CN107816009A - A kind of universal method for inquiring into multistage compound cross-section stage discharge relation - Google Patents
A kind of universal method for inquiring into multistage compound cross-section stage discharge relation Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
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- E02B—HYDRAULIC ENGINEERING
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Abstract
The present invention proposes a kind of universal method for inquiring into multistage compound cross-section stage discharge relation, comprises the following steps：The measurement data of target section is obtained, section is divided into M+N+1 sub- sections, and be further classified as 7 class components；Resistance division f is carried out to each sub- sectionk=fbk+fvk, wherein fvk=4 λkCDDkmkhkFor resistance coefficient caused by vegetation towing, the Manning coefficient of each sub- section of calculatingThe apparent shear stress of each element is calculated, the momentum balance relation of each sub- section is established, so as to obtain the matrix equation of tridiagonal coefficient matrix；Using " chasing method " solution matrix equation, the mean velocity in section of each sub- section is obtained, and then obtain the stage discharge relation of the section.Method proposed by the present invention has unified expression formula, it is easy to be calculated using Excel or programming, the stage discharge relation for all multistage compound cross-sections that can be applied to including two level compound cross-section is inquired into, and is the computational methods that a kind of calculating is easy but precision is high.
Description
Technical Field
The invention belongs to the technical field of hydraulic engineering, and particularly relates to a general method for calculating a multistage compound section water level flow relation.
Background
In order to adapt to the bed-making function of different flow rates, most of natural rivers are two-stage or multi-stage compound sections. In addition, urban rivers are also often designed into two-stage or multi-stage compound sections to reduce the impact of flood control measures on the landscape of river galleries and to increase the hydrophilic space for coastal residents. The compound section usually consists of a deep main trough which serves as a transport channel during dry periods and one or more relatively shallow beaches which serve as flood channels only when flood flow occurs during flood periods. Because the section is discontinuous, the beach is usually covered by vegetation, the roughness is larger than that of the main tank, and the flow velocity of the main tank is usually larger than that of the beach, so momentum exchange exists between the beach tanks. Momentum exchange between the beaches can increase water flow resistance, and further reduce the flow capacity of the cross section. Therefore, the computation methods such as the single section method and the section division method, which do not consider the momentum exchange between the beaches, cannot accurately calculate the water level flow relationship of the compound section. Therefore, many scientific and technological workers are dedicated to research on the complex cross-section water level flow relation calculation method, and a plurality of calculation methods with high precision are proposed, and are roughly divided into three categories, namely a hydraulics method (such as an apparent stress method, a zero stress interface method and the like), a statistical method (such as a multiple regression model and the like) and an artificial intelligence method (such as an artificial neural network, a genetic algorithm and the like). However, these methods are proposed for two-stage compound cross sections, and little attention is paid to a calculation method of the water level flow relationship of multi-stage compound cross sections.
In the flood control management of natural rivers, a water level flow relation is quickly and accurately established, and a flood level and a corresponding flood area under the peak flow can be forecasted, so that a reasonable and effective flood defense strategy can be adopted. In the engineering design of urban river regulation, establishing a water level flow relation is the basis for section design, particularly for determining key parameters such as main groove depth, beach land width, greening scheme (such as tree diameter, vegetation density and the like) and the like by comparison and selection. Therefore, in order to reasonably manage the river, a calculation method for deducing the multi-stage compound cross-section water level flow relationship is urgently needed.
Disclosure of Invention
The invention aims to provide a general method for calculating the water level and flow relationship of a multi-level compound cross section, which can conveniently, quickly and accurately calculate the water level and flow relationship of the multi-level compound cross section including a two-level compound cross section. The method is realized by the following technical scheme.
The invention provides a calculation method, in particular to a general method for calculating the water level flow relation of a multi-stage compound section, aiming at solving the technical problems, the technical scheme adopted by the invention is as follows:
step 1: and (4) analyzing the geometric dimension of the target section. Acquiring section measurement data (X) of a target section i ，Z i )(i＝1,2,…，K)，X i From the ith point to the cross section starting point X 1 Distance of, Z i As the elevation of the point, K is the section measuring pointThe number of (2); selecting points with obvious elevation change, dividing the cross section into M + N +1 sub-sections (as shown in figure 1) by vertical lines passing through the points, wherein the sub-section with the largest water depth is called a main trough, the rest are called beaches, M is the number of the beaches (sub-sections) on the left side of the main trough, N is the number of the beaches (sub-sections) on the right side of the main trough, M and N are natural numbers, and M + N is more than or equal to 1. And sequentially marking the sub-sections K (K is more than or equal to 1 and less than or equal to K-1) from the starting point side. The sub-section (k = M, M + 2) adjacent to the main groove is called a first-level beach, the bed surface elevation is called a first-level beach water depth, the sub-section (k = M-1, M + 3) adjacent to the first-level beach is called a second-level beach, the bed surface elevation is called a second-level beach water depth, and the like. Reading the width b of each sub-section k Step height d k Slope of beach land side slope, slope of left side slope of main trough S Lk And the slope S of the right side slope of the main groove Rk As in fig. 1.
