# Effects of Different In-Stream Structure Representations in Computational Fluid Dynamics Models—Taking Engineered Log Jams (ELJ) as an Example

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Governing Equations

#### 2.1.1. Hydrodynamic Model

#### 2.1.2. Porosity Model

#### 2.1.3. Drag Force Calculation

**τ**denotes the Reynolds stress tensor.

**n**is the surface normal vector, and ${\mathit{n}}_{x}=(1,0,0)$ denotes the streamwise direction. In this study, both methods were applied to the fully-resolved case and solid barrier case. For the porous media case, since there was no physical structure, only the second method was used. In fact, according to Equation (8), at steady state, the pressure and shear stress on the enclosing box should be balanced by the volume integration of ${S}_{i}$ within $CV$ if we assume other forces are small. This is also the foundation for the momentum analysis in previous studies [15,20,22].

#### 2.2. Geometry Preparation and Mesh Generation

#### 2.3. Boundary Conditions

#### 2.4. Configuration of the Porous Media Model

#### 2.5. Computational Platform

## 3. Results and Discussion

#### 3.1. Validation of the Fully-Resolved Configuration

#### 3.2. Calibration of Porous Media Model

#### 3.3. Evaluation of Different Representations in the CFD Model

#### 3.3.1. Flow Adjustment

#### 3.3.2. Near-Surface Velocity

#### 3.3.3. Near-Bed Turbulence

#### 3.3.4. Flow Structure

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ELJ | Engineered log jams |

LES | Large eddy simulation |

LWD | Large woody debris |

TKE | turbulent kinetic energy |

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**Figure 1.**The engineered log jam (ELJ) structure in the flume. In the 3D view, a fake free surface was added.

**Figure 4.**Comparison of the cross-sectional distributions of mean streamwise velocity and turbulent kinetic energy (TKE) between the numerical and experimental results for the background case without ELJ. The variables are made dimensionless with channel width B, water depth h and mean velocity ${u}_{0}$.

**Figure 5.**Comparison of the cross-sectional distributions of the mean streamwise velocity between the experiment and the fully-resolved case with ELJ.

**Figure 6.**Comparison of the cross-sectional distributions of TKE between the experiment and the fully-resolved case with ELJ.

**Figure 7.**Error distribution on the upstream and downstream cross-sections between the porosity cases and the fully-resolved case. The white blank region means that the values exceed the range of the colorbar.

**Figure 8.**Transverse distribution of the mean streamwise velocity and TKE on the upstream and downstream cross-sections at $z/h=0.4$.

**Figure 10.**Longitudinal profiles of cross-sectionally-averaged streamwise velocity and TKE within the adjustment and wake regions. The x coordinate is normalized by the length of ELJ (L). The gray area denotes ELJ.

**Figure 13.**Instantaneous flow field represented by streamlines in the wake zone. The streamlines are colored by the instantaneous velocity.

**Figure 15.**Zoom-in view of the instantaneous flow structure for the fully-resolved case with the isosurfaces of ${\lambda}_{2}=$ 3.

α | β | ${\mathit{d}}_{50}$ (mm) | K (m${}^{2}$) | ${\mathit{K}}_{\mathit{i}}$ (m${}^{2}$) | ${\mathit{F}}_{\mathit{d}}/{\mathit{F}}_{\mathit{fully}}$ | ${\mathit{\epsilon}}_{\mathit{u}/{\mathit{u}}_{0},\mathit{up}}$ | ${\mathit{\epsilon}}_{\mathit{u}/{\mathit{u}}_{0},\mathit{down}}$ | ${\mathit{\epsilon}}_{\mathit{k}/{\mathit{u}}_{0}^{2},\mathit{up}}$ | ${\mathit{\epsilon}}_{\mathit{k}/{\mathit{u}}_{0}^{2},\mathit{down}}$ |
---|---|---|---|---|---|---|---|---|---|

1000 | 1.1 | 32 | $2.34\times {10}^{-6}$ | $2.31\times {10}^{-8}$ | 1.111 | 0.065 | 0.117 | 0.341 | 1.295 |

1000 | 1.1 | 19 | $8.24\times {10}^{-7}$ | $1.37\times {10}^{-8}$ | 1.157 | 0.075 | 0.146 | 0.337 | 1.273 |

1000 | 1.1 | 1 | $2.28\times {10}^{-9}$ | $7.22\times {10}^{-10}$ | 1.113 | 0.131 | 0.162 | 0.673 | 2.570 |

200 | 2 | 32 | $1.17\times {10}^{-5}$ | $1.27\times {10}^{-8}$ | 1.134 | 0.070 | 0.129 | 0.347 | 1.267 |

200 | 2 | 19 | $4.12\times {10}^{-6}$ | $7.55\times {10}^{-8}$ | 1.153 | 0.079 | 0.146 | 0.369 | 1.252 |

200 | 2 | 1 | $1.14\times {10}^{-8}$ | $3.97\times {10}^{-10}$ | 1.148 | 0.126 | 0.168 | 0.649 | 2.584 |

solid | barrier | 0 | 0 | 1.246 | 0.145 | 0.238 | 0.636 | 3.123 |

${\mathit{L}}_{1}$ | ${\mathit{L}}_{\mathit{w}}$ | |
---|---|---|

Fully resolved | 6.1 | 11.3 |

Porosity ${d}_{50}=32$ mm | 7.8 | $10\sim 13$ |

Porosity ${d}_{50}=19$ mm | 6.3 | $10\sim 13$ |

Porosity ${d}_{50}=1$ mm | 4.6 | $10\sim 13$ |

Solid barrier | 4.5 | 7.6 |

Porosity | Solid Barrier | |
---|---|---|

near-bed TKE | under-predicted | over-predicted |

near-field flow structure | well-predicted | extremely weak |

far-field flow structure | too diffusive | well predicted |

flow structure inside ELJ | unpredictable | unpredictable |

wake length ${L}_{1}$ and ${L}_{w}$ | under-predicted | over-predicted |

computational efforts (of fully resolved) | about 1/200 | about 1/50 |

drag force (of fully resolved) | about 1.11 | about 1.25 |

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**MDPI and ACS Style**

Xu, Y.; Liu, X.
Effects of Different In-Stream Structure Representations in Computational Fluid Dynamics Models—Taking Engineered Log Jams (ELJ) as an Example. *Water* **2017**, *9*, 110.
https://doi.org/10.3390/w9020110

**AMA Style**

Xu Y, Liu X.
Effects of Different In-Stream Structure Representations in Computational Fluid Dynamics Models—Taking Engineered Log Jams (ELJ) as an Example. *Water*. 2017; 9(2):110.
https://doi.org/10.3390/w9020110

**Chicago/Turabian Style**

Xu, Yuncheng, and Xiaofeng Liu.
2017. "Effects of Different In-Stream Structure Representations in Computational Fluid Dynamics Models—Taking Engineered Log Jams (ELJ) as an Example" *Water* 9, no. 2: 110.
https://doi.org/10.3390/w9020110