A design method for water exchange and replenishment across the entire area of ​​a multi-island annular lake

Abstract

This invention discloses a design method for water exchange and replenishment of a multi-island annular lake. Based on the planned replenishment scale and path, a two-dimensional mathematical model coupling lake hydrodynamics and water exchange is used to simulate the replenishment process, determining the relationship between the average water exchange rate of the lake area and time, and obtaining the optimal simulated replenishment duration. A series of centralized replenishment points are set up in the island areas of the lake, and the replenishment process in the island areas is simulated under the optimal simulated replenishment duration. The head difference of each water flow channel in each centralized replenishment point in the island areas is determined, and the optimal centralized replenishment point in the island areas is determined based on the head difference of each water flow channel. A series of decentralized replenishment points are set up in the weak exchange zone of the main lake area, and the replenishment process in the main lake area is simulated under the optimal simulated replenishment duration. The water exchange rate in the weak exchange zone is determined, and the optimal decentralized replenishment point in the main lake area is determined based on the water exchange rate in the weak exchange zone, thereby improving the overall water exchange and replenishment effect of the lake.

Description

Technical Field

[0001] This invention belongs to the field of lake hydrodynamic numerical simulation technology, specifically, it relates to a design method for water exchange and replenishment of a multi-island annular lake. Background Technology

[0002] Water replenishment projects are currently the primary engineering method for addressing lake water quality issues and are widely used in various types of lakes worldwide. However, for multi-island annular lakes, due to their complex water and land area patterns, variable hydrodynamic characteristics, and diverse flow paths, determining the location of replenishment points during implementation is challenging, and accurately predicting the water exchange effects after the project is completed is difficult. Therefore, how to scientifically deploy replenishment points to effectively enhance the water exchange capacity of multi-island annular lakes has become a pressing technical challenge in the field of lake water environment hydrodynamics. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides a design method for water exchange and replenishment of a multi-island ring lake, offering a scientific and effective approach for the layout of water replenishment projects for multi-island ring lakes.

[0004] To achieve the above technical objectives, the present invention adopts the following technical solution: a design method for water exchange and replenishment of a multi-island annular lake, specifically including the following steps:

[0005] Step S1: Establish a two-dimensional mathematical model of the coupling of hydrodynamics and water exchange in the lake area;

[0006] Step S2: Based on the planned water replenishment scale and water replenishment path, use a two-dimensional mathematical model of lake hydrodynamics-water exchange coupling to simulate the water replenishment process, determine the relationship between the average water exchange rate of the lake area and time, and obtain the optimal simulated water replenishment duration.

[0007] Step S3: Set up a series of centralized water replenishment points in the island area of ​​the lake. Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling to simulate the water replenishment process in the island area, determine the head difference of each water flow channel in each centralized water replenishment point in the island area, and determine the optimal centralized water replenishment point in the island area based on the head difference of each water flow channel.

[0008] Step S4: Set up a series of decentralized water replenishment points in the weak exchange zone of the main lake area. Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake area hydrodynamic-water exchange coupling to simulate the water replenishment process of the main lake area, determine the water exchange rate of the weak exchange zone, and determine the optimal decentralized water replenishment points of the main lake area based on the water exchange rate of the weak exchange zone.

[0009] Step S5: The design schemes of the best centralized water replenishment point in the island area and the best decentralized water replenishment point in the main lake area are used as the water exchange and replenishment scheme for the entire lake area.

[0010] Furthermore, the two-dimensional mathematical model of the coupling of hydrodynamics and water exchange in the lake area is specifically as follows:

[0011]

[0012] Where h is the lake depth, u is the lake's flow velocity in the x-direction, v is the lake's flow velocity in the y-direction, q is a constant, g is the acceleration due to gravity, f is the Coriolis force coefficient, and p a ρ is the atmospheric pressure of the area where the lake is located; ρ is the density of the lake water; η is the elevation of the lakebed; τ is... ax τ ay These are the wind stress tensors in the x and y directions of the water surface, respectively, τ bx τ by Let τ be the stress tensor in the x and y directions at the bottom of the riverbed, respectively. sx τ sy The radiation stress components in the x and y directions are respectively, T xx T xy T yy The horizontal viscous stresses in the xx plane, xy plane, and yy plane are respectively, s is the flow rate at the water replenishment point, and u is the horizontal viscous stress in the xx plane, xy plane, and yy plane. x u y These represent the water flow velocities in the x and y directions at the water replenishment point, respectively; C represents the water exchange rate; and K represents the water exchange rate. x K y These are the diffusion coefficients in the x and y directions, respectively.

