Optimization of Liquid−Liquid Mixing in a Novel Mixer Based on Hybrid SVR-DE Model

Abstract

To solve the problem of evenly mixing flocculant and sewage, a new type of two-chamber mechanical pipe mixer was numerically calculated and its working principle was studied by means of the internal flow field. The single factor numerical simulation and analysis of some of the structural parameters in the mixer were carried out to determine the influence of different parameters on the results. Latin hypercube sampling was used to design 100 sets of test tables for the four variables of the branch pipe diameter, sewage flow rate, the installation height of the impeller, and the angle of the deflector. The results were optimized using the SVR-DE algorithm. After optimization, the variation coefficient of export flocculant mixing uniformity was 16.02%, which was increased by 74.94% compared with the initial 63.921%. The power consumption of the impeller was reduced by 8.30%. The concentration curves of the flocculant at different positions of the outlet tube could quickly converge to the target value.

1. Introduction

With rapid economic development and urbanization, sewage has increased sharply in recent years, and water environment problems have become increasingly prominent [1]. As the basis of sewage treatment, flocculant is put into the water to condense the colloidal substances into large particles and precipitate them, which can be removed in the subsequent process. The whole process has two working processes, the mixing stage and reaction stage. The time of the mixing stage should be controlled to reduce the reaction time of the flocculant and sewage in this stage, and the larger particles formed in the reaction process should avoid breaking as much as possible, and the quality of this step is directly related to whether the subsequent process can proceed smoothly [2,3,4]. Although the structure and principle of the flocculant mixer have been studied further, the commonly used mixing equipment still has certain room for improvement in the mixing efficiency and response speed [5]. In this paper, a numerical calculation of a new double-chamber pipe mixer has been carried out, which provides a certain theoretical basis for the application and structure optimization of liquid-liquid mixing in a sewage mixer.

At present, the commonly used sewage mixing devices are the static mixer and mechanical mixer. Scholars have done a lot of research on these two mixers. Zhen et al. [6] analyzed different arrangement angles of an SX static mixer and found that when the arrangement angle increased, the particle separation scale decreased and the dispersion effect increased. Zhang et al. [7] conducted a numerical simulation on a new static combination mixer of water and polymer produced in oil fields, and found that the model was suitable for mixing highly viscous fluids. Haddadi et al. [8] designed a new mixer suitable for Reynolds numbers ranging from 20 to 160, and tested the pressure drop ratio and coefficient of variation. However, the static pipe mixing pool has some problems, such as large head loss, difficulty adapting to flow changes, a narrow application range, and difficulty being widely used in sewage treatment. Different from the static mixer, a mechanical mixing tank is a mixer that uses an impeller to meet the requirements. Zhang et al. [9] found that changing the placement angle of an impeller in a sewage mixer can improve the circulation flow in the treatment tank and enhance the mixing effect. Mo et al. [10] used the standard k-ε model to study the impeller structure of a hyperbolic agitator, and found that the hollow and porous structure could increase the bottom velocity gradient, enhance the bottom fluid turbulence, and reduce the stirring dead zone. Tian et al. [11] found that the installation angle had little effect on the shaft power of the sewage agitator. When the installation angle was 15° away from the narrow side, the mixing area meeting the requirements was the maximum. Ni et al. [12] proposed a mixer with a reflux function to solve the problem of sedimentation blockage in a mechanical mixing pool. In the mixer of the mechanical mixing pool, the liquid far away from the impeller basically remained in a laminar flow state, which can easily produce a dead angle, resulting in becoming difficult to mix evenly and then causing a blockage. Moreover, the mechanical pool covers a large area and the cost is relatively high, so it is necessary to further optimize the structure of the mixing pool. In this regard, scholars have proposed different optimization schemes. Mansour et al. [13] conducted multi-objective optimization of spiral tubes with different parameters and proposed the correlation formula between the parameters and mixing coefficient. De et al. [14] used the differential evolution (DE) algorithm to optimize a filtered hydrocyclone and obtained a geometric model with the best efficiency. Hoseini et al. [15] combined the three optimization algorithms to optimize the impeller in the stirred tank reactor, and the results showed that the power number of V-shaped blades and U-shaped blades was reduced by 21% and 48%, respectively, compared with the six-blade turbine. Aguitoni et al. [16] used a combination of genetic algorithms and differential evolutionary optimization algorithms to find the best solution for heat exchange networks. Sujjaviriyasup et al. [17] proposed an SVR-DE model for energy consumption, which constructed a complex prediction model by using support vector regression, and used the DE algorithm to search for the optimal parameters of the support vector regression model, which was significantly better than the traditional single model at the significance level of 0.05. Although they used different optimization algorithms, they did not combine the power consumed by the system with the mixing effect.

