Method for calculating thermal characteristics of near space floating air ball

Abstract

The invention discloses a near space floating air ball thermal characteristic calculation method. Comprising the following steps: establishing a near space floating balloon thermal environment model, establishing a near space floating balloon skin and helium temperature thermal balance differential equation, and establishing a near space floating balloon kinematic model considering a wind field environment and volume change; the method comprises the following steps: establishing a thermal environment model of a floating air ball, simultaneously solving differential equations of skin temperature and helium temperature, and differential equations for controlling horizontal and vertical movement of the floating air ball, and the like, establishing a detailed thermal environment model of the floating air ball, and introducing the influence of an external wind field on an external convection environment. Helium temperature change caused by external acting of volume expansion in the balloon rising process and buoyancy weight balance change caused by helium leakage are considered in a helium temperature heat balance equation. According to the method, the changes of the external skin temperature, the internal helium temperature, the volume and the three-dimensional motion trail of the floating balloon in the whole rising and flat flying process can be obtained at the same time, and the calculation accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of aerostat design, and particularly to a method for calculating the thermal characteristics of a near-space floating balloon. Background Art

[0002] In recent years, long-endurance near-space floating balloons can provide a coverage area with a diameter of up to 1000 kilometers in the near space, and can complete tasks such as environmental monitoring, disaster relief, scientific experiments, and signal transmission. Many countries such as the United States, Japan, South Korea, and Europe have carried out theoretical research and experimental work on near-space floating balloons in terms of control, flight tests, structures, etc.

[0003] Computer simulation, with its characteristics of low cost and high speed, has become one of the important means for studying near-space floating balloons. Some organizations and researchers have independently proposed some flight simulation programs to predict the ascent and floating processes of balloons. Among them, the Scientific Balloon Analysis Model (SINBAD) and Balloon Ascent are two well-known projects developed by the Balloon Program Office of the National Aeronautics and Space Administration of the United States. SINBAD can be used to predict the flight profile of the balloon and provide assistance in the possible situations during the flight, while Balloon Ascent can analyze superpressure balloons and zero-pressure balloons respectively. In addition, the Italian Aerospace Research Center (CIRA) has developed the High Altitude Balloon Analysis Code (ACHAB) software, which is characterized by ballast and valve control, predicts the horizontal and vertical movements of the balloon, and has been successfully used for the trajectory prediction of stratospheric balloon flight tests.

[0004] The above software has greatly simplified the thermal environment of near-space floating balloons. Although the calculation efficiency has been improved, the calculation accuracy has been greatly reduced. Therefore, it is necessary to propose a calculation method that can accurately calculate the thermal characteristics of near-space floating balloons during the ascent process to provide a basis for the research of near-space floating balloons. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the thermal characteristics of a near-space floating balloon to solve the problem of insufficient calculation accuracy of foreign related calculation methods.

[0006] To achieve the above purpose, the present invention provides the following technical solution: A method for calculating the thermal characteristics of a near-space floating balloon, including the following steps:

[0007] Step S1: Establish a thermal environment model of a near-space floating balloon.

[0008] The thermal environment of a near-space aerostat can be divided into two parts: the external thermal environment and the internal thermal environment. The external thermal environment consists of direct solar radiation, atmospheric scattering, earth reflection, atmospheric infrared radiation, earth infrared radiation, and convective heat transfer between the aerostat and the external environment. The internal thermal environment consists of natural convection of internal helium and infrared radiation between the internal helium and the skin.

[0009] The direct solar radiation absorbed by the skin of the aerostat can be expressed as

[0010] q D = α·I D ·S projected ·(1 + τ / (1 - r))

[0011] where α, τ, and r represent the average visible light absorptivity, transmittance, and reflectivity of the skin, respectively, and S projected represents the longitudinal projected area of the airship. I D is the direct radiation from the sun and can be expressed as

[0012] I D = τ atm ·I sun

[0013] where τ atm is the transmittance of direct solar radiation in the earth's atmospheric environment, and I sun represents the intensity of direct solar radiation outside the earth's atmosphere. The intensity of direct solar radiation outside the earth I sun is

[0014]

[0015] where I0 is the solar radiation constant, I0 = 1367 W / m 2 , e earth is the eccentricity of the earth, e earth = 0.016708, is the true anomaly of the earth and can be expressed as

[0016]

[0017] where the solar angle θ day can be expressed as

[0018] θ day = 2π·(N - N0) / 365.2422

[0019] where N represents the number of days of the current date in a year. For example, N = 1 represents January 1st of each year, and N = 365 represents December 31st of each year. N0 represents the leap year correction term for the number of days.

