CFD study on the effect of particle properties on the performance of annular jet pump

The annular jet pump is a type of fluid mechanical pump that operates by exchanging momentum with the fluid. Annular jet pumps possess distinctive advantages in the transportation of solid particles. However, the efficiency of these pumps is significantly impacted by both the physical properties of the particles and their initial concentration, thereby limiting their practical applications. In this paper, by combining other scholars’ designs of annular jet pumps, the effects of different physical densities and different initial concentrations of particles on the flow field, pressure and efficiency of an annular jet pump were analysed based on the RNG k-ε turbulence model and the Mixture multiphase flow model. The efficiency of the annular jet pump decreases with a higher particle bulk density. Specifically, at an initial concentration of 20% and a flow ratio (M) of 0.5, the efficiency of the annular jet pump fluctuates as follows: it changes from 28.736% under single-phase flow conditions to 25.011%, 24.369%, 23.637%, 22.950%, and 21.733% as the density of particulate matter increases. The findings of this study offer valuable theoretical insights for the implementation of annular jet pumps in engineering discharge applications.


Introduce
Annular jet pump is a kind of fluid machinery and mixing reaction equipment that utilizes the shear and turbulent diffusion effect of the jet for mass and energy transfer.Jet pumps can be divided into two types: central jet pumps and annular jet pumps.Central jet pump nozzle placed in the middle of the suction chamber, the suction fluid surrounded by the nozzle at the outer end; annular jet pump using ring nozzle, the suction fluid from the ring nozzle through the inner ring.In annular jet pumps, the suction channel is in the central, coaxial with the throat, which is very favourable for the transport of solid particles such as live fish, capsules, potatoes, and onions [1].
The internal flow field of the annular jet pump is a complex three-bit finite space viscous turbulent jet motion, accompanied by the phenomena of volume suction, vortex and flow separation, numerical simulation methods based on Computational Fluid Dynamics (CFD) are often used by domestic and foreign scholars.Existing studies have shown that numerical analysis methods based on CFD theory can accurately explain the internal flow conditions of various jet phenomena and can provide accurate guidance for the optimization of annular jet pump performance.Deng et al. applied CFD computer analysis software to comparatively analysis the efficiency, solid ratio, velocity field distribution, and pressure field distribution of sand discharge jet pumps with diffusion tube outlet mutation structure and gradient structure [2].Mekahil et al. numerically simulated the internal flow field of a sand displacement jet pump and studied the pump characteristics under different nozzle diameters and driving pressures [3].Zhou et al. applied the CFD method to simulate its internal flow characteristics and investigated the three-dimensional liquid-solid two-phase flow characteristics and basic performance of the annular jet pump [4].ITOH et al. studied the basic external characteristics of sand displacement jet pumps under the conditions of different throat diameters and particle diameters, and made a comparative analysis with single-phase flow jet pumps [5].It can be seen that the current research is mostly focused on the operating fluid pressure, flow ratio and other operating parameters, as well as nozzles, throats, diffusion tubes and other structural parameters on the annular jet pump performance of the influence of the law of the particle density and the initial concentration of the role of the internal flow field of the annular jet pump and the external characteristics of the research is not common.
Since the particles in the suction fluid are the most important influence on the basic performance and efficiency degradation of annular jet pumps, therefore, it is of great significance to study the effects of different particle densities and initial particle concentrations on the internal flow field and external characteristics of the annular jet pump, and to optimize the structure of the annular jet pump in order to improve its operating efficiency and reduce energy consumption.This paper utilizes a numerical simulation method based on the RNG k-ε turbulence model and the Mixture multiphase flow model, to analysis the internal flow and external characteristics of different particle physical densities as well as different initial concentrations of particles during the operation of annular jet pumps, and to analysis the reasons for the performance and efficiency degradation, so as to provide theoretical guidance for the optimization of the structure and operating parameters of annular jet pumps.

Computational model
The annular jet pump is mainly composed of annular nozzle, intake nozzle, suction chambers, throat and diffuser (figure 1).The working fluid is ejected from the nozzle at a high speed and sucks the sucked fluid.The two fluids mix and exchange momentum in the throat, so that the kinetic energy of the transported fluid increases, and finally discharged through the diffuser after converting most of the kinetic energy into pressure energy.The performance parameters of the annular jet pump are flow ratio  =     , pressure ratio  = ( 0 −  ) (  −  ) and efficiency  = .Where: Q, P respectively for the volume flow and total pressure; subscript d, o, s respectively, the pump outlet, nozzle inlet and suction chamber inlet position.
Long [6] took the pump with the best performance among the 25 pumps with different structures used in Shimizu test [7] as an improved prototype, and used the experimental design method combined with numerical simulation to obtain the optimal size combination of the pump's performance (Table 1).In this paper, this optimal pump will be used as a prototype for numerical simulation of different particle densities and initial concentrations.