In view of the shortcomings of the static mixer and mechanical mixer in sewage treatment, a novel mixer was obtained by combining the two. The novel mixer can shorten the mixing time and improve the mixing efficiency through cooperation between the shitter pipe, the guide plate, and the impeller. Many studies have shown that fully mixing the flocculant with sewage in a short period of time is beneficial to improve its precipitation characteristics, effectively improve the level of water treatment, reduce the power consumption of the mixer, and make it possible to treat a large amount of sewage in a short time [18,19,20]. The ratio of flocculant to sewage should be adjusted according to the sewage situation, too high of a ratio will cause the waste of liquid medicine, while too low of a ratio will be difficult to achieve the intended effect. To explore the working principle and internal flow of the mixer, the ratio of flocculant to sewage is 1.4 × 10⁻⁵. Through the analysis of the fluid in the pipe, the flocculant and sewage are mixed in three steps in order to achieve the purpose of rapid mixing. To further improve its mixing efficiency, a single factor analysis was carried out on the new mixer. As support vector regression (SVR) can better solve high-dimensional problems than neural networks and perform well in predicting the performance of structures under the premise of a small number of samples [21,22], and the DE algorithm can better retain the characteristics of the child and parent generation, the SVR-DE algorithm was adopted to make multi-objective prediction and optimization of the structure, which provides theoretical support for improving the mixing efficiency of liquid−liquid mixing in mixer.

2. Calculation Model

2.1. Calculation Area and Grid Division

The mixer diagram and grid division are shown in Figure 1 below. It is mainly composed of the main pipe, flow guide plate, connecting pipe, dosing pipe, frequency conversion stirring device, etc. After the sewage enters the main pipe, the deflector discharges part of the water flow into the diversion pipe, and the flocculant is added to the shunt pipe to mix with the sewage for the first time, and after stirring by the impeller, the mixture will be discharged into the main pipe and mixed again in the main pipe. To improve mixing efficiency and increase turbulence intensity, five deflectors were placed in the pipe. The mixer and meshing are shown in Figure 1 below.

2.2. Data Processing

The mixing degree is expressed by the variation coefficient CV of the mixing uniformity, that is, the relative standard deviation of the mass volume fraction of the flocculant at the outlet. The smaller the data, the better the mixing effect:

$$CV=\frac{S}{\overline{X}}\times 100\%$$

(1)

where S is the standard deviation of data, and $\overline{X}$ is the average value of data.

An effective mixing ratio was adopted to reflect the proportion of areas with a predetermined effect η. The evaluation of the mixing performance is as follows:

$$\eta =\frac{S_1}{S_2}\times 100\%$$

(2)

where S₁ is the area of the area to achieve the mixing effect at the outlet and S₂ is the total area of the outlet.

Without considering the energy consumption of the shaft drive, replace the motor output torque with the torque on the impeller. The impeller consumption power P is used to represent the mixing consumption power [23]:

$$P=\frac{Mn}{9550}$$

(3)

where M is the torque on the impeller, n is the speed, and 9550 is the approximate constant obtained by unit conversion.

2.3. Grid Independence Verification

To prevent discrepancies between numerical simulation results due to the number of meshes, the grid independence was verified. The results are shown in

Table 1. Grid independence verification.

Number of Grids/106	1.51	2.00	2.86	3.64	4.39	5.45
CV/%	59.04	63.92	62.16	62.66	62.47	62.51
η/%	40.92	38.93	39.36	39.47	39.58	39.74

.

With the increase in the number of grids, the coefficient of variation is stable at 62~64%, and the effective mixing ratio is stable at 39~40%. To reduce the calculation amount and ensure the calculation accuracy, the number of grids selected is 2.00 × 10⁶.

2.4. Governing Equations

The flow movements inside the mixer satisfy the equations of conservation of mass, momentum, and energy. The medium calculated in this numerical calculation is an incompressible fluid with no internal and external heat exchange and temperature changes, so the energy conservation equation is not considered.

