Optimal Design of Diversion Piers of Lateral Intake Pumping Station Based on Orthogonal Test

To explore the rectiﬁcation parameters of the diversion piers optimized for the forebay of the pump station with a lateral angle of 45 ° , the orthogonal experiment and computational ﬂuid dynamics methods are used to analyze the ﬂow characteristics of the diversion piers under diﬀerent parameter combinations. The ﬂow pattern in the forebay of the side water inlet is improved. The rectiﬁcation eﬀect of the diversion piers under 16 schemes is analyzed, considering the length, width, radian, and relative height of the diversion piers. Combined with numerical simulation, a better rectiﬁcation scheme is provided, and ﬁnally, a reasonable range of values for the rectiﬁcation parameters of the forebay diversion pier of the side 45 ° bend angle pump station is obtained.


Introduction
e forebay of the pumping station is an important water diversion structure, and its hydraulic characteristics directly affect the performance of the pump. e forebay can be divided into frontal water intake and lateral water intake [1][2][3][4]. Some pumping stations can only adopt the form of lateral water intake because the layout of pumping stations is often restricted by objective factors, such as water flow characteristics and geographic location. If the water flow from the lateral inflow is oblique to the axis of the inlet pool, then backflow or vortex easily occurs. A number of studies have been carried out to analyze the flow pattern in the forebay and pump. At present, scholars mainly carried out a combination of model test and numerical simulation [5][6][7][8]. At the same time, substantial practical engineering problems have been solved using mathematical methods [9][10][11][12]. With the development of computer technology, the accuracy of numerical simulation is gradually enhanced and has become the main research method [13][14][15][16]. Sweeney [17] used narrow water distribution holes and splitter plate rectification measures to improve the bad flow pattern of the forebay of the lateral diversion pump station and obtained a stable forebay inlet flow pattern. e water inlet conditions of the pump are satisfied, and the hydraulic characteristics are significantly improved. Spence [18] used numerical simulation and model tests to optimize a series of parameters to explore the possible adverse effects of centrifugal pump operation. Various rectification measures are adopted to improve the flow pattern, which is beneficial to better manage the operation of the pump station. Zhou et al. [19] used the pump station model test to analyze the causes of the bad flow pattern in the forebay and proposed corresponding measures to improve the flow pattern. e first domestic research on the vortex at the inlet of the pump inlet channel was based on the Froude model to simulate the prototype flow pattern by increasing the flow velocity by approximately 0.5 times. e results are relatively satisfactory. Cheng et al. [20] quantitatively analyzed the influence of the position, height, angle, and length of the Y-shaped diversion pier on the flow pattern of the pump station's forebay by using Fluent software and obtained the optimal parameters of the Y-shaped diversion pier. Orthogonal experiment was used to analyze multifactor and multilevel experiments. Compared with the full-factor method, the number of experiments using orthogonal experiment was greatly reduced. Using the  standardized orthogonal table to design the test plan and  carry out the range and variance analysis of the test results,  the influence law of each factor on the index can be obtained. en, the optimized production conditions or process conditions can be obtained. Zhou et al. [21] used the orthogonal test method, selected four-factor three-level orthogonal table, analyzed the orthogonal test data, put forward an optimized design model pump scheme, and obtained the influence law of each geometric parameter on the index. Shi et al. [22][23][24] used a five-factor four-level orthogonal table to design the test plan for the relevant control dimensions of the pump device. Computational fluid dynamics (CFD) numerical simulation was used to calculate each plan, analyze the influence of each parameter on the hydraulic performance of the flow channel, and then verify it with a model test. Finally, the priority order of each control parameter to the index and the optimal plan were obtained. In the present study, numerical simulation is carried out for the forebay of the pumping station with a 45°lateral bending angle.
e orthogonal test method is used to design the geometric parameters of the diversion pier, and the optimized parameter combination is obtained. en, the CFX numerical calculation is used for analysis and verification. e improvement law of the parameters of the diversion pier on the flow pattern in the forebay of the lateral inlet is obtained.

