b, Shuang Han a, Yanlin Chen a

a State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, No. 28 Xianning West Road, Xi'an 710049, Chinab China Special Equipment Inspection and Research Institute, Beijing 100013, China

⁎ Corresponding author.E-mail address: wangys@mail.xjtu.edu.cn (Y. Wang).

http://dx.doi.org/10.1016/j.powtec.2014.12.0570032-5910/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 June 2014Received in revised form 9 December 2014Accepted 16 December 2014Available online 11 February 2015

Keywords:Liquid-particle two-phase flowErosionElbowCFD–DEMNumerical simulation

ACFD–DEM-based liquid-particle two-phaseflowerosion predictionmodel occurring over suchpipeline connec-tion as elbows, which takes the interaction of liquid–particle, particle–particle and particle–wall into account, isproposed in this study. The standard k− εmodel is adopted for fluid turbulent flow, the standard wall functionsfor near-wall zone treatment, and the Hertz–Mindlin (no slip) model for particle–particle and particle–wallcontact. Numerical simulations have been performed by combining CFD code ANSYS FLUENT with DEM codeEDEM to predict the maximum erosion rate and location in 90°, 60° and 45° elbows with diameter 40 mm. Thefluid is water with inlet velocity 3 m/s, and the particles are 150 μm in diameter and 2650 kg/m3 in density.While the maximum erosion rates of the three are found to be quite different, the maximum erosive locationshave been indicated to be at or near the exit of the elbows. In addition, the effect of bend-angle on erosion,particle motion and flow field has been discussed.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Erosion is a wear damage caused by the impact of small and loosemoving particles to the surface. In petroleum transportation systems,particles obtain the momentum from the carrier fluid and move withthe flow to impact and erode the inner wall of the pipes. Particularlyin such pipeline components as elbows, erosion could be more serious.One reason is that the pressure drop in elbows leads to the particle set-tling; the other is the centrifugal effects due to the curvature, for whichparticles tend to impact the concave wall of the elbows. In addition, thesecondary flow usually arises in the down-stream areas of the elbows,and it will change the main direction of particles and increase the im-pact of particles to the wall. These multiple effects make elbows mosteasily damaged by erosion.

Many investigators have carried out both experimental and numer-ical research of erosion of elbows, chokes and related geometries. In theearly stages, some typical experiments were conducted to investigatethe mechanism of erosion [1–7]. However, huge amount of experimen-tal parameterswhichmay have an effect on erosionmechanism, such asflow conditions, material attributions of particles and geometries [8],make experiments in realistic conditions hard to manage. Complexityand lack of predictability are characteristics for this kind of studies.Comparatively, with the rapid development of computer science andmodern numerical techniques, numerical modeling of its low costand controllability is proving fruitful. Computational fluid dynamics

(CFD) does well in modeling fluid flow and CFD-based erosion researchhas been very extensive. Mazumder [9] conducted CFD simulation tostudy the effect of liquid and gas velocities on location ofmaximumero-sion in a U-bend. The discrete phase model (DPM) was used to modelthe particlemotion, with particle interactions and any rebound ignored.Njobuenwu et al. [10] used a CFDmodel coupled to a Lagrangianparticletracking routine and erosionmodels to predict erosion of dilute particle-laden flow in 90° square cross-section bends. They took particle–wallinteraction into account, and the models performed well. But for theirfurther extension, four-way couplingwith particle–particle interactionswould be necessary to achieve improved agreement with experimentaldata. Chen et al. [11] proposed a comprehensive procedure to estimateerosion in elbows for gas/liquid/sand multiphase flow. They combinedthe mechanistic analysis of multiphase flow and application of asingle-phase CFD-based erosion prediction approach to simplify themultiphase flow erosion problem. The CFD-based erosion-predictionmodel neglected the particle interaction which was designed for dilutesystems. Zhang et al. [12] compared computed particle velocities anderosion in water and air flow with measured. The CFD-based erosionmodel adopted particle–wall rebound models and neglected particleinteraction. They obtained good agreement between data and CFD pre-diction for dilute flow. A near-wall modification [13] was introducedwith the turbulent particle interactions to improve the CFD-based parti-cle erosion modeling, while it was still at low solid particle concentra-tions. Li et al. [14] adopted discrete particle hard sphere model todescribe inter-particle collision. The behavior of all particles is simulatedby a Lagrangian approach and flow field simulation of continuous fluidby an Eulerian approach. For discrete particle hard sphere model is too

Fig. 1. In a soft-sphere model, the amount of normal overlap α and tangential displace-ment δ are assumed instead of considering deformation details.