[0013] Further, step S2 includes the following sub-steps:

[0014] Step S2.1: Divide the lake into grids based on its basic structure and topographic boundary conditions, and determine the grid boundary conditions based on the planned water replenishment scale and water replenishment path, including: the location of the water replenishment point and the flow rate of the water replenishment point;

[0015] Step S2.2: Based on the determined location and flow rate of the water replenishment point, run the two-dimensional mathematical model of the lake area's hydrodynamic-water exchange coupling to obtain the water exchange rate of the lake area for each grid at any time.

[0016] Step S2.3: Average the water exchange rate of all grids corresponding to the lake area to obtain the average water exchange rate of the lake area at any time.

[0017] Step S2.4: Perform curve fitting with time as the independent variable and the average water exchange rate of the lake area as the dependent variable to determine the relationship between the average water exchange rate of the lake area and time, and take the time corresponding to the maximum instantaneous average water exchange rate of the lake area as the optimal simulated water replenishment duration.

[0018] Furthermore, step S3 includes the following sub-steps:

[0019] Step S3.1: Select n centralized water replenishment points in the island area of ​​the lake, and set up m water flow channels at each centralized water replenishment point;

[0020] Step S3.2: Under the optimal simulated water replenishment duration, a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling is used to simulate the water replenishment process. Each time, only one water flow channel of a centralized water replenishment point is selected to simulate the water replenishment of the island area, determine the lake bottom elevation, and combine it with the lake water depth to obtain the head difference of the water flow channel used for water replenishment.

[0021] Step S3.3: Repeat step S3.2 for each water flow channel in the n centralized water replenishment points, calculate the root mean square error of the head difference of each water flow channel in each centralized water replenishment point, and take the centralized water replenishment point with the smallest root mean square error as the optimal centralized water replenishment point.

[0022] Furthermore, the calculation process for the root mean square error of the head difference in each water flow channel at each centralized water replenishment point in step S3.3 is as follows:

[0023]

[0024] Among them, S i Let denot ΔH represent the mean square error of the i-th centralized water replenishment point, m represent the number of water flow channels in the i-th centralized water replenishment point, j represent the index of m, and ΔH represent the mean square error of the i-th centralized water replenishment point. ij This represents the head difference of the j-th water flow channel among the i-th water replenishment points in the set. This represents the average head difference across all water flow channels at the i-th centralized water replenishment point.

[0025] Furthermore, step S4 includes the following sub-steps:

[0026] Step S4.1: Set up 1 to L gradually increasing decentralized water replenishment points in the weak exchange zone of the main lake area of ​​the lake as different water replenishment schemes for the weak exchange zone, and determine the flow rate of each decentralized water replenishment point under each water replenishment scheme.

[0027] Step S4.2: Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling to simulate the water replenishment process of the main lake area under different water replenishment schemes in sequence, and obtain the water exchange rate of the weak exchange zone.

[0028] Step S4.3: If the increase in the water exchange rate of the weak exchange zone under two adjacent water replenishment schemes is less than 3%, the former water replenishment scheme shall be taken as the best decentralized water replenishment point in the main lake area.

[0029] Furthermore, the flow rate Q at each decentralized water replenishment point in step S4.1 k=Q / k, and the flow rate of each decentralized water replenishment point does not exceed the water replenishment scale of the main lake area, where Q represents the total water replenishment flow rate of the weak exchange area, and k represents the number of decentralized water replenishment points set up, k∈{1,2,...,L].

[0030] Furthermore, in step S4.3, the increase in the water exchange rate ΔC in the weak exchange zone under two adjacent water replenishment schemes... k The calculation process is as follows:

[0031]

[0032] Among them, C k This represents the water exchange rate in the weak exchange zone under k dispersed water replenishment points.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) The water exchange and replenishment design method for the entire area of ​​multi-island ring lakes in this invention adds a water exchange component to describe the changes in substance concentration on the basis of the traditional hydrodynamic mathematical model, thereby establishing a two-dimensional mathematical model of lake area hydrodynamic-water exchange coupling, which can simulate the evolution process of water exchange in lake research and can directly show the distribution of water exchange rate in lake area.

[0035] (2) In this invention, the water exchange characteristics are mainly affected by friction resistance, and the effect of friction resistance is more significant in the island areas of lakes. Since there are many factors affecting friction resistance in the island areas of lakes, it is difficult to compare the flow resistance between different island channels through theoretical calculations. However, the head difference along the flow path, as a concrete manifestation of flow resistance, can be used as an indicative factor for judging the magnitude of flow resistance. Therefore, for the island areas of lakes, by setting up a series of centralized water replenishment points, simulating and comparing the head difference of each flow channel, and analyzing the uniformity of water diffusion, the optimal water replenishment point in the island areas is determined, thereby improving the water exchange capacity of the island areas of lakes.