Computational schemes and validation
The Mixture model is used to simulate the flow in the internal flow field of the annular jet pump, which needs to satisfy the hydrodynamic equations, mainly including the continuity equation and momentum conservation equation.
The continuity equation [8,9,10]: (2) Where:   is the mixed liquid density, / 3 ;  is the time, ; ∇ is the Hamiltonian operator; ̅  is the mass-averaged velocity matrix, /;  is the number of phases;   is the volume fraction of the th phase; and   is the average velocity of the th phase, /;   is the density of the th phase, / 3 .
Momentum conservation equation: , =   − ̅  (6) Where:  is the mixture pressure, ;  is the volume force, / 3 ;  is the gravitational acceleration, / 2 ;   is the th-phase viscosity,  • ; and  , is the drift velocity of the th phase, /.
The flow field inside the annular jet pump is considered as a constant incompressible flow and is axisymmetric.The details of the computational domain and structured grid are shown in figure 2. The inlet length of the computational domain is set to 1Ds0 and the outlet pipe length is set to 3D0 to ensure the stability of convergence, and other dimensions are given in the literature [2].
The controlling equations are the Reynolds-averaged N-S equation and the mass conservation equation; the RNG k-ɛ [11] turbulence model is used to close the equations; the standard wall function is used to handle the wall stresses; the medium of the annular jet pump is water, and the inlets of the working and sucked fluids are mass inflow ports; the outlet is used as a pressure boundary condition; the SIMPLE [12] algorithm is utilized to solve for the coupling of velocities and pressures; and the QUICK [13] format is used to reduce the effect of pseudo-dissipation.The criteria for convergence of the calculations are that the residuals of the individual calculations are less than 10 -5 and the relative error of the flow rate between the inlet and outlet is less than 0.5%.The validation of the irrelevance of the grid and the effectiveness of the simulation method have been verified in the literature and will not be repeated.In order to verify the reliability of the simulation results, this paper cites the dimensions of the annular jet pump used in the experiments of Wang [14] for numerical simulation.The efficiency curve of this annular jet pump is obtained by organizing the calculated and experimental results, and a comparison of the efficiency curves obtained from experiment and numerical simulation is shown in figure 3.

Figure 3. Efficiency comparison curve between emulation and experimental.
As can be seen from figure 3, the numerical simulation and experimentally obtained efficiency curve of the annular jet pump has the same trend, especially in the flow rate is relatively small conditions, the calculated results and the experimental results match to a higher degree, with the increase in the flow rate ratio of the error between the two is also correspondingly increased, but the maximum error is maintained within 5%.It can be seen that the numerical simulation scheme of annular jet pump used in this paper is accurate and reliable.

Physical properties of fluids and particles
The materials used include water, sand, resin and dust, with water as the working fluid and the inhalation fluid as the mix.Mixtures include water and grit, water and powder resin water and dust, each with three initial concentrations of 10%, 20% and 30% respectively.The density of sand is 2400/ 3 , the density of resin is divided into two types of 1000/ 3 and 1500/ 3 , and the density of dust is divided into two types of 100/ 3 and 500/ 3 .The particles used for numerical simulations were assumed to be uniformly sized spherical particles and their diameter was set to d=0.1mm.