The mass conservation equation, also known as the continuity equation [24], is expressed as follows:

$$\frac{\partial \rho }{\partial t}+\frac{\partial \left(\rho u_x\right)}{\partial x} +\frac{\partial \left(\rho u_y\right)}{\partial y}+\frac{\partial \left(\rho u_z\right)}{\partial z}=0$$

(4)

where ρ is the liquid density, t is time, u_x is the velocity of the fluid in the x direction, u_y is the velocity of the fluid in the y direction, and u_z is the velocity of the fluid in the z direction.

For an incompressible fluid [25], the equation for conservation of momentum is as follows:

$$\frac{\partial \left(\rho u_i\right)}{\partial i}+\frac{\partial \left(\rho u_i{u}_j\right)}{\partial x_j}=\frac{\partial }{\partial x_j}\left[\mu \left(\frac{\partial u_i}{\partial u_j}+\frac{\partial u_j}{\partial u_i}\right)\right]-\frac{\partial p}{\partial x_i}+f_i$$

(5)

where u_i is the velocity component, x_i is the coordinate component, μ is dynamic viscosity, and f_i is an external source item.

As the agent and raw water are soluble, a component transport model is used to simulate the mixing process [26]. The conservation equation is as follows:

$$\frac{\partial }{\partial t}(\rho Y_i)+\nabla \cdot (\rho \overrightarrow{\upsilon }{Y}_i)=-\nabla \cdot \overrightarrow{J_i}+R_{\mathrm{i}}+S_i$$

(6)

where ρ is the density of the fluid, Y_i is the mass fraction of the two liquids, υ is the velocity of the fluid, R_i is the velocity of producing the substance, and S_i is the velocity of generating the source by adding the dispersion. This time, R_i and S_i are both 0.

2.5. Turbulence Model

The standard k-ε model has a good robustness and economy, can make reasonable predictions of large-scale turbulence, and is suitable for turbulence calculation under a high Reynolds number [27,28]. The k equation and ε equation are as follows:

$$\frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial x_j}\left(\rho k{u}_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(7)

$$\frac{\partial }{\partial t}\left(\rho \epsilon \right)+\frac{\partial }{\partial x_i}\left(\rho \epsilon u_i\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial x_j}\right]+C_{1\epsilon }\frac{\epsilon }{k}\left(G_k+C_{3\epsilon }{G}_b\right)-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}+S_{\epsilon }$$

(8)

where k is the turbulent kinetic energy, ε is the turbulent dissipation rate, σ_k is Planck coefficient corresponding to turbulent kinetic energy, and σ_ε is the Prandtl coefficient corresponding to the turbulent energy dissipation rate. G_k is the turbulent kinetic energy generated by the average velocity gradient; G_b represents turbulent kinetic energy generated by buoyancy; Y_M is the contribution of wave expansion in compressible turbulence to the total dissipation rate; S_k and S_ε define source items for users; μ_t is the turbulent viscosity, ${\mu }_t=\rho C_{\mu }{k}^2/\epsilon$; and C_1ε, C_2ε, and C_μ are constant. The constant values [29] are: C_1ε = 1.44, C_2ε = 1.92, C_μ = 0.09, σ_k = 1.0, σ_ε = 1.3.

2.6. Experimental Verification

Sun B [30] experiment of mixing salt water with water was used to verify the adaptability of the turbulence model. The experimental setup and results are shown in Figure 2a–c. Using the standard k-ε turbulence model, for the component transport mode, the mixing ratio of salt water and water is 1%, and the results are shown in Figure 2 by adding purple ink to the salt water. The saltwater formed a trapezoidal shape after entering the main pipe, and the saltwater concentrated on the upper wall, and then tended to be stable with the increase in the length of the main pipe, which was consistent with the experimental results. The phenomenon of a phase concentrated on the pipe wall is easy to be produced in the liquid−liquid mixing of T-pipe, and it is difficult to mix fully. Therefore, the structure of the pipe is changed in this numerical calculation to improve its effect.

