This paper investigated the spacing threshold of nonsubmerged spur dikes with alternate layout to classify the impact scale of spur dikes. A mathematical model was built based on standard
Spur dikes are one of the most widely used structures in hydraulic engineering. They are introduced in rivers for channel regulation, flood prevention, and river diversion [
In the current work, flume experiments considering nonsubmerged spur dikes with ipsilateral and alternate layout were conducted firstly. Then, a numerical model which depends on the standard
The multifunction flume used in this study is 50 m long, 1.2 m wide, and 1.4 m deep, with a concrete floor and two toughened glass sidewalls. It is located in Jiangong, Test Hall of Zhejiang University, China, as shown in Figure
Multifunction flume and measuring instruments.
Spur dike layouts, monitoring cross sections, and monitoring points.
Ipsilateral layout
Alternate layout
The commercial computational fluid dynamics (CFD) code, FLUENT, is chosen to build the numerical model. Several auxiliary surfaces are added to divide the calculation area into regular blocks. Hexahedral structured meshes are adopted and refined in the vicinity of spur dikes. In our past research [
The pressure-based solver in FLUENT is used. The hydraulic diameter
The pressure-velocity coupling is achieved by SIMPLIC (semi-implicit method for pressure-linked equations consistent). The body force weighted method is used for pressure discretization and the first-order upwind method for the discrete format of momentum, turbulent kinetic energy, and turbulent dissipation rate. For boundary conditions, the mass-flow-inlet is used for approaching flow at the inlet, the outflow at the outlet, no-slip walls for the vertical and bottom faces of flume and dike bodies, and standard wall functions for the solution of
To verify the numerical model, two sets of experimental conditions, that is, ipsilateral (v1) and alternate (v2), listed in Table
Verification conditions.
No. | Category | Flow rate | Dike length | Water depth | Dike spacing |
---|---|---|---|---|---|
|
|
|
|
||
v1 | Ipsilateral | 0.0416 | 0.4 | 0.15 | 4.8 |
v2 | Alternate | 0.0603 | 0.4 | 0.3 | 2.4 |
Comparison of
v1 at horizontal plane
v2 at horizontal plane
Since the spur dike flow is regarded as fully turbulent, viscous effects (i.e., Reynolds number effects) can be neglected [
Based on (
Simulation conditions.
No. |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
c1 | 1.2 | 0.2 | 0.2 | 0.0336 | 0.1 | 6 | 6 |
c2 | 1.2 | 0.2 | 0.2 | 0.0672 | 0.2 | 6 | 6 |
c3 | 1.2 | 0.2 | 0.2 | 0.1008 | 0.3 | 6 | 6 |
c4 | 1.2 | 0.2 | 0.2 | 0.168 | 0.5 | 6 | 6 |
c5 | 1.2 | 0.2 | 0.2 | 0.2352 | 0.7 | 6 | 6 |
c6 | 1.2 | 0.5 | 0.2 | 0.0672 | 0.2 | 6 | 2.4 |
c7 | 1.2 | 0.4 | 0.2 | 0.0672 | 0.2 | 6 | 3 |
c8 | 1.2 | 0.3 | 0.2 | 0.0672 | 0.2 | 6 | 4 |
c9 | 1.2 | 0.2 | 0.2 | 0.0672 | 0.2 | 6 | 6 |
c10 | 1.2 | 0.1 | 0.2 | 0.0672 | 0.2 | 6 | 12 |
c11 | 0.6 | 0.1 | 0.3 | 0.0618 | 0.2 | 2 | 6 |
c12 | 1.2 | 0.2 | 0.3 | 0.1235 | 0.2 | 4 | 6 |
c13 | 1.2 | 0.2 | 0.2 | 0.0672 | 0.2 | 6 | 6 |
c14 | 1.8 | 0.3 | 0.2 | 0.1009 | 0.2 | 9 | 6 |
c15 | 2.4 | 0.4 | 0.2 | 0.1345 | 0.2 | 12 | 6 |
Note: c2, c9 and c13 are identical.
In our past research [
Spacing thresholds of c1–c15.
No. |
|
|
---|---|---|
c1 | 12.273 | 61.365 |
c2 | 9.699 | 48.495 |
c3 | 9.154 | 45.770 |
c4 | 8.271 | 41.355 |
c5 | 11.056 | 55.280 |
c6 | 13.330 | 26.660 |
c7 | 8.982 | 22.455 |
c8 | 9.280 | 30.933 |
c9 | 9.699 | 48.495 |
c10 | 14.402 | 144.020 |
c11 | 27.214 | 272.140 |
c12 | 18.667 | 93.335 |
c13 | 9.699 | 48.495 |
c14 | 6.545 | 21.817 |
c15 | 5.059 | 12.648 |
According to the data in Table
Variation of
The results of Figure
Figure
Testing conditions.
No. |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
t1 | 1 | 0.2 | 0.25 | 0.1566 | 0.4 | 4 | 5 |
t2 | 1.5 | 0.15 | 0.2 | 0.1051 | 0.25 | 7.5 | 10 |
t3 | 3 | 0.75 | 0.2 | 0.7564 | 0.9 | 15 | 4 |
t4 | 3 | 0.2 | 0.3 | 0.1235 | 0.08 | 10 | 15 |
Comparisons of
No. | CFD (m) | Equation ( |
RE (%) |
---|---|---|---|
t1 | 13.868 | 14.245 | 2.72 |
t2 | 12.605 | 12.448 | −1.25 |
t3 | 18.566 | 16.783 | −9.60 |
t4 | 48.785 | 51.212 | 4.98 |
Results of the regression analysis.
The dimensionless empirical formula of the spacing threshold of nonsubmerged double spur dikes with ipsilateral layout and same length is expressed in [
Figure
Comparison of empirical formulas between alternate spur dikes and ipsilateral spur dikes.
The empirical formula obtained in this paper can be used to determine the impact scale of spur dikes in straight and rectangular channel. Meanwhile, the empirical formula can be used to find the recovery section of velocities at the downstream of spur dike, and it can be also used for solving the local head loss of spur dike [
A numerical model combining the standard The three influencing factors of The dimensionless empirical formula of spacing threshold is obtained via multivariate regression analysis, and its accuracy is satisfactory. Compared with the spur dikes with ipsilateral layout, the spacing thresholds of alternate spur dikes are mostly smaller under the same conditions. The empirical formula proposed in this paper lays down a foundation for the research of cumulative impact of spur dikes and other river structures, for example, bridge, levee, wing-dike, navigational dam, and so forth, on river systems.
The study is supported by the National Natural Science Foundation of China (50909085, 51125034, and 51279046), the Department of Water Resources of Zhejiang Province (RC1106), and the Ministry of Water Resources of China (201101027).