Method for determining influence length of tailwater and height of side wall of fishway with equivalent open channel and vertical slot

Abstract

The application relates to the technical field of hydraulic engineering, and discloses a method for determining the tail water influence length and the side wall elevation of a vertical slit type fishway under an equivalent open channel, which comprises the following steps: extracting basic parameters and working condition parameters to establish an equivalent rectangular open channel; under the constraint of slow flow conditions, a spatial average resistance model is constructed by using a kinetic energy correction coefficient; an interval comprehensive correction coefficient is introduced to absorb structure conversion differences, and the interval comprehensive correction coefficient meeting the acceptance criterion is locked by combining the spatial average resistance model; an overall energy equation is constructed, and the output tail water influence length is calculated; the construction subinterval is divided according to the tail water influence length, the side wall top control elevation is calculated, the multi-working condition elevation envelope is extracted, and the boundary size data table is derived and generated. The application converts the periodic energy dissipation structure into a comprehensive resistance system, eliminates the multi-step recursive operation of each pool, realizes direct algebraic solution of the overall energy equation, and directly converts the theoretical hydraulic calculation result into the three-dimensional boundary size of the engineering anti-overflow envelope surface.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering technology, specifically to a method for determining the tailwater influence length and sidewall elevation of a vertically slotted fishway under an equivalent open channel. Background Technology

[0002] A conventional slotted fishway consists of a rectangular channel, transverse baffles along the flow path, continuous chambers, and vertical slots. Water flows through the slots, contracts, and forms a jet. This jet diffuses within the continuous chambers, creating backflow zones on both sides, while simultaneously generating turbulent energy loss. The energy loss along the flow path of a slotted fishway is composed of the slot contraction, jet diffusion, flow around the baffles, backflow within the chambers, turbulent energy loss, and wall friction.

[0003] When the outlet of a vertical slotted fishway connects to a downstream area of ​​fluctuating water levels, a rise in the downstream water level will cause tailwater backflow and backwater in the downstream section of the fishway. If the sidewall elevation is uniformly determined based on the baseline operating water depth unaffected by tailwater backflow, local safety freeboard issues will arise; if the sidewalls are uniformly raised according to the highest tailwater elevation along the entire line, the construction workload in areas unaffected by tailwater backflow will increase. During the engineering design phase, it is necessary to clearly define the length affected by tailwater backflow and the control elevation of the sidewall tops at each cross-section.

[0004] Conventional hydraulic calculation methods have limitations in handling tailrace backwater problems. Directly applying the roughness coefficient of conventional concrete materials for one-dimensional water surface line calculations ignores the comprehensive energy loss characteristics of periodic energy dissipation units, resulting in the calculation and analysis process failing to reflect the actual energy consumption level along the vertical slotted fishway. If iterative calculations are used for each chamber, the backwater curve in the gradually varied flow theory exhibits an asymptotic recovery state upstream, making it impossible to directly output the finite engineering impact endpoint and convert theoretical water depth data into an accurate range for sidewall heightening. Reconstructing complex flow patterns using three-dimensional numerical simulations and physical model experiments is time-consuming and increases computational costs. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for determining the tailwater impact length and sidewall elevation of an equivalent open channel vertical slotted fishway, solving the problems that the pool-by-pool recursive method cannot output the endpoint of finite engineering impact and that ordinary open channel systems cannot reflect the comprehensive energy consumption of periodic energy dissipation units.

[0006] To achieve the above objectives, this invention provides a method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway, comprising the following steps:

[0007] Extract basic design parameters and tailrace operating parameters to establish an equivalent rectangular open channel with equivalent comprehensive roughness;

[0008] Under the constraint of satisfying the steady and slow flow condition in the equivalent rectangular open channel, a spatial average resistance model is constructed using the kinetic energy correction coefficient;

[0009] An interval comprehensive correction coefficient is introduced to absorb the conversion difference between the equivalent rectangular open channel and the actual vertical slotted fishway structure. The interval comprehensive correction coefficient that satisfies the parameter acceptance criterion is locked by combining the spatial average resistance model.

[0010] The overall energy equation is constructed based on the interval comprehensive correction coefficient, and the tailwater influence length is calculated and output through the one-step estimation formula of the tailwater influence length.

[0011] The construction is divided into sections based on the length of the tailwater impact. The control elevation of the top of the sidewall corresponding to the construction section is calculated, and the design elevation envelope of the sidewall under multiple working conditions is extracted. A data table of three-dimensional boundary dimensions of the overflow envelope surface of the solidification project is then exported.

[0012] This invention maps the periodic energy dissipation structure of the vertically slotted fishway, with its repeating vertically slotted baffle chambers, into an equivalent rectangular open channel with comprehensive resistance. Based on the specific energy difference and the average friction gradient within the interval, the length of the tailrace influence is determined under stable, slow-flow conditions. By constructing a spatial average resistance model of the equivalent rectangular open channel, an interval comprehensive correction coefficient is introduced to integrate the conversion differences in spatial geometric dimensions and the conversion deviations in flow characteristics, thus maintaining a balance between the energy consumption level of the theoretically derived one-dimensional gradually varying flow and the energy consumption level of the actual three-dimensional flow. The overall energy equation independently extracts the tailrace influence length as a first-order algebraic term, eliminating the need for differential and integral operations on small water surface slices. This allows for direct algebraic calculations to solve independent tailrace operation conditions under multiple boundary conditions, establishing correlated data for the three-dimensional boundary dimensions of the engineering overflow envelope.

[0013] Preferably, the extraction of basic design parameters and tailrace operating parameters to establish an equivalent rectangular open channel with equivalent comprehensive roughness includes:

[0014] The static geometric boundary conditions of the equivalent rectangular open channel are defined by extracting the equivalent effective width, bottom slope, pool length, vertical joint width, diaphragm thickness, and downstream bottom plate elevation from the basic design parameters.

[0015] The equivalent energy slope of the multi-cycle measurement segment is generated by utilizing the total energy loss of the multi-cycle measurement segment, or the equivalent energy slope of the single-cycle measurement segment is obtained by calculating the energy loss of the single-cycle measurement segment. The reference water depth and the equivalent energy slope are determined based on the reference flow rate and the equivalent resistance rate, or the equivalent comprehensive roughness is obtained by back-calculating the equivalent comprehensive roughness through the equivalent comprehensive roughness calibration formula of the single-cycle equivalent energy slope.

[0016] Preferably, under the constraint that the equivalent rectangular open channel satisfies the steady and slow-flow condition, the spatial average resistance model constructed using the kinetic energy correction coefficient includes:

[0017] Based on the first set of pre-condition hydraulic conditions, which limit the reference operating water depth to be greater than the critical water depth, the second set of pre-condition hydraulic conditions, which limit the downstream control water depth to be greater than the critical water depth, and the third set of pre-condition hydraulic conditions, which limit the downstream control water depth to be greater than the reference operating water depth, the stable slow flow condition is determined to be met when all three pre-condition hydraulic conditions are met simultaneously.

[0018] By combining the kinetic energy correction coefficient to obtain the friction gradient ratio corresponding to the endpoint water depth of the engineering impact and the friction gradient ratio corresponding to the downstream control water depth, the spatial average resistance model is constructed.

[0019] Preferably, the calculation of the endpoint water depth affected by the project includes the relative proportion method and the absolute water depth method;

[0020] When using the relative proportion method, the endpoint water depth of the project impact is calculated based on the benchmark operating water depth, the downstream control water depth, and the relative control proportion constant, and the value range of the relative control proportion constant is defined between 0.025 and 0.10. When using the absolute water depth method, the endpoint water depth of the project impact is calculated based on the benchmark operating water depth and the absolute water depth threshold, and the absolute water depth threshold corresponds to the specified small water depth increment value.

