def ainslie(ct, u0, distance_parallel, distance_perpendicular):
# centreline = open('centreline.dat', 'w')
# velocity = open('velocity.dat', 'w')
h = 0.2
L = distance_parallel
n = int(L / h) + 1
Uc1 = [0.0 for x in range(n)]
d1 = [0.0 for x in range(n)]
I0 = 8.0 # Ambient turbulence intensity according to vanlucanee. 8% on average
k = 0.41 # von Karman constant
Ct = ct # Thrust coefficient
U0 = u0
# dr = 0.1
Y = distance_perpendicular
# m = int(Y / dr)
Dmi = Ct - 0.05 - (16.0 * Ct - 0.5) * I0 / 1000.0
def b(deficit): # Wake width measure
return (3.56 * Ct / (8.0 * deficit * (1.0 - 0.5 * deficit))) ** 0.5
def F(x): # Factor for near and far wake
if x >= 5.5:
return 1.0
if x < 5.5:
if x >= 4.5:
return 0.65 + ((x - 4.5) / 23.32) ** (1.0 / 3.0)
else:
return 0.65 - ((-x + 4.5) / 23.32) ** (1.0 / 3.0)
def E(x1, Uf, Ud, Dm): # Eddy viscosity term
return F(x1) * (0.015 * b(Dm) * (Uf - Ud)) + (k ** 2.0) * I0 / 100.0
Uc = U0 * (1.0 - Dmi) # Boundary condition at x = 2.0
d = Dmi
Uc1[0] = U0 * (1.0 - Dmi) # Boundary condition at x = 2.0
d1[0] = Dmi
for i in range(1, n): # For all positions in the wake centreline direction. Recursive. Whole grid
Uc1[i] = Uc1[i - 1] + (h * 16.0 * E(i * h, U0, Uc1[i - 1], d1[i - 1]) * (Uc1[i - 1] ** 3.0 - U0 * Uc1[i - 1] ** 2.0 - Uc1[i - 1] * U0 ** 2.0 + U0 ** 3.0) / (Uc1[i - 1] * Ct * U0 ** 2.0))
d1[i] = 1.0 - Uc1[i] / U0
########### Code to calculate wake deficit at a specific point instead of the whole grid. Namely, the rotor's centrepoint.
# U = U0 * (1.0 - d1[n-1] * exp(- 3.56 * (Y / b(d1[n-1])) ** 2.0))
##### Code to calculate average wake deficit in all area of the rotor ###############
## Define function to integrate.
def G(r, theta):
z = sqrt(Y ** 2.0 + r ** 2.0 + 2.0 * Y * r * cos(theta))
gauss = U0 * (1.0 - d1[n - 1] * exp(- 3.56 * (z / b(d1[n - 1])) ** 2.0))
return r * (U0 - gauss) ** 2.0
A = pi * 0.5 ** 2.0 ## Unitary diameter in this program.
U = U0 - sqrt((1.0 / A) * simpson_integrate2D(G, 0.0, 0.5, 5, 0.0, 2.0 * pi, 10))
return 1.0 - U / U0
def wake_deficit(U0, ct, A, x, r, c1):
return sqrt(
(1.0 / A) *
simpson_integrate2D(integrand, 0.0, 40.0, 5, 0.0, 2 * pi, 10)) / U0
def ainslie(ct, u0, distance_parallel, distance_perpendicular):
# centreline = open('centreline.dat', 'w')
# velocity = open('velocity.dat', 'w')
h = 0.2
L = distance_parallel
n = int(L / h) + 1
Uc1 = [0.0 for x in range(n)]
d1 = [0.0 for x in range(n)]
I0 = 8.0 # Ambient turbulence intensity according to vanlucanee. 8% on average
k = 0.41 # von Karman constant
Ct = ct # Thrust coefficient
U0 = u0
# dr = 0.1
Y = distance_perpendicular
# m = int(Y / dr)
Dmi = Ct - 0.05 - (16.0 * Ct - 0.5) * I0 / 1000.0
def b(deficit): # Wake width measure
return (3.56 * Ct / (8.0 * deficit * (1.0 - 0.5 * deficit)))**0.5
def F(x): # Factor for near and far wake
if x >= 5.5:
return 1.0
if x < 5.5:
if x >= 4.5:
return 0.65 + ((x - 4.5) / 23.32)**(1.0 / 3.0)
else:
return 0.65 - ((-x + 4.5) / 23.32)**(1.0 / 3.0)
def E(x1, Uf, Ud, Dm): # Eddy viscosity term
return F(x1) * (0.015 * b(Dm) * (Uf - Ud)) + (k**2.0) * I0 / 100.0
Uc = U0 * (1.0 - Dmi) # Boundary condition at x = 2.0
d = Dmi
Uc1[0] = U0 * (1.0 - Dmi) # Boundary condition at x = 2.0
d1[0] = Dmi
for i in range(
1, n
): # For all positions in the wake centreline direction. Recursive. Whole grid
Uc1[i] = Uc1[i - 1] + (h * 16.0 * E(i * h, U0, Uc1[i - 1], d1[i - 1]) *
(Uc1[i - 1]**3.0 - U0 * Uc1[i - 1]**2.0 -
Uc1[i - 1] * U0**2.0 + U0**3.0) /
(Uc1[i - 1] * Ct * U0**2.0))
d1[i] = 1.0 - Uc1[i] / U0
########### Code to calculate wake deficit at a specific point instead of the whole grid. Namely, the rotor's centrepoint.
# U = U0 * (1.0 - d1[n-1] * exp(- 3.56 * (Y / b(d1[n-1])) ** 2.0))
##### Code to calculate average wake deficit in all area of the rotor ###############
## Define function to integrate.
def G(r, theta):
z = sqrt(Y**2.0 + r**2.0 + 2.0 * Y * r * cos(theta))
gauss = U0 * (1.0 - d1[n - 1] * exp(-3.56 * (z / b(d1[n - 1]))**2.0))
return r * (U0 - gauss)**2.0
A = pi * 0.5**2.0 ## Unitary diameter in this program.
U = U0 - sqrt(
(1.0 / A) * simpson_integrate2D(G, 0.0, 0.5, 5, 0.0, 2.0 * pi, 10))
return 1.0 - U / U0
def wake_deficit(U0, ct, A, x, r, c1):
return sqrt((1.0 / A) * simpson_integrate2D(integrand, 0.0, 40.0, 5, 0.0, 2 * pi, 10)) / U0