changed basic thermal model, now realistic behavior
This commit is contained in:
parent
e011c90ad0
commit
d0d56c1fc9
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@ -0,0 +1,52 @@
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import cdsapi
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c = cdsapi.Client()
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r = c.retrieve(
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'reanalysis-era5-pressure-levels',
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{
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'product_type': 'reanalysis',
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'variable': [
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'fraction_of_cloud_cover', 'geopotential', 'relative_humidity',
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'specific_humidity', 'temperature', 'u_component_of_wind',
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'v_component_of_wind', 'vertical_velocity',
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],
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'pressure_level': [
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'1', '2', '3',
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'5', '7', '10',
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'20', '30', '50',
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'70', '100', '125',
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'150', '175', '200',
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'225', '250', '300',
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'350', '400', '450',
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'500', '550', '600',
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'650', '700', '750',
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'775', '800', '825',
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'850', '875', '900',
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'925', '950', '975',
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'1000',
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],
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'year': '2016',
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'month': '07',
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'day': [
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'11', '12', '13',
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'14', '15', '16',
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'17', '18',
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],
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'time': [
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'00:00', '01:00', '02:00',
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'03:00', '04:00', '05:00',
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'06:00', '07:00', '08:00',
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'09:00', '10:00', '11:00',
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'12:00', '13:00', '14:00',
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'15:00', '16:00', '17:00',
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'18:00', '19:00', '20:00',
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'21:00', '22:00', '23:00',
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],
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'area': [
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72, -111, 67,
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22,
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],
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'format': 'netcdf',
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})
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r.download('test.nc')
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@ -1,3 +0,0 @@
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# BASTET
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ESBO Balloon Simulation and Trajectory Evaluation Tool
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@ -0,0 +1,174 @@
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import numpy as np
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from astropy.time import Time
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# SIMPLE ATMOSPHERE MODEL
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def T_air(h):
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if h >= 0 and h <= 11000:
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res = 288.15 - 0.0065 * h
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return res
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elif h > 11000 and h <= 20000:
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res = 216.65
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return res
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elif h >= 20000:
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res = 216.65 + 0.0010 * (h - 20000)
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return res
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def p_air(h):
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if h >= 0 and h <= 11000:
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res = 101325 * ((288.15 - 0.0065 * h)/288.15) ** 5.25577
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return res
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elif h > 11000 and h <= 20000:
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res = 22632 * np.exp(-(h - 11000)/6341.62)
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return res
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elif h > 20000:
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res = 5474.87 * ((216.65 + 0.0010 * (h - 20000))/216.65) ** (-34.163)
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return res
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def rho_air(h):
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res = p_air(h)/(R_air * T_air(h))
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return res
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# USER INPUT
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start_height = 0
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start_utc = '2006-01-16 08:00:00.000'
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start_lat = 0 # start latitude in [deg]
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start_lon = 0 # start longitude in [deg]
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# INITIALISATION
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t = 0
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h = start_height
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lat = start_lat
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lon = start_lon
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utc = Time(start_utc)
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v_z = 0
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p_gas = p_air(h)
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T_gas = T_air(h)
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T_film = T_gas
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p_0 = 101325
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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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dT_gas = (Q_g/(c_pg * m_g) - (g * M_a * m_g * T_g)/(c_pg * T_a * M_g) * dz/dt) * dt
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V_b_new = m_gas * R_gas * T_gas_new/p_gas_new # r.h.s. with updated values!
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v_w = 0
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T_g1 = T_g
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T_a1 = T_a
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# Q_g1 = ???
