Universe water exchange water replenishing design method for multi-island annular lake

Abstract

The invention discloses a multi-island annular lake global water exchange water replenishing design method, which comprises the following steps of: according to a planned water replenishing scale and a water replenishing path, simulating a water replenishing process by using a lake region hydrodynamic force-water exchange coupled two-dimensional mathematical model, determining a change relation of a lake region average water body exchange rate along with time, and obtaining an optimal simulated water replenishing duration; setting a series of concentrated water replenishing points in the island area of the lake, simulating the water replenishing process of the island area under the optimal simulated water replenishing duration, determining the water head difference of each water flow channel in each concentrated water replenishing point of the island area, and determining the optimal concentrated water replenishing point of the island area according to the water head difference of each water flow channel; a series of dispersed water replenishing points are arranged in a weak exchange area of a main lake area of a lake, the water replenishing process of the main lake area is simulated under the optimal simulated water replenishing duration, the water body exchange rate of the weak exchange area is determined, the optimal dispersed water replenishing points of the main lake area are determined according to the water body exchange rate of the weak exchange area, and therefore the lake global water exchange water replenishing effect is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of lake hydrodynamic numerical simulation, and specifically relates to a design method for global water exchange and replenishment in a multi-island annular lake. Background Art

[0002] Water replenishment projects are currently the main engineering means to solve lake water quality problems and have been widely used in various lakes around the world. However, for multi-island circular lakes, due to their complex water and land patterns, variable hydrodynamic characteristics and water flow paths, it is difficult to determine the layout of water replenishment points when implementing water replenishment projects, and it is difficult to accurately predict the water exchange effect after the implementation of water replenishment projects. Therefore, how to scientifically arrange water replenishment points to effectively improve the water exchange capacity of multi-island circular lakes has become a technical problem that needs to be solved urgently in the field of lake water environment hydrodynamics. Summary of the invention

[0003] In response to the problems existing in the prior art, the present invention provides a design method for water exchange and replenishment in the entire area of ​​a multi-island circular lake, providing a scientific and effective method for the layout of water replenishment projects in multi-island circular 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 the entire area of ​​a multi-island circular lake, specifically comprising the following steps:

[0005] Step S1, establishing a two-dimensional mathematical model of lake hydrodynamics-water exchange coupling;

[0006] Step S2: according to the planned water replenishment scale and water replenishment path, a two-dimensional mathematical model of lake area 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 time;

[0007] Step S3, setting a series of centralized water replenishment points in the island area of ​​the lake, using a two-dimensional mathematical model of lake area hydrodynamics-water exchange coupling to simulate the water replenishment process of the island area under the optimal simulated water replenishment time, determining the head difference of each water flow channel in each centralized water replenishment point in the island area, and determining the optimal centralized water replenishment point in the island area according to the head difference of each water flow channel;

[0008] Step S4, setting a series of dispersed water replenishment points in the weak exchange area of ​​the main lake area of ​​the lake, using a two-dimensional mathematical model of lake area hydrodynamics-water exchange coupling to simulate the water replenishment process of the main lake area under the optimal simulated water replenishment duration, determining the water exchange rate of the weak exchange area, and determining the optimal dispersed water replenishment point of the main lake area according to the water exchange rate of the weak exchange area;

[0009] Step S5: Use the design plan of the best centralized water replenishment point in the island area and the best decentralized water replenishment point in the main lake area as the water exchange and replenishment plan for the entire lake area.

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

[0011]

[0012] where h is the water depth of the lake, u is the flow velocity in the x-direction of the lake, v is the flow velocity in the y-direction of the lake, q is a constant, g is the acceleration due to gravity, f is the Coriolis force coefficient, p a is the atmospheric pressure of the area where the lake is located; ρ is the density of the lake water, η is the lake bottom elevation, τ ax and τ ay are the wind stress tensors in the x-direction and y-direction of the water surface respectively, τ bx and τ by are the stress tensors in the x-direction and y-direction of the river bed bottom respectively, τ sx and τ sy are the radiation stress components in the x-direction and y-direction respectively, T xx and T xy and T yy are the horizontal viscous stresses in the xx plane, xy plane, and yy plane respectively, s is the flow rate of the water replenishment point, u x and u y are the water flow velocities of the water replenishment point in the x and y directions respectively, C is the water body exchange rate, K x and K y are the diffusion coefficients in the x and y directions respectively.

