Calculation method for resistance coefficient of plant filter bed for purifying non-point source pollution

Abstract

The present invention relates to a method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution, including determining the modified vegetation resistance F of aquatic vegetation d formula; determining the expressions of various vegetation factors; selecting the working conditions of different bending angles of the vegetation to obtain experimental data under different parameters and different working conditions; synthesizing the experimental data, fitting between the vegetation resistance coefficient and the bending angle, and constructing a resistance coefficient calculation model; using the coefficient of determination, root mean square error, and correlation coefficient to evaluate the accuracy of the resistance coefficient calculation model. By simulating the influence of water flow on vegetation under different natural conditions, analyzing the experimental data under different working conditions, and establishing a prediction calculation model for the vegetation resistance coefficient at different bending angles, the present invention provides a method for calculating the resistance coefficient of an aquatic plant filter bed for purifying non-point source pollution, provides support for the accurate calculation of the water flow resistance of vegetation, and thus optimizes the non-point source pollution treatment and pollutant interception mechanism

Description

Technical Field

[0001] The present invention relates to the fields of hydrodynamics and ecological restoration, and particularly to a method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution. Background Art

[0002] In the fields of hydrodynamics and ecological restoration, the study of the interaction between vegetation and water flow has always been an important and complex topic. In particular, the accurate understanding and quantification of the resistance characteristics of vegetation have received extensive attention. Vegetation resistance not only directly affects the flow velocity and direction of water flow, but also regulates the transport and distribution of non-point source pollutants, thus having a profound impact on the structure and function of river ecosystems.

[0003] On the one hand, vegetation resistance causes a decrease in the water flow velocity, enabling the sedimentation of solid pollutants in the water, thereby forming an interception effect of vegetation on solid pollutants. On the other hand, vegetation increases the water flow resistance, resulting in an increase in the hydraulic retention time, which promotes the purification of pollutants by vegetation. These two aspects can both provide support for the treatment of non-point source pollution and the interception of pollutants.

[0004] According to the morphological characteristics of the aquatic vegetation used in the plant filter bed, it can be divided into rigid vegetation and flexible vegetation. In the case of rigid vegetation, the vegetation resistance coefficient is relatively easy to determine. However, when the vegetation morphology changes, the relationship between the resistance coefficient and the water flow conditions changes, but the influence of the change range of vegetation morphology on the vegetation resistance coefficient has been ignored in existing studies.

[0005] Therefore, how to more accurately describe the influence of the change range of vegetation morphology on the vegetation resistance coefficient and complete the calculation of the calibration parameters for the influence of the change range of vegetation morphology on the resistance coefficient is a problem that needs to be solved. Summary of the Invention

[0006] (1) Object of the Invention: To solve the problems existing in the above-mentioned prior art, the object of the present invention is to provide a method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution.

[0007] (2) Technical Solution: To solve the above technical problems, the present technical solution provides a method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution, and the method includes the following steps:

[0008] Step 1: Determine the modified vegetation resistance F of the aquatic vegetation d formula;

[0009] Step 2: Through the analysis of the F d formula in Step 1, find out the vegetation factors that affect F d and determine the expressions of each vegetation factor;

[0010] Step 3: Through the experiment of simulating the conditions of the plant filter bed for purifying non-point source pollution, select the working conditions with different bending angles of the vegetation, and obtain the experimental data under different parameters and working conditions;

[0011] Step 4: Synthesize the experimental data, fit between the resistance coefficient and the bending angle of the vegetation, construct a calculation model of the vegetation resistance coefficient with respect to the bending angle, and obtain the vegetation resistance coefficient.

[0012] Furthermore, the formula in Step 1 is:

[0013]

[0014] In the formula, ρ is the density of water, A c is the projected area of the vegetation perpendicular to the direction of water flow, C d is the resistance coefficient of the vegetation cluster, u is the cross-sectional average flow velocity, β is the resistance coefficient, which is a calibration parameter for the influence of the vegetation form on the resistance.

[0015] Furthermore, the vegetation factors affecting F d in Step 2 include the projected area A of the vegetation perpendicular to the direction of water flow c , and its expression is:

[0016]

[0017] In the formula, h v is the vertical height after the vegetation is bent, and D is the diameter of the vegetation.

[0018] Furthermore, the vegetation factors affecting F d in Step 2 also include the resistance coefficient C d of the vegetation cluster, and its expression is:

[0019]

[0020] In the formula, Re v is the Reynolds number of the vegetation cluster, is the hydraulic radius caused by the vegetation cluster, and λ is the vegetation coverage.

[0021] Furthermore, the vegetation used in the experiment in Step 3 is non-submerged vegetation, eliminating the error introduced by the different velocity distributions between the free water layer and the vegetation layer.