Step 2: the Mannich coefficient of each fraction was determined. The Mannich roughness coefficient of the section k was calculated using the following formula:
in the formula: n is k The Manning roughness coefficient of the sub-section k; r k The hydraulic radius of the sub-section k is obtained by dividing the area of the sub-section k by the wet circumference of the sub-section; g is the acceleration of gravity, typically taken to be 9.81m/s 2 ；f k The total Darcy-Weisbach drag coefficient for the sub-section k. Since a vegetation density of 0 can be used to define a vegetation-free condition, the Darcy-Weisbach drag coefficient is composed of the drag coefficient due to the drag of vegetation and the bed-surface friction resistance according to the additivity principle, i.e.
f k ＝f bk +f vk (2)
In the formula: f. of bk The bed surface Darcy-Weisbach resistance coefficient, f of the sub-section k vk Drag coefficient due to drag of vegetation on sub-section k
f vk ＝4λ k C D D k m k h k (3)
In the formula: d k Is the diameter of the plant on the sub-section k; h is k Is the water depth of the sub-section k; m is k Is the number of plants per unit area on the sub-section k, i.e. the vegetation density, which for regularly planted plants is the reciprocal of the product of the row spacing and the plant spacing, i.e. m k ＝1/(L xk L yk )，L xk 、L yk The row spacing and the plant spacing of plants on the sub-section k; c D The drag force coefficient of the vegetation; lambda k In order to consider the correction coefficient of the vegetation inundation degree, the calculation formula is as follows:
wherein: s Dk The inundation degree of the vegetation on the sub-section k is defined as:
in the formula: h is a total of v The height of the plant on the sub section k;
and step 3: the elemental composition of the target section is identified. Any of the multiple levels of the compound cross-section can be constructed from the elements of figure 2. For example, the cross-section shown in FIG. 1 consists of 1 element I, M-1 element VI, 1 element IV, N-1 element VII, and 1 element II, with M + N +1 base elements. According to the specific situation of dividing the sub-sections of the target section, the elements corresponding to the sub-sections are selected in a contrast manner in fig. 2. The cross-sectional area A of each constituent element was calculated according to Table 1 k Wet week P k And hydraulic radius R k And determining the height h of the left and right side interfaces Lk And h Rk 。
TABLE 1 Hydraulic parameters of the elements constituting the multilevel complex section
And 4, step 4: and calculating an apparent shear stress coefficient. Apparent shear stress is adopted to measure momentum exchange between adjacent elements, and the calculation formula is
In the formula:respectively is the apparent shear stress between the sub-section k and the left sub-section k-1 and the right sub-section k +1; ρ is the density of water; h is a total of Lk ，h Rk The height of the interface of the sub-section k, the left sub-section k-1 and the right sub-section k +1 is shown; u. of k-1 ,u k ,u k+1 The average flow rate of the sub section k-1, k +1; xi k，k-1 ，ξ k，k+1 Respectively, the apparent shear stress coefficients of the sub-section k, the left sub-section k-1 and the right sub-section k + 1. The research of the second-level compound fracture surface shows that the value of the apparent shear stress coefficient is related to the relative water depth, the relative width, the relative roughness and the width-depth ratio of the main groove between the adjacent sub fracture surfaces. For a multi-stage compound section, j-stage flat beach water depth is used as a boundary (the left beach j = M-k +1 and the right beach j = k-M-1 of the main trough), the part below the depth is regarded as a new main trough, the part above the depth is regarded as a new edge beach (see figure 1 in detail), and the apparent shear stress coefficient is estimated by adopting a formula (7)
Wherein: r is an intermediate variable; h is the water depth of the new main tank; b is the width of the left part of the canal (comprising a half of the main channel and all the beaches on the left side); b is Mr The total width of the new main slot; h is r The water depth of the new beach; dr is the beach water depth of the new edge beach; n is a radical of an alkyl radical r The comprehensive roughness coefficient of the new edge beach; n is a radical of an alkyl radical r+1 The comprehensive roughness coefficient of the new main groove is obtained; psi is a proportionality coefficient related to section symmetry and vegetation. For vegetation-free symmetrical compound sections, psi =4.5 × 10 -4 (ii) a For an asymmetric compound cross-section without vegetation,ψ＝6.3×10 -4 (ii) a For symmetrical compound cross section of vegetation on beach land, psi =1.0 × 10 -4 (ii) a For asymmetric compound section with vegetation on beach, psi =1.4 × 10 -4 。
And 5: and calculating a coefficient matrix. Measuring and determining longitudinal slope gradient S of river reach 0 And respectively calculating the following parameters of each sub-section according to the element composition of the identified target section:
wherein: i is k ,J k ,X k ,Y k For calculated intermediate variables, n k ,R k ,ξ k,k-1 ,ξ k,k+1 ,h Lk ,h Rk And g has the same meaning as above.
