Reservoir density flow on-way evolution calculation method based on effective suspension work theory

Abstract

The invention discloses a reservoir density flow on-way evolution calculation method based on an effective suspension work theory. The method comprises the following steps: 1, calculating a reservoir density flow submergence point; 2, reservoir density current submerging characteristic calculation; 3, reservoir density flow on-way evolution simulation; and 4, carrying out reservoir density flow evolution processing and visual display. The method has the advantages that the effective suspension work is used for judging sedimentation or suspension of suspended sediment in the density current, and the critical effective suspension work is used as a judgment condition for the balance state of the density current; the evolution process of the flow velocity, the sand content and the density flow layer thickness from generation of the reservoir density flow to the front of the dam is rapidly and efficiently calculated by combining density flow submerging judgment conditions, a density flow submerging characteristic calculation formula, a density flow self-similarity theory, a density flow accumulation depth control equation and an effective suspension work theory; and support is provided for ultra-long-distance sediment transportation of density flow. Meanwhile, after upstream water and sand conditions and dam discharge flow are input, the density flow velocity, the sand content on-way change process and the warehouse-out sand content can be obtained.

Description

Technical Field

[0001] This invention relates to the field of reservoir capacity restoration and efficient sediment discharge technology, and in particular to a method for calculating the evolution of density currents along the reservoir based on the theory of effective suspension work. Background Technology

[0002] Reservoirs are effective tools for regulating runoff and developing and utilizing water resources. Strengthening water resource management and protection, optimizing water resource allocation, and improving the comprehensive utilization efficiency and benefits of water resources can support the sustainable development of the economy and society. Reservoir siltation is a common problem. After a reservoir is built, as the water level rises, backwater forms in the reservoir area, and the reduced water surface gradient and flow velocity lead to siltation. The distribution and morphology of reservoir siltation are influenced by factors such as the inflow of water and sediment, the characteristics of watershed sediment, and reservoir operation methods. During the construction and operation of reservoirs, siltation can encroach on flood control capacity, reduce the reservoir's regulation capacity, affect power generation, and make it difficult for the reservoir to maintain its effective storage capacity in the long term. Rivers with high sediment loads and large sediment transport volumes are characterized by severe siltation and reservoir capacity loss. Therefore, maintaining and utilizing reservoir capacity and achieving development goals are key scientific and technological issues in the design and operation of reservoirs in rivers with high sediment loads. By utilizing reservoirs to reduce siltation and promote beneficial use, problems such as rapid siltation and loss of reservoir capacity, limited silt-trapping capacity, and difficulties in power generation during the flood season can be solved.

[0003] Reservoirs often generate density currents during water and sediment regulation. Utilizing these density currents for efficient sediment removal and extending the reservoir's lifespan offers significant socio-economic benefits. The sediment removal efficiency of density currents is related to factors such as the reservoir's operation, the composition of the incoming sediment, and whether a turbid water reservoir was formed in the early stages. Density currents are beneficial for maintaining effective sediment retention capacity in reservoirs of sediment-rich rivers and can fully utilize the sediment transport efficiency of downstream channels, achieving long-term siltation reduction and shaping favorable medium-water channels. Currently, in reservoirs of sediment-rich rivers, density currents exhibit three motion states after submersion: disappearance, self-suspension, and excitation. However, there are still shortcomings in revealing the density current motion process during flood season sediment removal in reservoirs of sediment-rich rivers under different operating conditions. The lack of corresponding density current evolution prediction models during water and sediment regulation makes it impossible to predict the sediment removal effect of water and sediment regulation schemes, resulting in a lag in the effectiveness of water and sediment regulation. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the evolution of density current in reservoirs based on the theory of effective suspension work. This method aims to address the shortcomings in rapidly constructing the evolution process of density current in reservoirs and evaluating sediment discharge during the flood season using density current. It is particularly suitable for sediment-laden river reservoirs that discharge sediment using density current.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: The method for calculating the evolution of density currents in reservoirs based on the theory of effective suspension work, as described in this invention, includes the following steps: Step 1, Calculation of the ingress point of the density current in the reservoir: Collect the reservoir topographic distribution data, beach distribution data, or reservoir cross-sectional data to determine the water surface width and deep channel depth of each cross-section in the reservoir area at the designated reservoir dam water level, as well as the riverbed slope of the delta top section, front slope section, and dam front section in the reservoir area. Then calculate the penetration depth of the density current in the reservoir at the designated reservoir water level to determine the cross-section of the density current penetration point. Step 2, Calculation of reservoir density current intrusion characteristics: Based on the density flow velocity and density flow thickness calculated under uniform flow conditions, the density flow velocity and density flow thickness under different sediment concentration conditions are calculated according to different upstream water levels and ingress point cross sections. Step 3, Simulation of the evolution of the density current along the reservoir: A one-dimensional accumulation depth model of the density current in the reservoir was constructed using the control equations of density current, the theory of effective suspension work, and the theory of self-similarity. The parameters of the one-dimensional accumulation depth model were determined and the model was closed. The one-dimensional accumulation depth model was solved using the fourth-order Runge-Kutta method. Step 4, Reservoir density current evolution processing: The calculation results of the one-dimensional accumulation depth model of the heterogeneous flow are visualized using the self-similarity theory.

