sump pump jet

peng2020 slurry pump

ABSTRACT

Centrifugal slurry pumps are commonly used to convey solid materials in many industries including the mining, power, and marine industries. The solid particles in the slurry frequently impact the pump inner wall resulting in signicant wear of the ow passage. Frequent replace-ment of the pump components is not only expensive, but also wastes manpower and time. Therefore, many studies have sought to nd optimal designs of slurry pumps that are efcient and have less wear. This study used Eulerian-Eulerian mixture model to simulate the solid–liquid two- phase ow of quartz sand and water in a slurry pump. The impeller was optimized statistically. Then, the original pump design and the optimized pump design were manufactured for a geo-metric similarity ratio of 1:0.408. The wear rates in the two slurry pumps were then measured by weight loss measurements. The tests show that the optimized pump has less wear, longer service life and meets the design goals which shows that this optimization method is effective.

1.In tr od uc ti on

Slurry pumps are widely used to convey slurries containing solid particles. However, the solid particles in these slurries cause signicant wear of the ow passage which results in material loss and shortens the pump lifetime, which leads to large production losses. Therefore, industry needs slurry pump designs that are efcient, have little wear and have long lifetimes. The research on the movement of solid–liquid two-phase ows inside slurry pumps can be traced back to the 1920s. Some researchers have studied the move ment of solid particles inside centrifugal pumps from different angles through experiments and have analyzed the effects of particle size and slurry concentration on the slurry pump head and efciency. Shi et al. designed a slurry pump test bench that did not include stirring that allowed PIV measurements to study the solid–liquid two-phase ow in a centrifugal pump without the inuence of the high-speed rotation on the solid–liquid mixing process. Kumar et al. used Fluent to analyze the steady-state ow in a slurry pump at various spee ds with comparisons to experimental data. Huang et al. analyzed the particle trajectories and the resulting wear for various sedime nt types and inlets. They found that the wear on the impeller was mainly on the working surface and the rear cover. Kha et al. performed abrasion tests on a centrifugal pump impeller which showed that the erosion by the particles was the main reason for the impeller damage. The development of CFD tools in the 1980s led to many numerical studies of the internal ow elds in slurry pumps. Some studies simulated the solid–liquid two–phase ows of particles to predict the particle trajectories in the pumps. Roco et al. predicted the concentration and velocity distributions in the impeller region and the volute using a numerical model of the solid particle concentration in the slurry pump. Pagalthivarthi et al. predicted the velocities and concentrations of the solid particle phase in a radial section of a slurry pump with simulations of the s olid–liquid two-phase ow eld in a three-dimensional slurry pump model to predict the wear. Arakawa et al. calculated the solid particle velocity distribution in the volute using a nite element method and showed that the pressure loss in the volute was related to the volute prole, ow rate, solid particle concentration and boundary conditions. Rahu et al. used the Euler-Euler multiphase ow model with a sliding grid for unsteady simulations of the ow in a slurry pump to analyze the inuence of particle size and concentration on the ow eld in the impeller region and volute at the optimal efciency point. Cai et al. used particle and heterogeneous models to study the effect of various back blade shapes on the wear characteristics of the slurry pump with predictions of the wear based on the vorticity along the front and rear shrouds. For the optimization of slurry pumps, Derakhshan and Bashiri used Articial Neural Networks (ANN) and Eagle Strategy (ES) algorithms coupled with Eulerian-Eulerian model to optimize the impeller design, and the results indicated a reasonable improvement in the optimal design of pump impeller. Cellek and Engin used CFD to optimize the shroud type impeller, they found that the hydraulic efciency of the centrifugal slurry pump can be increased up to 9% by using the backward long blades. Gjernes used the Adaptive Response Surface Method algorithm with an Intelligent Space Exploration Strategy to minimize wear in the pump impeller, the optimum splitter conguration yielded an almost 19% decrease in the wear with a slight increase in efciency. Wang et al. successfully used RBF (radial basis function) neural network and NSGA-II algorithm to improve the hydraulic characteristics of the impeller and the performance of centrifugal slurry pump. Therefore, the combination of CFD and different optimization algorithms have been become a powerful way to optimal design the centrifugal slurry pump. Even lots of research on the ows in centrifugal slurry pumps has been carried out based on experiments and numerical simulations, but how to optimize the slurry pump hydraulics and wear is still a challenge work in pump design area. By using CFD and central composite circumscribed method, this study optimized a centrifugal pump impeller design to improve its wear characteristics using experimental and numerical models.