The apparent shear stress is proportional to the difference in flow velocity squared between the sub-sections. Recording the direction coefficients of apparent shear stress between the sub-section k and the adjacent sections on the left and right sides of the sub-section k as alpha k And beta k 。α k And beta k Taking values between-1, 0 and 1, and determining the values in the following three cases: (1) for a sub-section with a large flow velocity, the apparent shear stress is the resistance of the sub-section, namely the direction of the apparent shear stress is opposite to the direction of the gravity along the flow direction component, and the direction of the apparent shear stress is expressed as + 1'; (2) for the sub-section with smaller flow velocity, the apparent shear stress between the sub-section and the adjacent sub-section is dynamic, namely the direction of the apparent shear stress is the same as the direction of the gravity along the flow direction component, and the sub-section is expressed as "-1"; (3) for a side without adjacent sub-sections, this is indicated as "0". According to the above definition, 7 elements α shown in FIG. 2 k And beta k The values of (A) are shown in Table 1. When the method provided by the invention is used, after the element types of the sub-sections are identified, the values of alpha and beta can be determined according to the table 1. For example, when the section k belongs to the element IV, from Table 1, α k ＝1，β k =1; when the section k belongs to the element V, from Table 1, α k ＝1，β k =0, and so on.
According to the structure of the target section, the direction coefficient of apparent shear stress of each sub-section is determined in turn according to the table 1, and the following parameters are calculated
a k ＝α k X k ,b k ＝I k -α k X k -β k Y k ,c k ＝β k Y k (9)
Step 6: and establishing a matrix equation. For a multi-level complex section as shown in FIG. 1, solving the matrix to be a tri-diagonal matrix has elements of
ΦX＝J (10)
In the formula:is a flow velocity matrix; j = (J) 1 J 2 ... J M+N+1 ) T Is a momentum matrix; coefficient matrix with three diagonal phi
And 7: solving the formula (11) by adopting a pursuit method to obtain the average flow velocity u of each sub-section k Are multiplied by the corresponding sub-sectional areas A respectively k To obtain the flow Q of each sub-section k . Calculating the total flow Q of the target cross section according to the total flow equation, i.e.
Q＝AU T (12)
In the formula: u = (U) 1 u 2 … u M+N+1 ) T ,A＝(A 1 A 2 … A M+N+1 ) T 。
The invention has the advantages that:
compared with the prior art, the invention has the following advantages and effects: 1) The multistage compound cross section is divided into a plurality of sub cross sections along the vertical direction, any sub cross section and the boundary condition of the adjacent sub cross sections are divided into 7 categories, and any multistage compound cross section can be formed by 7 elements through a method of building blocks, so that the method provided by the invention can be applied to all multistage compound cross sections (including the two-stage compound cross sections); 2) The method provided by the invention fully considers the actual situation that the beach is generally covered by plants when calculating the Manning resistance coefficient, adopts the vegetation submergence correction coefficient to consider the variation of the vegetation additional resistance coefficient along with the fluctuation of the water level, and improves the calculation precision; 3) The method provided by the invention has a uniform expression, and is convenient for calculation by adopting Excel or programming; 4) Compared with the traditional methods such as a single section method, a section segmentation method and the like, the calculation method has higher calculation precision, and compared with a two-dimensional or three-dimensional hydraulics method and an artificial intelligence method, the required time (including the time for preparing input data) and the consumed manpower and material resources are less, so that the calculation method is simple and convenient in calculation and high in precision.
