# Effect of Topography Truncation on Experimental Simulation of Flow over Complex Terrain

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## Abstract

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## Featured Application

**This article analyzes the effect of topography truncation on wind characteristics of flow over complex terrain in a wind tunnel simulation.**

## Abstract

## 1. Introduction

## 2. Experimental Method

#### 2.1. Terrain Scale Model

^{2}, and the small one covered an area approximately one-fourth the size of the larger one. The terrain of the full island is shown in Figure 1, and two circles indicate the areas covered by the terrain model with diameters of 10 m and 5 m. The blockage ratio was approximately 3.27% for the terrain model with a diameter of 10 m, which is lower than the maximum allowable blockage ratio of 5% recommended by Holmes [33].

#### 2.2. Transition Sections

#### 2.3. Experimential Set-Up

^{−5}m

^{2}/s is the kinematic viscosity of air at 20 °C. The value of Reynolds numbers in this study was approximately 3.0 × 10

^{5}, which is in the range of 1.7 × 10

^{5}–4.6 × 10

^{5}studied by Kilpatrick et al. [1]. According to their research, the flow behavior is generally less affected by the Reynolds number. For the other nondimensional numbers determining the flow similarity between the wind tunnel and the real island, the Richardson number and the Eckert number similarities were satisfied due to the consideration of the neutrally stratified boundary layer, and the Prandtl number similarity was satisfied by the air working fluid. Depending on the early study of flow over complex terrain [34], the Rossby similarity was relaxed because of the practical difficulties of modeling the Coriolis force in the wind tunnel. The Froude similarity was also relaxed, because no thermal stratification was reproduced in the wind tunnel.

## 3. Mean wind Characteristics

#### 3.1. Mean Velocity

_{r}to reduce the influence of variation in incoming flow velocity, are shown in Figure 4 for four test cases with uniform inflow conditions but different forms of the transition section. For the convenience of analysis and interpretation, Figure 5 provides east-west cutting planes of measurement locations.

#### 3.2. Inclination Angle

## 4. Turbulence Characteristics

#### 4.1. Turbulence Intensity

#### 4.2. Velocity Spectra

_{u}(n)/σ

^{2}, where S

_{u}is the streamwise velocity spectra, n is the frequency, and σ is the standard deviation of velocity, are shown in Figure 8. The abscissa axis is the normalized frequency, expressed as f = nZ/U(Z), where Z is the height above ground and U(Z) is the mean velocity at height Z. The height of the spectrum shown in Figure 9 is 104 m, which is the hub height of most wind turbines.

## 5. Quantitative Analyses on Effect of Topographic Truncation

#### 5.1. Metrics on Profiles Differences

_{i}is the normalized streamwise mean velocity at i-th point above the ground, U

_{i,OT}is the normalized mean velocity at i-th point above the ground in the case of OT, Δh

_{i}is the height difference between i-th point and (i-1)-th point, H

_{w}is the total height at the measurement location, A

_{i}is the inclination angle at i-th point above the ground, A

_{i,OT}is the inclination angle at i-th point above the ground in the case of OT, I

_{i}is the turbulence intensity at i-th point above the ground, and I

_{i,OT}is the turbulence intensity at i-th point above the ground in the case of OT. It should be noted that in contrast to previous work [17], the absolute value is applied to Equations (2), (3), and (4) to quantify the overall differences. We also define a mean indicator (MI) to evaluate the topographic truncation effect in different cases, which can be calculated as:

_{x}means special indicators: U

_{x}, A

_{x}, and I

_{x}.

#### 5.2. Metrics on Spectra Shifts

_{l}, f

_{m,}and f

_{u}, which are the cut-off frequencies of the different energy intervals, can be calculated from Equations (6) and (7):

_{u}(n)/σ

^{2}is nonnegative and integrates to one in (−∞, +∞), and c = l, m, u. The value of a

_{c}varies with c, and a

_{l}= 0.05, a

_{m}= 0.5, and a

_{u}= 0.95. Hence, the bandwidth between f

_{l}and f

_{u}, which means 90% energy interval bandwidth, is calculated from Equation (8):

_{m,OT}and Δf

_{OT}mean median of normalized frequency and bandwidth of normalized frequency in the case of OT, respectively. As seen in Figure 10a, the normalized median of all cases and measurement locations shows values lower than 1. This indicates that the spectra obtained from the truncation terrain model show a higher value than that from OT, which also supports our analysis in Sect. 4.2. In addition, it can be concluded that energy shifts to a low-frequency range when using the truncation terrain model to obtain spectra.