2.Mode l and nume rica l met hod

2.1.Two-phase ow model

Solid-liquid two-phase ows can be simulated using the Eulerian-Eulerian method, Eulerian-Lagrangian method and Lagrangian- Lagrangian method. Euler’s method does not track the individual particle movements, but models the particles as a continuous ow eld dispersed inside the liquid ow eld to focus on the macroscopic effects. The Lagrange method predicts the movements of in-dividual particles over time to predict the movement of the entire ow eld, which has higher equipment for computer resources and consumes more time. In this study, since the particle diameter is only 0.16 mm, s o Eulerian-Eulerian method is suitable to calculate the ow features of small scale particles. Meanwhile, it also could facilitate the optimization design processes. Therefore, Eulerian- Eulerian method was adopted to carry out the following investigation. The turbulence predictions used a homogeneous ow model while the interphase mass and momentum transfer predictions used a heterogeneous ow model. The analysis of the solid–liquid two-phase ow in a slurry pump included prediction of the ow resistance and the turbulent dissipation. When particles move in a uid, the ow resistance is the most important interphase interaction force. Turbulent uctuations can cause additional resis-tance. The turbulent dissipation accelerates the particle diffusion from the high volume fraction region to the low volume fraction region. The Gidaspow model was used to predict the main ow resistance due to the particles.

2.2.Geometry model

This study analyzed a centrifugal slurry pump at the QBEP (Best Efciency Point, BEP) to represent the ow point at the rated operating conditions. The pump rotating speed is 1500 r/min, the ow rate is 18 m3/h, the head is 8 m, and the specic speed is 81.4. The inlet diameter is 62 mm, the outlet diameter is 40 mm, the impeller had 5 blades, and the impeller outer diameter was 162 mm. The main geometric parameters for the slurry pump are listed in Table 1. The uid domain model was split into the inlet, impeller, volute and outlet. The uid domain is shown in Fig. 1.

2.3.Grid independence analysis

Several meshes were used to e valuate the inuence of the number of elements based on the pump he ad and pump efciency for the same ow conditions. Table 2 compares the predictions for four grid schemes. Even with a large number of elements, the predicted heads were all within 0.3%, and the pump efciencies were within 2%. Thus, with 4.4 million elements, the predicted head and ef-ciency were within 1% of the results with the largest grid scheme, so the number of 4.4 million elements was considered appropriate.

2.4.Boundary conditions and two-phase ow settings

The ow was assumed to be steady with part of the impeller region set as a rotating domain with a rotational speed of 1500 r/min and the rest set as stationary. The scalable wall functions for smooth walls were used with the standard turbulence model. The inlet used the pressure inlet boundary condition while the outlet used the mass ow outlet. The interface between the inlet and the impeller and between the impeller and the volute used the frozen-rotor model for data transmission. The convection terms used the high resolution scheme for the ow equations and the rst-order method for the turbulence, the total number of steps is 3000, the uid time scale control used the physical time scale, and the residual limit was 10-5 for all the equations. The particle model in the Eulerian-Eulerian method was used to model the solid–liquid two-phase ow. In the rotating domain, the 0.165 mm solid particles were treated as discrete solids with the turbulence modeled using the discrete phase zero equation model. The Gidaspow and Favre averaged drag force models were used for the drag force and the turbulent dissipation force. The effects of lift, virtual mass force, and wall lubrication were neglected. The inlet was treated as a velocity inlet with a solid volume fraction of 0.3, the outlet was an average static pressure outlet, and the uid and solid phase wall boundary conditions were both no slip walls.

