Method for determining navigation level of mountainous channelized river channel

Abstract

The present application relates to mountainous river channel regulation technical field, specifically relates to a kind of mountainous canalization river channel navigation water level determination method, by collecting and analyzing power station operation and river hydrological data, form power station discharge comprehensive duration guarantee rate curve chart and reservoir water level flow relation diagram, determine minimum navigation flow and lowest submerged water level, based on the control section at the end of the regulated river section, establish two-dimensional hydrodynamics mathematical model to carry out multi-working condition test calculation;Determine the design lowest navigation water level and design highest navigation water level.The present application is aimed at the variable backwater area influenced by the regulation of cascade power station, uses water level flow combination guarantee rate to evaluate channel water depth condition, overcomes the defect that traditional method only considers single factor or selects extreme combination, improves the accuracy and economy of water level design, provides scientific and unified design standard for similar channel regulation engineering.

Description

Technical Field

[0001] This invention relates to the field of mountain river channel improvement technology, specifically to a method for determining the navigable water level of a canalized river channel in a mountainous area. Background Technology

[0002] Currently, methods for determining the minimum navigable design water level for natural rivers are relatively mature. Generally, calculations are performed using the comprehensive duration curve method and the guarantee rate frequency method based on multi-year water level data. However, there are fewer research results available on methods for determining the minimum navigable design water level in fluctuating backwater areas. The guarantee rate for the minimum navigable design water level is mainly statistically based on flow rate. However, the flow rate guarantee rate generally fails to meet the required standards. Some projects select guarantee rates based on the characteristics of the reservoirs studied, resulting in inconsistent values ​​and a lack of unified standards. This leads to a lack of comparability and standardization in the designs of different projects, posing difficulties for the overall planning of waterway improvement projects. Some projects select extreme working conditions according to the specifications. While this is safe, designing at such water levels requires large-scale excavation of the river channel, creating artificial deep channels within the existing channel. This causes a significant drop in the river level. Extending the excavation upstream to the downstream of the next-level dam will seriously affect the stability and safety of the dam, and also result in a huge waste of funds.

[0003] The current technology for determining the design navigable water level in the upstream section of a navigable river hub uses a combination of inflow rate with a guaranteed rate over many years and the corresponding drawdown level in front of the dam, as well as a combination of dead water level or minimum operating water level in front of the dam and the corresponding inflow rate at each level, to derive multiple backwater curves. The lower envelope of these curves is then taken as the minimum navigable water level at each point along the route. However, in selecting the design conditions, since the inflow rate of the cascade hydropower station and the water level in front of the dam are entirely subject to human control and have no direct relationship, it is difficult to determine the corresponding drawdown level in front of the dam in the combination of inflow rate with a guaranteed rate over many years, and the corresponding inflow rate in front of the dam in the combination of dead water level or minimum operating water level in front of the dam and the corresponding inflow rate at each level. If the inflow rate with a guaranteed rate over many years is combined with the lowest historical drawdown level in front of the dam, or the dead water level or minimum operating water level in front of the dam is combined with the lowest historical discharge, the representativeness may be insufficient. The standard does not consider the probability of the combination of the two factors. The selection of the combination of working conditions has a certain degree of randomness. This may result in the designed water level not being able to accurately reflect the lowest water level during actual navigation, thus affecting the normal navigation of the waterway.

[0004] Furthermore, for cascade hydropower stations, a low inflow rate does not necessarily indicate poor water depth conditions. During the non-flood season, the inflow rate is low, but the water level in front of the dam is high, and the water depth in the fluctuating backwater zone can meet navigation requirements. During the flood season, the water level in front of the dam is low, but the inflow rate is high, and the water depth in the fluctuating backwater zone can also meet navigation requirements. Therefore, considering only the flow rate guarantee rate cannot represent the actual design minimum navigation water level guarantee rate in the fluctuating backwater zone. In addition, in selecting the operating condition combination, when choosing the multi-year historical guarantee rate flow or the water level in front of the dam as the control factor, the determination of the other non-control factor has a certain degree of randomness, which reduces the reliability of the design results. Considering the above shortcomings, this invention proposes to use the water level and flow rate combination guarantee rate to determine the channel water depth guarantee rate.

[0005] To address the technical problems of the existing technologies, the invention team proposes a method for determining the design water level of canalized rivers in mountainous areas affected by cascade hydropower station regulation, especially for waterway improvement in variable backwater areas. This method aims to provide accurate and scientific water level parameters for waterway improvement in such special river sections. Summary of the Invention

[0006] In order to overcome the above-mentioned defects in the prior art, the purpose of this invention is to provide a method for determining the navigable water level of canalized river channels in mountainous areas.

[0007] The purpose of this invention is to provide a method for determining the navigable water level of a canalized river channel in a mountainous area. The navigable water level includes a maximum design navigable water level and a minimum design navigable water level. The determination method includes the following steps: S1. Collect data on the target sections of the waterway and the cascade hydropower stations. The data includes: statistical data on the water level and flow of the hydropower stations, measured data on the water level, gradient, and flow velocity of the engineering sections, topographic maps of the river channel, waterway grade and navigation periods; S2. Analyze the annual and daily variations of water level and flow in the reservoir area of ​​the hydropower station. S3. Based on the data collected in S1, take the end section of the regulated river section as the control section, calculate the design channel depth, and analyze the minimum navigable flow and the minimum inundation level. S4. Establish a two-dimensional hydrodynamic mathematical model to simulate the channel water depth distribution under different flow rate and water level combination conditions, and perform trial calculations for the flow rate-water level combination conditions. S5. Determine the navigable water level. S4. Calculate the flow-water level combination that meets the navigation requirements and select the lower envelope of its backwater curve as the design minimum navigable water level. Calculate the percentage of flow in the reservoir area and determine the design maximum navigable flow based on the flow statistics. Under the maximum navigable flow, obtain the design maximum navigable water level for each section through a two-dimensional hydrodynamic mathematical model.

