_{1}

The Duogu Wind Farm, China Huadian Group Corporation’s first wind project in Yunnan, China, has been approved by the Provincial Development and Reform Commission. The acquired site is in Mengzi, in the south-east of Yunnan Province. The developer has deployed thirty-three 1.5 MW turbines in this wind farm (49.5 MW), and the total cost of construction has been estimated to be CNY449.7 million ($69.61 million). The present study compared the prediction accuracy of two CFD software packages for simulating flow over an escarpment with a steep slope. The two software packages were: 1) Open FOAM (Turbulence model: SST k- <i>ω</i> RANS), which is a free, open source CFD software package developed by Open CFD Ltd at the ESI Group and distributed by the Open FOAM Foundation and 2) RIAM-COMPACT (Turbulence model: Standard Smagorinsky LES), which has been developed by the lead author of the present paper. Generally good agreement was obtained between the results from the simulations with Open FOAM and RIAM-COMPACT.

The author has developed the numerical wind diagnosis technique named RIAM-COMPACT [

On another front, open-source CFD software packages are more widely used than in the past. One of the most widely used software packages is OpenFOAM (Open Field Operation And Manipulation) [

In the present paper, simulations are performed for the airflow at a large-scale wind farm constructed above a steep escarpment using two software packages: RIAM-COMPACT (Turbulence model: Standard Smagorinsky LES) and OpenFOAM v.2.1.0 (Turbulence model selected for the present study: SST k-ω RANS). Subsequently, the results obtained from these simulations are compared.

In the present study, airflow at Duogu Wind Farm, a large-scale wind farm in China is investigated (

Numerical wind simulations are performed for airflow at Duogu Wind Farm, which is located above a steep escarpment (

model selected for the present study: SST k-ω RANS).

Next, the numerical simulation techniques and simulation set-ups that are used in the two software packages for the present study will be described. The present study uses the RIAM-COMPACT natural terrain version software package, which is based on a collocated grid in a general curvilinear coordinate system, to numerically predict local wind flow over complex terrain with high accuracy while avoiding numerical instability. In this collocated grid, the velocity components and pressure are defined at the grid cell centers, and variables that result from multiplying the contravariant velocity components by the Jacobian are defined at the cell faces. For the numerical simulation method, FDM (Finite-Difference Method) is adopted, and an LES (Large-Eddy Simulation) model is used for the turbulence model. In the LES model, a spatial filter is applied to the flow field to separate eddies of various scales into GS (Grid-Scale) components, which are larger than the computational grid cells, and SGS (Sub-Grid Scale) components, which are smaller than the computational grid cells. Large-scale eddies, i.e., the GS components of turbulence eddies, are directly numerically simulated without the use of a physically simplified model. In contrast, dissipation of energy, which is the main effect of small-scale eddies, i.e., the SGS components, is modeled according to a physics-based analysis of the SGS stress. For the governing equations of the flow, a filtered continuity equation for incompressible fluid and a filtered Navier-Stokes equation are used as follows.

∂ u ¯ i ∂ x i = 0

∂ u ¯ i ∂ t + u ¯ j ∂ u ¯ i ∂ x j = − ∂ p ¯ ∂ x i + 1 R e ∂ 2 u ¯ i ∂ x j ∂ x j − ∂ τ i j ∂ x j

τ i j ≈ u ′ i u ′ j ¯ ≈ 1 3 u ′ k u ′ k ¯ δ i j − 2 ν S G S S ¯ i j

ν S G S = ( C s f s Δ ) 2 | S ¯ |

| S ¯ | = ( 2 S ¯ i j S ¯ i j ) 1 / 2

S ¯ i j = 1 2 ( ∂ u ¯ i ∂ x j + ∂ u ¯ j ∂ x i )

f s = 1 − exp ( − z + / 25 )

Δ = ( h x h y h z ) 1 / 3

Because high wind conditions with mean wind speeds of 6 m/s or higher are considered in the present study, the effect of vertical thermal stratification, which is generally present in the atmosphere, is neglected (neutral atmosphere). The effect of the surface roughness is not taken into consideration, and the terrain surface, including the ground surface, is treated as a smooth surface. For the computational algorithm, a method similar to a FS (Fractional Step) method [

In contrast, the SST (Shear Stress Transport) k-ω model [

{ ∂ k ∂ t + U j ∂ k ∂ x j = P k − β * k ω + ∂ ∂ x j [ ( ν + σ k ν T ) ∂ k ∂ x j ] ∂ ω ∂ t + U j ∂ ω ∂ x j = α S 2 − β ω 2 + ∂ ∂ x j [ ( ν + σ ω ν T ) ∂ k ∂ x j ] + 2 ( 1 − F 1 ) α ω 2 1 ω ∂ k ∂ x i ∂ ω ∂ x i

P k = min ( τ i j ∂ U i ∂ x j , 10 β * k ω )

C D k ω = max [ 2 ρ σ ω 2 1 ω ∂ k ∂ x i ∂ ω ∂ x i , 10 − 10 ]

