- Email: [email protected]
Predicting erosion in a non-Newtonian shear-thinning jet flow with validated CFD models from PIV and PTV measurements
Wear 426–427 (2019) 501–506
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Predicting erosion in a non-Newtonian shear-thinning jet flow with validated CFD models from PIV and PTV measurements
T
⁎
Zhiguo Wanga, Jun Zhangb, , Siamack A. Shirazib, Yihua Doua a b
School of Mechanical Engineering, Xi'an Shiyou University, Xi'an 710065, China The Erosion/Corrosion Research Center, The University of Tulsa, Tulsa, OK 74104, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Non-Newtonian near wall flow field Particle transportation behavior Erosion prediction PIV and PTV measurements
In oil and gas industry, an increase in production is often achieved by injecting fracturing fluids with particles/ proppants into rocks and reservoirs. There are various fracking fluids that oil and gas companies use, and some of these fracturing fluids demonstrate non-Newtonian flow behavior. In this paper, sand erosion behavior in shearthinning carboxymethyl cellulose (CMC) solution is investigated with a jet impingement facility. Particularly, near wall flow speeds and particle impinging speeds are investigated in shear-thinning CMC fluids by Particle Image Velocimetery (PIV) and Particle Tracing Velocimetery (PTV) techniques. Computational Fluid Dynamics (CFD) are also used to predict the near wall particle impact information. The results indicate that different turbulence models resolve different near wall flow and particle impact characteristics. User Defined Functions (UDF) are developed and used to implement erosion ratio equations and simulate solid particle erosion behavior in the non-Newtonian fluid. The predictions are compared with experimental results. The results of this study can help improving erosion prediction in the hydraulic fracturing process utilizing CFD.
1. Introduction In the oil and gas industry, it is always necessary to increase production by injecting fracturing fluids embedded with particles/proppants into rocks and reservoirs. Severe erosion can take place in tubing and downhole tools during large-scale fracturing work since the fracturing injection rate can be up to 10–12 m3/min and the sand concentration may be up to 30–40% [1]. Wall thickness loss resulting from particles impacts can lead to equipment breakdown and be very costly, especially for high pressure and high temperature wells [2]. It is necessary to develop an accurate erosion model in order to prevent damaging erosion of tubing string and down-hole tools in large-scale fracturing processes. Erosion prediction models can be categorized into empirical models and semi-mechanistic models which are more physical than empirical models as they utilize particle impact information to calculate erosion. The earliest empirical models only use fluid information to estimate erosion which can be very conservative and involves little scientific justification. To improve empirical models, a 1-D semi-mechanistic model with a Newtonian fluid under low pressure condition was developed by Shirazi and McLaury [3,4]. The latest development has extended this model to low Stokes number conditions for Newtonian fluid. The procedure includes a 1-D particle tracking component to ⁎
determine representative particle impact speed, which is then applied in subsequent erosion calculation. However, the 1-D model confines the single representative particle along a stagnation line, which eliminates turbulence effect and misses flow velocities from other directions. The setup has limited applications of the 1-D model, therefore, Zhang et al. [5] developed a simplified CFD-based model which is known as a 2-D model to include turbulence effect on erosion prediction and has added another dimension to the problem. More powerful than the 2-D model, the most comprehensive CFD-based erosion model can consider many additional factors and has been utilized extensively to assess erosion in different flow lines and equipment. Many good practices can be found in the literature [6–8]. However, recently, investigators have found some limitations of the commercially available CFD-based models and have been worked on the models to improve the situation. Zhang et al. [9] has proposed a comprehensive CFD-based erosion simulation procedure which can be applied to a broader Stokes number conditions and is able to obtain good erosion prediction for all the available cases. Also, the authors have developed a procedure to utilize current limitations to improve erosion predictions especially for small particles in diluted gas [10]. The wide existing CFD studies mostly focus on Newtonian fluids that flow in the lines or equipment. Much less investigation has been made on erosion in non-Newtonian fluids. For example, Kowsari et al. [11]
Corresponding author. E-mail address: [email protected] (J. Zhang).
https://doi.org/10.1016/j.wear.2018.12.027 Received 7 September 2018; Received in revised form 4 December 2018; Accepted 12 December 2018 0043-1648/ © 2018 Elsevier B.V. All rights reserved.
Wear 426–427 (2019) 501–506
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made of stainless steel 316. The nozzle diameter (D) is about 7 mm. In the test, the specimen is put 28 mm away from the nozzle center which gives the off-set distance to 4D. The specimen is well mounted to the center of the nozzle. The average velocity exiting the nozzle is 16.8 m/s. The mixer is on during the entire test to avoid sand settlement and keep a homogenous slurry solution. However, for the erosion test, sand concentration in the nozzle is measured and monitored. The nozzle concentration is measured before erosion test, in the middle of the test and after test. The average nozzle concentration is about 0.5%. During the test, temperature is also monitored and it turns out the average temperature is 28 °C and there is no significant temperature change that can result in the change of CMC solution rheology. The total testing time is 24 h. But, the mass loss of the specimen in 3 h and 6 h are also measured and monitored to study erosion behavior for the non-Newtonian fluid. After the test is completed, the erosion profiles are obtained with a 3-D profilometer. In the analysis in order to get an accurate reference surface from the specimen, a code was developed to process the data. The detailed method can be referred to the work by Karimi et al. [14].
Fig. 1. Schematic of the erosion experiment setup.
studied erosion behavior of Al2O3 particles in water and a polymer solution. It is shown that low concentration polymer solution can effectively reduce erosion depth compared to water. In fact, the viscoelastic layer from the polymer can have some self-healing effects to alleviate erosion [12]. As an additional validation and improvement on predicting erosion in fracturing fluids, the present work uses PIV technique to measure flow field in a type of shear-thinning fluid. The data is used to validate current CFD models to simulate non-Newtonian fluid flow. The validated CFD model will then be used to generate flow information for particle tracking and erosion calculation. The particle tracking is also validated with PTV measurement. Finally, an existing erosion ratio equation is applied to evaluate the capability of current models for predicting erosion in the shear-thinning fluid.
