0   Introduction

Gas-solid two-phase particle injection is widely used in agriculture, industry and engineering.Dintwa et al.^[1] described a simulation model of a spinning disc fertilizer spreader, developed for incorporation into an automatic control system, and obtained the movement track and distribution characteristics of fertilizer throwing. Villette et al.^[2] defined a mathe-matical model of fertilizer particle motion on a spinning disc, and the study results in an analytical solution for a concave disc equipped with pitched straight vanes. Lei et al.^[3] designed a screw combined centralized fertilizer-feeding device for granular fertilizer and determined the key structural parameters of inclined spiral hole. Najjar et al.^[4] developed a flexible simulation framework, in which multiphase flow computations are performed that include three-way coupling among phases (mixture-droplet-smoke), conservative coupling approach, and full heat release for the burning mechanisms. Liu and Xing^[5] used Euler-Lagrangian method to simulate the gas-solid two-phase flow field in the thrust vector nozzle of solid rocket motor, and studied the effect of solid particles on the thrust vector performance of the nozzle. Xie et al.^[6]obtained the structural design formula of pneumatic conveying gas-solid ejector by using the hydrodynamics and empirical formulas of gas-solid two-phase flow, and studied the influence of structure and parameters on the performance of gas-solid ejector. In the primary air passage of a new type of once-through burner of a coal-fired boiler, Huang used a three-dimensional particle dynamic analyzer (3D-PDA) to measure the gas-particle two-phase flow. The gas-solid two-phase velocity distri-bution, turbulent kinetic energy distribution, particle diameter and particle concentration distribution were obtained in the primary air passage^[7]. Li et al.^[8] characterized the effect of oxidation temperatures on the microstructure and micro hardness of Ni/Al₂O₃ composite coatings, as-cold-sprayed and vacuum heat-treated. Hua et al. used discrete phase model and spray rate model to simulate the release and flow process of fire extinguishing agent particles, and analyzed the movement characteristics of ultra-fine particle fire extinguishing agent with particle size of 1~12 μm under obstacles. And the reference value R(t) and evaluation A were introduced to quantitatively evaluate the movement characteristics of 1~12 μm ultrafine particle fire extinguishers^[9]. Li et al.^[10] proposed a hybrid (deterministic/stochastic) fundamental model for the major physico-chemical processes involved in an industrial HVOF thermal spray process (Diamond Jet hybrid gun, Sulzer Metco, Westbury, NY, USA). Zhang et al. simu-lated the gas-solid ejector based on the particle trajectory model. The ejection performance was analyzed by using the number of particles ejected from the ejector, the number of remaining particles and the trajectory of particles. It is found that the inlet diameter of the contraction nozzle in the gas-solid ejector has a certain influence on the injection performance^[11]. Wang et al.^[12] used FLUENT software to simulate the hydrodynamic characteristics of gas-solid two-phase flow in a boiling bed of titanium slag spouted bed, and analyzed the flow characteristics and zoning characteristics of gas-solid two-phase flow under different blowing speeds.Wang et al. used a three-component particle-dynamics anemometer to measure the characteristics of two-phase gas-particle flows in a primary air nozzle using a gas/particle two-phase test facility. The jet trajectory of primary air velocities, Reynolds stress and particle concentration profiles were obtained. Based on this, the advantages and disadvantages of increasing the offset angle were analyzed to optimize performance^[13]. Wang et al.^[14] had presented a measurement method to obtain the solid phase particle size and the concentration of gas-solid two-phase flow, based on optical principle and image processing, and an experimental system was built.

With the development of gas-solid two-phase particle injection technology, it is of great value to study the factors affecting particle injection. Many scholars have studied particle injection factors such as nozzle exit velocity, nozzle distance, nozzle size, injection angle^[15-17]. However, the factors of the injection pressure and particle quality are not studied. Therefore, based on previous research, this paper combines numerical simulation with orthogonal design theory, and analyzes the influence of spray pressure and particle quality on gas-solid two-phase particle injection. Moreover, it is proved by experiments that this method provides a theoretical reference for the practical application of injection technology.