[0022] Furthermore, the vertical height after the non-submerged vegetation used in the experiment is bent is equal to the water depth.

[0023] Furthermore, the different parameters selected in the experiment in Step 3 include the bending angle and the vegetation density.

[0024] Further, the calculation model of the vegetation resistance coefficient with respect to the bending angle in step 4 is as follows:

[0025]

[0026] In the formula, θ is the bending angle of the vegetation.

[0027] Further, the coefficient of determination R 2 , root mean square error RMSE, and correlation coefficient r are used to compare the measured values and calculated values of F d under different working conditions, thereby evaluating the accuracy of the calculation model of the vegetation resistance coefficient with respect to the bending angle.

[0028] Further, the measured value of F d is obtained by actual measurement with an actual force measuring device, and the calculated value of F d is obtained by modifying the formula of the vegetation resistance F d .

[0029] (III) Beneficial effects: By simulating the water flow effects on vegetation under different natural conditions, analyzing the experimental data under different working conditions, and establishing a prediction calculation model for the vegetation resistance coefficient at different bending angles, the present invention provides a calculation method for the resistance coefficient of an aquatic plant filter bed for purifying non-point source pollution, provides support for the accurate calculation of the water flow resistance of vegetation, and thus optimizes the non-point source pollution treatment and pollutant interception mechanisms. Description of the Drawings

[0030] Figure 1 is the step flow chart of a calculation method for the resistance coefficient of a plant filter bed for purifying non-point source pollution according to the present invention;

[0031] Figure 2 is the relationship diagram of the vegetation resistance F d -section average flow velocity u according to the present invention;

[0032] Figure 3 is the relationship and fitting curve diagram of the resistance coefficient β and the bending angle θ according to the present invention. Specific Embodiments

[0033] The following further elaborates on the present invention in conjunction with preferred embodiments. More details are set forth in the following description for a full understanding of the present invention. However, the present invention can obviously be implemented in many other ways different from this description. Those skilled in the art can make similar extensions and deductions according to the actual application situation without departing from the connotation of the present invention. Therefore, the protection scope of the present invention should not be limited by the content of this specific embodiment.

[0034] The accompanying drawings are schematic diagrams of embodiments of the present invention. It should be noted that these drawings are only examples and are not drawn under the condition of equal proportions, and should not be used to limit the actual scope of protection required by the present invention.

[0035] A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution, as Figure 1 shown, includes the following steps:

[0036] Step 1: Determine the modified vegetation resistance F d formula;

[0037] Step 2: Through the analysis of the F d formula in Step 1, find out the vegetation factors that affect F d and determine the expressions of each vegetation factor;

[0038] Step 3: Through experiments simulating the conditions of a plant filter bed for purifying non-point source pollution, select working conditions with different bending angles of the vegetation, and obtain experimental data under different parameters and working conditions;

[0039] Step 4: Synthesize the experimental data, fit between the resistance coefficient and the bending angle of the vegetation, construct a calculation model of the vegetation resistance coefficient with respect to the bending angle, and obtain the vegetation resistance coefficient.

[0040] Vegetation resistance not only directly affects the flow velocity and direction of water flow, but also regulates the transport and distribution of non-point source pollutants, thus having a profound impact on the structure and function of the river ecosystem. On the one hand, vegetation resistance causes the flow velocity of water to decrease, enabling the sedimentation of solid pollutants in the water and forming the interception effect of vegetation on solid pollutants; on the other hand, vegetation increases the water flow resistance, increasing the hydraulic retention time and promoting the purification of pollutants by vegetation. Both of these aspects can provide support for the treatment of non-point source pollution and the interception of pollutants.

[0041] According to the research results of predecessors, aquatic vegetation can effectively reduce vegetation resistance through morphological changes. Based on this research result, the classical resistance formula of rigid vegetation is modified, and a new coefficient β is introduced to obtain the modified vegetation resistance formula:

[0042] (1),

[0043] where, ρ is the density of water; A c is the projected area of the vegetation perpendicular to the direction of water flow; C d is the vegetation cluster resistance coefficient; u is the cross-sectional average flow velocity; β is the resistance coefficient, which is a calibration parameter for the influence of vegetation morphology on resistance.

[0044] Based on considering parameters such as hydraulic radius and vegetation density, the vegetation cluster resistance coefficient C is proposed d The expression is as follows:

[0045] (2),

[0046] where Re v is the vegetation cluster Reynolds number.

[0047] Based on formula (2), it is simplified to obtain the vegetation cluster resistance coefficient formula:

[0048] (3),

[0049] where is the hydraulic radius caused by the vegetation cluster, and λ is the vegetation coverage.