[0036] (3) For the main lake area, the water area is vast, and it is difficult to completely exchange water throughout the entire area under the condition of limited water replenishment flow. Therefore, when designing the decentralized water replenishment points in the main lake area, it is necessary to give priority to the water replenishment effect in the weak exchange area. Therefore, for the main lake area, by analyzing the water exchange rate under different decentralized water replenishment schemes, the degree of improvement of water exchange effect in key areas is evaluated, and the best water replenishment scheme for the main lake area is determined.

[0037] By using the design scheme of the optimal centralized water replenishment point in the island area and the optimal decentralized water replenishment point in the main lake area as the water exchange and replenishment scheme for the entire lake area, the water exchange and replenishment capacity of the entire lake area can be improved. Furthermore, the lake water replenishment design scheme of this invention can be widely applied to the water replenishment engineering design of multi-island ring lakes, effectively solving the technical problems of difficulty in selecting water replenishment layout and inability to guarantee water replenishment effect, while enriching and developing the simulation method of lake hydrodynamics and water exchange. Attached Figure Description

[0038] Figure 1 A topographic map of Xinglin Bay;

[0039] Figure 2 This is a schematic diagram illustrating the grid division of Xinglin Bay.

[0040] Figure 3 A schematic diagram of a water replenishment scheme using the multi-island ring lake whole-area water exchange and replenishment design method of the present invention;

[0041] Figure 4 A graph showing the change in the average water exchange rate in the lake area;

[0042] Figure 5 Layout plan of centralized water replenishment points in the island area;

[0043] Figure 6 A schematic diagram of the water flow test along the route of water replenishment point No. 1 in the island area;

[0044] Figure 7 Rendering of the water exchange effect for the island area;

[0045] Figure 8 Diagram of the decentralized water replenishment layout scheme for the main lake area;

[0046] Figure 9 A statistical regional division map of the main lake area;

[0047] Figure 10 A diagram illustrating the water exchange effect in the main lake area;

[0048] Figure 11 A diagram showing the effect of water replenishment to the entire lake area. Detailed Implementation

[0049] The technical solution of the present invention will be further explained and described below with reference to the accompanying drawings.

[0050] This invention discloses a design method for water exchange and replenishment across the entire area of ​​a multi-island annular lake, specifically including the following steps:

[0051] Step S1: Traditional hydrodynamic models are mainly used for velocity distribution and sediment deposition / scouring studies in estuaries and coastal areas. This invention adds water exchange based on substance concentration to the traditional hydrodynamic model, establishing a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling. This model simulates the evolution of water exchange in lakes and can directly display the distribution of water exchange rates in lake areas. The two-dimensional mathematical model of lake hydrodynamic-water exchange coupling established in this invention is as follows:

[0052]

[0053] Where h is the lake depth, u is the lake's flow velocity in the x-direction, v is the lake's flow velocity in the y-direction, q is a constant, g is the acceleration due to gravity, f is the Coriolis force coefficient, and p a ρ is the atmospheric pressure of the area where the lake is located; ρ is the density of the lake water; η is the elevation of the lakebed; τ is... ax τ ay These are the wind stress tensors in the x and y directions of the water surface, respectively, τ bx τ by Let τ be the stress tensor in the x and y directions at the bottom of the riverbed, respectively. sx τ sy The radiation stress components in the x and y directions are respectively, T xx T xy T yy The horizontal viscous stresses in the xx plane, xy plane, and yy plane are respectively, s is the flow rate at the water replenishment point, and u is the horizontal viscous stress in the xx plane, xy plane, and yy plane. x u y These represent the water flow velocities in the x and y directions at the water replenishment point, respectively; C represents the water exchange rate; and K represents the water exchange rate. x K y These are the diffusion coefficients in the x and y directions, respectively.

[0054] Step S2: When simulating the water replenishment process using a two-dimensional mathematical model coupling lake hydrodynamics and water exchange, if the designed simulation replenishment duration is too short, the water exchange effect will be insignificant; if the designed simulation replenishment duration is too long, the economic cost will be high and the computational load will be large. Therefore, it is necessary to select an appropriate simulation replenishment duration to provide a scientific basis for the operation time of the water replenishment project. This invention, based on the planned water replenishment scale and path, uses a two-dimensional mathematical model coupling lake hydrodynamics and water exchange to simulate the water replenishment process, determines the relationship between the average water exchange rate of the lake area and time, and obtains the optimal simulation replenishment duration that can achieve both economic benefits and water replenishment effect; including the following sub-steps:

[0055] Step S2.1: Divide the lake into grids based on its basic structure and topographic boundary conditions, and determine the grid boundary conditions based on the planned water replenishment scale and water replenishment path, including: the location of the water replenishment point and the flow rate of the water replenishment point;

[0056] Step S2.2: Based on the determined location and flow rate of the water replenishment point, run the two-dimensional mathematical model of the lake area's hydrodynamic-water exchange coupling to obtain the water exchange rate of the lake area for each grid at any time.