3. Effect of Single Factor on Mixed Result

3.1. Working Principle

The sewage flow rate is set as 1000 m³/h, that is, the sewage inlet flow rate is 0.526 m/s and the flocculant inlet flow rate is 0.00234 m/s. The flocculant mixing process is shown in Figure 3. When the water flows from the inlet to the first deflector plate, part of the water is pushed into the branch pipe due to the obstruction effect. Two eddies are formed behind the deflector plate, and the water flow generates vertical and wall kinetic energy. After adding the flocculant, mixing with the flow in the branch pipe begins for the first time in zone A. After passing through the guide plate of the branch pipe, a violent small whirlpool is formed and the mixed fluid is pressed into the pipe directly above the impeller. Because of the hydraulic cooperation of the impeller, the water flow in region A flows into region B along the wall, resulting in a cavity and a reduced pressure. A partial backflow from zone B to zone A is generated, and remixing can be carried out in zone A. Different blade sizes exert different work on the mixed liquid. In region B, as shown in Figure 3b, the velocity of a single mixed liquid entering region B is different, resulting in different flow rates near the main wall of region B, thus affecting the mixing efficiency. In zone B, when the primary mixture enters the main pipe along the pipe wall, it gradually flows inward, forming a large eddy current and conducting secondary mixing. Because of the vortex, the velocity vector perpendicular to the main pipe becomes weaker and slower, forcing the flocculant to reach the bottom along the pipe wall and spread to the middle. After passing through the last section of the deflector plate, a vortex area is formed at the top and bottom of the discharge tube in zone C. The vortex at the top causes the downward velocity and the vortex at the bottom causes the upward velocity, which together affect the uniformity of the third mixing.

Through the analysis of the mixing process, it was found that the diameter of branch pipe (d₁), the angle of deflector (β) had a great influence on the internal flow field. The outer diameter of impeller (d₂), the installation height of impeller (h), the number of blades (z), the impeller speed (n), and so on affected the flow velocity and flow track of the flocculant. The data of the original model are shown in

Table 2. Model parameters and original data.

Variety	Size
diameter of branch pipe/d1	325 mm
angle of deflector/β	30°
impeller speed outer diameter/d2	300 mm
the installation height of impeller/h	607 mm
number of blades/z	3
impeller speed/n	200 r/min

. To further explore the influence of the single factor on the results, other parameters remain unchanged when a single parameter is modified.

3.2. Influence of Single Factor on Mixing Effect

The influences of different structural parameters on the results are shown in Figure 4. In Figure 4a, the branch pipe diameter is gradually increased, and the coefficient of variation first decreases to around 60% and then continues to decrease. The effective mixing ratio is the minimum when d₁ = 325 mm, and the impeller power consumption gradually decreases. This indicates that the overall lifting effect is more obvious when the branch pipe diameter is increased. It can be seen from groups 3, 4, and 5 that the branch pipe diameter is increased by 30 mm each time, and P is decreased by about 120 W. Although the power consumption P is decreasing, it also faces the problems of increasing the consumption of branch materials and expanding the occupied volume. Figure 4b shows the influence of β on the results. The guide plate plays a role in draining and increasing turbulence in the process of agitation, which can make the flow develop completely. The turbulence intensity generated by different angles of deflector is also different. At the same time, for the branch pipe, the angle of the deflector directly affects the amount of water entering the branch pipe, resulting in the difference between the primary mixing effect and the overall mixing quality deteriorating. From the comparison in Figure 4b below, the angle of the deflector influences CV, η, and P. In the process of gradually increasing β, the impeller power consumption increases about 5~7 W for every 5° increase, and β at 25° and 35° have the highest coefficient of variation. Compared with groups 1, 3, and 5, CV increases first and then remains unchanged. Under the premise of binding power, β = 20° corresponds to the best mixing effect.

It can be seen from Figure 4c that when the outer diameter increases, the coefficient of variation first shows a significant decreasing trend and then increases rapidly. The effective mixing ratio decreases first and then increases gradually. The power consumed on the impeller increases rapidly, by about 1.5~1.8 times each time. While raising the outer diameter, we can obtain better results, but the corresponding power will also increase at the same time. On the premise that the improvement effect is not significant, the gain is not worth the loss. To judge the influence of the impeller installation position on the results, take the main pipe axis as the horizontal line, set up five groups of installation schemes, as shown in Figure 4d. Obviously, too high or too low of an installation height of impeller will increase the coefficient of variation and make the effect worse. For the effective mixing ratio, the effect is best when h = 592 mm. The power consumed on the impeller almost does not change with the height, which is about 175~178 W.

