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Modeling of erodent particle trajectories in slurry flow
Wear 334-335 (2015) 49–55
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Wear journal homepage: www.elsevier.com/locate/wear
Modeling of erodent particle trajectories in slurry flow Liang Ma, Cheng Huang n, Yongsong Xie, Jiaren Jiang, Kidus Yoseph Tufa, Rob Hui, Zhong-Sheng Liu Energy, Mining and Environment Portfolio National Research Council Canada, 4250 Wesbrook Mall, Vancouver, BC, Canada V6T 1W5
art ic l e i nf o
a b s t r a c t
Article history: Received 17 February 2015 Received in revised form 21 April 2015 Accepted 22 April 2015 Available online 29 April 2015
This paper presents a method for calculating erodent particle trajectories in slurry flow. It involves computational fluid dynamics (CFD) for calculating fluid phase flow, the discrete phase method (DPM) for capturing the movement of erodent particles, and the volume of fluid method (VOF) for calculating interfaces between fluid phase and gas phase. The method is illustrated by application to a lab slurry jet testing system, which considers free water/air interface tracking, particle size distribution and local particle concentration. The validation of the modeling is done by comparing to a glass bead/water jet testing. Using the proposed method, further parametric studies are performed for calculating actual particle speeds and impingement angles under different operating conditions and physical explanations of the modeling results are provided in the end. Crown Copyright & 2015 Published by Elsevier B.V. All rights reserved.
Keywords: Slurry flow Particle trajectories Slurry jet erosion testing Computational fluid dynamics
1. Introduction Slurry flow is a very common phenomenon in mining operations for handling and/or transporting solid particles in bulk, where slurry is mainly a mixture of water and solid particles. Slurry flow through hydro-transport systems causes erosive and abrasive wear on pipelines, valves and pumps [1–5]. It becomes essential to design slurry flow that would reduce wear without compromising transport efficiency. With the rapid development of computational technology and numerical algorithms, some numerical simulation techniques, for example, computational fluid dynamics (CFD), the discrete phase method (DPM) along with erosion models have been developed for calculating particle motions and erosion rates. Turenne and Fiset [6] modeled particle trajectories in a slurry based on potential and stream functions. Edwards et al. [7] used CFD code to simulate solid particle trajectories and estimated erosion rate in elbows and plugged-tee geometries. Shah et al. [8] performed CFD modeling of slurry flow in coiled tubing for hydraulic fracturing and compared modeling results with experimental observations. In studying the effect of slurry flow on erosion rate of materials, a slurry jet erosion tester as illustrated in Fig. 1, has been often used at National Research Council Canada (NRC). In this testing setup, a slurry pump and a piping loop produce a slurry jet through a nozzle at controlled speed, which impacts a test specimen surface at a nominal pre-set impingement angle. It is apparent that actual n
Corresponding author. Tel.: þ 1 604 221 3050; fax: þ 1 604 221 3001. E-mail address: [email protected] (C. Huang).
http://dx.doi.org/10.1016/j.wear.2015.04.013 0043-1648/Crown Copyright & 2015 Published by Elsevier B.V. All rights reserved.
particle speeds and impingement angles at different locations of the test specimen surface are different from the nominal values. The overall erosion rate on the specimen surface is from the integral contribution of individual erodent particles, while the contribution of a single particle to the overall erosion rate is a function of its actual kinetic energy, shape, and impingement angle. In other words, the overall erosion rate is determined not only by each particle's motion but also their statistics. There are some published studies on the modeling of slurry jet testing. For example, Gnanavelu et al. [9] proposed a methodology to model a slurry jet erosion test and generate a material wear map through modeling particles' speeds and impingement angles. Moreover, Gnanavelu et al. [10] implemented CFD codes to determine par ticle motion and wear profile on various geometries. Zhang et al. [11] used a CFD model to calculate particles' radial and axial velocities for a slurry jet erosion testing and compared with measurement results using a laser Doppler velocity meter. However, these studies modeled basically slurry jet operating in a tank full of fluid at very low solid concentrations, allowing simplification and neglecting local concentration variations. The NRC slurry jet erosion tester operates in open air which is relatively easy for implementation and maintenance. The testing is usually conducted at relatively high solid concentrations, which more closely simulates many industrial applications and is more favorable than low concentration testing because shorter test duration is required for generating measurable wear volume loss. This has motivated us to track air/water interface and study the effects of local solid concentration. To the authors' knowledge, no studies have been reported in the literature that has simulated such systems.
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L. Ma et al. / Wear 334-335 (2015) 49–55
Fig. 1. Schematic of the NRC's slurry jet erosion tester.
In this paper, a coupled CFD and DPM model is proposed to calculate erodent particle trajectories in slurry flow with ANSYS Fluent and then is applied to simulate the NRC slurry jet erosion testing. In the study, free air/water interface tracking, particle size distribution and local particle concentration variations are all considered. The proposed model is validated by comparing the calculated results to the measured values in a specifically designed glass bead/water jet testing. Furthermore, parametric studies are performed by modeling and the physical explanations of the effect of slurry temperature, nominal impingement angle and even particle size on slurry jet erosion rate are provided based on the analysis of simulation results.
2. Modeling methodology The methodology proposed for modeling slurry flow with water/air interface is developed on ANSYS Fluent 14.5 with 4 parallel processes. For CFD modeling, ANSYS Fluent solves conservation equations for mass and momentum as follows: ⇀ ∂ρ + ∇⋅ ρv = Sm ∂t
(1)
⇀ ⇀ ⇀⇀ ⇀ ∂ ρv + ∇⋅ ρv v = − ∇p + ρg + F ∂t
(2)
( )
( )
( )
where ρ is the fluid density, ⇀ v is the fluid velocity, Sm is the ⇀ source term, p is the static pressure, and ρ⇀ g and F are the gravitational body force and external body forces, respectively. For the application in NRC slurry jet erosion testing, the inner diameter of the nozzle is 5 mm and the distance from the nozzle exit to the targeted surface is 100 mm. The CFD model in Fluent is used to simulate transient flow field from the inlet to the outlet of the computational domain which is shown in Fig. 2. These domains are for 90° impingement angle testing. For simplicity, only half of the real nozzle is modeled and the symmetric boundary conditions are applied. The total number of cells for calculation is 1,748,400. The inflation of meshing is applied on all walls and the estimated interface between water and air. The turbulence model is selected as the realizable k-epsilon model with enhanced wall treatment. Volume of fluid (VOF) is a numerical method which is able to track the shape and location of free surface based on the concept of a fractional volume of fluid [12]. A unity value of the volume fraction corresponds to a full element occupied by the fluid liquid, while a zero value indicates an empty element containing gas. The value of the volume fraction between zero and one indicates that the corresponding element is the surface element. So the interface between water and air for the slurry flow in open air is calculated by the VOF algorithm integrated in ANSYS Fluent.