[0050] Two kinds of vegetation resistance flume experiments with different parameters are carried out in the present invention. It includes the resistance experiment under different vegetation bending angles and the resistance experiment under different vegetation densities.

[0051] Experiment 1: Resistance experiment under different vegetation bending angles.

[0052] The experimental device of this experiment consists of a circulating rectangular open channel flume, simulated vegetation (cylindrical aluminum rod simulated vegetation), water gauge and underwater force measuring device. The selected circulating flume has a width of 0.5 m. During the experiment, the flow rate is adjusted to simulate different flow state conditions to complete the simulated experiment of vegetation flow at multiple flow velocities. Connect the PVC board with the fixed base of the force measuring device, then put the fixed base of the force measuring device and the PVC board into the experimental flume, connect the fixed base of the force measuring device with the underwater force measuring device, set the vegetation spacing to 6 cm×6 cm, the length L of the cylindrical aluminum rod simulated vegetation is 40 cm, the diameter D is 0.7 cm, and the drilling depth is 2 cm. Insert the cylindrical aluminum rod simulated vegetation with different bending angles into the PVC board to form multiple working conditions. It should be noted that the bent vegetation experiment in the embodiment is non-submerged vegetation to eliminate the possible error introduced by the different velocity distributions between the free water layer and the vegetation layer. The specific experimental working condition parameters are shown in Table 1.

[0053] Table 1

[0054]

[0055] where θ is the different bending angles of the cylindrical aluminum rod simulated vegetation, Q is the flume flow rate; h p is the water depth; u is the cross-sectional average flow velocity; Re v is the vegetation cluster Reynolds number; F d is the vegetation resistance.

[0056] Among them, since all five working conditions in this experiment are non-submerged states, the vertical height h after the vegetation bends v =h p , so the projected area of the vegetation perpendicular to the water flow direction is:

[0057] (4).

[0058] Experiment 2: Resistance experiment under different vegetation densities.

[0059] This experiment was carried out in the experimental flume based on Experiment 1. In this experiment, the water depth was fixed, and the upright and unbent cylindrical aluminum rods were used to simulate the vegetation as the experimental vegetation. The cylindrical aluminum rod simulated vegetation was inserted into the PVC board, and the spacing between the cylindrical aluminum rod simulated vegetation was adjusted to simulate the situation of vegetation clusters with different vegetation densities in natural water bodies. The specific vegetation cluster density parameters and experimental settings are shown in Table 2.

[0060] Table 2

[0061]

[0062] Among them, λ is the vegetation coverage.

[0063] Substitute the experimental data obtained in Experiments 1 and 2 into formulas (1), (3), and (4) to obtain the relationship diagram of vegetation resistance F d -section average velocity u and the fitting formulas under different working conditions, as Figure 2 shown, where the section average velocity u is set as the independent variable x, and the vegetation resistance F d is the dependent variable y.

[0064] Combining the experimental data of multiple working conditions, and at the same time according to Figure 2 the section average velocity u-vegetation resistance F d relationship diagram shown and the fitting formulas under different working conditions, fit between the vegetation resistance coefficient and the bending angle, and construct a calculation model of the vegetation resistance coefficient with respect to the bending angle:

[0065] (5),

[0066] and obtain the relationship and fitting curve between the vegetation resistance coefficient and the bending angle, as Figure 3 shown.

[0067] Using parameters such as the coefficient of determination R 2 , root mean square error RMSE, and correlation coefficient r, compare the measured values and calculated values of the vegetation resistance F d under different working conditions. Among them, the measured value of F d is obtained by actual measurement with a dynamometer, and the measured value of F dThe calculated value is obtained through formula (1), and the vegetation resistance coefficient is evaluated accordingly. β and the bending angle θ to determine the degree of fitting.

[0068] The coefficient of determination R 2 is expressed by the formula:

[0069]

[0070] When R² equals 1, it indicates that the model perfectly fits the data, that is, the model can explain all the variances of the dependent variable. When R² equals 0, it means that the model cannot explain any variance of the dependent variable, that is, the model cannot make any predictions or explanations for the data. When the value of R² is between 0 and 1, it shows that the model can explain part of the variance of the dependent variable. The closer R² is to 1, the better the model can fit the data and make more accurate predictions for the data.

[0071] The formula for the root mean square error RMSE is expressed as:

[0072]

[0073] RMSE is used to characterize the degree of fitting between the calculated value and the measured value curve. The smaller the root mean square error, the higher the degree of fitting.

[0074] The formula for the correlation coefficient r is as follows:

[0075]

[0076] where X i , Y i are two different variables (which are respectively represented as the calculated value and the measured value of F d in this embodiment); , are respectively the means of the variables X i , Y i ; N is the data length.

