import numpy as np
[docs]
def circular(diameter):
"""
Calculates the equivalent diameter and projected capture area of a
circular turbine
Parameters
------------
diameter : int/float
Turbine diameter [m]
Returns
---------
equivalent_diameter : float
Equivalent diameter [m]
projected_capture_area : float
Projected capture area [m^2]
"""
if not isinstance(diameter, (int, float)):
raise TypeError(f"diameter must be of type int or float. Got: {type(diameter)}")
equivalent_diameter = diameter
projected_capture_area = (1 / 4) * np.pi * (equivalent_diameter**2)
return equivalent_diameter, projected_capture_area
[docs]
def ducted(duct_diameter):
"""
Calculates the equivalent diameter and projected capture area of a
ducted turbine
Parameters
------------
duct_diameter : int/float
Duct diameter [m]
Returns
---------
equivalent_diameter : float
Equivalent diameter [m]
projected_capture_area : float
Projected capture area [m^2]
"""
if not isinstance(duct_diameter, (int, float)):
raise TypeError(
f"duct_diameter must be of type int or float. Got: {type(duct_diameter)}"
)
equivalent_diameter = duct_diameter
projected_capture_area = (1 / 4) * np.pi * (equivalent_diameter**2)
return equivalent_diameter, projected_capture_area
[docs]
def rectangular(h, w):
"""
Calculates the equivalent diameter and projected capture area of a
retangular turbine
Parameters
------------
h : int/float
Turbine height [m]
w : int/float
Turbine width [m]
Returns
---------
equivalent_diameter : float
Equivalent diameter [m]
projected_capture_area : float
Projected capture area [m^2]
"""
if not isinstance(h, (int, float)):
raise TypeError(f"h must be of type int or float. Got: {type(h)}")
if not isinstance(w, (int, float)):
raise TypeError(f"w must be of type int or float. Got: {type(w)}")
equivalent_diameter = np.sqrt(4.0 * h * w / np.pi)
projected_capture_area = h * w
return equivalent_diameter, projected_capture_area
[docs]
def multiple_circular(diameters):
"""
Calculates the equivalent diameter and projected capture area of a
multiple circular turbine
Parameters
------------
diameters: list
List of device diameters [m]
Returns
---------
equivalent_diameter : float
Equivalent diameter [m]
projected_capture_area : float
Projected capture area [m^2]
"""
if not isinstance(diameters, list):
raise TypeError(f"diameters must be of type list. Got: {type(diameters)}")
diameters_squared = [x**2 for x in diameters]
equivalent_diameter = np.sqrt(sum(diameters_squared))
projected_capture_area = 0.25 * np.pi * sum(diameters_squared)
return equivalent_diameter, projected_capture_area
[docs]
def tip_speed_ratio(rotor_speed, rotor_diameter, inflow_speed):
"""
Function used to calculate the tip speed ratio (TSR) of a MEC device with rotor
Parameters
-----------
rotor_speed : numpy array
Rotor speed [revolutions per second]
rotor_diameter : float/int
Diameter of rotor [m]
inflow_speed : numpy array
Velocity of inflow condition [m/s]
Returns
--------
TSR : numpy array
Calculated tip speed ratio (TSR)
"""
try:
rotor_speed = np.asarray(rotor_speed)
except:
"rotor_speed must be of type np.ndarray"
try:
inflow_speed = np.asarray(inflow_speed)
except:
"inflow_speed must be of type np.ndarray"
if not isinstance(rotor_diameter, (float, int)):
raise TypeError(
f"rotor_diameter must be of type int or float. Got: {type(rotor_diameter)}"
)
rotor_velocity = rotor_speed * np.pi * rotor_diameter
TSR = rotor_velocity / inflow_speed
return TSR
[docs]
def power_coefficient(power, inflow_speed, capture_area, rho):
"""
Function that calculates the power coefficient of MEC device
Parameters
-----------
power : numpy array
Power output signal of device after losses [W]
inflow_speed : numpy array
Speed of inflow [m/s]
capture_area : float/int
Projected area of rotor normal to inflow [m^2]
rho : float/int
Density of environment [kg/m^3]
Returns
--------
Cp : numpy array
Power coefficient of device [-]
"""
try:
power = np.asarray(power)
except:
"power must be of type np.ndarray"
try:
inflow_speed = np.asarray(inflow_speed)
except:
"inflow_speed must be of type np.ndarray"
if not isinstance(capture_area, (float, int)):
raise TypeError(
f"capture_area must be of type int or float. Got: {type(capture_area)}"
)
if not isinstance(rho, (float, int)):
raise TypeError(f"rho must be of type int or float. Got: {type(rho)}")
# Predicted power from inflow
power_in = 0.5 * rho * capture_area * inflow_speed**3
Cp = power / power_in
return Cp