Different blade numbers have a great effect on the power consumption on the impeller and the change in the internal flow field. The number of blades is set to be 2~6, respectively. The results are shown in Figure 4e. The number of leaves has a great effect on the coefficient of variation CV and effective mixing ratio η. It remains stable with increasing the number of blades, and the power consumption increases with increasing the torque, but the increment decreases. Among the five schemes, the effect is the best when z = 6, but the corresponding power is also the highest. Compared with z = 4, the effect is not improved much, but the power is increased by 33 W. Considering the comprehensive power, the result is the best when z = 4. In actual production, it is necessary to find the speed suitable for the current working condition to ensure that all indicators are as close to the predetermined target value as possible and can achieve the effect of energy conservation. For this reason, nine groups with an impeller speed of 100~300 r/min are uniformly selected for numerical calculation, as shown in Figure 4f. With the gradual increase in rotating speed, CV rapidly decreases to 60%. With the gradual increase in rotational speed, CV rapidly decreases to 60%, and when n = 225 r/min, CV gradually decreases after increasing to 75%. When η increases from 38% to about 40%, the rotational speed continues to increase, and the effective mixing ratio is expanded. Increasing the speed can strengthen the mixing strength of the flocculant and the sewage [31], shortening the mixing time, but the power consumed will increase rapidly. Based on the nine groups of data, the test results of n = 175 r/min and 200 r/min groups are better than those of the other two groups. As for the two groups, the coefficient of variation of the latter is increased by about 9%, but the power consumption is increased by 60 W.

4. SVR-DE Algorithm

4.1. SVR Algorithm

The basic idea of SVR is to create a separation plane on the premise of correctly distinguishing data to ensure the maximum separation data interval [32].

(1) Create hyperplane equations

$$f(x)=\omega ·x+b=0$$

(9)

(2) Hyperplane constraint

$$\begin{array}{l}\underset{\omega ,b}{\min }\frac{1}{2}{\Vert \omega \Vert }^2\\ y_i·({\omega }^T{x}_i+b)\ge 1,i=1,2,\dots \dots m\end{array}$$

(10)

(3) Separation decision function

$$f(x)=sign({\omega }^{*}·x+b^{*})$$

(11)

Nonlinear SVR requires the use of kernel functions to map the data to a new space corresponding to the linear classification, transforming the nonlinear problem into a linear problem. The selection of kernel function is the key to classification. The Gaussian kernel function has the characteristics of high stability and high precision [33,34], so the Gaussian kernel function K(x, z) is adopted.

$$K(x,z)=\exp (-\frac{{\Vert x-z\Vert }^2}{2{\sigma }^2})$$

(12)

The corresponding decision function is as follows:

$$f(x)=sign({\displaystyle \sum {}_{i=1}^N{\alpha }_i^{*}}{y}_i\exp (-\frac{{\Vert x-z\Vert }^2}{2{\sigma }^2})+b^{*})$$

(13)

4.2. DE Algorithm

The DE algorithm is an evolutionary algorithm using population variation, which is different from the genetic algorithm, in that the parent generation crosses to generate a new population. DE competes with the child generation to obtain a new population, enhance the approximation effect, and improve the convergence [35,36]. The algorithm steps are as follows:

(1)

Initialize the population, and set the population number, iteration number, variation factor, and crossover factor.

(2)

Evaluate the initial population and calculate the individual fitness of each sample.

(3)

Mutation, crossover, and boundary check will be conducted among populations.

(4)

Calculate the individual fitness of the new population and select the optimal solution.

(5)

Determine the parent’s result and the child’s result. If the child’s result is better than the parent’s, keep evolution or give up evolution.

4.3. Analysis of Optimization Results

By analyzing each factor separately, it can be found that different factors have different effects on the results. For the same working condition, the diameter of the branch pipe, angle of deflector, impeller installation height, etc., have obvious advantages. Considering the interaction between variables, it is necessary to design a test table to ensure that each parameter can reflect the effect. Latin hypercube sampling is adopted, which will homogenize the sample, avoid sample aggregation, and ensure the comprehensiveness of the sample [37,38]. Taking the angle of deflector, the diameter of the branch pipe, the installation height of impeller, and the flow ratio as variables, 100 groups of tests were conducted. Combined with the contents calculated in Section 3.1 and the actual working requirements, the range of β is 20°~40°, the range of d₁ is 293 mm~358 mm, the range of h is 562 mm~622 mm, and the range of Q is 0.6 km³/h~1.4 km³/h. The design table and numerical calculation table are shown in

Table 3. Latin hypercube sampling and numerical calculation table.