[0008] Furthermore, the analysis of the annual and daily changes in water level and flow in the hydropower station reservoir area described in S1 specifically involves statistically analyzing the relationship between water level and flow in the reservoir area to generate a comprehensive historical guarantee rate curve of the power station's outflow and a water level-flow relationship diagram in the reservoir area. This leads to the conclusion that there is a correlation between the changes in water level in the hydropower station reservoir area and the inflow. At the same time, the flow operation range and the percentage of flows exceeding a certain threshold are statistically analyzed, i.e., the proportion of flows exceeding this threshold in all statistical data.

[0009] Furthermore, as described in S3, the control section is obtained by drawing a cross-section of the downstream section of the regulated river using the end section of the regulated river as the control section, based on the river topographic map data. If the water depth at this cross-section is not less than the design navigable depth H, then the water depth of the regulated river section is considered to meet the design navigable depth requirements. The design navigable channel depth H is the minimum water depth of the channel within the channel width range under the design minimum navigable water level, and its calculation formula is: ; In the formula: H is the design channel depth; T is the ship's draft, which is the design draft of the ship or fleet or the draft when the ship is unloaded during the dry season; To ensure sufficient water depth, including the amount of sinking during ship navigation and the safety margin for bottoming out, the allowable water depth for Class III waterways is 0.3 to 0.4 meters. In addition, the allowable water depth for pebble and rocky riverbeds should be increased by 0.1 to 0.2 meters.

[0010] Furthermore, the minimum navigable flow was analyzed. and minimum flood level Specifically, when the discharge flow from the upstream power station exceeds its minimum navigable flow... At that time, the channel depth H met the requirements; the base flow was released from the upstream power station. conditions, This data pertains to hydroelectric power stations and can be collected to determine when the water level in front of the dam is higher than the minimum water level. The minimum navigable flow rate is the water level at which the designed navigable channel depth H within the regulated river section meets the design requirements. The initial judgment can be made based on the water level-discharge relationship diagram or by referring to the design flow of previous projects in this section of the waterway.

[0011] Therefore, as Figure 1 As shown, the discharge flow of the upstream power station is greater than its minimum navigable flow. Or the water level in front of the dam is higher than the minimum inundation level It is a sufficient condition for the variable backwater zone to meet the water depth requirements.

[0012] Furthermore, after the reservoir is filled, the water level in the reservoir area rises due to the backwater effect, forming backwater. The formula for calculating the cross-sectional water level is: ; In the formula, The water levels at the upstream and downstream sections are... Let g be the flow velocity at the upstream and downstream cross sections, and g be the acceleration due to gravity. For head loss along the route, This represents a localized head loss.

[0013] Furthermore, in waterway improvement projects, the establishment of a two-dimensional hydrodynamic mathematical model needs to consider the characteristics of water flow, topographic conditions, and engineering boundaries. Water flow simulation is achieved through a combination of theoretical equations and numerical methods. Specifically, the establishment of the two-dimensional hydrodynamic mathematical model includes: A finite element implicit discretization algorithm based on unstructured meshes is used to solve the two-dimensional shallow water flow control equations.

[0014] For planar two-dimensional water flow governing equations, where the vertical scale is generally much smaller than the planar scale for large-scale free surface flow, the shallow water hydrostatic pressure assumption can be introduced to simplify the basic governing equations. The hydrostatic pressure assumption assumes that the pressure along the water depth direction follows the hydrostatic pressure distribution. Simultaneously, by integrating the basic mass and momentum conservation equations along the water depth direction to introduce averaging, the following two-dimensional shallow water flow governing equations can be derived.

[0015] Continuity equation for water flow: ; Equations of motion: ; ; In the above equations, H represents water depth, u and v represent vertical average flow velocities, x, y, and t are planar coordinates and time, and C and... Here are the Chezy coefficient and the eddy viscosity coefficient; Coriolis force coefficient, water level function From water depth and riverbed elevation Sure; Finite element discretization of the governing equations: Based on unstructured networks, the equations are discretized using the finite element method. ; ; ; in , , , , For shape functions, , They are respectively , The source term of the direction.

[0016] While high-resolution schemes based on unstructured grids, such as the central difference discretization of the convection term, offer relatively high discretization accuracy, they fail to adequately account for the upwind effect of convection. This results in ill-conditioned discrete equations with severe asymmetry and off-diagonal dominance in the coefficient matrix, often leading to oscillating numerical solutions. Simple first-order upwind schemes can effectively eliminate numerical oscillations, but they often introduce excessive artificial viscosity. Recent high-resolution schemes, such as TVD and ENO, offer effective solutions to these problems. In constructing high-resolution schemes, the introduction of a Limiter, which relates to the properties of the solution, ensures both high discretization accuracy and avoids high-frequency oscillations in the solution. This invention employs a Limiter introduced under unstructured grid conditions to guarantee the high-resolution properties of the scheme—high discretization accuracy and monotonicity of the solution.

[0017] Take the following convection-diffusion equation as an example: ; Suppose that the above equation, after being semi-discretized in space, can be written in the form of a system of ordinary differential equations: ; Where M represents the lumped mass matrix, c represents the influence coefficient, b represents the source term, and j is the number of neighboring nodes surrounding node i, such as... Figure 4 As shown.