[0021] Preferably, the introduction of an interval comprehensive correction coefficient to absorb the conversion difference between the equivalent rectangular open channel and the actual vertical slotted fishway structure includes:

[0022] Import the reference tailwater condition with the measured cross-sectional position and corresponding measured water depth. Extract the reference benchmark position of the water depth mapping of the engineering impact endpoint from the reference tailwater condition. Combine the back calculation formula to calculate the actual average friction gradient ratio of the reference condition.

[0023] Based on the actual average friction gradient ratio under reference working conditions, the friction gradient ratio corresponding to the water depth at the endpoint of the engineering influence, and the friction gradient ratio corresponding to the water depth at the downstream control depth, the interval comprehensive correction coefficient is derived by back calculation. The interval comprehensive correction coefficient is then applied to the overall deviation absorption link between the one-dimensional equivalent analysis system and the three-dimensional real flow characteristics.

[0024] Preferably, locking the interval comprehensive correction coefficients that satisfy the parameter acceptance criteria includes:

[0025] The independent inspection working condition outputs the independent inspection predicted tailwater impact length. The independent inspection predicted tailwater impact length is compared with the independent inspection actual tailwater impact length, and the relative error of the impact length is calculated by combining the evaluation formula.

[0026] When the relative error of the affected length does not exceed the tolerance threshold, the interval comprehensive correction coefficient is determined to meet the parameter acceptance criterion and a locking operation is performed. The tolerance threshold is a preset value for numerical comparison.

[0027] Preferably, the overall energy equation is constructed based on the interval comprehensive correction coefficient, and the tailwater influence length is calculated and output using the one-step estimation formula, including:

[0028] Under the condition that the water flows from the endpoint of the engineering influence to the downstream control section, the overall energy equation is generated based on the balance condition of energy state and energy consumption along the path.

[0029] The tailwater influence length is separated as a linear algebraic term to be solved in the equality constraints. The analytical value is calculated by combining the one-step estimation formula of the tailwater influence length and the tailwater influence length is output within the range that meets the numerical fault tolerance criterion.

[0030] Preferably, the numerical fault tolerance criterion is jointly established by the denominator term anti-collapse condition and the flow continuity condition;

[0031] The anti-collapse condition for the denominator term requires that the value of the denominator judgment value be strictly greater than the minimum tolerance value. The flow continuity condition requires that the water depth between the downstream control section and the end point of the engineering influence maintain a monotonically decreasing characteristic along the counter-current direction and that there be no sudden jump or drop in the water surface elevation value.

[0032] Preferably, calculating the control elevation of the top of the sidewall corresponding to the construction segment interval includes:

[0033] Discretization is performed between the downstream control water depth and the water depth at the end point of engineering influence according to a fixed water depth increment to generate the control section water depth. The cumulative one-step spatial distance of the discrete control points is calculated using the control section water depth and the calculation formula is used to establish the spatial distribution grid of the discrete control points inside the equivalent rectangular open channel using the segmented standard step length calculation formula.

[0034] The design water surface elevation is calculated and output using the design water surface elevation generation formula for each control section. The safety superelevation parameter is superimposed on the associated design water surface elevation to calculate and output the control elevation of the top of the sidewall. The control elevation of the top of the sidewall corresponding to all discrete control points is traversed and compared within a single construction segment interval to extract the maximum value, and the maximum value is set as the unified control elevation.

[0035] Preferably, the extraction of the multi-condition sidewall design elevation envelope and the export of the data table for generating the three-dimensional boundary dimensions of the anti-overflow envelope surface of the curing project include:

[0036] Within the same construction segment, extract all unified control elevations and perform maximum value filtering. Combine the extraction formula to calculate and obtain the multi-condition sidewall design elevation envelope value to guide the construction of the project.

[0037] All construction sections are spliced ​​together based on their respective multi-condition sidewall design elevation envelope values ​​to form an engineering overflow prevention envelope. The horizontal starting point coordinates, horizontal ending point coordinates, and multi-condition sidewall design elevation envelope values ​​of all construction sections are spatially correlated to generate a data table.

[0038] This invention provides a method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway. It has the following beneficial effects:

[0039] 1. This invention extracts basic design parameters and tailrace operating parameters to establish an equivalent rectangular open channel with an equivalent comprehensive roughness. The equivalent comprehensive roughness is obtained by back-calculating the total energy loss of multi-period measurement sections. The local energy consumption characteristics of the repeated arrangement of pools, baffles and vertically slit periodic energy dissipation structures along the vertically slit fishway are calculated as a whole, avoiding the calculation deviation caused by applying the roughness of ordinary concrete materials. This provides input parameters that meet the boundary conditions for one-dimensional hydraulic calculations.

[0040] 2. This invention constructs a spatial average resistance model under the constraint of satisfying stable slow flow conditions, introduces an interval comprehensive correction coefficient to absorb the conversion deviation between the one-dimensional theoretical calculation system and the three-dimensional real flow characteristics, and combines the overall energy equation to independently separate the tailwater influence length as a first-order algebraic term to be solved. It directly calculates the analytical value using a one-step estimation formula, eliminating the need for the pool-by-pool recursive process and the integration calculation of small water surface slices, and realizes the algebraic solution of independent tailwater operation conditions under multiple boundary conditions.

[0041] 3. This invention divides the construction into sections based on the length of the tailrace influence. It generates the control section water depth by performing discretization processing with a fixed water depth increment between the downstream control water depth and the water depth at the end of the project influence. The safety freeboard parameter is superimposed on the associated design water surface elevation to calculate the control elevation of the top of the sidewall. The unified control elevation is extracted by comparison within a single construction section. A multi-condition sidewall design elevation envelope data table is exported. The hydraulic calculation results are transformed into the three-dimensional boundary dimensions of the engineering overflow envelope surface. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method of the present invention;

[0043] Figure 2 This is the equivalent dimension reduction mapping and integrated drag ratio determination logic block diagram of the present invention;

[0044] Figure 3 This is a determination diagram for the stable flow verification and backwater cutoff boundary establishment of the present invention;

[0045] Figure 4 This is a diagram showing the self-calibration and fault-tolerant closed-loop flow of the interval comprehensive correction coefficient in this invention.

[0046] Figure 5 This is a flowchart of the one-step influence length calculation and error prevention control algorithm of the present invention;

[0047] Figure 6 This is a nested loop diagram for multi-condition elevation envelope extraction and spatial discretization processing in this invention. Detailed Implementation

[0048] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] This invention provides a method for determining the tailwater influence length and sidewall elevation of a vertically slotted fishway under an equivalent open channel. This invention equates the periodic energy dissipation structure of the vertically slotted baffle chambers repeatedly arranged along the fishway to an equivalent rectangular open channel with comprehensive resistance. Based on the specific energy difference and the average friction gradient of the interval, the tailwater influence length, the design control water surface line, and the control elevation of the top of the sidewall of the downstream section of the fishway are determined under the condition of stable and slow flow.

[0050] A conventional vertical slotted fishway consists of an inlet section, a rectangular fishway body, and an outlet section. The rectangular fishway body connects the inlet and outlet sections and contains transverse baffles along the flow path. These baffles divide the rectangular fishway body into continuous chambers along the water flow direction, with the bottom of each continuous chamber forming the fishway floor. The fishway floor slopes continuously downstream, unlike the stepped floor primarily used for weir overflow. Each level of transverse baffles includes long and short baffles. The short baffles are connected to the sidewalls via short piers, while the long baffles connect to one sidewall and the short baffles connect to the opposite sidewall. A gap is left between the long and short baffles to form a vertical slot, which extends vertically from near the bottom of the chamber to above the design water level. The long baffles act as flow guides. The vertical slotted fishway relies on the continuous chambers and vertical slots to progressively distribute the upstream and downstream water level difference.