[0057] Step S2.3: Average the water exchange rate of all grids corresponding to the lake area to obtain the average water exchange rate of the lake area at any time.

[0058] Step S2.4: Using time as the independent variable and the average water exchange rate of the lake area as the dependent variable, curve fitting is performed to determine that the relationship between the average water exchange rate of the lake area and time is that it increases rapidly first and then slowly. That is, although the water exchange rate still increases after a certain period of water replenishment, the effect is not obvious. Therefore, this invention takes the time corresponding to the maximum instantaneous average water exchange rate of the lake area as the optimal simulated water replenishment time.

[0059] Step S3: Water exchange characteristics are mainly affected by friction loss, and the effect of friction loss is more significant in the island areas of lakes. For example, the width and shape of the channels between islands are closely related to the magnitude of friction loss. Narrow channels increase the water flow velocity and also generate greater local resistance, thus affecting the overall water exchange process. Since there are many factors affecting friction loss in lake island areas, it is difficult to compare the flow resistance between different island channels through theoretical calculations. However, the head difference along the flow, as a concrete manifestation of flow resistance, can serve as an indicative factor for judging the magnitude of flow resistance, greatly reducing the complexity of calculations. Simultaneously, the water area of ​​lake island areas is small, and decentralized water replenishment is not required. Therefore, a series of centralized water replenishment points are set up in the lake island areas. Under the optimal simulated water replenishment duration, a two-dimensional mathematical model of lake hydrodynamics-water exchange coupling is used to simulate the water replenishment process in the island areas, determining the head difference of each flow channel in each centralized water replenishment point in the island areas. Based on the head difference of each flow channel, the optimal centralized water replenishment point in the island areas is determined, thereby improving the water exchange capacity of the lake island areas. This includes the following sub-steps:

[0060] Step S3.1: Select n centralized water replenishment points in the island area of ​​the lake, and set up m water flow channels at each centralized water replenishment point;

[0061] Step S3.2: Under the optimal simulated water replenishment duration, a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling is used to simulate the water replenishment process. Each time, only one water flow channel of a centralized water replenishment point is selected to simulate the water replenishment of the island area, determine the lake bottom elevation, and combine it with the lake water depth to obtain the head difference of the water flow channel used for water replenishment.

[0062] Step S3.3: Repeat step S3.2 for each water flow channel in the n centralized water replenishment points, and calculate the root mean square error of the head difference of each water flow channel in each centralized water replenishment point. The smaller the root mean square error of the centralized water replenishment point, the closer the total resistance of each water flow channel in the centralized water replenishment point is. When the water flows, it will tend to flow into each water flow channel evenly. Therefore, in order to ensure that the water exchange in each water flow channel is uniform, the centralized water replenishment point with the smallest root mean square error is taken as the optimal centralized water replenishment point.

[0063] The calculation process for the root mean square error of the head difference in each water flow channel at each centralized water replenishment point is as follows:

[0064]

[0065] Among them, S i Let denot ΔH represent the mean square error of the i-th centralized water replenishment point, m represent the number of water flow channels in the i-th centralized water replenishment point, j represent the index of m, and ΔH represent the mean square error of the i-th centralized water replenishment point. ij This represents the head difference of the j-th water flow channel among the i-th water replenishment points in the set. This represents the average head difference across all water flow channels at the i-th centralized water replenishment point.

[0066] Step S4: For the main lake area, the water area is vast, and under the condition of limited water replenishment flow, it is difficult to completely exchange water throughout the entire area. Therefore, when designing the decentralized water replenishment points in the main lake area, the water replenishment effect of the weak exchange zone needs to be given priority. For the main lake area, human activities are frequent in the weak exchange zone, and the water quality is worse than in the center of the lake. Therefore, a series of decentralized water replenishment points are set up in the weak exchange zone of the main lake area. Under the optimal simulated water replenishment duration, a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling is used to simulate the water replenishment process of the main lake area, determine the water exchange rate of the weak exchange zone, and determine the optimal decentralized water replenishment points in the main lake area based on the water exchange rate of the weak exchange zone, thereby improving the water exchange effect of the main lake area; including the following sub-steps:

[0067] Step S4.1: In the weak exchange zone of the main lake area, set up 1 to L gradually increasing decentralized water replenishment points as different water replenishment schemes for the weak exchange zone, and determine the flow rate Q of each decentralized water replenishment point under each water replenishment scheme. k =Q / k, and the flow rate of each decentralized water replenishment point does not exceed the water replenishment scale of the main lake area, where Q represents the total water replenishment flow rate of the weak exchange area, and k represents the number of decentralized water replenishment points set up, k∈{1,2,...,L].

