Method for calculating position of main stream line of water flow in 90-degree curved river channel

Abstract

This invention discloses a method for calculating the position of the main flow line in a 90° bend river, belonging to the fields of hydraulics and river dynamics. By combining the geometric characteristics of the bend with hydrodynamic conditions, and introducing dimensionless parameters such as relative bend radius, Froude number, and relative water depth, a calculation formula for the lateral offset of the main flow line is established, thereby determining the spatial coordinates of the main flow line. This method has a clear calculation approach, well-defined physical meanings of the parameters, and readily available parameters. It is applicable to the hydrodynamic analysis of 90° bend rivers and can provide a reference for riverbed scouring and deposition analysis and engineering design in bend rivers, demonstrating good applicability and potential for wider application.

Description

Technical Field

[0001] This invention relates to the fields of hydraulics and river dynamics, and in particular to a method for calculating the position of the main flow line in a 90° curved river. Background Technology

[0002] Meandering rivers are a widespread river morphology in nature. The study of hydrodynamic characteristics and riverbed morphology evolution, especially in 90° bends, is of great significance in hydraulics and river management. The main flow line, i.e., the trajectory of the highest flow velocity in a river cross-section, is a crucial parameter for hydrodynamic analysis and morphological evolution of meandering rivers. Accurately determining the location of the main flow line is vital for hydraulic structure layout and riverbed scouring and deposition prediction in river design, flow analysis, and navigation channel improvement projects.

[0003] In existing technologies, the location of the main flow line is mostly estimated using experimental or field measurement data and empirical formulas. These methods are mostly applicable to river sections with small bends, but they are significantly insufficient for rivers with large bends (such as 90°). In rivers with large bends, the centrifugal force of the water flow is large, the secondary flow effect is significant, and the spatial distribution of flow velocity is complex. Traditional empirical formulas are difficult to accurately reflect this flow pattern change.

[0004] Therefore, it is necessary to propose a simple calculation method with readily available parameters that is applicable to the main channel position of rivers with a large bend angle of 90°, so as to provide a reference for the analysis of riverbed scouring and sedimentation and engineering design of meandering rivers. Summary of the Invention

[0005] The present invention aims to provide a method for calculating the position of the main flow line of a 90° curved river channel, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for calculating the position of the main flow line in a 90° curved river includes the following steps:

[0008] S1: Obtain the geometric parameters of a 90° curved river channel, including the channel width B and the radius of curvature R of the bend centerline. c ;

[0009] S2: Obtain hydrodynamic parameters of a 90° bend in the river channel, including water depth H and average flow velocity U at a representative cross-section;

[0010] S3: Based on the geometric and hydrodynamic parameters of the 90° bend in the river channel described in steps S1 and S2, determine the relative bend radius λ, the flow Froude number Fr, and the relative water depth η according to the following formulas:

[0011] (1)

[0012] (2)

[0013] (3)

[0014] In the formula, g is the acceleration due to gravity.

[0015] S4: Establish a rectangular coordinate system with the center of the 90° bend of the river as point O, the line connecting point O to the exit section of the bend as the x-axis, and the line connecting point O to the entry section of the bend as the y-axis.

[0016] S5: In the coordinate system established in step S4, with the entry section of the curve as the starting point, the relationship between the arc length s of the curve centerline and the turning angle θ is as follows:

[0017] s = R c ·θ (4)

[0018] S6: Determine the lateral offset δ of the main line relative to the centerline of the curve at the arc length position s. s :

[0019] (5)

[0020] S7: Based on the lateral offset δ of the main line at arc length position s relative to the center line of the curve in step S6. s Determine the spatial position coordinates (x, y) of the main line in the coordinate system established in step S4. s y s ):

[0021] (6)

[0022] In the formula, (x c y c ) represents the coordinates of the curve's centerline at the arc length position s; δ s sinθ is the lateral offset δ s The mapping on the x-axis, δ s ·cosθ is the lateral offset δ s Mapping on the y-axis.

[0023] Preferably, in step S1, the river width B refers to the representative cross-sectional width of the river channel bend, which is consistent with the river channel width before entering the bend.

[0024] Preferably, in step S2, the representative cross-sectional water depth H is the average water depth of the bend entry cross-section, and the average flow velocity U is the average flow velocity of the bend entry cross-section.

[0025] Preferably, in step S3, when the relative curvature radius λ ≤ 3, the river channel is a weakly curved river channel; when λ > 3, the river channel is a strongly curved river channel.

[0026] Preferably, in step S6, the function F(λ,Fr,η) is used to characterize the lateral offset δ of the geometric and hydrodynamic parameters of the 90° bend in the river channel relative to the main channel. s The effect is expressed as:

[0027] (7)

[0028] In the formula, a1, a2, and a3 are all coefficients that can be determined based on experimental or field data.

