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The present study compared the prediction accuracy of the three CFD software packages for simulating airflow around a three-dimensional, isolated hill with a steep slope: 1) WindSim (turbulence model: RNG k- ε RANS), 2) Meteodyn WT (turbulence model: k-L RANS), which are the leading commercially available CFD software packages in the wind power industry and 3) RIAM-COMPACT (turbulence model: standard Smagorinsky LES), which has been developed by the lead author of the present paper. Distinct differences in the airflow patterns were identified in the vicinity of the isolated hill (especially downstream of the hill) between the RANS results and the LES results. No reverse flow region (vortex region) characterized by negative wind velocities was identified downstream of the isolated hill in the result from the simulation with WindSim (RNG k- ε RANS) and Meteodyn WT ( k-L RANS). In the case of the simulation with RIAM-COMPACT natural terrain version (standard Smagorinsky LES), a reverse flow region (vortex region) characterized by negative wind velocities clearly forms. Next, an example of wind risk (terrain-induced turbulence) diagnostics was presented for a large-scale wind farm in China. The vertical profiles of the streamwise ( x) wind velocity do not follow the so-called power law wind profile; a large velocity deficit can be seen between the hub center and the lower end of the swept area in the case of the LES calculation (RIAM-COMPACT).

We have developed an unsteady and non-linear wind synopsis simulator called RIAM-COMPACT (Research Institute for Applied Mechanics, Kyushu University, Computational Prediction of Airflow over Complex Terrain) in order to simulate the airflow on a microscale, i.e., a few tens of km or less [

On another front, commercially available CFD software such as STAR-CCM+ [

The wind power industry has on its own developed and distributed CFD software designed for selecting sites appropriate for the installation of wind turbine generators. One such leading software package is Meteodyn WT [

In the present study, numerical simulations are performed for airflow over and around a three-dimensional, isolated hill with a steep slope angle using the three CFD software packages (WindSim, Meteodyn WT and RIAM-COMPACT). The results of the comparison are discussed. Next, the numerical simulations for airflow over a large-scale wind farm in China [

The numerical wind simulations in the present study are conducted for high Reynolds number airflow over and around a three-dimensional, isolated hill with a steep slope angle and a large-scale wind farm in China.

CFD model | RIAM-COMPACT | WindSim |
---|---|---|

Turbulence model | Standard Smagorinsky LES | RNG k-ε RANS |

Atmospheric stratification (Atmospheric stability) | Neutral atmosphere | |

Coriolis force | Not considered | |

Surface roughness | Not considered (Smooth surface) | Roughness length: 0.001 |

Ground surface boundary condition | Non-slip condition (Three wind velocity components at the ground surface are zero.) | Wall function |

Shape function of the isolated hill z (r) | 0.5h × {1 + cos(πr/a)}, r = (x^{2} + y^{2})^{1/2}, a = 2h | |

Height of the isolated hill h | 100 (m) | |

Reynolds number Re (=U_{in}h/ν) | 5 × 10^{4} and 1 × 10^{7} | 5 × 10^{4} and 1 × 10^{7} |

Time step Δt | 10^{−3} h/U_{in} (s) for Re = 5 × 10^{4} 10^{−7} h/U_{in} (s) for Re = 1 × 10^{7} | - |

Computational domain size | 13h (i) × 9h (j) × 8h (k) for Re = 5 × 10^{4} | 13h (i) × 9h (j) × 8h (k) |

19h (i) × 18h (j) × 8h (k) for Re = 1 × 10^{7} | ||

Number of computational grid points | 325 (i) × 226 (j) × 37 (k) (Approx. 2.7 million points) for Re = 5 × 10^{4} | 325 (i) × 226 (j) × 37 (k) (Approx. 2.7 million points) |

436 (i) × 325 (j) × 101 (k) (Approx. 14.3 million points) for Re = 1 × 10^{7} | ||

Streamwise (x) grid spacing (Δx) | 0.04 × h for Re = 5 × 10^{4} (0.035 - 0.5) × h for Re = 1 × 10^{7} | 0.04 × h |

Spanwise (y) grid spacing (Δy) | ||

Vertical (z) grid spacing (Δz) | (0.05 - 0.40) × h for Re = 5 × 10^{4} (0.000004 - 0.6) × h for Re = 1 × 10^{7} | (0.05 - 0.40) × h |

the present study: RIAM-COMPACT natural terrain version (turbulence model: LES) and WindSim (turbulence model: RANS).

