# Wind Pressure Distributions on Buildings Using the Coherent Structure Smagorinsky Model for LES

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## Abstract

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## 1. Introduction

## 2. SGS Models and Numerical Methods

#### 2.1. SGS Models

_{CSM}is a fixed model constant, F

_{CS}is the coherent structure function defined as the second invariant Q normalized by the magnitude of a velocity gradient tensor E in a GS flow field, and F

_{Ω}is the energy decay suppression function. $\overline{{W}_{ij}}$ is the vorticity tensor in a GS flow field. The wall damping effect is introduced by the coherent structure function F

_{CS}, which reflects the behavior of the second invariant Q [9].

_{CS}and F

_{Ω}have definite upper and lower limits [12]. Therefore, the CSM has small variance in the model parameter and the simulations performed using the CSM are more stable than the simulations that use other SGS models.

#### 2.2. Numerical Methods

## 3. Numerical Simulation for Isolated Buildings in Uniform Flow

#### 3.1. Experiments for Validation

_{0}= 10 m/s, and its turbulence intensity was less than 0.2%.

_{0}B/ν, B = 0.2 m) was about 112,000.

#### 3.2. Computational Model and Calculation Conditions

_{0}= 10 m/s. The outlet boundary was an open boundary with an inletOutlet condition [24]. The walls of the building model and the flat plate were no-slip boundaries. The other boundaries were slip boundaries.

^{−4}, 5 × 10

^{−5}, and 2.5 × 10

^{−5}(s), corresponding to the approximated Courant numbers ($Cr={U}_{0}\Delta t/\Delta $) of 2.0, 1.0, and 0.5, respectively. The simulations were conducted using the 6144 parallel CPUs in “The K Computer”, which was the world’s first-ranked supercomputer of the TOP500 Supercomputers in 2012. Peak pressure coefficients of the building models were calculated from the results of a real-time 1.0 s moving average—the same as the average calculated in the experiment.

#### 3.3. Results and Discussion

#### 3.3.1. Pressure Coefficients of Buildings

_{p}is calculated as follows:

_{0}and U

_{H}are the reference pressure at a 1.4 m height above the building and the wind speed at the eave height of the building, respectively. In this case, the inflow condition was set as the uniform flow, so the wind speed U

_{H}is equal to U

_{0}= 10 m/s.

#### 3.3.2. Flow Fields around Buildings

## 4. Numerical Simulation for a High-Rise Building in an Urban City with Turbulent Flow

#### 4.1. Validation Experiments

_{H}, of 11 m/s at the test model eaves height (H = 0.25 m), which corresponds to a basic wind speed of 36 m/s in terms of real-time conversion. The vertical wind profile at the center of the turntable was measured using a hot-wire anemometer. The mean wind profile was examined using a power law of exponent, α, of 0.2 and longitudinal wind turbulence intensity, I

_{u}, of 15% at the eaves height, H, of the building. The Reynolds number (Re = U

_{H}D/ν, D = 0.085 m) of the experiment was about 52,000.

#### 4.2. Computational Models and Calculation Conditions

_{H}, of 11 m/s—the same as in the wind tunnel experiment. The outlet boundary is an open boundary with an inletOutlet condition [24]. The walls of the building model and wind tunnel are no-slip boundaries.

^{+}for the SM in OpenFOAM using the wave propagation method resulted in a significantly higher computational cost due to the complex geometry of the unstructured mesh and the large-scale computational domain of several hundred million mesh cells.

