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windturbine.py
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import pandas as pd
import math
import matplotlib.pyplot as plt
import numpy as np
from scipy import interpolate
bn = 3 #Blades number [-]
hubr = 0.01 #Hub radius [m]
blade_min_radius = 0.05 #Blade min working radius [m]
blade_max_radius = 0.20 #Blade max working radius [m] (Rotor radius)
blade_sections_number = 9 #Blade sections [-]
uinf = 6 #Rated wind speed [m/s]
lamb = 6 #Rated lamda [-] (Omega*bmaxr/uinf)
rho=1.225 #Air density [kg/m3]
cilsec = True #If true output sections are on a cilindrical surface
pivotx = 0 #Pivot point x for airfoil rotation
pivoty = 0 #Pivot point y for airfoil rotation
# Instatntiate plot figure
fig = plt.figure()
# Read airfoil data from CSV
dataS822= pd.read_csv("dataS822.csv",header=0,names=['Re','alpha','cl','cd','eta'],sep=',')
# Data interpolation for calculation
# fcd = interpolate.interp2d(dataS822.Re, dataS822.alpha, dataS822.cd, kind='quintic')
# fcl = interpolate.interp2d(dataS822.Re, dataS822.alpha, dataS822.cl, kind='quintic')
# feta= interpolate.interp2d(dataS822.Re, dataS822.alpha, dataS822.eta, kind='quintic')
# Prepare data for interpolation
points = np.column_stack((dataS822.Re, dataS822.alpha)) # column_stack is used to stack 1-D arrays as columns into a 2-D array for example (a,b,c) and (d,e,f) will be (a,d),(b,e),(c,f)
fcd = interpolate.LinearNDInterpolator(points, dataS822.cd)
fcl = interpolate.LinearNDInterpolator(points, dataS822.cl)
feta = interpolate.LinearNDInterpolator(points, dataS822.eta)
# Create grid for plotting
Regrid = np.arange(50000, 525000, 25000) # Reynolds number grid for interpolation
alphagrid = np.arange(-10, 15, 1) # Angle of attack grid for interpolation
# Create meshgrid
Regrid, alphagrid = np.meshgrid(Regrid, alphagrid) # Create meshgrid for interpolation points
# Interpolate values
cdplot = fcd(Regrid, alphagrid)
clplot = fcl(Regrid, alphagrid)
etaplot = feta(Regrid, alphagrid)
# Plot of airfoil "cd"
ax221 = fig.add_subplot(221, projection='3d')
ax221.scatter(dataS822.Re, dataS822.alpha, dataS822.cd)
ax221.plot_surface(Regrid, alphagrid, cdplot)
# Plot of airfoil "cl"
ax222 = fig.add_subplot(222, projection='3d')
ax222.scatter(dataS822.Re, dataS822.alpha, dataS822.cl)
ax222.plot_surface(Regrid, alphagrid, clplot)
# Plot of airfoil "eta"
ax223 = fig.add_subplot(223, projection='3d')
ax223.scatter(dataS822.Re, dataS822.alpha, dataS822.eta)
ax223.plot_surface(Regrid, alphagrid, etaplot)
# If needed show airfoil plot
#plt.show()
# Rated angular speed calculation
omegar = lamb*uinf/blade_max_radius
print('Turbine rated speed: ' + str(omegar*60/(2*math.pi)))
# This function calculate for every section of the blade some parameters. This function must be called iteratively starting from the result
