CN115994396A - Construction method of water system connected mathematical model - Google Patents
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Abstract
The invention discloses a construction method of a water system communication mathematical model, which comprises the steps of firstly constructing a one-dimensional river network water sand mathematical model basic equation, and specifically comprises a water flow continuous equation, a water flow motion equation, a sediment continuous equation, a river bed deformation equation, a river network branch of a river point continuous equation and a river network branch of a river point motion equation; and constructing a two-dimensional mathematical model for simulating the water level and water flow change of the neglected layered two-dimensional free surface flow, and solving a continuous equation and a momentum conservation equation of the dynamic flow by using a finite difference method of ADI second-order precision. By applying the technical scheme of the invention, the water level of the cave lake region under different flow levels can be verified, and the average value of the relative errors of the water level is calculated; the model does not consider the interference of natural or artificial factors such as rainfall, evaporation, surrounding farmland irrigation water taking, resident domestic water and the like, and certain errors exist between the calculated value and the measured value, but the overall coincidence condition of the calculated value and the measured value is good, so that the model can be used for hydrodynamic force calculation of the cave lake region.
Description
Technical Field
The invention relates to the fields of river channel remediation, water environment treatment and water ecological restoration, in particular to a construction method of a water system communication mathematical model.
Background
The main targets of river and lake water system communication work are as follows: through efforts for 10-20 years, areas such as water resource shortage, water ecology weakness, water environment deterioration and the like are taken as important points, the national, regional and urban level layout is gradually constructed, the functions are complete, engineering optimization is realized, the powerful river and lake water system communication patterns are guaranteed, and the water resource overall allocation capacity, the water supply safety guarantee capacity, the flood control, waterlogging and disaster reduction capacity, the water ecology environment protection capacity and the emergency guarantee capacity are obviously improved.
The key point of river and lake water system communication is as follows: the method has the advantages that the functional requirements of water resource allocation, flood control, disaster relief, water ecological environment restoration, protection and the like on the communication of different types of river and lake water systems are highlighted, the regional characteristics of the communication of the river and lake water systems in eastern, middle and west regions and northeast regions are accurately mastered, and the communication characteristics of different layers such as countries, regions, cities and rural areas are emphasized.
The Dongting lake area is located on the south of Yangtze river, and spans two provinces of Hunan provinces and Hubei provinces. The perimeter of the lake basin is 803.2 km. The current numerical simulation of hydrodynamic force developed for a certain water system communication project is well done, but for a complex river network consisting of a natural water system, an artificial channel and a gate dam group in a cave lake region, a set of numerical models of hydrodynamic force, water quality elements capable of comprehensively visualizing, transplanting, rapidly calculating and other requirements is not yet available, so that the problems of water system communication project planning, project implementation process monitoring, water system communication front-back comparison evaluation and the like in practical application are solved.
Disclosure of Invention
The invention provides a construction method of a water system communication mathematical model, which comprises the following specific technical scheme:
the construction method of the water system communication mathematical model comprises the following steps:
constructing a one-dimensional river network water and sand mathematical model basic equation, wherein the basic equation comprises a water flow continuous equation, a water flow motion equation, a sediment continuous equation, a riverbed deformation equation, a river network branch of a river point continuous equation and a river network branch of a river point motion equation:
water flow continuity equation:
equation of motion of water flow:
sediment continuity equation:
river bed deformation equation:
the continuity equation at branch of a river:
the equation of motion at point branch of a river generally uses the same water level at each confluent river reach end point at point branch of a river as an approximation, namely:
Z m，1 ＝Z m，2 ＝…＝Z m，L(m) ＝Z m m＝1，2，…，M 6)；
wherein: x is the flow (m); t is time(s); z is the water level (m); q is flow (m) 3 S); u is the average flow velocity of the section; a is the cross-sectional area of water (m) 2 ) The method comprises the steps of carrying out a first treatment on the surface of the B is river width (m); s is S f Is hydraulic gradient; q l Is the lateral output flow (m 3 S), negative values indicate inflow; u (u) l A component (m) in the main flow direction of the lateral outflow flow rate per unit flow; alpha 1 Is a momentum correction coefficient; alpha is the recovery saturation coefficient; alpha 2 Correcting coefficients for the sand content distribution; q ls The lateral sand conveying rate (kg/(s.m)) in unit flow; s is the section sand content (kg/m 3); s is S * Sand entrainment for section (kg/m 3); a is that d Is the area (m) of the river bed on the section 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Gamma' is the dry volume weight (kg/m) of the bed sand 3 ) The method comprises the steps of carrying out a first treatment on the surface of the M is the total number of branch of a river points in the river network, L (M) is the number of river segments connected with M,
for the 1 st river reach connected with branch of a river point m to flow into (or out of) the branch of a river th river reach, the flow is ∈>
For other inflow flows except the confluent river reach at branch of a river point m, omega m A water storage capacity of branch of a river points m;
a two-dimensional mathematical model is constructed for simulating the water level and water flow variation of the two-dimensional free surface flow neglecting layering, and the continuous equation and the momentum conservation equation of the dynamic flow are solved by using a finite difference method of ADI second-order precision.