Fig. 2. (a) Modeling domains and boundary conditions. (b) Image of the mesh grids (totally 1,748,400 cells).
At the beginning, the transient CFD calculation coupled with the VOF goes through numerous iterations until convergence and stabilized mass flow rate at the outlet are reached. The time step in the analysis should be small enough to capture the physical phenomenon. After trials, the time step is set to 1e–5s and for each time step 200 maximum CFD interactions are adopted considering the calculation efficiency. This part of the modeling simulate the period from the time water exits the nozzle to when it hits the target wall (the specimen test surface). At the end of this transient calculation, the obtained values are used as initial inputs to perform a steady state analysis. The fluid interactions last for about 5000 steps and globally scaled residuals for all equations decrease below 0.001 and the mass flow rate at the outlet gets stabilized. Thus the stable interface between water and air is finalized, which means a free water flow in open air is formed. The solid particles are then released in the slurry and they are tracked by the DPM module, which uses the Lagrangian approach. Particle collisions are not considered in this study as the solid volume percentage is below 10%. The particles are divided into particle streams to pair each mesh surface at the domain inlet. The mass flow rate for each particle stream is calculated based on the paired mesh surface area. These particle streams are released to the flow at the domain inlet with their corresponding mass flow rate. All particle streams with their mass flow rates and simulated trajectories recorded by the coordinate values are tracked to consider the variations of the solid concentration at different locations in the fluid rather than assuming the concentration is even everywhere. The trajectories of these particle streams are calculated with the drag force due to fluid flow as the driving force using the Newton's Second Law. The change rate of particle velocity comes directly from the drag force as follows:
Fd = mp
d Vp dt
(3)
where Fd is the drag force vector acting on the particle, Vp is the particle velocity vector (combination of speed and direction) and mp is the particle mass. It should be mentioned that in the DPM
L. Ma et al. / Wear 334-335 (2015) 49–55
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calculation, the momentum exchange between particles and fluid is two-way coupled and turbulence dispersion should also be considered in modeling to improve accuracy and reliability. In the steady state simulation, 50 fluid interactions were performed between each particle trajectory interaction. Additional 2000 fluid interactions are performed to get all residuals below 0.001 and the mass flow rate at the outlet converges to the value from the inlet. Finally, the ANSYS Fluent 14.5 post-process module is used to extract information on local motion in all particle streams hitting on the specimen surface. The outputs of the calculation include, for example, the coordinate values, particle size, impact velocity (speed and impingement angle) and mass flow rate. When the solid particles approach the target wall surface, they must go through a thin layer of fluid near the wall that has relatively low velocity. In addition, they must squeeze the fluid between the particle and the wall to impinge the wall. The effect of the near wall fluid on the velocity of the solid particles is called the squeeze film effect. A simple mathematical model that can simulate this effect was proposed and developed by Clark et al. [13,14]. In order to implement this mathematical model in our study, a programmed post-process subroutine for the squeeze film effect was applied to adjust the particle speeds and impingement angles to get a more accurate prediction. The squeeze film effect depends mainly on particle Reynolds number Rep , which can be obtained from
Rep =
Vn dp ρ f μ
(4)
where Vn is the normal component of the particle velocity, dp is the particle diameter, μ is the dynamic viscosity of the fluid, and ρf is the fluid density. Another important number is critical particle Reynolds number Re* defined by
Re* =
3ξ 2 ⎛ ρp ⎞ 4 ⎜ ρ ⎟ + 2fav ⎝ f⎠
(5)
where ρp is the density of the solid particle, ξ is the particle shape related constant that equals to 10 and fav is set to 1.0 according to references [13,14]. If Rep ≤ Re*, it means that the particle does not touch the target wall surface. If Rep > Re*, then the particle is believed to penetrate the squeeze film and impact the sample surface. The particle normal component of the velocity is reduced to Vnreduced , which can be calculated by
V nreduced =
⎛ ⎞ a ⎜ Re* ⎟ 1− Vn ⎜ a +ξ⎝ Rep ⎟⎠
(6)
⎡ ⎛ ρp ⎞ ⎤ where a = 8 ⎢2 ⎜ ρ ⎟ + fav ⎥. ⎣ ⎝ f⎠ ⎦ After obtaining the velocity and mass flow rate of each particle stream, these results could be applied to an appropriate erosion model to evaluate the erosion rates of the sample, which is not presented in this paper. Finally, the modeling results could be validated by comparison with the measured erosion rate from a slurry jet erosion testing.
3. Model validation The speed and impingement angle of erodent particles are critical parameters for predicting erosion rate. Although the coupled CFD and DPM modeling technique has advanced significantly, its accuracy still needs to be assessed when applied to specific applications. At this stage, there is no technical solution to directly
Fig. 3. Impact craters produced on soft copper sample by 60–70 mesh glass beads in the slurry jet testing. (Black spot in the middle of (a) is the center point). (a) Impact craters produced on soft copper sample. (b) Typical impact craters.
measure the impact frequency distribution of actual particle speed and impingement angle in slurry jet testing, especially for the slurry jet operating in open air according to authors' knowledge. So a glass bead/water jet testing is specially designed to validate the proposed model. The normal component of round glass bead velocity on the surface of specimen in slurry jet testing was measured using a previously developed indirect measurement technique [15,16], and then compared with the simulated results. In this measurement, 60–70 mesh spherical glass beads were used as erodent particles to generate impact craters on polished soft copper which had a hardness of 60 HV. The flow rate of glass beads-water slurry was set at 17.6 L/min. This flow rate is used to generate the slurry flow at the speed of 16 m/s, which is used in the NRC standard procedure for accelerated slurry jet erosion testing. The concentration of glass beads was very low to ensure a clear and measurable image of crater distribution on the copper specimen surface. Fig. 3 shows the craters produced on soft copper sample surface in the glass bead-water jet testing. The normal impact velocity of a glass bead can be calculated from the diameter of the crater produced by the bead. According to solid mechanics, the diameter of the crater is related to the kinetic energy of the glass bead [17], which can be expressed as follows:
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1 mV n2 = 2
L. Ma et al. / Wear 334-335 (2015) 49–55
δ max
∫ 0
δ max
Pdδ ≈
∫ 0
1 2 πH (w max)4 πw Hdδ = 4 32D
(7)
where m is the mass of the glass beads; Vn means the normal impact velocity of the glass beads; P is the equivalent contact load at total (elastic and plastic) compression δ , H is the hardness of the sample; w is the diameter of the crater and D is the diameter of the glass beads. Due to the huge number of craters created on the copper surface, only a part of them, which includes a total of 255 craters in a 30° sector are observed and measured by using the measuring microscope on a micro hardness tester (BUEHLER 1600-6300). Then the normal impact velocities are calculated according to Eq. (5). The average of the distribution is 6.05 m/s and the standard deviation is 2.82 m/s. These normal impact velocities are finally normalized to a normal distribution using the above average and standard deviation, which predicts the distribution of all craters. This process is also adopted by Johnson [17]. Having performed the glass bead/water jet testing, the proposed CFD and DPM model was used to simulate the experiment. The normal velocity of the glass beads was obtained by running the subroutine in the post-processing module of ANSYS Fluent 14.5. The squeeze film effect was applied with its effect on the normal velocity considered. The total number of glass bead streams in the simulation was 7830. The normal impact velocity and the frequency for each particle stream were both recorded. The simulation results and experimentally measured particle normal velocity are compared in Fig. 4. In Fig. 4, the solid line shows the normalized distribution of the normal velocities measured using the glass bead method described above, while the columns show the impacting frequency calculated by the modeling. Each column represents the accumulated impact frequency in a 0.2 m/s normal velocity interval. The white columns represent the modeling calculated normal velocities without considering the squeeze film effect, from which the weighted average value is 7.27 m/s. The black columns show the modeling calculated results considering the squeeze film effect and the corresponding weighted average value is 5.89 m/s, which is very close to the average of the measured distribution 6.05 m/s. Here we should mention that according to the modeling almost all particles at the exit of the nozzle have reached velocities of about 16 m/s due to particle drag, which is consistent with the jet velocity at the nozzle exit. So the particles are significantly de-accelerated by drag force from the fluid flow when they are approaching the sample surface. The distribution from the measurement is wider than that from the modeling. The standard deviation from the modeling is 0.71 m/s compared with 2.82 m/s from the measurement. There
Fig. 4. The normal impact velocities of glass beads obtained from measurement and modeling.