[0006] Furthermore, the calculation of the reservoir density current ingress point includes calculating the ingress point location under different reservoir water level conditions based on the input topographic distribution data, upstream inflow, and inflow sediment concentration.

[0007] Furthermore, the simulation of the evolution of the density current along the reservoir involves a combination of three elements: the one-dimensional reservoir density current control depth equation, self-similar theory, and effective suspension work theory, which are solved using the fourth-order Runge-Kutta algorithm.

[0008] Furthermore, the reservoir density current evolution processing involves transforming the one-dimensional depth velocity and sediment concentration into a two-dimensional planar density current based on the reservoir density current simulation results using the self-similar theory, and calculating the sediment concentration and velocity distribution of the density current from the ingress point to the dam front.

[0009] The advantages of this invention lie in using effective suspension work as the criterion for determining whether suspended sediment in a density current settles or remains suspended, and using critical effective suspension work as the criterion for determining the equilibrium state of the density current. By combining the density current intrusion criterion, the density current intrusion characteristic calculation formula, the density current self-similarity theory, the density current accumulation depth control equation, and the effective suspension work theory, it achieves rapid and efficient calculation of the flow velocity, sediment concentration, and density current layer thickness evolution process of the density current from its generation to the dam, providing support for the ultra-long-distance sediment transport of density currents. Furthermore, the density current evolution calculation proposed in this invention differs from numerical simulation. After inputting upstream water and sediment conditions and dam discharge flow, it can quickly obtain the flow velocity, sediment concentration variation process along the flow path, and the outflow sediment concentration, predicting the density current intrusion point and the sediment concentration when the density current arrives at the dam. This provides strong technical support for the density current sediment discharge scheduling and decision-making during water and sediment regulation in reservoirs of sediment-rich rivers, and has broad application prospects and practical value. Attached Figure Description

[0010] Figure 1 This is a flowchart of the reservoir density flow evolution calculation method described in this invention.

[0011] Figure 2 The flowchart for calculating the ingress point of a reservoir density current as described in this invention.

[0012] Figure 3 The flowchart for calculating the intrusion characteristics of reservoir density currents described in this invention.

[0013] Figure 4 The flowchart of the simulation of the evolution of the density current along the reservoir described in this invention.

[0014] Figure 5 The flowchart of the reservoir density flow evolution process described in this invention.

[0015] Figure 6 This is a schematic diagram showing the comparison between the calculated values ​​of the density current theoretical model of Xiaolangdi Reservoir in 2010 and the measured values ​​(sediment content distribution) of each cross section, as described in Embodiment 1 of the present invention.

[0016] Figure 7 This is a schematic diagram showing the comparison between the calculated values ​​of the density current theoretical model of Xiaolangdi Reservoir in 2010 and the measured values ​​(water flow distribution) of each cross section, as described in Embodiment 1 of the present invention.

