Method for calculating resistance coefficient of plant filter bed for purifying non-point source pollution

Abstract

The invention relates to a method for calculating a resistance coefficient of a plant filter bed for purifying non-point source pollution. The method comprises the following steps: determining a formula of corrected vegetation resistance Fd of aquatic vegetation; determining an expression of each vegetation factor; working conditions of different bending angles of vegetation are selected, and experimental data of different parameters under different working conditions are obtained; integrating experimental data, performing fitting between the vegetation resistance coefficient and the bending angle, and constructing a resistance coefficient calculation model; and evaluating the resistance coefficient by adopting a decision coefficient, a root-mean-square error and a correlation coefficient to calculate the model precision. According to the method, the influence of water flow on vegetation under different natural conditions is simulated, experimental data under different working conditions are analyzed, a vegetation resistance coefficient prediction calculation model under different bending angles is established, the method for calculating the resistance coefficient of the aquatic plant filter bed for purifying non-point source pollution is provided, support is provided for accurate calculation of the water flow resistance of the vegetation, and the method is suitable for large-scale popularization and application. Therefore, a non-point source pollution treatment and pollutant interception mechanism is optimized.

Description

Technical Field

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

[0002] In the field of hydrodynamics and ecological restoration, the study of the interaction between vegetation and water flow has always been an important and complex topic, especially the precise understanding and quantification of vegetation resistance characteristics, which has always received widespread attention. Vegetation resistance not only directly affects the flow rate 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 reduces the flow velocity, causing solid pollutants in the water to settle, thus forming the vegetation’s interception effect on solid pollutants; on the other hand, vegetation increases water flow resistance, increasing hydraulic retention time, thus promoting the purification of pollutants by vegetation. Both aspects can provide support for the control of non-point source pollution and the interception of pollutants.

[0004] According to the morphological characteristics of aquatic vegetation used in plant filter beds, 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, while when the vegetation morphology changes, the relationship between the resistance coefficient and the water flow conditions changes. However, the influence of the amplitude of vegetation morphological changes on the vegetation resistance coefficient has been ignored in existing studies.

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

[0006] (I) Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the purpose 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] (II) Technical solution: In order to solve the above technical problems, this technical solution provides a method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution, and the method comprises the following steps: Step 1: Determine the corrected vegetation resistance F for aquatic vegetation d formula; Step 2: By the F d Analyze the formula and find out the d Influential vegetation factors, determine the expression of each vegetation factor; Step 3: Through the experiment of simulating the plant filter bed conditions for purifying non-point source pollution, the working conditions with different bending angles of vegetation are selected to obtain the experimental data under different parameters and different working conditions; Step 4: Based on the experimental data, fit the resistance coefficient and the bending angle of the vegetation, build a calculation model of the vegetation resistance coefficient with respect to the bending angle, and obtain the vegetation resistance coefficient.

[0008] Furthermore, the formula in step 1 is:

[0009] In the formula, ρ is the density of water, A c is the projection area of ​​vegetation perpendicular to the direction of water flow, C d is the vegetation resistance coefficient, u is the average flow velocity of the section, β is the drag coefficient, which is a calibration parameter for the effect of vegetation morphology on drag.

[0010] Furthermore, in step 2, d The influential vegetation factors include the projection area A of the vegetation perpendicular to the flow direction. c , whose expression is:

[0011] In the formula, h v is the vertical height of the vegetation after bending, and D is the diameter of the vegetation.

[0012] Furthermore, in step 2, d The vegetation factors that have an impact include the vegetation resistance coefficient C d , whose expression is:

[0013] In the formula, Re v is the vegetation Reynolds number, is the hydraulic radius caused by the vegetation cluster, and λ is the vegetation coverage.

[0014] Furthermore, the experimental vegetation in step 3 is non-submerged vegetation, which eliminates the error introduced by the different velocity distribution between the free water layer and the vegetation layer.

[0015] Furthermore, the vertical height of the non-submerged vegetation used in the experiment after bending is equal to the water depth.