[0018] Since the net transport in a uniform flow field is zero, it is easy to prove that the influence coefficient satisfies the following relationship. Therefore, when the influence of the source term is not considered, bi=0, and the semi-discrete transport equation can be written as: ; Assuming the influence coefficient is non-negative. Then the format is stable. Because if It is a local maximum, that is , then d Since dt ≤ 0, the local maximum value does not increase. Similarly, if It is a local minimum, that is , then d Since dt ≥ 0, the local minimum does not decrease. This exhibits the TVD property of a non-increasing maximum and a non-decreasing minimum. Alternatively, it preserves the monotonicity property, thus avoiding numerical oscillations in the solution.

[0019] For convection-dominated problems, central difference discretization or Galerkin finite element discretization typically lacks a positive influence coefficient. Artificial dissipation of the Laplace form can be added to the scheme to avoid numerical oscillations in the solution. For the discretized form, the artificial dissipation D can be written as: ; Positive definiteness requirements However, the artificial dissipation described above only has first-order accuracy. A high-resolution scheme can be understood as adding only the smallest possible artificial dissipation, so that the scheme has both high discretization accuracy and ensures that the solution does not oscillate.

[0020] First, taking the one-dimensional scalar transport equation as an example, consider its spatially semi-discrete equation: ; For convection-dominated problems, the influence coefficients of central difference or Galerkin finite element discretization are... or It might be negative; a first-order precision numerical dissipation d can be added to obtain a monotonic scheme. ; in, ; ; The superscripts + and - represent the difference, indicating the first and second differences, respectively. , ; It can be rewritten as: ; in: , , ,because , It does not oscillate.

[0021] High-precision non-oscillatory schemes can be obtained by introducing controllable anti-dissipation. ; If the anti-dissipation term is calculated from the average of the nearest differences: ; When C=1, Approximately This means the numerical dissipation has a third-order precision. Rewritten as: ; in, , .

[0022] Similarly, it can be exported The term can be used to derive the semi-discrete equation expressed by the improved influence coefficient: ; in, ; ; .

[0023] Clearly, the condition for maintaining a monotonic scheme is that the limiting factor φ(r) ≥ 0. Commonly used limiting factors include: a.Minmod: ; b.VanLeer: .

[0024] Therefore, for unstructured meshes, such as Figure 5 Higher-order dissipation is defined in the following form: ; ; in and The upstream and downstream differences representing i and j can be calculated through interpolation at nodes r, s, p, and q: , ; because , It can be done separately , and , Calculation, that is: ; ; And the coefficients can be proven. , , and It is non-negative. Therefore, the above formula can be rewritten as: ; φ(r) is the limiter, and r is the gradient ratio: ; Add higher-order dissipations to exportable components: ; Rewritten in a tighter form: .

[0025] It can be proven that when the restriction factor φ(r) ≥ 0 This ensures the high discrete accuracy of the scheme and the non-oscillatory nature of the solution.

[0026] Trial calculations were conducted, and the model considered factors such as river topography, roughness, flow continuity, and momentum conservation to simulate the channel depth under different flow rate and water level combinations. The critical inflow flow rate and upstream water level combination curve required to meet the design depth in the variable backwater zone were obtained through trial calculations.

[0027] Furthermore, based on the minimum navigable flow obtained from the analysis... and minimum flood level Establish scheduling rules for cascade hydropower stations: when the downstream discharge from the upstream hydropower station is less than... At that time, the water level in front of the dam shall not be lower than When the water level in front of the dam is lower than At that time, the downstream discharge flow of the upstream power station shall not be less than See the attached diagram for the power plant's cascade dispatch curve. Figure 2-3 The blue line represents the critical inflow rate and upstream water level combination curve required to meet the design water depth in the variable backwater zone, obtained through trial calculations. To meet the water depth requirements of the variable backwater zone, the ideal scheduling combination curve is shown as the blue line in the figure. However, scheduling based on this curve is extremely difficult in practice. Therefore, a scheduling rule for cascade power stations was developed, requiring the scheduling scheme to be set according to the red line. Although the design water depth guarantee rate is slightly reduced, the reduction is minimal, and the power station scheduling is highly operable. To further improve the power station's generating efficiency, the scheduling scheme can be further refined during actual scheduling, such as setting the scheduling curve as shown in the figure. Figure 3 The stepped curve.

[0028] Furthermore, according to the aforementioned scheduling rules, the situation where the water depth conditions of the regulated river section do not meet the requirements is when the discharge flow from the upstream power station is less than its minimum navigable flow. And the water level in front of the dam is lower than the minimum water level. The formula for calculating the navigation guarantee rate of the design channel depth requirement in the reservoir's variable backwater area is as follows: ; Where P is the navigation guarantee rate that the water depth in the reservoir area meets the requirements; P' is the rate at which the discharge flow from the upstream hydropower station is less than its minimum navigable flow. And the water level in front of the dam is lower than the minimum flood level. frequency.

[0029] Furthermore, the maximum design navigable flow is determined based on flow statistics, and the flow rate of reservoir area X is statistically analyzed. The above traffic accounts for 1%, which means X of this traffic As the highest air traffic volume.

[0030] The beneficial effects of this invention are: 1. This invention, by employing a method of guaranteeing the combined water level and flow rate, combined with the control effect of the end section of the regulated river, clarifies the design control benchmark, ensuring that the waterway can meet the navigation depth requirements under various reasonable combinations of operating conditions, thus guaranteeing navigation safety; it accurately determines the design water level of the waterway, avoiding the one-sidedness caused by determining the design water level based solely on a single factor such as flow rate or water level, and is more in line with the actual hydrological conditions of the variable backwater area, so that the design water level can truly reflect the minimum navigation requirements of the waterway, providing a unified reference basis for the design of waterway regulation in variable backwater areas of similar mountain canalized rivers.