Optionally, the building of the two-dimensional mathematical model is based on a shallow water equation of a two-dimensional numerical solution method, and uses a Navier-token equation as a numerical simulation calculation principle, wherein the two-dimensional shallow water equation set is as follows:
wherein: t-time; x, y, z-right hand Cartesian coordinate system; d, standing water depth; h=η+d—total water depth; η -water level; u, v, w—velocity component of flow velocity in x, y, z direction; f-Coriolis parameter, f=2Ω sin Φ; omega, phi-earth self-transmission angular rate, geographic dimension; ρ 0 -water density; p is p a -local atmospheric pressure;
-acceleration caused by earth rotation; s is(s) xx ，s xy ，s yx ，s yy -radiating stress components; t (T) xx ，T xy ，T yx ，T yy -a horizontal viscous stress term; s-source sink item; (u) s ，v s ) -source sink item water flow rate; bars represent average values, e.g.)>
Flow rate, which is the average depth, is defined as:
T ij is a horizontal viscous stress term, which is a vortex viscosity equation based on an average water depth flow velocity gradient:
by applying the technical scheme of the invention, the water level of the cave lake region under different flow levels can be verified, and the average value of the relative errors of the water level is calculated; the model does not consider the interference of natural or artificial factors such as rainfall, evaporation, surrounding farmland irrigation water taking, resident domestic water and the like, and certain errors exist between the calculated value and the measured value, but the overall coincidence condition of the calculated value and the measured value is good, so that the model can be used for hydrodynamic force calculation of the cave lake region.
Drawings
FIG. 1 is a schematic diagram of a great-pass lake connected water system in an embodiment of the invention;
FIG. 2 is a schematic view of a great-flux lake water grid and a great-flux lake water depth planar topography, specifically: FIG. 2 (a) shows a Datong lake water grid, and FIG. 2 (b) shows a Datong lake deep planar topography;
FIG. 3 shows the distribution of observation points of the Datong lake;
FIG. 4 is a graph of water level change under each scheduling scheme of Datong lake;
FIG. 5 is a graph of flow rate variation for each scheduling scheme for Datong lakes;
fig. 6 is a schematic diagram of a great lake outlet flow velocity point position, an initial average flow velocity, an average flow velocity when the outlet output flow rate and an average flow velocity when the water body is stable, specifically: (a) outlet flow rate point location (b) initial average flow rate (c) average flow rate when outlet output flow (d) average flow rate when water body is stable.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making clear and unambiguous the scope of the present invention.
Examples:
a construction method of a water system communication mathematical model, in particular to a water system communication project of a Datong lake area, comprising the following steps:
constructing a one-dimensional river network water and sand mathematical model basic equation, wherein the basic equation comprises a water flow continuous equation, a water flow motion equation, a sediment continuous equation, a riverbed deformation equation, a river network branch of a river point continuous equation and a river network branch of a river point motion equation:
water flow continuity equation:
equation of motion of water flow:
sediment continuity equation:
river bed deformation equation:
the continuity equation at branch of a river:
the equation of motion at point branch of a river generally uses the same water level at each confluent river reach end point at point branch of a river as an approximation, namely:
Z m，1 ＝Z m，2 ＝…＝Z m，L(m) ＝Z m m＝1，2，…，M 6)；
wherein: x is the flow (m); t is time(s); z is the water level (m); q is flow (m) 3 S); u is the average flow velocity of the section; a is the cross-sectional area of water (m) 2 ) The method comprises the steps of carrying out a first treatment on the surface of the B is river width (m); s is S f Is hydraulic gradient; q l Is the lateral output flow (m 3 S), negative values indicate inflow; u (u) l A component (m) in the main flow direction of the lateral outflow flow rate per unit flow; alpha 1 Is a momentum correction coefficient; alpha is the recovery saturation coefficient; alpha 2 Correcting coefficients for the sand content distribution; q ls The lateral sand conveying rate (kg/(s.m)) in unit flow; s is the section sand content (kg/m) 3 )；S * To the sand-carrying capacity of the section (kg/m) 3 )；A d Is the area (m) of the river bed on the section 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Gamma' is the dry volume weight (kg/m) of the bed sand 3 ) The method comprises the steps of carrying out a first treatment on the surface of the M is the total number of branch of a river points in the river network, L (M) is the number of river segments connected with M,
for the 1 st river reach connected with branch of a river point m to flow into (or out of) the branch of a river th river reach, the flow is ∈>
For other inflow flows except the confluent river reach at branch of a river point m, omega m A water storage capacity of branch of a river points m; />
A two-dimensional mathematical model is constructed for simulating the water level and water flow variation of the two-dimensional free surface flow neglecting layering, and the continuous equation and the momentum conservation equation of the dynamic flow are solved by using a finite difference method of ADI second-order precision.