3.Opti miza tion and desi gn

3.1.Opt imi zat ion meth ods

The central composite circumscribed method was used to design the experimental tests. In the central composite design method, the asterisk point is the main part of the quadratic term. How to determine the asterisk point, namely, the value of α, is particularly important. The formula for calculating the value of α is given below: α=F14 (2) F represents the total number of factors in the test. Fig. 3 is a schematic of the central composite design method, in which the asterisk represents the additional quadratic term of the response variable. The target variables were the head and efciency with the four impeller parameters for the number of blades, z, outer diameter, D2, wrap angle, φ, and blade width, b2, as the response variables. The impeller parameter ranges were based on the original pump impeller design for the number of blades (3, 5), the outer impeller diameter (151 mm, 159 m m), the wrap angle (100◦, 120◦), and the blade outlet width (24.5 m m, 28 mm). The response surface design used all the factors including the full-factor test and a set of extended axial points. The center point and an axial point were added to model the response variables with bending in the full- factor test and to estimate the signicance of the primary and secondary terms. 31 test designs were randomly generated with each design modeled separately using 3D uid dynamics modeling software.

3.2.Respon se surfac e anal ysis

The head and efciency were analyzed using the response surface variance. As shown in Table 3, linear combinations of three of the response variables are signicant to the target variable, the efciency, except for the wrap angle with P>0.05. The variance analysis for the head was the same as for the efciency and is not listed here. The regression equations for the head and efciency are: H=12.55\;0.264z+\;0.0258D2+\;0.921b2\;0.0585\;0.2566z20.02351b22+\;0.02297zD2\;0.00656z+\;0.00327b2 (3) η=\;146.68\;+\;8.18z\;0.602D2\;0.719b2+\;0.17291.022z2 (4) Figs. 4 to 9 show the relationships between the efciency and the various design factors. The diagrams show that the impeller diameter, blade outlet width and wrap angle signicantly affect the efciency. The relation between the impeller diameter and the efciency and between the blade outlet width and the efciency have the same linearly decreasing trend. The efciency is pro-portional to the wrap angle. The efciency is not linearly related to the number of blades, but rst increased and then decreased with the number of blades due to the z2 term. The curve type is similar to the parabola with an opening downward. Figs. 4 and 5 show that the maximum efciency occurs at 4 blades. The efciency response surface diagrams do not clearly show which response variable has the most signicant effect on the efciency. However, the efciency variance analysis in Table 2 shows that the impeller diameter has the most signicant effect, followed by the wrap angle, the blade outlet width, and nally the square of the number of blades. As with the efciency analysis, the variance analysis between the head and the various factors showed that the impeller diameter has the greatest inuence on the head, followed by the number of blades while the blade outlet width has little inuence on the head and the wrap angle has no inuence on the head. The coefcients of the squared terms in the head and efciency regression equations are all negative, which indicates that the head and efciency are maximized for the optimum values of b2 and z. The terms in the equations also show that the efciency can be improved without changing the head. The optimum four impeller design parameters are 4 blades with an impeller diameter of 155 mm, blade width of 26 mm, and wrap angle of 89◦ with a predicted head of 8.6 m and an efciency of 66.43%.

3.3.External ch aracteristics o f the optimized design and ow eld

Fig. 10 compares the solid phase slip velocities before and after optimization. The optimized pump impeller reduces the slip ve-locity at the blade outlet by changing the blade outlet shape. At the same time, the low-speed areas along the suction and pressure surfaces of the blade increases which effectively reduces the wear of the solid particles on the blade surface. Fig. 11 shows the solid phase volume fractions along the front and rear covers. The solid phase volume fraction distribution at the inlet of the optimized pump impeller is more uniform than in the original design. Fig. 12 compares the solid slip velocities along the rear cover of the original and optimized pump designs. The hydraulic optimization of the impeller increases the low speed area along the rear cover of the optimized pump impeller while reducing the slip velocity which reduces the abrasion along the rear cover and extends the pump life. Fig. 13 compares the slip velocities at the interface between the impeller and the volute which shows that the high slip velocity area along the interface near the front cover is apparently reduced. Fig. 14 compares the head and efciency before and after optimization. The head at the design point is increased from 8.06 m to 8.41 m while the efciency is increased from 53.25% to 60.6%, as listed in Table 4. Thus, this optimized impeller design improves the pump performance.