#### 4.3. Results and Discussion

#### 4.3.1. Wind Flow Characteristics

#### 4.3.2. Flow Fields around the Target Building

#### 4.3.3. Pressure Coefficients of the Target Building for a Specific Wind Direction

#### 4.3.4. Pressure Coefficients of the Target Building for All Wind Directions

## 5. Conclusions

- For an isolated rectangular building in uniform flow, the flow field around the building is generated by the horseshoe vortex and separated flow. Both SM and CSM show good agreement with the PIV results in the flow separation region as well as in the horseshoe vortex regions. The wind pressure coefficients calculated using both SM and CSM consistently agree with the experimental results (values within 20%).
- For an isolated building with a setback in uniform flow, a complex flow field is generated by a distinctive large horseshoe vortex interfering with the separated flow from the lower roof. A large negative pressure coefficient is found at the corner of the sidewall, near the interfered-with area. Although using the SM results in under-prediction, the predictions made using the CSM show good agreement with the PIV results for the flow field. This means that the CSM with the model parameter based on the coherent structure reflects the vortex behaviors and simulates well the complex flow fields due to the strong interference of the vorticities and flow separations. The CSM results also showed much better performance than the SM results for the wind pressure distribution on this building, being within 20% of the experimental results.
- For a high-rise building in an actual urban city with a turbulent boundary layer flow, we found that a strong three-dimensional complex wind flow occurs due to the strong influence of neighboring buildings, including interference of vortices and separated flows. We also found a distinctive wind pressure distribution that had strong positive and negative pressures simultaneously occurring on the front wall of the target building. The CSM also gives more accurate results with less variation than the SM, being within 20% of experimental results. In addition, LES with the CSM was conducted for all wind directions. The calculated largest positive and negative peak pressure coefficients were consistently in good agreement with experimental results (within 20%) in the relatively high-pressure region, at least similar to or less than the COVs of the wind tunnel test results [20].

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The experimental setup. (

**a**) Pressure experiment; (

**b**) particle image velocimetry (PIV) experiment.

**Figure 2.**The definition of the building models and pressure measurement regions. (

**a**) The building referred to as R01; (

**b**) the building referred to as SBL.

**Figure 3.**The definition of the building models and PIV measurement regions. (

**a**) The building R01; (

**b**) the building SBL.

**Figure 5.**The computational mesh and its close-up with refinement levels. (

**a**) The entire mesh in plane view; (

**b**) mesh of building R01; (

**c**) mesh of building SBL.

**Figure 6.**The pressure distribution on buildings obtained from the pressure experiments. (

**a**) Mean pressure coefficient of R01; (

**b**) negative peak pressure coefficient of R01; (

**c**) mean pressure coefficient of SBL; (

**d**) negative peak pressure coefficient of SBL.

**Figure 7.**The pressure coefficients obtained from the SM and CSM with Cr = 2.0 in comparison with experimental results. (

**a**) Mean pressure coefficient of R01; (

**b**) negative peak pressure coefficient of R01; (

**c**) mean pressure coefficient of SBL; (

**d**) negative peak pressure coefficient of SBL.

**Figure 8.**Pressure coefficients obtained from the CSM with different Cr values. (

**a**) Mean pressure coefficient of R01; (

**b**) negative peak pressure coefficient of R01; (

**c**) mean pressure coefficient of SBL; (

**d**) negative peak pressure coefficient of SBL.

**Figure 9.**The mean velocity vector and average vorticity contour obtained by the PIV experiments. (

**a**) The results of building R01 at the central cross section; (

**b**) results of building SBL at the central cross section; (

**c**) results of building R01 at the plane 5 mm away from the sidewall; (

**d**) results of building SBL at the plane 5 mm away from the sidewall.

**Figure 10.**The mean streamline around buildings as obtained using the CSM. (

**a**) Building R01; (

**b**) building SBL.

**Figure 11.**The mean velocity profile in the planes A1, A2, and A3 as obtained by the SM and the CSM in comparison with the PIV experiments. (

**a**) Results of building R01; (

**b**) partially enlarged view of results of building R01; (

**c**) results of building SBL; (

**d**) partially enlarged view of results of building SBL.

**Figure 12.**The mean velocity profile in the plane B1, 5 mm away from surface W1, obtained using the SM and the CSM in comparison with the PIV experiments. (