[0068] Step S4.2: Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling to simulate the water replenishment process of the main lake area under different water replenishment schemes in sequence, and obtain the water exchange rate of the weak exchange zone.

[0069] Step S4.3: If the increase in the water exchange rate of the weak exchange zone under two adjacent water replenishment schemes is less than 3%, the former water replenishment scheme shall be taken as the best decentralized water replenishment point in the main lake area.

[0070] The increase in water exchange rate ΔC in the weak exchange zone under two adjacent water replenishment schemes k The calculation process is as follows:

[0071]

[0072] Among them, C k This represents the water exchange rate in the weak exchange zone under k dispersed water replenishment points.

[0073] Step S5: Using the design schemes of the optimal centralized water replenishment point in the island area and the optimal decentralized water replenishment point in the main lake area as the overall water exchange and replenishment scheme for the lake can enhance the overall water exchange and replenishment capacity of the lake. Furthermore, the lake replenishment design scheme of this invention can be widely applied to the design of water replenishment projects for multi-island circular lakes, effectively solving the technical problems of difficulty in selecting water replenishment layouts and ensuring water replenishment effects. It also enriches and develops methods for simulating lake hydrodynamics and water exchange.

[0074] Example

[0075] Xinglin Bay is located in the central area of ​​Jimei District, Xiamen City, on the northwest side of Xiamen Island. Due to severe siltation at the bay's mouth, the water quality is poor, and tidal flow cannot improve the bay's hydrodynamic environment. Therefore, a water replenishment project is implemented to promote water exchange and improve water quality. Figure 1 Xinglin Bay is a typical multi-island ring-shaped lake. The left half of the bay is an island area, with six main islands arranged in a plum blossom pattern. The right side of the bay is the main lake area, with a wide water area. The method of this invention optimizes the layout of the water replenishment project for the entire lake area, ensuring uniform water replenishment at the centralized water replenishment points in the island area and improving the water exchange effect in the main lake area's secondary exchange zones. Specifically, it includes the following steps:

[0076] Step S1: Establish a two-dimensional mathematical model of the coupling of hydrodynamics and water exchange in the lake area:

[0077]

[0078] Where h is the lake depth, u is the lake's flow velocity in the x-direction, v is the lake's flow velocity in the y-direction, q is a constant, g is the acceleration due to gravity, f is the Coriolis force coefficient, and p a ρ is the atmospheric pressure of the area where the lake is located; ρ is the density of the lake water; η is the elevation of the lakebed; τ is... ax τ ay These are the wind stress tensors in the x and y directions of the water surface, respectively, τ bx τ by Let τ be the stress tensor in the x and y directions at the bottom of the riverbed, respectively.sx τ sy The radiation stress components in the x and y directions are respectively, T xx T xy T yy The horizontal viscous stresses in the xx plane, xy plane, and yy plane are respectively, s is the flow rate at the water replenishment point, and u is the horizontal viscous stress in the xx plane, xy plane, and yy plane. x u y These represent the water flow velocities in the x and y directions at the water replenishment point, respectively; C represents the water exchange rate; and K represents the water exchange rate. x K y These are the diffusion coefficients in the x and y directions, respectively.

[0079] In this embodiment, due to the complexity of the islands and water system within Xinglin Bay, the computational domain is discretized using an unstructured grid, which accurately reflects the outline of the shoreline and local engineering features. The basic structure of the lake includes the Xinglin Bay area and its internal islands, with a grid size of 6m to 8m to ensure computational accuracy. The total number of computational units is approximately 200,000. Figure 2 As shown.

[0080] Step S2: Based on the planned water replenishment scale and route, namely, replenishment from the end of Jiutian Lake and Houxi, with 80,000 cubic meters / day replenished to Jiutian Lake and 100,000 cubic meters / day replenished to Houxi, a two-dimensional mathematical model of lake hydrodynamics-water exchange coupling is used to simulate the water replenishment process, determine the relationship between the average water exchange rate of the lake area and time, and obtain the optimal simulated water replenishment duration.

[0081] like Figure 3 Based on the location of surrounding sewage treatment plants and their current purification capacity, assuming no water loss along the route, 180,000 cubic meters of purified water are used daily for the Xinglin Bay water replenishment project, of which 80,000 cubic meters / day are used in Jiutian Lake and 100,000 cubic meters / day in Houxi. To determine the duration of subsequent experimental simulations, a simulation calculation for a 180-day replenishment period was first performed on the design scheme. The average water exchange rate of the lake area was calculated and changed over time, as shown in Table 1: At the beginning of the replenishment, the average water exchange rate of the lake area increased rapidly. When the replenishment period reached 60 days, the average water exchange rate of the entire lake area reached more than 50%. Subsequently, the growth of the average water exchange rate of the lake area slowed down, and the water exchange rate reached about 80% after 180 days.