Drawings
FIG. 1 is a schematic diagram of a multi-stage compound section division of the method of the present invention;
FIG. 2 is a schematic diagram of the elements of a multi-stage compound cross section of the process of the present invention;
FIG. 3 is a schematic two-stage symmetrical compound cross-section of the beach of example 1 with no vegetation;
FIG. 4 is a water level/flow relationship of embodiment 1, which is obtained by the method of the present invention;
FIG. 5 is a schematic three-level asymmetric compound cross-section of the beach area with vegetation in example 2;
fig. 6 shows the relationship between water level and flow rate in example 2, which is obtained by the method of the present invention.
Detailed Description
Example 1
A symmetrical compound section (as shown in figure 3) with a section without vegetation on the beach, and a main groove bottom width b m =0.75m, groove depth d =0.15m, slope coefficient S =1, width of the beach b f =2.25m, the main trough and the beach are all made of concrete linings and are relatively smooth, the bed ratio of the river reach where the section is located is reduced to 1.027 ‰, and the water level flow of the section is calculatedAnd (4) relationship.
The steps of adopting the technical scheme of the invention to calculate the water level flow relation of the section are as follows:
step 1, selecting points C and F, dividing the section into 3 sub-sections along the vertical direction, and sequentially marking k =1,2,3, then b 1 ＝b 3 ＝2.25m，b 2 ＝1.50m，d 1 ＝d 3 ＝0.15m。
Step 2, the main trough and the beaches at the two sides of the main trough are relatively smooth and have no vegetation cover, namely m is taken k =0, and the Manning roughness coefficients of 3 sub-sections are all 0.010s/m 1/3 I.e. n 1 ＝n 2 ＝n 3 ＝0.010s/m 1/3 。
And 3, according to the sub-sections obtained by division, the sections are composed of 1 element I, 1 element IV and 1 element II, namely the elements of the target sections are I + IV + II. Depth of water h of current sub-section 2 (main trough) 2 When d =0.15m or less, all the water flow is conveyed by the main tank, the water level flow relation is directly calculated by a Manning formula, and when H is less than or equal to d =0.15m&At 0.15, the waterflow flood plain is a compound section, the water depth H is sequentially increased by 0.01m or 0.02m, and the section area A of each sub-section is calculated according to the table 1 k Wet week P k And hydraulic radius R k . From Table 1, it is determined that the sub-section 2 belongs to the element IV, and the heights of the sub-section interfaces with the left and right sub-sections are h L2 ＝h 2-1 ＝h 1 ，h R2 ＝h 2+1 ＝h 3 The calculation results are shown in Table 2.
Table 2 shows the calculation procedure and results of the present invention used in example 1
| H(m) | 0.160 | 0.170 | 0.180 | 0.190 | 0.200 | 0.220 | 0.240 | 0.260 | 0.280 | 0.300 |
| h 1 (m) | 0.010 | 0.020 | 0.030 | 0.040 | 0.050 | 0.070 | 0.090 | 0.110 | 0.130 | 0.150 |
| A 1 (＝A 3 )(m 2 ) | 0.041 | 0.082 | 0.123 | 0.164 | 0.205 | 0.287 | 0.369 | 0.451 | 0.533 | 0.615 |
| A 2 (m 2 ) | 0.266 | 0.284 | 0.302 | 0.320 | 0.338 | 0.374 | 0.410 | 0.446 | 0.482 | 0.518 |
| h L2 (＝h R1 ＝h R2 ＝h L3 )(m) | 0.010 | 0.020 | 0.030 | 0.040 | 0.050 | 0.070 | 0.090 | 0.110 | 0.130 | 0.150 |
| ξ 12 (＝ξ 21 ＝ξ 23 ＝ξ 32 ) | 0.082 | 0.044 | 0.031 | 0.024 | 0.021 | 0.016 | 0.014 | 0.012 | 0.011 | 0.010 |
| Q 1 (＝Q 3 )(m 3 /s) | 0.008 | 0.023 | 0.042 | 0.065 | 0.097 | 0.170 | 0.261 | 0.348 | 0.460 | 0.595 |
| Q 2 (m 3 /s) | 0.196 | 0.210 | 0.226 | 0.247 | 0.264 | 0.309 | 0.361 | 0.497 | 0.526 | 0.578 |
| Q(m 3 /s) | 0.211 | 0.255 | 0.310 | 0.378 | 0.459 | 0.649 | 0.884 | 1.193 | 1.446 | 1.769 |
And 4, step 4: and calculating the apparent shear stress coefficient. The section beach is symmetrical and has no vegetation cover, so the proportionality coefficient psi =4.5 × 10 -4 Let j =1 (only one step), the apparent shear stress coefficient is solved by equation (7). According to xi 21 And xi 23 The water depth H varies, and the values thereof are shown in table 2.