[0020]

[0021] In the formula, year represents the year corresponding to the calculation date.

[0022] The transmittance τ of direct solar radiation in the earth's atmospheric environment atm is

[0023] τ atm = 0.5·(1 + p h / p0)·(exp(-0.65λ AM ) + exp(-0.095λ AM ))

[0024] In the formula, p h and p0 represent the atmospheric pressure at height h and the atmospheric pressure at sea level respectively, and λ AM represents the air mass ratio when solar radiation passes through the atmosphere. The air mass ratio λ AM is related to the solar altitude angle θ ele . The air mass ratio corresponding to different altitude angles θ ele can be expressed as

[0025]

[0026] where θ DIP represents the airship section angle, defined as the angle between the tangent of the airship and the ground and the horizontal plane at the height where the airship is located. The solar altitude angle can be expressed as

[0027] θ ele = arcsin(sin(θ dec )·sin(Φ) + cos(θ dec )·cos(Φ)·cos(θ hour ))

[0028] where θ dec represents the solar declination angle, and θ hour represents the solar hour angle.

[0029] θ dec = [0.3723 + 23.2567·sin(θ day ) + 0.1149·sin(2θ day )

[0030] - 0.1712·sin(3θ day ) - 0.758·cos(θ day ) + 0.3656·cos(2θ day )

[0031] + 0.0201·cos(3θ day )]·π / 180

[0032] θ hour = 15(time + e t / 60 - 12.0)·π / 180

[0033] e t = 0.0028 - 1.9857·sin(θ day ) + 9.9059·sin(2θ day )

[0034] -7.0924·cos(θ day ) - 0.6882·cos(2θ day )

[0035] The atmospheric scattered radiation absorbed by the skin can be expressed as

[0036] q S = α·I s ·S surf ·(1 + τ / (1 - r))

[0037] where S surf represents the surface area of the bladder, and I s is the intensity of atmospheric scattered radiation, which can be expressed as

[0038]

[0039] The earth-reflected radiation absorbed by the skin can be expressed as

[0040] q R = α·I R ·S projected ·(1 + τ / (1 - r))

[0041] where I R is the intensity of earth-reflected radiation, which can be expressed as

[0042] I R = r e ·(I D ·sin(θ ele ) + I S )

[0043] where r e represents the earth surface reflectivity.

[0044] The infrared radiation from the atmosphere absorbed by the skin can be expressed as

[0045] q IR_atm = α IR ·I IR_atm ·S surf ·(1 + τ IR / (1 - r IR ))

[0046] where α IR , τ IR and r IR represent the infrared average absorptivity, transmittance and reflectivity of the skin respectively. Generally, assuming the atmosphere is a black body, according to the Stefan-Boltzman law, the atmospheric infrared radiation intensity I IR_atm can be expressed as

[0047] I IR_atm = σ·T sky

[0048] where T sky is the sky equivalent temperature, which can be expressed as a function of the sky emissivity ε sky and the atmospheric temperature T atm

[0049]

[0050] The infrared radiation of the earth absorbed by the skin can be expressed as

[0051] q IR_earth = α IR ·I IR_earth_h ·S projected ·(1 + τ IR / (1 - r IR ))

[0052] The direction of the surface radiation is perpendicular to the ground, and there are also losses during the radiation to the high altitude. In the space at the height of h, the earth infrared radiation intensity I IR_earth_h can be expressed as

[0053] I IR_earth_h = τ IR_gh ·I IR_earth

[0054] where I IR_earth is the ground infrared radiation, and the main energy comes from the long-wave radiation of the ground. The radiation intensity is related to the earth surface emissivity ε g and the earth surface temperature T g and can be expressed as

[0055]

[0056] where ε g is the emissivity of the earth surface, which is related to the surface properties. The emissivity in the desert area is about 0.85, the average emissivity of the earth surface is about 0.95, and it is taken as 0.98 in case of snow cover. T e0 is the earth surface temperature (the emissivity is low in the hot places on the ground and high in the cold places). τ IR_gh ​Denotes the transmittance of the surface radiation at height h in the atmosphere, and its expression is

[0057] τ IR_gh = 1.716 - 0.5(exp(-0.65p h / p0) + exp(-0.95p h / p0))

[0058] The infrared radiation of the internal helium gas absorbed by the skin can be expressed as

[0059] q IR_He = α IR ·I IR_He ·S surf ·(1 / (1 - r IR ))

[0060] where I IR_He is the infrared radiation between the internal helium and the skin, and can be expressed as

[0061]

[0062] where ε He denotes the emissivity of helium, T He and T f denote the temperatures of helium and the skin respectively.

