Application and experimental validation of a CFD based erosion prediction procedure for jet impingement geometry

Author’s Accepted Manuscript Application and experimental validation of a CFD based erosion prediction procedure for jet impingement geometry Jun Zhang, Brenton S. McLaury, Siamack A. Shirazi www.elsevier.com/locate/wear

PII: DOI: Reference:

S0043-1648(17)31071-2 https://doi.org/10.1016/j.wear.2017.10.001 WEA102264

To appear in: Wear Cite this article as: Jun Zhang, Brenton S. McLaury and Siamack A. Shirazi, Application and experimental validation of a CFD based erosion prediction procedure for jet impingement geometry, Wear, https://doi.org/10.1016/j.wear.2017.10.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Application and experimental validation of a CFD based erosion prediction procedure for jet impingement geometry Jun Zhang, Brenton S. McLaury, Siamack A. Shirazi The Erosion/Corrosion Research Center, Department of Mechanical Engineering, The University of Tulsa, Tulsa, OK, 74104, USA Abstract Computational Fluid Dynamics (CFD) based erosion prediction procedures are carried out to predict erosion for a submerged liquid jet impingement geometry. 3-D modeling with different near wall treatments are employed to simulate the wall bounded turbulent jet flow. Discrete Phase Model (DPM) is applied to track particles and obtain particle impact characteristics. Erosion is calculated using typical erosion ratio equations in the literature [1]. In this paper, two categories of near wall modeling approaches (wall functions and near wall models) are presented and examined. Particle impact parameters are extracted and compared with measured data to determine the most accurate near wall modeling approaches. A procedure for grid refinement particular for erosion simulations is proposed and followed by uncertainty analysis from the CFD predictions. Experimental data with uncertainty quantified for 300 μm large particles and 25 μm small particles are utilized to validate the proposed procedure. It is shown that following the proposed procedure yields very good erosion prediction from CFD regardless of particle size. Keywords: CFD; Erosion; Near-wall modeling; CFD based erosion modeling procedure; Uncertainty analysis 1.

Introduction

Being able to predict solid particle erosion is of significant importance to many industries including mining and oil and gas production. Computational Fluid Dynamics (CFD) has been widely used to predict erosion caused by solid particles. This technique consists of three components which are flow modeling, particle tracking and erosion calculation through erosion ratio equations. It has been acknowledged that the grid utilized in this technique affects both flow modeling and particle tracking [2], [3]. With respect to flow modeling, grids used, particularly in the near wall regions, affect the resolution of the near wall flow field. A coarse mesh is often used together with wall functions to approximate the near wall mean flow and turbulence field. This approach may be unable to provide sufficiently accurate flow field information in the region between the first near wall cell layer center and the wall. A fine mesh with near wall models, however, can solve the near-wall flow field all the way to the wall with boundary layer adequately resolved. Particle tracking also relies on the grids being used to calculate the flow field. A particle is re-located based on mesh topology information and advanced cell by cell. In turbulent flow, turbulent dispersion of particles is often modeled by an eddy interaction model (EIM) [4] in which particle dispersion is determined by a particle interacting with a succession of eddies of which velocity and time scales are calculated based on turbulent quantities within the local cell while the mean fluid velocity is constant. Currently, in most commercially available CFD codes that contain particle tracking procedures, particles are treated as a point mass in the algorithm. This treatment of particle size has several drawbacks in the present particle tracking models particularly near the wall with application to small particle erosion prediction [5]. An erosion ratio equation is often used to convert erosive particle impacts to material damage. The accuracy of this equation is also a crucial component that determines the confidence of predicted erosion. There are many erosion ratio equations in the literature. Most of them are derived with the approach of erosion testing and curvefitting which may limit the application of erosion ratio equations to the range of experimental conditions. Some erosion ratio equations can be very conservative while others are not. The discussion of different erosion ratio equations is complicated and requires a large erosion data bank to draw a conclusion which is beyond the scope of this paper. However, this paper can serve as a further progress to evaluate the applicability of a typical Erosion Corrosion Research Center (E/CRC) Angle Dependent Model for different geometries and particle sizes. Many CFD practices with application to erosion simulation exist in the literature. However, most of them do not involve a comprehensive evaluation and validation of CFD predictions versus experimental data [6]-[8]. Some good predictions can be obtained fortuitously as erosion is a function of multiple factors and different factors may offset each other to obtain good results. Whereas, key issues like conducting systematic grid refinement studies for CFD based erosion simulations while ensuring accurate prediction of particle impact parameters are seldom discussed and