[0017] Figure 8 This is a distribution diagram of sediment discharge efficiency under different reservoir water levels and upstream sediment inflow conditions during 50 years of operation of the Heishanxia Reservoir as described in Embodiment 2 of the present invention. Detailed Implementation

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] The reservoir density current evolution calculation method based on the effective suspension work theory described in this invention is applicable to the scheduling and decision-making process of density current sediment discharge during water and sediment regulation or sediment discharge in reservoirs of sediment-rich rivers. It can obtain the density current velocity, sediment concentration evolution process, and outflow sediment concentration based on topographic data (measured topographic data of the reservoir cross section), real-time water and sediment discharge process of the upstream reservoir, reservoir water level and discharge flow, and scheduling arrangements. It provides theoretical guidance and technical support for efficient sediment discharge in reservoirs of sediment-rich rivers, and provides guidance for the layout planning of water discharge structures of reservoirs of sediment-rich rivers (not yet constructed). That is, it calculates the evolution of the characteristics of the entire density current process (generation, infiltration, movement along the flow path, and outflow) during sediment discharge in different years of use.

[0020] The method for calculating the evolution of density currents in reservoirs based on the theory of effective suspension work described in this invention, such as... Figure 1-5 As shown, the specific steps include the following: Step 1, Calculation of the ingress point of the density current in the reservoir: Collect the reservoir topographic distribution data, beach distribution data, or reservoir cross-sectional data to determine the water surface width and deep channel depth of each cross-section in the reservoir area at the designated reservoir dam water level, as well as the riverbed gradient of the delta top section, front slope section, and dam front section. Then calculate the penetration depth of the density current in the reservoir at the designated reservoir water level to determine the density current penetration point cross-section.

[0021] Beneficially or exemplaryly, the reservoir density current ingress point calculation calculates the ingress point location and the distance from the ingress point to the dam under different reservoir water level conditions, based on the input topographic distribution data, upstream inflow, and inflow sediment content.

[0022] Because the transition from open channel flow to density current is not continuous, meaning the interface of the density current is abrupt at the intrusion point; therefore, after the density current intrudes, the thickness of the sediment-laden water flow rapidly decreases, and an inflection point appears on the density current surface line. At this inflection point... This is equivalent to the critical condition for the transition from a slow current to a rapid current in an open channel; the formula for calculating the depth of the intrusion point is as follows: (1) In the above formula h 0 represents the water depth required for the entry point into the density current; g represents the acceleration due to gravity. This is the gravity correction factor, i.e. , The density of turbid water, The density is that of clear water; due to the buoyancy of clear water, the gravitational acceleration of turbid water is reduced to [value missing]. times, and The magnitude is in the range of 10 -3 ~10 -1 Therefore, the gravitational effect of the density current is weakened; q For unit width flow, q= Q / B , Q This refers to the upstream water flow rate. B The width of the reservoir water surface at the dive point; based on the calculated... h By considering the topography of the reservoir area and the location of the dam, the distance from the ingress point to the dam can be determined.

[0023] Step 2, Calculation of reservoir density current intrusion characteristics: Based on the density flow velocity and density flow thickness calculated under uniform flow conditions, the density flow velocity and density flow thickness under different sediment concentration conditions are calculated according to different in-dam water levels and ingress point cross sections.

[0024] Assuming that the density current exhibits uniform flow motion after being submerged, then the density current velocity... With density flow thickness for: (2) (3) In the above formula, The drag coefficient representing the density flow (can be taken as 0.025). J b This refers to a deep channel or bottom slope of a reservoir.

[0025] because It is related to sediment content. If the sediment content of the upstream water is available, it can be directly used for calculation; otherwise, the relevant sediment content can be obtained from historical flood data, or a value can be determined by oneself.

[0026] Step 3, Simulation of the evolution of the density current along the reservoir: A one-dimensional accumulation depth model of the density current in the reservoir was constructed using the control equations of density current, the theory of effective suspension work, and the theory of self-similarity. The parameters of the one-dimensional accumulation depth model were determined and the model was closed. The one-dimensional accumulation depth model was solved using the fourth-order Runge-Kutta method.