1   Fundamental theory

1.1   Orthogonal experimental design principle

Orthogonal experimental design is a multi-factor and multi-level design method. According to the orthogonality, some representative points are selected from the comprehensive experiment to carry out the experiment. These points have the advantages of uniform dispersion, neatness and comparability^[18-20]. In this paper, there are two factors, the injection pressure and the particle mass, and each factor has four levels. The specified parameters of orthogonal table used is listed in Table 1.

表  1  具体参数的选取

Table  1  Specified parameters

Factors	Exp. 1	Exp. 2	Exp. 3	Exp. 4	Exp. 5	Exp. 6	Exp. 7	Exp. 8	Exp. 9	Exp.10	Exp.11	Exp.12	Exp.13	Exp.14	Exp.15	Exp.16
Pressure/MPa	0.2	0.2	0.2	0.2	0.3	0.3	0.3	0.3	0.4	0.4	0.4	0.4	0.5	0.5	0.5	0.5
Quality/g	1	2	3	4	1	2	3	4	1	2	3	4	1	2	3	4

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1.2   CFD-DEM model

The CFD-DEM model uses the averaged Navier-Stokes equation to describe the motion of the gas phase, and uses Newton's Second Law to describe the motion of the particle phase^[21]. The governing equation for the CFD-DEM model is ^[22]:

The equation of motion of the particles:

Where, m_a is the particle quality, r_a is the particle position, V_a is the particle volume, p is the pressure, β is the interphase drag coefficient, ε_g is the gas phase concentration, u_g is the gas phase macro speed, v_s is the speed of a single particle, g is the acceleration of gravity, F_{cont, a} is the contact force from the particles collision. F_{vdw, a} is van der Waals force, T_a is the moment, I_a is the moment of inertia, Ω_a is the rotational acceleration, and ω_a is the rotational speed.

The collision force between two particles is given by,

Where, F_{ab, n} is the normal contact force when the particles collide, k_n is the direction stiffness coefficient, δ_n is the shape variable when the particles collide, n_ab is the normal unit vector, η_n is the normal damping coefficient, v_{ab, n} is the normal relative speed, R_a and R_b represent the particle radii of the particle a and b, respectively. r_a and r_b are the positions of the particle a and b, respectively.

The mass conservation equation and the momentum conservation equation for the gas phase are as follows,

Where, ρ_g is the gas phase density and τ_g is the gas phase stress.

The gas-solid phase drag force is given by,

V_C is the volume of the calculation grid, and the phase drag coefficient β is given by,

The ideal gas state equation is as follow,

Where, d_p is the particle diameter, M_g is the molar mass of the gas, R is the molar gas constant, and T_g is the gas phase temperature.

The gas phase stress constitutive relationship is as follow,

Where, μ_g is the shear viscosity of the gas phase, and I represents an identity matrix.

2   Numerical simulation

2.1   Fluid calculation model

In this study, the average diameter of granules used in numerical simulation and experiment is 10.67 μm, spherical starch-like granules. When the pressure is 0.2~0.5 MPa, according to the Bernoulli equation^[23], the energy conservation equation of one-dimensional defined flow under isentropic conditions is^[24-25]:

The isentropic equation is:

According to Eq.(8) and Eq.(9), the jet velocity is:

For air, γ=1.4[24], ρ₀=1.185 kg/m³[26], p₀=0.1 MPa. When p=0.2 MPa, the substitution formula (10) calculates v_0.2=359.7 m/s. Similarly, we can get v_0.3=466.7 m/s, v_0.4=535.7 m/s, v_0.5=587.3 m/s. In addition, the diameter of the air compressor outlet pipe d₁=0.008 m, and the diameter of the nozzle d₂=0.05 m. v′ _0.2≈v_0.2×(d₁/d₂)²≈9.2 m/s, and the effective injection velocities v′ are 9.2, 11.9, 13.7 and 15.0 m/s, respectively. Since the flow rate is less than 0.6 to 0.8 times of the speed of sound, the air can be regarded as an incompressible fluid during the simulation^[27], and the reference atmospheric pressure is one atmosphere. The FLUENT is used to calculate the transient jet flow field under each pressure, and the CFD-DEM coupling method is used for the simulation calculation.