Variety	β (°)	d1 (mm)	h (mm)	Q (km3/h)	CV (%)	P/W
1	39.3	337.8	567.5	1.1	66.75	180.50
2	35.4	309.1	601.7	0.7	68.11	192.59
3	22.5	310.7	595.9	0.9	55.39	174.72
4	26.2	352.3	597.2	1.0	59.12	164.97
5	27.4	335.4	614.1	1.1	81.54	170.73
6	33.2	314.9	573.7	1.4	85.74	186.98
……	……	……	……	……	……	……
95	25.5	316.6	616.4	1.1	88.95	178.84
96	34.4	330.1	596.5	0.7	49.31	182.32
97	24.6	295.7	591.2	0.8	56.55	183.43
98	22.7	306.7	602.8	0.8	55.80	176.52
99	33.4	351.4	564.6	1.3	90.29	171.26
100	31.1	311.9	614.6	0.9	87.20	185.94

.

Normalize the numerical calculation results:

$$x_i{}^{\prime }=\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}$$

(14)

where x’_I is the processed data, x_i is the preprocessed data, x_min is the minimum value in the array, and x_max is the maximum value in the array.

Support vector regression is used to predict the children and parents, and the prediction results are optimized as fitness functions combined with the DE algorithm. As the mixer pays more attention to the mixing effect, the coefficient of variation and impeller power are considered as the objective function, and the weight ratio of the coefficient of variation and impeller power consumption is set as 8:2. The iteratives and the fitness of the objective function of DE algorithm are shown in Figure 5.

The value of each parameter under the optimal solution is, β = 23.81°, d₁ = 358 mm, h = 617.43 mm, and Q = 0.6 km³/h. Numerical calculation of the optimization results shows that the result is 16.18% and the power consumption of the impeller is 163.3 W. Under the optimal solution, the coefficient of variation is CV = 16.02% and the error compared with the numerical calculation is 1.02%. The consumed power of impeller P = 163.5 W and the error is less than 1%.

5. Comparison of Optimization Results

5.1. Mass Fraction of Flocculant for Export

Figure 6 shows a comparison of the mass fraction of flocculants at the outlet before and after optimization. The light color plane in Figure 6a,b is Fraction = 1.4 × 10⁻⁵, which is the target mixing plane. It can be seen from the figure that before optimization, there were three places with high quality scores and two places with low quality scores, leading to a poor overall effect. After optimization, there is one high and one low mass fraction, and the range is small, which greatly improves the overall mixing effect. In Figure 6a, the range with a mass fraction of about 3.5 × 10⁻⁵ affects each other, resulting in a large area far exceeding 1.4 × 10⁻⁵. In addition, the difference between the upper and lower limits has also become a factor of a poor mixing effect, and even some areas have a mixing effect close to zero. The improved effect is shown in Figure 6b. The contour lines are reduced to 5, the upper and lower limits are reduced to 1.6 × 10⁻⁵, and the reduction range is about 54.3%. The area higher than the target plane has increased significantly, mainly concentrated in the center of the outlet, and the area of the maximum and minimum areas has decreased significantly. At the same time, it can be ensured that the entire outlet can achieve a flocculant mixing effect higher than 8 × 10⁻⁶.

There are two obvious areas with a low mixing degree before optimization, which are mainly located on both sides above the mixer. On the one hand, this phenomenon is caused by the influence of the outlet splitter plate, and on the other hand, the flow state in front of the baffle plate. The outlet splitter plate remixes the fluid in the mixing area below the impeller, which can be remixed due to its certain inclination angle. Although the optimized geometric model still has a small range of areas where the concentration is not up to the standard, it has been significantly improved, and only the concentration of flocculant in the edge part is less than 1.4 × 10⁻⁵.

5.2. Comparison of Flocculant Concentration in Outlet Pipe

To judge the mixing effect along the way at different positions of the outlet pipe, as shown in Figure 7, place the monitoring curve P₁~P₉ according to the outlet position.

