# Experimental and Numerical Investigations of Turbulent Open Channel Flow over a Rough Scour Hole Downstream of a Groundsill

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## Abstract

**:**

## 1. Introduction

## 2. Background of the Experiments and Model Setups

#### 2.1. Experimental Equipment and Setups

^{2}/s), medium particle size (D

_{50}= 2.7 mm), and bed slope (S = 1%). One percent was selected because it is a typical slope value for mid-stream western rivers in Taiwan, e.g., Toucian River. Further, unit discharge corresponding to a 20 year return period and the medium value of particle size (D

_{50}) referred to the riverbed of Lung-En auxiliary Weir at a scale of 1:50, which is 2.7 mm. For a non-equilibrium scour hole, it is not easy to establish as the scale has a short scouring time and a small depth of scour hole. It is difficult to see the difference between a scour hole before equilibrium and one produced after a long scouring time but with a similar depth, as shown in Figure 3. Therefore, in this study, a time of 15 min was selected and the average for ten groups of scour holes was obtained in repeated experiments. Moreover, as Lu et al. presented, the scour hole reaches equilibrium less than 5 h [15]. Based on the above, the study selected 5 h as the dividing time. And considering the similarity theory for the Froude number, the length and depth of the scour hole before and after equilibrium were downscaled by half. Glass granules, which have a diameter of one-half of the median diameter of about 1.3 mm, were fixed to the bottom of the bed.

#### 2.2. Setups of Numerical Simulations

_{s}) and roughness constant (k

_{r}) were set for the bottom of the channel. For the roughness to take effect, one must specify a non-zero value for k

_{s}. A roughness height (k

_{s0}) of zero corresponds to smooth walls. For a uniform sand-grain roughness, the height of the sand-grains can simply be k

_{s}. The roughness height was set to be 0.0013 m of D

_{50}, referring to the experiment.

## 3. Results and Discussion

#### 3.1. Scour Hole Model and Measurement System Verification

_{s,m}) and the maximum scour depth (y

_{s,m}), respectively. The dimensionless equilibrium scour hole profiles reveal a considerable similarity among these experiments. Figure 6 also presents that experimental results of dimensionless analysis showed the high repeatability of the formation of the equilibrium scour hole. Lu et al. [20] defined the relations between dimensionless scour depth and its scouring time. Here, the depth of the non-equilibrium scour hole in this study is similar to the scour depth obtained from previous studies [20].

#### 3.2. Discussion of Experimental Results

#### 3.3. Comparison of Experimental and Simulation Results

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Experiment of Particle Image Velocimetry (PIV) with a high-speed camera (extract figure from Shih et al. [16]).

**Figure 7.**Comparison of fiber-optic laser doppler velocimeter (FLDV) and PIV velocity fields in: (

**a**) longitudinal velocity; (

**b**) vertical velocity.

**Figure 8.**Velocity profiles at each position measured with different discharges for scour holes under: (

**a**) equilibrium; (

**b**) non-equilibrium condition.

**Figure 9.**Longitudinal turbulence intensities at each position measured with different discharges for scour holes under: (

**a**) equilibrium; (

**b**) non-equilibrium condition.

**Figure 10.**Vertical turbulence intensities at each position measured with different discharges for scour holes under: (

**a**) equilibrium; (

**b**) non-equilibrium condition.

**Figure 11.**Reynolds stress at each position measured with different discharges for scour holes under: (

**a**) equilibrium; (

**b**) non-equilibrium condition.

**Figure 12.**Comparison of measured and simulated mean velocity profiles at each position with different discharges for scour holes under: (

**a**) equilibrium; and (

**b**) non-equilibrium condition.

**Figure 13.**Comparison of measured and simulated longitudinal turbulence intensities profiles at each position with Q = 0.0085 cm for scour holes under: (

**a**) equilibrium; and (

**b**) non-equilibrium condition.

**Figure 14.**Comparison of measured and simulated vertical turbulence intensities profiles at each position with Q = 0.0085 cm for scour holes under: (

**a**) equilibrium; and (

**b**) non-equilibrium condition.

**Figure 15.**Comparison of measured and simulated Reynolds stress values profiles at each position with Q = 0.0085 cm for scour holes under: (

**a**) equilibrium; and (

**b**) non-equilibrium condition.

Case | S (%) | h (cm) | Q (m ^{2}/s) | U (m/s) | ${\mathit{U}}_{*}$ (m/s) | F_{r} | R_{e} | B/h |
---|---|---|---|---|---|---|---|---|

S1H24 | 1/100 | 2.40 | 0.0030 | 0.50 | 0.0444 | 1.03 | 10,029 | 10.42 |

S1H31 | 1/100 | 3.10 | 0.0058 | 0.75 | 0.0494 | 1.36 | 18,559 | 8.06 |

S1H36 | 1/100 | 3.60 | 0.0085 | 0.94 | 0.0524 | 1.59 | 26,174 | 6.94 |

_{r}= Froude number = $\raisebox{1ex}{$U$}\!\left/ \!\raisebox{-1ex}{$\sqrt{gh}$}\right.$; R

_{e}= Reynolds number; B/h = aspect ratio (flume width: B = 0.25 m).

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**MDPI and ACS Style**

Chang, C.-K.; Lu, J.-Y.; Lu, S.-Y.; Wang, Z.-X.; Shih, D.-S.
Experimental and Numerical Investigations of Turbulent Open Channel Flow over a Rough Scour Hole Downstream of a Groundsill. *Water* **2020**, *12*, 1488.
https://doi.org/10.3390/w12051488

**AMA Style**

Chang C-K, Lu J-Y, Lu S-Y, Wang Z-X, Shih D-S.
Experimental and Numerical Investigations of Turbulent Open Channel Flow over a Rough Scour Hole Downstream of a Groundsill. *Water*. 2020; 12(5):1488.
https://doi.org/10.3390/w12051488

**Chicago/Turabian Style**

Chang, Cheng-Kai, Jau-Yau Lu, Shi-Yan Lu, Zhong-Xiang Wang, and Dong-Sin Shih.
2020. "Experimental and Numerical Investigations of Turbulent Open Channel Flow over a Rough Scour Hole Downstream of a Groundsill" *Water* 12, no. 5: 1488.
https://doi.org/10.3390/w12051488