In actual engineering, the air viscosity at room temperature υ=15.06×10^-6m²/s^[28], and the equivalent diameter D=0.05 m. The Reynolds number is calculated: Re=vD/υ>4000, so the realizable k-ε turbulence model equation is used^[29]. The kinetic energy k and the turbulent dissipation transport equation are shown in Eq.(11):

Where, , G_k represents the turbulent energy term produced by the laminar velocity gradient. G_b is the kinetic energy term generated by buoyancy. Y_m represents the contribution of the turbulent pulsation expan-sion to the dissipation rate in the global flow in the compressible flow, C_1ε, C₂, C_3ε are constants, σ_k and σ_ε are the turbulent Prandtl numbers of the k and ε equations, S_k and S_ε are user-defined kinetic energy terms and turbulent dissipation source terms. The turbulent viscosity , where C_μ is a constant.

2.2   Mesh and boundary conditions of model

2.2.1   Mesh generation

The trajectory of the particle jet into the box is studied. In order to facilitate the calculation, the model is calculated and analyzed by a two- dimensional model. The schematic diagram of the model is shown in Fig. 1(a). The geometric model has two parts, the upper part is a rectangle of 1.0 m, and the lower part of the nozzle has a diameter of 0.05 m and a length of 0.1 m.

图  1  模型简图

Fig.  1  Schematic diagram of the model

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In view of the uncomplicated characteristics of the particle injection model, a common grid structure is divided by the commonly used quadrilateral mesh, the mesh is divided by the workbench mesh, and the FLUENT software is imported for simulation calculation. The grid case is as follows: cell is 1268, face is 2611, and node is 1344. Fig. 1(b) is a schematic diagram of the mesh division.

2.2.2   Boundary conditions

Each boundary condition is set according to the conditions of the sprayed particles. The initialization method selects "Standard Initialization" and selects "All-Zones". The inlet boundary of the particle is set to "Velocity-Inlet", and the boundary of the other face is set to "Wall". The solid wall is no slip condition, the top wall is set to "Trap", and the other walls are set to "Reflect".

2.3   Analysis and discussion of simulation results

Particles were put into a rectangular frame with a diameter of 0.05 m and a length of 0.1 m. The simulation experiments were carried out according to the parameters in Table 1. The calculation steps were 500 and the particles were tracked. The simulation calculates the percentage of particle loss in each experiment, that is to say, the ratio of the number of tracked particles to the total number of tracked particles is the amount of particle loss in the simulation process. The data of the 16 computational simulations are shown in Table 2, and the percentage of loss is shown in Fig. 2.

表  2  追踪颗粒逃逸的数量和追踪总颗粒数量(500步)

Table  2  Tracking the number of particles trapping and the total number of particles (500 steps)

Factors	Exp.1	Exp.2	Exp.3	Exp.4	Exp.5	Exp.6	Exp.7	Exp.8	Exp.9	Exp.10	Exp.11	Exp.12	Exp.13	Exp.14	Exp.15	Exp.16
Trap number	40	74	81	66	42	21	39	31	44	30	35	41	66	45	42	87
Total number	321	327	259	251	186	215	146	349	146	151	93	114	143	190	140	179

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图  2  正交实验颗粒损失量

Fig.  2  Particle loss in orthogonal experiments

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By performing the range analysis of the 16 experiments, the mean value of pressure and mass was the smallest when the pressure was 0.3 MPa and the mass was 2 g. The range of the pressure and the mass are 20.1% and 12.4%, respectively, indicating that the magnitude of the pressure has the greatest impact. Then the variance analysis was performed on the two factors of the pressure and the mass, as shown in Table 3. The F ratios of the pressure and the mass obtained from the variance analysis table were 1.431 and 0.569, respectively, indicating that the influence of pressure was greater.