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

[0014] Step S2.1: Divide the grid according to the basic pattern and topographic boundary conditions of the lake, and determine the boundary conditions of the grid according to the planned water replenishment scale and water replenishment path, including: the position of the water replenishment point and the flow rate of the water replenishment point;

[0015] Step S2.2: Run the two-dimensional mathematical model of hydrodynamic-water exchange coupling in the lake water area according to the determined position of the water replenishment point and the flow rate of the water replenishment point, and obtain the water body exchange rate of each grid corresponding to the lake area at any time;

[0016] Step S2.3: Average the water body exchange rates of all grids corresponding to the lake area to obtain the average water body 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 body exchange rate of the lake area as the dependent variable to determine the change relationship of the average water body exchange rate of the lake area with time, and take the time corresponding to the maximum instantaneous average water body 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 m water flow channels at each centralized water replenishment point;

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

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

[0022] Furthermore, the calculation process of the mean square deviation of the head differences of each water flow channel in each centralized water replenishment point in Step S3.3 is as follows:

[0023]

[0024] where S i represents the mean square deviation of the i-th centralized water replenishment point, m represents the number of water flow channels in the i-th centralized water replenishment point, j represents the index of m, and ΔH ij represents the head difference of the j-th water flow channel in the i-th centralized water replenishment point, represents the average value of the head differences of all water flow channels in the i-th centralized water replenishment point,

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

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

[0027] Step S4.2: Use the 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 turn at the optimal simulated water replenishment duration to obtain the water body exchange rate in the weak exchange area;

[0028] Step S4.3: If the increase rate of the water body exchange rate in the weak exchange area between two adjacent water replenishment schemes is less than 3%, take the previous water replenishment scheme as the optimal decentralized water replenishment point in the main lake area.

[0029] Furthermore, the flow rate Q of 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 of the lake, where Q represents the total water replenishment flow rate of the weak exchange area, k represents the set number of decentralized water replenishment points, and k ∈ {1, 2,..., L}.

[0030] Furthermore, the increase ΔC in the water body exchange rate of the weak exchange area under two adjacent water replenishment schemes in step S4.3 k is calculated as follows:

[0031]

[0032] where C k represents the water body exchange rate of the weak exchange area under k decentralized water replenishment points.

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

[0034] (1) In the multi-island annular lake whole-region water exchange water replenishment design method of the present invention, on the basis of the traditional hydrodynamic mathematical model, a water body exchange part for describing the change of substance concentration is added, thereby establishing a two-dimensional mathematical model coupling hydrodynamic-water exchange in the lake area, which can simulate the evolution process of water body exchange in lake research and can directly display the distribution of the water body exchange rate in the lake area;

[0035] (2) In the present invention, the water body exchange characteristics are mainly affected by the frictional resistance along the way, and the effect of the frictional resistance along the way is more significant in the island area of the lake; since there are many factors affecting the frictional resistance in the island area of the lake, it is difficult to compare the water flow resistance between each island channel by theoretical calculation methods. And the head difference along the way, as the concrete manifestation of the water flow resistance, can be used as an indicative factor for judging the magnitude of the water flow resistance along the way. Therefore, for the island area of the lake, by setting a series of centralized water replenishment points, simulating and comparing the head differences of each water flow channel, and analyzing the uniformity of water flow diffusion, the optimal water replenishment points in the island area are determined, so as to improve the water body exchange ability of the island area of the lake;

[0036] (3) For the main lake area, the water area is wide, and it is difficult to completely exchange the entire area under the condition of limited water replenishment flow rate. Therefore, when designing the decentralized water replenishment points in the main lake area, the water replenishment effect of the weak exchange area needs to be considered first. Therefore, for the main lake area of the lake, by analyzing the water body exchange rate under different decentralized water replenishment point water replenishment schemes, evaluating the improvement degree of the water body exchange effect in the key area, and determining the optimal water replenishment scheme for the main lake area;