2.2. PIV and PTV experimental setup Fig. 3 presents the schematic of the PIV and PTV measurement system. The system includes a liquid jet impingement system, laser source, processor, synchronizer and computer to process the collected data. The flow field is measured through seeding particles. The doublepulsed laser sheet is produced from the laser source to light up the fluid and particles coming from the nozzle. The camera is used to capture pictures of these illuminated particles. In order to reach reasonable accuracy, for each test condition, more than 900 pairs of images are captured and analyzed. For the whole tests, the liquid velocity exiting the nozzle is 10.0 m/s and the CMC solution is 2.5% by weight as it provides more clear fluid to illuminate seeding particles. The test temperature is 23 °C. For the PTV measurement, instead of the seed particles, 300 μm sand particles are introduced to measure near wall particle velocities.
2. Experimental facility and procedure 2.1. Erosion test The erosion experiment is performed at E/CRC with a submerged impingement facility. Fig. 1 shows the schematic of the experimental setup. The experimental system consists of a recirculation pump, control valve, testing tank, impingement nozzle and mixer. Before testing, the CMC solution is prepared based on a weight concentration. The concentration chosen in the particular test is 4% by weight. After the 4% CMC solution is prepared, sand particles are added into the solution ensuring that sand concentration in the tank is 1% by weight. The sand used in the test has a mean diameter of 300 µm. Fig. 2 is the SEM image of the 300 µm sand. The sand density is 2650 kg/m3 and based on the SEM image the shape is considered as sharp. The test specimen is rectangular 70 mm × 45 mm (L × W) and
3. CFD modeling 3.1. Fluid rheology Rotational viscometer is used to measure the rheology of 4.0% CMC and 2.5% CMC solution under 28 °C and 23 °C respectively. The viscosity–shear rate curve is presented in Fig. 4. It is shown in Fig. 4 that the two solutions exhibit shear-thinning behavior as the shear rate increases. This phenomenon is also observed in reference [15]. And, it is found that under very low and very high shear rate the viscosity is approaching a limiting value. In order to accurately fit the experimental data, Cross model is used to regress the data and obtain the rheology equations. The formulation of Cross model is presented below:
Fig. 2. SEM micrograph of 300 µm sharp sand, SEM image was extracted from Zahedi, et al. [13].
Fig. 3. PIV and PTV test section setup for experiment. 502
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mass and pressure gradient forces are considered. The rebound model used in the simulations is from Grant and Tabakoff [18]. For this type of geometry and particle Stokes numbers, erosion results have been demonstrated insensitive to particle rebound model [9]. 3.2.4. Erosion ratio equations Many erosion ratio equations exist in the literature [19]. The typical Finnie-Bitter model [20,21] is a semi-mechanistic erosion model which classifies erosion into cutting and deformation based on erosion mechanism. Latest development on this typical model is conducted at E/ CRC by Arabnejad et al. [22] for different materials. The formulations are presented below: 2.41sin (θ )[2Kcos (θ ) − sin (θ )]
ERC = Fig. 4. Rheology of 2.5 wt% and 4.0 wt% CMC solution.
⎧C1 U ⎨ ⎩
2K2 U2.41cos 2 (θ ) C1 2
ERD = C2 (U sinθ − Utsh)2 η − η∞ 1 = , η0 − η∞ 1 + (λ c γ ̇)n
where, η is the viscosity under shear rate γ̇; η0 and η∞ are viscosities under zero and infinity shear; λc is the time constant, the reciprocal of shear rate which represents the timing when fluid takes on shearthinning behavior; n is the shear-thinning index, which is an indication of the strength of shear-thinning behavior; n = 0 represents Newtonian fluid while n = 1 means the shear-thinning effect is strong. Thus, based on Fig. 4, the fitting parameters for 2.5 wt% CMC solution and 4.0 wt% CMC solution are listed in Table 1.
As it is mentioned above, material mass loss is monitored at 3 h, 6 h and 24 h after tests. Fig. 6 shows the erosion testing results and corresponding relationship between material mass loss and sand throughput. It is observed in Fig. 6 that the mass loss and sand throughput present very good linear relationship which indicates that the slurry flow and particle properties almost have no changes during erosion tests. Erosion profiles of the specimen subjected to slurry flow for 3 h are examined using 3D profilometer. Fig. 7 presents the results. Compared to erosion profiles obtained for water by Mansouri et al. [23] the erosion profile of this non-Newtonian shearing-thinning fluid does not show significant change.
3.2.2. Flow modeling It is critical to select an appropriate flow model to simulate the turbulent jet flows. Previous study has demonstrated the turbulence models play an important role in predicting the jet flow in water [16]. Moreover, an optimized near wall treatment from reference [9] is also set for simulating the non-Newtonian jet flow. The first layer thickness near wall region should be set to the particle average size. Thus, Reynolds stress model, Realizable k-ε model and SST k-ω model with enhanced wall treatment are applied in this study. The fitted Cross model constants are implemented in ANSYS Fluent 17.2 in which the viscosity distribution over the domain will be resolved based on local shear rate. The simulated submerged impingement jet uses velocity inlet at the nozzle entrance and the outlets are set to pressure outlet that is atmospheric.