表  3  压强和质量影响方差分析表

Table  3  Variance analysis of pressure and quality impact

Factors	Square of deviance	Degree of freedom	F ratio	F critical-value
Pressure	0.093	3	1.431	4.760
Quality	0.037	3	0.569	4.760
Error	0.130	6	—	—

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3   Experimental verification

3.1   Experimental device diagram

This experiment mainly observes the flow trajectory of particles under different injection pressures (The dimensions of main instruments in the experiment are shown in Fig. 1). The experimental diagram is shown in Fig. 3, where A is a compressed air mercury, B is a gas storage chamber, C is a pulse valve, and D is an imaging system, E is where the particles are stored. Using the pulse valve C to eject particles at E. And the instruments used in this experiment are shown in Table 4.

图  3  喷射实验示意图

Fig.  3  Schematic diagram of injection experiment

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表  4  实验测量仪器清单

Table  4  Experimental measurement instrument list

Serial number	Device name	Model number	Manufacturing company
1	Air compressor	OD1012	FujianJuba Machinery Co. LTD
2	Ball valve	FG-55658	FEGEER
3	DMF-Z	DMF-Z-20	CHCR
4	Powder particle	——	HenanSuhe Biotechnology Co. LTD
5	Electronic scales	JM1003	Yuyao Jiming Weighing and Verifying Equipment Co. LTD
6	High-speed camera	Fastcam Ultima APX	Photron Corporation of Japan

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3.2   Analysis of experimental results

Through the above numerical simulation calcu-lation and experimental orthogonal analysis, the results are obtained. When the pressure is 0.3 MPa and the mass is 2 g, the loss optimization is achieved. The experimental parameters were taken as the above results, and the spray experiment was carried out with the designed particle ejection device, and then the image was taken by the imaging system.

Finally, the image color histogram processing was performed on the captured image^[30-31], and the ejection trajectory diagram is shown in the left of Fig. 4. Select the captured particle ejection images to perform image color histogram processing. Considering that the RGB color space does not conform to the human perception of color, the HSV space is visually sensed to quantify the HSV space and then its histogram is calculated to reduce the amount of calculation. The color space is converted from RGB to HSV by the rgb2hsv function in MATLAB. The HSV grayscale image obtained by processing the image is shown in the right of Fig. 4.

图  4  喷射颗粒的数值模拟图和拍摄轨迹图(P=0.3 MPa，m=2 g)

Fig.  4  Numerical simulations of the sprayed particles and the trajectory of the shot (P=0.3 MPa, m=2 g)

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From Fig. 2, we can see that Exp.1, Exp. 6 and Exp.8 are the three groups with the lowest particle loss, which are 12.46%, 9.76% and 8.88% respectively. However, the optimal combination obtained by variance analysis is Exp.6. Then the injection experiment was taken on the spot when the pressure was 0.3 MPa and the mass was 2 g. At this time, the whole process of particle injection from the beginning to the top of the box could be captured, so the shooting effect was considered to be the best. The results are in agreement with those obtained by orthogonal experimental simulation, as shown in Fig. 4.

4   Conclusion

The two factors, the pressure and the mass, which affect the gas-solid two-phase jet particles were studied and analyzed. The 16 simulation experiments were arranged based on the principle of orthogonal experimental design. Then, based on CFD-DEM model, FLUENT was used for numerical simulation, and the simulation results were analyzed by orthogonal test. Finally, a set of gas-solid injection device was designed to carry out the injection experiment, and the color histogram of the image was processed. The following conclusions are drawn:

The range of the pressure and the mass is 20.1% and 12.4%, respectively. The F ratios of pressure and mass are 1.431 and 0.569, respectively. Both methods show that the effect of pressure is greater than that of mass, and the mean value is the smallest when the pressure is 0.3 MPa and the mass is 2 g.

The image of the particle injection trajectory captured by the injection experiment was processed by color histogram and compared with the trajectory obtained by numerical simulation. The results show that when the pressure is 0.3 MPa and the mass is 2 g, the injection effect is optimized, and the shooting effect is the best.