[0051] As water flows from the previous continuous chamber through the vertical slit into the next continuous chamber, it contracts and forms the main jet. The main jet diffuses within the continuous chamber, creating backflow and low-velocity zones on both sides of the long and short baffles. Simultaneously, turbulent energy loss occurs within the continuous chamber. The energy loss along the vertical slit fishway involves the combined effects of vertical slit contraction, jet diffusion, flow around the baffles, backflow within the chamber, turbulent energy loss, and wall friction, unlike ordinary open channels where energy loss is characterized solely by the surface roughness of the materials.

[0052] The inlet section of a vertical slotted fishway connects to the downstream river channel, reservoir, or sluice gate area. When the water level rises, causing backwater to form in the downstream section of the vertical slotted fishway, it creates a tailrace backwater effect, causing the backwater curve to gradually recover upstream of the fishway. Without the tailrace backwater effect, the vertical slotted fishway corresponds to a reference operating depth. Since uniformly raising the sidewalls according to the highest tailrace depth would increase the engineering workload, and uniformly determining the sidewall top control elevation according to the reference operating depth would lead to insufficient freeboard in some areas, an equivalent rectangular open channel is used to clarify the upstream location where the tailrace backwater effect reaches, the cross-section of the downstream section of the vertical slotted fishway where the sidewalls need to be raised, and the corresponding sidewall top control elevation.

[0053] After obtaining the equivalent comprehensive roughness and related structural data, the flow state within the equivalent rectangular open channel is determined to meet the steady-flow condition. Under the constraint of the steady-flow condition, a one-dimensional energy equation is established within the equivalent rectangular open channel. The one-dimensional energy equation relates the downstream control section to the upstream engineering influence endpoint. The downstream control section corresponds to the starting position of the tailrace backwater, and the engineering influence endpoint corresponds to the cutoff position of the backwater curve in the upstream asymptotic recovery extension direction. At this point, the remaining backwater depth at the engineering influence endpoint is less than the engineering control threshold, thus transforming the theoretically infinitely asymptotically recoverable backwater curve into a finite length.

[0054] By combining the specific energy of the cross-section and the average friction gradient of the interval, the specific energy difference between the downstream control section and the endpoint of the engineering influence is calculated using a one-dimensional energy equation. The tailwater influence length, representing the horizontal distance along the route between the downstream control section and the endpoint of the engineering influence, is then calculated using the specific energy difference and the average friction gradient of the interval. After determining the tailwater influence length, a corresponding control water surface line is generated between the downstream control section and the endpoint of the engineering influence. The design water surface elevation of each section is combined with the safety freeboard to generate the control elevation of the sidewall top of each section. For different downstream tailwater conditions, multiple control elevations of the sidewall top corresponding to different flow rates and downstream water depths are used to generate a multi-condition sidewall elevation envelope, which serves as the design benchmark for the heightening of the sidewall of the downstream section of the vertical slotted fishway.

[0055] See attached document Figure 1 The method for determining the tailrace length and sidewall elevation of an equivalent open channel vertical slotted fishway provided by this invention specifically includes the following steps:

[0056] S1. Before establishing the equivalent rectangular open channel, extract the basic design parameters and tailrace condition parameters of the vertical slot fishway. Establish the longitudinal coordinates along the vertical slot fishway with the downstream end as the origin and extending upstream as the positive direction. The bottom slope is taken as positive value in the upstream direction. The water flow direction in the vertical slot fishway is from upstream to downstream and is opposite to the positive direction of the longitudinal coordinates.

[0057] The basic design parameters include the net width of the pool chamber, the equivalent calculated effective width, the pool chamber length, the vertical joint width, the baffle thickness, the bottom slope, the downstream bottom elevation, and the safety freeboard. The equivalent calculated effective width is the net width of the pool chamber corresponding to the representative cross-section in the middle of the pool chamber. When the mainstream effective width is less than the net width of the pool chamber, the net width of the pool chamber is multiplied by the effective width coefficient to obtain the equivalent calculated effective width. The effective width coefficient is greater than 0 and less than or equal to 1, and is determined based on the three-dimensional velocity field measurement data of the vertical joint fishway, measured data from physical model tests, numerical simulation results, or historical data from similar projects. The equivalent calculated effective width, bottom slope, pool chamber length, vertical joint width, baffle thickness, and downstream bottom elevation together define the static geometric boundary conditions of the equivalent rectangular open channel.

[0058] The downstream control depth and actual flow rate are obtained for multiple design tailrace conditions. For conditions where the flow rate changes due to downstream water level, the actual flow rate data after the tailrace condition is modified is used. The actual flow rate, together with the downstream control depth, constitutes the downstream dynamic boundary input of the one-dimensional energy equation. At the same time, the reference operating depth unaffected by tailrace backwater is obtained to provide a backwater-free reference for asymptotic calculations.

[0059] See attached document Figure 2 After obtaining the design tailrace conditions and baseline operating depth, representative cross-sections of the same origin are established in the periodic energy dissipation structure, defined as the cross-sections at the middle of each continuous chamber. These representative cross-sections are defined as water-passing sections with identical relative positions to the baffles and vertical joints in adjacent periodic units. Upstream and downstream representative cross-sections of the same origin are extracted from the continuously distributed representative cross-sections to define multi-cycle measurement sections with sufficient length. Within each multi-cycle measurement section, the total energy loss is calculated using the difference between the specific energy of the upstream and downstream representative cross-sections. The formula for calculating the total energy loss of the multi-cycle measurement section is as follows:

[0060] ;

[0061] In the formula, Total energy loss over multiple measurement cycles; This represents the water surface elevation of the upstream representative section; This is the kinetic energy correction factor for the upstream representative section; The average cross-sectional velocity is the representative cross-section of the upstream source. It is the acceleration due to gravity; This represents the water surface elevation of a downstream representative section. This is the kinetic energy correction coefficient for the downstream representative section; The average cross-sectional velocity is the representative cross-section of the downstream co-source.

[0062] Under the condition that the differences in water depth, average flow velocity, and kinetic energy correction coefficient between the upstream and downstream representative cross sections are negligible, the total energy loss of the multi-cycle measurement segment is equivalent to the difference in water surface elevation between the upstream and downstream representative cross sections. The equivalent energy slope of the multi-cycle measurement segment is generated using the total energy loss of the multi-cycle measurement segment. Within the interval where only a single vertical slit baffle chamber unit is extracted, the equivalent energy slope is obtained by calculating the energy loss in a single cycle. The formula for calculating the equivalent energy slope is divided into a multi-cycle equivalent energy slope calculation formula and a single-cycle equivalent energy slope calculation formula. The multi-cycle equivalent energy slope calculation formula is as follows:

[0063] ;

[0064] In the formula, Equivalent energy slope; Total energy loss over multiple measurement cycles; The length of the measured segment.

[0065] The formula for calculating the single-cycle equivalent energy slope is as follows:

[0066] ;

[0067] In the formula, Equivalent energy slope; This represents energy loss per cycle. This is the length of the pool / chamber.

[0068] The equivalent energy slope establishes the energy attenuation boundary of the equivalent rectangular open channel, which, together with the static geometric boundary conditions of the equivalent rectangular open channel, supports the calibration of the equivalent comprehensive resistance. The equivalent rectangular open channel establishes cross-sectional geometric constraints based on the extracted equivalent effective width. The cross-sectional geometric quantities are strictly constrained by the equivalent effective width and any water depth. These cross-sectional geometric constraints correspond to the calculation of the flow area, wetted perimeter, hydraulic radius, and water surface width. The formulas for the flow area, wetted perimeter, hydraulic radius, and water surface width are as follows:

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] In the formula, This represents the cross-sectional area corresponding to any water depth. For any water depth; To calculate the effective width equivalently; The wetted perimeter corresponds to any water depth; The hydraulic radius corresponding to any water depth; The width of the water surface corresponding to any water depth.

