- Email: [email protected]
A comprehensive CFD-based erosion prediction for sharp bend geometry with examination of grid effect
Wear 430–431 (2019) 191–201
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
A comprehensive CFD-based erosion prediction for sharp bend geometry with examination of grid effect
T
Jun Zhang∗, Farzin Darihaki, Siamack A. Shirazi The Erosion/Corrosion Research Center, Department of Mechanical Engineering, The University of Tulsa, Tulsa, OK, 74104, USA
ARTICLE INFO
ABSTRACT
Keywords: CFD Sharp bend Small particle erosion CFD based erosion prediction procedure Liquid-solid flow
A comprehensive CFD-based erosion prediction procedure developed previously is applied to predict erosion in a 90° sharp bend. This paper serves as a further validation of the proposed Computational Fluid Dynamics (CFD) based erosion prediction procedure for a different geometry, flow and particle conditions to examine the generalization of this comprehensive CFD-based approach to other geometries. Special emphasis is played on the strong effects of the grids on the resulting erosion profile representation. Detailed meshing information is provided for repeatable and further improved CFD studies in future. In the process, erosion predictions for both large (256 µm ) and small particles (25 µm ) in a sharp bend geometry are performed by applying the comprehensive CFD-based erosion prediction procedure. Results are compared with data from the literature and are found to be in a good agreement with data which demonstrates the success of the applied CFD-based erosion prediction procedure. It is shown that appropriate meshing, selection of turbulence model and near wall modeling approach are crucial for obtaining good erosion prediction results utilizing CFD, especially for small particle erosion prediction under the present flow and geometry conditions.
1. Introduction Many engineering applications involve material damage due to particle impacts. Erosion is referred to a type of wear due to fluid-induced particle impacts. Predicting impact parameters is then critical to obtain accurate erosion prediction, which is extremely important for engineering design and integrity management. Though simplified semimechanistic procedures have been developed and improved over the time [1–4], the models are limited to simple geometries with simple flow fields. As for a complex geometry or geometries with complicated flow field, CFD is often used to aid in erosion prediction. Early works of CFD-based erosion prediction are conducted by Edwards et al. [5,6] and Forder et al. [7]. Since then, predicting erosion utilizing CFD is thriving in the literature [8–15]. However, most of the investigations are only limited to applications of existing different models for modeling flow and particle behaviors. Few studies have looked into the details and limitations of the models. By far, several limitations have been found in the Discrete Phase Model (DPM) based erosion prediction model based upon very limited references. The pioneering work by Zhang et al. [16] explored consequences of the point-particle assumption made within most commercial CFD codes and showed that the assumption has re-
∗
sulted in unphysical multiple impacts within a small region in many cases. In order to overcome this limitation, in that study, near wall particle trajectories were modified through a User Defined Function (UDF) to account for particle size in the near wall region. In the implementation, particles are rebounded at radius before impacting the wall. This helps to obtain more physical small particle near wall trajectories and hence has improved erosion prediction. Also, results from the default CFD near wall flow solution and the implemented near wall velocity profiles based on law of the wall were compared and have demonstrated that more resolved near-wall flow field can significantly improve small particle erosion prediction. Though reasonably good results can be achieved through these modifications, the compensated measures are not generalized and can't be extended to other geometries, flow and particle conditions. Fard et al. [17] investigated more on the overall particle tracking component and pointed out another limitation of the commercial DPM based erosion prediction model which is eddy size is effectively limited to grid size. As a result, grid sizes govern particle dispersion and near wall behavior. This phenomenon has been validated in the recent work of Zhang et al. [18] and could be used further to improve erosion prediction.
Corresponding author. E-mail address: [email protected] (J. Zhang).
https://doi.org/10.1016/j.wear.2019.04.029 Received 31 December 2018; Received in revised form 28 April 2019; Accepted 29 April 2019 Available online 10 May 2019 0043-1648/ © 2019 Elsevier B.V. All rights reserved.
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Table 2 Meshes designed for grid configuration and near-wall optimization. First Layer Thickness (µm )
Mesh Set
Number of Nodes on N1
Number of Nodes on N2
Number of Nodes on N3
Number of Nodes on N4
25
Mesh Mesh Mesh Mesh Mesh Mesh
16 32 16 16 54 16
16 32 16 16 48 16
54 54 54 856 107 54
428 428 856 428 107 428
0.5 256
1 2 3 4 5 6
other flow and particle conditions to further evaluate the method performance. 2. Experimental background and CFD setup Previously, investigators of Baker Oil Tools (BOT) [20] have conducted erosion experiments with four testing conditions for a sharp bend geometry which resembles the fluid flows that can be experienced in the flow ports of valves in the well. Erosion of several materials were studied for the geometry. In each testing condition, five 1-inch, 90° sharp bends were placed in series with different materials. The following figure presents the schematic of the testing facilities (Fig. 1). The test are designed to mimic field operation conditions. The blender is used to prepare the slurry flow. Constant flow rate is maintained during the tests and sand particles are replaced every 2 h. Material weight and volume loss is obtained after all the tests and erosion depth is inspected at locations every 30° radial increment and 12.7 mm axial increment shown in Fig. 2. From Fig. 1, it can be seen that the 90° sharp bend is made up of two short straight pipes intersecting along a plane that is cut 45° to the pipe axis. Fig. 2 shows the dimensions of each tested pipe section that constitutes the sharp elbow geometry. From Table 2, it is observed that the sand concentration is relatively very low that the slurry is treated as a dilute liquid-solid flow. Thus, particle modulation of flow field and particle-particle interaction are neglected in the modeling. DPM-based erosion prediction procedure is applied. In the Phase I test, investigators have developed an erosion ratio equation for Inconel 718. The developed erosion ratio equation can be found in Ref. [16]. Thus, this erosion ratio equation is employed in the CFD predictions. For particle tracking component, drag, virtual mass, and pressure gradient forces are considered and Forder rebound model is employed. All the CFD cases are run in second-order accuracy. Pressure, momentum and turbulence equations are discretized with second-order spatial accuracy.
Fig. 1. Schematic diagram of testing facilities from Ref. [20].