are several possible reasons for the wider distribution from the measurement. First of all, the actual slurry flow rate in the testing was not constant at 17.6 L/min as indicated by the recorded flow rate data in Fig. 5, where the fluctuations were due to the pulsated operation of the dual diaphragm slurry pump used in the testing. In Fig. 5, a total of 7062 data points are collected for two hours used as the NRC standard procedure, the average of the flow rate is 17.578 L/min while the standard deviation is 0.902 L/min. Secondly, the glass beads were treated in this modeling to have an identical diameter of 231 μm, but 60–70 mesh glass beads actually have a size distribution with their diameters ranging from 212 μm to 250 μm. Due to the limitation of Eq. (7), we can only assume the particles have a constant diameter to evaluate the distribution of normal velocity, as we cannot know what is the exact size of a particular particle which creates the corresponding crater in Fig. 3. In addition, the glass beads have a much smaller distribution (212–250 μm, average 231 μm) than the sand (the size distribution will be shown in the following section) we used for standard SJE testing. So at current stage, we use the uniform size (the average diameter 231 μm) and round shape particles to validate the modeling results. The good agreement of the weighted average of the normal impact velocities from the modeling with the average of the normalized ones from measurement indicates that this CFD and DPM modeling methodology is able to provide a reasonable prediction for particle motions in slurry flow in open air.
4. Parametric studies In hard rock mining applications, the slurries are usually transported at ambient temperature. However, in Canadian oil sand operations the slurry is heated to an elevated temperature heated up to 60 °C. The nominal impingement angle in a slurry jet erosion testing is usually between 20° and 90° for evaluating the wear resistance of materials under different operating conditions. Therefore in our parametric studies, we use the validated modeling technique to investigate the effect of slurry temperature and nominal impingement angle under the following conditions: 1. Slurry of 90° 2. Slurry of 90° 3. Slurry of 20°
temperatures of 20 °C and nominal impingement angle (20 °C 90°). temperatures of 60 °C and nominal impingement angle (60 °C 90°). temperatures of 20 °C and nominal impingement angle (20 °C 20°).
Fig. 5. Recorded actual slurry flow rate during the 2 h testing showing considerable fluctuations.
L. Ma et al. / Wear 334-335 (2015) 49–55
For above three scenarios, both of the modeling and the testing are performed. Here we should mention again that there are no measuring techniques that can measure the distributions of actual particle speeds and impingement angles for slurry jet system operating in open air at this stage. So we use the proposed modeling technique to calculate the distributions of particle speeds and impingement angles under these three conditions and try to explain how the slurry temperature and nominal impingement angle affect the mass loss rate of the specimen measured from the corresponding testing. EN30B steel was used as the test specimen and AFS 50–70 silica sand was used as the erodent. The standard NRC procedure for accelerated slurry jet erosion testing are followed: (1) the weight ratio of sand to water in the slurry was 1:10; (2) the slurry flow rate was controlled at 17.6 L/min to generate the slurry flow at the speed of 16 m/s; and (3) the erosion test duration was two hours. The total mass loss results of the EN30B steel specimens for three scenarios are measured and summarized in Table 1. The physical properties of fluid phase (water) at 20 °C and 60 °C are listed in Table 2. In the modeling, the size distribution of the erodent particles is considered based on the actual AFS 50–70 silica sand used in the laboratory test, which is shown in Fig. 6. The silica density is 2640 kg/m3. To reduce the calculation time while maintaining reasonable accuracy, all the sand particles are divided into 8 different particle size groups and the flow rate for each size group is calculated based on the particle size distribution chart in Fig. 6. The group size information and the corresponding mass flow rate are listed in Table 3. The calculated distributions of actual particle speeds on the specimen surface are plotted in Fig. 7, which shows the effect of slurry temperature and nominal impingement. In addition, the calculated distributions of actual particle impingement angles under three scenarios are provided in Fig. 8. Fig. 7 shows that for small size particles, the mean particle speed is slightly lower in the scenario (60 °C 90°) than in the scenario (20 °C 90°). However, for the large particle size groups, the mean particle speed remains unchanged at the different temperatures, while the speed distribution in the scenario (60 °C 90°) is narrower as compared with that in the scenario (20 °C 90°). The modeling results also indicate that for all size groups, the scenario (20 °C 90°) testing is associated with wider particle speed distribution than that for the scenario (20 °C 20°). From Fig. 8, the actual impingement angles of individual erodent particles hitting the specimen surface are not identical but rather have a distribution in a certain range of angles. The peak and average impingement angles are lower than the nominal impingement Table 1 Total mass loss of the specimen in two hours. Scenario
(20 °C 90°)
(60 °C 90°)
(20 °C 20°)
Operating conditions
Temperature: 20 °C Nominal impingement angle: 90° 0.5426
Temperature: 60 °C Nominal impingement angle: 90° 0.4417
Temperature: 20 °C Nominal impingement angle: 20° 0.6050
Mass loss (g)
Table 2 Physical properties of water at 20 °C and 60 °C for slurry jet testing. Scenario
(20 °C 90°), (20 °C 20°)
(60 °C 90°)
Temperature Density Viscosity Surface tension
20 °C 0.9982 g/cm3 1.003 g/m/s 0.0735 N/m
60 °C 0.9832 g/cm3 0.47 g/m/s 0.0662 N/m
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Fig. 6. Size distribution of AFS 50–70 silica sand.