[0074] After establishing the cross-sectional geometric constraints and the equivalent energy slope, the local energy dissipation inside the vertical slot fishway is converted into the equivalent comprehensive roughness. Based on the given reference flow rate, equivalent drag rate, reference water depth, and equivalent energy slope, the equivalent comprehensive roughness is obtained by back-calculation using the equivalent comprehensive roughness calibration formula, which is as follows:

[0075] ;

[0076] In the formula, Equivalent comprehensive roughness; The cross-sectional area corresponding to the reference water depth for the equivalent drag ratio; To determine the reference water depth for the equivalent drag ratio; The hydraulic radius corresponding to the reference water depth is used to determine the equivalent drag ratio; Equivalent energy slope; For reference traffic.

[0077] The calculation of the equivalent comprehensive roughness ensures that the energy loss diameter is completely consistent with the diameter of the measured section length. Under the condition that the reference state corresponding to the equivalent drag rate reference water depth is equivalent to the baseline uniform operating state, the value of the equivalent energy slope is equivalent to the value of the bottom slope. When the effective width of the equivalent calculation differs from the equivalent comprehensive roughness, it is treated as an unconstrained free parameter and can be arbitrarily adjusted. For intervals where the back-calculated values ​​of the equivalent comprehensive roughness differ significantly, parameters in the form of partitions, operating conditions, or functions are used to avoid unconditional extrapolation. The equivalent comprehensive roughness establishes the comprehensive drag attribute of the equivalent rectangular open channel, providing a dimension-reduced one-dimensional model parameter for calculating slow-flow conditions and defining the endpoint of influence.

[0078] See attached document Figure 3 S2, after obtaining the equivalent comprehensive roughness and establishing the comprehensive resistance attribute of the equivalent rectangular open channel, a kinetic energy correction coefficient is introduced to check whether the flow state in the equivalent rectangular open channel meets the steady-flow condition. The determination of the steady-flow condition depends on the critical water depth. The critical state corresponding to the critical water depth satisfies the critical water depth discriminant, which is as follows:

[0079] ;

[0080] In the formula, This is the kinetic energy correction factor; Design traffic; The critical water depth; This represents the width of the water surface corresponding to the critical water depth. It is the acceleration due to gravity; This represents the cross-sectional area corresponding to the critical water depth.

[0081] With the kinetic energy correction coefficient extracted from the equivalent calculation equal to 1, the critical water depth discriminant degenerates into the commonly used critical flow discriminant, and numerical comparisons are performed between the reference operating water depth and the critical water depth, as well as between the downstream control water depth and the critical water depth. The slow-flow backwater calculation relies on multiple pre-existing hydraulic conditions. The first pre-existing hydraulic condition limits the reference operating water depth to be greater than the critical water depth; the second pre-existing hydraulic condition limits the downstream control water depth to be greater than the critical water depth; and the third pre-existing hydraulic condition limits the downstream control water depth to be greater than the reference operating water depth. When all three pre-existing hydraulic conditions are met simultaneously, the equivalent rectangular open channel is determined to be under local control with no hydraulic jump and pressurized flow, thus establishing the boundary basis for the slow-flow backwater calculation and ensuring a reliable output of the endpoint water depth for engineering impact.

[0082] After establishing the boundary conditions for calculating the slow-flow backwater, the tailrace backwater curve is determined to extend upstream along the equivalent rectangular open channel, with the water depth asymptotically recovering to the reference operating depth. Since the tailrace backwater curve asymptotically recovering to the reference operating depth corresponds to an infinite length in the absence of boundary disturbances, thus hindering the coordinate positioning of the end of the tailrace influence length, a one-dimensional energy equation is introduced to introduce an engineering cutoff criterion to limit the upstream cutoff endpoint of the tailrace backwater curve within the equivalent rectangular open channel, establishing the engineering influence endpoint water depth corresponding to the upstream cutoff endpoint. The value of the engineering influence endpoint water depth is greater than the reference operating depth, and the difference is constrained by the set engineering control parameters. The calculation of the engineering influence endpoint water depth includes the relative proportion method and the absolute depth method. The formula for defining the engineering influence endpoint water depth using the relative proportion method is as follows:

[0083] ;

[0084] In the formula, The project affects the final water depth; The reference operating water depth; It is the relative control proportional constant; To control water depth downstream.

[0085] The formula for defining the endpoint water depth of engineering influence using the absolute water depth method is as follows:

[0086] ;

[0087] In the formula, The project affects the final water depth; The reference operating water depth; This is the absolute water depth threshold.

[0088] The relative control proportional constant is defined between 0.025 and 0.10, and the water depth threshold corresponds to a specified small water depth increment. The endpoint water depth of the engineering impact, together with the downstream control water depth, defines the upstream and downstream water depth boundary conditions of the tailrace impact section, providing endpoint constraint parameters for calculating the cross-sectional specific energy along the channel. After establishing the upstream and downstream water depth boundary conditions of the tailrace impact section, the cross-sectional specific energy and water conveyance capacity corresponding to any water depth are calculated along the equivalent rectangular open channel. The cross-sectional specific energy characterizes the energy possessed by the water flow through the equivalent cross-section and is calculated using a formula. The water conveyance capacity characterizes the flow properties of the water transported by the equivalent rectangular open channel and is calculated using a function formula. The formula for cross-sectional specific energy is as follows:

[0089] ;

[0090] In the formula, The cross-sectional specific energy corresponding to any water depth; For any water depth; This is the kinetic energy correction factor; Design traffic; It is the acceleration due to gravity; This represents the cross-sectional area corresponding to any water depth.

[0091] The formula for the water conveyance capacity function is as follows:

[0092] ;

[0093] In the formula, This represents the water conveyance capacity at any water depth. This represents the cross-sectional area corresponding to any water depth. Let be the hydraulic radius corresponding to any water depth.

[0094] Based on the assumption that the equivalent comprehensive roughness remains constant, the friction gradient at any water depth is calculated using the following formula:

[0095] ;

[0096] In the formula, For any water depth, the friction gradient is given. Design traffic; For reference traffic; Equivalent comprehensive roughness; This represents the water conveyance capacity at any water depth. Equivalent energy slope; The water conveyance capacity corresponding to the reference water depth is determined for the equivalent resistance rate.

[0097] The friction gradient ratio is calculated under the following conditions: the reference water depth is equal to the reference operating water depth and the equivalent energy slope is equal to the bottom slope. The formula for the friction gradient ratio is as follows:

[0098] ;

[0099] In the formula, For any water depth, the friction gradient ratio is given. For any water depth, the friction gradient is given. It is a bottom slope; Design traffic; For reference traffic; The water conveyance capacity corresponding to the benchmark operating water depth; This represents the water conveyance capacity for any water depth.

[0100] By combining the friction slope ratio with the endpoint weighted approximation formula, a strictly spatially average friction slope ratio from the downstream control section to the endpoint of the engineering influence is constructed. Based on the endpoint weighted calculation law, it is transformed into an endpoint weighted approximation form based on the boundary water depth. The integral formula and endpoint weighted approximation formula of the strictly spatially average friction slope ratio are as follows:

[0101] ;

[0102] In the formula, For a strictly spatially average friction gradient ratio; The length affected by the tailwater; For the integral variable along the path space; This refers to the frictional gradient along the path. It is a bottom slope; This is the interval comprehensive correction coefficient; The friction gradient ratio corresponding to the final water depth affected by the project. The friction gradient ratio corresponding to the downstream control water depth.