In RIAM-COMPACT, a collocated grid in a general curvilinear coordinate system is used in order to numerically predict local wind flow over complex terrain with high accuracy while avoiding numerical instability. For the numerical simulation method, a FDM is adopted, and an LES model is used for the turbulence model. For the computational algorithm, a method similar to a FS method [

For discretization of all the spatial terms in the governing equations except for the convective term in the Navier-Stokes equation, a second-order central difference scheme is applied. For the convective term, a third-order upwind difference scheme is used. An interpolation technique based on four-point differencing and four-point interpolation by Kajishima [

Regarding the boundary conditions adopted for the simulations with RIAM-COMPACT, the same inflow profile as used for the simulations with WindSim (_{in}h/ν) = 10^{7}, the number of grid points is changed to 101 in the vertical direction, and the minimum vertical grid spacing in is set to Δz_{min}/h = 4 × 10^{−7} according to the equation below (see

Δ z min / h = 0.1 Re (1)

In contrast to RIAM-COMPACT, WindSim uses RANS models. In the present study, the RNG k-ε RANS model is selected for the simulations. Refer to [

(Re = 5 × 10^{4} and 5 × 10^{7}) did a reverse flow region (vortex region), in which the values of the streamwise wind velocity are negative, form downstream of the isolated hill. Instead, a potential-flow-like pattern formed in both simulations.

^{4} and 1 × 10^{7}). An examination of these simulation results reveals the clear presence of a reverse flow region (vortex region), in which the values of the streamwise wind velocity are negative, downstream of the isolated hill.

For the present study, numerical simulations are conducted for high Reynolds number flow around a three-dimensional, isolated hill with a steep slope angle using RIAM-COMPACT, which is based on an LES turbulence model, and

Meteodyn WT, which is based on a RANS turbulence model (see

CFD model | RIAM-COMPACT | Meteodyn WT |
---|---|---|

Turbulence model | Standard Smagorinsky LES | k-L RANS (A single equation model) |

Atmospheric stratification (Atmospheric stability) | Neutral atmosphere | |

Coriolis force | Not considered | |

Surface roughness | Not considered (Smooth surface) | Roughness length: 0.05 (For the ground surface not on the isolated hill: 0.001) |

Ground surface boundary condition | Non-slip condition (Three wind velocity components at the ground surface are zero.) | |

Shape function of the isolated hill z (r) | 0.5h × {1 + cos(πr/a)} r = (x^{2} + y^{2})1/2, a = 2h | |

Height of the isolated hill h | 100 (m) | |

Reynolds number Re (=U_{in}h/ν) | 10^{6} | 10^{7} |

Time step Δt | 10^{−5} h/U_{in} (s) | - |

Computational domain size | 19h (i) × 18h (j) × 8h (k) | |

Number of computational grid points | 436 (i) × 325 (j) × 101 (k) (Approx. 14.3 million points) | 436 (i) × 325 (j) × 37 (k) (Approx. 5.2 million points) |

Streamwise (x) grid spacing (Δx) | (0.035 - 0.5) × h | |

Spanwise (y) grid spacing (Δy) | ||

Vertical (z) grid spacing (Δz) | (0.0001 - 0.6) × h | (0.005 - 1.2) × h |

Since simulations for a flow with Re (=U_{in}h/ν) = 10^{7} were not feasible with the RIAM-COMPACT natural terrain version software because of the time step, a numerical wind simulation is performed at Re = 10^{6}, which is an order of magnitude smaller than the flow simulated with Meteodyn WT. For this simulation, the number of grid points in the vertical direction is set to 101 (37 for the simulation with Meteodyn WT), and the minimum vertical spacing is set to Δz_{min}/h = 10^{−4} based on the Equation (1) (Δz_{min}/h = 5.0 × 10^{−3} for the simulation with Meteodyn WT, see ^{−5} h/U_{in} (refer to

Figures 10-12 show results from the simulation with the Meteodyn WT software package (turbulence model: k-L RANS). These results (for a flow at Re = 10^{7}) indicate that a reverse flow region (vortex region) characterized by negative values of wind velocity does not form downstream of the isolated hill, and a pattern resembling potential flow is present there. _{in}h/ν) = 10^{6}.