not well resolved. For many years, E/CRC has utilized CFD techniques to run erosion simulations under both single and multiphase flow conditions [9]-[13]. Yet, a more or less systematic application and validation of CFD techniques for erosion simulation can only be found within the work of Chen et al. [14], [15] and Zhang et al [16], [17]. Still, none of the studies have combined grid refinement study with ensuring accurate particle impact information prediction. The significance of this work is to form a CFD based erosion prediction procedure in which both aspects are considered and incorporated. The investigation is carried out first by investigating different near wall modeling approaches for erosion simulation and determining the appropriate model combination that is capable of predicting particle impact parameters and erosion accurately for the investigated cases. Then, based on the findings, a systematic procedure is proposed and utilized to perform a grid refinement study followed by uncertainty analysis of the CFD predictions from different models. This comprehensive procedure is carried out for both small particles (< 50 μm and relatively large particles (> 100 μm) respectively. Experimental data with uncertainty quantified is utilized to validate the proposed procedures. 2.

CFD predictions

2.1 CFD model and procedure Flow modeling for the CFD based erosion prediction model is first conducted utilizing Reynolds stress model (RSM). By changing near wall grid spacing while keeping other parameters the same, the effect of near wall modeling approaches on solid particle erosion prediction is investigated with employment of enhanced wall treatment. Other details of the CFD approach for this study are described in the following table. In the study, due to low sand concentration, one way coupling is used for tracking sand particles and Discrete Random Walk (DRW) model is applied to include the effect of turbulence on particles. Table 1. Parameters set for investigating the effect of different near wall modeling approaches on erosion prediction Flow Modeling Particle Tracking Erosion Ratio Equation

Reynolds stress model, 2nd order accuracy Enhanced wall treatment Velocity inlet and pressure outlet Drag law: Spherical Virtual mass and pressure gradient forces included Particle rebound model: Grant and Tabakoff (1975) E/CRC Zhang et al. (2009)

The geometry used for the present study is a submerged normal liquid jet impingement geometry as sufficient experimental data is available for validating CFD models. A schematic of the simulated submerged jet impingement geometry is given below.

D

Domain of interest r L

U z

L Fig. 1. 2-D schematic of jet impingement geometry used in CFD simulation and experimental testing

Where, D is the round jet diameter. L is the stand-off distance, and, U is the average velocity at the exit of the nozzle. In order to obtain measurable erosion utilizing current facilities, the nozzle diameter used in the experiments is 8 mm, the average liquid velocity at the exit of the nozzle in experiments is 14 m/s, and the stand-off distance is 12.7 mm. The domain of interest is pointed out in Figure 1, and the near wall meshes within the domain of interest are designed to be biased towards the wall so that the wall adjacent cell height can be accurately controlled. The control of wall adjacent cell height enables modeling the jet impingement flow with different near wall modeling approaches without changing the total number of cells used to discretize the domain. Based on the above description, the following geometry and representative mesh are created to run CFD simulations.

Velocity inlet

Nozzle wall

Pressure outlet

Zoomed in

Impingement wall Fig. 2. Representative computational domain using hexahedral meshes It can be seen in Figure 2 that the computational domain is discretized with hexahedral meshes. A uniform velocity of 14 m/s is used for the velocity inlet. Also for the inlet, the turbulence specification method is through turbulence intensity and hydraulic diameter using the following formula for turbulent pipe correlation [18].

Where, I is turbulent intensity, and is Reynolds number based on nozzle diameter, D. For the outlet boundaries, pressure is set to atmospheric pressure. In the study, four mesh types are designed for simulations with different near wall modeling approaches. The mesh types are given in the following table.

Table 2. Meshes used in the near wall modeling approach study Mesh

Total number of elements

First layer thickness (FLT) ( )

Maximum Y+

1

136,000

300

140

2

136,000

25

13

3

136,000

3

1.5

4

136,000

0.3

0.15

Near wall modeling approach Standard wall function Enhanced wall function Low Reynolds number modeling Low Reynolds number modeling

It is observed from Table 2 that all the mesh types have the same total number of elements but different wall adjacent cell heights which will represent different near wall modeling approaches being used in the simulations. Generally, Mesh 1 employs a typical standard wall function near wall modeling approach, and Mesh 2 uses enhanced wall function near wall modeling approach. Mesh 3 and Mesh 4 both use a low Reynolds number near wall modeling approach. The detailed formulations of the near wall models can be found in Reference [19]. The application of different near wall modeling approaches will result in different near wall flow field resolutions which will in return affect particle near wall trajectories and impact characteristics when predicting erosion due to particle impacts. 2.2 Effect of near wall modeling approach on erosion prediction Investigation is first carried out for 300 μm large particles. The sand used in the investigation and experiments has a size distribution which can be found in Reference [20]. In the CFD simulations, Rosin-Rammler method is adopted to represent the sand size distribution. The actual particle size distribution and the fit are shown in Figure 3. 1 0.9

Mass Fraction >d, Yd

0.8 Particle size data

0.7 0.6 0.5

RosinRammler curve fit

0.4 0.3 0.2 0.1 0 0

200

400

600

800

Diameter, d (µm) Fig. 3. Rosin-Rammler curve fit for the particle size data

Results obtained from CFD based erosion predictions are a function of number of hits, average impact speed and average impact angle at a given location. Thus, in the process of predicting erosion, particle impact characteristics from different meshes (different near wall modeling approaches) are extracted and compared to

investigate how different near wall modeling approaches affect erosion prediction results. The erosion representation at different locations is an accumulation of erosion due to many particle impacts. Figure 4 provides CFD predictions for 300 large particles.