[0103] The range of values ​​for the interval comprehensive correction coefficient is defined between 0 and 1. Combined with the friction gradient ratio corresponding to the water depth at the endpoint of the engineering impact and the friction gradient ratio corresponding to the downstream control water depth, the equivalent rectangular open channel spatial average resistance model is constructed, providing dimensionality reduction constraint parameters for one-step rapid analysis of the tailrace impact length.

[0104] See attached document Figure 4 S3. After constructing the spatial average resistance model, import the reference tailrace condition, which includes the measured friction section locations and corresponding measured water depths. Extract the reference benchmark location mapped to the endpoint water depth of the engineering impact from this reference benchmark location. Combine the measured friction section locations and measured water depths to perform linear interpolation to obtain the horizontal friction distance corresponding to the endpoint water depth of the engineering impact, thus establishing the numerical value of the reference benchmark location. Combining the reference benchmark location, downstream control water depth, and endpoint water depth of the engineering impact, calculate the actual average friction gradient ratio of the reference condition using the inverse calculation formula, as follows:

[0105] ;

[0106] In the formula, The actual average friction gradient ratio is used as a reference. For downstream control section specific energy; To affect the specific energy of the endpoint section; It is a bottom slope; This serves as a reference point.

[0107] After obtaining the actual average friction gradient ratio under the reference working condition, the comprehensive correction coefficient for the interval is derived by back-calculating based on the actual average friction gradient ratio under the reference working condition, the friction gradient ratio corresponding to the water depth at the endpoint of the engineering influence, and the friction gradient ratio corresponding to the downstream control water depth. The derivation formula is as follows:

[0108] ;

[0109] In the formula, This is the interval comprehensive correction coefficient; The actual average friction gradient ratio is used as a reference. The friction gradient ratio corresponding to the downstream control water depth; The friction gradient ratio corresponds to the water depth at the endpoint of the project's impact.

[0110] The inversely calculated interval comprehensive correction coefficient establishes the weighting weights in the endpoint weighted approximation, providing a basis for parameter migration calculations of the one-dimensional energy equation to unknown independent operating conditions. In the absence of measured water depth data as a reference tailrace condition, the interval comprehensive correction coefficient is set at 0.50 as the initial estimate for equal weighting of the two endpoints, or obtained through migration from similar hydraulic engineering projects. After extracting the interval comprehensive correction coefficient, it is applied to the overall deviation absorption stage between the one-dimensional equivalent analysis system and the three-dimensional real flow characteristics.

[0111] Because the long and short partitions and vertical slots inside the vertical slot fishway cause the actual width of the water flow channel to change along the direction of water flow, while the equivalent rectangular open channel uses a single equivalent effective width to replace it, a difference in spatial geometric dimension is generated between the two structures. The difference in spatial geometric dimension is integrated and compensated by the interval comprehensive correction coefficient.

[0112] In reality, the vertical slotted fishway has three-dimensional flow characteristics consisting of mainstream jet, local backflow and strong turbulent mixing. The equivalent rectangular open channel reduces the three-dimensional flow characteristics to a one-dimensional gradually varying flow state with a uniform cross-sectional average velocity distribution, thus generating a flow characteristic conversion deviation. The interval comprehensive correction coefficient absorbs the flow characteristic conversion deviation into a single constant term.

[0113] The interval comprehensive correction coefficient ensures that the spatial average resistance level calculated by the endpoint weighted approximation formula remains consistent with the actual energy consumption level shown by the reference tailrace conditions. The basic data errors generated from a single measurement are also aggregated into the interval comprehensive correction coefficient, thus uniformly quantifying and absorbing the overall deviation. The interval comprehensive correction coefficient establishes a conversion balance between the equivalent rectangular open channel and the actual vertical slotted fishway structure, preventing interference from local parameter settings on the accuracy of the overall tailrace influence length calculation. This allows the one-dimensional energy equation to complete an adaptive calibration closed loop based on the interval comprehensive correction coefficient.

[0114] After completing the overall deviation absorption setting of the interval comprehensive correction coefficient, an independent test condition is introduced that is different from the reference tailwater condition and has measured water depth data and corresponding actual tailwater influence length. This condition is used to perform prediction accuracy tolerance test and provide an objective comparison benchmark.

[0115] The interval comprehensive correction coefficient is used to calculate and output the corresponding predicted tailwater impact length for independent inspection conditions. The predicted tailwater impact length is compared with the actual tailwater impact length for independent inspection to perform deviation quantification. The relative error of the impact length is calculated using the evaluation formula as follows:

[0116] ;

[0117] In the formula, To affect the relative error of length; To independently test the predicted tailwater impact length; To independently verify the actual length of the tailwater impact.

[0118] After generating the relative error of the influence length, the preset tolerance threshold is extracted and numerically compared. If the relative error of the influence length is less than or equal to the tolerance threshold, the corresponding fault tolerance test is qualified. The comprehensive correction coefficient of the judgment interval meets the parameter acceptance criteria and is locked. The result is output to the influence length prediction calculation stage of the unknown independent tailrace condition.

[0119] If the relative error of the affected length exceeds the tolerance threshold, the corresponding fault tolerance test fails to meet the standard. The determination of the interval comprehensive correction coefficient violates the parameter acceptance criterion, thereby triggering the parameter reset condition. This blocks the deduction and calculation of the current unknown independent tailrace working condition and forces a return to the parameter extraction stage to recalibrate the effective width of the equivalent calculation. The spatial average resistance model is reconstructed to prevent the interval comprehensive correction coefficient that exceeds the boundary from entering the subsequent calculation stage of the sidewall elevation.

[0120] See attached document Figure 5After locking the interval comprehensive correction coefficients that satisfy the parameter acceptance criteria, an energy conservation model is constructed between the downstream control section and the endpoint of the engineering influence, mathematically linking the energy states at both ends with the energy consumption along the flow path. Under the condition that the water flows from the endpoint of the engineering influence to the downstream control section along an equivalent rectangular open channel, the sum of the specific energy of the endpoint section and the potential energy increment generated by the bottom slope is equal to the sum of the specific energy of the downstream control section and the energy consumption due to friction along the flow path.

[0121] The frictional energy loss along the route is obtained by multiplying the strictly spatial average frictional gradient ratio, the bottom slope, and the length of influence of the tailwater. The potential energy increment generated by the bottom slope is obtained by multiplying the bottom slope and the length of influence of the tailwater. Based on the balance condition of energy state and frictional energy loss, the overall energy equation is generated. The overall energy equation from the downstream control section to the endpoint of influence is as follows:

[0122] ;

[0123] In the formula, To affect the specific energy of the endpoint section; It is a bottom slope; The length affected by the tailwater; For downstream control section specific energy; It is the strict spatial average friction gradient ratio.

[0124] The overall energy equation extracts the tailrace influence length as a first-order algebraic term to avoid differential slicing and integration on the water surface line. The downstream control water depth and actual flow rate establish the precise value of the specific energy at the downstream control section, while the basic design parameters combined with the water depth at the engineering influence endpoint establish the precise value of the specific energy at the influence endpoint section. The overall energy equation replaces the strictly spatially average friction gradient ratio with an endpoint-weighted approximation based on a comprehensive interval correction coefficient, forming an equality constraint condition that only includes known endpoint boundary parameters and the tailrace influence length. This provides a fundamental analytical framework for a one-step direct solution of the tailrace influence length under unknown operating conditions.