Fig. 2. Schematic diagram of the testing specimen from Ref. [20]. The four testing conditions consisting of two flow conditions and two particle sizes are listed in Table 1. Table 1 BOT phase II testing conditions. Conditions
Test 1
Test 2
Test 3
Test 4
Carrier Fluid Sand Size (µm ) Sand Type
Water 256 rounded quartz 15.2 10 1%
25 sharp silica 15.2 10 1%
25 sharp silica 26.2 2 1%
256 rounded quartz 26.2 2 1%
Inlet Velocity (m/s) Testing Duration (hours) Sand Concentration (by weight of liquid)
3. Results and discussions 3.1. Grid configuration and near-wall treatment optimization Simulations in the present work are carried out for the first sharp bend of which material is Inconel 718. This simplifies the problem and has ruled out the effects of other available sharp bends on flow modeling and erosion prediction. From Ref. [18], it is understood that the current CFD codes limit eddy size to cell size which affects particle trajectories and particle dispersion. Also, first layer thickness plays an important role in determining particle impact characteristics which has been fully discussed in Ref. [19]. Thus, a careful study and selection of grids used for erosion simulation is of supreme importance to have reasonable and accurate erosion predictions. Moreover, predicting erosion resulting from small particles is very challenging as small particles can be easily affected by turbulence and mean flow field. Under this context, both small particle
This work is an application and validation of the previously developed CFD-based erosion prediction procedure [19] for a new geometry where data is available and different Stokes number conditions. Following the comprehensive procedure, a systematic grid sensitivity study is carried out to obtain a reasonably good mesh for running erosion simulations. Detailed gird information is presented so that the CFD results are repeatable and can be examined. Then, the mesh is run with different turbulence models and results are compared with experimental data to reach a suitable combination of models for predicting erosion. Finally, the established mesh and model are applied to 192
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Fig. 3. a. The simulated sharp bend geometry.b. Cross-sectional mesh notation.
Fig. 4. a. Typical CFD predicted erosion contour for Test 3. b. Effect of mesh density on erosion prediction and comparison with data. c. Effect of mesh density on particle trajectories. (Mesh 1 to Mesh 4, Test 3, dp = 25 µm ). d. Effect of upstream mesh density on erosion representation.
(Test 3) and large particle (Test 4) erosion data are used to investigate the effect of grid configuration on erosion prediction so as to obtain an optimized mesh, particularly along the wall normal direction for running erosion simulation. Based on above discussion, the modeled sharp bend geometry is created and different mesh sets are examined to obtain the representative mesh set that can appropriately resolve flow field and do particle tracking. Fig. 3a and b, and Table 2 present the geometry and the selected mesh information.
It is to be noted that during mesh generation, The first layer thickness is controlled to the desired scale for all the mesh sets. It is critical to select the most appropriate near wall modeling approach based on the flow condition and the first layer thickness. The estimated Y+ for all the experimental testing conditions are around 20–50 when first layer thickness is set to be particle diameter. Under this circumstances, enhanced wall treatment and non-equilibrium wall function can all be applicable. However, as the flow in the sharp bend involves reattachment and recirculation towards downstream, non-equilibrium 193
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Fig. 4. (continued)
wall function is expected to have better performance in modeling this type of flow as it considers viscous sublayer and pressure gradient effects according to ANSYS Fluent documentation. Based on this, nonequilibrium wall function is applied in the first stage of CFD modeling to examine the effect of mesh sets on erosion prediction from Mesh 1 to
Mesh 4. Fig. 4a-c present the prediction results and comparison to experimental data. Fig. 4a shows the typical erosion contour obtained from CFD which gives a general picture of how erosion distributes under the conditions simulated. The predicted results in Fig. 4b are normalized with the 194
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Fig. 4. (continued)
Fig. 4. (continued)
grid refinement. By comparing the downstream erosion profiles, it is found that the predicted results experience almost no changes to this grid refinement. Both predictions are very similar to experimental results for the downstream regions. Mesh 3 provides refinement to the downstream section. The obtained results also demonstrate negligible changes to the resulting erosion profiles. By comparing Mesh 1 with Mesh 4 which refers to axial refinement in the upstream section, it is observed the resulting predictions of the downstream section have been changed. Compared to experimental downstream profile, the results from Mesh 4 is not as good as Mesh 1 with relatively large over-prediction for both upstream and downstream sections. Moreover, the erosion pattern of the downstream has been changed. By examining trajectories in Fig. 4c for Mesh 1 and Mesh 4, the particle trajectories and velocities are very similar. The different representations of erosion profiles can be dominantly caused by the changing of upstream cell sizes. Table 3 sumarizes the behaviors described above, quantitatively.
Table 3 Predicted maximum erosion over data ratios and maximum erosion location (Mesh 1 to Mesh 4). Mesh Set
Upstream CFD/ Data
Downstream CFD/ Data
Maximum erosion location
Mesh Mesh Mesh Mesh
6.16 5.30 6.16 38.11
1.59 1.67 1.76 4.14
Downstream Downstream Downstream Upstream
1 2 3 4
experimental data. For the downstream results, the normalization is done with the downstream experimental maximum erosion data. And, for the upstream, this process is achieved with the upstream experimental maximum erosion data. Mesh 1 provides a reference which other mesh sets are compared with. Mesh 2 represents cross-sectional 195
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Fig. 5. Effect of first layer thickness on erosion prediction (Test 3, dp = 25 µm ).
work. For example, the particle-eddy interaction model implemented in the current commercial CFD codes is unable to model turbulent dispersion of particles very well. Based on these predictions and comparisons, the grid configuration of Mesh 1 will be applied to predict the rest of the testing conditions except for the first layer thickness which is changed according to the particle size in each test. In order to present the effect of first layer thickness on erosion prediction, Mesh 1, Mesh 5 and Mesh 6 are utilized to further demonstrate that it is needed to set the first layer thickness to an appropriate scale which is the particle diameter for running erosion simulations. 25 µm particle erosion is simulated with first layer thickness of 0.5 µm (Mesh 5), 25 µm (Mesh 1), 256 µm (Mesh 6) respectively. In the event, based on the average Y+ appropriate near wall treatment is set for running each case. Thus, Mesh 1 is run with low Reynolds number modeling and Mesh 5 and Mesh 6 are simulated with wall functions so as to appropriately simulate the near wall flow field. Fig. 5 shows the results. Fig. 5 and Table 4 prove that for the 25 µm small particle erosion simulation the first layer thickness shouldn't be too fine and too coarse.
Table 4 Predicted maximum erosion over data ratios and maximum erosion location (Test 3, dp = 25 µm ). Mesh Set
Upstream CFD/ Data
Downstream CFD/ Data
Maximum erosion location
Mesh 1 Mesh 5 Mesh 6
6.16 18.20 63.33
1.59 47.17 9.96
Downstream Downstream Downstream
Thus, the systematic grid structure study indicates that Mesh 1 can predict erosion with good accuracy and generally much less computational cost. However, even by applying Mesh 1, it is found that the erosion pattern of the upstream section can't be predicted very well. Both the magnitude and erosion pattern have deviated from the experiment a lot. It is also found that by refining the upstream grids of Mesh 1, erosion representation by CFD deteriorates which is presented in Fig. 4d. This may be due to some additional deficiencies in the commercial CFD codes that are not within the scope of this present 196
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Fig. 6. Effect of near wall treatment on erosion prediction (Test 3, dp = 25 µm ).