[0037] By taking 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 water replenishment scheme for the overall water exchange of the lake, the water replenishment capacity for the overall water exchange of the lake can be improved. Moreover, the lake water replenishment design scheme of the present invention can be widely applied to the water replenishment engineering design of multi-island annular lakes, effectively solving the technical problems of difficult selection of water replenishment layout and inability to guarantee water replenishment effect, and meanwhile enriching and developing the simulation methods of lake hydrodynamics and water body exchange. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the topographic map of the current situation of Xinglin Bay;

[0039] Figure 2 is the schematic diagram of dividing Xinglin Bay into grids;

[0040] Figure 3 is the schematic diagram of the water replenishment scheme using the overall water exchange water replenishment design method for multi-island annular lakes of the present invention;

[0041] Figure 4 is the curve graph of the change in the average water exchange rate of the lake area;

[0042] Figure 5 is the layout diagram of the centralized water replenishment points in the island area;

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

[0044] Figure 7 is the water exchange effect diagram in the island area;

[0045] Figure 8 is the layout scheme diagram of the decentralized water replenishment in the main lake area;

[0046] Figure 9 is the statistical area division diagram of the main lake area;

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

[0048] Figure 11 is the water replenishment effect diagram of the whole lake area. DETAILED DESCRIPTION OF THE EMBODIMENTS

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

[0050] The present invention discloses an overall water exchange water replenishment design method for multi-island annular lakes, which specifically includes the following steps:

[0051] Step S1. Traditional hydrodynamic models are mainly used for research related to the flow velocity distribution and sediment erosion and deposition in estuary and coastal areas. Based on the traditional hydrodynamic model, the present invention adds water body exchange based on substance concentration to establish a two-dimensional mathematical model coupling lake hydrodynamic and water exchange, which is used to simulate the evolution process of water body exchange in the lake and can directly display the distribution of the water body exchange rate in the lake area. The two-dimensional mathematical model coupling lake hydrodynamic and water exchange established in the present invention is as follows:

[0052]

[0053] where h is the water depth of the lake, u is the flow velocity of the lake in the x direction, v is the flow velocity of the lake in the y direction, q is a constant, g is the acceleration due to gravity, f is the Coriolis force coefficient, p a is the atmospheric pressure of the area where the lake is located; ρ is the density of lake water, η is the lake bottom elevation, τ ax 、τ ay are the wind stress tensors in the x direction and y direction on the water surface respectively, τ bx 、τ by are the stress tensors in the x direction and y direction at the bottom of the riverbed respectively, τ sx 、τ sy are the radiation stress components in the x direction and y direction respectively, T xx 、T xy 、T yy are the horizontal viscous stresses in the xx plane, xy plane, and yy plane respectively, s is the flow rate of the water supply point, u x 、u y are the water flow velocities of the water supply point in the x and y directions respectively, C is the water body exchange rate, K x 、K y are the diffusion coefficients in the x and y directions respectively.

[0054] Step S2. When using the two-dimensional mathematical model coupling lake hydrodynamic and water exchange to simulate the water supply process, if the designed simulation water supply duration is too short, the water body exchange effect is not significant; if the designed simulation water supply duration is too long, the economic cost is high and the calculation amount is large. Therefore, it is necessary to select an appropriate simulation water supply duration to provide a scientific basis for the operation time of the water supply project. According to the planned water supply scale and water supply path, the present invention uses the two-dimensional mathematical model coupling lake hydrodynamic and water exchange to simulate the water supply process, determines the variation relationship of the average water body exchange rate in the lake area with time, and obtains the optimal simulation water supply duration that can balance economic benefits and water supply effect; it includes the following sub-steps:

[0055] Step S2.1. Divide the grid according to the basic pattern and topographic boundary conditions of the lake, and determine the boundary conditions of the grid according to the planned water supply scale and water supply path, including: the position of the water supply point and the flow rate of the water supply point;

[0056] Step S2.2: Run the two-dimensional mathematical model of hydrodynamic-water exchange coupling in the lake area according to the determined position and flow rate of the water replenishment points, and obtain the water body exchange rate of each grid corresponding to the lake area at any time;