Table 3 Sand groups divided by particle size. Group number
Particle diameter (μm)
Volume %
Mass flow rate (g/s)
1 2 3 4 5 6 7 8
182 209 240 275 316 363 417 479
4.1 8.6 15.7 21.1 21.1 16.1 9.0 4.3
1.21 2.55 4.65 6.26 6.26 4.79 2.67 1.27
angle. They are also higher in the scenario (60 °C 90°) than those of the scenario (20 °C 90°), especially for the large particle size groups. For all the size groups, the distribution of real impingement angles for the scenario (20 °C 20°) testing is much narrower than the results for the scenario (20 °C 90°). Most of the particle impingement angles are below the nominal impingement angle. The above simulation results can be applied to explain the experimentally observed phenomenon that erosion rate of the EN30B steel was lower at the elevated temperature of 60 °C than at 20 °C. In the temperature range from 20 °C to 60 °C, temperature should have little effect on the material properties of the EN30B steel. Therefore, the decrease in erosion rate when the slurry temperature increases from the scenario (20 °C 90°) to the scenario (60 °C 90°) can be attributed mainly to the change in the impact conditions of the erodent particles. The erosion rate of metallic materials is usually dependent on the particle speed by a power law Vn, where n ¼ 2.3–3 [18–20]. So the decline of the particle speed from small particle size groups for the high temperature scenario (Fig. 7(a) and (b)) could explain our experimental observation that erosion rate gets lower when slurry temperature goes up. In addition, the higher temperature leads to relatively smaller reduction in actual impingement angles of the individual particles with respect to their nominal angle as the parametric study shows in Fig. 8. This could be another reason why higher temperature resulted in lower erosion rate, because relatively higher impingement angles (greater than about 30°) can result in relatively smaller cutting effect for ductile materials and, as a consequence, lower erosion rate. It is thus not unreasonable to believe that the effect of temperature on erosion rate is from the effect of temperature on water viscosity. The reduced water viscosity at higher temperature leads the decreased particle speeds
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L. Ma et al. / Wear 334-335 (2015) 49–55
Fig. 7. The calculated distributions of particle speed under three scenarios. (a) Size group 1, D =182 μm; (b) Size group 4, D =275 μm; (c) Size group 5, D =316 μm and (d) Size group 8, D =479 μm and (e) averages and standard deviations.
and increased actual impingement angles, which work together to reduce the erosion rate (Table 1). For comparison in terms of the nominal impingement angle, the particle speed is higher in the scenario (20 °C 20°) (Fig. 8) which directly contributes to the higher erosion rate as compared with the testing of the scenario (20 °C 90°). Moreover, the actual
Fig. 8. The calculated distributions of particle impingement angle under three scenarios. (a) Size group 1, D =182 μm; (b) Size group 4, D =275 μm; (c) Size group 5, D =316 μm; (d) Size group 6, D = 479 μm and (e) averages and standard deviations.
impingement angles in the scenario (20 °C 20°) are much lower than those in the scenario (20 °C 90°), leading to considerably higher cutting effect. As a result, the total erosion rate in the scenario (20 °C 20°) testing is higher than that in the scenario (20 °C 90°) testing (Table 1). 5. Physical explanations Now we try to further explain physically the three main phenomena that the above parametric simulation studies have shown.
L. Ma et al. / Wear 334-335 (2015) 49–55
(1) The parametric studies show that the distribution of the particle speeds at higher temperature is narrower than that for lower temperature and the average of the actual impingement angles increases with slurry temperature under the same conditions of nominal impingement angle and particle size distributions. This can be explained based on the variation in viscosity of water. When temperature increases, the viscosity of the slurry decreases. This leads to the decrease in the drag force. Before approaching to the sample surface, the velocities of the erodent particles in the slurry are very uniform and are close to the velocity of the liquid phase. But in the region near the sample surface, the flow field (speed and direction) of the liquid phase changes rapidly, which leads to a change in the motion of erodent particles via drag force. With a weaker drag force at higher temperature, the erodent particles are acted upon with less force to change their motion in speed and direction, which means less disturbance and strong tendency to keep their original motion. Thus the particle speed distribution becomes narrower. Note that the drag forces are in the direction that would always make the actual impingement angles smaller than their nominal impingement angle. The higher drag force due to higher viscosity results in smaller actual impingement angles. (2) The parametric studies also show that the distribution of the particle speeds of large particle size groups is narrower and the average value of particle impingement angles is larger than those of small particle size groups, when the other variables are the same. This can be largely attributed to the effect of particle inertia. Since larger particles have higher inertia compared to smaller ones, the larger particles tend to keep their original motion. On the other hand, the smaller particles are less able to keep their original motion and are more affected by drag force, which contributes to the wider particle speed distribution. Moreover, the larger inertia would make the actual impingement angles closer to the nominal angle; the smaller inertia would make the actual impingement angles more affected leading to smaller actual impingement angles than the nominal angle. (3) The last phenomenon the parametric study has shown that when keeping the other variables such as particle size and slurry temperature unchanged, the distribution of particle speed is narrower and the average value changes less (closer to the original speed in the straight part of the slurry jet) at low nominal impingement angles than those at high impingement angles. In addition, the actual impingement angles in the scenario (20 °C 20°) are very close to the nominal value; but it is not the case for the scenario (20 °C 90°) and the scenario (60 °C 90°). This is mainly related to the difference in the flow fields at the different impingement angles. In the scenario (20 °C 20°), the flow field of fluid phase near the sample surface in terms of speed and direction is not much different from the erodent particles' speed and direction. But for the scenario (20 °C 90°) and the scenario (60 °C 90°), the flow field near the sample surface is very different from the particles' speed and direction. As a result, the erodent particles in the scenario (20 °C 20°) receive less drag force thus they still can keep their original motion in terms of speed and direction without much disturbance. However, the direction of liquid flow in the scenario (20 °C 90°) and the scenario (60 °C 90°) changes dramatically near the sample surface and thus the erodent particles are dragged relatively strongly to change their motions in terms of speed and direction.
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6. Conclusions The model provided in this paper has enabled us to calculate the erodent particles' trajectories in the slurry jet flow, offering some insights into why and how operating conditions affect erosion rate of specimen surface. Compared to the glass bead/water jet testing, the simulation results reasonably agree with experimental observations in terms of normal impact velocities on the specimen surface. Furthermore, the model has been applied to explain the effect of temperature and nominal impingement angle change on the particle velocities and then the erosion rate on the specimen, which were not well understood before. It is envisioned that the proposed model would able to predict erosion rate when integrated with reliable erosion models for specific materials, which gives the relation/correlation between erosion rates, material properties, and erosion conditions such as particle speeds and impingement angles. Further investigations coupled with such erosion models to predict erosion rate are being conducted and the results will be presented in the future.