It is shown that predictions deteriorate significantly as the first layer thickness decreased to 0.5 µm (Mesh 5) with an over-prediction factor of 47 and erosion pattern also changed compared to data. Also, the predictions become inaccurate when the first layer thickness goes up to 256 µm . Significant over-prediciton is observed for the upstream section. Though the downstream pattern is somehow retained, it overpredicts maximum erosion by a factor of 10. Generally, the first layer scale set to particle diameter 25 µm has yielded a lot better results and are very comparable to the data particularly for the downstream section. The results and discussions have validated the previously developed theory that it is recommended to set the first layer thickness to particle diameter for erosion simulation utilizing current CFD codes in order to obtain good predictions. There can be more than one wall function or near wall model that is applicable for a specific case. In the subsequent discussion, the effect of different near wall modeling approaches is presented to screen out the best model for erosion simulation. It is found that enhanced wall treatment can be very flexible and is applicable for Test 3 condition. Thus, the results from non-equilibrium wall function and enhanced wall treatment are compared. Fig. 6 demonstrates the results. Fig. 6 shows that both the models can predict the maximum erosion downstream fairly well but can't capture the upstream erosion profile. And, examining the downstream erosion profile, it is seen that nonequilibrium wall function performs better than enhanced wall treatment by correctly predicting two erosion hotspots. Thus, non-equilibrium wall function is applied in the following investigation for all the cases. By far, the comprehensive discussion has reached the best grid configuration and near wall treatment for running erosion simulation which is Mesh 1 and non-equilibrium wall function respectively for this
sharp bend geometry. 3.2. Effect of turbulence model on erosion simulation The effect of different turbulence models is investigated to evaluate the overall performance of commonly used turbulence models with application to erosion simulation for this type of geometry. Besides Reynolds stress model, SST k , RNG k , Realizable k and Standard k are examined. Non-equilibrium wall function is applied to each case. Experimental data of Test 3 is used to determine which model has the best performance in predicting the overall erosion profile. Fig. 7 presents the results for Test 3. It is observed from Fig. 7 that Reynolds Stress Model (RSM) offers the best prediction of erosion pattern and magnitude for both upstream comes as the secondary and downstream sections. Realizable k candidate for modeling erosion in the sharp bend. However, further compared to experimental data, the overall erosion profiles predicted are not as good as Reynolds Stress Model. All the other models can't predict erosion profiles that follow the measured erosion pattern and present highly localized erosion hotspots, which are not physical. All the models seem to predict downstream erosion magnitude better than upstream and there are significant over-predictions of maximum erosion upstream of the sharp bend, but because of the smaller maximum erosion for the upstream, this is compromised. In experiment, it is noticed that for the upstream section particles appears to be fully mixed with fluid that upstream experimental erosion profile is more dispersed and randomly distributed. But, erosion simulations always show significant erosion localization for the upstream section which indicates the deficiencies of current CFD codes on modeling particle-fluid interaction. 197
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Fig. 7. Effect of turbulence model on erosion prediction (Test 3, dp = 25 µm ).
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acceptable accuracy in predicting erosion pattern and the location of hotspots at downstream. However, CFD is not able to capture the erosion pattern at the upstream section. Figs. 10 and 11 present the results for the small particle cases. For fine particles also the same performance is observed. Overall, for all the four tests downstream section erosion profile is captured better than the upstream section erosion profile by current CFD codes. The overall ratios of maximum erosion predicted over experimental data are listed in Table 6 to present a more straightforward evaluation of the proposed CFD based erosion prediction procedure. Table 6 points out the accuracy of the magnitude of the calculated erosion. A factor of 0.53 has been applied for cases with rounded quartz particles to consider particle shape on the resulting erosion. In all cases, maximum erosion belongs to the downstream section of the sharp bend. Two large over-predictions at upstream refer to the cases with smaller particles in which erosion at downstream is significantly greater than upstream. The comprehensive approach previously proposed contains creating meshes with first layer thickness that is capable of predicting particle impact parameters (which can be obtained by examining the resulting predictions and comparing with data), conducting grid refinement along all the relevant directions with the fixed first layer thickness and incorporating different turbulence model induced uncertainties. The summary of predictions presented by Table 6 shows that proposed procedure works very well in predicting both large and small particle erosion for sharp bend geometry. Also, it is observed that the current CFD model package is mostly conservative in predicting erosion which can be favored in practical engineering design.
Table 5 Comparison of predicted maximum erosion from models with data (Test 3). Models
Upstream CFD/Data
Downstream CFD/Data
Maximum erosion location
Standard k- ε RNG k- ε Realizable k- ε SST k-ω RSM with nonequilibrium wall function
58.89 9.74 7.31 15.47 6.16
8.49 2.77 1.39 7.24 1.59
Downstream Downstream Downstream Downstream Downstream
As for the downstream section, experiment presents a symmetric erosion profile with erosion hotspot on each side which is caused by the strong secondary flow inside the downstream pipe. Simulations are able to replicate the same behavior especially results from Reynolds Stress Model can follow experimental data very well. Table 5 compares the maximum values of raw calculated erosion data with the experimental data points. It shows that RSM and Realizable k- ε model perform better in predicting maximum erosion. Reynold Stress Model is the best model in that it can both predict the pattern and magnitude. 3.3. Application and validating the model for all the cases Following figures (Figs. 8–11) present CFD predictions for all the four tests. Grid configuration of Mesh 1 is used but based on the particle size available, first layer thickness is changed to adapt to different particle conditions. First, comparisons are made for large particle represented by Test 1 and Test 4. Next, small particle erosion results (Test 2 and Test 3) are also compared to data. Finally, a table is given to demonstrate the ratio of predicted maximum erosion over experimental data for all four cases. Figs. 8 and 9 show the results for Test 1 and Test 4. It is observed that for larger particle size cases, the measured thickness loss keeps a similar pattern; this consistency is also represented by CFD results. The presented approach has provided an
4. Conclusions The present study suggested that the particle erosion in a sharp bend geometry could be resolved by utilizing available CFD models, however, it was shown that the predictions could be affected drastically by factors including mesh cell size and near wall modeling. The calculations confirmed the validity of the proposed comprehensive procedure for sharp bend geometry. The results following this procedure yielded
Fig. 8. Comparison of erosion profiles for Test 1 (Vinlet =15.2 m/s, dp = 256 μm).