[0027] Furthermore, the simulation of the evolution of the density current along the reservoir combines the one-dimensional reservoir density current control depth equation, self-similar theory, and effective suspension work theory, and uses the fourth-order Runge-Kutta algorithm for solution calculation.

[0028] The reservoir density current evolution simulation model uses the calculation of the density current intrusion point and the density current intrusion characteristics as prerequisites, or performs inversion and calculation of the density current evolution along the course under known intrusion characteristics and intrusion location. This allows for the rapid acquisition of sediment content, flow velocity and layer thickness in front of the dam in the density current, providing a reference for guiding reservoir operation.

[0029] In constructing the governing equations for density current in a reservoir, it is assumed that the cross-section of the river channel flowing through the reservoir is rectangular with a large width-to-depth ratio (greater than 10). The lateral distribution characteristics of the density current are not considered, and the riverbed slope remains constant with a gradient less than (less than 0.01). Therefore, the density current can be viewed as a two-dimensional planar motion. xz Plane, in which x The axis is positive along the downstream of the river channel. z The axis is perpendicular to the riverbed and upwards is positive; using the Boussinesq assumption, the dynamic viscosity coefficient of the sand-laden layer is... υ Similar to the clear water layer; the upper clear water layer is thicker than the lower sediment-laden layer, and the density current layer is thicker. h The density current changes along the course due to mixing with the upper clear water. Driven by density differences, the average particle size of the suspended sediment is... d The angle between the riverbed and the horizontal plane is θ The main parameter of density flow is the time-averaged velocity. u ( z ), sediment content c ( z ), turbulent kinetic energy k ( z The interaction between density currents and the substrate includes sedimentation. D ) and erosion E The settling velocity of the sediment is w s The mixing speed of the clear water layer is w e The corresponding governing equations for density currents are: (4a) (4b) (4c) (4d) k turbulent kinetic energy ;in This refers to the instantaneous volumetric sand content of the sand-bearing layer. The instantaneous flow velocity of the sand layer; Instantaneous pressure; , g It is the acceleration due to gravity. S For the slope, ρ The density of the stationary fluid. ρ s The density of sediment particles, R =( ρ s / ρ -1); The velocity of suspended sediment can be considered as the water flow velocity and the sediment settling velocity in still water. w s sum; For Kronecker numbers.

[0030] In constructing the accumulation depth equation for density currents, the two-dimensional density current motion process is approximated using a boundary layer, neglecting variations along the lateral width; in the Cartesian coordinate system, we have... , The relationship between the friction velocity and the vertical velocity in a density flow is as follows: u >> w In a quasi-equilibrium state, there is ∂ / ∂z >> ∂ / ∂x At the same time, the density current is in a state of complete turbulence ( Uh / v >3000, U The vertical average velocity, h For the thickness of the density flow, v The dynamic viscosity coefficient is 1.01 × 10⁻⁶. -6 m 2 / s), the viscous term can be ignored, but the Reynolds stress term, i.e., the viscous dissipation term caused by turbulence, is retained, and there is The equation for the depth of density current accumulation can be obtained as follows: (5a) (5b) (5c) (5d) In the above formula , , , , z = b It is near the riverbed, so it can be taken. b =0.05 h , C a =2.69 C , To account for the approximate virtual vertical velocity at the upper interface of the density flow, we have: ,in The rate of change of the density flow thickness over time. w e It can be represented as ew U , e w The mixing coefficient of clear and turbid water; F b This represents the suspension rate of sediment carried away from the bed surface due to the influence of turbulence (sediment entrainment rate), introducing a dimensionless sediment entrainment rate. E s Defined as: F b = w s E s , E s It can be represented as e s and w s The product of, i.e. E s = e s w s cos θ .

