Designing method of test flume with special-shaped cross section and application thereof

Abstract

A method for forming a test flume usable in hydraulic engineering and debris-flow hazard mitigation is provided. The test flume has a foundation flume and an expansion flume. The expansion flume has a lower edge connected to an upper edge of the foundation flume. A hydraulic radius of the test flume is determined based on a model test. A width of the foundation flume is selected based on a size of the test site of the model test. A coefficient is obtained and a width of the test flume is obtained. A cross section curve equation of the expansion flume is obtained based on the hydraulic radius of the test flume, the coefficient, the width of the test flume and the width of the foundation flume. The test flume is formed based on the cross section curve equation of the expansion flume.

Claims

1. A method for forming a test flume usable in hydraulic engineering and debris-flow hazard mitigation, wherein the test flume comprises: a foundation flume having a bottom wall and at least two side walls, and an expansion flume above the foundation flume; wherein the expansion flume has a lower edge connected to an upper edge of the foundation flume; wherein the foundation flume has a cross section that is rectangular, semicircular or triangular, and the expansion flume has a cross section that comprises two axisymmetric curves, the method comprising: determining a hydraulic radius R of the test flume based on a model test; selecting a width b of the foundation flume based on a size of the test site of the model test, wherein the width b and the hydraulic radius R satisfies b>2R; wherein when it is determined that 2R<b<4R, selecting the cross section of the foundation flume to be rectangular, and calculating a depth d by using formula $d=\frac{Rb}{b-2R};$ wherein when it is determined that b=4R, selecting the cross section of the foundation flume to be semicircular, and calculating the depth d by using formula d=b/2; wherein when it is determined that b>4R, selecting the cross section of the foundation flume to be triangular, and calculating the depth d by using formula $d=\frac{2Rb}{\sqrt{b^2-16R^2}};$ obtaining a coefficient C by using formula $C=\mathrm{ar}\cosh \left(\frac{b}{2R}\right);$ obtaining a width B of the test flume by using formula B=k.Math.b, wherein k is a coefficient; obtaining a cross section curve equation of the expansion flume by using formula: $\left\{\begin{array}{c}y=R.Math.\left[\mathrm{ar}\cosh \left(\frac{-x}{R}\right)-C\right],-B/2\le x\le -b/2\\ y=R.Math.\left[\mathrm{ar}\cosh \left(\frac{x}{R}\right)-C\right],b/2\le x\le B/2\end{array}\right\}$ where R is the hydraulic radius of the test flume, C is the coefficient, B is the width of the test flume and b is the width of the foundation flume; and forming the test flume based on the cross section curve equation of the expansion flume.

2. A method of using the method of claim 1, wherein the test flume is used with a simulated test fluid of clear water flow, hyperconcentration flow or debris flow.

3. A method of using the method of claim 1, wherein the test flume is used to design a flume with a test slope of 5%-30%.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a structural diagram of a test flume with a special cross section.

(2) FIG. 2 is a cross section of a test flume with a flat bottom.

(3) FIG. 3 is a cross section of a test flume with a round bottom.

(4) FIG. 4 is a cross section diagram of a test flume with a sharp bottom.

(5) 1 Foundation flume 2 Expansion flume 3 Hopper 4 Flume inlet gate 5 Special section test flume 6 Flume support 7 Flume slope regulator 8 Speed camera 9 LED shadowless lamp 10 Tailing pool b Width of the foundation flume d Depth of the foundation flume B Width of the flume h Water depth (debris-flow depth)

DESCRIPTION OF THE EMBODIMENT

(6) The embodiment of the invented design method of a test flume with a special-shaped cross section is shown in FIG. 1, FIG. 2, FIG. 3 and FIG. 4. To explore the relationship between the average velocity of the debris flow section and the hydraulic radius of the flow section, the design method of the special section test flume proposed in the invention is used to make three special section test flumes (5) and then build three test flume devices.

(7) In the test flume device, the special cross section test flume (5) includes a foundation flume (1) and an expansion flume (2) above the foundation flume (1); the lower edge of the expansion flume (2) is connected to the upper edge of the flume wall of the foundation flume (1); the cross-sectional shape of the foundation flume (1) is rectangular, or semicircular or triangular, and the flume wall of the expansion flume (2) is two axisymmetric curves. The design method and steps of the special section test flume (5) are as follows:

(8) In the first step, according to the experimental design, the design hydraulic radius R of three special section test flumes (5) is determined to be 0.05 m, 0.1 m and 0.15 m; according to the test site, the width b of three foundation flumes (1) is selected as 0.25 m, 0.4 m and 0.45 m; and the length of three special section test flumes (5) is 20 m.

(9) For the first special section test flume (5), because b=0.25 m, R=0.05 m, and b>4R, the cross-sectional shape of the foundation flume (1) is triangular (as shown in FIG. 4). Then, R and b are substituted into formula

(10) $d=\frac{2Rb}{\sqrt{b^2-16R^2}},$
and the depth d of the foundation flume (1) is calculated to be 0.167 m.

