3.1. Mechanism Description
In the DDPM calculation process, the solid–liquid two-phase flow shows a fine interaction mechanism. As with most Euler methods, the continuous phase (water flow) sweeps all the grids in the form of quasi-uniform fields, evolving with the continuity equation of non-phase transitions. Unlike conventional methods, DDPM is compatible with continuous and discrete computations.
Figure 3 shows the forces and motions of the particle phase during the calculation of the self-defined model in this study.
In the granular particle tracing system, the tailings particles migrate in the model cell in three modes: The entry mode, the reflection mode, and the escape mode. In the incident phase, each element of the inlet is taken as a channel, and the tailing particles enter the flow field in the order of the Rosin–Rammler particle size distribution, as shown in Equation (5). The calculated value of particle size distributions with the calculated curve fitting in
Figure 2c is 0.026 mm. In the flow field, the particle-phase interaction is shown by the following formula:
Figure 3 shows the flow field on the role of particles, which are mainly gravitational and interphase drag forces (interphase mass transfer as 0), as follows:
The particles exhibit the reflection mode and escape mode at the cell junction. The reflection mode is the main form of particle phase interactions with wall units, which is characterized by the erosion of tailings particles or the dissipation of kinetic energy after sedimentation. This concentrated area tends to form erosion and sedimentation zones of the particle phase, which is obviously different from the homogeneous field simulation. When the particle flow is close to the boundary and the outlet of the flow field, the contact surface adopts the escape mode and the flow field enters the next action phase. Particle phase and kinematic characteristics are recorded in real time using a Granular tracking system in the form of node information feedback.
The results of pressure, flow field, and discrete phase distributions of the filling process with different slurry concentrations and flow rates were calculated using the UDF model of DDPM, as shown below.
3.2. Concentration Analyses
The slurry concentration was controlled within 50%~70%, and slurry transportation flow within 50~70 m3/h to accord with the practical needs of mine filling system optimization. In the first stage of the simulation, the initial volume flow was fixed for 70 m3/h, slurry transportation simulation analyses of different concentrations were conducted in this condition.
The internal pressure distribution for the slurry concentration was 70%, and the conveying flow rate as 70 m
3/h, shown in
Figure 4 and
Figure 5. This shows that the flow field static pressure decreases step-by-step from entrance to the export, in addition to a certain degree of recovery at the elbow. The dynamic pressure is stable because of the traffic flow field. The maximum dynamic pressure appears at the center of the pipe, but is relatively concentrated at the bend; therefore, the wear of the elbow is more serious. The overall dynamic pressure in the flow field is stable due to the stable flow control. The flow field characteristics, without significant velocity gradients, are also consistent with the properties of high-concentration slurry transport. The maximum dynamic pressure is 9.53 kPa, which appeared at the pipeline axis. Baseline conveying pressure of the scheme with slurry concentrations of 50%, 55%, 60%, 55%, and 70% were extracted, as shown in
Figure 6.
It is clearly observed from
Figure 6 that the flow field static pressure decreases gradually from entrance to export. The lower the slurry concentration is, the lower the inlet pressure, which is contrary to the outlet pressure. Both peak values of positive pressure and negative pressure appeared in the transmission scheme with a slurry concentration of 70% and a flow rate of 70 m
3/h. The inlet and outlet pressures are 98.6 kPa and −201.5 kPa, respectively. According to the Bernoulli equation, the dynamic pressure is maintained in a stable state, thus, the static pressure difference is the pipeline resistance loss of backfilling transportation. The calculation results are shown in
Table 1.