[0031] In the self-similarity theory of density flows, since the velocity, sediment concentration, and turbulent kinetic energy of density flows are similar, the shape functions of the velocity, sediment concentration, and turbulent kinetic energy of the corresponding density flows can be obtained. , They are respectively: (6a) (6b) (6c) U, C and K These are the vertical average velocity, sediment concentration, and turbulent kinetic energy, respectively; substituting equation (6) into equation (5) yields: (7a) (7b) (7c) (7d) In the above formula, Using the Kolmogorov assumption , The dimensionless turbulence coefficient is related to the flow state. I 1 = 1.002, I 2 = 1.003, I 3 = 1.446 I4 = 1.466 I 5 = 0.255 I 6 = 1.150 I 7 = 1.010 I 8 = 0.335 I 9 = 0.631 I 10 =4.199; In the quasi-steady state, we have .

[0032] In the theory of effective suspension work, it is assumed that the underwater weight of sediment per unit volume is... , γ s and γ 0 The bulk density of silt and sand and the bulk density of water are respectively. C This refers to the volumetric sediment content; due to the high density of sediment particles, their energy velocity... U = u + w s J ,in u The velocity is the kinetic energy velocity, which is the same as the water flow velocity. w s J Potential energy velocity; J For hydraulic gradient; in order to maintain the suspension of sediment, the turbulence surrounding the sediment particles should provide power to the sediment particles. W 1 (Work for sediment suspension) is: (8a) During the movement of sediment particles, the effective potential energy provided to the water flow due to the change in potential energy is: (8b) To maintain the suspension equilibrium of sediment per unit volume in a density current, the net power generated by turbulence per unit underwater weight of sediment particles is: W c ; (8a) For the entire water column, the average vertical volume can be obtained: W c = w s - UJ (8b) In the above formula J Available J b Instead; when suspended sediment particles in turbid water are in a self-suspended state, that is, in the theory of effective suspension work. W cWhen the ratio is 0, the suspended sediment particles are in a critical suspension state. UJ = w s This refers to the critical state in which density currents can maintain a suspended state and achieve long-distance sediment transport.

[0033] The one-dimensional accumulation depth model of the density flow is closed, as shown in equation (7). e w , e s , u * , β , w s Not yet determined; w s It can be represented as: (9) In the above formula Rp Particle Reynolds number . e w and e s They are respectively: (10) (11) In the above formula, Ri Richardson number (= RgCh / U 2 ); u * With vertical average turbulent kinetic energy ( K This can be represented as: (12) In the above formula α For the coefficient, it can be taken as 0.1; for the parameter β This can be obtained by considering that the turbulent kinetic energy is in a state of spatial equilibrium, that is: (13) In the above formula, the subscript * indicates a spatial equilibrium state; introducing the spatial equilibrium state... Ri * Then the above formula can be written as: (14) Furthermore, under spatial equilibrium, we can obtain from equation (7c): e s = C a ;when e s >C a At that time, the density current is in an accelerated state; when e s < C a At that time, the density current is in a state of extinction; when e s = C a At that time, the density current is in equilibrium; considering the critical effective suspension work ( W s =0), that is, there is w s* = U * J ,consider u * 2 = C f* U * 2 Substituting the above equation into equation (14) yields: (15) That is, when considering the critical effective suspension work, When a density flow is in a turbulent state, the dissipation value of the turbulence is always positive, meaning that the energy in the turbulence is converted into heat energy and dissipated through small-scale eddies. β It must be a positive value; under spatial equilibrium, from equation (7b), we can obtain: u * 2 = RgI 2 JCh ,Right now Ri * = C f* / I 2 J ,when Ri When =1, the density current is in a critical state; Ri When the value is greater than 1, the density flow is a subcritical flow or a slow flow; Ri When <1, the density flow is a supercritical flow or a rapid flow; substitute equations (9) to (15) into equation 7 and use the fourth-order Runge-Kutta method to solve it.

