Average Wind Power Density

The averageWindPowerDensity field represents the average wind power density (in W/m²) over a specified period (annual, seasonal, or monthly, depending on simulation settings). It combines CFD results from multiple wind directions with statistical wind data to quantify the energy potential of the wind across the computational domain.

How is it computed?

1. Wind Directions

   • The simulation runs for 8 or 16 directions, evenly spaced over 360°.
   • Each direction provides local wind speed results on the computational mesh.

2. Wind Statistics (Weibull Distribution)

   • For each wind direction, the observed wind climate is described using Weibull parameters:
     • Shape factor \(k\)
     • Scale factor \(c\)
   • These parameters define the distribution of wind speeds from that direction.

3. Expected Cubed Speed

   • The average cubed wind speed for each direction is derived analytically from the Weibull distribution:

     $$ \mathbb{E}[S^3] = c^3 \cdot \Gamma\left(1 + \frac{3}{k}\right) $$

   • This ensures the computation accounts for the full variability of the wind, not just discrete speed bins.

4. Local Wind Power Density Contribution

   • For each wind direction, the contribution at a location is:

     $$ WPD_{\theta} = \frac{occurrence_{\theta}}{100} \times \frac{1}{2}\rho \left(\frac{U_{\text{local, simulated}}}{U_{\text{met, simulated}}}\right)^3 \cdot \mathbb{E}[S^3] $$

   • Where:

     • \(\rho\) is air density (1.225 kg/m³ by default).
     • \(U_{\text{local, simulated}}\) is the CFD wind speed at the site.
     • \(U_{\text{met, simulated}}\) is the reference speed used in simulations.
     • \(occurrence_{\theta}\) is the statistical frequency of that wind direction.

5. Aggregation

   • The contributions from all wind directions are summed to form the averageWindPowerDensity field.

Why it matters

The averageWindPowerDensity field provides actionable insight into the energy potential of the wind at a site:

• Wind Farm Prospecting and Planning: Identifies high-potential zones for turbine siting.
• Urban and Industrial Studies: Helps assess renewable energy opportunities in built environments.
• Comparative Analysis: Enables consistent evaluation across different time periods (monthly, seasonal, annual).

By combining CFD simulations with site-specific wind statistics, this field bridges local flow patterns and long-term wind climate data.