[0031] 2. The water level and flow rate combination guarantee rate of this invention avoids large-scale river channel excavation caused by selecting extreme working conditions for design, and reduces project investment. For example, in the application of Goupitan Reservoir, it is not necessary to design according to the extreme combination of inflow and dead water level with a 98% guarantee rate, thereby avoiding the waste of funds caused by large-scale excavation and the impact on the stability of the upstream hub. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of power plant dispatching. Figure 2 This is a rectangular dispatch curve diagram for the power plant. Figure 3 This is a diagram of the power plant's ladder-shaped dispatch curve. Figure 4 A schematic diagram of the elements and nodes surrounding i; Figure 5 This is a schematic diagram of the upstream and downstream differences for nodes i and j; Figure 6 This is a graph showing the relationship between the water level and inflow rate in Pengshui Reservoir during the period from 8:00 to 22:00. Figure 7 This is a curve showing the comprehensive duration guarantee rate of the discharge flow from Shatuo. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention. Example 1

[0034] A method for determining the navigable water level of a canalized river channel in a mountainous area, wherein the navigable water level includes a maximum design navigable water level and a minimum design navigable water level, and the method includes the following steps: S1. Collect data on the target sections of the waterway and the cascade hydropower stations. The data includes: statistical data on the water level and flow of the hydropower stations, measured data on the water level, gradient, and flow velocity of the engineering sections, topographic maps of the river channel, waterway grade, and navigation periods.

[0035] S2. Analyze the annual and daily variations of water level and flow in the hydropower station reservoir area; statistically analyze the relationship between water level and flow in the power station reservoir area, and generate a comprehensive historical guarantee rate curve of the power station's outflow and a water level-flow relationship diagram in the reservoir area. Then, derive the correlation between the water level changes in the hydropower station reservoir area and the inflow. At the same time, statistically analyze the flow operation range and the proportion of flows exceeding a certain flow rate, that is, the proportion of flows exceeding this flow rate in all statistical data.

[0036] S3. Using the end section of the regulated river section as the control section, calculate the design channel depth H and analyze the minimum navigable flow. and minimum flood level ; Using the downstream section of the regulated river segment as the control section, a control section is obtained by drawing the downstreammost section of the regulated river segment based on river topographic map data. If the water depth at this section is not less than the design navigable depth H, the water depth of the regulated river segment is considered to meet the design navigable depth requirement. The design navigable depth H is the minimum water depth within the navigable channel width under the design minimum navigable water level, and its calculation formula is: ; In the formula: H is the design channel depth; T is the ship's draft, which is the design draft of the ship or fleet or the draft when the ship is unloaded during the dry season; To ensure sufficient water depth, including the amount of sinking during ship navigation and the safety margin for bottoming out, the allowable water depth for Class III waterways is 0.3 to 0.4 meters. In addition, the allowable water depth for pebble and rocky riverbeds should be increased by 0.1 to 0.2 meters.

[0037] After the reservoir is filled, the water level in the reservoir area rises due to the backwater effect, forming backwater, which is the minimum submerged water level. The calculation formula is: ; In the formula, The water levels at the upstream and downstream sections are... Let g be the flow velocity at the upstream and downstream cross sections, and g be the acceleration due to gravity. For head loss along the route, This represents a localized head loss.

[0038] Analysis of minimum air traffic flow and minimum flood level Specifically, when the discharge flow from the upstream power station exceeds its minimum navigable flow... At that time, the channel depth H met the requirements; the base flow was released from the upstream power station. conditions, This data pertains to hydroelectric power stations and can be collected to determine when the water level in front of the dam is higher than the minimum water level. The design navigation channel depth H within the regulated river section is the water level at which the design requirements are met. A sufficient condition for the variable backwater zone to meet the water depth requirements is that the discharge flow of the upstream power station exceeds its minimum navigable flow Qmin or the water level in front of the dam is higher than the minimum water level H.

[0039] S4. Based on the analysis, the minimum navigable flow rate is... and minimum flood level Calculate the navigation guarantee rate based on the combined flow rate and water level; Based on the analysis of the minimum navigable flow and minimum flood level Establish scheduling rules for cascade hydropower stations: when the downstream discharge from the upstream hydropower station is less than... At that time, the water level in front of the dam shall not be lower than When the water level in front of the dam is lower than At that time, the downstream discharge flow of the upstream power station shall not be less than See the attached diagram for the power plant's cascade dispatch curve. Figure 2-3 The blue line represents the critical inflow rate and upstream water level combination curve required to meet the design water depth in the variable backwater zone, obtained through trial calculations. To meet the water depth requirements of the variable backwater zone, the ideal scheduling combination curve is shown as the blue line in the figure. However, scheduling based on this curve is extremely difficult in practice. Therefore, a scheduling rule for cascade power stations was developed, requiring the scheduling scheme to be set according to the red line. Although the design water depth guarantee rate is slightly reduced, the reduction is minimal, and the power station scheduling is highly operable. To further improve the power station's generating efficiency, the scheduling scheme can be further refined during actual scheduling, such as setting the scheduling curve as shown in the figure. Figure 3 The stepped curve.

[0040] According to the aforementioned scheduling rules, the situation where the water depth conditions of the regulated river section do not meet the requirements is when the discharge flow from the upstream power station is less than its minimum navigable flow. And the water level in front of the dam is lower than the minimum water level. The formula for calculating the navigation guarantee rate of the design channel depth requirement in the reservoir's variable backwater area is as follows: ; Where P is the navigation guarantee rate that the water depth in the reservoir area meets the requirements; P' is the rate at which the discharge flow from the upstream hydropower station is less than its minimum navigable flow. And the water level in front of the dam is lower than the minimum flood level. frequency.