[0082] Table 1. Variation of Average Water Exchange Rate under Lake Area Design Scheme

[0083]

[0084]

[0085] The curve showing the relationship between the average water exchange rate and the water replenishment time in the fitted lake area is shown below. Figure 4 Therefore, its expression is P = -0.00003t. 2+0.01t+0.0093, where P is the average water exchange rate of the lake area, t is the water replenishment duration, ΔP=P'=-0.00006t+0.01, setting ΔP>0.6%, we get t<66. That is, for Xinglin Bay, the water replenishment effect is too low after the water replenishment duration exceeds 66 days. Considering the economic benefits of water replenishment and the calculation time of the two-dimensional mathematical model of the lake area's hydrodynamic-water exchange coupling, the optimal water replenishment duration for Xinglin Bay is considered to be 60 days, and the duration of water replenishment simulations for all subsequent schemes is set to 60 days.

[0086] Step S3: Set up a series of centralized water replenishment points in the island area of ​​the lake. Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake hydrodynamics-water exchange coupling to simulate the water replenishment process in the island area, determine the head difference of each water flow channel in each centralized water replenishment point in the island area, and determine the optimal centralized water replenishment point in the island area based on the head difference of each water flow channel. For example... Figure 5 As shown, three centralized water replenishment points were selected in the island area. One of the replenishment points was selected in turn to conduct water replenishment simulation. In order to make the experimental phenomenon obvious, the water replenishment flow rate can be appropriately increased and set to 50 times the daily water replenishment flow rate, that is, 4 million cubic meters / day.

[0087] In each set of simulation tests, only one outflow channel is retained, and the remaining channels between islands are set to not cross the water boundary. There are five outflow channels in the Xinglin Bay island area, resulting in a total of five sets of tests under one water replenishment point. The test paths for the five sets of tests at water replenishment point #1 are as follows: Figure 6 As shown in the figure. After a constant flow field is formed in the island area, the water level along the flow path of each outlet channel is measured. The head loss along the flow path represents the magnitude of the friction resistance. The head difference of different channels is obtained through the above method. Subsequently, the water supply point is changed and the simulation is performed again to obtain the head difference of each channel under water supply points #2 and #3. After 6 hours of simulated water supply, the water level along the flow path under each scheme is basically constant. The head difference of each flow channel in Xinglin Bay island area under the scheme of taking water supply points #1, #2, and #3 is measured as shown in Table 2 below.

[0088] Table 2. Head difference of each channel at different water supply points.

[0089]

[0090]

[0091] The root mean square error of the friction resistance along different flow channels at each centralized water replenishment point is calculated using the following formula: Among them, S i Let denot ΔH represent the mean square error of the i-th centralized water replenishment point, m represent the number of water flow channels in the i-th centralized water replenishment point, j represent the index of m, and ΔH represent the mean square error of the i-th centralized water replenishment point. ij This represents the head difference of the j-th water flow channel among the i-th water replenishment points in the set. This represents the average head difference across all water flow channels at the i-th centralized water replenishment point. The calculation results are shown in Table 3 below. The frictional resistance at water replenishment point #1 is the smallest, indicating that water exchange in the island area is more uniform under water replenishment at this point, and its water replenishment effect is as follows: Figure 7 As shown, therefore, Xinglin Bay Island Area selected No. 1 water replenishment point as the best water replenishment point.

[0092] Table 3. Calculation of the root mean square error of friction resistance.

[0093]

[0094] Step S4: Set up a series of decentralized water replenishment points in the weak exchange zone of the main lake area. Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake area hydrodynamic-water exchange coupling to simulate the water replenishment process of the main lake area, determine the water exchange rate of the weak exchange zone, and determine the optimal decentralized water replenishment points of the main lake area based on the water exchange rate of the weak exchange zone.

[0095] To explore the optimal layout of decentralized water replenishment points in the main lake area, a decentralized water replenishment experiment was conducted in the main lake area to observe the distribution of replenishment rates under different flow rates. Since the maximum replenishment volume of Houxi is 100,000 cubic meters per day, the total replenishment flow rate used in the main lake area during the experiment was 100,000 cubic meters per day.

[0096] Due to the shielding effect of the three island chains to the northeast, the water in the right coastal area of ​​Xinglin Bay has not been effectively exchanged. At the same time, in order to ensure the water exchange effect in the Houxi direction, the water replenishment flow in the Houxi water area should not be less than 40,000 cubic meters / day. Therefore, 60,000 cubic meters / day of water replenishment will be transferred to the right coastal area of ​​Xinglin Bay.