4.2. PIV measurement and CFD flow field validation The non-Newtonian jet flow field is measured by PIV to validate CFD models. The 2.5 wt% CMC solution is used in the PIV/PTV measurement as it is clearer than the 4.0 wt% CMC solution which facilitates measurements. Thus, the rheology equation is first input in the CFD model and Fig. 8 presents the viscosity distribution over the domain. Fig. 8 demonstrates the shear thinning behavior especially in the near wall region. It shows that the viscosity is reduced while approaching the wall. In order to validate whether this rheology equation can capture the entire flow field characteristics, the jet flow is measured with PIV. The average nozzle velocity is 10 m/s. Fig. 9 shows the axial jet velocity decay from the nozzle outlet to the specimen wall predicted by different turbulence models. It is observed from Fig. 9 that CFD is able to predict the velocity decay along the nozzle center axis. All three turbulence models can predict well compared to the PIV data but the SST k-ω model predicts higher fluid velocity near the wall which is in a better agreement with PIV data as approaching the wall. For particle tracking and erosion prediction, near wall flow field is more important and it is critical to have an accurate prediction on the near wall flow information [24]. Thus, the data is further extracted and analyzed with different
3.2.3. Particle tracking The sand concentration is relatively low (0.5% by weight). Particle effects on fluid and interparticle interaction are not considered in the current particle tracking. The classical DPM based particle tracking is applied. Shape factor for the sand particles in the non-spherical drag law being used is 0.66 based on the findings in reference [17], virtual Table 1 Cross model constants of CMC solutions. η0 [Pa s]
η∞ [Pa s]
Temperature/°C
R2
2.5 4.0
0.0112 0.0075
0.582 0.532
0.100 0.150
0.03 0.03
23 28
0.873 0.866
(3)
4.1. Erosion testing results in shear-thinning CMC fluid
3.2.1. Geometry and CFD Meshing In this study, an optimized mesh is designed for erosion simulations as demonstrated by Zhang, et al. [9]. The geometry and representative meshing strategy is presented in the following figure. Fig. 5
n (-)
Usinθ > > Utsh
(2)
4. Results and discussion
3.2. Mesh and model setup
λc [s]
θ > tan−1 (K )
Where ERC and ERD are cutting and deformation erosion respectively, and C1,C2, K and Utsh are empirical constants and for stainless steel 316 is 4.58 × 10−8, 5.56 × 10−8, 0.4 and 5.8, respectively. If the component Usin θ is below the threshold velocity, then the deformation erosion is set to zero in the implementation. The total erosion is the summation of cutting erosion and deformation erosion
(1)
CMC [%]
θ < tan−1 (K )
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Fig. 5. CFD geometry and meshing.
Fig. 8. Viscosity distribution for the 2.5 wt% CMC solution (Vjet = 10.0 m/s). Fig. 6. Specimen mass loss versus sand mass exiting the nozzle.
Fig. 9. Comparison of axial jet velocity decay profile for 2.5% CMC solution between PIV measurement and CFD predictions (Vjet = 10.0 m/s).
Fig. 7. 3D erosion profiles viewed from the mid-plane after 3 h erosion test.
turbulence models. Fig. 10 compares the near wall flow field results from PIV measurement and CFD models. The off-distance from the wall is only 2.47 mm in the figure. Fig. 10 demonstrates that generally the implemented Cross model for 2.5% CMC solution is capable of predicting reasonable good near wall flow field. For non- Newtonian CMC fluid, Realizable k-ε predicts the lowest level of average velocities near the wall while SST k-ω predicts the highest level and Reynolds stress model is in between. Although Fig. 10 indicates a better agreement of the maximum velocity at the center by the RSM model, the SST model has a better agreement with the data trend for the radial distribution of velocity. Thus, both Figs. 9 and 10 indicate that SST k-ω model is more capable of predicting the velocity distribution near the wall.
4.3. PTV measurement and CFD particle tracking validation For erosion prediction, more importantly, it is essential to successfully capture particle near wall behavior and this relies on accurate flow modeling and particle tracking. Thus, in this part, the DPM-based particle tracking formulation is validated through comparing particle impact speeds obtained from PTV measurement and CFD predictions. Fig. 11 presents the average particle speed distribution in the nonNewtonian jet flow obtained from 900 images of PTV data. It is shown that particles can be accelerated by the flow and when approaching the wall particles are generally experienced a velocity reduction process. To make clear and accurate comparison, particle impact speeds are extracted and compared to CFD predictions with the three turbulence 504
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Fig. 12. Comparison of particle impact speeds from PTV measurement (≤ 300 µm from the wall) and CFD predictions (Vjet = 10.0 m/s). Fig. 10. Near the wall (2.47 mm from the wall) velocity distribution from CFD and PIV for 2.5% CMC solution (Vjet = 10.0 m/s).
Table 2 Total weight loss predicted by different models (Exp. data is 0.1597 g).
models. Fig. 12 presents the results. Fig. 12 shows that different models result in different predicted impact speeds. Compared to data, SST k-ω model with the current nonNewtonian model agrees better with PTV measurements particularly for predicting those particles with higher impact speeds. While RSM and Realizable k-ε (RKE) model are comparable in the resulting particle impact speeds predictions, the models have demonstrated a tendency of underprediciton of the impact speeds. Also, Fig. 12 have further proved the findings in references [9,10,25] that it is critical to set the first layer thickness to the particle size for erosion prediction so as to obtain reasonably good impact parameters for erosion prediction. This is also further demonstrated in Ref. [26].
Number
λc [s]
n (-)
η0 [Pa s]
η∞ [Pa s]
Total weight loss
Error (%)
1 2 3 4
0.0075 0.0075 0.0075 0.0060
0.532 0.532 0.684 0.532
0.150 0.120 0.150 0.150
0.03 0.03 0.03 0.03
0.141 0.144 0.104 0.137
− 11.8 − 10.07 − 34.7 − 14.3
4.4. Sensitivity of Cross model parameters on erosion prediction The comprehensive CFD models are validated with PIV and PTV measurements. SST k-ω model agrees better with both PIV and PTV measurements. It is then applied to predict erosion for the testing case with 4.0 wt% CMC solution. To show that the accuracy of the nonNewtonian Cross model used in this study, a sensitivity study is performed by varying the used parameters in Cross model. The main three parameters, the zero shear viscosity η0, the time constant λ and the index of shear thinning n are changed by 20% based on the results of the 4.0% CMC solutions in Table 1. Table 2 listed the matrix for the sensitivity analysis of CFD prediction. The results of simulations are shown in Fig. 13 and the error analysis of weight loss is also listed in
Fig. 13. Effect of Cross model parameters on erosion prediction.