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Fig. 9. Comparison of erosion profiles for Test 4 (Vinlet =26.2 m/s, dp = 256 μm).
Fig. 10. Comparison of upstream erosion profile for Test 2 (Vinlet =15.2 m/s, dp = 25 μm).
the near-wall treatment should also be changed according to the resulting Y+ value. For this work, it turned out non-equilibrium wall function can best simulate near wall particle behavior and the resulting erosion profile. CFD simulations suggested that turbulence modeling is a very important component especially in fully mixing the particles with fluids. The current investigation pointed out that current RANS based CFD models are limited in simulating mixing of particles in straight pipes which resulted in unsatisfactory erosion pattern prediction for the upstream section. For this geometry, Reynolds stress model is the best one to successfully have downstream erosion profile predicted.
fairly good agreement with experimental data especially for the downstream pipe. Though the downstream predictions were around ±50% of the experimental data, considering the fact that erosion phenomenon is complicated and affected by a multitude of factors this level of accuracy is acceptable in many engineering applications. Grid refinement study revealed that increasing mesh density will not always result in more accurate erosion prediction and in some cases, significant over-prediction could be observed. Alongside this comprehensive procedure, this paper also highlights how critical the first layer thickness is by simulating with different first layer thickness scales. To obtain good erosion prediction results, the first layer thickness is recommended to be set to particle diameter and
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Fig. 11. Comparison of upstream erosion profile for Test 3 (Vinlet =26.2 m/s, dp = 25 μm). Table 6 Ratio of maximum predicted erosion to experimental data. Sand condition
256 µm rounded quartz
Test number
Test 1
Test velocity (m/s) Section CFD/Experiment
15.2 Up 0.49
25 µm sharp silica flour Test 4
Down 0.85
Test 2
26.2 Up 0.76
Down 1.47
Acknowledgments
15.2 Up 9.31
Test 3 Down 1.44
26.2 Up 6.16
Down 1.59
[10] P. Zahedi, J. Zhang, H. Arabnejad, B.S. McLaury, S.A. Shirazi, CFD simulation of multiphase flows and erosion predictions under annular flow and low liquid loading conditions, Wear 376–377 (2017) 1260–1270. [11] C. Duarte, F. de Souza, R. Salvo, V. dos Santos, The role of inter-particle collisions on elbow erosion, Int. J. Multiph. Flow 89 (2017) 1–22. [12] H. Zhu, J. Zhu, J. Zhang, H.-Q. Zhang, Sand Erosion Model Prediction, Selection and Comparison for Electrical Submersible Pump (ESP) Using CFD Method, FEDSM 2018-83179, ASME FEDSM, Montreal, Canada, July 14-20, 2018. [13] Z. Wang, J. Zhang, S.A. Shirazi, Yihua Dou, Experimental and numerial study of erosion in a non-Newtonain hydraulic fracturing fluid, Wear 422–423 (2019) 1–8. [14] J. Zhang, B.S. McLaury, S.A.Shirazi, Effect of near wall modeling approaches on solid particle erosion prediction, FEDSM2017-69374, Proceedings of the ASME 2017 Fluids Engineering Summer Meeting, Waikoloa, Hawaii, USA. [15] Xianghui Chen, Brenton S. McLaury, Siamack A. Shirazi, Application and experimental validation of a computational fluid dynamics (CFD) based erosion prediciton model in elbows and plugged tees, Comput. Fluids 33 (2004) 1251–1272. [16] Yongli Zhang, Brenton S. McLaury, Siamack A. Shirazi, Improvements of particle near-wall velocity and erosion predictions using a commercial CFD code, J. Fluids Eng. 131 (3) (2009) 031303. [17] F.N. Fard, B.S. McLaury, S.A.Shirazi, Effect of cell size on particle-eddy interaction and erosion predictions using commercial CFD software (FLUENT), FEDSM201272294, Proceedings of the ASME 2012 Fluids Engineering Summer Meeting, Rio Grande, Puerto Rico. [18] J. Zhang, B.S. McLaury, S.A. Shirazi, Modeling sand fines in elbows mounted in series, Wear 402–403 (2018) 196–206. [19] J. Zhang, B.S. McLaury, S.A. Shirazi, Application and experimental validation of a CFD based erosion prediction procedure for jet impingement geometry, Wear 394–395 (2018) 11–19. [20] R. Russell, S.A. Shirazi, J. Macrae, A new computational fluid dynamics model to predict flow profiels and erosion rates in downhole completion equipment, Proceedings of SPE Annual Technical Conference and Exhibition, 2004 Paper no. SPE 90734.
The authors wish to acknowledge all the member companies that have supported E/CRC research for many years. References [1] S.A. Shirazi, J.R. Shadley, B.S. McLaury, E.F. Rybicki, A procedure to predict solid particle erosion in elbows and tees, J. Press. Vessel Technol. 117 (1) (1995) 45–52. [2] B.S. McLaury, S.A. Shirazi, Predicting erosion in straight pipes, FEDSM 98: Production Operations and Engineering-General, 1999 Houston, Oct3-6. [3] B.S. McLaury, S.A. Shirazi, Generalization of API RP 14E for Erosive Service in Multiphase Production, SPE ATCE: Production Operations and EngineeringGeneral, Houston, 1999 Oct3-6. [4] Y. Zhang, B.S. McLaury, S.A. Shirazi, E.F. Rybicki, A Two-Dimensional Mechanistic Model for Sand Erosion Prediction Including Particle Impact Characteristics, Corrosion, San Antonio, 2010 Paper no. 10378. [5] Edwards, J.K., McLaury, B.S., Shirazi, S.A., Supplementing a CFD Code with Erosion Prediction Capabilities, Paper FEDSM 98-5229 in ASME FED Summer Meeting Proceedings 1998, Wahsington D.C., June 21-25. [6] J.K. Edwards, Development, Validation, and Application of A Three-Dimensional, CFD-Based Erosion Prediction Procedure, PhD Dissertaion, The University of Tulsa, 2000. [7] A. Forder, M. Thew, D. Harrison, A numerical investigation of solid particle erosion experienced within oilfield control valves, Wear 216 (1998) 184–193. [8] Christopher B. Solnordal, Chong Y. Wong, Joan Boulanger, An experimental and numerical analysis of erosion caused by sand pneumatically conveyed through a standard pipe elbow, Wear 336–337 (2015) 43–57. [9] C. Duarte, F. de Souza, V. dos Santos, Numerical investigation of mass loading effects on elbow erosion, Powder Technol. 283 (2015) 593–606.