[0034] Step 4, Reservoir density current evolution processing: The calculation results of the one-dimensional depth model of the density flow are visualized using the self-similar theory. Based on the simulation results of the density flow in the reservoir, the one-dimensional depth velocity and sediment concentration are transformed into a two-dimensional density flow in the vertical plane according to the self-similar theory. The velocity and vertical distribution of the density flow from the ingress point to the front of the dam are calculated. The calculation results are displayed in a two-dimensional vertical plane. That is, the dimensionless mileage and water depth are multiplied by the water depth at the ingress point to obtain the actual distance from the dam and the change of water depth along the path. The dimensionless density flow velocity, sediment concentration, turbulent kinetic energy and layer thickness are multiplied by the relevant parameters at the ingress point. The velocity, sediment concentration and turbulent kinetic energy of the density flow are obtained by using equation (6) to obtain the distribution of velocity, sediment concentration and turbulent kinetic energy along the vertical line. Furthermore, the sediment concentration and sediment discharge ratio at the dam site can be obtained.

[0035] Example 1: The reservoir density current evolution calculation method based on the effective suspension work theory described in this invention is applied to the Xiaolangdi Reservoir as follows: S1, Collect actual measurement data on the topography and density currents in the Xiaolangdi Reservoir area: Based on the topography of the Xiaolangdi Reservoir area, data on slope, water surface width variation, and reservoir water level at the intrusion point were obtained. Based on actual density current measurement data from the Xiaolangdi Reservoir, the density current velocity, sediment concentration, layer thickness, and suspended particle size distribution characteristics at the intrusion section were obtained. The corresponding vertical average values ​​of the density current measurements at the downstream measurement section of the intrusion point were calculated, and dimensionless values ​​were obtained using the vertical average values ​​of the corresponding density current parameters at the intrusion point. For example, the average suspended sediment particle size at the density current intrusion point of the Xiaolangdi Reservoir in 2010 was... d s =0.031mm, slope J =0.0012, thickness of the density flow h 0 = 3.3m, average of perpendicular lines U =3.24m / s, vertical average volumetric sand content C 0 = 0.057, vertical average turbulent kinetic energy K 0 = 0.09m 2 / s 2 .

[0036] S2, the evolution of the density flow along the path is calculated by incorporating the effective suspension work theory: The data obtained in the first step were substituted into the reservoir density current evolution simulation. The calculation time was 0.1s. The calculation results and the measured results are as follows: Table 1 Comparison of Calculated and Measured Results of One-Dimensional Accumulation Depth Model for Nitrogen Flow Table 1 Comparison of Calculated and Measured Results of One-Dimensional Accumulation Depth Model for Nitrogen Flow S3, the calculation results are displayed in a two-dimensional elevation view: Using the dimensionless density current results obtained in step 2, such as dimensionless distance from the dam, dimensionless vertical average sediment concentration, and dimensionless vertical average velocity, these parameters are multiplied by the density current ingress point depth, vertical average sediment concentration, and vertical average velocity, respectively. Then, using the density current self-similarity theory, two-dimensional elevation results of the density current velocity and sediment concentration along the flow path are obtained. The inversion results of the sediment concentration distribution from the 2010 Xiaolangdi Reservoir density current theoretical model are shown below. Figure 6 As shown; the inversion results of the flow distribution of the density current theoretical model in Xiaolangdi Reservoir in 2010 are as follows. Figure 7 As shown.

[0037] Example 2: The reservoir density current evolution calculation method based on the effective suspension work theory described in this invention is applied to the Heishanxia Reservoir, which is planned but not yet built. The specific application process is as follows: S1, Obtain data on the topography and flood season dispatching patterns of the Heishanxia Reservoir: Obtain the topography of the Heishanxia Reservoir and its flood season operation mode; calculate the riverbed slope and water surface width at each measurement section under different reservoir water levels; and calculate the unit width discharge at each measurement section based on the flood season operation mode. q Analysis of sediment particle size distribution in the Heishanxia Reservoir bed and at relevant hydrological stations during floods.

[0038] S2, Calculation of the ingress point of the density current in the reservoir: Based on the slope, water surface width, and unit width flow rate at each measurement section obtained in step 1, and assuming different inflow sediment concentrations, the required water depth and the section where the density current intrusion point of the reservoir is located are calculated at different water levels.