And 5: and calculating a coefficient matrix. Longitudinal slope gradient S of target section 0 ＝1.027×10 -3 Respectively calculating I from the formula (8) k ，J k 、X k And Y k . From the elemental composition of the identified target section, the orientation coefficients of the various sub-sections are determined from table 1: subface 1 (element I): alpha is alpha 1 ＝0，β 1 = -1; subface 2 (element IV): alpha is alpha 2 ＝1，β 2 =1; subface 3 (element II): alpha (alpha) ("alpha") 3 ＝-1，β 3 And =0. A is calculated from the formula (9) k 、b k And c k 。
Step 6: and establishing a matrix equation. And (5) establishing a matrix equation according to the three-diagonal coefficient matrix phi obtained by calculation in the step 5.
And 7: solving the formula (A2) by adopting a 'catch-up method' to obtain the average flow velocity u of each sub-section k Are multiplied by the corresponding cross-sectional areas A respectively k To obtain the flow Q of each sub-section k . Calculating the total flow Q of the target section according to a total flow equation,see table 2 and fig. 4 for details.
FIG. 4 is a water level flow relationship of the cross section of the embodiment 1, which is obtained by applying the method provided by the present invention, and the calculation result is verified by using the actually measured data, which indicates that the calculation accuracy of the present invention is high.
Example 2
A river is an asymmetric compound section with three levels and the beach land is covered by vegetation, and is shown in figure 5. The total width of the target section is 100m, wherein the width of the second-level beach is b 1 =25m, step height d 1 =1.4m, first-level edge width b 2 =25m, step height d 2 =1.0m, main slot width b 3 =50m, and the slope coefficients are all 0. Rigid vegetation is regularly planted on the second-level beach land, the height of plants is 1.2m, the diameter is 0.06m, the row spacing is 0.25m, the plant spacing is 0.5m, the river bed ratio of a river reach where the section is located is 0.4 per thousand, and the water level flow relation of the section is calculated.
The steps of adopting the technical scheme of the invention to calculate the water level flow relation of the cross section shown in the embodiment 2 are as follows:
step 1: selecting points C and E, dividing the target section into 3 sub-sections along the vertical direction, sequentially marking k =1,2,3, and then b 1 ＝b 2 ＝25m，b 3 ＝50m，d 1 ＝13.6m，d 2 ＝10.6m。
Step 2: all the beach lands are covered by vegetation cover h v ＝1.2m，D＝0.06m，L x ＝0.25m，L y =0.5m, vegetation density m 1 ＝m 2 =1/0.25/0.5=8, the main trough is not covered by vegetation, i.e. m 3 And =0. The roughness of the beach according to equation (4) increases with the rise of the water level, and the roughness of the beach at different water levels is detailed in table 3.