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T_e1 = T_e
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# T_g2 = T_g1 + dt * (Q_g1/(c_pg * m_g1) - g * M_a * T_g1 * dh/(c_pg * T_a1 * M_g))
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# T_e2 = T_e1 + Q_e/(c_env * m_e) * dt
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T_gn = T_g + dt * (Q_g/(c_pg * m_g) - g * M_a * T_g * dh/(c_pg * T_a * M_g))
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T_en = T_e + Q_e/(c_env * m_e) * dt
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s_n = s + dt * v + 0.5 * a * dt ** 2
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v_n = v - v_w + dt * a
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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 = v_n
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V = m_g * R_g * T_g / (p_g)
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dV_b = V_b_new - V_b # calculating volume increment
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dT_gas = Q_ConvInt/(c_v * m_g) * dt + (gamma - 1) * T_g * (dm_g/m_g - dV_b/V_b)
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V_b = V_b_new # updating current volume
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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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m_balloon = A_balloon * rho_envelope
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m_gas = Vol_balloon * (M_gas * p_gas)/(R_c * T_gas)
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m_gross = m_balloon + m_payload
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m_tot = m_balloon + m_gas + m_payload
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GI = F_buoyant - g * (rho_a - rho_g) * Vol_balloon
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W = m_gross * g
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m_virtual = m_tot + C_virtual * rho_a * Vol_balloon
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R_z = GI + T_z - D_z - W
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dV_A = (R_z * dt)/m_virtual
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F_Drag = 0.5 * C_D * rho * np.abs(V) * V * A_cross
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Re = (rho * V * l)/my
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C_D = 24/Re
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my = my_0 * (T_0 + C)/(T + C) * (T/T_0) ** (3/2)
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C_D = 0.23175 - 0.15757 * f + 0.04744 * f ** 2 - 7.0412 * 10 ** (-3) * f ** 3 + 5.1534 * 10 ** (-4) * f ** 4 - 1.4835 * 10 ** (-5) * f ** 5
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Vol_balloon = m_g * R_g * T_g/p_g
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Vol_ballon_new = m_g * R_g * T_g/p_g # r.h.s. with updated values!
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dVol = Vol_ballon_new - Vol_balloon # calculating volume increment
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Vol_ballon = Vol_ballon_new # updating current volume
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L_z = g * (M_atm * p_atm/(R * T_atm) - M_gas * p_gas/(R * T_gas)) * Vol_balloon
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dT_g = Q_ConvInt/(c_v * m_g) * dt + (gamma - 1) * T_g * (dm_g/m_g - dVol/Vol)
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dT_e = (Q_sun + Q_albedo + Q_IREarth + Q_IRsky + Q_ConvExt - Q_ConvInt + Q_IRout)/(c_e * m_e)
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Pr_g = my_g * c_pg/kappa_g
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Pr_a = my_a * c_pa/kappa_a
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beta_g = 1/T_g
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beta_a = 1/T_a
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Gr_g = d_b ** 3 * rho_g ** 2 * g * beta_g * (T_e - T_g)/(my_g ** 2)
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Gr_a = d_b ** 3 * rho_a ** 2 * g * beta_a * (T_e - T_a)/(my_a ** 2)
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h = h + dt * V + 0.5 * a * dt ** 2
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V = V + dt * a
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Binary file not shown.