Fig. 11. Particle speeds distribution through PTV measurement (Vjet = 10.0 m/s). 505
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Table 2. Fig. 13 and Table 2 present that the radial location of maximum erosion and the weight loss will be affected by 10–35% if the parameters of Cross model are changed by about 20%. The effects are more pronounced on the weight loss predictions if the shear thinning power index increases. Therefore, it is important to obtain accurate rheology parameters for shear thinning fluids before CFD-based erosion prediction can be performed for non-Newtonian fluids.
hydraulic fracturing, Annu. Rev. Chem. Biomol. Eng. 7 (2016) 415–453. [2] J. Zhang, J. Kang, J. Fan, J. Gao, Study on erosion wear of fracturing pipeline under the action of multiphase flow in oil & gas industry, J. Nat. Gas. Sci. Eng. 32 (2016) 334–346. [3] B.S. McLaury, S.A. Shirazi, An alternate method to API RP 14E for predicting solids erosion in multiphase flow, J. Energy Resour. Technol. 122 (2000) 115–122. [4] S.A. Shirazi, B.S. Mclaury, H. Arabnejad, T. Erosion, A semi-mechanistic model for predicting sand erosion threshold velocities in gas and multiphase flow production, SPE-181487-MS, ATCE,Dubai, UAE, 2016. [5] Y. Zhang, B.S. McLaury, S.A. Shirazi, E.F. Rybicki, A two-dimensional mechanistic model for sand erosion prediction including particle impact characteristics, in: Proceedings of the NACE International Corrosion Conference Exposition 2010, pp. 1–19. [6] T.N. Hunter, T. Unsworth, S.R. Biggs, The influence of system scale on impinging jet sediment erosion: observed using novel and standard measurement techniques The influence of system scale on impinging jet sediment, Chem. Eng. Res. Des. 91 (4) (2013) 722–734. [7] G.V. Messa, S. Malavasi, The effect of sub-models and parameterizations in the simulation of abrasive jet impingement tests, Wear 370–371 (2017) 59–72. [8] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear (2015) 332–333. [9] 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. [10] J. Zhang, B.S. McLaury, S.A. Shirazi, Modeling sand fines erosion in elbows mounted in series, Wear 402–403 (2018) 196–206. [11] K. Kowsari, D.F. James, M. Papini, J.K. Spelt, The effects of dilute polymer solution elasticity and viscosity on abrasive slurry jet micro-machining of glass, Wear 309 (2014) 112–119. [12] M.W. Keller, K. Hampton, B. Mclaury, Self-healing of erosion damage in a polymer coating, Wear 307 (2013) 218–225. [13] P. Zahedi, S. Parvandeh, A. Asgharpour, B.S. McLaury, S.A. Shirazi, B.A.McKinney.random forest regression prediction of solid particle erosion in elbows, Powder Technol. 338 (2018) 983–992. [14] S. Karimi, A. Mansouri, S.A. Shirazi, B.S. McLaury, Experimental Investigation on the Influence of Particle Size in a Submerged Slurry Jet on Erosion Rates and Patterns, in: Proceedings of the ASME 2017 Fluids Engineering Division Summer Meeting, 2017,p. 11. FEDSM2017-69350. [15] A. Benchabane, K. Bekkour, Rheological properties of carboxymethyl cellulose (CMC) solutions, Colloid Polym. Sci. 286 (2008) 1173–1180. [16] Y. Zhang, E.P. Reuterfors, B.S. McLaury, S.A. Shirazi, E.F. Rybicki, Comparison of computed and measured particle velocities and erosion in water and air flows, Wear 263 (2007) 330–338. [17] A. Haider, O. Levenspiel, Drag coefficient and terminal velocity of spherical and non-spherical particles, Powder Technol. 58 (1) (1989) 63–70. [18] G. Grant, W. Tabakoff, Erosion prediction in turbomachinery resulting from environmental solid particles, J. Aircr. 12 (1975) 471–478. [19] Y.I. Oka, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact. Part 2: mechanical properties of materials directly associated with erosion damage, Wear 259 (2005) 102–109. [20] I. Finnie, Erosion of surfaces by solid particles, Wear 3 (2) (1960) 87–103. [21] J.G.A. Bitter, A study of erosion phenomena part I, Wear 6 (1) (1963) 5–21. [22] H. Arabnejad, A. Mansouri, S.A. Shirazi, B.S. McLaury, Development of mechanistic erosion equation for solid particles, Wear 332–333 (2015) 1044–1050. [23] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear 332–333 (2015) 1090–1097. [24] J. Zhang, Improvements to a semi-mechanistic erosion prediction procedure, (Ph.D. Dissertation), Department of Mechanical Engineering, The University of Tulsa, Tulsa, OK, USA. [25] J. Zhang, B.S. McLaury, S.A. Shirazi, Effect of near wall modeling approaches on solid particle erosion prediction, in: Proceedings of the ASME 2017 Fluids Engineering Divison Summer Meeting. 2017: p. V01CT15A009. [26] G.V. Messa, Y. Wang, Importance of accounting for finite particle size in CFD-based erosion prediction, in: Proceedings of the ASME Pressure Vessels & Piping Conference PVP: 2018,p. V004T04A028.