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Wear journal homepage: www.elsevier.com/locate/wear
Modeling of erodent particle trajectories in slurry flow Liang Ma, Cheng Huang n, Yongsong Xie, Jiaren Jiang, Kidus Yoseph Tufa, Rob Hui, Zhong-Sheng Liu Energy, Mining and Environment Portfolio National Research Council Canada, 4250 Wesbrook Mall, Vancouver, BC, Canada V6T 1W5
art ic l e i nf o
a b s t r a c t
Article history: Received 17 February 2015 Received in revised form 21 April 2015 Accepted 22 April 2015 Available online 29 April 2015
This paper presents a method for calculating erodent particle trajectories in slurry flow. It involves computational fluid dynamics (CFD) for calculating fluid phase flow, the discrete phase method (DPM) for capturing the movement of erodent particles, and the volume of fluid method (VOF) for calculating interfaces between fluid phase and gas phase. The method is illustrated by application to a lab slurry jet testing system, which considers free water/air interface tracking, particle size distribution and local particle concentration. The validation of the modeling is done by comparing to a glass bead/water jet testing. Using the proposed method, further parametric studies are performed for calculating actual particle speeds and impingement angles under different operating conditions and physical explanations of the modeling results are provided in the end. Crown Copyright & 2015 Published by Elsevier B.V. All rights reserved.
Keywords: Slurry flow Particle trajectories Slurry jet erosion testing Computational fluid dynamics
1. Introduction Slurry flow is a very common phenomenon in mining operations for handling and/or transporting solid particles in bulk, where slurry is mainly a mixture of water and solid particles. Slurry flow through hydro-transport systems causes erosive and abrasive wear on pipelines, valves and pumps [1–5]. It becomes essential to design slurry flow that would reduce wear without compromising transport efficiency. With the rapid development of computational technology and numerical algorithms, some numerical simulation techniques, for example, computational fluid dynamics (CFD), the discrete phase method (DPM) along with erosion models have been developed for calculating particle motions and erosion rates. Turenne and Fiset [6] modeled particle trajectories in a slurry based on potential and stream functions. Edwards et al. [7] used CFD code to simulate solid particle trajectories and estimated erosion rate in elbows and plugged-tee geometries. Shah et al. [8] performed CFD modeling of slurry flow in coiled tubing for hydraulic fracturing and compared modeling results with experimental observations. In studying the effect of slurry flow on erosion rate of materials, a slurry jet erosion tester as illustrated in Fig. 1, has been often used at National Research Council Canada (NRC). In this testing setup, a slurry pump and a piping loop produce a slurry jet through a nozzle at controlled speed, which impacts a test specimen surface at a nominal pre-set impingement angle. It is apparent that actual n
Corresponding author. Tel.: þ 1 604 221 3050; fax: þ 1 604 221 3001. E-mail address: [email protected] (C. Huang).
http://dx.doi.org/10.1016/j.wear.2015.04.013 0043-1648/Crown Copyright & 2015 Published by Elsevier B.V. All rights reserved.
particle speeds and impingement angles at different locations of the test specimen surface are different from the nominal values. The overall erosion rate on the specimen surface is from the integral contribution of individual erodent particles, while the contribution of a single particle to the overall erosion rate is a function of its actual kinetic energy, shape, and impingement angle. In other words, the overall erosion rate is determined not only by each particle's motion but also their statistics. There are some published studies on the modeling of slurry jet testing. For example, Gnanavelu et al. [9] proposed a methodology to model a slurry jet erosion test and generate a material wear map through modeling particles' speeds and impingement angles. Moreover, Gnanavelu et al. [10] implemented CFD codes to determine par ticle motion and wear profile on various geometries. Zhang et al. [11] used a CFD model to calculate particles' radial and axial velocities for a slurry jet erosion testing and compared with measurement results using a laser Doppler velocity meter. However, these studies modeled basically slurry jet operating in a tank full of fluid at very low solid concentrations, allowing simplification and neglecting local concentration variations. The NRC slurry jet erosion tester operates in open air which is relatively easy for implementation and maintenance. The testing is usually conducted at relatively high solid concentrations, which more closely simulates many industrial applications and is more favorable than low concentration testing because shorter test duration is required for generating measurable wear volume loss. This has motivated us to track air/water interface and study the effects of local solid concentration. To the authors' knowledge, no studies have been reported in the literature that has simulated such systems.
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L. Ma et al. / Wear 334-335 (2015) 49–55
Fig. 1. Schematic of the NRC's slurry jet erosion tester.
In this paper, a coupled CFD and DPM model is proposed to calculate erodent particle trajectories in slurry flow with ANSYS Fluent and then is applied to simulate the NRC slurry jet erosion testing. In the study, free air/water interface tracking, particle size distribution and local particle concentration variations are all considered. The proposed model is validated by comparing the calculated results to the measured values in a specifically designed glass bead/water jet testing. Furthermore, parametric studies are performed by modeling and the physical explanations of the effect of slurry temperature, nominal impingement angle and even particle size on slurry jet erosion rate are provided based on the analysis of simulation results.
2. Modeling methodology The methodology proposed for modeling slurry flow with water/air interface is developed on ANSYS Fluent 14.5 with 4 parallel processes. For CFD modeling, ANSYS Fluent solves conservation equations for mass and momentum as follows: ⇀ ∂ρ + ∇⋅ ρv = Sm ∂t
(1)
⇀ ⇀ ⇀⇀ ⇀ ∂ ρv + ∇⋅ ρv v = − ∇p + ρg + F ∂t
(2)
( )
( )
( )
where ρ is the fluid density, ⇀ v is the fluid velocity, Sm is the ⇀ source term, p is the static pressure, and ρ⇀ g and F are the gravitational body force and external body forces, respectively. For the application in NRC slurry jet erosion testing, the inner diameter of the nozzle is 5 mm and the distance from the nozzle exit to the targeted surface is 100 mm. The CFD model in Fluent is used to simulate transient flow field from the inlet to the outlet of the computational domain which is shown in Fig. 2. These domains are for 90° impingement angle testing. For simplicity, only half of the real nozzle is modeled and the symmetric boundary conditions are applied. The total number of cells for calculation is 1,748,400. The inflation of meshing is applied on all walls and the estimated interface between water and air. The turbulence model is selected as the realizable k-epsilon model with enhanced wall treatment. Volume of fluid (VOF) is a numerical method which is able to track the shape and location of free surface based on the concept of a fractional volume of fluid [12]. A unity value of the volume fraction corresponds to a full element occupied by the fluid liquid, while a zero value indicates an empty element containing gas. The value of the volume fraction between zero and one indicates that the corresponding element is the surface element. So the interface between water and air for the slurry flow in open air is calculated by the VOF algorithm integrated in ANSYS Fluent.