Performance analysis
As can be seen from the Figure 4, with the increase of the initial concentration of particles, the flow rate of the annular jet pump to reach the highest point of efficiency is decreasing, and every 10% increase in the initial concentration, the corresponding flow rate of the annular jet pump to reach the highest point of efficiency decreases by 0.1.For example, when the initial concentration is 10%, the flow rate of the annular jet pump reaches the highest point of efficiency is 0.6, which is the same as the efficiency of the single-phase flow; when the initial concentration is 20%, the flow rate is 0.5, and the mixed fluid operates most efficiently in the annular jet pump; and when the initial concentration is 30%, the flow rate is 0.4, and the mixed fluid operates most efficiently in the annular jet pump.
It can be seen from Figure 3: as the flow ratio increases, the efficiency line of the annular jet pump increases and then decreases.The presence of particles makes the pressure ratio curve and efficiency curve of the annular jet pump shift downward, indicating that when conveying mixtures containing solid particles, the pressure ratio and efficiency of the annular jet pump are reduced compared with the singlephase flow, and the larger the flow ratio and the higher the initial concentration, the larger the decrease.At an initial concentration of 10% and a flow ratio of 0.6, the efficiency of the annular jet pump changes from 29.48% at the optimum condition of single-phase flow operation to 27.41%, 26.97%, 26.56%, 26.14%, and 25.41% as the density of particulate properties increases, with the magnitude of change being 7.05%, 8.54%, 9.93%, 11.34%, and 13.84%;At an initial concentration of 20% and a flow ratio of 0.5, the efficiency of the annular jet pump changes from 29.48% at the optimum condition of singlephase flow operation to 25.01%, 24.37%, 23.64%, 22.95%, and 21.73% as the density of the particulate matter increases, with the values of 15.17%, 17.35%, 19.83%, 22.16%, 22.16%, and 26.29%.and 26.29%;At an initial concentration of 30% and a flow ratio of 0.4, the efficiency of the annular jet pump changed from 29.48% at the optimum condition of single-phase flow operation to 22.33%, 21.52%, 20.57%, 19.75%, and 18.44% as the density of the particulate matter increased, with the magnitude of change being 24.27%, 27.01%, 30.22%, 33.01%, 33.01%, and 37.47%.and 37.47%.The reason for this result is that the particle densities during the numerical simulation are all greater than the pure water density, making the average density of the absorbed fluid increase.From the basic characteristic equations of the annular jet pump, it can be seen that when the power fluid with lower density pumps the suction fluid with higher density, the pressure ratio and efficiency are reduced; The presence of particles makes collision friction losses between particles and between particles and the inner wall of the pump body increase, which also leads to a decrease in pressure ratio and efficiency.
When the initial concentration is 10% and smaller flow ratio (M=0.1)condition, the annular jet pump efficiency value changes from 10.53% in pure water operation condition to 10.74%, 10.52%, 10.45%, 10.40%, 10.36% with the increase of particulate bulk density, with the change of -1.99%, 0.1%, 0.76%, 1.23% and 1.61%.In which the suction liquid contains small density particles, the efficiency change amplitude is negative, mainly due to the particle diameter of only 0.1mm and density is small, less affected by the volume effect, and the liquid phase to follow the ability to be strong, triggered by the volume effect of the solid extrusion of the liquid phase speed increases and additional friction loss is very small, and at the same time, due to the increase in the density of the liquid-solid two-phase mixtures, which makes the annular jet pump inlet Pressure value is less than the export, so the efficiency will be slightly higher than the single-phase flow conditions.

Effect of particle density and concentration on velocity in the flow channel
Figure 5 presents a plot of the velocity variation along the central axis of the annular jet pump for different densities of particles operating at the highest efficiency at different initial concentrations.As can be seen from the figure, after the fluid through the nozzle, the speed in the suction chamber will rise sharply, leaving the suction chamber in the throat has been to maintain high-speed movement, out of the throat into the diffusion tube after the speed began to gradually decline, with the mixing process, the final speed tends to stabilize, the mixed fluid is discharged together with the annular jet pump When the suctioned fluid contains particles, the velocity of the mixed fluid in the suction and mixing chambers will be higher than in single-phase flow operation, and the velocity of the mixed fluid will increase as the concentration increases.This is due to the fact that the density of the mixed fluid is higher than that of the single-phase flow at the same flow ratio, and therefore the flow rate will be faster.When the concentration is unchanged, as the density of particles increases, the loss generated by friction with the working fluid in the suction chamber and the head of the throat becomes larger, so the acceleration ability in the suction chamber and the head of the throat is gradually weakened.And the mixing of the two fluids causes the velocity of the mixed fluid to decline to different degrees in both the throat and the diffuser tube.The greater the particle density the lesser the degree of decline, the lesser the particle density the greater the degree of decline.This is due to when the particle density increases, the quality of the larger particles by the inertial force is greater, making its followability worse, the working fluid to be sucked into the fluid mass transfer, energy transfer is not sufficient, the mixed fluid through the diffusion tube only a small portion of the kinetic energy is converted into pressure energy.Thus, causing the basic performance and efficiency of the annular jet pump to decrease with increasing particle density and concentration.For this phenomenon, when the annular jet pump is used to transport density and concentration of larger particles, the length of the throat should be increased appropriately to reduce the extra loss caused by the uneven velocity of the solid-liquid two-phase at the outlet of the diffuser tube, in order to improve its conveying efficiency.