Table 3 is a table of the calculation process of the present invention applied to example 2
| H(m) | 1.10 | 1.20 | 1.40 | 1.60 | 1.80 | 2.00 | 2.20 | 2.40 | 2.60 | 2.80 | 3.00 | 3.20 | 3.40 |
| h 1 (m) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.20 | 0.40 | 0.60 | 0.80 | 1.00 |
| h 2 (m) | 0.10 | 0.20 | 0.40 | 0.60 | 0.80 | 1.00 | 1.20 | 1.40 | 1.60 | 1.80 | 2.00 | 2.20 | 2.40 |
| A 1 (m 2 ) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 10 | 15 | 20 | 25 |
| A 2 (m 2 ) | 2.5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 30 | 35 | 40 | 45 | 50 |
| A 3 (m 2 ) | 55 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 |
| n 1 | - | - | - | - | - | - | - | 0 | 0.039 | 0.061 | 0.080 | 0.096 | 0.112 |
| n 2 | 0.026 | 0.039 | 0.061 | 0.080 | 0.096 | 0.112 | 0.126 | 0.127 | 0.128 | 0.129 | 0.130 | 0.131 | 0.132 |
| ξ 12 (＝ξ 21 ) | - | - | - | - | - | - | - | - | 0.003 | 0.002 | 0.002 | 0.001 | 0.001 |
| ξ 23 (＝ξ 32 ) | 0.007 | 0.005 | 0.003 | 0.003 | 0.002 | 0.002 | 0.002 | 0.002 | 0.003 | 0.002 | 0.002 | 0.001 | 0.001 |
| Q 1 (m 3 /s) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.7 | 1.8 | 2.6 | 3.4 | 4.2 |
| Q 2 (m 3 /s) | 0.4 | 0.9 | 1.8 | 2.7 | 3.5 | 4.4 | 5.3 | 6.8 | 8.3 | 10 | 11.8 | 13.5 | 15.2 |
| Q 3 (m 3 /s) | 57.0 | 65.8 | 84.9 | 105.8 | 128.4 | 152.7 | 178.5 | 205.9 | 249.1 | 278.8 | 312.0 | 347.1 | 383.9 |
| Q(m 3 /s) | 57.4 | 66.7 | 86.7 | 108.5 | 131.9 | 157.1 | 183.8 | 212.7 | 258.1 | 290.6 | 326.4 | 364.0 | 403.3 |
And 3, according to the sub-sections obtained by division, the sections are composed of 1 element I, 1 element VI and 1 element V, namely the elements of the target section are I + VI + V. When H is less than or equal to d =1.0m, all water flow is conveyed by the main tank, and the water level flow relation is directly calculated by a Manning formula; when 1.0m&When H is less than or equal to 2.4m, the water flows to the first-class beach land compound section; when H is present&And when the water flow reaches the second-level beach land at 2.4 m. The water depth H is increased by 0.1m or 0.2m in turn, and the cross-sectional area A of each sub-section is calculated according to the table 1 k Wet week P k And hydraulic radius R k . From Table 1, it is determined that the sub-section 2 belongs to element IV, and the heights of the sub-section interfaces with the left and right sides are h L2 ＝h 2-1 ＝h 1 ，h R2 ＝h 2+1 ＝h 2 The calculation results are shown in Table 2.
And 4, step 4: and calculating the apparent shear stress coefficient. The section beach land is asymmetric and covered by vegetation, so the proportionality coefficient psi =1.4 × 10 -4 . When j =1, higher than d 2 The sub-section 1 (second-level beach) and the sub-section 2 (first-level beach) are regarded as 'new edge beach', and are lower than d 2 The sub-section 3 (main groove) is a new main groove; when j =2, higher than d 1 +d 2 The sub-section 1 (second-level beach) is regarded as a new edge beach and is lower than d 1 +d 2 The sub-section 2 (first-stage beach) and the sub-section 3 (main groove) are "new main grooves", and the apparent shear stress coefficients are respectively calculated by adopting the formula (7), which is shown in table 3.
And 5: and calculating a coefficient matrix. Longitudinal slope gradient S of target section 0 ＝0.4×10 -3 Respectively calculating I from the formula (8) k ，J k 、X k And Y k . From the elemental composition of the identified target section, the orientation coefficients of the various sub-sections are determined from table 1: subface 1 (element I): alpha (alpha) ("alpha") 1 ＝0，β 1 = -1; subface 2 (element VI): alpha is alpha 2 ＝1，β 2 = -1; subface 3 (element V): alpha is alpha 3 ＝1，β 3 And =0. A is calculated from the formula (9) k 、b k And c k 。
Step 6: and establishing a matrix equation. And (5) establishing a matrix equation according to the three diagonal matrix phi obtained by calculation in the step 5.
And 7: solving the formula (A2) by adopting a pursuit method to obtain the average flow velocity u of each sub-section k Are multiplied by the corresponding cross-sectional areas A respectively k To obtain the flow Q of each sub-section k . The total flow Q of the target cross section is calculated according to the total flow equation, detailed in table 3 and fig. 6.