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

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

[0059] The water body exchange characteristics are mainly affected by the frictional resistance along the way, and the effect of the frictional resistance along the way is more significant in the island area of the lake. For example, the channel width and shape between the island branches are closely related to the magnitude of the frictional resistance along the way. Narrow channels will increase the water flow velocity and also generate a large local resistance, thus affecting the overall water body exchange process. Since there are many factors affecting the frictional resistance along the way in the lake island area, it is difficult to compare the water flow resistance between each island channel by theoretical calculation methods. And the head difference along the way, as the concrete manifestation of the water flow resistance, can be used as an indicative factor for judging the magnitude of the water flow resistance along the way, greatly reducing the complexity of the calculation. At the same time, the water area of the lake island area is small and there is no need for decentralized water replenishment. Therefore, a series of centralized water replenishment points are set in the island area of the lake. Under the optimal simulated water replenishment duration, use the two-dimensional mathematical model of hydrodynamic-water exchange coupling in the lake area 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 according to the head difference of each water flow channel, so as to improve the water body exchange ability of the lake island area. It includes the following sub-steps:

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

[0061] Step S3.2: When using the two-dimensional mathematical model of hydrodynamic-water exchange coupling in the lake area to simulate the water replenishment process under the optimal simulated water replenishment duration, each time only select one water flow channel of one centralized water replenishment point for water replenishment simulation in the island area, determine the lake bottom elevation, and combine the water depth of the lake to obtain the head difference of the water flow channel for water replenishment;

[0062] Step S3.3: Repeat Step S3.2 for each water flow channel in the n centralized water replenishment points, calculate the mean square deviation of the head differences of each water flow channel in each centralized water replenishment point. The smaller the mean square deviation of a centralized water replenishment point, the closer the total resistance of each water flow channel in the centralized water replenishment point is. When water is flowing, it tends to flow evenly into each water flow channel. Therefore, to ensure uniform water replacement in each water flow channel, select the centralized water replenishment point with the smallest mean square deviation as the optimal centralized water replenishment point.

[0063] The calculation process of the mean square deviation of the head differences of each water flow channel in each centralized water replenishment point is as follows:

[0064]

[0065] where S i represents the mean square deviation of the i-th centralized water replenishment point, m represents the number of water flow channels in the i-th centralized water replenishment point, j represents the index of m, and ΔH ij represents the head difference of the j-th water flow channel in the i-th centralized water replenishment point, represents the average value of the head differences of all water flow channels in the i-th centralized water replenishment point,

[0066] Step S4: For the main lake area, with a vast water area, it is difficult to completely exchange 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. For the main lake area, human activities are frequent in the weak exchange area, and the water quality is worse than that in the center of the lake. Therefore, set a series of decentralized water replenishment points in the weak exchange area of the main lake area. Use the two-dimensional mathematical model of lake hydrodynamic-water exchange coupling to simulate the water replenishment process of the main lake area under the optimal simulated water replenishment duration, determine the water body exchange rate in the weak exchange area, and determine the optimal decentralized water replenishment points in the main lake area according to the water body exchange rate in the weak exchange area, so as to improve the water body exchange effect in the main lake area; it includes the following sub-steps:

[0067] Step S4.1: Set 1 to L gradually increasing decentralized water replenishment points in the weak exchange area of the main lake area as different water replenishment schemes in the weak exchange area, and determine the flow rate Q k =Q / k for each decentralized water replenishment point under each water replenishment scheme, 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 in the weak exchange area, k represents the number of decentralized water replenishment points set, and k ∈ {1, 2,..., L}.

[0068] Step S4.2: Use the 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 turn under the optimal simulated water replenishment duration to obtain the water body exchange rate in the weak exchange area;

[0069] Step S4.3: If the increase rate of the water body exchange rate in the weak exchange area under two adjacent water replenishment schemes is less than 3%, use the previous water replenishment scheme as the optimal decentralized water replenishment point in the main lake area.

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

[0071]

[0072] where C k represents the water body exchange rate in the weak exchange area under k decentralized water replenishment points.

[0073] Step S5: Use 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 water replenishment scheme for the overall lake area water exchange, which can improve the water replenishment capacity of the overall lake area water exchange. And the lake water replenishment design scheme of the present invention can be widely applied to the water replenishment project design of multi-island annular lakes, effectively solving the technical problems of difficult selection of water replenishment layout and inability to guarantee water replenishment effect, and at the same time enriching and developing the simulation methods of lake hydrodynamics and water body exchange.