[0029] Preferably, in step S7, the coordinate x of the curve centerline at the arc length position s is... c = R c ·sinθ,y c =R c ·coθ.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] This invention proposes a method for calculating the position of the main flow line in a 90° bend river. By combining the geometric characteristics of the bend with hydrodynamic conditions, and introducing dimensionless parameters such as relative bend radius, Froude number, and relative water depth, a calculation formula for the lateral offset of the main flow line is established, thereby determining the spatial coordinates of the main flow line. This method has a clear calculation approach, well-defined physical meanings of the parameters, and readily available parameters. It is applicable to the hydrodynamic analysis of 90° bend rivers and can provide a reference for riverbed scouring and deposition analysis and engineering design in bend rivers, demonstrating good applicability and potential for wider application. Attached Figure Description

[0032] Figure 1 A simplified schematic diagram of a 90° curved river channel in a specific embodiment;

[0033] Figure 2 This is a schematic diagram of the coordinate system for a 90° curved river channel in a specific embodiment;

[0034] Figure 3 Here is a diagram showing the layout of the test model in a specific embodiment;

[0035] Figure 4 Here are schematic diagrams of the main water flow path under different operating conditions in a specific embodiment: (a) 35 L / s, (b) 52 L / s, (c) 80 L / s;

[0036] Figure 5 In a specific embodiment, the calculated and measured values ​​of the main flow line position of the 90° curved river proposed in this invention are compared: (a) 35 L / s, (b) 52 L / s, (c) 80 L / s. Figure 5In the diagram, dashed lines represent calculated values, and solid lines represent measured values.

[0037] Figure 6 This is a flowchart of the method of the present invention. Detailed Implementation

[0038] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0039] like Figure 6 As shown, this invention provides a method for calculating the position of the main flow line in a 90° curved river, comprising the following steps:

[0040] S1: Determine the geometric parameters of the 90° bend in the river channel, including the channel width B and the radius of curvature R of the bend centerline. c ;

[0041] S2: Determine the hydrodynamic parameters of a 90° bend in the river channel, including the water depth H and the average flow velocity U at a representative cross-section;

[0042] S3: Based on the geometric and hydrodynamic parameters of the 90° bend in the river channel described in steps S1 and S2, determine the relative bend radius λ, the flow Froude number Fr, and the relative water depth η according to the following formulas:

[0043] (1)

[0044] (2)

[0045] (3)

[0046] In the formula, g is the acceleration due to gravity.

[0047] S4: Establish a rectangular coordinate system with the center of the 90° bend of the river as point O, the line connecting point O to the exit section of the bend as the x-axis, and the line connecting point O to the entry section of the bend as the y-axis.

[0048] S5: In the coordinate system established in step S4, with the entry section of the curve as the starting point, the relationship between the arc length s of the curve centerline and the turning angle θ is as follows:

[0049] s = R c ·θ (4)

[0050] S6: Determine the lateral offset δ of the main line relative to the centerline of the curve at the arc length position s. s :

[0051] (5)

[0052] In the formula, the function F(λ,Fr,η) is used to characterize the lateral offset δ of the geometric and hydrodynamic parameters of a 90° bend in the main channel with respect to the main channel. s The impact, The coefficients a1, a2, and a3 can be determined based on experimental or field data.

[0053] S7: Based on the lateral offset δ of the main line at arc length position s relative to the center line of the curve in step S6. s Determine the spatial position coordinates (x, y) of the main line in the coordinate system established in step S4. s y s ):

[0054] (6)

[0055] In the formula, (x c y c Let x be the coordinate of the curve's centerline at the arc length s. c = R c ·sinθ,y c = R c ·coθ;δ s sinθ is the lateral offset δ s The mapping on the x-axis, δ s ·cosθ is the lateral offset δ s Mapping on the y-axis.

[0056] In one specific embodiment, a flume test method is used to verify whether the proposed method for calculating the position of the main flow line of a 90° curved river is accurate and effective.

[0057] Test methods

[0058] The test flume is a 90° curved flume constructed from transparent plexiglass and a steel truss. It consists of two straight sections and one curved section, each 0.6 m wide, 0.8 m high, and 19.4 m long, with a slope of 5‰. The upstream straight section is 10.5 m long, the downstream straight section is 6.5 m long, and the radius of curvature R at the center of the curved section is... c = 1.5 m. In the model test, the water level was controlled by adjusting the opening of the tailrace gate at the end of the flume. The test model was arranged as follows: Figure 3 As shown.

[0059] In one specific embodiment, the model test arranged nine measurement sections at the bend, with 11 vertical measuring lines at each section. Velocity measuring points were placed along each vertical measuring line in the direction of water depth, and the water velocity was measured using an acoustic Doppler current meter (ADV). The model test group and corresponding flow parameters are shown in Table 1. In the table, Re represents the Reynolds number.