183J. Chen et al. / Powder Technology 275 (2015) 182–187

simplified, the CFD-based erosion prediction model may not be quitesuitable for very dense flow. Zhang et al. [15] described the particletrajectory with discrete element method (DEM) and adopted a fluiddensity-based buoyancy model to calculate the solid–fluid interactionforce. Moreover, they adopted particle–wall interaction force but notthe erosion rate to represent the erosion severity. In conclusion, mostcurrent CFD-based erosion research uses a one-way or two-waycoupling method that neglects the effect of particles to fluid flow andthe particle–particle interactions. Such erosion prediction models aresuitable for dilute flow. But in practice, dense flow is also encounteredfrequently, for which the particle interactions cannot be neglected anymore. A trend is a model of more general usage.

In recent years, with the improvement in particle simulation tech-nique, the particle science and technology have been developing rapid-ly. The discrete element method (DEM), as one of the mainstreamdiscrete modeling techniques, has the capacity to provide individualparticle dynamic information [16], which shows huge potential in theresearch of pneumatic conveying and particle erosion. Markus Vargaet al. [17] conducted a CFD–DEM approach for simulation of particulateflow in feed pipes. They concluded that prediction results of localizedhigh particle–wall conclusions agreed with higher wear rates from theerosion tests in lab-scale. Kuang et al. [18] presented a 2D CFD + 3DDEM model to study horizontal gas–solid slug flow. Chu and Yu [19,20] combined the DEM code with CFD software (combined continuumand discrete method, CCDM) and applied it successfully to simulationof particle–fluid flow in complex three-dimensional systems. What'smore, Chu et al. [21] adopted the CFD–DEM method and the Finniewear model to predict the wear rate of dense medium cyclones undermultiphaseflow condition. Theirwork suggested the CFD–DEMmethodcould be a helpful tool to study wear and particle–fluid flow.

This work combines DEMwith CFD and takes the interactions ofliquid–particle, particle–particle and particle–wall into account.The CFD–DEM coupled approach is able to model the liquid–parti-cle two-phase flow, from dense to dilute regimes. Simulation ofparticle motion is at particle-scale. An empirical erosion model isapplied to simulate erosion rate according to the data of particle–wall collisions. In addition, considering that in long-distance trans-portation pipelines wide-bend-angle elbows like 90° elbows oftentend to be replaced by smaller bending angle elbows, as 60° and 45°elbows, the research on which has caught very little attention, thisstudy aims to predict erosion in such bend-angle elbows by meansof numerical simulation.

(a) normal force (b) tangential force

Fig. 2. Spring–damper system to model contact forces.

2. Numerical model

The numerical model consists of three components: the fluid flowmodel, the particle motion model and the erosion model. Each ofthem will be briefly discussed, respectively.

2.1. Fluid flow modeling

Taking the volume fraction of the continuous phase and the particle–fluid interaction force into account, the continuous carrier fluid flowequations consists of volume averaging continuity and momentumequations, with the forms respectively

∂∂t α fρ f

� �þ∇ � α fρ fu f

� �¼ 0 ð1Þ

∂∂t α fρ fu f

� �þ∇ � α fρ fu fu f

� �¼ −α f∇pþ∇ � α f τ f

� �þ α fρ fg−fdrag

ð2Þ

As the flow in elbows is usually turbulent flow, the standard k − εequations are adopted,

∂∂t α fρ f k� �

þ∇ � α fρ fu f k� �

¼ ∇ � α f Γk∇k� �

þ α f G−α fρ f ε ð3Þ

∂∂t α fρ f ε� �

þ∇ � α fρ fu f ε� �

¼ ∇ � α f Γε∇ε� �

þ α fεk

c1G−c2ρ f ε� �

ð4Þ

The subscript f is for the fluid phase. These equations are so well-known that they won't be explained in this article.

2.2. Discrete particle motion modeling

While theflowoffluid as a continuumphase is described by the localaveraged Navier–Stokes equations on a computational cell scale, themotion of particles is modeled as a discrete phase, described by theNewton's laws of motion on an individual scale. When a particle is inmotion, it may collide with other particles nearby or wall and will bealways being dragged by carrier fluid. The motion of a particle in fluid(without contact with other particles or wall) is affected by the gravity,drag force and so on [22]. The governing equation is as shown below:

mpdup

dt¼ mpgþ Fdrag þ Fvm þ Fpg þ Fsl þ Fb þ Fm ð5Þ

Fdrag, Fvm, Fpg, Fsl, Fb and Fm represent the drag force, virtual massforce, pressure gradient force, Saffman lift force, Basset force, andMagnus force, respectively. The literature [23,24] suggests that thedrag force plays the major role in the force acting on the particles bythe fluid, and thus, in this paper we just focus on the gravity and thedrag force. The widely used Di Felice Drag Model [25] is applied todescribe the interaction between fluid and particles. The model isformulated as below:

Fdrag ¼ Cd0

8πd2pρ f u f−up

��� ��� u f−up

� �α− χþ1ð Þ

f

χ ¼ 3:7−0:65exp − 1:5− logRep� �2

=2� � ð6Þ

Fig. 5. Collision frequency distribution at the maximum erosive locations of the threeelbows.

Fig. 3. Average erosion rate of the concave wall of the elbows.

184 J. Chen et al. / Powder Technology 275 (2015) 182–187

where αf is the volume fraction of the fluid, and Cd0 and Rep are the dragcoefficient and Reynolds number of the particle, respectively:

Cd0 ¼ 0:63þ 4:8Re0:5p

!2

;Rep ¼α fρ f dp u f−up

��� ���μ f

ð7Þ

The vertical mass force,

Fvm

mpdup

dt

¼12ρ f Vp

d u f−up

� �dt

ρpVpdup

dt

¼ 12ρ f

ρp

d u f−up

� �dup

ð8Þ

will be important when ρf N ρp but not the case in this paper. It also ap-plies to the pressure gradient force,

Fpg

mpdup

dt

¼ Vp∇p

ρpVpdup

dt

∼ρ f

du f

dt

ρpdup

dt

: ð9Þ

Fig. 4. Relative erosion rate distribution at the maximum erosive locations of the threeelbows.

In addition, the pressure gradient that arises from the flow field isquite small especially for not very dense flow. And the pressure variesvery slightly over a distance of one particle diameter due to reasonablysmall particles. For the two reasons, we neglect the pressure gradientforce. The reason for neglecting the other force won't be discussedhere owing to the limited space.

As shown in dashed lines, Fig. 1, particle i driven by inertia orexternal forces contacts with particle j at point C. With the subse-quent relative motion, the particles actually deform. However, insoft-sphere model, the amount of normal overlap α and tangentialdisplacement δ are assumed as shown in Fig. 1 instead of consideringdeformation details. As a result, a normal force and a tangential forceare involved, composing of the contact forces. The model is com-posed of mechanical elements such as a spring, damper and frictionslider as shown in Fig. 2. The spring simulates the damp of deforma-tion and the damper simulates the damping effect. The couplerconnects the two particles when they are in contact but allowsthem to separate under the influence of repulsive force. If the diam-eter of one particle is set equal to infinity, the model reduces to aparticle–wall collision. The effects of these mechanical componentson particle motion mainly manifest in the parameters, namely springstiffness k and damping coefficient η.

Fig. 6. Probability distribution of particle–wall incidence speed of the three elbows.

Fig. 7. Probability distribution of particle–wall incidence angle of the three elbows.

185J. Chen et al. / Powder Technology 275 (2015) 182–187

The normal component of the contact force Fnij acting on particle i isgiven by the sum of the forces due to the spring and the damper. Forsphere particles in the three dimensional coordinate, it is given by

Fni j ¼ −knα32−ηniGn

� �n ð10Þ

where α is the displacement of the amount of normal overlap; G is therelative velocity vector of particle i to particle j, G = vi − vj; and n isthe unit vector in the direction of the line from the center of particle ito that of particle j.

With the similar form, the tangential component of the contact forceFtij is given by

Fti j ¼ −ktδ−ηt jGct ð11Þ

where kt and ηtj are the stiffness and damping coefficient, respectively,in the tangential direction; Gct is the slip velocity at the contact point,which is given by

Gct ¼ G− G � nð Þnþ aiΩi � nþ ajΩ j � n ð12Þ

where ai and aj are the radius of particle i and particle j, respectively;Ωi

and Ωj are the angular velocity of particle i and particle j, respectively.

(a) 45-degree elbow (b) 6

Fig. 8. Contours of turbulent intensity in th

In conclusion, the total force and torque acting on particle i aregiven by

Fi ¼ Fni j þ Fti j ; Ti ¼ ain� Fti j ð13Þ

For high concentration of particles, while several particles are incontact with particle i at the same time, the total force and torque actingon particle i are obtained by taking the sum of the forces as

Fi ¼Xj

Fni j þ Fti j� �

; Ti ¼Xj

ain� Fti j� �

ð14Þ

2.3. Erosion modeling

It proves that particle erosion is a very complicated process in viewof its mechanism and huge amounts of factors. Though there is nomodel with general application as previously mentioned, many empiri-cal formulas to predict erosion have been presented based on somespecific application under different conditions. An employable erosionprediction model should take as many factors into account as possibleto meet some given service requirement.