Erosion (micrometer/kg)

2.5

Nozzle

2

Mesh1

r

1.5

Mesh2

Specimen

Mesh3

1

Mesh4 0.5 0 0

2

4

6

8

10

12

14

Radial Position, r (mm) Fig. 4. CFD predictions for 300 μm solid particle erosion utilizing different near wall modeling approaches In Figure 4, the values on the horizontal axis represent radial position of the specimen where 0 is the centerline of the jet impingement. It is observed that regardless of the near wall modeling approach CFD has predicted similar erosion trends. A certain amount of erosion is predicted at the center of the jet impingement and erosion gradually increases as radial position moves away from the impingement center and reaches a maximum erosion value at approximately 5 mm. Then, erosion magnitude decreases rapidly as distance moves further away from the impingement center. Examining the effects of different near wall modeling approaches on erosion magnitude, it is observed that the standard wall function modeling approach, Mesh 1, predicts the largest erosion followed by the enhanced wall function modeling approach, Mesh 2. The low Reynolds number modeling approach predicts the least erosion, Meshes 3 and 4. It is observed that Mesh 3 and Mesh 4 have converged to the same erosion profile which may indicate numerical convergence in CFD for the erosion simulation. Following the same procedure, erosion predictions are run for 25 μm small particles. Since the particle size distribution information is unknown from the references, a uniform sand size distribution is assumed and adopted in the erosion simulations. The results are given in Figure 5.

Erosion (micrometer/kg)

2.5

Nozzle

2

r 1.5

Specimen

Mesh1 Mesh2

1

Mesh3 Mesh4

0.5

0 0

2

4

6

8

10

12

14

16

Radial Position, r (mm) Fig. 5a. CFD predictions for 25 μm solid particle erosion utilizing different near wall modeling approaches

Erosion (micrometer/kg)

0.25

Nozzle

0.2

r

0.15

Specimen

Mesh2 Mesh3

0.1

Mesh4 0.05

0 0

2

4

6

8

10

12

14

16

Radial Position, r (mm) Fig. 5b. CFD predictions for 25 μm solid particle erosion utilizing different near wall modeling approaches excluding standard wall function approach CFD has predicted different erosion profiles for 25 μm small particles compared with 300 large particles. First of all, erosion prediction at the impingement center is significantly different between small and large particles. Much less erosion appears near the impingement center for small particles, since the smaller particles do not have as much momentum to travel through the stagnation region to impact the wall. Second, the maximum erosion location

is shifted to a larger radial location for small particles, and the erosion profile after the maximum location does not appear to drop as rapidly compared to large particles. Third, predicting erosion for small particles seems to be much more sensitive to different near wall modeling approaches. Figure 5a shows over a factor of 20 difference between Mesh 1 (standard wall function near wall modeling approach) and Mesh 4 (low Reynolds number modeling approach) while for 300 μm large particles the difference is only a factor of 3. Despite these differences, at least two common phenomena can be observed for both large particle and small particle erosion predictions. One is that by reducing first layer thickness (changing from wall function modeling approach to low Reynolds number modeling approach), the predicted erosion magnitudes from CFD reduce. However, the degree of change in the predicted erosion magnitude depends on particle size as shown in previous the figures. The other is that when an adequately small first layer thickness is used in CFD erosion simulations the results converge such that predicted erosion profiles will remain the same regardless of further refinement of the first layer thickness. Furthermore, it is observed that when Mesh 1 (standard wall function near wall modeling approach) is used to predict erosion for both large (> 100 μm) and small (< 50 μm) particle erosion, the obtained maximum erosion for small particles appears to be comparable to large particle result, which is not physical. Thus, this indicates that a coarse mesh with standard wall function near wall modeling approach is inaccurate for running small particle erosion simulations, while switching to a more accurate near wall modeling approach by near wall mesh refinement helps improve small particle erosion prediction. Or, generally, near wall mesh refinement helps reduce the predicted maximum erosion magnitude until it converges and remains unchanged. It is still necessary to determine if the predicted results agree with experimental data. In order to explain and validate the numerical variations and pick the best numerical model combinations for erosion simulation, particle impact speed and angle from different meshes (i.e. different near wall modeling approaches) are extracted and compared with available experimental data. The same mesh sets in Table 2 (Mesh1 to Mesh4) are used for running simulations. The experimental data was collected recently at E/CRC utilizing Particle Image Velocimetry (PIV) technique. Details of the experimental facilities and measurements can be found in the Reference [20]. In the corresponding experiment, the nozzle exit velocity is 8.15 m/s, and the experiment is conducted with the same 300 μm particles. In the process, enough particles are tracked to obtain statistically stable impact characteristics. And, average impact speed and angle are used to represent particle impacts at each location. The averaging is summation of each impacting history and then divided by total number of impacts at a given location which is in line with the method used in the experiments. The following figures show the obtained numerical results and comparison with data.