5. Conclusion This work has presented a systematic procedure for predicting erosion in a non-Newtonian shear-thinning CMC solution. The following conclusions can be made: (1) CMC solutions can exhibit non-Newtonian shear-thinning behavior. Erosion profiles of 300 µm sand particle in the CMC shear-thinning fluid are not dramatically different from those in water. (2) The implemented Cross model with CFD can resolve the nonNewtonian flow field that is comparable to PIV measurement. (3) Current particle tracking scheme can well handle predicting particle impact speeds in the CMC shear-thinning fluid. Amongst, SST k-ω can yield a better prediction with PTV measurement. PIV and PTV results have indicated that SST k-ω can provide better predictions of the flow field and particle speeds compared to other models. More measurements are required to draw a deterministic conclusion. (4) For this specific case considered, with all corresponding settings of the CFD-based erosion prediction model, the results from SST k-ω and a non-Newtonian Cross model can agree with the experimental data trend. (5) A sensitivity study is performed for the current non-Newtonian model used here in this study. The results indicate that it is important to obtain accurate rheology parameters for shear thinning fluids before CFD-based erosion prediction can be performed for non-Newtonian fluids. Acknowledgements The authors wish to acknowledge the support of National Natural Science Foundation of China (No. 51674199) and the University of Tulsa and the Erosion/Corrosion Research Center (E/CRC) member companies. Dr. Wang also acknowledges the Visiting Scholar Plan by Young Teachers for Advanced Study Abroad of SXYU. Thanks to Matthew Fulton for his help in conducting the PIV and PTV experiments at E/CRC. References [1] A.C. Barbati, J. Desroches, A. Robisson, G.H. McKinley, Complex fluids and
506
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Predicting erosion in a non-Newtonian shear-thinning jet flow with validated CFD models from PIV and PTV measurements
T
⁎
Zhiguo Wanga, Jun Zhangb, , Siamack A. Shirazib, Yihua Doua a b
School of Mechanical Engineering, Xi'an Shiyou University, Xi'an 710065, China The Erosion/Corrosion Research Center, The University of Tulsa, Tulsa, OK 74104, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Non-Newtonian near wall flow field Particle transportation behavior Erosion prediction PIV and PTV measurements
In oil and gas industry, an increase in production is often achieved by injecting fracturing fluids with particles/ proppants into rocks and reservoirs. There are various fracking fluids that oil and gas companies use, and some of these fracturing fluids demonstrate non-Newtonian flow behavior. In this paper, sand erosion behavior in shearthinning carboxymethyl cellulose (CMC) solution is investigated with a jet impingement facility. Particularly, near wall flow speeds and particle impinging speeds are investigated in shear-thinning CMC fluids by Particle Image Velocimetery (PIV) and Particle Tracing Velocimetery (PTV) techniques. Computational Fluid Dynamics (CFD) are also used to predict the near wall particle impact information. The results indicate that different turbulence models resolve different near wall flow and particle impact characteristics. User Defined Functions (UDF) are developed and used to implement erosion ratio equations and simulate solid particle erosion behavior in the non-Newtonian fluid. The predictions are compared with experimental results. The results of this study can help improving erosion prediction in the hydraulic fracturing process utilizing CFD.
1. Introduction In the oil and gas industry, it is always necessary to increase production by injecting fracturing fluids embedded with particles/proppants into rocks and reservoirs. Severe erosion can take place in tubing and downhole tools during large-scale fracturing work since the fracturing injection rate can be up to 10–12 m3/min and the sand concentration may be up to 30–40% [1]. Wall thickness loss resulting from particles impacts can lead to equipment breakdown and be very costly, especially for high pressure and high temperature wells [2]. It is necessary to develop an accurate erosion model in order to prevent damaging erosion of tubing string and down-hole tools in large-scale fracturing processes. Erosion prediction models can be categorized into empirical models and semi-mechanistic models which are more physical than empirical models as they utilize particle impact information to calculate erosion. The earliest empirical models only use fluid information to estimate erosion which can be very conservative and involves little scientific justification. To improve empirical models, a 1-D semi-mechanistic model with a Newtonian fluid under low pressure condition was developed by Shirazi and McLaury [3,4]. The latest development has extended this model to low Stokes number conditions for Newtonian fluid. The procedure includes a 1-D particle tracking component to ⁎
determine representative particle impact speed, which is then applied in subsequent erosion calculation. However, the 1-D model confines the single representative particle along a stagnation line, which eliminates turbulence effect and misses flow velocities from other directions. The setup has limited applications of the 1-D model, therefore, Zhang et al. [5] developed a simplified CFD-based model which is known as a 2-D model to include turbulence effect on erosion prediction and has added another dimension to the problem. More powerful than the 2-D model, the most comprehensive CFD-based erosion model can consider many additional factors and has been utilized extensively to assess erosion in different flow lines and equipment. Many good practices can be found in the literature [6–8]. However, recently, investigators have found some limitations of the commercially available CFD-based models and have been worked on the models to improve the situation. Zhang et al. [9] has proposed a comprehensive CFD-based erosion simulation procedure which can be applied to a broader Stokes number conditions and is able to obtain good erosion prediction for all the available cases. Also, the authors have developed a procedure to utilize current limitations to improve erosion predictions especially for small particles in diluted gas [10]. The wide existing CFD studies mostly focus on Newtonian fluids that flow in the lines or equipment. Much less investigation has been made on erosion in non-Newtonian fluids. For example, Kowsari et al. [11]
Corresponding author. E-mail address: [email protected] (J. Zhang).
https://doi.org/10.1016/j.wear.2018.12.027 Received 7 September 2018; Received in revised form 4 December 2018; Accepted 12 December 2018 0043-1648/ © 2018 Elsevier B.V. All rights reserved.
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made of stainless steel 316. The nozzle diameter (D) is about 7 mm. In the test, the specimen is put 28 mm away from the nozzle center which gives the off-set distance to 4D. The specimen is well mounted to the center of the nozzle. The average velocity exiting the nozzle is 16.8 m/s. The mixer is on during the entire test to avoid sand settlement and keep a homogenous slurry solution. However, for the erosion test, sand concentration in the nozzle is measured and monitored. The nozzle concentration is measured before erosion test, in the middle of the test and after test. The average nozzle concentration is about 0.5%. During the test, temperature is also monitored and it turns out the average temperature is 28 °C and there is no significant temperature change that can result in the change of CMC solution rheology. The total testing time is 24 h. But, the mass loss of the specimen in 3 h and 6 h are also measured and monitored to study erosion behavior for the non-Newtonian fluid. After the test is completed, the erosion profiles are obtained with a 3-D profilometer. In the analysis in order to get an accurate reference surface from the specimen, a code was developed to process the data. The detailed method can be referred to the work by Karimi et al. [14].
Fig. 1. Schematic of the erosion experiment setup.
studied erosion behavior of Al2O3 particles in water and a polymer solution. It is shown that low concentration polymer solution can effectively reduce erosion depth compared to water. In fact, the viscoelastic layer from the polymer can have some self-healing effects to alleviate erosion [12]. As an additional validation and improvement on predicting erosion in fracturing fluids, the present work uses PIV technique to measure flow field in a type of shear-thinning fluid. The data is used to validate current CFD models to simulate non-Newtonian fluid flow. The validated CFD model will then be used to generate flow information for particle tracking and erosion calculation. The particle tracking is also validated with PTV measurement. Finally, an existing erosion ratio equation is applied to evaluate the capability of current models for predicting erosion in the shear-thinning fluid.