The concentration of the monitoring curve before and after optimization is shown in Figure 8. Before optimization, the concentration of the flocculant at the center point and around it is difficult to converge. The outlet deflector is located at Z = 0.55~0.6 m. There is a sharp drop in the area where the concentration is higher than 1.5 × 10⁻⁵ after passing the deflector, and then it gradually increases. However, each curve is difficult to stabilize near 1.5 × 10⁻⁵, and the concentration difference between different locations is large. P₃ and P₇ gradually stabilize with the increase in outlet pipe length, but there is still a distance from the target mixing line of 1.5 × 10⁻⁵ for the flocculant concentration. Figure 8b shows the flocculant concentration curves at different positions of the outlet pipe after optimization. Each curve quickly approaches 1.4 × 10⁻⁵, and the fluctuation is reduced, which is significantly improved compared with that before optimization. Compared with that before optimization, the monitoring point is in a slow and stable state within 1~2 m after passing through the outlet deflector.

To further analyze the internal micro-mixing process, the flow state of the flocculant in the pipe is studied by combining the turbulence intensity contour, static pressure contour, and outlet pipe mixing contour. It can be seen from the static pressure contour of Figure 9a that there is a circular static pressure area at the bottom left of the impeller outlet, combined with the turbulence intensity contour of Figure 9b, indicating that the turbulent intensity state here is stronger than that in the main pipe, combined with Figure 3 before optimization, indicating that a small vortex has appeared, and the vortex is increased; that is, as the impeller is mixed for the first time, the high-concentration flocculant liquid is slowly mixed with the sewage here, further promoting homogeneous mixing. Because of the certain inclination angle of the outlet pipe deflector, the turbulence intensity in the outlet pipe is gradually reduced due to the blocking of the mixed liquid, indicating that most of the mixing processes are completed just as they enter the outlet pipe and the outlet flow is stable, which can increase the difficulty of reducing the subsequent process. To study the flow of the outlet pipe, place cross-sections A−E [39,40]. Figure 10 shows the mixing of the outlet pipes before and after optimization, it can be seen that the difference between the two on cross-sections A is not large, but as the mixing progresses, the gap between the two gradually widens; the flocculant concentration is at cross-sections C and the optimized structure is basically mixed. Compared with before optimization, it can be seen in Figure 3 that the speed of the mixture in the outlet tube is mostly parallel to the pipe wall, resulting in uneven mixing, and the mixing effect of cross-sections B−E is very small, and it is directly discharged without mixing and there is a dead zone. The main reason for the improvement in the effect after optimization is that the pipe diameter of the shunt pipe is increased, resulting in an increase in the flow of the shunt pipe. The increase of the installation height of the impeller increases the work of the impeller in the first mixture, which is conducive to increasing the size of the vortex, and the different inclination angles of deflector make the shape and position of the vortex change slightly, which together improve the mixing efficiency.

6. Conclusions

In this paper, the flow field of the novel two-chamber mechanical pipe mixer is numerically simulated and analyzed, and the SVR-DE algorithm is used to optimize it, and the optimal size and mixing conditions are obtained. The main conclusions are as follows:

(1)

Under the effect of deflector, branch pipe, and impeller, the new structure can mix the flocculant in three steps, step by step, which can effectively mix the flocculant with sewage, and the outlet pipe basically has no dead zone.

(2)

For a single working condition, the diameter of the branch pipe, the angle of deflector, and the installation height of impeller have a high influence on the internal flow and mixing characteristics. The SVR-DE algorithm was used to optimize the structure and the optimal solution was obtained as the diameter d₁ = 358 mm, the angle of deflector β = 23.81°, and the installation height of impeller h = 617.43 mm. Currently, the most suitable sewage flow is Q = 600 m³/h.

(3)

After optimization, the coefficient of variation and the volume fraction of flocculant at the outlet is 16.02%, which is 74.94% higher than the initial 63.92%. The power consumption of impeller is reduced by 8.30%. The flocculant concentration curve at different positions of the outlet pipe can quickly converge to the target value, reducing the consumption of the outlet pipe and saving materials.

At present, the analysis of the algorithm design is not in-depth enough and has not been compared with other hybrid algorithms, and follow-up research can start from this aspect to study the advantages and disadvantages of different hybrid algorithms in multi-objective prediction and optimization of geometric models. The equation of the energy and reaction process is not added to this calculation, considering that the mixing process of the temperature and flocculant may produce floc precipitation problems, which may affect the mixing effect of the mixer, and subsequent calculations can add the necessary reaction process equations according to the actual situation.