8

Nozzle

Impact Speed (m/s)

7 6

r

Experiment

5

Mesh1

Specimen 4

Mesh2

3

Mesh3

2

Mesh4

1 0 0

5

10

15

20

25

Radial Distance from Jet Impingement Center, r (mm) Fig.6. Comparison of particle impact speeds from CFD predictions and experimental data (𝑉𝑗𝑒𝑡 =8.15 m/s, 𝑑𝑝 =300 μm)

90

Impact Angle (degree)

80

Nozzle

70 60

Experiment

r

Mesh1

50

Specimen

40

Mesh2

30

Mesh3

20

Mesh4

10 0 0

5

10

15

20

25

Radial Distance from Jet Impingement Center, r (mm) Fig.7. Comparison of particle impact angles from CFD predictions and experimental data (𝑉𝑗𝑒𝑡 =8.15 m/s, 𝑑𝑝 =300 μm) Figures 6 and 7 demonstrate that variation of different near wall modeling approaches results in different particle impact characteristics hence different erosion profiles. For the erosion prediction convergence utilizing Mesh 3 and Mesh 4 as seen in Figures 4 and 5, the extracted impact information shows that these meshes have nearly the same impact speed and angle predicted which lead to almost the same erosion profile. However, it is observed that the numerical schemes represented by Meshes 3 and 4 underpredict impact speeds everywhere which can directly result in erosion underprediction. The impact angles at most locations are overpredicted, which can also result in erosion underprediction for ductile materials. Thus, it is believed that the previous converged erosion profile for the 300 μm particles may be inaccurate with predicted erosion magnitude below experimental data. Similarly, this gives rise to concerns for the accuracy of the converged erosion results for 25 μm particles. By comparing particle impact speed and angle with experimental data, it is observed that only Mesh 1 is capable of predicting the impact speed profile which follows closely with data, while the other meshes all tend to underpredict impact speed which is detrimental for erosion calculation and can result in significant erosion underprediction. For impact angles, it is also observed that only Mesh 1 is able to predict the impact angle profile which gives the best representation of experimental data compared with the other meshes. Thus considering particle impact information, Mesh 1 which represents a typical standard wall function modeling approach is the only near wall modeling approach that is able to accurately predict impact parameters for the 300 μm particles. Other modeling approaches which are achieved by near wall mesh refinement all tend to underpredict impact speed and overpredict impact angle which can result in erosion underprediction for ductile materials. These comparisons and observations can lead to several meaningful and important findings. One is that accurate flow modeling achieved by mesh refinement especially near the wall does not always guarantee accurate impact characteristics and therefore erosion prediction. Generally for large particle erosion simulations, it is not recommended to apply near wall mesh refinement while for small particle erosion simulation, it is highly recommended to use small near wall grid spacing. Also, converged CFD based erosion prediction results are not always accurate. Unfortunately, there is no experimental data available for validating impact speed and angle for the 25 μm particle case, but particle near wall information can be used to help judge the results. Thus, for Mesh 1, near wall (~ 3μm) particle velocity and fluid velocity applied to track particles are plotted in Figures 8 and 9:

Nozzle

r

14 12

Specimen

Speed (m/s)

10 8 6 4 2 0 5.78E-03 5.79E-03 5.87E-03 5.87E-03 5.91E-03 5.95E-03 6.00E-03 6.03E-03

Radial Position, r (m) Fluid Velocity Particle Velocity Fig.8. Comparison of near wall particle velocity and fluid velocity for 25 μm particles based on Mesh 1 (𝑉𝑗𝑒𝑡 =14 m/s) Figure 8 presents the particle velocity versus fluid velocity (used for calculating particle velocity) at 3 μm away from the wall. The jet velocity is 14 m/s. Fluid and particle velocities near the wall were extracted through a userdefined-function. It is shown that unphysically high fluid velocity is used for particle tracking regardless of location of particle in cell. And, this has resulted in very high particle impact speeds for small particles. Particle Velocities