[0041] S4. Establish a two-dimensional hydrodynamic mathematical model to simulate the channel depth distribution under different flow and water level combinations. Combined with the navigation period regulations, calculate the flow-water level combination conditions and evaluate the channel depth satisfaction and corresponding improvement engineering volume. The model considers factors such as river topography, roughness, flow continuity and momentum conservation to simulate the channel depth under different flow and water level combinations.

[0042] In waterway improvement projects, the establishment of a two-dimensional hydrodynamic mathematical model requires consideration of water flow characteristics, topographic conditions, and engineering boundaries. Water flow simulation is achieved through a combination of theoretical equations and numerical methods. Specifically, the establishment of the two-dimensional hydrodynamic mathematical model includes: A finite element implicit discretization algorithm based on unstructured meshes is used to solve the two-dimensional shallow water flow control equations.

[0043] For planar two-dimensional water flow governing equations, where the vertical scale is generally much smaller than the planar scale for large-scale free surface flow, the shallow water hydrostatic pressure assumption can be introduced to simplify the basic governing equations. The hydrostatic pressure assumption assumes that the pressure along the water depth direction follows the hydrostatic pressure distribution. Simultaneously, by integrating the basic mass and momentum conservation equations along the water depth direction to introduce averaging, the following two-dimensional shallow water flow governing equations can be derived.

[0044] Continuity equation for water flow: ; Equations of motion: ; ; In the above equations, H represents water depth, u and v represent vertical average flow velocities, x, y, and t are planar coordinates and time, and C and... Here are the Chezy coefficient and the eddy viscosity coefficient; Coriolis force coefficient, water level function From water depth and riverbed elevation Sure; Finite element discretization of the governing equations: Based on unstructured networks, the equations are discretized using the finite element method. ; ; ; in , , , , For shape functions, , They are respectively , The source term of the direction.

[0045] While high-resolution schemes based on unstructured grids, such as the central difference discretization of the convection term, offer relatively high discretization accuracy, they fail to adequately account for the upwind effect of convection. This results in ill-conditioned discrete equations with severe asymmetry and off-diagonal dominance in the coefficient matrix, often leading to oscillating numerical solutions. Simple first-order upwind schemes can effectively eliminate numerical oscillations, but they often introduce excessive artificial viscosity. Recent high-resolution schemes, such as TVD and ENO, offer effective solutions to these problems. In constructing high-resolution schemes, the introduction of a Limiter, which relates to the properties of the solution, ensures both high discretization accuracy and avoids high-frequency oscillations in the solution. This invention employs a Limiter introduced under unstructured grid conditions to guarantee the high-resolution properties of the scheme—high discretization accuracy and monotonicity of the solution.

[0046] Trial calculations were conducted, and the model, taking into account factors such as river topography, roughness, flow continuity, and momentum conservation, simulated the channel depth under different flow rate and water level combinations. The critical inflow rate versus dam-front water level combination curve required to achieve the design depth in the variable backwater area was obtained through these calculations.

[0047] S5. Determine the navigable water level. S4. Calculate the flow-water level combination that meets navigation requirements, and select the lower envelope of its backwater curve as the design minimum navigable water level; calculate the percentage of flow in the reservoir area, and calculate the X-value of the reservoir area. The above traffic accounts for approximately 1%, which is equivalent to X% of the traffic. The design maximum navigable flow rate is determined based on flow statistics. Under the maximum navigable flow rate, the design maximum navigable water level for each cross section is obtained through a two-dimensional hydrodynamic mathematical model. Example 2

[0048] This embodiment was implemented in the Wujiangdu section of the river. The section from Wujiangdu to Gongtan is divided into four segments by the Wujiangdu, Goupitan, Silin, Shatuo, and Peng hydropower stations. Due to the daily regulation of the power stations and the fluctuation of the water level upstream of the dams, the hydrological conditions are complex. The backwater areas of each reservoir are affected by both the discharge from the upstream power stations and the water level in front of the downstream power station dams. Determining the minimum design navigable water level in these backwater areas is crucial to the design of the waterway improvement project, directly affecting the cost of waterway improvement, the safety of navigation, and the stability of surrounding water conservancy facilities.

[0049] The planned navigation channel in the Goupitan Reservoir area of ​​the Wujiang River is classified as Class III. According to regulations, the minimum navigable water level in the Goupitan Reservoir area should be the inflow rate with a 98% guarantee rate (112...). The combination of the dam's upstream drawdown level and the minimum operating water level (590m) with the corresponding inflow rates at each level is used, and their envelope is taken as the design minimum navigable water level. Since 10 years of actual operation, the inflow rate has maintained a 98% guarantee rate ( The extreme combination of 590m and dead water level did not occur. If extreme conditions are selected, the inflow rate with a 98% guarantee rate (112) is taken. Combining the water level with the dead water level (590m) is a safe approach, but designing based on this water level would require extensive excavation of the river channel, creating an artificial deep channel within the existing channel. This would lead to a significant drop in the river level, and extending the river channel excavation upstream to the dam of the next higher-level hub would seriously affect the stability and safety of the next higher-level hub, while also resulting in a huge waste of funds.