Effect of particle density and concentration on the distribution of turbulent kinetic energy in a flow channel
The turbulent kinetic energy distribution law of the annular jet pump is studied to gain a deeper understanding of its internal flow mechanism, to analyse the reasons for the low efficiency of the annular jet pump applied to transport particles from the perspective of turbulent kinetic energy, and to provide theoretical guidance for the optimization of the annular jet pump.
The axial turbulence energy scores for different particle densities at different concentrations are shown in figure 6.As can be seen from the figure, the region of high turbulent kinetic energy is mainly concentrated in the working and suction fluid inhalation chamber, mainly due to the existence of two streams of fluid in the inhalation chamber of the complex energy exchanges, with the mixing of turbulent kinetic energy is gradually reduced or even disappeared, indicating that the two streams of fluid mixing is gradually completed.However, with the increase of particle density and concentration, the turbulent kinetic energy of the basin gradually weakened, indicating that the degree of mixing in the region is weakened with the increase of particle density and concentration, so the position of the mixing completion moves downstream, and the corresponding friction loss increases, and the efficiency decreases.

Effect of particle density and concentration on pressure in the flow channel
The distribution of the wall static pressure coefficient Cp along the flow direction is given in figure 7. Due to the large velocity of the working fluid, Cp decreases more in the nozzle of the annular jet pump, the pressure decreases sharply in the suction chamber and becomes slower in the throat, and the pressure is further recovered when the mixed fluid enters the diffuser.From figure 7, it can be seen that the higher the density of particles contained in the sucked fluid, the higher the Cp number in the nozzle and inhalation chamber.The opposite is true for Cp in the throat and diffusion tube, where the higher the particle density contained in the suction fluid, the lower the Cp number.The higher the concentration of particles contained in the suction fluid, the lower the Cp coefficient at the transition between the suction chamber and the mixing chamber, and the higher the fluctuation of Cp.The fluctuations in Cp are caused by the impingement of the mixed fluid on the walls of the inhalation chamber.The higher the density and concentration of the mixed particles, the more violent the pressure wave and the stronger the impact.

Conclusion
By simulating and calculating the table of the performance of the annular jet pump under different particle properties and different initial concentrations of particles, and analysing and comparing the pressure ratio curves and efficiency curves under different flow ratios, the following conclusions are drawn: (1) In this paper, the effects of different physical densities and different initial concentrations of particles on the flow field, pressure and efficiency of an annular jet pump are analysed based on the RNG k-ɛ turbulence model and the Mixture multiphase flow model.(2) When the initial concentration of particles is unchanged, the higher the density of particles contained in the mixed fluid as the mass flow ratio increases, the lower the pressure ratio and efficiency.At an initial concentration of 20% and a flow ratio M of 0.5, the annular jet pump efficiency changes from 28.736% at single-phase flow condition to 25.011%, 24.369%, 23.637%, 22.950% and 21.733% as the density of particulate nature increases, decreasing by 12.97%, 15.19%, 17.74%, 20.14% and 24.37%.When the particle density is constant, the higher the initial concentration, the lower the mixed fluid pressure ratio and efficiency.The maximum efficiencies that can be achieved by the mixed fluid containing sand particles at initial particle concentrations of 10%, 20%, and 30% show a decrease in efficiency of 14.01%, 26.29%, and 37.47%, respectively, when compared to the maximum efficiencies of the single-phase flow condition.(3) As the initial concentration of particles increases, the flow rate ratio at which the annular jet pump reaches its peak efficiency decreases, and for every 10% increase in initial concentration, the corresponding flow rate ratio at which the annular jet pump reaches its peak efficiency decreases by 0.1.(4) The higher the density and concentration of the particles contained in the suction fluid, the greater the fluctuation of Cp in the transition section between the suction chamber and the mixing chamber, which indicates that the pressure fluctuation is more intense, i.e., the stronger the impact, the greater the consumption of the capacity, and thus the efficiency decreases.

Figure 2 .
Figure 2. Computational domain and mesh.In order to verify the reliability of the simulation results, this paper cites the dimensions of the annular jet pump used in the experiments of Wang[14] for numerical simulation.The efficiency curve of this annular jet pump is obtained by organizing the calculated and experimental results, and a comparison of the efficiency curves obtained from experiment and numerical simulation is shown in figure3.