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@ -1,7 +1,8 @@
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g = 9.81 # local gravitational acceleration in [m/s^2]
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c_v = 3115.89 # [J/(kg * K)]
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R_air = 287.1 # Specific Gas Constant Dry Air in [J/(kg * K)]
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R_gas = 2077.1 # Specific Gas Constant Helium in [J/(kg * K)]
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R_E = 6378000 # Earth Radius in [m]
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e = 0.016708 # Eccentricity of Earth's Orbit
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sigma = 5.670374419 * 10 ** -8 # Stefan-Boltzmann-Constant
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gamma = 1.4
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gamma = 1.667 # 1.44 # 1.6
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@ -1,8 +1,9 @@
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# BALLOON
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m_pl = 10.0 # payload mass in [kg]
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m_film = 1.0 # mass balloon film in [kg]
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m_gas = 1.7645 # 1.60391061452 # lifting gas mass in [kg]
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V_max = 9999999 # maximum fillable balloon volume in [m^3]
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m_pl = 417.57 # payload mass in [kg]
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m_film = 7.74 # mass balloon film in [kg]
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m_gas = 5 * 74.98539754298822 # 1.60391061452 # lifting gas mass in [kg]
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V_design = 334705 # maximum fillable balloon volume in [m^3]
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L_goreDesign = 1.914 * V_design ** (1/3)
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# THERMO-OPTICAL
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alpha_VIS = 0.024
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@ -16,19 +17,19 @@ r_IR = 0.04
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c_f = 2092 # [J/(kg*K)]
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epsilon_ground = 0.9
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Albedo = 0.2
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Albedo = 0.1
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T_ground = 273.15
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# DRAG
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c_d = 0.47 # drag coefficient balloon (spherical) [-]
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c_virt = 0
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c_virt = 0.37
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# SIMULATION
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t_end = 10000 # maximum simulation time in [s]
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dt = 0.1 # simulation time step in [s]
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start_height = 0.0 # start altitude in [m]
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start_lat = 0.0 # start latitude in [deg]
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start_lon = 0.0 # start longitude in [deg]
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start_utc = '2020-12-13 12:00:00.000' # start date and time in UTC
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p_0 = 1013.25 # sea-level pressure
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t_end = 10000 #5000 # maximum simulation time in [s]
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dt = 0.01 #0.01 # simulation time step in [s]
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start_height = 0.0 # start altitude in [m]
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start_lat = 39.9161 # start latitude in [deg]
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start_lon = 9.6889 # start longitude in [deg]
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start_utc = '2006-01-16 08:00:00.000' # start date and time in UTC
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p_0 = 101325 # sea-level pressure
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52
main.py
52
main.py
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@ -20,9 +20,6 @@ lon = start_lon # deg
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date = Time('2020-12-13 12:00:00.000')
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AZ = sun_angles_astropy(45.0, 45.0, 0, date)[0]
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ELV = sun_angles_astropy(45.0, 45.0, 0, date)[1]
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# INITIALISATION
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@ -45,9 +42,9 @@ while t <= t_end and h >= 0:
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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_max:
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V_b = V_max
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m_gas = V_max * rho_gas
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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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@ -55,7 +52,12 @@ while t <= t_end and h >= 0:
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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 = (6.0 * V_b / np.pi) ** (1/3) # calculate diameter of balloon from its volume
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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_z) # calculate drag force
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@ -68,12 +70,6 @@ while t <= t_end and h >= 0:
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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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A_surf = 4.94 * V_b ** (2/3)
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A_eff = A_surf
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#A_surf1 = 4.94 * V_b
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# AirMass(x, p_0, ELV, h)
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# CALCULATIONS FOR THERMAL MODEL
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@ -129,19 +125,31 @@ while t <= t_end and h >= 0:
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RoC = -v_z
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dT_gas = (Q_ConvInt / (gamma * R_gas) - (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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# 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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###
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v_w = 0
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v = v_z
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s = h
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dv_z = F/m_virt * dt # velocity increment
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a = F/m_virt
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v_z += dv_z * dt # velocity differential
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h += v_z * dt # altitude differential
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s_n = s + dt * v + 0.5 * a * dt ** 2
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dh = s_n - s
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v_n = v - v_w + dt * a
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p_gas = p_air(h)
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T_gas = T_gas + dT_gas * dt
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T_film = T_film + dT_film * dt
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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 = 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 * u.second
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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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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.drag import drag, c_d
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from models.simple_atmosphere import T_air, p_air, rho_air
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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 u
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from models.thermal import AirMass
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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
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h = start_height
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utc = Time(start_utc)
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v_z = 0
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p_gas = p_air(h)
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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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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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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
|
||||
|
||||
D = drag(c_d, rho_air(h), d_b, v_z) # calculate drag force
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||||
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)
|
||||
|
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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)))
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||||
|
||||
# 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 * m_gas * c_v) - (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()
|
||||
Loading…
Reference in New Issue