With different concentrations, the filling slurry shows different transport characteristics. As can be seen from the calculation of the loss of resistance in
Table 1, the maximum value of the pipeline resistance loss is 300.1 kPa (concentration 70%) and the minimum is 258.9 kPa (50% concentration). With the decrease of slurry concentration, the absolute value of pipeline transportation pressure became smaller, and the resistance loss decreased. The difference of inlet pressure between the solutions is low (about 4 kPa), but the difference in the outlet pressure is increased (up to nearly 10 kPa). This indicates that the increase of the slurry concentration increases the viscous resistance between the pipe wall and particle flow at the same flow rate. When the slurry concentration is less than 60%, the resistance loss is reduced to below 10 kPa. The main reason for this is that, with continuous dilution, the slurry fluidity is improved. However, with the decrease of the tailing sand content, the decreasing trend of the fluid density slows and the magnitude of the improvement decreases. A comparison between the two schemes shows that the decrease of the slurry concentration in the steady flow field can help the fluidity, but, when the slurry concentration is lower than 60%, the effect is not obvious.
Since the particle collision angle function proposed by Huser and Kvernvold [
22] is used by the CFD model, and a number of erosion empirical models, we applied this model for erosion calculations.
where
is the wall erosion rate, kg/m
2·s;
N is the number of particle collisions;
is the mass flow rate of particles kg/s;
is the particle size function;
is the relative velocity function;
is the area of the unit, m
2; and
is the wall collision angle, wherein:
The results of the wall erosion rate under different concentrations were extracted, as shown in
Figure 7.
The erosion rate is calculated by counting the cumulative damage of each particle to the wall. It can be seen from the erosion diagram of the different concentration schemes that the main scope of erosion influence is in the range of about 8 m from the elbow; the closer to the elbow, the more obvious the increase in erosion rate. The maximum erosion rate appears in the origin, the minimum value is kg/m2·s (concentration 50%), the maximum value is kg/m2·s (concentration 70%). From the comparison of the maximum erosion rate and the influence range of different schemes, it can be seen that, when the slurry concentration is less than 60%, the erosion rate and influence range increase slowly, and the average erosion rate is below kg/m2·s. When the concentration is higher than 60%, the erosion rate increases significantly, and the average erosion rate exceeds kg/m2·s, the maximum erosion rate exceeds kg/m2·s. In the scheme of a slurry concentration of 70%, the erosion rate obviously fluctuated, and the grain flow shows an unstable state, indicating that the erosion area is no longer concentrated in the pipeline bus, and obvious diffusion occurs. There is a significant turbulence in the elbow, which presents a risk of slurry leakage.
The erosion contrast chart was developed in order to show the erosion range in different scenarios. It can be seen that, with the increase of slurry concentration, the median value of the erosion rate experiences a near-linear growth, indicating that, with the increase of concentration, the erosion of particles continue to accumulate. With the removal of outliers, the minimum erosion rate of schemes with slurry concentrations of 65% and 70% exceed kg/m2·s, significantly exceeding other schemes, which is not conducive to transport stability. When the concentration does not exceed 60%, the erosion box diagrams are stable at a low level. The erosion of the filling pipeline is a long-term effect, and the erosion of the solid phase on the pipeline will continue until the bottom of the pipe is damaged. It can be seen from the comparison that, under the conditions of gravity transport, the control of slurry concentrations (not more than 60%) is helpful to maintain the stability of the flow field and lower erosion damage.
Different from the pressure and velocity distributions, the flow of backfilling particles are heterogeneous, although initial velocity boundary conditions of the particle phase were fixed for a uniform flow. This is mainly caused by the interphase coupling effect, collision, and friction with the pipe shell in the flow field. With slurry particle size parameters set, the discrete phase particle movement of schemes with different slurry concentrations was simulated. Results are shown in
Figure 8.
Figure 8 shows the movement and distribution of dispersed phase particles in the pipeline (cross-sectional and longitudinal). Measurements of 0.002~0.07 mm (content more than 90%) were set up as the particle size constraints for demonstration of accurate analysis results. As shown, particle motion is relatively stable in the vertical pipe section, in addition to a certain degree of separation at the end, mainly due to the viscous forces of the wall. Particle size distribution is obviously changed at the elbow, showing a non-linear mixed flow state. At this stage, interphase interactions and erosion effects of the tube wall are obviously increased. The ultimate appearance of flow field characteristics in the horizontal branch is an unsteady particle mixing flow. Particle flow characteristics of the flow field were accurately simulated using the dense phase particle model.