[0074] Embodiment

[0075] Xinglin Bay is located in the central area of Jimei District, Xiamen City, on the northwest side of Xiamen Island. Due to serious sediment deposition and poor water quality environment at the mouth of Xinglin Bay, the hydrodynamic water environment in the bay cannot be improved by tidal intake and drainage means, so a water replenishment project is adopted to promote water body exchange in the bay and improve the water quality. As Figure 1 , Xinglin Bay is a typical multi-island annular lake. The left half of the bay is the island area, and six main islands stand in a plum blossom shape; the right side of the bay is the main lake area with a wide water area. Using the method of the present invention to optimize the water replenishment project layout of the whole lake area can not only make the water replenishment of each water flow channel of the centralized water replenishment point in the island area uniform, but also improve the water replacement effect of the weak exchange area in the main lake area. The specific steps are as follows:

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

[0077]

[0078] where h is the water depth of the lake, u is the flow velocity of the lake in the x direction, v is the flow velocity of the lake in the y direction, q is a constant, g is the acceleration of gravity, f is the Coriolis force coefficient, p a is the atmospheric pressure of the area where the lake is located; ρ is the density of lake water, η is the lake bottom elevation, τ ax , τ ay are the wind stress tensors in the x direction and y direction of the water surface respectively, τ bx , τ by are the stress tensors in the x direction and y direction of the river bed bottom respectively, τsx and τ sy are the radiation stress components in the x - direction and y - direction respectively, and T xx , T xy , T yy are the horizontal viscous stresses in the xx - plane, xy - plane and yy - plane respectively, s is the flow rate of the water replenishment point, and u x , u y are the water flow velocities of the water replenishment point in the x - and y - directions respectively, C is the water body exchange rate, and K x , K y are the diffusion coefficients in the x - and y - directions respectively.

[0079] In this embodiment, due to the complexity of the internal islands and the water system in Xinglin Bay, unstructured grids are used for the discretization of the calculation area, which can more accurately reflect the shoreline and the contour of local projects; the basic pattern of the lake includes the Xinglin Bay Lake area and its internal islands, and the grid scale is divided into 6m - 8m to ensure the calculation accuracy. The total number of calculation units is about 200,000, as Figure 2 shown.

[0080] Step S2: According to the planned water replenishment scale and water replenishment path, that is, replenishing from the terminal ends of Jiutian Lake and Houxi, with 80,000 cubic meters of water replenished to Jiutian Lake per day and 1,000,000 cubic meters of water replenished to Houxi per day, use the two - dimensional mathematical model of lake hydrodynamic - water exchange coupling to simulate the water replenishment process, determine the variation relationship of the average water body exchange rate of the lake area with time, and obtain the optimal simulated water replenishment duration.

[0081] As Figure 3 , combined with the location of the surrounding sewage treatment plants and their current water purification capabilities, assuming no loss of water during the transportation process, 180,000 cubic meters of purified water is used for the Xinglin Bay water replenishment project every day, including 80,000 cubic meters of water in the Jiutian Lake area and 1,000,000 cubic meters of water in the Houxi area. To determine the subsequent test simulation duration, first conduct a set of simulation calculations with a water replenishment duration of 180 days for the design scheme, and calculate the variation of the average water exchange rate of the lake area with time, as shown in Table 1: At the beginning of water replenishment, the average water exchange rate of the lake area increases rapidly. When the water replenishment duration reaches 60 days, the average water exchange rate of the entire lake area reaches more than 50%, and then the growth of the average water exchange rate of the lake area slows down. When the water replenishment duration reaches 180 days, the water exchange rate reaches about 80%.

[0082] Table 1 Variation table of the average water exchange rate under the design scheme of the lake area

[0083]

[0084]

[0085] Fit the relationship curve between the average water exchange rate of the lake area and the water replenishment time, as Figure 4 , and obtain its expression as P=-0.00003t 2+0.01t + 0.0093, where P is the average water replacement rate of the lake area, t is the water replenishment duration, ΔP = P’ = -0.00006t + 0.01. Let ΔP > 0.6%, then 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 lake hydrodynamic-water exchange coupling, it is considered that the optimal water replenishment duration for Xinglin Bay is 60 days, and the water replenishment simulation of each subsequent plan is set to a duration of 60 days.