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Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
A comprehensive CFD-based erosion prediction for sharp bend geometry with examination of grid effect
T
Jun Zhang∗, Farzin Darihaki, Siamack A. Shirazi The Erosion/Corrosion Research Center, Department of Mechanical Engineering, The University of Tulsa, Tulsa, OK, 74104, USA
ARTICLE INFO
ABSTRACT
Keywords: CFD Sharp bend Small particle erosion CFD based erosion prediction procedure Liquid-solid flow
A comprehensive CFD-based erosion prediction procedure developed previously is applied to predict erosion in a 90° sharp bend. This paper serves as a further validation of the proposed Computational Fluid Dynamics (CFD) based erosion prediction procedure for a different geometry, flow and particle conditions to examine the generalization of this comprehensive CFD-based approach to other geometries. Special emphasis is played on the strong effects of the grids on the resulting erosion profile representation. Detailed meshing information is provided for repeatable and further improved CFD studies in future. In the process, erosion predictions for both large (256 µm ) and small particles (25 µm ) in a sharp bend geometry are performed by applying the comprehensive CFD-based erosion prediction procedure. Results are compared with data from the literature and are found to be in a good agreement with data which demonstrates the success of the applied CFD-based erosion prediction procedure. It is shown that appropriate meshing, selection of turbulence model and near wall modeling approach are crucial for obtaining good erosion prediction results utilizing CFD, especially for small particle erosion prediction under the present flow and geometry conditions.
1. Introduction Many engineering applications involve material damage due to particle impacts. Erosion is referred to a type of wear due to fluid-induced particle impacts. Predicting impact parameters is then critical to obtain accurate erosion prediction, which is extremely important for engineering design and integrity management. Though simplified semimechanistic procedures have been developed and improved over the time [1–4], the models are limited to simple geometries with simple flow fields. As for a complex geometry or geometries with complicated flow field, CFD is often used to aid in erosion prediction. Early works of CFD-based erosion prediction are conducted by Edwards et al. [5,6] and Forder et al. [7]. Since then, predicting erosion utilizing CFD is thriving in the literature [8–15]. However, most of the investigations are only limited to applications of existing different models for modeling flow and particle behaviors. Few studies have looked into the details and limitations of the models. By far, several limitations have been found in the Discrete Phase Model (DPM) based erosion prediction model based upon very limited references. The pioneering work by Zhang et al. [16] explored consequences of the point-particle assumption made within most commercial CFD codes and showed that the assumption has re-
∗
sulted in unphysical multiple impacts within a small region in many cases. In order to overcome this limitation, in that study, near wall particle trajectories were modified through a User Defined Function (UDF) to account for particle size in the near wall region. In the implementation, particles are rebounded at radius before impacting the wall. This helps to obtain more physical small particle near wall trajectories and hence has improved erosion prediction. Also, results from the default CFD near wall flow solution and the implemented near wall velocity profiles based on law of the wall were compared and have demonstrated that more resolved near-wall flow field can significantly improve small particle erosion prediction. Though reasonably good results can be achieved through these modifications, the compensated measures are not generalized and can't be extended to other geometries, flow and particle conditions. Fard et al. [17] investigated more on the overall particle tracking component and pointed out another limitation of the commercial DPM based erosion prediction model which is eddy size is effectively limited to grid size. As a result, grid sizes govern particle dispersion and near wall behavior. This phenomenon has been validated in the recent work of Zhang et al. [18] and could be used further to improve erosion prediction.
Corresponding author. E-mail address: [email protected] (J. Zhang).
https://doi.org/10.1016/j.wear.2019.04.029 Received 31 December 2018; Received in revised form 28 April 2019; Accepted 29 April 2019 Available online 10 May 2019 0043-1648/ © 2019 Elsevier B.V. All rights reserved.
Wear 430–431 (2019) 191–201
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Table 2 Meshes designed for grid configuration and near-wall optimization. First Layer Thickness (µm )
Mesh Set
Number of Nodes on N1
Number of Nodes on N2
Number of Nodes on N3
Number of Nodes on N4
25
Mesh Mesh Mesh Mesh Mesh Mesh
16 32 16 16 54 16
16 32 16 16 48 16
54 54 54 856 107 54
428 428 856 428 107 428
0.5 256
1 2 3 4 5 6
other flow and particle conditions to further evaluate the method performance. 2. Experimental background and CFD setup Previously, investigators of Baker Oil Tools (BOT) [20] have conducted erosion experiments with four testing conditions for a sharp bend geometry which resembles the fluid flows that can be experienced in the flow ports of valves in the well. Erosion of several materials were studied for the geometry. In each testing condition, five 1-inch, 90° sharp bends were placed in series with different materials. The following figure presents the schematic of the testing facilities (Fig. 1). The test are designed to mimic field operation conditions. The blender is used to prepare the slurry flow. Constant flow rate is maintained during the tests and sand particles are replaced every 2 h. Material weight and volume loss is obtained after all the tests and erosion depth is inspected at locations every 30° radial increment and 12.7 mm axial increment shown in Fig. 2. From Fig. 1, it can be seen that the 90° sharp bend is made up of two short straight pipes intersecting along a plane that is cut 45° to the pipe axis. Fig. 2 shows the dimensions of each tested pipe section that constitutes the sharp elbow geometry. From Table 2, it is observed that the sand concentration is relatively very low that the slurry is treated as a dilute liquid-solid flow. Thus, particle modulation of flow field and particle-particle interaction are neglected in the modeling. DPM-based erosion prediction procedure is applied. In the Phase I test, investigators have developed an erosion ratio equation for Inconel 718. The developed erosion ratio equation can be found in Ref. [16]. Thus, this erosion ratio equation is employed in the CFD predictions. For particle tracking component, drag, virtual mass, and pressure gradient forces are considered and Forder rebound model is employed. All the CFD cases are run in second-order accuracy. Pressure, momentum and turbulence equations are discretized with second-order spatial accuracy.
Fig. 1. Schematic diagram of testing facilities from Ref. [20].