Claims (5)
1. A general method for estimating a multi-stage compound section water level flow relation is characterized by comprising the following steps:
step 1: the geometric dimension analysis of the target section is realized as follows:
acquiring section measurement data X of target section i ，Z i ，i＝1,2,…，K，X i From the ith point to the cross section starting point X 1 Distance of, Z i The elevation of the point is taken as K is the number of section measuring points;
selecting points with obvious elevation change, dividing the cross section into M + N +1 sub-sections by vertical lines passing through the points, wherein the sub-section with the largest water depth is called a main groove, the rest are called a beach, M is the number of the sub-sections of the beach on the left side of the main groove, N is the number of the sub-sections of the beach on the right side of the main groove, M and N are natural numbers, and M + N is more than or equal to 1;
marking the sub-sections k from the starting point side in sequence, wherein k is more than or equal to 1 and less than or equal to M + N +1;
the elevation of the sub-section next to the primary beach land is called a primary beach water depth, the elevation of the sub-section next to the primary beach land is called a secondary beach land, the elevation of the bed surface is called a secondary beach water depth, and the rest can be done in the same way;
reading the width b of each sub-section k Height of step d k Slope of beach land side slope, slope of main trough left side slope S Lk And the slope S of the right side slope of the main groove Rk ；
And 2, step: determining the Mannich roughness coefficient of each part, and concretely realizing the following steps:
the Mannich roughness coefficient of the section k was calculated using the following formula:
in the formula: n is k The Manning roughness coefficient of the sub-section k; r k The hydraulic radius of the sub-section k is obtained by dividing the area of the sub-section k by the wet circumference of the sub-section; g is the acceleration of gravity; f. of k The total Darcy-Weisbach resistance coefficient of the sub-section k;
and step 3: identifying the basic element composition of a target section, and concretely realizing the following steps:
any multi-stage compound section can be composed of one or more of the following seven elements:
element I: the left side near shore beach; and (3) element II: the right side near shore beach; element III: a left main near-shore tank; and element IV: a main offshore launder; element V: a right main near-shore trough; element VI: left-side offshore beach; and (3) element VII: the right offshore beach;
selecting elements corresponding to the sub-sections according to the specific situation of dividing the sub-sections of the target section;
the cross-sectional area A of each constituent element is calculated k Wet week P k And hydraulic radius R k And determining the height h of the left and right side interfaces Lk And h Rk ；
And 4, step 4: calculating the apparent shear stress coefficient, and concretely realizing the following steps:
apparent shear stress is adopted to measure momentum exchange between adjacent elements, and the calculation formula is
In the formula:respectively is the apparent shear stress between the sub-section k and the left sub-section k-1 and the right sub-section k +1; ρ is the density of water; h is Lk ，h Rk The height of the interface of the sub-section k, the left sub-section k-1 and the right sub-section k +1 is shown; u. u k-1 ，u k ，u k+1 The average flow rate of a sub section k-1, k +1; xi shape k，k-1 ，ξ k，k+1 Respectively representing the apparent shear stress coefficients of the sub-section k, the left sub-section k-1 and the right sub-section k +1;
and 5, calculating a coefficient matrix, wherein the specific implementation is as follows:
measuring and determining longitudinal slope gradient S of river reach 0 And respectively calculating the following parameters of each sub-section according to the element composition of the identified target section:
wherein: I.C. A k ,J k ,X k ,Y k For calculated intermediate variables, n k The Manning coefficient of the sub-section k, g is the acceleration of gravity, h Lk And h Rk The height of the interface between the left and right sides of each constituent element, R k Is the hydraulic radius, xi, of each constituent element k，k-1 ，ξ k，k+1 Respectively representing the apparent shear stress coefficients of the sub-section k, the left sub-section k-1 and the right sub-section k +1;
recording the direction coefficients of apparent shear stress between the sub-section k and the adjacent sections on the left and right sides of the sub-section k as alpha k And beta k (ii) a When the section k belongs to the element I, alpha k ＝0，β k = -1; when the section k belongs to the element II, alpha k ＝-1，β k =0; when the section k belongs to the element III, alpha k ＝0，β k =1; when the section k belongs to the element IV, alpha k ＝1，β k =1; when the section k belongs to the element V, alpha k ＝1，β k =0; when the section k belongs to the element VI, alpha k ＝1，β k = -1; when the section k belongs to the element VII, alpha k ＝-1，β k ＝1；
According to the structure of the target section, the direction coefficient of the apparent shear stress of each sub-section is determined in turn, and the following parameters are calculated
a k ＝α k X k ,b k ＝I k -α k X k -β k Y k ,c k ＝β k Y k ；
Step 6: establishing a matrix equation, specifically realizing the following steps:
for multi-level compound section, solving the matrix equation with coefficient matrix as three diagonal matrix
ΦX＝J
In the formula:is a flow velocity matrix; j = (J) 1 J 2 ... J M+N+1 ) T Is a momentum matrix; coefficient matrix with phi being three diagonal
And 7: solving the coefficient matrix phi of the three opposite angles by adopting a pursuit method to obtain the average flow velocity u of each sub-section k Are multiplied by the corresponding sub-cross-sectional areas A respectively k To obtain the flow Q of each sub-section k (ii) a Calculating the total flow Q of the target cross section according to the total flow equation, i.e.