[0125] After generating the overall energy equation, an algebraic equivalent transformation is performed. The tailwater influence length is separated as a linear algebraic term to be solved in the equality constraints. An algebraic relationship for directly solving the tailwater influence length is derived, replacing the traditional iterative calculation by traversing each pool. Combined with the one-step estimation formula for the tailwater influence length, the tailwater influence length is calculated. The estimation formula is as follows:

[0126] ;

[0127] In the formula, The length affected by the tailwater; For downstream control section specific energy; To affect the specific energy of the endpoint section; It is a bottom slope; This is the interval comprehensive correction coefficient; The friction gradient ratio corresponding to the final water depth affected by the project. The friction gradient ratio corresponding to the downstream control water depth.

[0128] The one-step estimation formula for the tailrace influence length maps the known endpoint boundary parameters into a single continuous equation, eliminating the need to divide the water surface into small slices along the equivalent rectangular open channel and perform cyclical calculations. By inputting the cross-sectional energy state parameters and friction gradient parameters corresponding to a single tailrace condition, the exact analytical value of the tailrace influence length is directly output.

[0129] The upstream cutoff coordinates are located within the equivalent rectangular open channel based on analytical values, defining the spatial range in which the tailwater backwater phenomenon decreases along the course and gradually recovers towards the reference operating depth, providing a clear horizontal distance indicator for the sidewall elevation of different sections of the vertical slot fishway.

[0130] After extracting the analytical values ​​of the tailrace influence length, applicability boundary error prevention control is implemented for the estimation formula. The solution is subject to numerical preconditions including the anti-collapse condition of the denominator term and the flow continuity condition. The anti-collapse condition of the denominator term is used to constrain the denominator calculation term in the formula, which consists of the bottom slope and the combined algebraic term. The combined algebraic term is calculated by the interval comprehensive correction coefficient and the friction slope ratio. The difference between the combined algebraic term value and the constant 1 is calculated to generate the denominator judgment value. A preset tolerance minimum value is used to ensure that the value of the denominator judgment value is strictly greater than the tolerance minimum value. If it is less than or equal to the tolerance minimum value, the calculation of the tailrace influence length under the current working condition is blocked to prevent overall divergence.

[0131] The flow continuity condition limits the water depth from the downstream control section to the endpoint of the engineering influence to maintain a monotonically decreasing characteristic along the counter-current direction, with no abrupt jumps or drops in water surface elevation. Since the presence of water depth abrupt changes violates the pre-established theoretical framework of steady, gradually varying flow, the water depth continuity is used to verify the interception of tailrace conditions with non-gradual transitions. The denominator anti-collapse condition and the flow continuity condition together establish a numerical fault tolerance criterion, ensuring the output of effective tailrace influence length values ​​within a range where the flow boundary is not distorted and algebraic operations do not overflow. This provides accurate horizontal mileage input parameters for the subsequent determination of the sidewall elevation distribution.

[0132] See attached document Figure 6 S5, after outputting the effective tailrace influence length value, establishes discrete control points between the downstream control section and the endpoint of the engineering influence. The control section water depth is generated by performing discretization processing on the water depth between the downstream control depth and the endpoint of the engineering influence using a fixed water depth increment. Based on the control section water depth, the cumulative spatial coordinates of the discrete control points are calculated using a calculation formula. The cumulative one-step spatial distance calculation formula is as follows:

[0133] ;

[0134] In the formula, For the first The cumulative one-step spatial distance of each control section; For downstream control section specific energy; For the first Specific energy of each control section; It is a bottom slope; This is the interval comprehensive correction coefficient; For the first The friction gradient ratio corresponding to the water depth at each control section; The friction gradient ratio corresponding to the downstream control water depth.

[0135] After obtaining the cumulative one-step spatial distance, the spacing between adjacent control sections is calculated using the segmented standard step size calculation formula. This establishes the spatial distribution grid of discrete control points within the equivalent rectangular open channel. The segmented standard step size calculation formula is as follows:

[0136] ;

[0137] In the formula, For the first Standard step size for each control section segment; For the first The cumulative one-step spatial distance of each control section; For the first The cumulative one-step spatial distance of each control section.

[0138] Based on a spatially distributed grid of discrete control points, the design water surface elevation data for each control section is calculated and output using the design water surface elevation generation formula along an equivalent rectangular open channel in reverse direction. The formula overlays the underlying topographic coordinates, bottom slope increments, and water depth at the control section. The design water surface elevation generation formula is as follows:

[0139] ;

[0140] In the formula, For the first Design water surface elevation of each control section; The starting elevation of the bottom plate of the downstream control section; It is a bottom slope; For the first The cumulative one-step spatial distance of each control section; For the first Water depth at each control section.

[0141] The design constructs a spatial distribution model of the water surface line, which shows the trajectory of the tailrace water attenuation along the extension from the downstream control section to the upstream. This model provides a three-dimensional coordinate data source for the subsequent extraction of the sidewall elevation envelope, thus supporting the calibration of the structural dimensions of the physical engineering within the tailrace-affected section.

[0142] After constructing the spatial distribution model of the water surface line, a single-condition height increase response calculation is performed. The independently set safety freeboard parameter used to prevent overflowing water flow is superimposed onto the design water surface elevation associated with each discrete control point. Combined with the generation formula, the control elevation of the sidewall top corresponding to the discrete control point is calculated and output. The formula for generating the control elevation of the sidewall top is as follows:

[0143] ;

[0144] In the formula, For the first The control elevation of the top of the sidewall of each control section; For the first Design water surface elevation of each control section; Extremely high parameters for safety.

[0145] After calculating and outputting the control elevation of the top of the sidewall, a construction segmentation rule is introduced. The continuous tailwater-affected section along the process is divided into multiple independent construction segment intervals based on the horizontal distance. Within a single construction segment interval, the control elevation of the top of the sidewall corresponding to all discrete control points is traversed and compared to extract the maximum value. The maximum value is set as the unified control elevation to eliminate minor elevation differences, so that the top of the sidewall within a single construction segment interval presents a horizontal straight-line spatial distribution that matches the flush assembly conditions of the wall template of the solid structure.

[0146] Multiple construction segments continuously distributed along an equivalent rectangular open channel are combined with corresponding unified control elevations to generate a stepped sidewall protection boundary. The output sidewall solid elevation scale provides underlying spatial benchmark data for envelope extraction in the context of multiple tailrace operation conditions. Subsequently, a multi-condition array is introduced, encompassing all hydrological combinations faced by the vertical slotted fishway. Each hydrological combination maps to an independent tailrace operation condition. The unified control elevation is calculated and output for each independent tailrace operation condition.

[0147] Within the same construction segment, all unified control elevations are extracted and filtered for maximum values. Low elevation data submerged by high water levels are removed, and the value with the highest elevation is locked. The extraction formula is then used to calculate and obtain the multi-condition sidewall design elevation envelope to guide the construction project. The extraction formula is as follows:

[0148] ;

[0149] In the formula, For the first The design elevation envelope values ​​of the sidewall under multiple working conditions in each construction segment; This represents the total number of independent tailrace operation conditions contained in the multi-condition array; An incremental index variable for independent tailrace operation conditions; For the first The construction section is in the first The unified control elevation corresponding to each independent tailrace operation condition.

[0150] For the upstream section unaffected by tailrace backwater, within the range where the coordinates along the route exceed the tailrace influence length corresponding to the tailrace operating condition, the elevation of the upstream section's sidewall is controlled and verified using the benchmark operating water depth superimposed with safety freeboard parameters to ensure the safety of the entire sidewall section. All construction segments continuously distributed along the equivalent rectangular open channel are spliced ​​together based on their respective multi-condition sidewall design elevation envelope values ​​to form the engineering overflow protection envelope. The horizontal starting and ending coordinates of all construction segments are spatially correlated with the multi-condition sidewall design elevation envelope values, generating a data table of solidified three-dimensional boundary dimensions for the engineering overflow protection envelope. This provides quantitative elevation data constraints for the drawing and on-site construction of the vertical slotted fishway solid sidewall.