Fig. 2. Schematic diagram of the testing specimen from Ref. [20]. The four testing conditions consisting of two flow conditions and two particle sizes are listed in Table 1. Table 1 BOT phase II testing conditions. Conditions
Test 1
Test 2
Test 3
Test 4
Carrier Fluid Sand Size (µm ) Sand Type
Water 256 rounded quartz 15.2 10 1%
25 sharp silica 15.2 10 1%
25 sharp silica 26.2 2 1%
256 rounded quartz 26.2 2 1%
Inlet Velocity (m/s) Testing Duration (hours) Sand Concentration (by weight of liquid)
3. Results and discussions 3.1. Grid configuration and near-wall treatment optimization Simulations in the present work are carried out for the first sharp bend of which material is Inconel 718. This simplifies the problem and has ruled out the effects of other available sharp bends on flow modeling and erosion prediction. From Ref. [18], it is understood that the current CFD codes limit eddy size to cell size which affects particle trajectories and particle dispersion. Also, first layer thickness plays an important role in determining particle impact characteristics which has been fully discussed in Ref. [19]. Thus, a careful study and selection of grids used for erosion simulation is of supreme importance to have reasonable and accurate erosion predictions. Moreover, predicting erosion resulting from small particles is very challenging as small particles can be easily affected by turbulence and mean flow field. Under this context, both small particle
This work is an application and validation of the previously developed CFD-based erosion prediction procedure [19] for a new geometry where data is available and different Stokes number conditions. Following the comprehensive procedure, a systematic grid sensitivity study is carried out to obtain a reasonably good mesh for running erosion simulations. Detailed gird information is presented so that the CFD results are repeatable and can be examined. Then, the mesh is run with different turbulence models and results are compared with experimental data to reach a suitable combination of models for predicting erosion. Finally, the established mesh and model are applied to 192
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Fig. 3. a. The simulated sharp bend geometry.b. Cross-sectional mesh notation.
Fig. 4. a. Typical CFD predicted erosion contour for Test 3. b. Effect of mesh density on erosion prediction and comparison with data. c. Effect of mesh density on particle trajectories. (Mesh 1 to Mesh 4, Test 3, dp = 25 µm ). d. Effect of upstream mesh density on erosion representation.
(Test 3) and large particle (Test 4) erosion data are used to investigate the effect of grid configuration on erosion prediction so as to obtain an optimized mesh, particularly along the wall normal direction for running erosion simulation. Based on above discussion, the modeled sharp bend geometry is created and different mesh sets are examined to obtain the representative mesh set that can appropriately resolve flow field and do particle tracking. Fig. 3a and b, and Table 2 present the geometry and the selected mesh information.
It is to be noted that during mesh generation, The first layer thickness is controlled to the desired scale for all the mesh sets. It is critical to select the most appropriate near wall modeling approach based on the flow condition and the first layer thickness. The estimated Y+ for all the experimental testing conditions are around 20–50 when first layer thickness is set to be particle diameter. Under this circumstances, enhanced wall treatment and non-equilibrium wall function can all be applicable. However, as the flow in the sharp bend involves reattachment and recirculation towards downstream, non-equilibrium 193
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Fig. 4. (continued)
wall function is expected to have better performance in modeling this type of flow as it considers viscous sublayer and pressure gradient effects according to ANSYS Fluent documentation. Based on this, nonequilibrium wall function is applied in the first stage of CFD modeling to examine the effect of mesh sets on erosion prediction from Mesh 1 to
Mesh 4. Fig. 4a-c present the prediction results and comparison to experimental data. Fig. 4a shows the typical erosion contour obtained from CFD which gives a general picture of how erosion distributes under the conditions simulated. The predicted results in Fig. 4b are normalized with the 194
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Fig. 4. (continued)
Fig. 4. (continued)
grid refinement. By comparing the downstream erosion profiles, it is found that the predicted results experience almost no changes to this grid refinement. Both predictions are very similar to experimental results for the downstream regions. Mesh 3 provides refinement to the downstream section. The obtained results also demonstrate negligible changes to the resulting erosion profiles. By comparing Mesh 1 with Mesh 4 which refers to axial refinement in the upstream section, it is observed the resulting predictions of the downstream section have been changed. Compared to experimental downstream profile, the results from Mesh 4 is not as good as Mesh 1 with relatively large over-prediction for both upstream and downstream sections. Moreover, the erosion pattern of the downstream has been changed. By examining trajectories in Fig. 4c for Mesh 1 and Mesh 4, the particle trajectories and velocities are very similar. The different representations of erosion profiles can be dominantly caused by the changing of upstream cell sizes. Table 3 sumarizes the behaviors described above, quantitatively.
Table 3 Predicted maximum erosion over data ratios and maximum erosion location (Mesh 1 to Mesh 4). Mesh Set
Upstream CFD/ Data
Downstream CFD/ Data
Maximum erosion location
Mesh Mesh Mesh Mesh
6.16 5.30 6.16 38.11
1.59 1.67 1.76 4.14
Downstream Downstream Downstream Upstream
1 2 3 4
experimental data. For the downstream results, the normalization is done with the downstream experimental maximum erosion data. And, for the upstream, this process is achieved with the upstream experimental maximum erosion data. Mesh 1 provides a reference which other mesh sets are compared with. Mesh 2 represents cross-sectional 195
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Fig. 5. Effect of first layer thickness on erosion prediction (Test 3, dp = 25 µm ).
work. For example, the particle-eddy interaction model implemented in the current commercial CFD codes is unable to model turbulent dispersion of particles very well. Based on these predictions and comparisons, the grid configuration of Mesh 1 will be applied to predict the rest of the testing conditions except for the first layer thickness which is changed according to the particle size in each test. In order to present the effect of first layer thickness on erosion prediction, Mesh 1, Mesh 5 and Mesh 6 are utilized to further demonstrate that it is needed to set the first layer thickness to an appropriate scale which is the particle diameter for running erosion simulations. 25 µm particle erosion is simulated with first layer thickness of 0.5 µm (Mesh 5), 25 µm (Mesh 1), 256 µm (Mesh 6) respectively. In the event, based on the average Y+ appropriate near wall treatment is set for running each case. Thus, Mesh 1 is run with low Reynolds number modeling and Mesh 5 and Mesh 6 are simulated with wall functions so as to appropriately simulate the near wall flow field. Fig. 5 shows the results. Fig. 5 and Table 4 prove that for the 25 µm small particle erosion simulation the first layer thickness shouldn't be too fine and too coarse.
Table 4 Predicted maximum erosion over data ratios and maximum erosion location (Test 3, dp = 25 µm ). Mesh Set
Upstream CFD/ Data
Downstream CFD/ Data
Maximum erosion location
Mesh 1 Mesh 5 Mesh 6
6.16 18.20 63.33
1.59 47.17 9.96
Downstream Downstream Downstream
Thus, the systematic grid structure study indicates that Mesh 1 can predict erosion with good accuracy and generally much less computational cost. However, even by applying Mesh 1, it is found that the erosion pattern of the upstream section can't be predicted very well. Both the magnitude and erosion pattern have deviated from the experiment a lot. It is also found that by refining the upstream grids of Mesh 1, erosion representation by CFD deteriorates which is presented in Fig. 4d. This may be due to some additional deficiencies in the commercial CFD codes that are not within the scope of this present 196
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Fig. 6. Effect of near wall treatment on erosion prediction (Test 3, dp = 25 µm ).