Fig. 2. (a) Modeling domains and boundary conditions. (b) Image of the mesh grids (totally 1,748,400 cells).
At the beginning, the transient CFD calculation coupled with the VOF goes through numerous iterations until convergence and stabilized mass flow rate at the outlet are reached. The time step in the analysis should be small enough to capture the physical phenomenon. After trials, the time step is set to 1e–5s and for each time step 200 maximum CFD interactions are adopted considering the calculation efficiency. This part of the modeling simulate the period from the time water exits the nozzle to when it hits the target wall (the specimen test surface). At the end of this transient calculation, the obtained values are used as initial inputs to perform a steady state analysis. The fluid interactions last for about 5000 steps and globally scaled residuals for all equations decrease below 0.001 and the mass flow rate at the outlet gets stabilized. Thus the stable interface between water and air is finalized, which means a free water flow in open air is formed. The solid particles are then released in the slurry and they are tracked by the DPM module, which uses the Lagrangian approach. Particle collisions are not considered in this study as the solid volume percentage is below 10%. The particles are divided into particle streams to pair each mesh surface at the domain inlet. The mass flow rate for each particle stream is calculated based on the paired mesh surface area. These particle streams are released to the flow at the domain inlet with their corresponding mass flow rate. All particle streams with their mass flow rates and simulated trajectories recorded by the coordinate values are tracked to consider the variations of the solid concentration at different locations in the fluid rather than assuming the concentration is even everywhere. The trajectories of these particle streams are calculated with the drag force due to fluid flow as the driving force using the Newton's Second Law. The change rate of particle velocity comes directly from the drag force as follows:
Fd = mp
d Vp dt
(3)
where Fd is the drag force vector acting on the particle, Vp is the particle velocity vector (combination of speed and direction) and mp is the particle mass. It should be mentioned that in the DPM
L. Ma et al. / Wear 334-335 (2015) 49–55
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calculation, the momentum exchange between particles and fluid is two-way coupled and turbulence dispersion should also be considered in modeling to improve accuracy and reliability. In the steady state simulation, 50 fluid interactions were performed between each particle trajectory interaction. Additional 2000 fluid interactions are performed to get all residuals below 0.001 and the mass flow rate at the outlet converges to the value from the inlet. Finally, the ANSYS Fluent 14.5 post-process module is used to extract information on local motion in all particle streams hitting on the specimen surface. The outputs of the calculation include, for example, the coordinate values, particle size, impact velocity (speed and impingement angle) and mass flow rate. When the solid particles approach the target wall surface, they must go through a thin layer of fluid near the wall that has relatively low velocity. In addition, they must squeeze the fluid between the particle and the wall to impinge the wall. The effect of the near wall fluid on the velocity of the solid particles is called the squeeze film effect. A simple mathematical model that can simulate this effect was proposed and developed by Clark et al. [13,14]. In order to implement this mathematical model in our study, a programmed post-process subroutine for the squeeze film effect was applied to adjust the particle speeds and impingement angles to get a more accurate prediction. The squeeze film effect depends mainly on particle Reynolds number Rep , which can be obtained from
Rep =
Vn dp ρ f μ
(4)
where Vn is the normal component of the particle velocity, dp is the particle diameter, μ is the dynamic viscosity of the fluid, and ρf is the fluid density. Another important number is critical particle Reynolds number Re* defined by
Re* =
3ξ 2 ⎛ ρp ⎞ 4 ⎜ ρ ⎟ + 2fav ⎝ f⎠
(5)
where ρp is the density of the solid particle, ξ is the particle shape related constant that equals to 10 and fav is set to 1.0 according to references [13,14]. If Rep ≤ Re*, it means that the particle does not touch the target wall surface. If Rep > Re*, then the particle is believed to penetrate the squeeze film and impact the sample surface. The particle normal component of the velocity is reduced to Vnreduced , which can be calculated by
V nreduced =
⎛ ⎞ a ⎜ Re* ⎟ 1− Vn ⎜ a +ξ⎝ Rep ⎟⎠
(6)
⎡ ⎛ ρp ⎞ ⎤ where a = 8 ⎢2 ⎜ ρ ⎟ + fav ⎥. ⎣ ⎝ f⎠ ⎦ After obtaining the velocity and mass flow rate of each particle stream, these results could be applied to an appropriate erosion model to evaluate the erosion rates of the sample, which is not presented in this paper. Finally, the modeling results could be validated by comparison with the measured erosion rate from a slurry jet erosion testing.
3. Model validation The speed and impingement angle of erodent particles are critical parameters for predicting erosion rate. Although the coupled CFD and DPM modeling technique has advanced significantly, its accuracy still needs to be assessed when applied to specific applications. At this stage, there is no technical solution to directly
Fig. 3. Impact craters produced on soft copper sample by 60–70 mesh glass beads in the slurry jet testing. (Black spot in the middle of (a) is the center point). (a) Impact craters produced on soft copper sample. (b) Typical impact craters.
measure the impact frequency distribution of actual particle speed and impingement angle in slurry jet testing, especially for the slurry jet operating in open air according to authors' knowledge. So a glass bead/water jet testing is specially designed to validate the proposed model. The normal component of round glass bead velocity on the surface of specimen in slurry jet testing was measured using a previously developed indirect measurement technique [15,16], and then compared with the simulated results. In this measurement, 60–70 mesh spherical glass beads were used as erodent particles to generate impact craters on polished soft copper which had a hardness of 60 HV. The flow rate of glass beads-water slurry was set at 17.6 L/min. This flow rate is used to generate the slurry flow at the speed of 16 m/s, which is used in the NRC standard procedure for accelerated slurry jet erosion testing. The concentration of glass beads was very low to ensure a clear and measurable image of crater distribution on the copper specimen surface. Fig. 3 shows the craters produced on soft copper sample surface in the glass bead-water jet testing. The normal impact velocity of a glass bead can be calculated from the diameter of the crater produced by the bead. According to solid mechanics, the diameter of the crater is related to the kinetic energy of the glass bead [17], which can be expressed as follows:
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1 mV n2 = 2
L. Ma et al. / Wear 334-335 (2015) 49–55
δ max
∫ 0
δ max
Pdδ ≈
∫ 0
1 2 πH (w max)4 πw Hdδ = 4 32D
(7)
where m is the mass of the glass beads; Vn means the normal impact velocity of the glass beads; P is the equivalent contact load at total (elastic and plastic) compression δ , H is the hardness of the sample; w is the diameter of the crater and D is the diameter of the glass beads. Due to the huge number of craters created on the copper surface, only a part of them, which includes a total of 255 craters in a 30° sector are observed and measured by using the measuring microscope on a micro hardness tester (BUEHLER 1600-6300). Then the normal impact velocities are calculated according to Eq. (5). The average of the distribution is 6.05 m/s and the standard deviation is 2.82 m/s. These normal impact velocities are finally normalized to a normal distribution using the above average and standard deviation, which predicts the distribution of all craters. This process is also adopted by Johnson [17]. Having performed the glass bead/water jet testing, the proposed CFD and DPM model was used to simulate the experiment. The normal velocity of the glass beads was obtained by running the subroutine in the post-processing module of ANSYS Fluent 14.5. The squeeze film effect was applied with its effect on the normal velocity considered. The total number of glass bead streams in the simulation was 7830. The normal impact velocity and the frequency for each particle stream were both recorded. The simulation results and experimentally measured particle normal velocity are compared in Fig. 4. In Fig. 4, the solid line shows the normalized distribution of the normal velocities measured using the glass bead method described above, while the columns show the impacting frequency calculated by the modeling. Each column represents the accumulated impact frequency in a 0.2 m/s normal velocity interval. The white columns represent the modeling calculated normal velocities without considering the squeeze film effect, from which the weighted average value is 7.27 m/s. The black columns show the modeling calculated results considering the squeeze film effect and the corresponding weighted average value is 5.89 m/s, which is very close to the average of the measured distribution 6.05 m/s. Here we should mention that according to the modeling almost all particles at the exit of the nozzle have reached velocities of about 16 m/s due to particle drag, which is consistent with the jet velocity at the nozzle exit. So the particles are significantly de-accelerated by drag force from the fluid flow when they are approaching the sample surface. The distribution from the measurement is wider than that from the modeling. The standard deviation from the modeling is 0.71 m/s compared with 2.82 m/s from the measurement. There
Fig. 4. The normal impact velocities of glass beads obtained from measurement and modeling.