[0086] Step S3: Set a series of centralized water replenishment points in the island area of the lake. Use the two-dimensional mathematical model of lake hydrodynamic-water exchange coupling to simulate the water replenishment process in the island area under the optimal simulated water replenishment duration, determine the head differences 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 according to the head differences of each water flow channel. As Figure 5 shown, 3 centralized water replenishment points are selected in the island area, and one of the water replenishment points is selected in turn for water replenishment simulation. To make the test 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 per day.

[0087] In each group of simulation tests, only one outflow channel is retained, and the remaining inter-island channels are set as non-water-passing boundaries. There are five outflow channels in the island area of Xinglin Bay. Therefore, there are a total of five groups of tests under one water replenishment point. The five test paths of the 1# water replenishment point are as Figure 6 shown. After a steady flow field is formed in the island area, measure the water levels along the way of each outflow channel. The head loss along the way represents the magnitude of the resistance along the way. Through the above method, the head differences of different channels are obtained. Subsequently, change the water replenishment point and conduct the simulation again, and the head differences of each channel under the 2# and 3# water replenishment points can be obtained. After 6 hours of simulated water replenishment, the water levels along the way under each plan are basically constant. Under the plans with 1#, 2#, and 3# as the water replenishment points in the island area of Xinglin Bay, the head differences of each water flow channel are shown in Table 2 below.

[0088] Table 2 Head differences of each channel under different water replenishment points

[0089]

[0090]

[0091] Calculate the mean square deviation of the resistance along the way of different water flow channels under each centralized water replenishment point. The calculation formula is: where S i represents the mean square deviation of the i-th centralized water replenishment point, m represents the number of water flow channels in the i-th centralized water replenishment point, j represents the index of m, ΔH ij represents the head difference of the j-th water flow channel in the i-th centralized water replenishment point, represents the average value of the head differences of all water flow channels in the i-th centralized water replenishment point, The calculation results are shown in Table 3 below. The mean square deviation of the frictional resistance at the 1# water replenishment point is the smallest, indicating that the water exchange in each channel of the lower island area through this point is more uniform. Its water replenishment effect is as Figure 7 shown. Therefore, the 1# water replenishment point is selected as the optimal water replenishment point in the Xinglin Bay island area.

[0092] Table 3 Calculation Table of Mean Square Deviation of Frictional Resistance along the Route

[0093]

[0094] Step S4: Set a series of decentralized water replenishment points in the weak exchange area of the main lake area of the lake. Use the two-dimensional mathematical model coupling lake hydrodynamics and water exchange to simulate the water replenishment process in the main lake area under the optimal simulated water replenishment duration, determine the water exchange rate in the weak exchange area, and determine the optimal decentralized water replenishment points in the main lake area according to the water exchange rate in the weak exchange area.

[0095] To explore the layout of the optimal decentralized water replenishment points in the main lake area, a decentralized water replenishment test was carried out in the main lake area to observe the distribution of the water replenishment rate at each flow rate. Since the maximum water replenishment volume of Houxi is 100,000 cubic meters per day, the total water replenishment flow rate used in the main lake area in the test is 100,000 cubic meters per day.

[0096] Due to the shielding effect of the three island chains on the northeast side, the water body in the right coastal area of Xinglin Bay fails to be effectively exchanged. At the same time, to ensure the water exchange effect in the Houxi direction water area, the water replenishment flow rate in the Houxi water area is not less than 40,000 cubic meters per day. Therefore, 60,000 cubic meters per day of the water replenishment volume is transferred to the right coastal area of Xinglin Bay.

[0097] Set k new decentralized water replenishment points respectively in the right coastal area of the main lake area, where k = 1, 2, 3, 4, 5. The flow rates of each water replenishment point are 60,000 cubic meters per day, 30,000 cubic meters per day, 20,000 cubic meters per day, 15,000 cubic meters per day, and 12,000 cubic meters per day respectively. The layout of the decentralized water replenishment points is as Figure 8 shown.