Dougu wind farm is located in the city of Mengzi, Honghe prefecture, Yunnan province, China (see

ranges from around 1850 to 2200 meters. The cliff has a height of around 900 m with slopes exceeding 60 degrees in places. Aerial photos from Google Earth indicate vegetation is abundant at the bottom of the cliff but scarce along the cliff and in the vicinity of turbines. Since the start of operations, one of the wind turbines, turbine No.12 (T12) has experienced vibration problems. Wind farm operator Yunnan Huadian Dougu Wind Power Corporation (YUDWPC) suspected the vibration issue is related to wind conditions. In the present study, the simulations are performed with RIAM-COMPACT, which is based on an LES turbulence model, and WindSim, which is based on a RANS turbulence model. The results from the simulations are compared.

The vibration problem of turbine T12 was investigated by the operator YUDWPC and a report was issued in April 2014 [

For LES simulation, the RIAM-COMPACT natural terrain version software package was employed. The software uses a standard Smagorinsky turbulence model. For the simulation, SRTM 90 m data was used for elevation data. Wind direction is set to true north at 247 degrees and the computational domain constructed is shown in

− Domain size: 14.0 km × 13.3 km × 8.3 km

− Elevation: 1275 m (Min) - 2232 m (Max)

− Calculation grid points: 300 × 400 × 60

− Total number of grid points: 7.2 million

− Grid spacing: 8 m - 957 m (x), 13 m - 72 m (y), 1 m - 470 m (z)

To increase calculation accuracy, the mesh is concentrated around the turbine positions in both the x and y direction as shown in

The simulation results also indicate that the wind flow is relatively undisturbed above hub height level. The U component wind speed time series during the ten minute simulation at rotor top (106.3 m), hub center (65 m), rotor bottom (23.7 m) and surface level (10 m) positions are plotted in

Referring to

wind is flowing in reverse direction. During the ten minute simulation, negative values account for 62% of the total data at rotor bottom. When the rotor bottom wind speed is at its minimum of negative 6.2 m/s the wind speed at rotor top is at 18.1 m/s, hence a very large absolute wind speed difference of 24.3 m/s. Excluding the negative wind speed data, the wind speed difference across the rotor face (between rotor top and rotor bottom) has a maximum value of 18.7 m/s and an average of 17.4 m/s. The maximum wind shear exponent is calculated to be 5.8 with an average value of 2.5, far exceeding the IEC standard average shear value of 0.2.

The average, minimum and maximum values of the U component wind speed at turbine T12 are shown in

In this study, the commercial software Meteodyn WT (turbulence model: k-L RANS) was employed and its results were compared with the results calculated by the RIAM-COMAPCT. The calculation parameters are shown in

Wind direction | 247 degrees |
---|---|

Thermal stability class | 2 |

Smoothing-Whole domain | 1 |

Forest model | Robust model |

Minimum horizontal spacing | 5 m |

Minimum vertical spacing | 2 m |

Horizontal expansion coefficient | 1.1 |

Vertical expansion coefficient | 1.2 |

Grid points | 225 (i) × 237 (j) × 44 (k) (Approx. 2.3 million points) |

Maximum iteration number | 25 |

Convergence | 99.3 % |

Meteodyn WT’s calculation output includes the speed-up factor from height 20 m to 200 m at an interval of 20 m at turbine T12. These values are shown in

Height (m) | Speed-up factor | Wind speed (m/s) |
---|---|---|

20 | 1.850 | 17.58 |

40 | 1.952 | 18.54 |

60 | 2.002 | 19.02 |

80 | 2.013 | 19.12 |

100 | 2.008 | 19.08 |

120 | 1.998 | 18.98 |

140 | 1.987 | 18.88 |

160 | 1.977 | 18.78 |

180 | 1.968 | 18.70 |

200 | 1.959 | 18.61 |

speed at different heights can be calculated based on the speed-up factor and the results are shown in