are several possible reasons for the wider distribution from the measurement. First of all, the actual slurry flow rate in the testing was not constant at 17.6 L/min as indicated by the recorded flow rate data in Fig. 5, where the fluctuations were due to the pulsated operation of the dual diaphragm slurry pump used in the testing. In Fig. 5, a total of 7062 data points are collected for two hours used as the NRC standard procedure, the average of the flow rate is 17.578 L/min while the standard deviation is 0.902 L/min. Secondly, the glass beads were treated in this modeling to have an identical diameter of 231 μm, but 60–70 mesh glass beads actually have a size distribution with their diameters ranging from 212 μm to 250 μm. Due to the limitation of Eq. (7), we can only assume the particles have a constant diameter to evaluate the distribution of normal velocity, as we cannot know what is the exact size of a particular particle which creates the corresponding crater in Fig. 3. In addition, the glass beads have a much smaller distribution (212–250 μm, average 231 μm) than the sand (the size distribution will be shown in the following section) we used for standard SJE testing. So at current stage, we use the uniform size (the average diameter 231 μm) and round shape particles to validate the modeling results. The good agreement of the weighted average of the normal impact velocities from the modeling with the average of the normalized ones from measurement indicates that this CFD and DPM modeling methodology is able to provide a reasonable prediction for particle motions in slurry flow in open air.
4. Parametric studies In hard rock mining applications, the slurries are usually transported at ambient temperature. However, in Canadian oil sand operations the slurry is heated to an elevated temperature heated up to 60 °C. The nominal impingement angle in a slurry jet erosion testing is usually between 20° and 90° for evaluating the wear resistance of materials under different operating conditions. Therefore in our parametric studies, we use the validated modeling technique to investigate the effect of slurry temperature and nominal impingement angle under the following conditions: 1. Slurry of 90° 2. Slurry of 90° 3. Slurry of 20°
temperatures of 20 °C and nominal impingement angle (20 °C 90°). temperatures of 60 °C and nominal impingement angle (60 °C 90°). temperatures of 20 °C and nominal impingement angle (20 °C 20°).
Fig. 5. Recorded actual slurry flow rate during the 2 h testing showing considerable fluctuations.
L. Ma et al. / Wear 334-335 (2015) 49–55
For above three scenarios, both of the modeling and the testing are performed. Here we should mention again that there are no measuring techniques that can measure the distributions of actual particle speeds and impingement angles for slurry jet system operating in open air at this stage. So we use the proposed modeling technique to calculate the distributions of particle speeds and impingement angles under these three conditions and try to explain how the slurry temperature and nominal impingement angle affect the mass loss rate of the specimen measured from the corresponding testing. EN30B steel was used as the test specimen and AFS 50–70 silica sand was used as the erodent. The standard NRC procedure for accelerated slurry jet erosion testing are followed: (1) the weight ratio of sand to water in the slurry was 1:10; (2) the slurry flow rate was controlled at 17.6 L/min to generate the slurry flow at the speed of 16 m/s; and (3) the erosion test duration was two hours. The total mass loss results of the EN30B steel specimens for three scenarios are measured and summarized in Table 1. The physical properties of fluid phase (water) at 20 °C and 60 °C are listed in Table 2. In the modeling, the size distribution of the erodent particles is considered based on the actual AFS 50–70 silica sand used in the laboratory test, which is shown in Fig. 6. The silica density is 2640 kg/m3. To reduce the calculation time while maintaining reasonable accuracy, all the sand particles are divided into 8 different particle size groups and the flow rate for each size group is calculated based on the particle size distribution chart in Fig. 6. The group size information and the corresponding mass flow rate are listed in Table 3. The calculated distributions of actual particle speeds on the specimen surface are plotted in Fig. 7, which shows the effect of slurry temperature and nominal impingement. In addition, the calculated distributions of actual particle impingement angles under three scenarios are provided in Fig. 8. Fig. 7 shows that for small size particles, the mean particle speed is slightly lower in the scenario (60 °C 90°) than in the scenario (20 °C 90°). However, for the large particle size groups, the mean particle speed remains unchanged at the different temperatures, while the speed distribution in the scenario (60 °C 90°) is narrower as compared with that in the scenario (20 °C 90°). The modeling results also indicate that for all size groups, the scenario (20 °C 90°) testing is associated with wider particle speed distribution than that for the scenario (20 °C 20°). From Fig. 8, the actual impingement angles of individual erodent particles hitting the specimen surface are not identical but rather have a distribution in a certain range of angles. The peak and average impingement angles are lower than the nominal impingement Table 1 Total mass loss of the specimen in two hours. Scenario
(20 °C 90°)
(60 °C 90°)
(20 °C 20°)
Operating conditions
Temperature: 20 °C Nominal impingement angle: 90° 0.5426
Temperature: 60 °C Nominal impingement angle: 90° 0.4417
Temperature: 20 °C Nominal impingement angle: 20° 0.6050
Mass loss (g)
Table 2 Physical properties of water at 20 °C and 60 °C for slurry jet testing. Scenario
(20 °C 90°), (20 °C 20°)
(60 °C 90°)
Temperature Density Viscosity Surface tension
20 °C 0.9982 g/cm3 1.003 g/m/s 0.0735 N/m
60 °C 0.9832 g/cm3 0.47 g/m/s 0.0662 N/m
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Fig. 6. Size distribution of AFS 50–70 silica sand.