The distribution of dispersed phase particles 8~10 m out the bend is shown on the right side of
Figure 8 (corresponding to the results in
Table 2). This region is a high turbulence area for pipeline transportation. It can be seen that the coarse particles concentrate at the center of the pipe; the closer to the wall, the more obvious the fine particle distributions are, due to the smaller viscosities. The particle size distribution at different slurry concentrations is shown in
Table 2. It was found that the particle diameter range of the 65% scheme is 0.007–0.17 mm, and in the concentration range of the 70% scheme, it is 0.011–0.25 mm. Under the conditions of high concentration transportation, the coarse particle distribution is obvious and the weighted average diameter is more than 0.045 mm. With the decrease in concentration, the trace amounts of coarse particles decrease, as with the content of coarse particles. The particle size range of the 50% scheme is 0.002–0.049 mm, with coarse particle content decreases.
Different slurry concentration schemes showed different grain size characteristics in the post-eroded zone, and the reasons can be summarized as follows:
In schemes with 65% and 70% concentrations, the tailing erosion is obvious and local turbulence is formed near the elbow. The original particle size structures of the particles re broken and the distribution is obviously uneven, resulting in a concentrated distribution of coarse particles. Siltation and plugging may be caused by the long-term erosion effect of the particle flow. In the 55% and 50% schemes, although the fluidity is good, there is obvious shear thinning in the post-eroded area due to the low content of particles and the poor viscosity, leading to particle size separation, which is not conducive to backfill integrity.
These two conditions are not conducive to the continuity of the filling operation due to the uniform content of the total particles during transport. By comparing the particle size characteristics of the post-eroded zone, it can be seen that the weighted average particle diameter values increase with concentration, and the average particle diameter of the 60% slurry concentration is 0.027 mm, the closest to the particle size curve fitting characterization of 0.026 mm. After erosion, the flow field gradually returns to a laminar flow state. Particle flow mixing and separation are reduced. The scheme with a 60% concentration keeps the homogeneity of the slurry and the integrity of the flow field, which are the most favorable schemes.
By summarizing the analysis results of resistance loss, erosion rate, and particle size distributions, the scheme with a slurry concentration 60% satisfies the demand of high concentration, ultrafine backfilling transportation, with little resistance loss, erosion rate, and good particle uniformity. The scheme can guarantee the transmission stability and cemented backfill integrity.
3.3. Slurry Flow Analyses
Backfilling pipeline flow optimization was conducted based on the results of the concentration analysis. In the first stage of simulation, the initial slurry concentration was set to 60%, slurry transportation simulation analyses of different slurry flows (50, 55, 60, 65, and 70 m
3/h) were conducted under these conditions. Pressure calculation results are shown in
Table 3.
When the flow rate is not the same, filling transportation shows different resistance characteristics. From the results of the resistance loss calculation in
Table 2, it can be seen that the maximum value of pipeline resistance loss is 271.6 kPa (flow 70 m
3/h), the minimum value is 179.3 kPa (flow 50 m
3/h). With the decrease of the conveying flow, the absolute value of the pipe conveying pressure becomes smaller, and the resistance loss gradually decreases. The loss difference between the two schemes is about 20 kPa, indicating that the resistance loss of the two-phase flow will increase with an increase in the slurry flow rate under the same concentration conditions. According to
Figure 8, when the slurry flow continues to decrease, the pipe resistance loss showed a near-linear trend. The results of
Figure 8 show that the maximum value of the shear stress is 229.7 Pa with a flow rate of 70 m
3/h and a minimum value 148.4 Pa with flow rate of 50 m
3/h. With the increase in the conveying flow, the shear stress of the wall is obviously increased.