In this embodiment, the two-dimensional mathematical model is built on the basis of a shallow water equation of a two-dimensional numerical solution method, and a Navier-token equation is used as a numerical simulation calculation principle, and a two-dimensional shallow water equation set is as follows:
wherein: t-time; x, y, z-right hand Cartesian coordinate system; d, standing water depth; h=η+d—total water depth; η -water level; u, v, w—velocity component of flow velocity in x, y, z direction; f-Coriolis parameter, f=2Ω sin Φ; omega, phi-earth self-transmission angular rate, geographic dimension; ρ 0 -water density; p is p a -local atmospheric pressure;
-acceleration caused by earth rotation; s is(s) xx ，s xy ，s yx ，s yy -radiating stress components; t (T) xx ，T xy ，T yx ，T yy -a horizontal viscous stress term S-a source sink term; (u) s ，v s ) -source of originSink water flow rate; bars represent average values, e.g.)>
Flow rate, which is the average depth, is defined as:
T ij is a horizontal viscous stress term, which is a vortex viscosity equation based on an average water depth flow velocity gradient:
the specific application cases are as follows:
1. study area overview
The inland river lake water system of the Datong lake is various and mainly comprises the Datong lake, the tile sentry lake, the Wuqi river, the Jinshen river, the Saiyang canal and other river lakes. The Datong lake is located in the middle of the cave lake region and is the largest inland freshwater lake in the region, and is shown in figure 1. The east-west length of the lake surface reaches 15.75km, the north-south width is 13.7km, the lake surface is triangular, the area of the lake surface reaches 89.9km2, and the average water depth is 2.5m. The water level of Datong lake is controlled between 25.28m and 27.08m by adopting the national elevation reference plane of 1985.
1.1 model building
According to the actual condition of the model, the inlet boundary adopts a flow boundary, is set at the position where the fixed ecological water quantity is introduced from the grass tail river into the five-seven canal by the five-seven sluice, and the outlet boundary is set at the big east sluice, and mainly aims at controlling the water level of the big ventilation lake, so that the water level boundary is adopted. Because the large-pass lake area is large, a long time is required from diversion to overall water level stabilization according to the model simulation result, so the simulation step length is set to 600s, and the simulation step number is 25380 steps.
The water level flow data are set according to various working conditions by referring to a preliminary design report of a five-seven-river first-period treatment project in Hunan province; since the great general lake minimum water level is 25.28m, the initial water level is set to 25.28m, and it is assumed that the entire simulation area starts from a stationary condition, i.e., the initial flow rate is 0; the terrain of the great general lake is flat, no boulder exists at the bottom, the roughness is set to be 0.03 according to the condition of the lake bottom, the soil condition adopted by the bottom of a river newly revised by the five-seven canal in engineering planning is considered, the final roughness of the five-seven canal is set to be 0.02, the plug Yang He is set to be 0.046, and the Jin Penhe is set to be 0.036; the vortex viscosity coefficient is calculated by adopting a Smogorinsky formula, and the value of Cs is 0.28; to prevent the model from overflowing in the dry area, the dry water depth was set to 0.01m and the wet water depth was set to 0.1m in the dry and wet judgment (fig. 2).
Because of the engineering case implemented by the case source and the lack of measured data, the measured data of the document [2] is selected to model the part not implemented by the engineering case source.