Particle Trajectories

1.2

r

Rebounding particle

4.90E-03 4.80E-03

0.8 Nozzle z

Specimen

4.70E-03

0.6 0.4

4.60E-03

Incoming particle

4.50E-03

0.2

4.40E-03

0 0.012699 0.0126992 0.0126994 0.0126996 0.0126998

Radial r Position r, (m)

Speed (m/s)

1

5.00E-03

4.30E-03

0.0127

Axial Position, z (m) Fig.9. Near wall particle trajectories and particle speed for 25 μm particle based on Mesh 3 Figure 9 shows that Mesh 3 predicts very low impact speeds at most locations. Many impact speeds are approaching zero. This is detrimental and dangerous for predicting erosion severity and has a great tendency of underpredicting the results. So, based on above analysis, it can be seen that different near wall meshes and models can lead to significant differences in particle impact speeds. While not all the near wall modeling approaches or mesh types can be used to predict particle near wall behavior and run erosion simulations. One needs to first examine different mesh and model

combinations either by comparison with measured data or by investigation of near wall information to choose the most appropriate approach that is able to represent particle near wall behavior and impact characteristics. 2.3 Uncertainties of CFD predictions Erosion simulation utilizing CFD involves multiple components. A change of one component can bring a change in the predicted results as shown in previous sections. This section attempts to quantify the overall uncertainty of CFD predictions by carrying out a grid refinement study and changing the key parameters set for erosion simulations while fixing the wall adjacent cell height. The key and basis of quantifying CFD erosion prediction uncertainties is that CFD erosion prediction models must utilize the most accurate near wall modeling approaches to have impact characteristics reasonably predicted. Based on previous validations and discussions, Mesh 1 is believed to be the most accurate configuration for the 300 μm particle erosion prediction. Similarly, for the 25 μm particle erosion prediction case, apparently, Mesh 1 should not be used for predicting small particle erosion as it predicts the same amount of erosion as 300 μm large particles under the same flow condition. Meshes 3 and 4 are also inappropriate for small particle erosion simulation based on investigating near wall particle behaviors shown above which can cause significant underprediction. Thus, the following discussions for 25 μm particle erosion simulation will focus on Mesh 2. The previous sections have addressed the effect of different near wall modeling approaches on erosion simulations for both large and small particles while the effects of grid density in all related directions on erosion prediction under the appropriate near wall modeling approach have not been discussed. In order to carry out this grid refinement study, the following notation is specified in Figure 10, where N1 represents mesh number in the wall normal direction, N2 represents grid number in the radial direction, N 3 represents mesh number for every 45 degrees around the cylindrical domain of interest.

3

Zoomed in

Fig. 10. Grid refinement notation Table 3. Meshes used in grid refinement study

Case

300 large particle FLT=300

25

small particle FLT=25

Mesh 5 1 (previous Mesh 1) 6 7 8 9 2 (previous Mesh 2) 10 11

Near wall modeling approaches

55

Azimuthal number of divisions (N3) 5

30

55

10

184,000 385,600 788,800 63,000

42 42 42 30

55 115 235 55

10 10 10 5

Standard wall function

136,000

30

55

10

496,000 2,224,000

120 120

55 235

10 10

Total number of elements

Wall normal number of divisions (N1)

Radial number of divisions (N2)

63,000

30

136,000

Enhanced wall function

The predicted results for particles sizes of 300 and 25 μm are provided in Figures 11 and 12. For all the simulations in this section, the jet velocity is 14 m/s.

Erosion (micrometer/kg)

2.5

2

Nozzle Mesh5

1.5

r

Mesh1 Mesh6

Specimen

1

Mesh7 Mesh8

0.5

0 0

2

4

6

8

10

12

14

Radial Position, r (mm) Fig. 11. Grid refinement studies for 300 μm solid particle erosion

Erosion (micrometer/kg)

0.25

Nozzle

0.2

Mesh9

r

0.15

Mesh2

Specimen

Mesh10 Mesh11

0.1

0.05

0 0

2

4

6

8

10

12

14

16

Radial Position, r (mm)