In this paper, taking the liquid–solid two-phase fluid dynamics aswell as the geometric characters of elbow and material properties intoaccount, the erosion protection model developed at the Erosion Corro-sion Research Center at the University of Tulsa is adopted, as following(according to Zhang et al., University of Tulsa, 2007 [12]):

E ¼ C BHð Þ−0:59 FsVnp F αð Þ ð15Þ

F αð Þ ¼X5i¼1

Aiαi ð16Þ

where E is erosion ratio defined as the mass removed from a surfacedivided by the total mass of particles impinging on the surface; BH isthe Brinell hardness of the wall material; Fs is the particle shape coeffi-cient, and Fs =0.2 for fully rounded sand particles; Vp is the particle in-cidence speed in m/s; α is the particle incidence angle in radians; andn = 2.41 and C = 2.17 × 10−7 are empirical constants. Values of Ai fori = 1 − 5 are 5.40,−10.11, 10.93,−6.33, and 1.42, respectively.

3. Implementation

As has been noted, the two-phase flowmodeling taking the interac-tion of liquid–particle, particle–particle, and particle–wall into account

0-degree elbow (c) 90-degree elbow

e exit sections of three kinds of elbow.

186 J. Chen et al. / Powder Technology 275 (2015) 182–187

was completed via CFD coupling DEM. The CFD code, ANSYS FLUENT,was employed to model the continuous phase flow. A pressure-based, transient-in-time solver was adopted, together with a stan-dard k − ε model for turbulence and standard wall functions forthe near-wall zone treatment. The discrete particle motion modeling

(a) 45-degree elbow

(b) 60-degree elbow

(c) 90-degree elbow

Fig. 9. Velocity vectors in the exit sections of three kinds of elbow.

was accomplished by the DEM code EDEM. The Hertz–Mindlin (noslip) contact model [26] was selected for particle–particle or parti-cle–wall contact. The individual particle motion characteristicswere revealed as well as particle–particle and particle–wall colli-sions are tracked.

The simulation of fluid flow and particle motion provided the indi-vidual particle motion characteristics, in which the information of parti-cle–wall collisionwas just concerned, such as the collision positions andincidence speeds of the particles to the wall. The incidence angles wereobtained by their tangent values, which equaled to the ratios of thenormal components to the tangential components of the particle inci-dence speeds. With the application of the erosion model, the individualparticle erosion rate was calculated. The frequency statistics of particleimpacts at various positions on side wall of the elbow were carriedout, and then it came to the average erosion rate of the elbow sidewall in various positions.

4. Verification

Erosion in elbows by particles entrained in water was experimen-tally analyzed by Blanchard et al. in 1984 [27]. They tested varioussand particle sizes ranging from 95 μm to 605 μm in diameter andpresented the location of maximum erosion to be 85° in average,measured from the beginning of the curve. Chen studied erosion inelbows caused by water/sand flow via CFD simulation under thecase of water velocity of 3 m/s and sand diameter of 150 μm, andthe result was that maximum erosion occurred at the exit region ofthe elbow [28]. In order to verify the current proposed model, onecase has been simulated under the same water velocity and sanddiameter as Chen's, and the details of settings are described in thefollowing paragraph.

Erosion prediction of 90° standard elbow has been implemented.The inner diameter of the elbow D = 40 mm and the radius meets r/D = 1.5. The 10D-length straight pipes are added both at the inletand the outlet of the elbow. The former is to reach a fully developedflow and a sufficient dispersion of the particles in the stream, beforereaching the elbow zone. The latter is to avoid possible reversed flowat the outlet surface of the domain. Water is selected as the fluid inthe pipe, at the speed of 3m/s flowing into the pipe. The discrete par-ticles are assumed to be spherical with the diameter 150 μm, injectedat the same speed with the fluid and positioned randomly at the inletsurface of the pipe. The density of the particles is 2650 kg/m3, and thenumber is 50,000 particles per second.

Erosion rate of individual particle is simulated, and through statisticthe average erosion rate was then obtained. The average erosion rate ofthe concavewall of 90° elbow along the curve is as shown in dashed linein Fig. 3. It can be seen that, the maximum average erosion rate with avalue of 4.38 × 10−9kg/(m2 ⋅ s) occurs in Φ = 86° in the elbow,where Φ is the bend-angle measured from the beginning of the curve.This result is confirmed by both the simulation observations of Chenand the experimental observations of Blanchard.

