278 lines
8.6 KiB
Python
278 lines
8.6 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from datetime import datetime
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start = datetime.now()
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print(start)
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begin_time = datetime.now()
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from models.sun import sun_angles_analytical
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from models.sun import sun_angles_astropy
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from models.simple_atmosphere import T_air, p_air, rho_air
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from models.drag import drag, c_d
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from input.user_input import *
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from input.natural_constants import *
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from astropy.time import Time
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import astropy.units as unit
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from models.thermal import AirMass
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from netCDF4 import Dataset
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#data = Dataset("test2021.nc", "r", format="NETCDF4")
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#ERAtime = data.variables['time'][:] # time
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#ERAlat = data.variables['latitude'][:] # latitude
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#ERAlon = data.variables['longitude'][:] # longitude
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#ERAz = data.variables['z'][:]/g # geopotential to geopotential height
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#ERApress = data.variables['level'][:] # pressure level
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#ERAtemp = data.variables['t'][:]
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#vw_x = data.variables['u'][:] # v_x
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#vw_y = data.variables['v'][:] # v_y
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#vw_z = data.variables['w'][:] # v_z
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# t: simulation time (0 .. t_max) in [s]
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# utc = Time(start_utc) + t * u.second # current time (UTC)
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lat = start_lat # deg
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lon = start_lon # deg
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# date = Time('2020-12-13 12:00:00.000')
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# INITIALISATION
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t = 0 # simulation time in seconds
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h = start_height
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utc = Time(start_utc)
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#epoch_diff = (Time(start_utc).jd - Time('1900-01-01 00:00:00.0').jd) * 24.000000
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#t_epoch = epoch_diff
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#sq_diff_lat = (ERAlat - lat) ** 2
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#sq_diff_lon = (ERAlon - lon) ** 2
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#sq_diff_time = (ERAtime - t_epoch) ** 2
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#min_index_lat = sq_diff_lat.argmin()
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#min_index_lon = sq_diff_lat.argmin()
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#min_index_time = sq_diff_time.argmin()
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#sq_diff_h = (ERAz[min_index_time, :, min_index_lat, min_index_lon] - h) ** 2
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#min_index_h = sq_diff_h.argmin()
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#h_grid = ERAz[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#p_grid = ERApress[min_index_h] * 100
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#T_grid = ERAtemp[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#u_grid = vw_x[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#v_grid = vw_y[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#w_grid = -1/g * vw_z[min_index_time, min_index_h, min_index_lat, min_index_lon] * R_air * T_grid / p_grid
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#v = v_grid
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#u = u_grid
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#w = w_grid
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#T_air = T_grid
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#p_air = p_grid
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#rho_air = p_air/(R_air * T_air)
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v_x = 0
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v_y = 0
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v_z = 0
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T_gas = T_air(h)
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T_film = T_gas
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t_list = []
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h_list = []
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lat_list = []
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lon_list = []
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p_list = []
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Temp_list = []
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rho_list = []
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while t <= t_end and h >= 0:
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t_list.append(t)
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h_list.append(h)
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lat_list.append(lat)
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lon_list.append(lon)
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p_list.append(p_air(h))
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Temp_list.append(T_air(h))
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rho_list.append(rho_air(h))
