windpowerlib.density.ideal_gas¶

windpowerlib.density.ideal_gas(pressure, pressure_height, hub_height, temperature_hub_height)[source]¶

Calculates the density of air at hub height using the ideal gas equation.

This function is carried out when the parameter density_model of an instance of the ModelChain class is ‘ideal_gas’.

Parameters:	pressure (pandas.Series or numpy.array) – Air pressure in Pa. pressure_height (float) – Height in m for which the parameter pressure applies. hub_height (float) – Hub height of wind turbine in m. temperature_hub_height (pandas.Series or numpy.array) – Air temperature at hub height in K.
Returns:	Density of air at hub height in kg/m³. Returns a pandas.Series if one of the input parameters is a pandas.Series.
Return type:	pandas.Series or numpy.array

Notes

The following equations are used [1] [2] [3]:

$\rho_{hub}=p_{hub}/ (R_s T_{hub})$

and [4]:

$p_{hub}=\left(p/100-\left(h_{hub}-h_{p,data}\right)\cdot \frac{1}{8}\right)\cdot 100$

with:: T: temperature [K], $\rho$ : density [kg/m³], p: pressure [Pa]

$h_{p,data}$ is the height of the measurement or model data for pressure, $R_s$ is the specific gas constant of dry air (287.058 J/(kg*K)) and $p_{hub}$ is the pressure at hub height $h_{hub}$ .

References

[1]	Ahrendts J., Kabelac S.: “Das Ingenieurwissen - Technische Thermodynamik”. 34. Auflage, Springer-Verlag, 2014, p. 23

[2]	Biank, M.: “Methodology, Implementation and Validation of a Variable Scale Simulation Model for Windpower based on the Georeferenced Installation Register of Germany”. Master’s Thesis at RLI, 2014, p. 57

[3]	Knorr, K.: “Modellierung von raum-zeitlichen Eigenschaften der Windenergieeinspeisung für wetterdatenbasierte Windleistungssimulationen”. Universität Kassel, Diss., 2016, p. 97

[4]	Deutscher Wetterdienst: http://www.dwd.de/DE/service/lexikon/begriffe/D/Druckgradient_pdf.pdf?__blob=publicationFile&v=4