As can be seen from the results shown in
Figure 9, at a flow rate of 50~70 m
3/h, the pipeline resistance loss and wall shear stress exhibit a linear growth trend. The main reason for this is that, in the solid and liquid two-phase full flow state, the concentration and flow are relatively stable; when the flow changes, the frequency of the particle phase experiences flow field changes. As the flow rate increases, the wall resistance, the interphase drag force, and the internal collision of the dispersed phase will increase, leading to increased energy consumption and resistance loss. At the same time, the collisions and friction between the particle flow and the wall increase, which leads to an increase of wall shear stress. This result shows that, unlike the concentration change, the impact of the change of the conveying flow on the resistance and wear of a pipeline is direct. If the flow velocity is too large, the transportation consumption and the wall wear will increase. Long-term work is liable to cause slurry and leakage. Through comparison of the schemes, it is shown that, under the premise of satisfying the conveying capacity of filling slurry, the conveying flow should be minimized in order to reduce the resistance loss of pipeline transportation, thus reducing the energy consumption and pipe wear.
Slurry flow, not only related to the size of the conveyor resistance loss, also affects pipeline stress and the distribution of the solid phase. The elbow branch was set as the research domain for analyses on shear stress and discrete phase mass fraction of schemes with different volume flows, as shown in
Figure 10.
Figure 10 shows the mass distribution of the discrete phase with different flow rates. During the filling process, the distribution of the discrete phase is relatively uniform in the front part of the elbow. After the elbow, due to erosion and sedimentation, the dispersed phase particles concentrated at the bottom of the pipeline. During this period, particle flow has undergone the biggest erosion stage during the transportation process. In the slurry, some tailing particles settled due to a depletion of kinetic energy. As can be seen from the nephogram in
Figure 10, the mass fraction of the upper part of the pipeline is significantly lower than the bottom, so that the bottom of the pipeline at this time experienced particle aggregation. When disturbed by turbulence in the flow field, tailings particles restarted movement, but, if the flow is insufficient, siltation occurs in tailing particles that cannot be transported. The curve shows the maximum mass fraction at the elbow at different flows. When the flow rate decreases, the mass fraction of the dispersed phase increases. When the flow rate is less than 55 m
3/h, the mass fraction obviously increases. When the flow rate reaches 50 m
3/h, the maximum mass fraction reaches 2450 kg/m
3, and the particle aggregation range is also larger than in other schemes. The red line shows the solid phase density (2500 kg/m
3), indicating that, in this scheme, the filling slurry is likely to form dehydration deposition.
As the filling slurry is a two-phase mixed flow with high solid content, the high content of the tailings may cause sedimentation of the pipeline during transportation. As a key part of pipeline transportation, the probability of silt deposition is highest at the bend, and it is also a problem for areas of high obstruction, which directly affects the operation of the filling system. Moreover, accumulative siltation will greatly reduce the service life of a pipeline. The problem of tailing sedimentation depends on the velocity of pipeline transportation. Excessive flow velocity will cause erosion damage and resistance loss of a pipeline, and can even cause pipeline leakage. A flow rate that is too low will cause the tailings to be deposited in the transportation process, not only causing pipe blockage, but can also reduce the quality of backfills. For the purpose of reducing energy consumption and pipe wear, a lower flow rate should be selected when the filling demand has been met. From analyses of the mass fraction of the dispersed phase, it can be concluded that a flow rate of 50 m3/h leads to obvious concentrations of particle phase mass distribution. With an increase in conveying distance, the slurry can be dehydrated. When the flow rate reaches 55 m3/h, the concentration trend of the discrete phase is not obvious, and the maximum mass fraction decreased significantly. Therefore, in order to reduce resistance loss, while controlling the deposition of the discrete phase, and to ensure filling efficiency, the transport scheme with a flow rate of 55 m3/h was selected for reasonable delivery. The requirements of the backfilling system capacity at the Mercury Cave gold mine is 300 m3/d, setting an effective work time of six hours will meet the requirements.
The numerical simulation work established the pipeline flow field model using the CFD-DDPM (computational fluid dynamics-dense discrete phase model) method, with interface drag forces and particle size distribution characteristics of the imported transmission. Accuracy of calculation results was guaranteed by function fitting and the UDF method. Different from the optimization method, by only reducing the concentration and flow rate [
21], a variety of factors were considered in the analysis. Combining the conclusions, mentioned above, transportation parameters with a slurry concentration of 60%, a volume flow 55 m
3/h was selected as the optimal transportation scheme.