5. Results and discussion

As mentioned, the 60° elbow and 45° elbow are also widely usedin petroleum exploitation and transportation engineering. The pre-dictions of the maximum erosion and its location of the two havebeen carried out as shown in Fig. 3. The maximum erosion rate of60° elbow is 3.45 × 10−9kg/(m2 s) located in Φ = 60°. Those of 45°elbow are 2.60 × 10−9kg/(m2 s) and Φ = 44°. It can be seen that,the maximum erosive locations of different bend-angle elbows areat or near the exit, while the maximum erosion rate decreased withsmall bend-angle. Next the effect of bend-angle on erosion, particlemotion and fluid flow will be discussed.

187J. Chen et al. / Powder Technology 275 (2015) 182–187

5.1. Erosion and collision frequency distribution

Relative erosion rate is defined as

E ¼ Mass removed from a surfaceTotal mass of particles impinging on a surface

ð17Þ

Figs. 4 and 5 show the distributions of relative erosion rate andcollision frequency at the maximum erosive locations of the three,respectively. As the bend-angle ranged from 45° to 90°, erosion andcollision distribution spread from the concentrated bottom of theconcave wall to the whole domain. That is because at the exit of45° elbow, in addition to the leading role of mainstream drag force,particle motion is strongly affected by the gravity, leading to particlesedimentation to increase collision and erosion at the bottom of theelbow. Near the exit of 90° elbow, the turbulent flow has been moredeveloped with greater secondary flow, which increases the circum-ferential and radial motion of particles and results more collisions tothe side wall and top wall. It turns out to be a wider erosive area. Inshort, besides the mainstream drag force, gravitational effect con-tributes a lot to particle motion in 45° and 60° elbows, while turbu-lence and secondary flow weigh more in 90° elbow.

5.2. Particle motion

In order to discuss the effect of bend-angle on particle motion, atten-tion has been focused on the probability distributions of particle–wallincidence speed and incidence angle in the whole elbows. The resultsare presented in Figs. 6 and 7. Fig. 6 shows that in 90° elbow there aremuch more particles impacting on the wall at lower velocities. The prob-ability of particle incidence speed within 2–3 m/s is more than twice asmuch as that of 90° elbow. To the contrary, the probability of higher par-ticle incidence angle (≥15°) of 90° elbow is much higher than the othertwo. That is due to the increasing rebounds, more inter-particle collisionsand greater developed turbulence in 90° elbow. The former twoweakensthe energy of particles, lowering the incidence speed, and the last deviat-ed particles from mainstream direction to impact on the wall at morevariable angles. According to Humphrey's review [8], the maximumerosion is at an incidence angle within 20–30°. So it is indicated that par-ticle–wall incidence angle is more erosive in 90° elbow.

5.3. Flow field

Fig. 8 shows the contours of turbulent intensity in the exitsections of the three elbows, respectively. In the contours, the reduc-tion in blue region and the increase in red region meant the increaseof turbulent intensity. Thus, a much more intense turbulence arisesin 90° elbow. Velocity vectors at the exit sections of the three inFig. 9 are observed for the secondary flow paths. According to thevelocity vectors, it is obvious that the fully developed secondaryflow contributed to push the particles to impact on the extrados,outer side wall of the 90° elbow. Those results support the interpre-tations on the distributions of erosion and collision frequency nearthe exit of the elbow.

6. Conclusions

Numerical simulations based on CFD-coupling-DEM have been per-formed to predict erosion of liquid–particle two-phase flow in commonlyused 45°, 60° and 90° elbows. The result of maximum erosive locationprediction in 90° elbow is in reasonable agreement with both the simula-tion and experimental observations presented. The results show that,the maximum erosive locations are all near or at the exit of the threeelbows. Whereas, the effect of bend-angle on the maximum erosionrate is quite significant. The critical influences on particle motion are

different among the three elbows. The probability distributions of parti-cle–wall incidence speed and incidence angle in the three elbows indicatethat 90° elbow possesses more erosive incidence angle of particle–wallimpact. Thus, it will be advisable for suitable cases to replace widebend-angle (e.g. 90°) elbows with small bend-angle (e.g. 45° and 60°)elbows.

Acknowledgment

This work is supported by the National High Technology Researchand Development Program of China (863 Program) (grant no.2012AA040105-01) and the Foundation for Innovative ResearchGroups of the National Natural Science Foundation of China (grantno. 51121092).

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