[0050] S1. Collect data on the target sections of the waterway and the cascade hydropower stations. The data includes: statistical data on the water level and flow of the hydropower stations, measured data on the water level, gradient, and flow velocity of the engineering sections, topographic maps of the river channel, waterway grade and navigation periods; S2. Analyze the annual and daily changes in water level and flow in the hydropower station reservoir area; statistically analyze the relationship between water level and flow in the power station reservoir area, and form a comprehensive historical guarantee rate curve of the power station's outflow and a water level and flow relationship diagram in the reservoir area. Then, derive the correlation between the changes in water level in the hydropower station reservoir area and the inflow. At the same time, statistically analyze the flow operation range and the proportion of flows exceeding a certain flow, that is, the proportion of flows exceeding this flow in all statistical data.

[0051] Navigation is prohibited at night during the flood season in the backwater fluctuation sections of each reservoir area. Navigation is permitted from 8:00 AM to 10:00 PM. For an example, please refer to the diagram showing the relationship between water level and inflow in Pengshui Reservoir from 8:00 AM to 10:00 PM. Figure 6 Please refer to the comprehensive duration guarantee rate curve of the Shatuo River discharge flow. Figure 7 .

[0052] Currently, all cascade hydropower stations along the river section of the project have been completed and are operating under joint scheduling. Analysis of data collected from each reservoir area shows that the discharge flow from each station generally follows a regular pattern. During the main flood season, the characteristics of rapid rises and falls typical of mountain rivers remain. Due to the impounding effect of the hydropower stations, the flood discharge duration is generally short, ranging from several hours to twenty-four hours, except in special years, and rarely exceeding two days. According to the analysis, the Goupitan Reservoir area has a discharge capacity of 1200 cubic meters per second. The above flow rate accounts for only 0.2%, with the Shatuo Reservoir area at 1800. The above flow rate accounts for only 1%, Pengshui Reservoir area 1950 The above traffic accounts for only 1%.

[0053] S3. Using the end section of the regulated river section as the control section, calculate the design channel depth H and analyze the minimum navigable flow. and minimum flood level ; Using the downstream section of the regulated river segment as the control section, a control section is obtained by drawing the downstreammost section of the regulated river segment based on river topographic map data. If the water depth at this section is not less than the design navigable depth H, the water depth of the regulated river segment is considered to meet the design navigable depth requirement. The design navigable depth H is the minimum water depth within the navigable channel width under the design minimum navigable water level, and its calculation formula is: ; In the formula: H is the design channel depth; T is the ship's draft, which is the design draft of the ship or fleet or the draft when the ship is unloaded during the dry season; To ensure sufficient water depth, including the amount of sinking during ship navigation and the safety margin for bottoming out, the allowable water depth for Class III waterways is 0.3 to 0.4 meters. In addition, the allowable water depth for pebble and rocky riverbeds should be increased by 0.1 to 0.2 meters.

[0054] After the reservoir is filled, the water level in the reservoir area rises due to the backwater effect, forming backwater, which is the minimum submerged water level. The calculation formula is: ; In the formula, The water levels at the upstream and downstream sections are... Let g be the flow velocity at the upstream and downstream cross sections, and g be the acceleration due to gravity. For head loss along the route, This represents a localized head loss.

[0055] Analysis of minimum air traffic flow and minimum flood level Specifically, when the discharge flow from the upstream power station exceeds its minimum navigable flow... At that time, the channel depth H met the requirements; the base flow was released from the upstream power station. conditions, This data pertains to hydroelectric power stations and can be collected to determine when the water level in front of the dam is higher than the minimum water level. The water level at which the designed navigation depth H in the regulated river section meets the design requirements is determined. Based on this, the critical inflow rate and upstream water level combination curve required for the variable backwater zone to meet the design depth are obtained through trial calculations. Therefore, a discharge rate greater than the minimum navigable flow rate Qmin from the upstream power station or an upstream water level higher than the minimum water level H submerging the area are sufficient conditions for the variable backwater zone to meet the water depth requirements.

[0056] S4. Establish a two-dimensional hydrodynamic mathematical model to simulate the channel depth distribution under different flow and water level combinations. Combined with the navigation period regulations, calculate the flow-water level combination conditions and evaluate the channel depth satisfaction and corresponding improvement engineering volume. The model considers factors such as river topography, roughness, flow continuity and momentum conservation to simulate the channel depth under different flow and water level combinations.

[0057] In waterway improvement projects, the establishment of a two-dimensional hydrodynamic mathematical model requires consideration of water flow characteristics, topographic conditions, and engineering boundaries. Water flow simulation is achieved through a combination of theoretical equations and numerical methods. Specifically, the establishment of the two-dimensional hydrodynamic mathematical model includes: A finite element implicit discretization algorithm based on unstructured meshes is used to solve the two-dimensional shallow water flow control equations.

[0058] For planar two-dimensional water flow governing equations, where the vertical scale is generally much smaller than the planar scale for large-scale free surface flow, the shallow water hydrostatic pressure assumption can be introduced to simplify the basic governing equations. The hydrostatic pressure assumption assumes that the pressure along the water depth direction follows the hydrostatic pressure distribution. Simultaneously, by integrating the basic mass and momentum conservation equations along the water depth direction to introduce averaging, the following two-dimensional shallow water flow governing equations can be derived.

[0059] Continuity equation for water flow: ; Equations of motion: ; ; In the above equations, H represents water depth, u and v represent vertical average flow velocities, x, y, and t are planar coordinates and time, and C and... Here are the Chezy coefficient and the eddy viscosity coefficient; Coriolis force coefficient, water level function It is determined by the water depth H(x, y, t) and the riverbed elevation h(x, y); Finite element discretization of the governing equations: Based on unstructured networks, the equations are discretized using the finite element method. ; ; ; in , , , , For shape functions, , They are respectively , The source term of the direction.