[0016] Furthermore, the different parameters selected for the experiment in step 3 include bending angle and vegetation density.

[0017] Furthermore, the calculation model of the vegetation resistance coefficient with respect to the bending angle in step 4 is:

[0018] In the formula, θ is the bending angle of the vegetation.

[0019] Furthermore, the determination coefficient R 2 , root mean square error RMSE and correlation coefficient r, and the F d The measured values ​​and calculated values ​​were compared to evaluate the accuracy of the calculation model of vegetation resistance coefficient with respect to bending angle.

[0020] Furthermore, F d The measured value of F is obtained by actual force measurement device. d The calculated value is corrected by the vegetation resistance F d The formula is obtained.

[0021] (III) Beneficial effects: The present invention simulates the influence of water flow on vegetation under different natural conditions, analyzes experimental data under different working conditions, and establishes a prediction and calculation model for the vegetation resistance coefficient under different bending angles. It provides a method for calculating the resistance coefficient of aquatic plant filter beds for purifying non-point source pollution, and provides support for the accurate calculation of vegetation resistance to water flow, thereby optimizing non-point source pollution control and pollutant interception mechanisms. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the steps of a method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to the present invention; Figure 2 is the vegetation resistance F of the present invention d -Relationship diagram of average flow velocity u in cross section; Figure 3 is the drag coefficient of the present invention β With bending angle θ Relationship and fitting curve diagram. DETAILED DESCRIPTION

[0023] The present invention is further described in detail below in conjunction with preferred embodiments. More details are elaborated in the following description to facilitate a full understanding of the present invention. However, the present invention can obviously be implemented in a variety of other ways different from the description. Those skilled in the art can make similar generalizations and deductions based on actual application situations without violating 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.

[0024] The accompanying drawings are schematic diagrams of embodiments of the present invention. It should be noted that the drawings are only examples and are not drawn to scale, and should not be used to limit the actual protection scope of the present invention.

[0025] A method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution, such as Figure 1 As shown, the following steps are included: Step 1: Determine the corrected vegetation resistance F for aquatic vegetation d formula; Step 2: By the F d Analyze the formula and find out the d Influential vegetation factors, determine the expression of each vegetation factor; Step 3: Through the experiment of simulating the plant filter bed conditions for purifying non-point source pollution, the working conditions with different bending angles of vegetation are selected to obtain the experimental data under different parameters and different working conditions; Step 4: Based on the experimental data, fit the resistance coefficient and the bending angle of the vegetation, build a calculation model of the vegetation resistance coefficient with respect to the bending angle, and obtain the vegetation resistance coefficient.

[0026] Vegetation resistance not only directly affects the 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. On the one hand, vegetation resistance causes the water flow velocity to decrease, causing solid pollutants in the water to settle, thus forming the vegetation's interception effect on solid pollutants; on the other hand, vegetation increases water flow resistance, increasing the hydraulic retention time, thus promoting the purification of pollutants by vegetation. Both aspects can provide support for the control of non-point source pollution and the interception of pollutants.

[0027] According to previous research results, 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: (1), in, ρ is the density of water; A c C is the projection area of ​​vegetation perpendicular to the direction of water flow; d is the resistance coefficient of vegetation; u is the average flow velocity of the section; β is the drag coefficient, which is a calibration parameter for the effect of vegetation morphology on drag.

[0028] Based on the consideration of parameters such as hydraulic radius and vegetation density, the vegetation resistance coefficient C is proposed. d The specific formula is as follows: (2), Among them, Re v is the vegetation thicket Reynolds number.

[0029] Based on formula (2), we simplify it and get the formula of vegetation resistance coefficient: (3), in, is the hydraulic radius caused by the vegetation cluster, and λ is the vegetation coverage.

[0030] The present invention conducts two vegetation resistance flume experiments under different parameters, including resistance experiments under different vegetation bending angles and resistance experiments under different vegetation densities.

[0031] Experiment 1: Resistance experiment under different vegetation bending angles.