**a**) Results of building R01; (

**b**) partially enlarged view of results of building R01; (

**c**) results of building SBL; (

**d**) partially enlarged view of results of building SBL.

**Figure 13.**Wind tunnel experiment. (

**a**) Wind tunnel model setup; (

**b**) target building and pressure measurement point layers.

**Figure 16.**The computational mesh of the building model, its vicinity, and an enlarged view. (

**a**) Mesh A (140 million cells); (

**b**) Mesh B (1.1 billion cells).

**Figure 17.**The wind flow characteristics as obtained by the experiments and LES (Mesh A without buildings). (

**a**) Mean wind speed; (

**b**) longitudinal turbulence intensity, Iu; (

**c**) lateral turbulence intensity, Iv; (

**d**) vertical turbulence intensity, Iw; (

**e**) power spectrum density, Su; (

**f**) power spectrum density, Sv; (

**g**) power spectrum density, Sw.

**Figure 18.**The mean wind speed contours. (

**a**) Section z = 0.2H; (

**b**) section z = 0.5H; (

**c**) section z = 0.9H.

**Figure 19.**The flow field around the target building as obtained by the CSM with Mesh A. (

**a**) Mean streamline; (

**b**) instantaneous Q-criterion isosurface (Q = 300,000).

**Figure 20.**The mean pressure coefficient. (

**a**) Experimental values; (

**b**) result of the SM with Mesh A; (

**c**) result of the CSM with Mesh A; (

**d**) result of the CSM with Mesh B.

**Figure 21.**The comparisons of the mean pressure coefficients between the experiments and LES. (

**a**) Result of the SM with Mesh A; (

**b**) result of the CSM with Mesh A; (

**c**) results of the CSM with Mesh B.

**Figure 22.**The comparisons between experiments and LES of the largest negative peak pressure coefficients. (

**a**) SM with Mesh A; (

**b**) results of the CSM with Mesh A; (

**c**) results of the CSM with Mesh B.

**Figure 23.**The pressure coefficients as obtained by the experiments and LES using CSM (Mesh A, five samples). (

**a**) Mean coefficient; (

**b**) standard deviation coefficient; (

**c**) largest positive peak pressure coefficient; (

**d**) largest negative peak pressure coefficient.

**Figure 24.**The comparison of the peak pressure coefficients estimated for all wind directions (CSM, Mesh A). (

**a**) Largest positive peak pressure coefficient; (

**b**) largest negative peak pressure coefficient.

**Figure 25.**The pressure coefficients for all wind directions calculated from experiments and LES using the CSM. (

**a**) Largest positive peak pressure coefficient; (

**b**) largest negative peak pressure coefficient.

Type | B | D | H | H_{1} | H_{2} | D_{1} |
---|---|---|---|---|---|---|

R01 | 0.20 | 0.10 | 0.20 | |||

SBL | 0.20 | 0.10 | 0.20 | 0.15 | 0.05 | 0.35 |

Subgrid-Scale (SGS) Model | Smagorinsky Model (SM) | Coherent Structure Smagorinsky Model (CSM) |
---|---|---|

Mesh cells (millions) | 570 | 570 |

Time increment Δt (s) | 10^{−4} | 10^{−4}, 5 × 10^{−5}, 2.5 × 10^{−5} |

Courant number Cr | 2.0 | 2.0, 1.0, 0.5 |

Initial run-up time (s) | 3 | 3 |

Evaluation time (s) | 8 | 8 |

Number of parallel CPUs | 6144 | 6144 |

SGS Model Use in Large Eddy Simulation (LES) | SM | CSM | CSM |
---|---|---|---|

Mesh type | A | A | B |

Mesh cells (millions) | 140 | 140 | 1100 |

Wind direction θ (degree) | 60 | 60 (0, .., 350) | 60 |

Time increment Δt (s) | 2.5 × 10^{−5} | 2.5 × 10^{−5} | 1.25 × 10^{−5} |

Courant number Cr | 1 | 1 | 1 |

Initial run-up time (s) | 3 | 3 | 3 |

Evaluation time (s) | 18 | 30 (6) | 6 |

Number of samples in ten-minute record in real-time conversion for evaluation | 3 | 5 (1) | 1 |

Number of parallel CPUs | 768 | 768 | 6144 |

Computational time for one sample (days) | 40 | 20 | 20 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Phuc, P.V.; Nozu, T.; Kikuchi, H.; Hibi, K.; Tamura, Y.
Wind Pressure Distributions on Buildings Using the Coherent Structure Smagorinsky Model for LES. *Computation* **2018**, *6*, 32.
https://doi.org/10.3390/computation6020032

**AMA Style**

Phuc PV, Nozu T, Kikuchi H, Hibi K, Tamura Y.
Wind Pressure Distributions on Buildings Using the Coherent Structure Smagorinsky Model for LES. *Computation*. 2018; 6(2):32.
https://doi.org/10.3390/computation6020032

**Chicago/Turabian Style**

Phuc, Pham Van, Tsuyoshi Nozu, Hirotoshi Kikuchi, Kazuki Hibi, and Yukio Tamura.
2018. "Wind Pressure Distributions on Buildings Using the Coherent Structure Smagorinsky Model for LES" *Computation* 6, no. 2: 32.
https://doi.org/10.3390/computation6020032