[0097] K new decentralized water replenishment points will be set up along the right bank of the main lake area, where k = 1, 2, 3, 4, and 5. The flow rates at each replenishment point will be 60,000 cubic meters / day, 30,000 cubic meters / day, 20,000 cubic meters / day, 15,000 cubic meters / day, and 12,000 cubic meters / day, respectively. The decentralized water replenishment points will be arranged as follows: Figure 8 As shown.

[0098] The main lake area of ​​Xinglin Bay has a vast water area. Due to human activities, the water quality along the right bank is poor, making it a weak water exchange zone. The focus is on the water exchange efficiency along the right bank. To compare and select the best decentralized water replenishment scheme for the main lake area, a statistical area has been defined as follows: Figure 9 As shown in Table 4, the average water exchange rate and its increase within the statistical area are as follows: When the number of decentralized water replenishment points on the right side of Xinglin Bay increases to 5, the increase in water exchange effect becomes less significant. Considering economic benefits and construction feasibility, selecting 4 decentralized water replenishment points along the right side of Xinglin Bay is the optimal solution. Therefore, the final water replenishment layout scheme for the main lake area of ​​Xinglin Bay is: 40,000 cubic meters / day replenishment from Houxi, and 15,000 cubic meters / day replenishment from each of the 4 decentralized water replenishment points along the right side of the lake. The water replenishment effect of the main lake area of ​​Xinglin Bay is as follows: Figure 10 As shown.

[0099] Table 4. Calculation of Water Exchange Rate for Various Decentralized Water Replenishment Schemes in the Main Lake Area

[0100] Dispersed water supply points 1 2 3 4 5 <![CDATA[Average water change rate C k > 82.16％ 85.24％ 88.03％ 91.37％ 93.25％ <![CDATA[Solution amplification ΔC k > 3.75％ 3.27％ 3.79％ 2.06％

[0101] Step S5: Using the design schemes of the optimal centralized water replenishment point in the island area and the optimal decentralized water replenishment point in the main lake area as the overall water exchange and replenishment scheme for the entire lake area, the water exchange effect after the overall lake area water replenishment project is obtained, such as... Figure 11 The experimental results show that after combining the optimal schemes for the island area and the main lake area, the water in the entire Xinglin Bay lake area was effectively exchanged, with more than 70% of the water area achieving a water exchange rate of 30%. The overall water exchange effect is equivalent to the superposition of the effects of the two schemes, which demonstrates the independence of the island area and the main lake area in responding to the water replenishment project, and also confirms the scientific nature of the regional study and selection of water replenishment points in this invention.

[0102] In summary, under the existing water replenishment scale, the optimal layout for Xinglin Bay is to centrally replenish the island areas, replenish 80,000 cubic meters / day in Jiutian Lake, disperse water replenishment in the main lake area, replenish 40,000 cubic meters / day in Houxi Lake, and add four additional water replenishment points along the right bank of the lake area, each replenishing 15,000 cubic meters / day. After 60 days of replenishment using this scheme, the water area with a water exchange rate exceeding 30% accounts for 75% of the total lake area, indicating a good water exchange effect. Through this invention, the water exchange capacity of Xinglin Bay is effectively improved, solving the problems of difficulty in selecting water replenishment points and unpredictable replenishment effects when using water replenishment projects for multi-island ring lakes.

[0103] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A design method for water exchange and replenishment across the entire area of ​​a multi-island annular lake, characterized in that, Specifically, the steps include the following: Step S1: Establish a two-dimensional mathematical model of the coupling of hydrodynamics and water exchange in the lake area: in, Due to the depth of the lake, Lake Flow velocity in direction Lake Flow velocity in direction q It is a constant. It is the acceleration due to gravity. The Coriolis force coefficient, The atmospheric pressure in the area where the lake is located; For the density of the lake water, The elevation of the lake bottom. , They are water surfaces direction, Wind stress tensor in direction, , The bottom of the riverbed direction, Stress tensor in the direction, , They are respectively direction, Radiation stress components in the direction, , , They are respectively xx flat, xy flat, yy Horizontal viscous stress in a plane For the flow rate at the water replenishment point, , The water replenishment points are respectively at , The velocity of water flow in the direction, For water exchange rate, , They are respectively and Diffusion coefficient in the direction of diffusion; Step S2: Based on the planned water replenishment scale and water replenishment path, use a two-dimensional mathematical model of lake hydrodynamics-water exchange coupling to simulate the water replenishment process, determine the relationship between the average water exchange rate of the lake area and time, and obtain the optimal simulated water replenishment duration. Step S3: Set up a series of centralized water replenishment points in the island area of ​​the lake. Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling to simulate the water replenishment process in the island area, determine the head difference of each water flow channel in each centralized water replenishment point in the island area, and determine the optimal centralized water replenishment point in the island area based on the head difference of each water flow channel. Step S4: Set up a series of decentralized water replenishment points in the weak exchange zone of the main lake area. Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake area hydrodynamic-water exchange coupling to simulate the water replenishment process of the main lake area, determine the water exchange rate of the weak exchange zone, and determine the optimal decentralized water replenishment points of the main lake area based on the water exchange rate of the weak exchange zone. Step S5: The design schemes of the best centralized water replenishment point in the island area and the best decentralized water replenishment point in the main lake area are used as the water exchange and replenishment scheme for the entire lake area.