Fig. 12. CFD grid refinement study for 25 μm solid particle erosion It is found in the fixed first layer thickness (FLT) grid refinement study that different particles sizes respond differently to changes in the grid. Generally, it shows that grid refinement in the azimuthal direction has little effect for both small and large particles. The small particle (<50 μm) results show negligible response to grid refinement in all directions with a fixed first layer thickness. While, the large particle (>100 μm) shows a noticeable response to grid refinement in the radial direction. This is due to one of the limitations in the current commercial CFD codes where eddy sizes are limited to cell sizes and particles are tracked cell by cell. Changes in the grid change the particle-eddy interaction model, since the cell size is effectively limiting the eddy size. So, within a given region, more grids means that particles interact with more eddies which help large particles disperse spreading them over the domain and hence affect large particle impact characteristics. While this does not affect small particles as much since small particles can be easily transported and dispersed by the flow field and quickly adopt fluid velocities due to much lower inertia. Thus, based on the above analysis, Mesh 7 and Mesh 2 can adequately embrace the uncertainties resulting from grid refinement for 300 μm and 25 μm solid particles, respectively. Analysis of uncertainties from other factors like different turbulence models will be quantified based on Mesh 7 for 300 μm particles and Mesh 2 for 25 μm particles. Five turbulence models are applied to examine the differences for both large and small particles: SST model, Reynolds stress model (RSM), Realizable model, RNG model and Standard model. Figures 13 and 14 present the predicted erosion results obtained by applying the various turbulence models for large and small particles, respectively.

Erosion (micrometer/kg)

2.5

Nozzle

2

SST 𝑘−𝜔

r

1.5

RSM

Specimen

Realizable 𝑘−𝜀

1

RNG 𝑘−𝜀 0.5

Standard 𝑘−𝜀

0 0

2

4

6

8

10

12

14

Radial Position, r (mm) Fig. 13. Effect of turbulence models on CFD based erosion predictions for 300 μm particles

0.25

Nozzle

Erosion (mcrion/kg)

0.2

SST 𝑘−𝜔

r 0.15

RSM

Specimen

Realizable 𝑘−𝜀 0.1

RNG 𝑘−𝜀 Standard 𝑘−𝜀

0.05

0 0

2

4

6

8

10

12

14

16

Radial Position, r (mm) Fig.14. Effect of turbulence models on CFD based erosion predictions for 25 μm particle It is observed from Figures 13 and 14 that large and small particles demonstrate different responses to different turbulence models. For each case, five different turbulence models are applied to the same mesh with Mesh 7 for 300 μm particles and Mesh 2 for 25 μm particles. For these conditions, the SST produces a noticeably weaker turbulence field than the other turbulence models, while the RSM produces a noticeably stronger turbulence field. For the larger particles shown in Figure 13, the weaker turbulence field results in less dispersion of the particles, so the impact area is more concentrated for the SST model, which causes the higher erosion seen in the figure. For the smaller particles shown in Figure 14, the more energetic eddies modeled from the higher turbulence

predicted by the RSM model cause particles to repeatedly impact the wall. This causes the higher predicted erosion seen in the figure. Even if the same flow field is used, different near wall particle behaviors are predicted for small and large particles. Figure 15 and 16 show different particle near wall behaviors for 300 and 25μm, respectively, using the same flow filed obtained using Mesh 1 and the Realizable turbulence model.

Particle trajectory with turbulence effect

Particle trajectory without turbulence effect

Radial Position, r (m)

0.06

r

0.05

Rebounding particle

0.04

Specimen

Nozzle z

0.03 0.02

Incoming particle

0.01 0 0.0109

0.0112

0.0115

0.0118

0.0121

0.0124

0.0127

Axial Position, z (m) Fig. 15. 300 μm particle response to turbulence field based on Mesh 1 and Realizable

model

0.008

Radial Position, r (m)

Particle trapped

r

0.007

t

0.006 0.005

Nozzle z

Specimen

0.004 0.003

Incoming particle

0.002 0.001 0 0.0123

0.0124

0.0125

0.0126

0.0127

Axial Position, z (m) Fig. 16. 25 μm particle response to turbulence field based on Mesh 1 and Realizable

model

Figure 15 demonstrates that particle-turbulence interaction can increase the number of impacts but due to rebounding momentum are able to escape the near wall region for the 300 μm larger particles. Whereas, Figure 16 shows that turbulence can push small particles (25 μm) toward the wall where they become trapped, and it is predicted that they impact the wall repeatedly.

Based on the above discussion, it can be inferred that the relatively strong particle-eddy interaction provided in RSM model contributes to the distinguished difference in erosion profile predicted for small particles. Whereas, the SST model produces a relatively weak particle-eddy interaction which causes distinguished difference in erosion profile for both large and small particles in which for large particles unlike other turbulence models particle impacts are concentrated in a narrower region with much higher erosion predicted and for small particles it causes noticeable lower erosion prediction since the particle dispersion is less compared with all the other models. Turbulence modeling is complicated and there are many models available in the literature that when utilized to model turbulent dispersion of particles provide different particle behaviors and therefore different erosion results will be expected. However, as it can be seen in the figures that variants of models provide very similar erosion prediction results for both large and small particles. Since the impingement surface is simply a flat specimen for the jet impingement geometry, it would be expected that particle rebound behavior should have a negligible effect on erosion profile. For thorough validation, an investigation is carried out for large particles using RSM model with four different rebound models: perfectly elastic rebound model, Tabakoff rebound model [21], Tabakoff stochastic rebound model [22] and Forder rebound model [23]. Each model differs from each other in the formulation of the coefficients of restitutions. The stochastic model has utilized a stochastic approach to obtain the coefficient of restitutions. Figure 17 presents the predicted results. 1.8 1.6