It is shown that predictions deteriorate significantly as the first layer thickness decreased to 0.5 µm (Mesh 5) with an over-prediction factor of 47 and erosion pattern also changed compared to data. Also, the predictions become inaccurate when the first layer thickness goes up to 256 µm . Significant over-prediciton is observed for the upstream section. Though the downstream pattern is somehow retained, it overpredicts maximum erosion by a factor of 10. Generally, the first layer scale set to particle diameter 25 µm has yielded a lot better results and are very comparable to the data particularly for the downstream section. The results and discussions have validated the previously developed theory that it is recommended to set the first layer thickness to particle diameter for erosion simulation utilizing current CFD codes in order to obtain good predictions. There can be more than one wall function or near wall model that is applicable for a specific case. In the subsequent discussion, the effect of different near wall modeling approaches is presented to screen out the best model for erosion simulation. It is found that enhanced wall treatment can be very flexible and is applicable for Test 3 condition. Thus, the results from non-equilibrium wall function and enhanced wall treatment are compared. Fig. 6 demonstrates the results. Fig. 6 shows that both the models can predict the maximum erosion downstream fairly well but can't capture the upstream erosion profile. And, examining the downstream erosion profile, it is seen that nonequilibrium wall function performs better than enhanced wall treatment by correctly predicting two erosion hotspots. Thus, non-equilibrium wall function is applied in the following investigation for all the cases. By far, the comprehensive discussion has reached the best grid configuration and near wall treatment for running erosion simulation which is Mesh 1 and non-equilibrium wall function respectively for this
sharp bend geometry. 3.2. Effect of turbulence model on erosion simulation The effect of different turbulence models is investigated to evaluate the overall performance of commonly used turbulence models with application to erosion simulation for this type of geometry. Besides Reynolds stress model, SST k , RNG k , Realizable k and Standard k are examined. Non-equilibrium wall function is applied to each case. Experimental data of Test 3 is used to determine which model has the best performance in predicting the overall erosion profile. Fig. 7 presents the results for Test 3. It is observed from Fig. 7 that Reynolds Stress Model (RSM) offers the best prediction of erosion pattern and magnitude for both upstream comes as the secondary and downstream sections. Realizable k candidate for modeling erosion in the sharp bend. However, further compared to experimental data, the overall erosion profiles predicted are not as good as Reynolds Stress Model. All the other models can't predict erosion profiles that follow the measured erosion pattern and present highly localized erosion hotspots, which are not physical. All the models seem to predict downstream erosion magnitude better than upstream and there are significant over-predictions of maximum erosion upstream of the sharp bend, but because of the smaller maximum erosion for the upstream, this is compromised. In experiment, it is noticed that for the upstream section particles appears to be fully mixed with fluid that upstream experimental erosion profile is more dispersed and randomly distributed. But, erosion simulations always show significant erosion localization for the upstream section which indicates the deficiencies of current CFD codes on modeling particle-fluid interaction. 197
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Fig. 7. Effect of turbulence model on erosion prediction (Test 3, dp = 25 µm ).
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acceptable accuracy in predicting erosion pattern and the location of hotspots at downstream. However, CFD is not able to capture the erosion pattern at the upstream section. Figs. 10 and 11 present the results for the small particle cases. For fine particles also the same performance is observed. Overall, for all the four tests downstream section erosion profile is captured better than the upstream section erosion profile by current CFD codes. The overall ratios of maximum erosion predicted over experimental data are listed in Table 6 to present a more straightforward evaluation of the proposed CFD based erosion prediction procedure. Table 6 points out the accuracy of the magnitude of the calculated erosion. A factor of 0.53 has been applied for cases with rounded quartz particles to consider particle shape on the resulting erosion. In all cases, maximum erosion belongs to the downstream section of the sharp bend. Two large over-predictions at upstream refer to the cases with smaller particles in which erosion at downstream is significantly greater than upstream. The comprehensive approach previously proposed contains creating meshes with first layer thickness that is capable of predicting particle impact parameters (which can be obtained by examining the resulting predictions and comparing with data), conducting grid refinement along all the relevant directions with the fixed first layer thickness and incorporating different turbulence model induced uncertainties. The summary of predictions presented by Table 6 shows that proposed procedure works very well in predicting both large and small particle erosion for sharp bend geometry. Also, it is observed that the current CFD model package is mostly conservative in predicting erosion which can be favored in practical engineering design.
Table 5 Comparison of predicted maximum erosion from models with data (Test 3). Models
Upstream CFD/Data
Downstream CFD/Data
Maximum erosion location
Standard k- ε RNG k- ε Realizable k- ε SST k-ω RSM with nonequilibrium wall function
58.89 9.74 7.31 15.47 6.16
8.49 2.77 1.39 7.24 1.59
Downstream Downstream Downstream Downstream Downstream
As for the downstream section, experiment presents a symmetric erosion profile with erosion hotspot on each side which is caused by the strong secondary flow inside the downstream pipe. Simulations are able to replicate the same behavior especially results from Reynolds Stress Model can follow experimental data very well. Table 5 compares the maximum values of raw calculated erosion data with the experimental data points. It shows that RSM and Realizable k- ε model perform better in predicting maximum erosion. Reynold Stress Model is the best model in that it can both predict the pattern and magnitude. 3.3. Application and validating the model for all the cases Following figures (Figs. 8–11) present CFD predictions for all the four tests. Grid configuration of Mesh 1 is used but based on the particle size available, first layer thickness is changed to adapt to different particle conditions. First, comparisons are made for large particle represented by Test 1 and Test 4. Next, small particle erosion results (Test 2 and Test 3) are also compared to data. Finally, a table is given to demonstrate the ratio of predicted maximum erosion over experimental data for all four cases. Figs. 8 and 9 show the results for Test 1 and Test 4. It is observed that for larger particle size cases, the measured thickness loss keeps a similar pattern; this consistency is also represented by CFD results. The presented approach has provided an
4. Conclusions The present study suggested that the particle erosion in a sharp bend geometry could be resolved by utilizing available CFD models, however, it was shown that the predictions could be affected drastically by factors including mesh cell size and near wall modeling. The calculations confirmed the validity of the proposed comprehensive procedure for sharp bend geometry. The results following this procedure yielded
Fig. 8. Comparison of erosion profiles for Test 1 (Vinlet =15.2 m/s, dp = 256 μm).
