diff --git a/main.py b/main.py new file mode 100644 index 0000000..e74871c --- /dev/null +++ b/main.py @@ -0,0 +1,150 @@ +import numpy as np +import matplotlib.pyplot as plt +from datetime import datetime +begin_time = datetime.now() +from models.sun import sun_angles_analytical +from models.sun import sun_angles_astropy +from models.drag import drag, c_d +from models.simple_atmosphere import T_air, p_air, rho_air +from input.user_input import * +from input.natural_constants import * +from astropy.time import Time +import astropy.units as u +from models.thermal import AirMass + +# t: simulation time (0 .. t_max) in [s] +# utc = Time(start_utc) + t * u.second # current time (UTC) + +lat = start_lat # deg +lon = start_lon # deg + +date = Time('2020-12-13 12:00:00.000') + +AZ = sun_angles_astropy(45.0, 45.0, 0, date)[0] +ELV = sun_angles_astropy(45.0, 45.0, 0, date)[1] + + +# INITIALISATION + +t = 0 +h = start_height +utc = Time(start_utc) +v_z = 0 +p_gas = p_air(h) +T_gas = T_air(h) +T_film = T_gas + +t_list = [] +h_list = [] + +while t <= t_end and h >= 0: + t_list.append(t) + h_list.append(h) + + rho_gas = p_gas/(R_gas * T_gas) # calculate gas density through ideal(!) gas equation + + V_b = m_gas/rho_gas # calculate balloon volume from current gas mass and gas density + + if V_b > V_max: + V_b = V_max + m_gas = V_max * rho_gas + else: + pass + + m_gross = m_pl + m_film + m_tot = m_pl + m_film + m_gas + m_virt = m_tot + c_virt * rho_air(h) * V_b + + d_b = (6.0 * V_b / np.pi) ** (1/3) # calculate diameter of balloon from its volume + A_top = np.pi/4 * d_b ** 2 + + D = drag(c_d, rho_air(h), d_b, v_z) # calculate drag force + I = g * V_b * (rho_air(h) - rho_gas) # calculate gross inflation + W = g * m_gross # calculate weight (force) + F = I - W - D * np.sign(v_z) + + v_zrel = v_z + + AZ, ELV = sun_angles_analytical(lat, lon, utc) + + A_proj = A_top * (0.9125 + 0.0875 * np.cos(np.pi - 2 * np.deg2rad(ELV))) + A_surf = 4.94 * V_b ** (2/3) + + A_eff = A_surf + #A_surf1 = 4.94 * V_b + + # AirMass(x, p_0, ELV, h) + + # CALCULATIONS FOR THERMAL MODEL + + if ELV >= -(180 / np.pi * np.arccos(R_E / (R_E + h))): + 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))) + tau_atmIR = 1.716 - 0.5 * (np.exp(-0.65 * p_air(h) / p_0) + np.exp(-0.095 * p_air(h) / p_0)) + else: + tau_atm = 0 + tau_atmIR = 0 + + doy = int(utc.doy) + + MA = (357.52911 + 0.98560028 * (utc.jd - 2451545)) % 360 # in degree, reference: see folder "literature" + TA = MA + 2 * e * np.sin(np.deg2rad(MA)) + 5 / 4 * e ** 2 * np.sin(np.deg2rad(2 * MA)) + I_Sun = 1367.5 * ((1 + e * np.cos(np.deg2rad(TA))) / (1 - e ** 2)) ** 2 + I_SunZ = I_Sun * tau_atm + q_sun = I_SunZ + q_IRground = epsilon_ground * sigma * T_ground ** 4 + q_IREarth = q_IRground * tau_atmIR + + if ELV <= 0: + q_Albedo = 0 + else: + q_Albedo = Albedo * I_Sun * np.sin(np.deg2rad(ELV)) + + my_air = (1.458 * 10 ** -6 * T_air(h) ** 1.5) / (T_air(h) + 110.4) + my_gas = 1.895 * 10 ** -5 * (T_gas / 273.15) ** 0.647 + k_air = 0.0241 * (T_air(h) / 273.15) ** 0.9 + k_gas = 0.144 * (T_gas / 273.15) ** 0.7 + Pr_air = 0.804 - 3.25 * 10 ** (-4) * T_air(h) + Pr_gas = 0.729 - 1.6 * 10 ** (-4) * T_gas + + Gr_air = (rho_air(h) ** 2 * g * np.abs(T_film - T_air(h)) * d_b ** 3) / (T_air(h) * my_air ** 2) + Nu_air = 2 + 0.45 * (Gr_air * Pr_air) ** 0.25 + HC_free = Nu_air * k_air / d_b + Re = np.abs(v_zrel) * d_b * rho_air(h) / my_air + + HC_forced = k_air / d_b * (2 + 0.41 * Re ** 0.55) + HC_internal = 0.13 * k_gas * ((rho_gas ** 2 * g * np.abs(T_film - T_gas) * Pr_gas) / (T_gas * my_air ** 2)) ** ( + 1 / 3) + HC_external = np.maximum(HC_free, HC_forced) + + HalfConeAngle = np.arcsin(R_E / (R_E + h)) + ViewFactor = (1 - np.cos(HalfConeAngle)) / 2 + + Q_Sun = alpha_VIS * A_proj * q_sun * (1 + tau_VIS / (1 - r_VIS)) + Q_Albedo = alpha_VIS * A_surf * q_Albedo * ViewFactor * (1 + tau_VIS / (1 - r_VIS)) + Q_IREarth = alpha_IR * A_surf * q_IREarth * ViewFactor * (1 + tau_IR / (1 - r_IR)) + Q_IRfilm = sigma * epsilon * alpha_IR * A_surf * T_film ** 4 * 1 / (1 - r_IR) + Q_IRout = sigma * epsilon * A_surf * T_film ** 4 * (1 * tau_IR / (1 - r_IR)) + Q_ConvExt = HC_external * A_eff * (T_air(h) - T_film) + Q_ConvInt = HC_internal * A_eff * (T_film - T_gas) + + RoC = -v_z + + dT_gas = (Q_ConvInt / (gamma * R_gas) - (gamma - 1) / gamma * rho_air(h) * g / (rho_gas * R_gas) * RoC) * dt + dT_film = ((Q_Sun + Q_Albedo + Q_IREarth + Q_IRfilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film)) * dt + + ### + + dv_z = F/m_virt * dt # velocity increment + + v_z += dv_z * dt # velocity differential + h += v_z * dt # altitude differential + + p_gas = p_air(h) + T_gas = T_gas + dT_gas * dt + T_film = T_film + dT_film * dt + + t += dt # time increment + utc = Time(start_utc) + t * u.second + +plt.plot(t_list, h_list) +plt.show()