Nozzle Erosion (micrometer/kg)

1.4

r

1.2 1

Perfectly elastic

Specimen

Tabakoff stochastic

0.8

Tabakoff 0.6 Forder

0.4 0.2 0 0

2

4

6

8

10

12

14

Radial Position, r (mm) Fig.17. Effect of rebound models on CFD based erosion predictions for 300 μm particle The results are consistent with the expectation that for this geometry the erosion profile is insensitive to the particle rebound model. 3.

Validation with experimental data

Previous investigators at E/CRC collected erosion data for submerged normal liquid jet impingement. Mansouri [24] collected erosion data for 300 μm particles. Karimi et al. [25] collected erosion data for 25 μm particles. Data collected by Mansouri and Karimi are used to evaluate the CFD predictions obtained from the proposed procedures. The jet velocity for all the erosion data collected is 14 m/s. The latest experimental results are presented with uncertainty obtained by repeating the experiments multiple times (mostly 3 to 5 times) or estimated with available information. It should be noted that for erosion the experimental uncertainty can be large for some cases but obvious data outliers can be discarded using appropriate statistical approaches.

CFD predictions are compared with experimental data with uncertainties denoted. The CFD predictions are based on the selected mesh types which are believed to be capable of accurately predicting particle impact characteristics. Thus, for this work, the 300 μm particle erosion predictions are based on Mesh 7 while the 25 μm particle erosion predictions are based on Mesh 2. Results are shown in the following figures.

Erosion (micrometer/kg)

2.5

Nozzle

2

Experiment SST 𝑘−𝜔

r

1.5

RSM

Specimen 1

Realizable 𝑘−𝜀 RNG 𝑘−𝜀

0.5

Standard 𝑘−𝜀

0 0

2

4

6

8

10

12

14

Radial Position, r (mm) Fig. 18. Validation for 300 μm solid particle erosion prediction utilizing CFD

0.25

Erosion (mcriometer/kg)

0.2

Nozzle Experiment

r

0.15

SST 𝑘−𝜔 RSM

Specimen

Realizable 𝑘−𝜀

0.1

RNG 𝑘−𝜀 Standard 𝑘−𝜀

0.05

0 0

2

4

6

8

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Radial Position, r (mm) Fig. 19. Validation for 25 μm solid particle erosion prediction utilizing CFD By comparing with experimental data, it is observed that for the large particle case following the procedures described above that most models can predict erosion fairly well except for the SST model with an overprediction factor of 1.5. Whereas, for the small particle case, RSM shows a relatively large overprediction (a

factor of 4) and deviation from other models, while SST has underpredicted erosion everywhere. For both large particles and small particles, it turns out that models are the most robust and consistent models which are capable of predicting turbulent dispersion of particles and hence erosion profile reasonably well compared with experimental data. Thus, applying proposed procedures which create meshes with first layer thickness that are capable of predicting particle impact parameters reasonably well (can be obtained based on experimental data or examining particle impact information as discussed previously), doing grid refinement based on the fixed layer thickness in all relevant directions and incorporating different model induced uncertainties, have demonstrated their success in predicting solid particle erosion regardless of particle size. Application of this comprehensive procedure can help improve the confidence of CFD based erosion predictions and offers an approach for engineers to perform decisionmaking accounting for several factors. 4.

Conclusions

This study of erosion prediction utilizing the proposed procedure leads to the following conclusions: (1) Small near wall grid spacing is not recommended for relatively large particle erosion simulation, while large near wall grid spacing is not recommended for relatively small particle erosion simulation. (2) Converged erosion simulation results obtained through near wall grid refinement can be deceiving and particle impact speed can be significantly underpredicted. (3) Grid refinement study for erosion simulations should be based on accurate near wall modeling resulting in particle impact parameters being predicted well. Otherwise, a mesh independent study for erosion simulation is meaningless. (4) Enhanced wall treatment is highly recommended for running erosion simulations. This near wall treatment offers a hybrid near wall modeling approach which depends on near wall mesh resolution. It provides the maximum flexibility in adapting to the change of near wall mesh resolution while ensuring an adequately accurate flow field. (5) Turbulence modeling is an important component in determining particle distribution and impact characteristics over the impingement wall. In this work, different particle sizes have shown different responses to the turbulence field. Small particles are easily captured and trapped by turbulence, while turbulence helps large particles spread more uniformly throughout the flow domain. (6) It has been demonstrated that as long as particle impact characteristics can be accurately predicted, change of physical models will not cause significant deviations in predicted results and can agree well with experimental data which proves the validity of the proposed CFD based erosion procedure. Acknowledgements The authors wish to acknowledge all the member companies that have supported E/CRC research for many years. References [1] [2]