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#t_epoch = epoch_diff + t/3600
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#sq_diff_lat = (ERAlat - lat) ** 2
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#sq_diff_lon = (ERAlon - lon) ** 2
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#sq_diff_time = (ERAtime - t_epoch) ** 2
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#min_index_lat = sq_diff_lat.argmin()
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#min_index_lon = sq_diff_lat.argmin()
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#min_index_time = sq_diff_time.argmin()
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#sq_diff_h = (ERAz[min_index_time, :, min_index_lat, min_index_lon] - h) ** 2
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#min_index_h = sq_diff_h.argmin()
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#h_grid = ERAz[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#p_grid = ERApress[min_index_h] * 100
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#T_grid = ERAtemp[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#u_grid = vw_x[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#v_grid = vw_y[min_index_time, min_index_h, min_index_lat, min_index_lon]
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#w_grid = -1/g * vw_z[min_index_time, min_index_h, min_index_lat, min_index_lon] * R_air * T_grid / p_grid
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# p_air = p_grid
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p_gas = p_air(h)
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# rho_air = p_air / (R_air * T_air)
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u = 0
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v = 0
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w = 0
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v_relx = u - v_x
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v_rely = v - v_y
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v_relz = w - v_z
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v_rel = (v_relx ** 2 + v_rely ** 2 + v_relz ** 2) ** (1/2)
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p_gas = p_air(h)
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rho_gas = p_gas/(R_gas * T_gas) # calculate gas density through ideal(!) gas equation
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V_b = m_gas/rho_gas # calculate balloon volume from current gas mass and gas density
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if V_b > V_design:
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V_b = V_design
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m_gas = V_design * rho_gas
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else:
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pass
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m_gross = m_pl + m_film
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m_tot = m_pl + m_film + m_gas
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m_virt = m_tot + c_virt * rho_air(h) * V_b
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d_b = 1.383 * V_b ** (1/3) # calculate diameter of balloon from its volume
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L_goreB = 1.914 * V_b ** (1/3)
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h_b = 0.748 * d_b
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A_surf = 4.94 * V_b ** (2/3)
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A_surf1 = 4.94 * V_design ** (2/3) * (1 - np.cos(np.pi * L_goreB/L_goreDesign))
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A_eff = 0.65 * A_surf + 0.35 * A_surf1
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A_top = np.pi/4 * d_b ** 2
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D = drag(c_d, rho_air(h), d_b, v_rel) # calculate drag force
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if v_rel == 0:
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Drag_x = 0
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Drag_y = 0
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Drag_z = 0
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else:
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Drag_x = D * v_relx / v_rel
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Drag_y = D * v_rely / v_rel
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Drag_z = D * v_relz / v_rel
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I = g * V_b * (rho_air(h) - rho_gas) # calculate gross inflation
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W = g * m_gross # calculate weight (force)
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F = I - W + Drag_z
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AZ, ELV = sun_angles_analytical(lat, lon, utc)
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A_proj = A_top * (0.9125 + 0.0875 * np.cos(np.pi - 2 * np.deg2rad(ELV)))
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# CALCULATIONS FOR THERMAL MODEL
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if ELV >= -(180 / np.pi * np.arccos(R_E / (R_E + h))):
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tau_atm = 0.5 * (np.exp(-0.65 * AirMass(p_air(h), p_0, ELV, h)) + np.exp(-0.095 * AirMass(p_air(h), p_0, ELV, h)))
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tau_atmIR = 1.716 - 0.5 * (np.exp(-0.65 * p_air(h) / p_0) + np.exp(-0.095 * p_air(h) / p_0))
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else:
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tau_atm = 0
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tau_atmIR = 0
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doy = int(utc.doy)
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MA = (357.52911 + 0.98560028 * (utc.jd - 2451545)) % 360 # in degree, reference: see folder "literature"
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TA = MA + 2 * e * np.sin(np.deg2rad(MA)) + 5 / 4 * e ** 2 * np.sin(np.deg2rad(2 * MA))
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I_Sun = 1367.5 * ((1 + e * np.cos(np.deg2rad(TA))) / (1 - e ** 2)) ** 2
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I_SunZ = I_Sun * tau_atm
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q_sun = I_SunZ
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q_IRground = epsilon_ground * sigma * T_ground ** 4