[0077] The absolute value of r ranges from 0 to 1. Generally speaking, the closer r is to 1, the stronger the correlation between the two quantities X and Y. On the contrary, the closer r is to 0, the weaker the correlation between the two variables X and Y.

[0078] Table 3

[0079]

[0080] According to Figure 2 , 3 and Table 3, it can be seen that there is a high degree of consistency between the measured vegetation resistance F d and the theoretical model of the resistance coefficient, revealing the vegetation resistance Fd There is a power function relationship with the cross-sectional average velocity u. When the vegetation is not bent (i.e., the bending angle is 0°), the vegetation resistance is proportional to the square of the cross-sectional average velocity; after the vegetation form changes, the relationship between the vegetation resistance and the cross-sectional average velocity begins to change, and this change is reflected in the change of the resistance coefficient. Moreover, as the bending angle of the vegetation in the experiment increases, the vegetation resistance under the same flow velocity shows a gradually decreasing trend, indicating that the vegetation resistance is greatly affected by the vegetation form.

[0081] According to the determination coefficient R 2 , root mean square error RMSE, correlation coefficient r and other parameters, it can be evaluated that the resistance coefficient of the plant filter bed resistance coefficient calculation method for purifying non-point source pollution proposed by the present invention β Regarding the bending angle θ The calculation model has a good fitting degree, provides a calculation method for the resistance coefficient of the aquatic plant filter bed for purifying non-point source pollution, provides support for the accurate calculation of the vegetation resistance to water flow, and thus optimizes the non-point source pollution control and pollutant interception mechanism.

[0082] The above content is an illustration of the preferred embodiments of the present invention, which can help those skilled in the art to more fully understand the technical solution of the present invention. However, these embodiments are only examples and cannot be considered that the specific implementation of the present invention is limited to the description of these embodiments. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions and transformations can be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution, characterized in that, The method includes the following steps: Step 1: Determine the corrected vegetation drag force F of aquatic vegetation d Formula Step 2: By analyzing the F described in Step 1 d formula, find out the vegetation factors that affect F d and determine the expressions of each vegetation factor; Step 3: Through experiments simulating the conditions of a plant filter bed for purifying non-point source pollution, select the working conditions with different bending angles of the vegetation, and obtain the experimental data under different parameters and different working conditions; Step 4: Synthesize the experimental data, fit between the resistance coefficient and the bending angle of the vegetation, construct a calculation model of the vegetation resistance coefficient with respect to the bending angle, and obtain the vegetation resistance coefficient; The calculation model of the vegetation resistance coefficient with respect to the bending angle in Step 4 is: ， In the formula, θ is the bending angle of the vegetation; The resistance experiment in Step 3 includes resistance experiments under different vegetation densities, and the resistance experiments under different vegetation densities use upright and unbent cylindrical aluminum rods to simulate vegetation as the experimental vegetation.

2. The method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 1, wherein The formula in Step 1 is: ， Wherein, ρ is the density of water, A c is the projected area of the vegetation perpendicular to the direction of water flow, C d is the vegetation cluster resistance coefficient, u is the cross-sectional average flow velocity, β is the resistance coefficient, which is a calibration parameter for the influence of vegetation morphology on resistance.

3. The method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 1, characterized in that, In Step 2, for F d The vegetation factors that have an impact include the projected area A of the vegetation perpendicular to the direction of water flow c , and its expression is: ， where h v is the vertical height after the vegetation bends, and D is the diameter of the vegetation.

4. A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 1, characterized in that, In Step 2, for F d The vegetation factors that have an impact also include the vegetation cluster resistance coefficient C d , and its expression is: ， where Re v is the Reynolds number of the vegetation cluster, is the hydraulic radius caused by the vegetation cluster, and λ is the vegetation coverage.

5. The calculation method of the resistance coefficient of the plant filter bed for purifying non-point source pollution according to claim 1, characterized in that, The experimental vegetation in Step 3 is non-submerged vegetation, eliminating the error introduced by the different flow velocity distributions between the free water layer and the vegetation layer.

6. A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 3 or 5, characterized in that, The vertical height of the bent non-submerged vegetation used in the experiment is equal to the water depth.

7. A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 1, characterized in that The different parameters selected in the experiment in Step 3 include the bending angle and the vegetation density.

8. A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 1, characterized in that, Using the coefficient of determination R 2 , the root mean square error RMSE, and the correlation coefficient r, the measured and calculated values of F d under different working conditions were compared to evaluate the accuracy of the calculation model of the vegetation drag coefficient with respect to the bending angle.

9. A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 8, characterized in that, F d The measured value of F is obtained through actual force measurement by an actual force measuring device. d The calculated value of F is obtained by correcting the vegetation drag d using the formula.

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