[3]

[4] [5] [6]

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. 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), FEDSM2012-72294, Proceedings of the ASME 2012 Fluids Engineering Summer Meeting, Rio Grande, Puerto Rico. Jun Zhang, Brenton S. McLaury, Siamack A. Shirazi, Predicting erosion from small particles in sudden contraction and expansion geometries with improved near wall treatment, Corrosion 2016, 6-10 March, Vancoouver, British Columbia, Canada. D.I. Graham, P.W. James, Turbulent dispersion of particles using eddy interaction models, International Journal of Multiphase Flow, 22, 1996, 157-175. F. Najafifard, Predicting near wall particle behavior with application to erosion simulation, Ph.D. Dissertation, Department of Mechanical Engineering, The University of Tulsa, 2014. Chong Y.Wong, Christopher Solnordal, Anthony Swallow, Jie Wu, Experimental and computational modeling of solid particle erosion in a pipe annular cavity, Wear 303 (2013), 109-129.

[7] [8]

[9] [10]

[11]

[12] [13]

[14]

[15]

[16] [17] [18] [19] [20]

[21] [22] [23] [24] [25]

Praveen Kumar G, Byron Simith R J, Damodaran Vedapuri, Sand fines erosion in gas pipelines-experiments and CFD modeling., Corrosion, 2014, San Antonio, Texas, U.S.A. Christopher B. Solnordal, Chong Y. Wong, Amir Zamberi, Maharon Jadid, Zurita Johar, Determination of erosion rate characteristic for particles with size distributions in the low Stokes number range, Wear 305 (2013), 205-215. Wang J, Shirazi S, Shadley J, Rybicki E., Application of flow modeling and particle tracking to predict sand erosion rates in elbows, ASME FEDSM, 1996, 236:725-734. Edwards, J.K., McLaury, B.S., Shirazi, S.A., Erosion prediction in elbows and plugged tees, Paper No. ETCE00-ER-033, ETCE 2000/OMAE 2000 Joint Conference of ASME Petroluem Division, February 14-17, 2000. Edwards JK., Development, validation, and application of a three-dimensional, CFD-based erosion prediction procedure. PhD Dissertation, Department of Mechanical Engineering, The University of Tulsa, 2000. J. Zhang, B.S. McLaury, S.A. Shirazi, CFD simulation and 2-D modeling of solid particle erosion in annular flow, 10th North American Conference on Multiphase Technology, Banff, Canada, 8-10 June, 2016. . Peyman Zahedi, Jun Zhang, Hadi Arabnejad, Brenton S. McLaury, Siamack A. Shirazi, CFD simulation of multiphase flows and erosion predictions under annular flow and low liquid loading conditions, Wear, 376377, Part B (2017), 1260-1270. Xinghui 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, Computers & Fluids, 33(2004) 1251-1272. X. Chen, Application of computational fluid dynamics (CFD) to single-phase and multiphase flow simulation and erosion prediction, Ph.D. Dissertation, Department of Mechanical Engineering, The University of Tulsa, 2004. 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. Y. Zhang, Application and improvements of computational fluid dynamics (CFD) in solid particle erosion modeling, Ph.D. Dissertation, Department of Mechanical Engineering, The University of Tulsa, 2006. ANSYS Fluent, Fluent 17.2 User’s Guide, ANSYS Inc., 2017. ANSYS Fluent, Fluent 17.2 Theory Guide, ANSYS Inc., 2017. A. Mansouri, A combined CFD-Experimental method for developing an erosion ratio equation for both gassand and liquid-sand flows, Ph.D. Dissertation, Department of Mechanical Engineering, The University of Tulsa, 2016. X. Chen, B.S. McLaury, S.A. Shirazi, Effect of applying a stochastic rebound model in erosion prediction of elbow and plugged tee, ASME FED. 257(2002) 247-254. A. Forder, M. Thew, D. Harrison, Numerical investigation of solid particle erosion experienced within oilfield valves, Wear 216 (1998) 184-193. G. Grant, W. Tabakoff, Erosion prediction in turbomachinery resulting from environmental solid particles, J. Aircraft 12(5) (1975) 471-478. A. Mansouri, H. Arabnejad, S.A. Shirazi, B.S. McLaury, A combined CFD/experimental methodology for erosion prediction, Wear 332-333 (2015), 1090-1097. Soroor Karimi, Siamack A. Shirazi, Brenton S. Mclaury, Predicting fine particle erosion utilizing computational fluid dynamics, Wear 376-377, Part B (2017), 1130-1137.