## 6. Conclusions

- (1)
- Experimental results show that the effect of topographic truncation on profiles of mean velocity and turbulence intensity is different for different regions. A greater impact of the truncation was found in windward and leeward regions. The truncation of the terrain leads to a change in topographic features, causing a change in flow behavior upwind, and is the main reason for this difference. Accurate simulation of flow behavior upwind is crucial for repeating mean velocity and turbulence intensity profiles at target locations.
- (2)
- By comparing the mean velocity and turbulence intensity, profiles of the inclination angle are more sensitive to topographic changes upstream, or they are more sensitive to changes in upstream flow behavior.
- (3)
- Overestimation of streamwise velocity spectra was found in cases with the truncated terrain model in the low-frequency range but underestimated in the high-frequency range. Meanwhile, the slope of the spectra is influenced by a less negative value at the inertial subrange. Moreover, the normalized bandwidth representing the 90% energy interval is influenced by the topographic truncation, but the effect relates to the measurement locations. The bandwidth of windward and leeward regions narrows down, while the bandwidth of the valley region broadens.
- (4)
- Transition sections used in this study have only limited effectiveness. Transition sections can only curb flow separation at the edge of the terrain model, but the change in flow behavior caused by the absence of topographic features due to topographic truncation cannot be resolved. In addition, the implementation of transition sections at the model edge may introduce additional errors into the experiment.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

LES | Large Eddy Simulation |

URANS | Unsteady Reynolds-averaged Navier-Stokes |

OT | Original topography |

WTS | Without transition section |

WTC | Witozinsky transition curve |

RTC | Ramp transition curve |

α | A constant coefficient and equal to 50 |

H | Altitude difference between model edge and wind tunnel floor |

L | Length of transition curve at the certain points corresponding to H |

Re | Reynolds number |

h | Model height |

ν | Kinematic viscosity |

U | Streamwise velocity |

U_{r} | Mean velocity at the top height of each location |

I_{u} | Turbulence intensity |

S_{u} | Streamwise velocity spectra |

n | Frequency |

σ | Standard deviation of velocity |

f | Normalized frequency |

Z | Height above ground |

U(Z) | Mean velocity at height Z |

U_{x} | Special indicator for mean velocity profiles |

A_{x} | Special indicator for inclination angle profiles |

I_{x} | Special indicator for turbulence intensity profiles |

N | Total number of measurement points alone height at each measurement location |

U_{i} | Normalized streamwise mean velocity at i-th point above the ground |

U_{i,OT} | Normalized mean velocity at i-th point above the ground in case OT |

Δh_{i} | Height difference between i-th point and (i-1)-th point |

H_{w} | Total height at the measurement location |

A_{i} | Inclination angle at i-th point above the ground |

A_{i,OT} | Inclination angle at i-th point above the ground in case OT |

I_{i} | Turbulence intensity at i-th point above the ground |

I_{i,OT} | Turbulence intensity at i-th point above the ground in case OT |

MI | Mean indicators |

f_{l} | Cutoff frequency of 0.05 energy interval |

f_{m} | Cutoff frequency of 0.5 energy interval |

f_{u} | Cutoff frequency of 0.95 energy interval |

Δf | 90% energy interval bandwidth |

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**Figure 4.**Profiles of mean velocity at measurement locations: (A1) location A1; (A2) location A2; (A3) location A3; (A4) location A4; (A5) location A5.

**Figure 5.**East-West cutting planes of measurement locations: (A1) location A1; (A2) location A2; (A3) location A3; (A4) location A4; (A5) location A5.

**Figure 6.**Profiles of inclination angle at measurement locations: (A1) location A1; (A2) location A2; (A3) location A3; (A4) location A4; (A5) location A5.

**Figure 7.**Profiles of turbulence intensity at measurement locations: (A1) location A1; (A2) location A2; (A3) location A3; (A4) location A4; (A5) location A5.

**Figure 8.**Normalized streamwise spectra for measurement locations at a height of 104 m: (A1) location A1; (A2) location A2; (A3) location A3; (A4) location A4; (A5) location A5.

**Figure 9.**Special indexes at measurement locations: (

**a**) mean velocity; (

**b**) inclination angle; (

**c**) turbulence intensity.

**Figure 10.**Metrics on spectra shifts at measurement locations: (

**a**) median of the normalized frequency; (

**b**) the bandwidth of the normalized frequency.

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**MDPI and ACS Style**

Wang, Z.; Zou, Y.; Yue, P.; He, X.; Liu, L.; Luo, X.
Effect of Topography Truncation on Experimental Simulation of Flow over Complex Terrain. *Appl. Sci.* **2022**, *12*, 2477.
https://doi.org/10.3390/app12052477

**AMA Style**

Wang Z, Zou Y, Yue P, He X, Liu L, Luo X.
Effect of Topography Truncation on Experimental Simulation of Flow over Complex Terrain. *Applied Sciences*. 2022; 12(5):2477.
https://doi.org/10.3390/app12052477

**Chicago/Turabian Style**

Wang, Zhen, Yunfeng Zou, Peng Yue, Xuhui He, Lulu Liu, and Xiaoyu Luo.
2022. "Effect of Topography Truncation on Experimental Simulation of Flow over Complex Terrain" *Applied Sciences* 12, no. 5: 2477.
https://doi.org/10.3390/app12052477