Study Area.
A pumping station hub with lateral water intake is considered an example. ree pump units are installed in the pump room; each pump has a design flow of 4.0 m /s, and the flow channel inlet size is 2.36 m (width) × 1.8 m (length). e intake level of the pumping station is 1.9 m, the elevation of the bottom of the drainage canal is 0.0 m, and the elevation of the forebay bottom is −1.0 m. e main functions of the project are flood control and drainage. e left side of the pumping station is a self-draining culvert. When the pumping station is in operation, the self-draining culvert control gate is closed. e total width of the outlet of the forebay is B, and the length from the center of the inlet of the forebay to the center of the outlet is L. Figure 1 shows the plan layout of the intake building of the pumping station, where the lateral bend angle is 45°.

Study
Method. CFX is used to numerically simulate the model, and the overall calculation domain is divided into unstructured grids. e hydraulic loss is used as the evaluation index. After grid independence verification, when the total grid number is 3.58 million, the hydraulic loss is relatively small. erefore, the influence of the number of grids on the numerical calculation can be ignored. e inlet boundary condition adopts the quality inlet, the inlet flow channel outlet is selected as the calculated outlet boundary, the standard atmosphere is set to 1, and the "steel cover assumption" is selected for the surface of the water body, that is, symmetry surface boundary treatment and nonslip walls.

Selection of Test Factors and Levels.
Diversion piers are used to improve the flow pattern of the forebay. e geometric parameters of the diversion piers have a certain influence on the inlet channel and the water inlet conditions. e axial uniformity and weighted average angle of the inlet section of the inlet flow passage are used as the quantitative indicators of the test, and the geometric parameters of the diversion pier greatly affect the indicators, which need to be integrated for orthogonal test design. e results of the orthogonal test are analyzed, the optimal parameter combination of the diversion pier is determined, and then the influence of various geometric parameters of the diversion pier on the hydraulic performance of the forebay is studied.
e key to this research is to reasonably select the range of geometric parameters of the diversion pier.
For the forebay with different lateral bends, the length of the diversion piers is mainly selected according to the range of its bad flow patterns. e maximum horizontal width of the diversion pier is 1.0 m because the distance between 1# and 2# inlet channels is 1.0 m. e arc-shaped diversion pier can play a good diversion function, and the range of the diversion pier's radian should be selected through repeated trials. e relative height of the diversion pier is used to study the influence of the height of the diversion pier on the hydraulic characteristics of the flow pattern in the forebay, considering that different water levels may occur in the forebay. e schematic of the geometric parameters of the diversion pier is shown in Figure 2, where l is the length of the diversion pier, b is the width of the diversion pier, α is the radian of the diversion pier, and h is the relative height of the diversion pier. e expression is as follows: h � H 1 /H 2 . In the formula, H 1 is the actual height of the diversion pier, m; H 2 is the water depth in the forebay, m. Table. In this study, the parameters of the orthogonal experiment are the length, width, radian, and relative height of the diversion pier. e factors are determined according to the design scope. e length of the diversion pier is based on the length of the swing zone in the forebay in the original design. e level of the test factor is determined according to the possible variation range of each factor parameter in the actual project. When the lateral angle is 45°, the orthogonal design of the geometric parameters of the diversion pier in the forebay selects four factors, and each factor selects four levels. e specific parameters of the factor level are shown in Tables 1 and 2. e factor codes A, B, C, and D in the table represent the length (m), width (m), radian (°), and relative height of the diversion pier, respectively.

Orthogonal
According to the selected factors and the number of levels, the orthogonal table L16 (4 5 ) is selected for orthogonal design, and one column is the error column.