[0098] The water area of the main lake area of Xinglin Bay is wide. Affected by human activities, the water quality in the right coastal area is poor and it is a weak exchange area. Focus on the water exchange efficiency in the right coastal area. To compare the optimal decentralized water replenishment schemes in the main lake area, delimit the statistical area as Figure 9 shown. The average water exchange rate and the increase rate of the water exchange rate in the statistical area are shown in Table 4 below: When the number of decentralized water replenishment points on the right side of Xinglin Bay increases to 5, the increase in its water exchange effect is not very significant. Considering economic benefits and construction feasibility, taking 4 decentralized water replenishment points on the right coastal area of Xinglin Bay is the optimal scheme. Therefore, the final water replenishment layout scheme for the main lake area of Xinglin Bay is: 40,000 cubic meters per day of water replenishment from Houxi, and 4 decentralized water replenishment points are taken on the right coastal area, each with a water replenishment of 15,000 cubic meters per day. The water replenishment effect of the main lake area of Xinglin Bay is as Figure 10 shown.

[0099] Table 4 Calculation Table of Water Exchange Rates for Each Decentralized Water Supply Scheme in the Main Lake Area

[0100] Number of decentralized water replenishment points 1 2 3 4 5 <![CDATA[Average water change rate C k > 82.16％ 85.24％ 88.03％ 91.37％ 93.25％ <![CDATA[Program Amplification ΔC k > 3.75％ 3.27％ 3.79％ 2.06％

[0101] Step S5: Take the design schemes of the optimal centralized water supply point in the island area and the optimal decentralized water supply point in the main lake area as the water exchange and supply scheme for the entire lake area, and obtain the water body exchange effect after the water supply project in the entire lake area. For example Figure 11 , the test results show that after combining the optimal schemes in the island area and the main lake area, the water bodies in the entire Xinglin Bay lake area are basically effectively exchanged, and the water exchange rate of more than 70% of the water areas reaches 30%. Its overall water exchange effect is equivalent to the superposition of the effects of the two schemes, which illustrates the independence of the responses of the island area and the main lake area to the water supply project, and also confirms the scientific nature of selecting water supply points through sub-region research in the present invention.

[0102] In summary, under the existing water supply scale of Xinglin Bay, the optimal layout scheme is to conduct centralized water supply in the island area, supply 80,000 cubic meters of water per day in the Jiutian Lake water area, conduct decentralized water supply in the main lake area, supply 40,000 cubic meters of water per day in the Houxi water area, and add 4 new water supply points with 15,000 cubic meters of water per day each along the right bank of the lake area. After 60 days of water supply with this scheme, the water area with a water exchange rate exceeding 30% accounts for 75% of the total water area of the entire lake area, and the water body exchange effect is good. Through the method of the present invention, the water body exchange capacity of Xinglin Bay is effectively improved, solving the problems that it is difficult to select water supply points and it is impossible to grasp the water supply effect when using water supply projects for such multi-island ring-shaped lakes.

[0103] The above is only the preferred implementation mode of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake, characterized in that: The specific steps include: Step S1, establishing a two-dimensional mathematical model of lake hydrodynamics-water exchange coupling; Step S2: according to the planned water replenishment scale and water replenishment path, a two-dimensional mathematical model of lake area 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 time; Step S3, setting a series of centralized water replenishment points in the island area of ​​the lake, using a two-dimensional mathematical model of lake area hydrodynamics-water exchange coupling to simulate the water replenishment process of the island area under the optimal simulated water replenishment time, determining the head difference of each water flow channel in each centralized water replenishment point in the island area, and determining the optimal centralized water replenishment point in the island area according to the head difference of each water flow channel; Step S4, setting a series of dispersed water replenishment points in the weak exchange area of ​​the main lake area of ​​the lake, using a two-dimensional mathematical model of lake area hydrodynamics-water exchange coupling to simulate the water replenishment process of the main lake area under the optimal simulated water replenishment duration, determining the water exchange rate of the weak exchange area, and determining the optimal dispersed water replenishment point of the main lake area according to the water exchange rate of the weak exchange area; Step S5: Use the design plan of the best centralized water replenishment point in the island area and the best decentralized water replenishment point in the main lake area as the water exchange and replenishment plan for the entire lake area.

