def flowprandtlmeyer(gamma, prandtlmeyer_array, mtype='mach'):
"""
Calculate Prandtl-Meyer functions for expansion waves.
http://www.mathworks.nl/help/aerotbx/ug/flowprandtlmeyer.html
"""
M, V, U = aerotbx.flowprandtlmeyer(**{'gamma':gamma,
mtype:prandtlmeyer_array})
return M, V, U
def flowprandtlmeyer(gamma, prandtlmeyer_array, mtype='mach'):
"""
Calculate Prandtl-Meyer functions for expansion waves.
http://www.mathworks.nl/help/aerotbx/ug/flowprandtlmeyer.html
"""
M, V, U = aerotbx.flowprandtlmeyer(**{
'gamma': gamma,
mtype: prandtlmeyer_array
})
return M, V, U
plot_pres_c = True
plot_regions = True
plot_chars = True
plot_s = True
plot_pres_s = True
import matplotlib # Set graph font size
matplotlib.rcParams.update({'font.size': 16})
# Initialise the flow variables
phi = np.zeros(n + 1 + 3 * int(round(n * (n + 1) / 2.)))
nu = np.zeros(n + 1 + 3 * int(round(n * (n + 1) / 2.)))
M = np.zeros(n + 1 + 3 * int(round(n * (n + 1) / 2.)))
mu = np.zeros(n + 1 + 3 * int(round(n * (n + 1) / 2.)))
# Compute PM angle and Mach angle in the exit
M[0], nu[0], mu[0] = aerotbx.flowprandtlmeyer(gamma=gamma, M=M_e)
# Compute the total pressure ratio in the exit
P_eP_t = aerotbx.flowisentropic(gamma=gamma,
M=M_e)[2] # Outputs [mach, T, P, rho, area]
# Compute total pressure ratio in the ambient after the expansion
P_aP_t = P_eP_t / P_eP_a
# With the total pressure ratio, compute the Mach number behind the expansion fan (region 3)
M[n] = aerotbx.flowisentropic(gamma=gamma, p=P_aP_t)[0][0]
# Compute the flow angle in the region behind the expansion fan (region 3)
(_, nu[n], mu[n]) = aerotbx.flowprandtlmeyer(gamma=gamma, M=M[n])
phi[n] = nu[n] - nu[0] + phi[0]
gamma = 1.4
M0 = 2.0
phi0 = 0.0 # Degrees
n = 3 # Number of characteristics
h = 0.1
#Plotting
plot_pres_c = False
plot_mach = False
phi = np.zeros(n + 1 + 2 * round(n * (n + 1) / 2.))
nu = np.zeros(n + 1 + 2 * round(n * (n + 1) / 2.))
M = np.zeros(n + 1 + 2 * round(n * (n + 1) / 2.))
mu = np.zeros(n + 1 + 2 * round(n * (n + 1) / 2.))
(M[0], nu[0], mu[0]) = aerotbx.flowprandtlmeyer(gamma=gamma,
M=M0) # Output: [m,nu,mu]
# # First calculate the Mach number in region n using the pressure ratio since the expension is isentropic
p_0_p_t = aerotbx.flowisentropic(gamma=gamma,
M=M0)[2] # Output: [mach,T,P,rho,area]
p_n_p_t = p_0_p_t * (1 / p0_pa
) # Calculate ratio total pressure vs pressure in 3
p_a_p_t = p_n_p_t
#
# # Using this total pressure ratio the mach number in section 3 can be determined
M[n] = aerotbx.flowisentropic(
gamma=gamma, p=p_n_p_t)[0][0] # Returns an array of mach numbers
(_, nu[n], mu[n]) = aerotbx.flowprandtlmeyer(gamma=gamma, M=M[n])
phi[n] = nu[n] - nu[0] + phi[0]
import aerotbx
h = 0.5 #outlet height [m]
p0_pa = 2.0
gamma = 1.4
M0 = 2.0
phi0 = 0.0 # Degrees
nu0 = aerotbx.flowprandtlmeyer(gamma=gamma, M=M0)[1] # Output: [m,nu,mu]
# Know from common knowledge
phi4 = phi7 = phi9 = 0.0
# First use 3 characteristcs solving the problem
# See drawn figure
# First calculate the Mach number in region 3 using the pressure ratio since the expension is isentropic
p_0_p_t = aerotbx.flowisentropic(gamma=gamma,
M=M0)[2] # Output: [mach,T,P,rho,area]
p_3_p_t = p_0_p_t * (1 / p0_pa
) # Calculate ratio total pressure vs pressure in 3
p_a_p_t = p_3_p_t
# Using this total pressure ratio the mach number in section 3 can be determined
M3 = aerotbx.flowisentropic(
gamma=gamma, p=p_3_p_t)[0][0] # Returns an array of mach numbers
nu3 = aerotbx.flowprandtlmeyer(gamma=gamma, M=M3)[1][0]
# Use MOC to obtain mu3 (gamma + from 0 to 3)
phi3 = nu3 - nu0 + phi0
# No go back through expansion fan
dphi_I = (phi3 - phi0) / 3.0 # Phi step over fan I