Selecting 2 observation points as shown in FIG. 3, taking the measured water level data of the two points as inlet and outlet boundary control water levels respectively, inputting actual flow data as boundary conditions of the actual flow data into the model after the inlet and outlet water levels are determined, and taking the flow of 3.9m 3 And/s, and correcting the roughness value of a part of river channels to obtain the flow velocity of the two points in water body stability theoretically, and comparing the flow velocity with the actually measured flow velocity of the two points, wherein the comparison result is shown in Table 1.
TABLE 1 comparison of flow simulation and actual measurement
| Observation point serial number | Measured water level/m | Actual measurement value of flow velocity V (m/s) | Flow velocity analog value V (m/s) | Relative error/% |
| 1 | 26.50 | 0.07 | 0.0732 | 4.5 |
| 2 | 26.49 | 0.10 | 0.0976 | 2.4 |
Because the water is mainly drained through the five-seven gate drainage in the flood season, the water is drained through the five-seven canal coastal pump gate, and the flow change is not single, the influence of the engineering on the water system connectivity in the flood season of the great-pass lake is considered.
According to the planning of the five-seven canal management engineering, the water level of the connected great-pass lake in the flood season is controlled to be 25.48-26.08m.
The influence of each runoff and other pump stations, electric rows and gates is not considered in the non-flood period, and the maximum water diversion quantity of the five-seven gates is 28.92m 3 And/s, setting three diversion flows of 10m respectively according to the ecological water quantity required by the great lake in the non-flood period, wherein the five-seven gates are respectively arranged 3 /s、20m 3 /s、30m 3 And/s, controlling the outlet water level of the big east to be 25.48m and 26.08m respectively (table 2).
TABLE 2 different conditions of hydrodynamic simulation
1.2 analysis of simulation results
Through simulation calculation, 7 points uniformly distributed in the Datong lake are selected for water level analysis. Because the great lake is large and the internal flow rate change is not obvious, 6 points of the outlet section of the gold basin river are selected for flow rate analysis, and the average water level and the average flow rate under various working conditions in the flood season are calculated.
The water level in the water diversion period is raised to a certain height along with the increase of the communication time and then is in a stable state (figure 4). Before stabilization, water automatically flows from the five-seven canal to the great-passage lake to raise the water level, the water level in the early stage is raised faster, the output flow starts when the water level is controlled, and the water level at the outlet of the great-passage lake is limited between 25.48 and 26.08m by a great-east gate at the outlet of the golden basin. Because the water body is kept in a flowing state all the time, when the water level of the Datong lake is in balance, the water level difference between the water level of the lake area and the water level of the outlet is between 0.13 and 0.61 m. Excluding intermediate errors, the slope of the water level-time curve is 0, which is considered to be fluid stable.
Considering the communication dynamics, the fluid stability from the start of water diversion to the time when the slope of the curve of fig. 4 is 0 is regarded as the communication time. The later water level is still raised with a very small amplitude until it eventually stabilizes, which is in part negligible due to the small lifting amount of ten-thousandths. In the process that the fluid tends to be stable, the total amount of inflow water and the total amount of outflow water are different, and the total amount of inflow water and the total amount of outflow water of the fluid are basically consistent during the stability, and the water changing efficiency in the fluid stabilization process is mainly considered.
The fluid takes a certain time to draw water from the fifth and seventh canals to the great general lake, the initial flow rate of water diversion is almost 0m/s (fig. 6 (b)), and the flow rate begins to increase when the water body flows through the outlet. During the period, when the water level in the great lake is raised and the section is unchanged, the flow speed is in a sharp increasing state. When the lake water level reaches the control water level, the output flow rate of the outlet (fig. 6 (c)) is reduced, the flow rate increasing speed is reduced in the process that the difference value between the water diversion amount and the water yield is gradually reduced, the flow rate reaches the maximum value when the water diversion amount and the water yield are equal (fig. 6 (d)), and the average flow rate at the moment can be regarded as the water changing efficiency. When the water reaches an equilibrium state, the water flow rate basically tends to be stable, and the flow rate change trend under various diversion conditions is basically consistent. The larger the diversion flow rate, the earlier the flow rate tends to stabilize under the condition that the section is unchanged, and the larger the flow rate is during stabilization (figure 5).