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q_IREarth = q_IRground * tau_atmIR
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if ELV <= 0:
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q_Albedo = 0
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else:
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q_Albedo = Albedo * I_Sun * np.sin(np.deg2rad(ELV))
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my_air = (1.458 * 10 ** -6 * T_air(h) ** 1.5) / (T_air(h) + 110.4)
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my_gas = 1.895 * 10 ** -5 * (T_gas / 273.15) ** 0.647
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k_air = 0.0241 * (T_air(h) / 273.15) ** 0.9
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k_gas = 0.144 * (T_gas / 273.15) ** 0.7
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Pr_air = 0.804 - 3.25 * 10 ** (-4) * T_air(h)
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Pr_gas = 0.729 - 1.6 * 10 ** (-4) * T_gas
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Gr_air = (rho_air(h) ** 2 * g * np.abs(T_film - T_air(h)) * d_b ** 3) / (T_air(h) * my_air ** 2)
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Nu_air = 2 + 0.45 * (Gr_air * Pr_air) ** 0.25
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HC_free = Nu_air * k_air / d_b
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Re = np.abs(v_relz) * d_b * rho_air(h) / my_air
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HC_forced = k_air / d_b * (2 + 0.41 * Re ** 0.55)
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HC_internal = 0.13 * k_gas * ((rho_gas ** 2 * g * np.abs(T_film - T_gas) * Pr_gas) / (T_gas * my_air ** 2)) ** (
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1 / 3)
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HC_external = np.maximum(HC_free, HC_forced)
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HalfConeAngle = np.arcsin(R_E / (R_E + h))
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ViewFactor = (1 - np.cos(HalfConeAngle)) / 2
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Q_Sun = alpha_VIS * A_proj * q_sun * (1 + tau_VIS / (1 - r_VIS))
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Q_Albedo = alpha_VIS * A_surf * q_Albedo * ViewFactor * (1 + tau_VIS / (1 - r_VIS))
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Q_IREarth = alpha_IR * A_surf * q_IREarth * ViewFactor * (1 + tau_IR / (1 - r_IR))
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Q_IRfilm = sigma * epsilon * alpha_IR * A_surf * T_film ** 4 * 1 / (1 - r_IR)
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Q_IRout = sigma * epsilon * A_surf * T_film ** 4 * (1 * tau_IR / (1 - r_IR))
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Q_ConvExt = HC_external * A_eff * (T_air(h) - T_film)
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Q_ConvInt = HC_internal * A_eff * (T_film - T_gas)
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# RoC = -v_z
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# dT_gas = (Q_ConvInt / (gamma * m_gas * c_v) - (gamma - 1) / gamma * rho_air(h) * g / (rho_gas * R_gas) * RoC) * dt
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# dT_film = ((Q_Sun + Q_Albedo + Q_IREarth + Q_IRfilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film)) * dt
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# v_w = w
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# v = v_z
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s = h
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a_x = Drag_x/m_virt
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a_y = Drag_y/m_virt
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a_z = F/m_virt
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# DIFFERENTIAL EQUATIONS
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dx = dt * v_x + 0.5 * a_x * dt ** 2 # lon
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dy = dt * v_y + 0.5 * a_y * dt ** 2 # lat
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lon = lon + np.rad2deg(np.arctan(dx/((6371229.0 + h) * np.cos(np.deg2rad(lat)))))
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lat = lat + np.rad2deg(np.arctan(dy/(6371229.0 + h)))
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v_xn = v_x + dt * a_x
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v_yn = v_y + dt * a_y
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s_n = s + dt * v_z + 0.5 * a_z * dt ** 2
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dh = s_n - s
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v_n = v_z + dt * a_z
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T_gn = T_gas + dt * (Q_ConvInt / (gamma * c_v * m_gas) - g * R_gas * T_gas * dh / (c_v * gamma * T_air(s) * R_air))
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T_en = T_film + (Q_Sun + Q_Albedo + Q_IREarth + Q_IRfilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film) * dt
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T_g = T_gn
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T_e = T_en
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s = s_n
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v_x = v_xn
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v_y = v_yn
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v_z = v_n
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h = s
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T_gas = T_g
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T_film = T_e
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# v_z = v
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t += dt # time increment
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utc = Time(start_utc) + t * unit.second
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end = datetime.now()
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print(end)
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plt.plot(t_list, h_list, 'k-')
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plt.plot(t_list, p_list, 'r-')
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plt.plot(t_list, Temp_list, 'b-')
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plt.plot(t_list, rho_list, 'g-')
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plt.show() |