[0032] The experimental device of this experiment consists of a circulating rectangular open channel flume, simulated vegetation (cylindrical aluminum rod simulated vegetation), a water ruler and an underwater force measuring device. This experiment uses a circulating flume with a width of 0.5m. During the experiment, the flow rate was adjusted to simulate different flow conditions to complete the simulation experiment of vegetation water flow at multiple flow rates. The PVC board is connected to the fixed base of the force measuring device, and then the fixed base of the force measuring device and the PVC board are placed in the experimental flume, and the fixed base of the force measuring device is connected to the underwater force measuring device. The vegetation spacing is set to 6cm×6cm, the length L of the cylindrical aluminum rod simulated vegetation is 40cm, the diameter D is 0.7cm, and the drilling depth is 2cm. The cylindrical aluminum rod simulated vegetation with different bending angles is inserted into the PVC board to form multiple working conditions. It is worth noting that the bent vegetation experiment done in the embodiment is non-submerged vegetation to eliminate the error that may be introduced due to the different flow velocity distribution between the free water layer and the vegetation layer. The specific experimental working condition parameters are shown in Table 1.

[0033] Table 1

[0034]

[0035] in, θ is the different bending angles of the cylindrical aluminum rod simulating vegetation, Q is the flow rate of the water tank; h p is the water depth; u is the average flow velocity of the cross section; Re v is the vegetation Reynolds number; F d is vegetation resistance.

[0036] Among them, because the five working conditions in this experiment are all non-flooded, the vertical height of the vegetation after bending h v =h p , so the projection area of ​​vegetation perpendicular to the flow direction is: (4).

[0037] Experiment 2: Resistance experiment under different vegetation densities.

[0038] This experiment was conducted in an experimental water tank based on Experiment 1. The water depth was fixed in this experiment. Vertical unbent cylindrical aluminum rods were used as experimental vegetation. The cylindrical aluminum rods were inserted into the PVC board and the spacing between the cylindrical aluminum rods was adjusted to simulate the vegetation clusters with different vegetation densities in natural water bodies. The specific vegetation cluster density parameters and experimental settings are shown in Table 2.

[0039] Table 2

[0040] Among them, λ is the vegetation coverage.

[0041] Substituting the experimental data obtained in Experiments 1 and 2 into formulas (1), (3), and (4), we can obtain the vegetation resistance F d -Relationship diagram of average flow velocity u in cross section and fitting formula under different working conditions, such as Figure 2 As shown in the figure, the average flow velocity u of the cross section is assumed to be the independent variable x, and the vegetation resistance F d is the dependent variable y.

[0042] Combining multiple working condition experimental data, Figure 2 Average flow velocity u of the cross section shown - vegetation resistance F d The relationship diagram and the fitting formula under different working conditions are used to fit the vegetation resistance coefficient and the bending angle, and a calculation model of the vegetation resistance coefficient with respect to the bending angle is constructed: (5), And the relationship between vegetation resistance coefficient and bending angle and the fitting curve are obtained, such as Figure 3 shown.

[0043] The coefficient of determination R 2 , root mean square error RMSE and correlation coefficient r, etc., to calculate the vegetation resistance F under different working conditions. d The measured value and calculated value are compared, among which, F d The measured value of F is obtained by measuring with a dynamometer. d The calculated value of is obtained by formula (1), and the vegetation resistance coefficient is evaluated by β With bending angle θ The degree of fit between them.

[0044] Coefficient of determination R 2 The formula is:

[0045] When R² is equal to 1, it means that the model fits the data perfectly, that is, the model can explain all the variance of the dependent variable. When R² is equal to 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 means 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.

[0046] The root mean square error RMSE formula is expressed as:

[0047] RMSE is used to characterize the degree of fit between the calculated value and the measured value curve. The smaller the root mean square error, the higher the degree of fit.

[0048] The correlation coefficient r formula is as follows:

[0049] Among them, X i , Y i are two different variables (represented as F d Calculated and measured values ​​of , The variables X i , Y i The mean of; N is the data length.

[0050] The absolute value of r is between 0 and 1. Generally speaking, the closer r is to 1, the stronger the correlation between X and Y. Conversely, the closer r is to 0, the weaker the correlation between X and Y.

