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7_3.py
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from math import *
import numpy as np
#single stage turbine on free vortex theory
m_dot = 36 #[kg/s]
T_01 = 1200 #[K]
p_01 = 8 #[bar]
deltaT_013 = 150 #[K]
eta_t = 0.9
U_m = 320 #[m/s]
N = 250 #[rev/s]
V3 = 400 #[m/s] axial
alpha_3 = radians(0) #[radians]
#Calculate:
#blade height and radius ratio of the annulus from the outlet conditions
#Assuming nozzle loss below, calculate the inlet Mach number relative to the rotor blade at the root radius
nozzle_loss = 0.07
V2a = 346 #[m/s]
#constant
cp = 1148
gamma = 1.333
aux = gamma/(gamma-1)
R = 0.287
pr = 1/((-(deltaT_013/(eta_t*T_01) -1))**(aux))
p_03 = p_01/pr
T_03 = T_01 - deltaT_013
T_3 = T_03 - ((V3**2)/(2*cp))
p_3 = p_03*((T_3/T_03)**aux)
rho_3 = (p_3*100)/(R*T_3)
A = m_dot/(V3*rho_3)
r_m = U_m/(2*pi*N)
h = A/(2*pi*r_m)
print("Blade height: ", h)
r_root = r_m - (h/2)
r_tip = r_m + (h/2)
r_ratio = r_tip/r_root
print("Radius ratio: ", r_ratio)
U_r = 2*pi*N*r_root
flow_coeff_r = V2a/U_r
temp_drop_coeff_r = (2*cp*deltaT_013)/(U_r**2)
tg_beta_3_r = tan(alpha_3) + (1/flow_coeff_r)
tg_beta_2_r = (cp*deltaT_013/(U_r*V2a)) - tg_beta_3_r
beta_2_r = atan(tg_beta_2_r)
tg_alpha_2_r = (1/flow_coeff_r) + tg_beta_2_r
alpha_2_r = atan(tg_alpha_2_r)
V2 = V2a/cos(alpha_2_r)
W2 = V2a/cos(beta_2_r)
#reaction_r = ((tg_beta_3_r*2*flow_coeff_r) - (temp_drop_coeff_r/2))/2
#print(reaction_r)
T_02 = T_01 #no change in absolute temperature at nozzle
T_2_prime = T_02 - (V2**2)/(2*cp)
T_2 = T_2_prime + (nozzle_loss*((V2**2)/(2*cp)))
a = sqrt(gamma*R*T_2*1000)
M = W2/a
print("Relative Mach number at rotor inlet in root radius: ", M)