Q＝AU T
In the formula: u = (U) 1 u 2 … u M+N+1 ) T ,A＝(A 1 A 2 … A M+N+1 ) T 。
2. The universal method for estimating a multi-level compound cross-section water level flow relationship as claimed in claim 1, wherein:
in step 2, since the vegetation density is 0, which can be used to define the vegetation-free condition, the Darcy-Weisbach drag coefficient is composed of drag coefficient due to drag force of vegetation and frictional resistance of the bed surface, i.e., the drag coefficient is determined by the additivity principle
f k ＝f bk +f vk
In the formula: f. of bk The bed surface Darcy-Weisbach resistance coefficient, f of the sub-section k vk Coefficient of resistance due to drag of vegetation on sub-section k
f vk ＝4λ k C D D k m k h k
In the formula: d k Is the diameter of the plant on the sub-section k; h is k Is the water depth of the sub-section k; m is k Is the number of plants per unit area on the sub-section k, i.e. the vegetation density, which for regularly planted plants is the reciprocal of the product of the row spacing and the plant spacing, i.e. m k ＝1/(L xk L yk )，L xk 、L yk The row spacing and the plant spacing of the plants on the sub-section k are shown; c D The drag force coefficient of the vegetation; lambda [ alpha ] k In order to consider the correction coefficient of the vegetation inundation degree, the calculation formula is as follows:
wherein: s Dk Is the vegetation submergence on the sub-section k.
3. The universal method for estimating a multi-level compound cross-section water level flow relationship as claimed in claim 2, wherein:
in step 2, the submergence degree S of the vegetation on the sub-section k Dk Defined as:
in the formula: h is v Is the height of the plant on the subplanar k, h k The depth of water of the sub-section k.
4. The universal method for estimating a multi-level compound cross-section water level flow relationship as claimed in claim 1, wherein:
in step 4, regarding the multilevel compound section, taking j-level spread water depth as a boundary, regarding the section lower than the j-level spread water depth as a new main groove, regarding the section higher than the j-level spread water depth as a new edge beach, and estimating the apparent shear stress coefficient by adopting the following formula
Wherein: r is an intermediate variable; h is the water depth of the new main tank; b is the left part of the canal, including half of the main channel and the width of all the side beaches on the left side; b is Mr The total width of the new main slot; h is r The water depth of the new beach; dr is the beach water depth of the new edge beach; n is r The comprehensive roughness coefficient of the new edge beach; n is r+1 The comprehensive roughness coefficient of the new main groove is obtained; psi is a scale factor related to section symmetry and vegetation.
5. The universal method for estimating a multi-stage compound cross-section water level flow relationship as claimed in claim 4, wherein:
in step 4, ψ =4.5 × 10 for a symmetrical double section without vegetation -4 (ii) a For an unerased asymmetric compound section, ψ =6.3 × 10 -4 (ii) a For symmetrical compound section with vegetation on beach, psi =1.0 × 10 -4 (ii) a For asymmetric compound section with vegetation on beach, psi =1.4 × 10 -4 。
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| CN108827871A (en) * | 2018-08-17 | 2018-11-16 | 河海大学 | Silt surface shearing stress determines method in a kind of tubular type soil erosion experimental rig |
| CN109736259A (en) * | 2019-03-04 | 2019-05-10 | 四川大学 | The hydraulics of the compound beach utilization scope of mountain stream and flood control safety position determines method |
| CN111400974A (en) * | 2020-04-27 | 2020-07-10 | 中国水利水电科学研究院 | Method for estimating tangential stress of wall surface and bed surface of rectangular canal |
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| CN109736259A (en) * | 2019-03-04 | 2019-05-10 | 四川大学 | The hydraulics of the compound beach utilization scope of mountain stream and flood control safety position determines method |
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| CN115222115A (en) * | 2022-07-07 | 2022-10-21 | 珠江水利委员会珠江水利科学研究院 | Comprehensive roughness calculation method and system for plant-containing river channel |
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