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ISAfunction.py
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ISAfunction.py
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# -*- coding: utf-8 -*-
"""
Created on Sat Nov 28 15:32:16 2020
@author: Matko
"""
def ISAfunny(Z): # in meters
"""
Atmospheric model according to 1976 (give more source)
Returns temperature, pressure, density, kinematic viscosity,
and speed of sound at given altitude.
Parameters
----------
Z : float
Altitude [m]
Returns
-------
list [T,P,rho,mu,a]
in SI units: [K], [Pa], [kg/m3], [m2/s], [m/s]
"""
import numpy as np
g0 = 9.807 # [m/s2]
R = 8.314472 # [J/molK]
bs = 1.458e-6
S = 110.4
Ga = 1.4
Mo = 28.9647e-3 # [kg/mol]
Hb = np.array([0,11,20,32,47,51,71]) # [km]
bet = np.array([-6.5,0,1,2.8,0,-2.8,-2])
Tb = np.array([288.15,216.65,216.65,228.65,270.65,270.65,214.65]) # [K]
pb = np.array([101325,22632.1,5474.89,868.019,110.906,66.9389,3.95642]) # [Pa]
R1 = 6356.766e3; # [m]
hb = Hb*1000 # converts belts' altitudes from km to m
bet = bet/1000 # [K/m]
H = (Z*R1)/(Z+R1) # [m]
if H <= hb[1]:
T = Tb[0] + bet[0]*(H-hb[0])
P = pb[0]*( Tb[0]/( Tb[0]+bet[0]*(H-hb[0]) ) )**( (g0*Mo)/(R*bet[0]) )
elif H > hb[1] and H <= hb[2]:
T = Tb[1] + bet[1]*( H-hb[1])
P = pb[1]*np.exp( (-g0*Mo*(H-hb[1]))/(R*Tb[1]) )
elif H > hb[2] and H <= hb[3]:
T = Tb[2] + bet[2]*(H-hb[2])
P = pb[2]*( Tb[2]/( Tb[2]+bet[2]*( H-hb[2] ) ) )**( ( g0*Mo )/(R*bet[2]) )
elif H > hb[3] and H <= hb[4]:
T = Tb[3] + bet[3]*( H-hb[3] )
P = pb[3]* ( Tb[3]/( Tb[3]+bet[3]*(H-hb[3]) ) )**( ( g0*Mo )/(R*bet[3]) )
elif H > hb[4] and H <= hb[5]:
T = Tb[4] + bet[4]*(H-hb[4])
P = pb[4] * np.exp( (-g0*Mo*(H-hb[4]))/(R*Tb[4]) )
elif H > hb[5] and H <= hb[6]:
T = Tb[5] + bet[5]*(H - hb[5])
P = pb[5] * ( Tb[5]/( Tb[5]+bet[5]*( H-hb[5] ) ) )**( ( g0*Mo )/(R*bet[5]) )
elif H > hb[6]:
T = Tb[6] + bet[6]*( H-hb[6] )
P = pb[6] * ( pb[6]*( Tb[6]/( Tb[6]+bet[6]*(H-hb[6]) ) ) )**( ( g0*Mo )/(R*bet[6]) )
else:
print('this message should never appear')
rho = ( P*Mo )/( R*T ) # Density
mu = bs* ( T**1.5 )/( T+S ) # Viscosity
a = np.sqrt( Ga*286.9*T ) # Speed of sound
return [T,P,rho,mu,a]
# return P
# return rho
# return mu
# return a
#%% PLOTS plt.gca().set_xlim(0, .14);
# import matplotlib.pyplot as plt
# plt.figure(1)
# plt.plot(P/1000,H/1000)
# plt.gca().set_xlim(0,120)
# plt.gca().set_ylim(0,90)
# plt.xticks(np.arange(0,120,step=10),rotation=0)
# plt.xlabel('Pressure [kPa]')
# plt.yticks(np.arange(0,100,step=10),rotation=0)
# plt.ylabel('Altitude [km]')
# plt.gca().grid('on')
# plt.figure(2)
# plt.plot(rho/1,H/1000)
# # plt.gca().set_xlim(0,120)
# plt.gca().set_ylim(0,90)
# # plt.xticks(np.arange(0,120,step=10),rotation=0)
# plt.xlabel('Density [kg/m3]')
# plt.yticks(np.arange(0,100,step=10),rotation=0)
# plt.ylabel('Altitude [km]')
# plt.gca().grid('on')
# plt.figure(3)
# plt.plot(T/1,H/1000)
# # plt.gca().set_xlim(0,120)
# plt.gca().set_ylim(0,90)
# # plt.xticks(np.arange(0,120,step=10),rotation=0)
# plt.xlabel('Temperature [K]')
# plt.yticks(np.arange(0,100,step=10),rotation=0)
# plt.ylabel('Altitude [km]')
# plt.gca().grid('on')
# plt.figure(4)
# plt.plot(mu/1,H/1000)
# # plt.gca().set_xlim(0,120)
# plt.gca().set_ylim(0,90)
# # plt.xticks(np.arange(0,120,step=10),rotation=0)
# plt.xlabel('Viscosity [m2/s]')
# plt.yticks(np.arange(0,100,step=10),rotation=0)
# plt.ylabel('Altitude [km]')
# plt.gca().grid('on')
# plt.figure(5)
# plt.plot(a/1,H/1000)
# # plt.gca().set_xlim(0,120)
# plt.gca().set_ylim(0,90)
# # plt.xticks(np.arange(0,120,step=10),rotation=0)
# plt.xlabel('Speed of sound [m/s]')
# plt.yticks(np.arange(0,100,step=10),rotation=0)
# plt.ylabel('Altitude [km]')
# plt.gca().grid('on')
# plt.figure(6)
# plt.plot(P/max(P),H/1000,T/max(T),H/1000,rho/max(rho),H/1000,mu/max(mu),H/1000,a/max(a),H/1000,)
# print('ISAfunction done successfully')