F 1 = tanh [ ( min ( max ( k β * ω y , 500 ν y 2 ω ) , 4 α ω 2 k C D k ω y 2 ) ) 4 ]

F 2 = tanh [ ( max ( 2 k β * ω y , 500 ν y 2 ω ) ) 2 ]

S = [ 1 2 ( ∂ j u i + ∂ i u j ) ] , ν T = α 1 k max ( α 1 ω , F 2 S )

α 1 = 5 9 , α 2 = 0.44 , β 1 = 3 40

β 2 = 0.0828 , β * = 9 100 , σ k 1 = 0.85

σ k 2 = 1 , σ k 1 = 0.5 , σ k 2 = 0.856

a k-ω model is applied for airflow in and in the vicinity of the boundary layer. The specific equations that are used for the models are shown as follows. As is the case for many existing commercial software packages, the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) method, which is a simultaneous relaxation method, is adopted for the pressure-velocity coupling algorithm in OpenFOAM. The present study uses pisoFoam, which is one of the incompressible flow solvers available for OpenFOAM. The pisoFoam solver is based on the PISO (Pressure Implicit with Splitting of Operators) algorithm [

_{in} is the wind velocity (m/s) at the inflow boundary at height z_{max}. In the present study, the Reynolds number, U_{in}h/ν, is set to 10^{4} for the simulations in both software packages, where ν is the kinematic viscosity of

air (m^{2}/s). In addition, the same boundary conditions are set for the simulations in both software packages. At the inflow boundary, a vertical wind velocity profile is given with a power law exponent of 5. At the side and upper boundaries, slip conditions are applied, and convective outflow conditions are applied at the outflow boundary. On the terrain surface, a viscous boundary condition (no-slip boundary condition) is imposed. The time step is set to Δt = 2 × 10^{−3} h/U_{in} for RIAM-COMPACT and to Δt = 10^{−4} h/U_{in} for OpenFOAM.

Figures 4-6 show comparisons of the simulation results from RIAM-COMPACT (Turbulence model: Standard Smagorinsky LES) and those from OpenFOAM (Turbulence model: SST k-ω RANS).

Next, the influence of the spatial grid resolution on the vertical profile of streamwise (x) wind velocity (non-dimensional) at the location of the wind turbine under investigation (No.12) was considered. For this purpose, the RIAM-COMPACT natural terrain version software package based on a large-eddy simulation (LES) was done (see

Case 1 | Case 2 | Case 3 | |
---|---|---|---|

Wind turbine | No. 12 | ||

Grid points | 101 × 101 × 51 | 301 × 301 × 51 | 1001 × 1001 × 51 |

Time step | 2 × 10^{−3} h/U_{in} | 1 × 10^{−3} h/U_{in} | 1 × 10^{−4} h/U_{in} |

Minimum horizontal grid spacing | Δx = Δy = 37 m | Δx = Δy = 12 m | Δx = Δy = 4 m |

Minimum vertical grid spacing | Δz = 3 m | ||

Domain size | 10.0 × 10.0 × 4.7 km | ||

Others | Same conditions |

Recently, it has been reported that the utilization rates of wind turbines on wind farms situated on complex terrain fall short of expectations; that is, reports of damage and breakage of the exteriors and interiors of wind turbines as well as wind turbines with notably low power output have surfaced. Terrain-induced turbulence is considered as the major cause of these issues from the author’s research results [

(x) × 2.0 (y) × 4.7 (z) km, and the number of grid points is 501 × 101 × 101 points (approximately five million points). The minimum horizontal and vertical grid widths are 7.5 m and 2.75 m, respectively. Other simulation settings are the same as those used for the above simulation.

As shown in

In the present study, numerical wind simulations were performed for a large-scale wind farm (33 wind turbines) located above a steep escarpment in China.

For the simulations, the RIAM-COMPACT software package (Turbulence model: Standard Smagorinsky LES) and the Open FOAM software package (Turbulence model: SST k-ω RANS, selected from various turbulence model options available in this software package) were used. Comparisons of the simulation results revealed that their tendencies were in good agreement. Of particular note, the vertical profiles of the streamwise wind velocity from both of the simulations showed local increases (terrain effects on wind) at the investigated wind turbine location. Next, the influence of the spatial grid resolution on the vertical profile of streamwise (x) wind velocity (non-dimensional) at the location of the wind turbine under investigation was considered. As a result, in order to predict the vertical profile of wind velocity at the location of the wind turbine location precisely, the minimum horizontal grid spacing should be at least 12 m. Finally, an example of wind risk (terrain-induced turbulence) diagnostics was presented. The vertical profiles of the streamwise (x) wind velocity (non-dimensional) do not follow the so-called wind profile power law; a large velocity deficit can be seen between the hub center and the lower end of the swept area.

This work was supported by JSPS KAKENHI Grant Number 17H02053. The author expresses appreciation to them.

Uchida, T. (2017) CFD Prediction of the Airflow at a Large-Scale Wind Farm above a Steep, Three-Dimensional Escarpment. Energy and Power Engineering, 9, 829-842. https://doi.org/10.4236/epe.2017.913052