2.2. PIV and PTV experimental setup Fig. 3 presents the schematic of the PIV and PTV measurement system. The system includes a liquid jet impingement system, laser source, processor, synchronizer and computer to process the collected data. The flow field is measured through seeding particles. The doublepulsed laser sheet is produced from the laser source to light up the fluid and particles coming from the nozzle. The camera is used to capture pictures of these illuminated particles. In order to reach reasonable accuracy, for each test condition, more than 900 pairs of images are captured and analyzed. For the whole tests, the liquid velocity exiting the nozzle is 10.0 m/s and the CMC solution is 2.5% by weight as it provides more clear fluid to illuminate seeding particles. The test temperature is 23 °C. For the PTV measurement, instead of the seed particles, 300 μm sand particles are introduced to measure near wall particle velocities.
2. Experimental facility and procedure 2.1. Erosion test The erosion experiment is performed at E/CRC with a submerged impingement facility. Fig. 1 shows the schematic of the experimental setup. The experimental system consists of a recirculation pump, control valve, testing tank, impingement nozzle and mixer. Before testing, the CMC solution is prepared based on a weight concentration. The concentration chosen in the particular test is 4% by weight. After the 4% CMC solution is prepared, sand particles are added into the solution ensuring that sand concentration in the tank is 1% by weight. The sand used in the test has a mean diameter of 300 µm. Fig. 2 is the SEM image of the 300 µm sand. The sand density is 2650 kg/m3 and based on the SEM image the shape is considered as sharp. The test specimen is rectangular 70 mm × 45 mm (L × W) and
3. CFD modeling 3.1. Fluid rheology Rotational viscometer is used to measure the rheology of 4.0% CMC and 2.5% CMC solution under 28 °C and 23 °C respectively. The viscosity–shear rate curve is presented in Fig. 4. It is shown in Fig. 4 that the two solutions exhibit shear-thinning behavior as the shear rate increases. This phenomenon is also observed in reference [15]. And, it is found that under very low and very high shear rate the viscosity is approaching a limiting value. In order to accurately fit the experimental data, Cross model is used to regress the data and obtain the rheology equations. The formulation of Cross model is presented below:
Fig. 2. SEM micrograph of 300 µm sharp sand, SEM image was extracted from Zahedi, et al. [13].
Fig. 3. PIV and PTV test section setup for experiment. 502
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mass and pressure gradient forces are considered. The rebound model used in the simulations is from Grant and Tabakoff [18]. For this type of geometry and particle Stokes numbers, erosion results have been demonstrated insensitive to particle rebound model [9]. 3.2.4. Erosion ratio equations Many erosion ratio equations exist in the literature [19]. The typical Finnie-Bitter model [20,21] is a semi-mechanistic erosion model which classifies erosion into cutting and deformation based on erosion mechanism. Latest development on this typical model is conducted at E/ CRC by Arabnejad et al. [22] for different materials. The formulations are presented below: 2.41sin (θ )[2Kcos (θ ) − sin (θ )]
ERC = Fig. 4. Rheology of 2.5 wt% and 4.0 wt% CMC solution.
⎧C1 U ⎨ ⎩
2K2 U2.41cos 2 (θ ) C1 2
ERD = C2 (U sinθ − Utsh)2 η − η∞ 1 = , η0 − η∞ 1 + (λ c γ ̇)n
where, η is the viscosity under shear rate γ̇; η0 and η∞ are viscosities under zero and infinity shear; λc is the time constant, the reciprocal of shear rate which represents the timing when fluid takes on shearthinning behavior; n is the shear-thinning index, which is an indication of the strength of shear-thinning behavior; n = 0 represents Newtonian fluid while n = 1 means the shear-thinning effect is strong. Thus, based on Fig. 4, the fitting parameters for 2.5 wt% CMC solution and 4.0 wt% CMC solution are listed in Table 1.
As it is mentioned above, material mass loss is monitored at 3 h, 6 h and 24 h after tests. Fig. 6 shows the erosion testing results and corresponding relationship between material mass loss and sand throughput. It is observed in Fig. 6 that the mass loss and sand throughput present very good linear relationship which indicates that the slurry flow and particle properties almost have no changes during erosion tests. Erosion profiles of the specimen subjected to slurry flow for 3 h are examined using 3D profilometer. Fig. 7 presents the results. Compared to erosion profiles obtained for water by Mansouri et al. [23] the erosion profile of this non-Newtonian shearing-thinning fluid does not show significant change.
3.2.2. Flow modeling It is critical to select an appropriate flow model to simulate the turbulent jet flows. Previous study has demonstrated the turbulence models play an important role in predicting the jet flow in water [16]. Moreover, an optimized near wall treatment from reference [9] is also set for simulating the non-Newtonian jet flow. The first layer thickness near wall region should be set to the particle average size. Thus, Reynolds stress model, Realizable k-ε model and SST k-ω model with enhanced wall treatment are applied in this study. The fitted Cross model constants are implemented in ANSYS Fluent 17.2 in which the viscosity distribution over the domain will be resolved based on local shear rate. The simulated submerged impingement jet uses velocity inlet at the nozzle entrance and the outlets are set to pressure outlet that is atmospheric.