2. A method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake according to claim 1, characterized in that: The two-dimensional mathematical model of the lake area hydrodynamic-water exchange coupling is specifically: Where h is the depth of the lake, u is the velocity of the lake in the x direction, v is the velocity of the lake in the y direction, q is a constant, g is the acceleration of gravity, f is the Coriolis force coefficient, and p is the velocity of the lake in the y direction. a is the atmospheric pressure in the area where the lake is located; ρ is the density of the lake water, η is the elevation of the lake bottom, τ ax , τ ay are the wind stress tensors in the x and y directions of the water surface, τ bx , τ by are the stress tensors in the x and y directions of the riverbed bottom, τ sx , τ sy are the radiation stress components in the x-direction and y-direction, T xx , T xy , T yy are the horizontal viscous stresses in the xx plane, xy plane, and yy plane, s is the flow rate at the water replenishment point, u x 、u y are the water flow velocities at the water replenishment point in the x and y directions, C is the water exchange rate, K x , K y are the diffusion coefficients in the x and y directions, respectively.

3. A method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake according to claim 2, characterized in that: Step S2 includes the following sub-steps: Step S2.1, dividing the grid according to the basic pattern and terrain boundary conditions of the lake, and determining the boundary conditions of the grid according to 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, running the two-dimensional mathematical model of lake area hydrodynamics-water exchange coupling according to the determined location of the water replenishment point and the flow rate of the water replenishment point, and obtaining the water exchange rate of each grid corresponding to the lake area at any time; Step S2.3, averaging the water exchange rates of the lake areas corresponding to all grids 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 changing 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.

4. A method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake according to claim 3, characterized in that: Step S3 includes the following sub-steps: Step S3.1, select n centralized water replenishment points in the island area of ​​the lake, and set m water flow channels at each centralized water replenishment point; Step S3.2, using the two-dimensional mathematical model of lake area hydrodynamics-water exchange coupling to simulate the water replenishment process under the optimal simulated water replenishment duration, each time only one water flow channel of a centralized water replenishment point is selected to simulate the water replenishment of the island area, the elevation of the lake bottom is determined, and the head difference of the water flow channel used for water replenishment is obtained in combination with the water depth of the lake; Step S3.3, repeat step S3.2 for each water flow channel in the n centralized water replenishment points, calculate the mean square deviation 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 mean square deviation as the optimal centralized water replenishment point.

5. A method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake according to claim 4, characterized in that: The calculation process of the mean square error of the head difference of each water flow channel in each centralized water replenishment point in step S3.3 is: Among them, S i represents the mean square error of the ith concentrated water replenishment point, m represents the number of water flow channels in the ith concentrated water replenishment point, j represents the index of m, ΔH ij represents the head difference of the j-th water flow channel in the i-th concentrated water replenishment point, represents the average water head difference of all water flow channels in the i-th concentrated water replenishment point, 6. A method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake according to claim 4, characterized in that: Step S4 includes the following sub-steps: Step S4.1, setting 1 to L gradually increasing dispersed water replenishment points in the weak exchange area of ​​the main lake area as different water replenishment schemes for the weak exchange area, and determining the flow rate of each dispersed water replenishment point under each water replenishment scheme; Step S4.2, using the two-dimensional mathematical model of lake area hydrodynamics-water exchange coupling to simulate the water replenishment process of the main lake area under different water replenishment schemes under the optimal simulated water replenishment time, and obtaining the water exchange rate of the weak exchange area; Step S4.3: If the increase in the water exchange rate in the weak exchange zone under two adjacent water replenishment schemes is less than 3%, the previous water replenishment scheme is used as the optimal dispersed water replenishment point in the main lake area.

7. A method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake according to claim 6, characterized in that: The flow rate Q of each dispersed 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 in the weak exchange area, k represents the number of decentralized water replenishment points set, k∈{1,2,...,L].

8. The method for designing water exchange and replenishment for the entire area of ​​a multi-island circular lake according to claim 6 is characterized in that: The increase ΔC of the water exchange rate in the weak exchange zone under two adjacent water replenishment schemes in step S4.3 k The calculation process is: Among them, C k It represents the water exchange rate in the weak exchange zone under k dispersed water replenishment points.

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