(11) For the second special cross section test flume (5), because b=0.4 m, R=0.1 m, and b=4R, the cross-sectional shape of the foundation flume (1) is semicircular (as shown in FIG. 3), and then substituting b into formula d=b/2, the depth d of the foundation flume (1) is calculated to be 0.2 m.

(12) For the third special section test flume (5), since b=0.45 m, R=0.15 m, and 2R<b<4R, the cross-sectional shape of the foundation flume (1) is rectangular (as shown in FIG. 2). Then, R and b are substituted into formula

(13) $d=\frac{Rb}{b-2R},$
and the depth d of the foundation flume (1) is calculated to be 0.45 m.

(14) In the second step, the design hydraulic radius R and the width b of the foundation flume (1) obtained in the first step are substituted into formula

(15) $C=\mathrm{ar}\cosh \left(\frac{b}{2R}\right),$
and the three undetermined coefficients C are arc osh (2.5), arc osh (2) and arc osh (1.5).

(16) In the third step, for the first special section test flume (5), the coefficient k is selected as 5 according to the test site conditions, the width b of the foundation flume (1) obtained in the first step is substituted into formula B=k.Math.b, and the width B of the flume is calculated to be 1.25 m. For the second special section test flume (5), the coefficient k is selected as 4 according to the test site conditions. The width b of the foundation flume (1) obtained in the first step is substituted into formula B=k.Math.b, and the width B of the flume is calculated to be 1.6 m. For the third special section test flume (5), the coefficient k is selected as 3 according to the test site conditions. The width b of the foundation flume (1) obtained in the first step is substituted into formula B=k.Math.b, and the width B of the flume is calculated to be 1.35 m.

(17) In the fourth step, the design hydraulic radius R of the three special section test flumes (5), the width b of the three foundation flumes (1) determined in the first step, the three undetermined coefficients C determined in the second step, and the three flume widths B determined in the third step are substituted into the following formula:

(18) $\left\{\begin{array}{c}y=R.Math.\left[\mathrm{ar}\cosh \left(\frac{-x}{R}\right)-C\right],-B/2\le x\le -b/2\\ y=R.Math.\left[\mathrm{ar}\cosh \left(\frac{x}{R}\right)-C\right],b/2\le x\le B/2\end{array}\right\}$

(19) The cross section curve equations of three expansion flumes (2) are obtained:

(20) The first special section test flume (5) is as follows:

(21) $\left\{\begin{array}{c}y=0.05\times \left[ar\cosh \left(-20x\right)-\mathrm{ar}\cosh \left(2.5\right)\right],-0.625\le x\le -0.125\\ y=0.05\times \left[ar\cosh \left(20x\right)-\mathrm{ar}\cosh \left(2.5\right)\right],0.125\le x\le 0.625\end{array}\right\}$

(22) The second special section test flume (5) is as follows:

(23) $\left\{\begin{array}{c}y=0.1\times \left[ar\cosh \left(-10x\right)-\mathrm{ar}\cosh \left(2\right)\right],-0.8\le x\le -0.2\\ y=0.1\times \left[ar\cosh \left(10x\right)-\mathrm{ar}\cosh \left(2\right)\right],0.2\le x\le 0.8\end{array}\right\}$

(24) The third special section test flume (5) is as follows:

(25) $\left\{\begin{array}{c}y=0.15\times \left[\mathrm{ar}\cosh \left(\frac{-20x}{3}\right)-\mathrm{ar}\cosh \left(1.5\right)\right],-0.675\le x\le -0.225\\ y=0.15\times \left[\mathrm{ar}\cosh \left(\frac{20x}{3}\right)-\mathrm{ar}\cosh \left(1.5\right)\right],0.225\le x\le 0.675\end{array}\right\}$

(26) According to the width b, depth d of the foundation flume (1), width B of the flume and cross-sectional curve of the expansion flume obtained in the first, third and fourth steps, three special section test flumes (5) are made. As shown in FIG. 1, the special section test flume (5) overlaps with the hopper (3), flume inlet gate (4), flume support (6), flume slope regulator (7), speed camera (8), LED shadowless lamp (9) and tailing pool (10) as three special cross section test flume devices with a constant hydraulic radius.

(27) The test fluid enters the special cross section test flume (5) from the hopper (3) through the flume inlet gate (4). The special cross section test flume (5) is supported by the flume support (6), and the flume slope regulator (7) is installed at the lower end of flume support (6), which is used to adjust the change in the flume slope in the range of 5%-30%. After the test fluid enters the special section test flume (5), with the cooperation of the LED shadowless lamp (9), the speed camera (8) records the speed of the test fluid. The test fluid passes through the whole special cross section test flume (5) and enters the tailings pool (10) through the outlet of the flume.