[0060] Table 1 Test Conditions

[0061]

[0062] Test results

[0063] The main flow path is the horizontal projection of the line connecting the points of maximum longitudinal water depth and average velocity at each measurement section along the flow path, reflecting the variation of the main flow path along the flow path. Based on the measurement results, the main flow paths for different test groups can be obtained as follows: Figure 4 As shown. For the 90° curved river in this embodiment, in the straight section entering the bend, the water flow basically maintains the basic form of a straight open channel flow. When the water enters the bend, the flow direction is forced to deflect, and the flow field in the bend is adjusted before entering the bend, resulting in a significant change in the flow structure. Due to the centrifugal force acting on the water flow in the bend, the flow velocity on the convex bank increases while the flow velocity on the concave bank decreases. Under different test groups, the dynamic axis of the water flow begins to deflect towards the convex bank until it reaches its limit near the bend crest. After passing the bend crest, this trend begins to decrease, and the mainstream begins to slowly move towards the concave bank and continues to shift towards the concave bank. Due to inertia, even after exiting the bend, when there is no centripetal force acting on the water flow, the mainstream still deflects towards the concave bank.

[0064] To verify the method for calculating the position of the main flow line of a 90° curved river proposed in this invention, flume test data from the embodiment of this invention were selected, and the formula coefficients a1, a2, and a3 in step S6 were calibrated, yielding a1 = 1.98, a2 = -0.02, and a3 = -0.13. Figure 5 A comparison was made between the proposed method for calculating the position of the main flow line in a 90° curved river and the experimentally measured position of the main flow line. It was found that the two were not significantly different. The correlation between the calculated value and the measured value of the lateral offset of the main flow line was 86%, indicating that the present invention can accurately calculate and predict the spatial position of the main flow line in a 90° curved river.

[0065] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for calculating the position of the main flow line in a 90° bend river, characterized in that: The calculation method includes the following steps: S1: Obtain the geometric parameters of the 90° curved river channel, including the river channel width B and the center line curvature radius R of the curved channel c ; S2: Obtain hydrodynamic parameters of a 90° bend in the river channel, including water depth H and average flow velocity U at a representative cross-section; S3: Based on the geometric and hydrodynamic parameters of the 90° bend in the river channel described in steps S1 and S2, determine the relative bend radius λ, the flow Froude number Fr, and the relative water depth η according to the following formulas: （1） （2） （3） In the formula, g is the acceleration due to gravity; S4: Establish a rectangular coordinate system with the center of the 90° bend of the river as point O, the line connecting point O to the exit section of the bend as the x-axis, and the line connecting point O to the entry section of the bend as the y-axis. S5: In the coordinate system established in step S4, with the entry section of the curve as the starting point, the relationship between the arc length s of the curve centerline and the turning angle θ is as follows: s = R c • θ (4) S6: determining the lateral offset δ of the main flow line at the arc length position s relative to the center line of the curve s : （5） S7: determining the spatial position coordinates (x, y) of the main flow line in the coordinate system established in step S4 in dependence on the lateral offset δ of the main flow line at the arc length position s relative to the center line of the curve s s s ​​​ （6） where (x c , y c ) are the coordinates of the centerline of the bend at arc length position s; δ s · sinθ is the mapping of the lateral offset δ s in the x-axis, and δ s · cosθ is the mapping of the lateral offset δ s in the y-axis.

2. The method for calculating the position of the main flow line in a 90° curved river as described in claim 1, characterized in that: In step S1, the river width B refers to the representative cross-sectional width of the river channel bend, which is consistent with the river channel width before entering the bend.

3. The method for calculating the position of the main flow line in a 90° curved river as described in claim 1, characterized in that: In step S2, the representative cross-sectional water depth H is the average water depth at the bend entry section, and the average flow velocity U is the average flow velocity at the bend entry section.

4. The method for calculating the position of the main flow line in a 90° curved river as described in claim 1, characterized in that: In step S3, when the relative curvature radius λ ≤ 3, the river channel is a weakly curved river channel; when λ > 3, the river channel is a strongly curved river channel.

5. The method for calculating the position of the main flow line in a 90° curved river as described in claim 1, characterized in that: In step S6, the function F(λ,Fr,η) is used to characterize the lateral offset δ of the main channel by the geometric and hydrodynamic parameters of the 90° bend. s The effect of is expressed as: （7） In the formula, a1, a2, and a3 are all coefficients that can be determined based on experimental or field data.

6. The method for calculating the position of the main flow line in a 90° curved river as described in claim 1, characterized in that: In step S7, the coordinate x of the curve centerline at the arc length position s is... c = R c ·sinθ,y c = R c ·coθ.

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