[0060] While high-resolution schemes based on unstructured grids, such as the central difference discretization of the convection term, offer relatively high discretization accuracy, they fail to adequately account for the upwind effect of convection. This results in ill-conditioned discrete equations with severe asymmetry and off-diagonal dominance in the coefficient matrix, often leading to oscillating numerical solutions. Simple first-order upwind schemes can effectively eliminate numerical oscillations, but they often introduce excessive artificial viscosity. Recent high-resolution schemes, such as TVD and ENO, offer effective solutions to these problems. In constructing high-resolution schemes, the introduction of a Limiter, which relates to the properties of the solution, ensures both high discretization accuracy and avoids high-frequency oscillations in the solution. This invention employs a Limiter introduced under unstructured grid conditions to guarantee the high-resolution properties of the scheme—high discretization accuracy and monotonicity of the solution.

[0061] Based on the analysis of the minimum navigable flow and minimum flood level Establish scheduling rules for cascade hydropower stations: when the downstream discharge from the upstream hydropower station is less than... At that time, the water level in front of the dam shall not be lower than When the water level in front of the dam is lower than At that time, the downstream discharge flow of the upstream power station shall not be less than See the attached diagram for the power plant's cascade dispatch curve. Figure 2-3 The blue line represents the critical inflow rate and upstream water level combination curve required to meet the design water depth in the variable backwater zone, obtained through trial calculations. To meet the water depth requirements of the variable backwater zone, the ideal scheduling combination curve is shown as the blue line in the figure. However, scheduling based on this curve is extremely difficult in practice. Therefore, a scheduling rule for cascade power stations was developed, requiring the scheduling scheme to be set according to the red line. Although the design water depth guarantee rate is slightly reduced, the reduction is minimal, and the power station scheduling is highly operable. To further improve the power station's generating efficiency, the scheduling scheme can be further refined during actual scheduling, such as setting the scheduling curve as shown in the figure. Figure 3 The stepped curve.

[0062] According to the aforementioned scheduling rules, the situation where the water depth conditions of the regulated river section do not meet the requirements is when the discharge flow from the upstream power station is less than its minimum navigable flow. And the water level in front of the dam is lower than the minimum water level. The formula for calculating the navigation guarantee rate of the design channel depth requirement in the reservoir's variable backwater area is as follows: ; Where P is the navigation guarantee rate that the water depth in the reservoir area meets the requirements; P' is the rate at which the discharge flow from the upstream hydropower station is less than its minimum navigable flow. And the water level in front of the dam is lower than the minimum flood level. frequency.

[0063] S5. Determine the navigable water level. Based on S4, calculate the flow-water level combination that meets navigation requirements. Select the lower envelope of its backwater curve as the minimum design navigable water level. Calculate the percentage of flow in the reservoir area. Based on the flow statistics, determine the maximum design navigable flow. Calculate the X flow rate in the reservoir area. The above traffic accounts for approximately 1%, which is equivalent to X% of the traffic. As the maximum navigable flow rate, the design maximum navigable water level for each cross section is obtained through a two-dimensional hydrodynamic mathematical model at the maximum navigable flow rate.

[0064] For the Goupitan Reservoir area, the water level in front of the dam ranges from 592 to 630 meters. When the water level in front of the dam rises to 621 meters, the backwater flows to the Wujiangdu Wharf. Considering the fluctuating water depth in the Goupitan backwater area, when the inflow is less than 400 cubic meters per second... At that time, the navigation channel required extensive excavation, resulting in a significant drop in water level. A two-dimensional hydrodynamic mathematical model was established, selecting an upstream flow rate of 0... This corresponds to a downstream water level of 621m and an upstream flow rate of 402m. The two working conditions correspond to a downstream water level of 595m. Statistical analysis shows that under these two working conditions, the percentage of time that the channel depth meets the design navigation depth requirement, i.e., the navigation guarantee rate, is 60%. This guarantee rate can meet the navigation needs while avoiding the increased costs and safety hazards caused by excessive dredging. Therefore, the lower envelope of these two working conditions is determined as the design minimum navigation water level for the Goupitan Reservoir area.

[0065] In the Shatuo Reservoir area, when the water level in front of the dam is 362m, no downstream discharge is required. When the upstream inflow is 270... At that time, trial calculations were conducted when the water level in front of the Shatuo Dam was between 356.7 and 362 meters; when the upstream flow rate was 570... At that time, the corresponding water level in front of the Shatuo Dam was 353.5m. Using the same mathematical model, the water depth under different combinations was simulated. Combined with the calculation of the improvement project volume (including excavation volume, engineering material usage, etc.), and considering both economic rationality and navigation safety, a discharge flow of 270 was adopted. Corresponding to the water level 360m upstream of the dam and 570m The flow rate corresponds to two working conditions at 353.5m upstream of the dam, and the lower envelope of the flow rate is taken as the minimum navigable water level designed for the Shatuo Reservoir area. For the Pengshui Reservoir area, when the water level in front of the dam is 289m, no downstream discharge is required; the upstream inflow is 270m. Calculations were conducted with the water level in front of the Pengshui Dam between 283.9 and 289 m. When the upstream inflow was 600 m³ / s, the corresponding water level in front of the Pengshui Dam was 279.5 m. Through mathematical modeling, the water depth and engineering volume under different working conditions were analyzed, and a discharge flow of 270 m³ / s was adopted. Corresponding to a water level of 287m upstream of the dam and 600m The flow rate corresponds to two working conditions at 279.5m upstream of the dam, and the lower envelope of the flow rate is taken as the minimum design navigable water level for the Pengshui Reservoir area.