4.2. PIV measurement and CFD flow field validation The non-Newtonian jet flow field is measured by PIV to validate CFD models. The 2.5 wt% CMC solution is used in the PIV/PTV measurement as it is clearer than the 4.0 wt% CMC solution which facilitates measurements. Thus, the rheology equation is first input in the CFD model and Fig. 8 presents the viscosity distribution over the domain. Fig. 8 demonstrates the shear thinning behavior especially in the near wall region. It shows that the viscosity is reduced while approaching the wall. In order to validate whether this rheology equation can capture the entire flow field characteristics, the jet flow is measured with PIV. The average nozzle velocity is 10 m/s. Fig. 9 shows the axial jet velocity decay from the nozzle outlet to the specimen wall predicted by different turbulence models. It is observed from Fig. 9 that CFD is able to predict the velocity decay along the nozzle center axis. All three turbulence models can predict well compared to the PIV data but the SST k-ω model predicts higher fluid velocity near the wall which is in a better agreement with PIV data as approaching the wall. For particle tracking and erosion prediction, near wall flow field is more important and it is critical to have an accurate prediction on the near wall flow information [24]. Thus, the data is further extracted and analyzed with different
3.2.3. Particle tracking The sand concentration is relatively low (0.5% by weight). Particle effects on fluid and interparticle interaction are not considered in the current particle tracking. The classical DPM based particle tracking is applied. Shape factor for the sand particles in the non-spherical drag law being used is 0.66 based on the findings in reference [17], virtual Table 1 Cross model constants of CMC solutions. η0 [Pa s]
η∞ [Pa s]
Temperature/°C
R2
2.5 4.0
0.0112 0.0075
0.582 0.532
0.100 0.150
0.03 0.03
23 28
0.873 0.866
(3)
4.1. Erosion testing results in shear-thinning CMC fluid
3.2.1. Geometry and CFD Meshing In this study, an optimized mesh is designed for erosion simulations as demonstrated by Zhang, et al. [9]. The geometry and representative meshing strategy is presented in the following figure. Fig. 5
n (-)
Usinθ > > Utsh
(2)
4. Results and discussion
3.2. Mesh and model setup
λc [s]
θ > tan−1 (K )
Where ERC and ERD are cutting and deformation erosion respectively, and C1,C2, K and Utsh are empirical constants and for stainless steel 316 is 4.58 × 10−8, 5.56 × 10−8, 0.4 and 5.8, respectively. If the component Usin θ is below the threshold velocity, then the deformation erosion is set to zero in the implementation. The total erosion is the summation of cutting erosion and deformation erosion
(1)
CMC [%]
θ < tan−1 (K )
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Fig. 5. CFD geometry and meshing.
Fig. 8. Viscosity distribution for the 2.5 wt% CMC solution (Vjet = 10.0 m/s). Fig. 6. Specimen mass loss versus sand mass exiting the nozzle.
Fig. 9. Comparison of axial jet velocity decay profile for 2.5% CMC solution between PIV measurement and CFD predictions (Vjet = 10.0 m/s).
Fig. 7. 3D erosion profiles viewed from the mid-plane after 3 h erosion test.
turbulence models. Fig. 10 compares the near wall flow field results from PIV measurement and CFD models. The off-distance from the wall is only 2.47 mm in the figure. Fig. 10 demonstrates that generally the implemented Cross model for 2.5% CMC solution is capable of predicting reasonable good near wall flow field. For non- Newtonian CMC fluid, Realizable k-ε predicts the lowest level of average velocities near the wall while SST k-ω predicts the highest level and Reynolds stress model is in between. Although Fig. 10 indicates a better agreement of the maximum velocity at the center by the RSM model, the SST model has a better agreement with the data trend for the radial distribution of velocity. Thus, both Figs. 9 and 10 indicate that SST k-ω model is more capable of predicting the velocity distribution near the wall.
4.3. PTV measurement and CFD particle tracking validation For erosion prediction, more importantly, it is essential to successfully capture particle near wall behavior and this relies on accurate flow modeling and particle tracking. Thus, in this part, the DPM-based particle tracking formulation is validated through comparing particle impact speeds obtained from PTV measurement and CFD predictions. Fig. 11 presents the average particle speed distribution in the nonNewtonian jet flow obtained from 900 images of PTV data. It is shown that particles can be accelerated by the flow and when approaching the wall particles are generally experienced a velocity reduction process. To make clear and accurate comparison, particle impact speeds are extracted and compared to CFD predictions with the three turbulence 504
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Fig. 12. Comparison of particle impact speeds from PTV measurement (≤ 300 µm from the wall) and CFD predictions (Vjet = 10.0 m/s). Fig. 10. Near the wall (2.47 mm from the wall) velocity distribution from CFD and PIV for 2.5% CMC solution (Vjet = 10.0 m/s).
Table 2 Total weight loss predicted by different models (Exp. data is 0.1597 g).
models. Fig. 12 presents the results. Fig. 12 shows that different models result in different predicted impact speeds. Compared to data, SST k-ω model with the current nonNewtonian model agrees better with PTV measurements particularly for predicting those particles with higher impact speeds. While RSM and Realizable k-ε (RKE) model are comparable in the resulting particle impact speeds predictions, the models have demonstrated a tendency of underprediciton of the impact speeds. Also, Fig. 12 have further proved the findings in references [9,10,25] that it is critical to set the first layer thickness to the particle size for erosion prediction so as to obtain reasonably good impact parameters for erosion prediction. This is also further demonstrated in Ref. [26].
Number
λc [s]
n (-)
η0 [Pa s]
η∞ [Pa s]
Total weight loss
Error (%)
1 2 3 4
0.0075 0.0075 0.0075 0.0060
0.532 0.532 0.684 0.532
0.150 0.120 0.150 0.150
0.03 0.03 0.03 0.03
0.141 0.144 0.104 0.137
− 11.8 − 10.07 − 34.7 − 14.3
4.4. Sensitivity of Cross model parameters on erosion prediction The comprehensive CFD models are validated with PIV and PTV measurements. SST k-ω model agrees better with both PIV and PTV measurements. It is then applied to predict erosion for the testing case with 4.0 wt% CMC solution. To show that the accuracy of the nonNewtonian Cross model used in this study, a sensitivity study is performed by varying the used parameters in Cross model. The main three parameters, the zero shear viscosity η0, the time constant λ and the index of shear thinning n are changed by 20% based on the results of the 4.0% CMC solutions in Table 1. Table 2 listed the matrix for the sensitivity analysis of CFD prediction. The results of simulations are shown in Fig. 13 and the error analysis of weight loss is also listed in
Fig. 13. Effect of Cross model parameters on erosion prediction.