Orthogonal Test Results of the Geometric Parameters of the Diversion Pier.
e preliminary research analysis shows the position of the bad flow pattern in the forebay, the reason for its formation, and the approximate range of the recirculation zone when the lateral angle is 45°. e bad flow pattern mainly affects the 1# inlet flow passage and causes harm to the inlet conditions of the 1# inlet flow passage, thereby threatening the normal stability of the pump unit. erefore, the engineering measures of adding diversion piers between the 1# and 2# inlet channels are considered to improve the flow pattern of the forebay, and the influence of the geometric parameters of the diversion piers on the hydraulic performance of the forebay is studied. e four geometric parameters and levels of the selected diversion piers are designed according to the orthogonal table L16 (45), and each plan is numerically simulated by CFD.
Moreover, the axis of the inlet section of the 1# inlet channel under each plan is obtained. e uniformity and weighted average angle of flow velocity, test plan, and calculation results are shown in Table 2. Intuitive analysis and variance analysis of the orthogonal test results are carried out, and the influence trend of various factors on the improvement of the inlet conditions of the inlet channel is analyzed. en, the parameter combination of the optimization of the geometric parameters of the diversion pier is obtained. Finally, the optimized parameter combination obtained is analyzed and verified through numerical calculation to obtain the improvement law of the flow characteristics of the forebay by the geometric parameters of the diversion pier.

Visual Analysis.
Range refers to the difference between the maximum value and the minimum value of the sum of each level index in the same factor, that is,  uniformity of the flow velocity at the inlet of the inlet flow channel. Table 2 shows that the difference between the parameters and the uniformity of axial flow velocity is D> B > A > C. e order of the factors is as follows: the relative height of the diversion pier, the width of the diversion pier, the length of the diversion pier, and the radian of the diversion pier. e research shows that, among the four factors that affect the rectification effect of the diversion pier, the relative height of the diversion pier is the key factor, the length of the diversion pier, the width of the diversion pier are general factors, and the radian of the diversion pier is the secondary factor.
A trend chart is drawn to analyze the specific influence trend of the changes in various factors on improving the uniformity of the flow velocity of the inlet section of the inlet flow channel. e abscissa is the level of each factor, and the ordinate is the average of the sum of the results of the corresponding factors. e relationship among the k i value, the factors, and the uniformity of the flow velocity of the inlet section of the inlet flow channel is shown in Figure 3. Figure 3 shows that, within the range of the number of factors studied, various factors have different effects on the uniformity of the axial flow velocity of the inlet section of the 1# inlet channel. When the length of the diversion pier is 8 m, the index is the smallest, and the index increases below 8 m and above 8 m. e 20°radian of the diversion pier leads to the smallest index, and the index is lower than 20°and higher than 20°. As the width of the diversion pier increases, the index gradually increases, forming a trend that the index increases when the width of the diversion pier continues to increase. When the relative height of the diversion pier changes from 0.4 to 1.0, the index also increases continuously.
is finding indicates that the index reaches the maximum value when the height of the diversion pier is flush with the water surface.

Analysis of Variance.
Variance analysis should be performed on the test results to estimate the size of the error in the test process and analyze whether the influence of various factors on the uniformity of the axial flow velocity at the inlet section of the 1# inlet flow passage is significant. e orthogonal table leaves an error column to calculate the experimental error. e sum of squared deviations excludes the difference between the factor levels and only represents the size of the experimental error because this column is blank.
e results of variance calculation are shown in Table 3. e results show that the variance of the error term is smaller than the variance of each factor. is finding indicates that each factor affects the test index, and no factor is included in the error term. In addition, if the variance and error of the radian of the diversion pier are small, then the change in this factor level has no significant impact on the test results. In addition, the variance and error of other factors are large. us, the change in the factor level affects the test results, which have a significant impact. e significant degree of the specific influence of each factor can be judged on the basis of the comparison of the variance ratio and the critical value of F. Table 3 shows that the change in the length of the diversion pier has a certain influence on the index, that is, the uniformity of the axial flow velocity of the inlet section of the 1# inlet channel. e change in the width of the diversion pier significantly affects the index. e change in the radian level of the diversion pier has no significant impact on the index, and the parameters can be arbitrarily selected within the test range according to the specific situation. e change in the relative height of the diversion pier has a very significant impact on the index.