# of previus call of the same function. The process may converge.
def bladesection(a_arr,a1_arr,c_arr):
print('{:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10} {:<10}'.format('r', 'w', 'phi', 'Re', 'alpha', 'cd', 'cl', 'chord', 'cx', 'cy', 'newa', 'newa1', 'DeltaCp', 'Twist'))
print('---------------------------------------------------------------------------------------------------------------------------------------------------------------')
out_a_arr = np.empty(blade_sections_number)
out_a1_arr = np.empty(blade_sections_number)
out_c_arr = np.empty(blade_sections_number)
out_cp_arr = np.empty(blade_sections_number)
out_twist_arr = np.empty(blade_sections_number)
for i in range(blade_sections_number):
r = sector_radius[i]
a = a_arr[i] #axial induction factor
a1 = a1_arr[i] #angular induction factor
c = c_arr[i] #chord
w = math.sqrt((uinf*(1-a))**2 + (omegar*r*(1+a1))**2) #relative wind speed
phi = math.atan((uinf*(1-a))/(omegar*r*(1+a1))) #angle of attack
re = w*c/1.45e-5 #Reynolds number
if re < 50000:
re = 50000
alphas = np.linspace(-10,14,100) #angle of attack range
etas = feta(re,alphas) #efficiency
#plt.plot(alphas,etas)
#plt.show()
bestalpha = alphas.item(np.argmax(etas)) #best angle of attack for efficiency
cdrags = fcd(re,alphas) #drag coefficient for every angle of attack
clifts = fcl(re,alphas) #lift coefficient for every angle of attack
bestcd = cdrags.item(np.argmax(etas)) #drag coefficient for best angle of attack
bestcl = clifts.item(np.argmax(etas)) #lift coefficient for best angle of attack
newc = ((8*(2*math.pi*blade_max_radius))/(9*lamb**bestcl*bn))/(math.sqrt((4/9)+((lamb**2)*((r/blade_max_radius)**2)*(1+2/(9*(lamb**2)*((r/blade_max_radius)**2)))**2))) #new chord
out_c_arr[i]=newc #save chord value obtained from airfoil series theoric calculation
cy=bestcl*math.cos(phi)+bestcd*math.sin(phi) #cy and cx are the lift and drag components of the force
cx=bestcl*math.sin(phi)-bestcd*math.cos(phi)
#B=((bn*c)/(2*math.pi*r)*((cy**2)-(((bn*newc)/(2*math.pi*r)*cx**2)/(4*(math.sin(phi))**2))/(4*(math.sin(phi))**2)))
sigmar = bn*newc/(2*math.pi*r)
B=(sigmar/(4*(math.sin(phi)**2)))*((cy**2)-((sigmar*(cx**2))/(4*math.sin(phi)**2)))
newa=B/(B+1)
out_a_arr[i]=newa
F=((bn*newc)/(2*math.pi*r)*cx/(4*math.sin(phi)*math.cos(phi)))
newa1=F/(1-F)
out_a1_arr[i]=newa1
deltacp=((4*math.pi*rho*uinf*(omegar**2)*r*newa1*(1-newa)*(r**2)*((blade_max_radius-blade_min_radius)/blade_sections_number))-(0.5*rho*(w**2)*bestcd*math.cos(phi)*newc*bn*omegar*r*((blade_max_radius-blade_min_radius)/blade_sections_number)))/(0.5*rho*math.pi*(blade_max_radius**2)*(uinf**3))
out_cp_arr[i]=deltacp
twist_ang = phi-(bestalpha*0.017453)
out_twist_arr[i] = twist_ang
print('{:<10.2f} {:<10.2f} {:<10.2f} {:<10.0f} {:<10.2f} {:<10.2f} {:<10.2f} {:<10.3f} {:<10.2f} {:<10.2f} {:<10.2f} {:<10.2f} {:<10.3f} {:<10.3f}'.format(r, w, phi/0.01745, re, bestalpha, bestcd, bestcl, newc, cx, cy, newa, newa1, deltacp, twist_ang/0.017453))
print()
results = [out_a_arr,out_a1_arr,out_c_arr,out_cp_arr,out_twist_arr]
return results
# First attempt values:
cp_0 = 0.44 #First attempt power coefficient
a_0 = 0.333 #First attempt axial induction factor