Fig. 11. Particle speeds distribution through PTV measurement (Vjet = 10.0 m/s). 505
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Table 2. Fig. 13 and Table 2 present that the radial location of maximum erosion and the weight loss will be affected by 10–35% if the parameters of Cross model are changed by about 20%. The effects are more pronounced on the weight loss predictions if the shear thinning power index increases. Therefore, it is important to obtain accurate rheology parameters for shear thinning fluids before CFD-based erosion prediction can be performed for non-Newtonian fluids.
hydraulic fracturing, Annu. Rev. Chem. Biomol. Eng. 7 (2016) 415–453. [2] J. Zhang, J. Kang, J. Fan, J. Gao, Study on erosion wear of fracturing pipeline under the action of multiphase flow in oil & gas industry, J. Nat. Gas. Sci. Eng. 32 (2016) 334–346. [3] B.S. McLaury, S.A. Shirazi, An alternate method to API RP 14E for predicting solids erosion in multiphase flow, J. Energy Resour. Technol. 122 (2000) 115–122. [4] S.A. Shirazi, B.S. Mclaury, H. Arabnejad, T. Erosion, A semi-mechanistic model for predicting sand erosion threshold velocities in gas and multiphase flow production, SPE-181487-MS, ATCE,Dubai, UAE, 2016. [5] Y. Zhang, B.S. McLaury, S.A. Shirazi, E.F. Rybicki, A two-dimensional mechanistic model for sand erosion prediction including particle impact characteristics, in: Proceedings of the NACE International Corrosion Conference Exposition 2010, pp. 1–19. [6] T.N. Hunter, T. Unsworth, S.R. Biggs, The influence of system scale on impinging jet sediment erosion: observed using novel and standard measurement techniques The influence of system scale on impinging jet sediment, Chem. Eng. Res. Des. 91 (4) (2013) 722–734. [7] G.V. Messa, S. Malavasi, The effect of sub-models and parameterizations in the simulation of abrasive jet impingement tests, Wear 370–371 (2017) 59–72. [8] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear (2015) 332–333. [9] 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. [10] J. Zhang, B.S. McLaury, S.A. Shirazi, Modeling sand fines erosion in elbows mounted in series, Wear 402–403 (2018) 196–206. [11] K. Kowsari, D.F. James, M. Papini, J.K. Spelt, The effects of dilute polymer solution elasticity and viscosity on abrasive slurry jet micro-machining of glass, Wear 309 (2014) 112–119. [12] M.W. Keller, K. Hampton, B. Mclaury, Self-healing of erosion damage in a polymer coating, Wear 307 (2013) 218–225. [13] P. Zahedi, S. Parvandeh, A. Asgharpour, B.S. McLaury, S.A. Shirazi, B.A.McKinney.random forest regression prediction of solid particle erosion in elbows, Powder Technol. 338 (2018) 983–992. [14] S. Karimi, A. Mansouri, S.A. Shirazi, B.S. McLaury, Experimental Investigation on the Influence of Particle Size in a Submerged Slurry Jet on Erosion Rates and Patterns, in: Proceedings of the ASME 2017 Fluids Engineering Division Summer Meeting, 2017,p. 11. FEDSM2017-69350. [15] A. Benchabane, K. Bekkour, Rheological properties of carboxymethyl cellulose (CMC) solutions, Colloid Polym. Sci. 286 (2008) 1173–1180. [16] Y. Zhang, E.P. Reuterfors, B.S. McLaury, S.A. Shirazi, E.F. Rybicki, Comparison of computed and measured particle velocities and erosion in water and air flows, Wear 263 (2007) 330–338. [17] A. Haider, O. Levenspiel, Drag coefficient and terminal velocity of spherical and non-spherical particles, Powder Technol. 58 (1) (1989) 63–70. [18] G. Grant, W. Tabakoff, Erosion prediction in turbomachinery resulting from environmental solid particles, J. Aircr. 12 (1975) 471–478. [19] Y.I. Oka, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact. Part 2: mechanical properties of materials directly associated with erosion damage, Wear 259 (2005) 102–109. [20] I. Finnie, Erosion of surfaces by solid particles, Wear 3 (2) (1960) 87–103. [21] J.G.A. Bitter, A study of erosion phenomena part I, Wear 6 (1) (1963) 5–21. [22] H. Arabnejad, A. Mansouri, S.A. Shirazi, B.S. McLaury, Development of mechanistic erosion equation for solid particles, Wear 332–333 (2015) 1044–1050. [23] A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear 332–333 (2015) 1090–1097. [24] J. Zhang, Improvements to a semi-mechanistic erosion prediction procedure, (Ph.D. Dissertation), Department of Mechanical Engineering, The University of Tulsa, Tulsa, OK, USA. [25] J. Zhang, B.S. McLaury, S.A. Shirazi, Effect of near wall modeling approaches on solid particle erosion prediction, in: Proceedings of the ASME 2017 Fluids Engineering Divison Summer Meeting. 2017: p. V01CT15A009. [26] G.V. Messa, Y. Wang, Importance of accounting for finite particle size in CFD-based erosion prediction, in: Proceedings of the ASME Pressure Vessels & Piping Conference PVP: 2018,p. V004T04A028.
5. Conclusion This work has presented a systematic procedure for predicting erosion in a non-Newtonian shear-thinning CMC solution. The following conclusions can be made: (1) CMC solutions can exhibit non-Newtonian shear-thinning behavior. Erosion profiles of 300 µm sand particle in the CMC shear-thinning fluid are not dramatically different from those in water. (2) The implemented Cross model with CFD can resolve the nonNewtonian flow field that is comparable to PIV measurement. (3) Current particle tracking scheme can well handle predicting particle impact speeds in the CMC shear-thinning fluid. Amongst, SST k-ω can yield a better prediction with PTV measurement. PIV and PTV results have indicated that SST k-ω can provide better predictions of the flow field and particle speeds compared to other models. More measurements are required to draw a deterministic conclusion. (4) For this specific case considered, with all corresponding settings of the CFD-based erosion prediction model, the results from SST k-ω and a non-Newtonian Cross model can agree with the experimental data trend. (5) A sensitivity study is performed for the current non-Newtonian model used here in this study. The results indicate that it is important to obtain accurate rheology parameters for shear thinning fluids before CFD-based erosion prediction can be performed for non-Newtonian fluids. Acknowledgements The authors wish to acknowledge the support of National Natural Science Foundation of China (No. 51674199) and the University of Tulsa and the Erosion/Corrosion Research Center (E/CRC) member companies. Dr. Wang also acknowledges the Visiting Scholar Plan by Young Teachers for Advanced Study Abroad of SXYU. Thanks to Matthew Fulton for his help in conducting the PIV and PTV experiments at E/CRC. References [1] A.C. Barbati, J. Desroches, A. Robisson, G.H. McKinley, Complex fluids and
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