Determination of Optimal Solution.
For the uniformity of axial flow velocity, the larger value is better. General calculation and analysis are performed on the orthogonal test results and the trend graph of the relationship between various factors and indicators, and then, a better test plan is obtained. e maximum average value k i of the axial flow velocity uniformity of the inlet section of the inlet channel of 1# is selected under the level i of the diversion pier. Figure 3 shows that, among the four levels considered by the length of the diversion pier, the k i value is the largest when the length is 7 m. Among the four levels considered by the width of the diversion pier, the k i value is the largest when the width is 1.0 m. Among the four levels considered by the radian of the diversion pier, the k i value is the largest when the radian is 25°. Among the four levels considered by the relative height of the diversion pier, the k i value is the largest when the relative height is 1.0 m. erefore, the optimal plan is as follows: the length of the diversion pier is 7 m; the width of the diversion pier is 1.0 m; the radian of the diversion pier is 25°; the relative height of the diversion pier is 1.0. erefore, the design scheme is plan A 1 B 4 C 4 D 4 .

Feature Section Selection.
Two characteristic sections of the horizontal section of the front pond are selected for flow field analysis, namely, two horizontal longitudinal sections of the front pond surface layer and bottom layer. Figure 4 shows the horizontal section, namely, the surface layer a-a and the bottom layer b-b to study the flow pattern and axial velocity distribution of the forebay surface layer and bottom layer, respectively. Among them, the surface layer a-a section is 0.05 m away from the water surface, and the coordinates of the surface layer and bottom layer are Z a � 1.85 m and Z b � 0.05 m, respectively.

Selection of the Flow Pattern Scheme for the Horizontal
Profile of the Forebay. e optimal combination of diversion pier parameters is obtained in accordance with the calculation of orthogonal experiment. According to this parameter setting, several schemes are numerically simulated again, and the data of the scheme with the highest axial flow velocity uniformity among the 16 schemes are compared. e 16 schemes in the orthogonal experimental design are named L 1 ∼L 16 . e program parameter settings are shown in Table 4.
A representative scheme is selected for numerical simulation analysis to study the flow pattern of the water in the forebay. e accuracy of the orthogonal experiment results is analyzed and verified to further confirm the effect of the orthogonal experiment, and the selected typical schemes are shown in Table 5.      e recirculation zone formed at the bottom layer is far from the inlet of the 1# inlet channel. us, it slightly affects the flow pattern of the water in front of the 1# inlet channel. e axial flow field diagrams of the surface layer and bottom layer horizontal section of each typical scheme are compared and analyzed, as shown in Figure 5. In the L 4 scheme of Figures 5(a) and 5(b), the surface layer and bottom layer have the smoothest flow lines and the best flow pattern, which is the optimal scheme. For the excellent scheme directly observed in the orthogonal experiment, the design scheme is observed when the index is the largest, that is, the fourth scheme A 1 B 4 C 4 D 4 . e maximum flow rate uniformity is 90.75%, which is 7.29% higher than the original scheme. is conclusion shows that the results of orthogonal experimental design and numerical simulation analysis are consistent.

Conclusion
e rectification measures for the forebay of the pump station with a 45°lateral bending angle are studied. e orthogonal test method is used to design the various geometric parameters of the diversion pier, and the optimized parameter combination is obtained by analyzing the orthogonal test results. en, CFX numerical calculation is used to verify the analysis. Conclusions are as follows: (1) Adding diversion piers between the 1# and 2# inlet channels can effectively improve the flow pattern of the forebay. rough the orthogonal experiment, the different geometric parameters of the diversion pier lead to a large difference in the uniformity of the flow velocity at the inlet section of the 1# inlet channel.
(2) rough the analysis, the range indicates that the factors from primary to secondary are DBAC. at is, among the four factors that affect the rectification effect of the diversion pier, the relative height of the diversion pier is the key factor, the length of the diversion pier and the width of the diversion pier are the general factors, and the radian of the diversion pier is the secondary factor. (3) Various factors have different effects on the uniformity of the axial flow velocity at the inlet section of the inlet flow channel. e length of the diversion pier at 8 m leads to the smallest index, and the indexes below 8 m and above 8 m are large. Similarly, the diversion pier radian of 20°leads to the smallest index, and the indexes below 20°and higher than 20°a re large. As the width of the diversion pier increases, the index gradually increases, forming a trend that when the width of the diversion pier continues to increase, the index also increases. Similarly, when the relative height of the diversion pier is from 0.4 to 1.0, the index also increases, that is, when the height of the diversion pier is flushed with the water surface, the index reaches the maximum value.

Data Availability
e curve data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.