[0151] In the application scenario, the physical structure dimensions and working condition boundary values ​​are imported to build a test benchmark. The physical structure dimensions that provide internal fixed space constraints include bottom slope, net width of pool chamber, length of pool chamber, thickness of partition, and width of vertical joint.

[0152] In the test baseline, the bottom slope is assigned a value of 1%, the net width of the pool chamber is assigned a value of 2m, the length of the pool chamber is assigned a value of 3m, the thickness of the partition is assigned a value of 0.2m, and the width of the vertical joint is assigned a value of 0.3m, and the equivalent effective width is calculated accordingly. The working condition boundary values ​​that define the internal energy movement state include the design flow rate, reference flow rate, reference operating water depth, equivalent comprehensive roughness, and kinetic energy correction factor.

[0153] In the test benchmark, the design flow rate is assigned to 0.5 m³ / s, the benchmark operating water depth is assigned to 1.5 m, the equivalent comprehensive roughness is assigned to 0.04, and the kinetic energy correction coefficient is assigned to 1. Under the condition that the equivalent resistance calibration reference water depth is equal to the benchmark operating water depth and the equivalent energy slope is equal to 1% of the bottom slope, the reference flow rate is determined to be approximately 0.56872 m³ / s based on the equivalent comprehensive roughness calibration relationship.

[0154] The combination of physical structure dimensions and operating condition boundary values ​​forms definite boundary constraints, providing underlying basic parameters for the cross-sectional specific energy formula and the water conveyance capacity function formula. For each independent tailrace operating condition included in the multi-condition array, a test range for the downstream control water depth is set, with the lower limit equal to 1.5m corresponding to the benchmark operating water depth and the upper limit limited to 3.0m. The established closed numerical computation environment intercepts interference from out-of-bounds parameters and supports error screening calculations for the multi-condition sidewall design elevation envelope results.

[0155] After establishing a closed computational environment, the equivalent resistance and flow boundary instantiation calculations were performed. The equivalent effective width was extracted from the test baseline and assigned a value of 0.45m, and the equivalent comprehensive roughness was assigned a value of 0.04. Combining the equivalent comprehensive roughness, the equivalent effective width, and the baseline operating water depth, the friction gradient under the tailrace-free backwater condition was calculated. The friction gradient value was equal to the bottom slope, and the bottom slope was assigned a value of 1%, thus establishing the basic calibration origin of the spatial average resistance model.

[0156] After completing the equivalent resistance calibration, the critical water depth and endpoint numerical verification conditions were introduced. Under the conditions that the design flow rate is equal to 0.5 m³ / s and the equivalent effective width is equal to 0.45 m, the calculated value of the critical water depth is 0.5 m. The comparison shows that the reference operating water depth of 1.5 m is greater than the calculated value of the critical water depth. This verifies that the water flow inside the equivalent rectangular open channel maintains a slow flow state that meets the flow continuity conditions and prevents abnormal interruption of the calculation.

[0157] After confirming the slow-flow regime, the water depth at the endpoint of the engineering impact is calculated and defined as 1.05 times the baseline operating water depth, with an output of 1.575m. This ensures that the specific energy of the impact endpoint section is within the effective real number domain. The water depth at the engineering impact endpoint is locked as a forced cutoff boundary to limit the unlimited upstream transmission of downstream control water depth fluctuations. The intermediate calculated values ​​generated by the instantiated calculation are combined to form the input source data for discrete control points, which is transmitted to the sidewall top control elevation generation stage to support the accurate extraction of the sidewall design elevation envelope results under multiple working conditions.

[0158] After completing the instantiation calculation, the reference validation set data is imported to perform data fitting and parameter convergence calculation. The reference validation set data comes from the interpolation table of measured water depths along the reference tailrace condition with a downstream control water depth of 2.4m. Under the operating conditions of a downstream control water depth of 2.4m and a design flow rate of 0.5m³ / s, the interpolation table of measured water depths along the tailrace records water depth data from equidistant sampling points extending upstream from the downstream control section with a spacing of approximately 12.2358m.

[0159] The water depth at the downstream control section at 0m is 2.4m. The water depths at subsequent locations are as follows: 2.33m at 12.236m, 2.26m at 24.472m, 2.19m at 36.707m, 2.12m at 48.943m, 2.05m at 61.179m, 1.98m at 73.415m, 1.91m at 85.650m, 1.84m at 97.886m, 1.77m at 110.122m, 1.70m at 122.358m, 1.63m at 134.593m, and 1.575m at 146.829m, corresponding to the water depth at the endpoint of the project's influence. The reference tailwater influence length measured at the reference reference location is approximately 146.829 m.

[0160] The friction slope ratio calculated based on a downstream control water depth of 2.4m is approximately 0.282397, and the friction slope ratio calculated based on an engineering impact endpoint water depth of 1.575m is approximately 0.695269.

[0161] Retrieving the corresponding specific energy parameters, under the conditions that the kinetic energy correction coefficient is equal to 1, the design flow rate is equal to 0.5 m³ / s, and the equivalent effective width is equal to 0.45 m, the specific energy of the downstream control section is approximately 2.410924 m, the specific energy of the affected endpoint section is approximately 1.600366 m, and the specific energy difference between sections is approximately 0.810558 m.

[0162] Substituting the specific energy difference, the 1% bottom slope, and the reference tailwater influence length of approximately 146.829m into the back calculation relationship, the actual average friction slope ratio under the reference working condition is calculated to be approximately 0.447959. Subsequently, substituting the actual average friction slope ratio under the reference working condition, the friction slope ratio corresponding to the downstream control water depth of approximately 0.282397, and the friction slope ratio corresponding to the engineering influence endpoint water depth of approximately 0.695269 into the interval comprehensive correction coefficient back calculation relationship, the back calculation value is approximately equal to 0.401.

[0163] The stable parameter back-calculation results confirm that the comprehensive correction coefficient of the interval is between 0 and 1, thus satisfying the requirements of the endpoint weighted approximation form for the value of the weighting weight, and providing parameter basis for performing one-step prediction for unknown independent tailrace conditions.

[0164] After confirming that the comprehensive correction coefficient of the interval has the characteristic of constant value migration, abnormal working condition traversal monitoring is performed to scan the equivalent calculated effective width corresponding to the size of the entity structure. When there is a step change parameter, it is determined to trigger the sudden cross section working condition to prevent the destruction of the boundary condition with consistent bottom width.

[0165] The critical water depth is calculated based on the design flow rate and the equivalent effective width, and compared with the reference operating water depth. When the reference operating water depth is less than the critical water depth, the flow continuity condition is interrupted, and a rapid flow condition is triggered. Due to the rapid flow condition, the downstream control water depth cannot be transmitted to the upstream space. Under the conditions of triggering abrupt cross-section conditions or rapid flow conditions, segmented calculation degradation operations are initiated, and global calls to formulas are stopped. The coordinates of the step change nodes of the equivalent effective width and the coordinates of the flow regime transition nodes are extracted, and the equivalent rectangular open channel is divided into multiple independent equivalent calculation sub-intervals.

[0166] Within the equivalent calculation sub-interval, the effective width and equivalent comprehensive roughness of the equivalent calculation are retrieved again, and the equivalent resistance and flow boundary are instantiated and calculated independently. For each independent equivalent calculation sub-interval, the downstream control section and the engineering influence endpoint of the sub-interval are established. The critical water depth and the specific energy of the influence endpoint section of the sub-interval are calibrated, and the formula is independently called to calculate and output the tailwater influence length of the sub-interval.