[0051] Table 3

[0052] according to Figure 2 , 3 From Table 3, we can see that the measured vegetation resistance F d There is a high degree of consistency between the theoretical model of the resistance coefficient and the vegetation resistance F d There is a power function relationship between the resistance coefficient and the average flow velocity u of the cross section. When the vegetation is not bent (i.e. the bending angle is 0°), the vegetation resistance is proportional to the square of the average flow velocity of the cross section; when the vegetation morphology changes, the relationship between the vegetation resistance and the average flow velocity of the cross section begins to change, and this change is reflected in the change of the resistance coefficient. And as the bending angle of the vegetation increases in the experiment, the vegetation resistance shows a trend of gradually decreasing at the same flow velocity, which shows that the vegetation resistance is greatly affected by the vegetation morphology.

[0053] According to the coefficient of determination R 2, root mean square error RMSE and correlation coefficient r and other parameters evaluation show that the resistance coefficient of the plant filter bed resistance coefficient calculation method for purifying non-point source pollution proposed in the present invention is β About bending angle θ The calculation model has a good fit and provides a method for calculating the resistance coefficient of aquatic plant filter beds for purifying non-point source pollution, providing support for the accurate calculation of vegetation resistance to water flow, thereby optimizing non-point source pollution control and pollutant interception mechanisms.

[0054] The above content is an explanation 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 merely illustrative, and it cannot be determined that the specific implementation methods of the present invention are limited to the description of these embodiments. For ordinary technicians 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 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 comprises the following steps: Step 1: Determine the corrected vegetation resistance F for aquatic vegetation d formula; Step 2: By the F d Analyze the formula and find out the d Influential vegetation factors, determine the expression of each vegetation factor; Step 3: Through the experiment of simulating the plant filter bed conditions for purifying non-point source pollution, the working conditions with different bending angles of vegetation are selected to obtain the experimental data under different parameters and different working conditions; Step 4: Based on the experimental data, fit the resistance coefficient and the bending angle of the vegetation, build a calculation model of the vegetation resistance coefficient with respect to the bending angle, and obtain the vegetation resistance coefficient.

2. The method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 1 is characterized in that: The formula described in step 1 is: ， In the formula, ρ is the density of water, A c is the projection area of ​​vegetation perpendicular to the direction of water flow, C d is the vegetation resistance coefficient, u is the average flow velocity of the section, β is the drag coefficient, which is a calibration parameter for the effect of vegetation morphology on drag.

3. The method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 1 is characterized in that: Step 2 d The influential vegetation factors include the projection area A of the vegetation perpendicular to the flow direction. c , whose expression is: ， In the formula, h v is the vertical height of the vegetation after bending, and D is the diameter of the vegetation.

4. 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: Step 2 d The influencing vegetation factors also include the vegetation resistance coefficient C d , whose expression is: ， In the formula, Re v is the vegetation Reynolds number, is the hydraulic radius caused by the vegetation cluster, and λ is the vegetation coverage.

5. 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 3, the experimental vegetation used is non-submerged vegetation to eliminate the error introduced by the different flow velocity distribution between the free water layer and the vegetation layer.

6. The 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 non-submerged vegetation used in the experiment after bending is equal to the water depth.

7. 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: The different parameters selected for the experiment in step 3 include bending angle and vegetation density.

8. 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: The calculation model of vegetation resistance coefficient with respect to bending angle in step 4 is: ， In the formula, θ is the bending angle of the vegetation.

9. 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: The coefficient of determination R 2 , root mean square error RMSE and correlation coefficient r, and the F d The measured values ​​and calculated values ​​were compared to evaluate the accuracy of the calculation model of vegetation resistance coefficient with respect to bending angle.

10. The method for calculating the resistance coefficient of a plant filter bed for purifying non-point source pollution according to claim 9, characterized in that: F d The measured value of F is obtained by actual force measurement device. d The calculated value is corrected by the vegetation resistance F d The formula is obtained.

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