a1_0 = 0 #First attempt angular induction factor
ci_0 = 0.02 #First attempt airfoil chord
# Fill of first attemp arrays
sector_radius = np.linspace(blade_min_radius,blade_max_radius,blade_sections_number)
a_i=np.empty(blade_sections_number)
a_i.fill(a_0)
a1_i=np.empty(blade_sections_number)
a1_i.fill(a1_0)
ci_i=np.empty(blade_sections_number)
ci_i.fill(ci_0)
#Instead of having a while cycle to convergence there is a for cycle (usually 10 iteration are enought)
for i in range(10):
results = bladesection(a_i,a1_i,ci_i)
a_i = results[0]
a1_i = results[1]
ci_i = results[2]
# Iteration turbine Cp (sum of section Cp)
print('Turbine Cp: ' + str(sum(results[3])))
# Read of airfoil shape from CSV
shapeS822= pd.read_csv("shapeS822.csv",header=0,names=['x','y'],sep=',')
ax224 = fig.add_subplot(224,projection='3d')
# If needed plot the loaded shape
#ax224.plot(shapeS822.x,shapeS822.y)
# Function that scale, rotate, and project airfoil shape based on a pivot point
# It save 3 series of CSV files, the first series without suffix contains the full shape for every blade section,
# the one with suffix "_A" contains the first half shape of the airfoil for every blade section,
# the one with suffix "_B" contains the other half shape of the airfoil for every blade section
def bladeddraw(c_arr,twist_arr,pivot_x,pivot_y):
fig2 = plt.figure()
fig2.tight_layout()
ax111 = fig2.add_subplot(111,projection='3d')
for j in range(blade_sections_number):
x = (shapeS822.x-pivot_x)*c_arr[j]
y = (shapeS822.y-pivot_y)*c_arr[j]
x1 = x*math.cos(twist_arr[j])-y*math.sin(twist_arr[j])
y1 = y*math.cos(twist_arr[j])+x*math.sin(twist_arr[j])
#ax224.plot(x1,y1)
#sigma = (x/secr[j])*2*math.pi
sigma = np.empty(len(x1))
x2 = np.empty(len(x1))
y2 = np.empty(len(x1))
z2 = np.empty(len(x1))
for k in range(len(x1)):
sigma[k] = x1[k]/sector_radius[j]
if cilsec:
x2[k] = 100*sector_radius[j]*math.sin(sigma[k]) #100 convert the coordinate in [cm] but importing it in Fusion360
y2[k] = 100*y1[k] #leads to [mm] dimensions!!!!!
z2[k] = 100*sector_radius[j]*math.cos(sigma[k])
else:
x2[k] = 100*x1[k]
y2[k] = 100*y1[k]
z2[k] = 100*sector_radius[j]
ax224.scatter(x2,y2,z2)
coord = { 'x': x2,
'y': y2,
'z': z2
}
df = pd.DataFrame(coord, columns= ['x', 'y','z'])
fn = 'output/coord_{:.2f}'.format(sector_radius[j]) + '.csv'
df.to_csv (fn, index = False, header=True, float_format='%.3f')
print (df)
coord_a = {'x': x2[0:31],
'y': y2[0:31],
'z': z2[0:31]
}
df = pd.DataFrame(coord_a, columns= ['x', 'y','z'])
fn = 'output/coord_{:.2f}'.format(sector_radius[j]) + '_A.csv'
df.to_csv (fn, index = False, header=True, float_format='%.3f')
print (df)
coord_b = { 'x': x2[30:61],
'y': y2[30:61],
'z': z2[30:61]
}
df = pd.DataFrame(coord_b, columns= ['x', 'y','z'])
fn = 'output/coord_{:.2f}'.format(sector_radius[j]) + '_B.csv'
df.to_csv (fn, index = False, header=True, float_format='%.3f')
print (df)
ax111.scatter(x2,y2,z2)
ax111.set_xlim3d([-50,50])
ax111.set_ylim3d([-50,50])
ax111.set_zlim3d([0,100])
# Call of bladedraw with calculated chords length, angles with a specific pivot point
bladeddraw(ci_i,results[4],pivotx,pivoty)
plt.tight_layout()
# Show the plot with cd, cl, eta and blade subplots
plt.show()