[0167] By combining the tailwater influence length of the sub-interval with reverse deduction, local water surface elevation data of the equivalent calculation sub-interval is generated. This forces the water level values ​​of adjacent equivalent calculation sub-intervals to match at the node coordinates. The local water surface elevation data are then stitched together to form a continuous overall water surface elevation data covering the dimensions of the entity structure. This data is then used in the single-condition heightening response calculation to provide the underlying spatial reference data under abnormal conditions.

Claims

1. A method for determining the tailrace length and sidewall elevation of an equivalent open channel vertical slotted fishway, characterized in that... Includes the following steps: Extract basic design parameters and tailrace operating parameters to establish an equivalent rectangular open channel with equivalent comprehensive roughness; Under the constraint that the equivalent rectangular open channel satisfies the steady and slow flow condition, a spatial average resistance model is constructed using the kinetic energy correction coefficient; An interval comprehensive correction coefficient is introduced to absorb the conversion difference between the equivalent rectangular open channel and the actual vertical slot fishway structure. The interval comprehensive correction coefficient that satisfies the parameter acceptance criterion is locked in combination with the spatial average resistance model. The overall energy equation is constructed based on the comprehensive correction coefficient of the interval, and the tailwater influence length is calculated and output using the one-step estimation formula of the tailwater influence length. The construction is divided into sections based on the length of the tailwater impact. The control elevation of the top of the sidewall corresponding to the construction section is calculated, and the design elevation envelope of the sidewall under multiple working conditions is extracted. A data table of three-dimensional boundary dimensions of the anti-overflow envelope surface of the solidification project is then exported.

2. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 1, characterized in that, Extracting the basic design parameters and the tailrace operating parameters to establish the equivalent rectangular open channel with the equivalent comprehensive roughness includes: The equivalent effective width, bottom slope, pool length, vertical joint width, diaphragm thickness, and downstream bottom elevation are extracted from the basic design parameters to define the static geometric boundary conditions of the equivalent rectangular open channel. The equivalent energy slope of the multi-cycle measurement segment is generated by utilizing the total energy loss of the multi-cycle measurement segment, or the equivalent energy slope of the single-cycle measurement segment is calculated by utilizing the energy loss of the single-cycle measurement segment. The equivalent comprehensive roughness is obtained by back-calculating the equivalent comprehensive roughness calibrating formula based on the reference flow rate, the equivalent resistance rate, and the equivalent energy slope or the single-cycle equivalent energy slope.

3. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 1, characterized in that, Under the constraint that the equivalent rectangular open channel satisfies the stable flow condition, the spatial average resistance model constructed using the kinetic energy correction coefficient includes: Based on the first set of pre-condition hydraulic conditions, which limit the reference operating water depth to be greater than the critical water depth, the second set of pre-condition hydraulic conditions, which limit the downstream control water depth to be greater than the critical water depth, and the third set of pre-condition hydraulic conditions, which limit the downstream control water depth to be greater than the reference operating water depth, the stable slow flow condition is determined to be satisfied when all three pre-condition hydraulic conditions are met simultaneously. The spatial average resistance model is constructed by combining the kinetic energy correction coefficient to obtain the friction gradient ratio corresponding to the endpoint water depth of the engineering influence and the friction gradient ratio corresponding to the downstream control water depth.

4. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 3, characterized in that, The calculation of the water depth at the endpoint affected by the project includes the relative proportion method and the absolute water depth method; When using the relative proportion method, the endpoint water depth of the project impact is calculated based on the benchmark operating water depth, the downstream control water depth, and the relative control proportion constant, and the value range of the relative control proportion constant is defined between 0.025 and 0.

10. When using the absolute water depth method, the endpoint water depth of the project impact is calculated based on the benchmark operating water depth and the absolute water depth threshold, and the absolute water depth threshold corresponds to a specified small water depth increment value.

5. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 3, characterized in that, The introduction of the interval comprehensive correction coefficient to absorb the conversion difference between the equivalent rectangular open channel and the actual vertical slotted fishway structure includes: Import the reference tailwater condition with the measured cross-sectional location and corresponding measured water depth, extract the reference benchmark location of the water depth mapping at the end point of the engineering influence, and calculate the actual average friction gradient ratio of the reference condition using the back calculation formula. The interval comprehensive correction coefficient is obtained by back-calculation based on the actual average friction gradient ratio of the reference working condition, the friction gradient ratio corresponding to the water depth at the endpoint of the engineering influence, and the friction gradient ratio corresponding to the downstream control water depth. The interval comprehensive correction coefficient is then applied to the overall deviation absorption link between the one-dimensional equivalent analysis system and the three-dimensional real flow characteristics.

6. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 1, characterized in that, Locking the interval comprehensive correction coefficients that satisfy the parameter acceptance criteria includes: An independent inspection condition is introduced to output the predicted tailwater impact length. The predicted tailwater impact length is compared with the actual tailwater impact length in the independent inspection, and the relative error of the impact length is calculated by combining the evaluation formula. When the relative error of the influence length is less than or equal to the tolerance threshold, the interval comprehensive correction coefficient is determined to meet the parameter acceptance criterion and locked. The tolerance threshold is a preset value for numerical comparison.

7. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 5, characterized in that, Based on the aforementioned interval comprehensive correction coefficient, the overall energy equation is constructed. The tailwater influence length is calculated and output using the one-step estimation formula, including: The overall energy equation is generated based on the balance condition of energy state and energy consumption along the flow path when the water flows from the endpoint of the engineering influence to the downstream control section. The tailwater influence length is separated as a linear algebraic term to be solved in the equality constraints. The analytical value is calculated by combining the tailwater influence length one-step estimation formula and the tailwater influence length is output within the range that meets the numerical fault tolerance criterion.

8. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 7, characterized in that, The numerical fault tolerance criterion is jointly established by the denominator term anti-collapse condition and the flow continuity condition; The anti-collapse condition for the denominator term limits the value of the denominator judgment value to be strictly greater than the minimum tolerance value. The flow continuity condition limits the water depth between the downstream control section and the endpoint of the engineering influence to maintain a monotonically decreasing characteristic along the counter-current direction and the water surface elevation value has no sudden jump or drop step point.

9. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 7, characterized in that, Calculating the control elevation of the top of the sidewall corresponding to the construction segment interval includes: Discretization is performed between the downstream control water depth and the water depth at the end point of engineering influence according to a fixed water depth increment to generate the control section water depth. The cumulative one-step spatial distance of the discrete control points is calculated using the control section water depth and the segmented standard step length calculation formula is used to establish the spatial distribution grid of the discrete control points inside the equivalent rectangular open channel. The design water surface elevation is calculated and output using the design water surface elevation generation formula for each control section. The safety superelevation parameter is superimposed on the associated design water surface elevation to calculate and output the control elevation of the top of the side wall. The control elevation of the top of the side wall is extracted by traversing and comparing all discrete control points within a single construction segment interval. The maximum value is then set as the unified control elevation.

10. The method for determining the tailrace influence length and sidewall elevation of an equivalent open channel vertical slotted fishway according to claim 1, characterized in that, The data table for extracting the elevation envelope of the multi-condition sidewall design and exporting the three-dimensional boundary dimensions of the overflow prevention envelope surface of the curing project includes: Within the same construction segment interval, extract all unified control elevations and perform maximum value filtering. Combine the extraction formula to calculate and obtain the multi-condition sidewall design elevation envelope value to guide the construction of the project. All the construction segment intervals are spliced ​​together according to their respective multi-condition sidewall design elevation envelope values ​​to form an engineering overflow prevention envelope surface. The horizontal starting point coordinates and horizontal ending point coordinates of all the construction segment intervals are spatially correlated with the multi-condition sidewall design elevation envelope values ​​to generate the data table.

Images