[0066] Using the methods described above, the Wujiang River waterway exhibits typical characteristics of a mountainous river, with large fluctuations between dry and flood seasons, short flood durations, and a sharp increase in flow velocity within the channel during floods, resulting in poor navigation conditions. Based on the aforementioned analysis, the Goupitan Reservoir area (1200 km) The above flow rate accounts for only 0.2%, with the Shatuo Reservoir area at 1800. The above flow rate accounts for only 1%, Pengshui Reservoir area 1950 The above flow rate accounts for only 1%, therefore, a flow rate of 1200m is recommended for the Goupitan Reservoir area. As the maximum navigable flow rate, the Shatuo Reservoir area adopts a 1800m... As the maximum navigable flow rate, the Pengshui Reservoir area adopts a flow rate of 1950m. As the highest air traffic volume.

[0067] Although the present invention has been described in detail above with general descriptions, specific embodiments, and accompanying drawings, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for determining the navigable water level of a canalized river channel in a mountainous area, characterized in that, The navigation water level includes the maximum design navigation water level and the minimum design navigation water level, and the determination method includes the following steps: S1. Collect data on the target sections of the waterway and the cascade hydropower stations. The data includes: statistical data on the water level and flow of the hydropower stations, measured data on the water level, gradient, and flow velocity of the engineering sections, topographic maps of the river channel, waterway grade and navigation periods; S2. Analyze the annual and daily variations of water level and flow in the reservoir area of ​​the hydropower station. S3. Based on the data collected in S1, take the end section of the regulated river section as the control section, calculate the design channel depth, and analyze the minimum navigable flow and the minimum inundation level. S4. Establish a two-dimensional hydrodynamic mathematical model to simulate the channel water depth distribution under different flow rate and water level combination conditions, and perform trial calculations for the flow rate-water level combination conditions. S5. Determine the navigable water level. S4. Calculate the flow-water level combination that meets the navigation requirements and select the lower envelope of its backwater curve as the design minimum navigable water level. Calculate the percentage of flow in the reservoir area and determine the design maximum navigable flow based on the flow statistics. Under the maximum navigable flow, obtain the design maximum navigable water level for each section through a two-dimensional hydrodynamic mathematical model.

2. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 1, characterized in that, The analysis of the annual and daily changes in water level and flow in the reservoir area of ​​the hydropower station described in S2 involves statistically analyzing the relationship between water level and flow in the reservoir area, generating a comprehensive historical guarantee rate curve of the outflow from the power station and a water level-flow relationship diagram in the reservoir area, thereby deriving the correlation between water level changes in the reservoir area and inflow, and simultaneously calculating the flow operation range and the percentage of times the flow exceeds a certain level.

3. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 1, characterized in that, As described in S3, the control section is the downstream section of the regulated river segment. Based on river topographic data, a cross-section of the downstreammost part of the regulated river segment is drawn to obtain the control section. If the water depth at this section is not less than the design navigable depth H, then the water depth of the regulated river segment is considered to meet the design navigable depth requirements. The design navigable depth H is the minimum water depth within the navigable channel width under the design minimum navigable water level, and its calculation formula is: ； In the formula: H is the design channel depth; T is the ship's draft, which is the design draft of the ship or fleet or the draft when the ship is unloaded during the dry season; The water depth is considered to be sufficient, including the amount of water sinking during navigation and the safety margin for bottoming.

4. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 1, characterized in that, Analysis of minimum air traffic flow and minimum flood level Specifically, the minimum navigable flow rate is obtained based on the water level-discharge relationship diagram. When the discharge flow of the upstream power station exceeds its minimum navigable flow... At that time, the channel depth H met the requirements; the base flow was released from the upstream power station. Under these conditions, when the water level in front of the power station dam is higher than the minimum inundation level At that time, the water level at which the designed navigation channel depth H in the regulated river section meets the design requirements.

5. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 4, characterized in that, Based on the analysis of the minimum navigable flow and minimum flood level Establish scheduling rules for cascade hydropower stations: when the downstream discharge from the upstream hydropower station is less than... At that time, the water level in front of the dam shall not be lower than When the water level in front of the dam is lower than At that time, the downstream discharge flow of the upstream power station shall not be less than .

6. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 1, characterized in that, The formula for calculating the navigation guarantee rate of the design channel depth requirement in the reservoir's variable backwater area is as follows: ； Where P is the navigation guarantee rate that the water depth in the reservoir area meets the requirements; P' is the rate at which the discharge flow from the upstream hydropower station is less than its minimum navigable flow. And the water level in front of the dam is lower than the minimum flood level. frequency.

7. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 1, characterized in that, The establishment of the two-dimensional hydrodynamic mathematical model is specifically as follows: Continuity equation for water flow: ； Equations of motion: ； ； In the above equations, H represents water depth, u and v represent vertical average flow velocities, x, y, and t are planar coordinates and time, and C and... Here are the Chezy coefficient and the eddy viscosity coefficient; Coriolis force coefficient, water level function From water depth and riverbed elevation Sure; Based on unstructured networks, the equations are discretized using the finite element method: ； ； ； in , , , , For shape functions, , They are respectively , The source term of the direction, where j is the number of neighboring nodes surrounding node i.

8. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 7, characterized in that, The critical inflow rate and upstream water level combination curve required to meet the design water depth in the variable backwater zone were obtained through trial calculations.

9. The method for determining the navigable water level of a canalized river channel in a mountainous area according to claim 1, characterized in that, The maximum design navigable flow is determined based on flow statistics, and the flow rate of reservoir area X is statistically analyzed. The above traffic accounts for 1%, which means X of this traffic As the highest air traffic volume.

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