[0039] S3, Calculation of reservoir density current intrusion characteristics: Based on the intrusion section determined in step 2, the thickness and vertical average velocity of the intrusion of the density current in the reservoir are calculated using the intrusion characteristics of the density current in the reservoir under different reservoir water levels and sediment concentrations.

[0040] S4, Simulation of the evolution of density current along the reservoir: Based on the slope, thickness of the density current after intrusion, average vertical velocity, average vertical sediment concentration, and average suspended sediment particle size at the cross section where the intrusion point is located, calculated in S1 and S3, the turbulent kinetic energy and drag coefficient are calculated. The above parameters are then substituted into the reservoir density current evolution simulation module to calculate the changes in density current velocity, sediment concentration, and layer thickness along the flow path.

[0041] S5, Calculate the sediment discharge ratio using reservoir density current evolution processing: The sediment flux at the dam site (sediment flux at the dam site = flow velocity × sediment concentration × thickness) is calculated based on different water levels and upstream sediment loads. The sediment discharge efficiency is the ratio of the sediment flux at the dam site to the upstream sediment flux (upstream sediment flux = flow rate × sediment concentration). Figure 8 The figure shows the distribution of sediment discharge efficiency under different reservoir water levels and upstream sediment inflows over 50 years of operation of the Heishanxia Reservoir. The figure indicates that when the upstream sediment inflow... S v0 =0.008, the highest sediment discharge efficiency is achieved when the reservoir water level is 1310m; this invention can provide reference for the scheduling and arrangement of the Heishanxia Reservoir and the layout of the sediment discharge tunnel.

Claims

1. A method for calculating the evolution of density currents in a reservoir based on the theory of effective suspension work, characterized in that, Includes the following steps: Step 1, Calculation of the ingress point of the density current in the reservoir: By processing reservoir topography and beach distribution data, the water surface width and water depth at the deep channel of each cross section in the reservoir area at the designated reservoir dam water level are determined, as well as the riverbed slope of the delta top section, front slope section, and dam front section in the reservoir area; then, the penetration depth of the density current in the reservoir at the designated reservoir water level is calculated, thus determining the cross section of the density current penetration point. Step 2, Calculation of reservoir density current intrusion characteristics: Based on the density flow velocity and density flow thickness calculated under uniform flow conditions, the density flow velocity and density flow thickness under different sediment concentration conditions are calculated according to different upstream water levels and ingress point cross sections. Step 3, Simulation of the evolution of the density current along the reservoir: A one-dimensional accumulation depth model of the density current in a reservoir was constructed using the control equations of density current, the theory of effective suspension work, and the theory of self-similarity. The parameters of the one-dimensional accumulation depth model were determined and the one-dimensional accumulation depth model was closed. The fourth-order Runge-Kutta method was used to solve the one-dimensional accumulation depth model. Step 4, Reservoir density current evolution processing: The calculation results of the one-dimensional accumulation depth model of the heterogeneous flow are visualized using the self-similarity theory.

2. The method for calculating the evolution of density currents in a reservoir based on the theory of effective suspension work as described in claim 1, characterized in that: The calculation of the ingress point of the density current in the reservoir includes calculating the location of the ingress point under different reservoir water level conditions based on the input topographic distribution data, upstream inflow, and inflow sediment concentration.

3. The method for calculating the evolution of density currents in a reservoir based on the theory of effective suspension work as described in claim 1, characterized in that: The simulation of the evolution of the density current along the reservoir combines the one-dimensional reservoir density current control depth equation, self-similar theory, and effective suspension work theory, and uses the fourth-order Runge-Kutta algorithm for solution calculation.

4. The method for calculating the evolution of density currents in a reservoir based on the theory of effective suspension work as described in claim 1, characterized in that: The reservoir density current evolution processing involves using self-similarity theory to obtain the sediment content and velocity distribution of the two-dimensional density current from the ingress point to the dam front using the one-dimensional density current motion results.

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