The wind speed figures in

Referring to

Simulations were performed for airflow around a three-dimensional, isolated hill with a steep slope angle in order to compare the flow pattern simulated in the vicinity of the hill by three software packages. For the simulations, three software packages were used: 1) WindSim (turbulence model: RNG k-ε RANS), 2) Meteodyn WT (turbulence model: k-L RANS), which are the leading commercially available CFD software packages in the wind power industry and 3) RIAM-COMPACT (turbulence model: standard Smagorinsky LES). Comparisons of the simulated results revealed a distinct difference in the simulated flow patterns in the vicinity of the isolated hill (especially downstream of the hill). No reverse flow region (vortex region) characterized by negative wind velocities was identified downstream of the isolated hill in the result from the simulation with WindSim (RNG k-ε RANS) and Meteodyn WT (k-L RANS). In the case

RIAM-COMPACT | Meteodyn WT | |
---|---|---|

Wind speed near rotor bottom at height (m/s) | 0.11 (23.7 m) | 17.58 (20 m) |

Wind speed near rotor top at height (m/s) | 18.0 (102.6 m) | 19.08 (100 m) |

Wind speed difference (m/s) | 17.9 | 1.5 |

Average shear exponent | 3.5 | 0.025 |

Average shear exponent exceeding IEC standard | YES | NO |

of the simulation with RIAM-COMPACT (standard Smagorinsky LES), a reverse flow region (vortex region) characterized by negative wind velocities clearly forms.

Next, a turbine which has vibration problems was simulated using the Meteodyn WT (k-L RANS) and RIAM-COMPACT (standard Smagorinsky LES). It was deduced from the vibration and turbine operation data that a possible reverse flow region near the rotor bottom was the direct cause of the vibration. Simulation results from LES-based code RIAM-COMPACT predict a flow separation upstream and a reverse flow region at the rotor bottom. Simulation results from RANS-based software Meteodyn WT produced a very different shear profile which suggests the reverse flow and the associated flow separation were not predicted.

This work was supported by JSPS KAKENHI Grant Number 17H02053.

The authors declare no conflicts of interest regarding the publication of this paper.

Uchida, T. and Li, G. (2018) Comparison of RANS and LES in the Prediction of Airflow Field over Steep Complex Terrain. Open Journal of Fluid Dynamics, 8, 286-307. https://doi.org/10.4236/ojfd.2018.83018

As discussed in the above text of the present paper, no reverse flow region (vortex region) characterized by negative wind velocities was identified downstream of the isolated hill in the result from the simulation with WindSim (RNG k-ε RANS) and Meteodyn WT (k-L RANS), in which the Reynolds number was set to Re = 10^{7} (the default value for Meteodyn WT). Accordingly, in order to investigate if a flow pattern similar to that simulated with Meteodyn WT (k-L RANS) can also be formed with the use of RIAM-COMPACT (standard Smagorinsky LES), a simulation is conducted with RIAM-COMPACT in which the method for setting the surface boundary conditions is modified. Specifically, the values of the three components of the wind velocity from k = 2 on the computational grid of Meteodyn WT (k-L RANS) (k = 1 corresponds to the surface of the ground or the isolated hill in Meteodyn WT) are assigned as the values for the surface boundary conditions (k = 1) for the simulation with RIAM-COMPACT (standard Smagorinsky LES) (_{in}h/ν) = 10^{4}, and the computational grids shown in ^{−3} h/U_{in}. The results obtained from this simulation are compared to those from a simulation which is identical to the simulation described in this addendum, except that non-slip conditions are applied at the surfaces of the ground and the isolated hill, that is, the three components of the wind velocity are all set to zero as Dirichlet boundary conditions. For convenience, the simulation in which non-zero wind velocities are applied as a Dirichlet boundary condition is denoted as Case 1, and the simulation in which all three components of the wind velocity are set to zero is denoted as Case 2. A comparison of the simulation results is shown in

An examination of

Thus, the flow pattern which forms in the vicinity of the isolated hill varies significantly according to the velocity boundary conditions applied for the surfaces of the ground and the isolated hill.