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Fig. 9. Comparison of erosion profiles for Test 4 (Vinlet =26.2 m/s, dp = 256 μm).
Fig. 10. Comparison of upstream erosion profile for Test 2 (Vinlet =15.2 m/s, dp = 25 μm).
the near-wall treatment should also be changed according to the resulting Y+ value. For this work, it turned out non-equilibrium wall function can best simulate near wall particle behavior and the resulting erosion profile. CFD simulations suggested that turbulence modeling is a very important component especially in fully mixing the particles with fluids. The current investigation pointed out that current RANS based CFD models are limited in simulating mixing of particles in straight pipes which resulted in unsatisfactory erosion pattern prediction for the upstream section. For this geometry, Reynolds stress model is the best one to successfully have downstream erosion profile predicted.
fairly good agreement with experimental data especially for the downstream pipe. Though the downstream predictions were around ±50% of the experimental data, considering the fact that erosion phenomenon is complicated and affected by a multitude of factors this level of accuracy is acceptable in many engineering applications. Grid refinement study revealed that increasing mesh density will not always result in more accurate erosion prediction and in some cases, significant over-prediction could be observed. Alongside this comprehensive procedure, this paper also highlights how critical the first layer thickness is by simulating with different first layer thickness scales. To obtain good erosion prediction results, the first layer thickness is recommended to be set to particle diameter and
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Fig. 11. Comparison of upstream erosion profile for Test 3 (Vinlet =26.2 m/s, dp = 25 μm). Table 6 Ratio of maximum predicted erosion to experimental data. Sand condition
256 µm rounded quartz
Test number
Test 1
Test velocity (m/s) Section CFD/Experiment
15.2 Up 0.49
25 µm sharp silica flour Test 4
Down 0.85
Test 2
26.2 Up 0.76
Down 1.47
Acknowledgments
15.2 Up 9.31
Test 3 Down 1.44
26.2 Up 6.16
Down 1.59
[10] P. Zahedi, J. Zhang, H. Arabnejad, B.S. McLaury, S.A. Shirazi, CFD simulation of multiphase flows and erosion predictions under annular flow and low liquid loading conditions, Wear 376–377 (2017) 1260–1270. [11] C. Duarte, F. de Souza, R. Salvo, V. dos Santos, The role of inter-particle collisions on elbow erosion, Int. J. Multiph. Flow 89 (2017) 1–22. [12] H. Zhu, J. Zhu, J. Zhang, H.-Q. Zhang, Sand Erosion Model Prediction, Selection and Comparison for Electrical Submersible Pump (ESP) Using CFD Method, FEDSM 2018-83179, ASME FEDSM, Montreal, Canada, July 14-20, 2018. [13] Z. Wang, J. Zhang, S.A. Shirazi, Yihua Dou, Experimental and numerial study of erosion in a non-Newtonain hydraulic fracturing fluid, Wear 422–423 (2019) 1–8. [14] J. Zhang, B.S. McLaury, S.A.Shirazi, Effect of near wall modeling approaches on solid particle erosion prediction, FEDSM2017-69374, Proceedings of the ASME 2017 Fluids Engineering Summer Meeting, Waikoloa, Hawaii, USA. [15] Xianghui Chen, Brenton S. McLaury, Siamack A. Shirazi, Application and experimental validation of a computational fluid dynamics (CFD) based erosion prediciton model in elbows and plugged tees, Comput. Fluids 33 (2004) 1251–1272. [16] Yongli Zhang, Brenton S. McLaury, Siamack A. Shirazi, Improvements of particle near-wall velocity and erosion predictions using a commercial CFD code, J. Fluids Eng. 131 (3) (2009) 031303. [17] F.N. Fard, B.S. McLaury, S.A.Shirazi, Effect of cell size on particle-eddy interaction and erosion predictions using commercial CFD software (FLUENT), FEDSM201272294, Proceedings of the ASME 2012 Fluids Engineering Summer Meeting, Rio Grande, Puerto Rico. [18] J. Zhang, B.S. McLaury, S.A. Shirazi, Modeling sand fines in elbows mounted in series, Wear 402–403 (2018) 196–206. [19] J. Zhang, B.S. McLaury, S.A. Shirazi, Application and experimental validation of a CFD based erosion prediction procedure for jet impingement geometry, Wear 394–395 (2018) 11–19. [20] R. Russell, S.A. Shirazi, J. Macrae, A new computational fluid dynamics model to predict flow profiels and erosion rates in downhole completion equipment, Proceedings of SPE Annual Technical Conference and Exhibition, 2004 Paper no. SPE 90734.
The authors wish to acknowledge all the member companies that have supported E/CRC research for many years. References [1] S.A. Shirazi, J.R. Shadley, B.S. McLaury, E.F. Rybicki, A procedure to predict solid particle erosion in elbows and tees, J. Press. Vessel Technol. 117 (1) (1995) 45–52. [2] B.S. McLaury, S.A. Shirazi, Predicting erosion in straight pipes, FEDSM 98: Production Operations and Engineering-General, 1999 Houston, Oct3-6. [3] B.S. McLaury, S.A. Shirazi, Generalization of API RP 14E for Erosive Service in Multiphase Production, SPE ATCE: Production Operations and EngineeringGeneral, Houston, 1999 Oct3-6. [4] Y. Zhang, B.S. McLaury, S.A. Shirazi, E.F. Rybicki, A Two-Dimensional Mechanistic Model for Sand Erosion Prediction Including Particle Impact Characteristics, Corrosion, San Antonio, 2010 Paper no. 10378. [5] Edwards, J.K., McLaury, B.S., Shirazi, S.A., Supplementing a CFD Code with Erosion Prediction Capabilities, Paper FEDSM 98-5229 in ASME FED Summer Meeting Proceedings 1998, Wahsington D.C., June 21-25. [6] J.K. Edwards, Development, Validation, and Application of A Three-Dimensional, CFD-Based Erosion Prediction Procedure, PhD Dissertaion, The University of Tulsa, 2000. [7] A. Forder, M. Thew, D. Harrison, A numerical investigation of solid particle erosion experienced within oilfield control valves, Wear 216 (1998) 184–193. [8] Christopher B. Solnordal, Chong Y. Wong, Joan Boulanger, An experimental and numerical analysis of erosion caused by sand pneumatically conveyed through a standard pipe elbow, Wear 336–337 (2015) 43–57. [9] C. Duarte, F. de Souza, V. dos Santos, Numerical investigation of mass loading effects on elbow erosion, Powder Technol. 283 (2015) 593–606.
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