Table 3 Sand groups divided by particle size. Group number
Particle diameter (μm)
Volume %
Mass flow rate (g/s)
1 2 3 4 5 6 7 8
182 209 240 275 316 363 417 479
4.1 8.6 15.7 21.1 21.1 16.1 9.0 4.3
1.21 2.55 4.65 6.26 6.26 4.79 2.67 1.27
angle. They are also higher in the scenario (60 °C 90°) than those of the scenario (20 °C 90°), especially for the large particle size groups. For all the size groups, the distribution of real impingement angles for the scenario (20 °C 20°) testing is much narrower than the results for the scenario (20 °C 90°). Most of the particle impingement angles are below the nominal impingement angle. The above simulation results can be applied to explain the experimentally observed phenomenon that erosion rate of the EN30B steel was lower at the elevated temperature of 60 °C than at 20 °C. In the temperature range from 20 °C to 60 °C, temperature should have little effect on the material properties of the EN30B steel. Therefore, the decrease in erosion rate when the slurry temperature increases from the scenario (20 °C 90°) to the scenario (60 °C 90°) can be attributed mainly to the change in the impact conditions of the erodent particles. The erosion rate of metallic materials is usually dependent on the particle speed by a power law Vn, where n ¼ 2.3–3 [18–20]. So the decline of the particle speed from small particle size groups for the high temperature scenario (Fig. 7(a) and (b)) could explain our experimental observation that erosion rate gets lower when slurry temperature goes up. In addition, the higher temperature leads to relatively smaller reduction in actual impingement angles of the individual particles with respect to their nominal angle as the parametric study shows in Fig. 8. This could be another reason why higher temperature resulted in lower erosion rate, because relatively higher impingement angles (greater than about 30°) can result in relatively smaller cutting effect for ductile materials and, as a consequence, lower erosion rate. It is thus not unreasonable to believe that the effect of temperature on erosion rate is from the effect of temperature on water viscosity. The reduced water viscosity at higher temperature leads the decreased particle speeds
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L. Ma et al. / Wear 334-335 (2015) 49–55
Fig. 7. The calculated distributions of particle speed under three scenarios. (a) Size group 1, D =182 μm; (b) Size group 4, D =275 μm; (c) Size group 5, D =316 μm and (d) Size group 8, D =479 μm and (e) averages and standard deviations.
and increased actual impingement angles, which work together to reduce the erosion rate (Table 1). For comparison in terms of the nominal impingement angle, the particle speed is higher in the scenario (20 °C 20°) (Fig. 8) which directly contributes to the higher erosion rate as compared with the testing of the scenario (20 °C 90°). Moreover, the actual
Fig. 8. The calculated distributions of particle impingement angle under three scenarios. (a) Size group 1, D =182 μm; (b) Size group 4, D =275 μm; (c) Size group 5, D =316 μm; (d) Size group 6, D = 479 μm and (e) averages and standard deviations.
impingement angles in the scenario (20 °C 20°) are much lower than those in the scenario (20 °C 90°), leading to considerably higher cutting effect. As a result, the total erosion rate in the scenario (20 °C 20°) testing is higher than that in the scenario (20 °C 90°) testing (Table 1). 5. Physical explanations Now we try to further explain physically the three main phenomena that the above parametric simulation studies have shown.
L. Ma et al. / Wear 334-335 (2015) 49–55
(1) The parametric studies show that the distribution of the particle speeds at higher temperature is narrower than that for lower temperature and the average of the actual impingement angles increases with slurry temperature under the same conditions of nominal impingement angle and particle size distributions. This can be explained based on the variation in viscosity of water. When temperature increases, the viscosity of the slurry decreases. This leads to the decrease in the drag force. Before approaching to the sample surface, the velocities of the erodent particles in the slurry are very uniform and are close to the velocity of the liquid phase. But in the region near the sample surface, the flow field (speed and direction) of the liquid phase changes rapidly, which leads to a change in the motion of erodent particles via drag force. With a weaker drag force at higher temperature, the erodent particles are acted upon with less force to change their motion in speed and direction, which means less disturbance and strong tendency to keep their original motion. Thus the particle speed distribution becomes narrower. Note that the drag forces are in the direction that would always make the actual impingement angles smaller than their nominal impingement angle. The higher drag force due to higher viscosity results in smaller actual impingement angles. (2) The parametric studies also show that the distribution of the particle speeds of large particle size groups is narrower and the average value of particle impingement angles is larger than those of small particle size groups, when the other variables are the same. This can be largely attributed to the effect of particle inertia. Since larger particles have higher inertia compared to smaller ones, the larger particles tend to keep their original motion. On the other hand, the smaller particles are less able to keep their original motion and are more affected by drag force, which contributes to the wider particle speed distribution. Moreover, the larger inertia would make the actual impingement angles closer to the nominal angle; the smaller inertia would make the actual impingement angles more affected leading to smaller actual impingement angles than the nominal angle. (3) The last phenomenon the parametric study has shown that when keeping the other variables such as particle size and slurry temperature unchanged, the distribution of particle speed is narrower and the average value changes less (closer to the original speed in the straight part of the slurry jet) at low nominal impingement angles than those at high impingement angles. In addition, the actual impingement angles in the scenario (20 °C 20°) are very close to the nominal value; but it is not the case for the scenario (20 °C 90°) and the scenario (60 °C 90°). This is mainly related to the difference in the flow fields at the different impingement angles. In the scenario (20 °C 20°), the flow field of fluid phase near the sample surface in terms of speed and direction is not much different from the erodent particles' speed and direction. But for the scenario (20 °C 90°) and the scenario (60 °C 90°), the flow field near the sample surface is very different from the particles' speed and direction. As a result, the erodent particles in the scenario (20 °C 20°) receive less drag force thus they still can keep their original motion in terms of speed and direction without much disturbance. However, the direction of liquid flow in the scenario (20 °C 90°) and the scenario (60 °C 90°) changes dramatically near the sample surface and thus the erodent particles are dragged relatively strongly to change their motions in terms of speed and direction.
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6. Conclusions The model provided in this paper has enabled us to calculate the erodent particles' trajectories in the slurry jet flow, offering some insights into why and how operating conditions affect erosion rate of specimen surface. Compared to the glass bead/water jet testing, the simulation results reasonably agree with experimental observations in terms of normal impact velocities on the specimen surface. Furthermore, the model has been applied to explain the effect of temperature and nominal impingement angle change on the particle velocities and then the erosion rate on the specimen, which were not well understood before. It is envisioned that the proposed model would able to predict erosion rate when integrated with reliable erosion models for specific materials, which gives the relation/correlation between erosion rates, material properties, and erosion conditions such as particle speeds and impingement angles. Further investigations coupled with such erosion models to predict erosion rate are being conducted and the results will be presented in the future.
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