Under the condition that the control water levels of the outlets of the large-pass lakes in the non-flood period are the same, the time required for the communication to stabilization is shortened along with the increase of the diversion flow, the water level of the large-pass lakes in the stabilization is increased, the average flow velocity of the outlets is obviously increased, and the water changing efficiency is improved. Compared with working conditions 1 and 4, 2 and 5, and 3 and 6, the diversion flow is the same, when the control water level of the outlet of the big east is 26.08m, the water level of the big general lake is higher in the stable state, but when the control water level is 25.48m, the average flow velocity at the outlet is larger in the stable state. The difference in water level at the outlet had a slightly smaller effect on water efficiency at the time of stabilization than the diversion flow, and the difference was 6.68%, 29.84%, 35.56%, respectively, and this difference became more remarkable as the diversion flow was increased (table 3).
TABLE 3 mean water level and mean flow rate at stability under different conditions
The foregoing description is only illustrative of the present invention and is not intended to limit the scope of the invention, and all equivalent structures or equivalent processes or direct or indirect application in other related technical fields are included in the scope of the present invention.
Claims (2)
1. The construction method of the water system communication mathematical model is characterized by comprising the following steps of:
constructing a one-dimensional river network water and sand mathematical model basic equation, wherein the basic equation comprises a water flow continuous equation, a water flow motion equation, a sediment continuous equation, a riverbed deformation equation, a river network branch of a river point continuous equation and a river network branch of a river point motion equation:
water flow continuity equation:
equation of motion of water flow:
sediment continuity equation:
river bed deformation equation:
the continuity equation at branch of a river:
the equation of motion at point branch of a river generally uses the same water level at each confluent river reach end point at point branch of a river as an approximation, namely:
Z m,1 ＝Z m,2 ＝…＝Z m,L(m) ＝Z m m＝1,2,…,M 6)；
wherein: x is the flow (m); t is time(s); z is the water level (m); q is flow (m) 3 S); u is the average flow velocity of the section; a is the cross-sectional area of water (m) 2 ) The method comprises the steps of carrying out a first treatment on the surface of the B is river width (m); s is S f Is hydraulic gradient; q l Is the lateral output flow (m 3 S), negative values indicate inflow; u (u) l A component (m) in the main flow direction of the lateral outflow flow rate per unit flow; alpha 1 Is a momentum correction coefficient; alpha is the recovery saturation coefficient; alpha 2 Correcting coefficients for the sand content distribution; q ls The lateral sand conveying rate in unit flow (kg/(s.m)); s is the section sand content (%/m) 3 )；S * To the sand-carrying capacity of the section (kg/m) 3 )；A d Is the area (m) of the river bed on the section 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Gamma' is the dry volume weight (kg/m) of the bed sand 3 ) The method comprises the steps of carrying out a first treatment on the surface of the M is the total number of branch of a river points in the river network, L (M) is the number of river segments connected with M,
for the first river reach connected to point branch of a river m, the flow to (or from) point branch of a river is->
For other inflow flows except the confluent river reach at branch of a river point m, omega m A water storage capacity of branch of a river points m;
a two-dimensional mathematical model is constructed for simulating the water level and water flow variation of the two-dimensional free surface flow neglecting layering, and the continuous equation and the momentum conservation equation of the dynamic flow are solved by using a finite difference method of ADI second-order precision.
2. The method for constructing a water system connected mathematical model according to claim 1, wherein the construction of the two-dimensional mathematical model is based on a shallow water equation of a two-dimensional numerical solution method, and uses a Navier-token equation as a numerical simulation calculation principle, and the two-dimensional shallow water equation set is as follows:
wherein: t-time; x, y, z-right hand Cartesian coordinate system; d, standing water depth; h=η+d—total water depth; η -water level; u, v, w—velocity component of flow velocity in x, y, z direction; f-Coriolis parameter, f=2Ω sin Φ; omega, phi-earth self-transmission angular rate, geographic dimension; ρ 0 -water density; p is p a -local atmospheric pressure;
-acceleration caused by earth rotation; s is(s) xx ,s xy ,s yx ,s yy -radiating stress components; t (T) xx ,T xy ,T yx ,T yy -a horizontal viscous stress term; s-source sink item; (u) s ,v s ) -source sink item water flow rate; bars represent average values, e.g.)>
Flow rate, which is the average depth, is defined as:
T ij is a horizontal viscous stress term, which is a vortex viscosity equation based on an average water depth flow velocity gradient:
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| CN116362162B (en) * | 2023-05-30 | 2023-08-01 | 湖南百舸水利建设股份有限公司 | Underwater high-concentration sludge conveying method, system, computer equipment and storage medium |
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