2. The design method for water exchange and replenishment of a multi-island annular lake according to claim 1, characterized in that, Step S2 includes the following sub-steps: Step S2.1: Divide the lake into grids based on its basic structure and topographic boundary conditions, and determine the grid boundary conditions based on the planned water replenishment scale and water replenishment path, including: the location of the water replenishment point and the flow rate of the water replenishment point; Step S2.2: Based on the determined location and flow rate of the water replenishment point, run the two-dimensional mathematical model of the lake area's hydrodynamic-water exchange coupling to obtain the water exchange rate of the lake area for each grid at any time. Step S2.3: Average the water exchange rate of all grids corresponding to the lake area to obtain the average water exchange rate of the lake area at any time. Step S2.4: Perform curve fitting with time as the independent variable and the average water exchange rate of the lake area as the dependent variable to determine the relationship between the average water exchange rate of the lake area and time, and take the time corresponding to the maximum instantaneous average water exchange rate of the lake area as the optimal simulated water replenishment duration.

3. The design method for water exchange and replenishment of a multi-island annular lake according to claim 2, characterized in that, Step S3 includes the following sub-steps: Step S3.1: Select the island area in the lake. n There are 1 centralized water supply point, and each centralized water supply point is set up with m One water flow channel; Step S3.2: Under the optimal simulated water replenishment duration, a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling is used to simulate the water replenishment process. Each time, only one water flow channel of a centralized water replenishment point is selected to simulate the water replenishment of the island area, determine the lake bottom elevation, and combine it with the lake water depth to obtain the head difference of the water flow channel used for water replenishment. Step S3.3, will n For each water flow channel in each centralized water replenishment point, repeat step S3.2 to calculate the root mean square error of the head difference in each water flow channel in each centralized water replenishment point, and select the centralized water replenishment point with the smallest root mean square error as the optimal centralized water replenishment point.

4. The design method for water exchange and replenishment of a multi-island annular lake according to claim 3, characterized in that, The calculation process for the root mean square error of the head difference in each water flow channel at each centralized water replenishment point in step S3.3 is as follows: in, S i Indicates the first i The mean square error of the centralized water replenishment points m Indicates the first i The number of water flow channels in each centralized water replenishment point j express m index, Indicates the first i The first of the centralized water replenishment points j The head difference in each water flow channel Indicates the first i The average head difference of all water flow channels in a centralized water replenishment point .

5. The design method for water exchange and replenishment of a multi-island annular lake according to claim 3, characterized in that, Step S4 includes the following sub-steps: Step S4.1: Set up 1~ in the weak exchange zone of the main lake area of ​​the lake. L A series of gradually increasing decentralized water replenishment points were selected as different water replenishment schemes for the weak exchange area, and the flow rate of each decentralized water replenishment point under each water replenishment scheme was determined. Step S4.2: Under the optimal simulated water replenishment duration, use a two-dimensional mathematical model of lake hydrodynamic-water exchange coupling to simulate the water replenishment process of the main lake area under different water replenishment schemes in sequence, and obtain the water exchange rate of the weak exchange zone. Step S4.3: If the increase in the water exchange rate of the weak exchange zone under two adjacent water replenishment schemes is less than 3%, the former water replenishment scheme shall be taken as the best decentralized water replenishment point in the main lake area.

6. The design method for water exchange and replenishment of a multi-island annular lake according to claim 5, characterized in that, Flow rate at each decentralized water supply point in step S4.1 Furthermore, the flow rate at each decentralized water replenishment point does not exceed the water replenishment scale of the main lake area. This indicates the total water replenishment flow in the weak exchange zone. This indicates the number of decentralized water supply points set. .

7. The design method for water exchange and replenishment of a multi-island annular lake according to claim 5, characterized in that, The increase in the water exchange rate of the weak exchange zone under two adjacent water replenishment schemes in step S4.3 The calculation process is as follows: in, express k Water exchange rate in weak exchange zones under decentralized water replenishment points.

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