[0063] The convective heat transfer between the skin and the external environment can be expressed as

[0064] q conv_ex = h ex ·S surf ·(T atm - T f )

[0065] where h ex is the convective heat transfer coefficient between the floating balloon and the external environment, and can be expressed as

[0066]

[0067] where h ex_force is the external forced convective heat transfer coefficient, h ex_natural is the external natural convective heat transfer coefficient. The external forced convective heat transfer coefficient h ex_force can be expressed as

[0068]

[0069] where Re atm denotes the atmospheric Reynolds number, k atmh denotes the atmospheric thermal conductivity at height h, and L0 denotes the characteristic length of the floating balloon.

[0070]

[0071] Among them, D represents the characteristic diameter of the floating air balloon, υ atm represents the air flow velocity, ρ atmh , μ atmh and T atmh respectively represent the atmospheric density, atmospheric viscosity coefficient and atmospheric temperature at height h.

[0072] The external natural convection heat transfer coefficient h ex_natural can be expressed as

[0073]

[0074] where Nu atm_natural is the external atmospheric Nusselt number, and L0 is the characteristic length of the floating air balloon.

[0075]

[0076] In the formula, Gr atmh and Pr atmh respectively represent the atmospheric Grashof number and Prandtl number at height h.

[0077]

[0078] Pr atmh = 0.804 - 3.25·10 -4 ·T atmh

[0079] The convective heat transfer between the skin and helium can be expressed as

[0080] q conv_in = h in ·S surf ·(T He - T f )

[0081] Step S2: Establish the differential equation of thermal equilibrium for the skin and helium temperatures of the near-space floating air balloon.

[0082] Based on the thermal model in step S1, establish the differential equations for the skin temperature T f and the helium temperature T He , expressed as

[0083]

[0084] where m f , c f and T f respectively represent the mass, specific heat capacity and temperature of the skin; m He , c v_Herespectively represent the mass and specific heat capacity at constant volume of helium, γ = c p_He / c v_He , and V represents the volume of the stratospheric aerostat.

[0085] Step S3: Establish a kinematic model of the stratospheric aerostat considering the wind field environment and volume change.

[0086] The volume of the stratospheric aerostat can be expressed as

[0087]

[0088] where P He represents the pressure of helium, R represents the radius of the fully formed stratospheric aerostat, and ΔP represents the pressure difference between helium and the external atmosphere, which can be expressed as

[0089] ΛP = P He -P atm

[0090] The total buoyancy B and drag D acting on the stratospheric aerostat can be expressed as

[0091] B = ρ atm ·g·V

[0092]

[0093] where ρ atm is the atmospheric density at the corresponding altitude, C d represents the drag coefficient, S represents the reference area, and v r represents the wind speed relative to the stratospheric aerostat.

[0094]

[0095] where v rx , v ry and v rh represent the components of the relative wind speed in three directions and can be expressed as

[0096]

[0097] where v wx , v wy and v wh represent the components of the absolute wind speed in three directions, v x , v y and v h represent the absolute velocities of the stratospheric aerostat in three directions. Therefore, the drag acting on the stratospheric aerostat can be expressed as

[0098]

[0099] Therefore, the differential equations for controlling the horizontal and vertical motions of the aerostat are obtained as follows

[0100]

[0101] where x, y, and h represent the coordinate positions of the aerostat in three directions, m represents the total mass of the aerostat, and m add represents the added mass, which can be expressed as

[0102] m add = C V ·ρ atm ·V

[0103] where C V is the drag coefficient, and its value can be C V = 0.5.

[0104] Step S4: Simultaneously solve the differential equations of the skin temperature T f and the helium temperature T He in Step S2 and the differential equations for controlling the horizontal and vertical motions of the aerostat in Step S3.

[0105] Compared with the prior art, the beneficial effects of the present invention are as follows: By establishing an accurate thermal model of the near-space aerostat and considering the relative motion between the aerostat and the surrounding wind field during the ascent process, the thermal characteristics of the aerostat during the ascent process and its motion characteristics along with the wind field environment can be obtained more accurately, and at the same time, the calculation efficiency is greatly improved. Description of the Drawings

[0106] Figure 1 is a schematic diagram of the thermal environment of a near-space aerostat according to the present invention.

[0107] Figure 2 is a flowchart of the calculation of the thermal characteristics of a near-space aerostat according to the present invention. Detailed Embodiments

[0108] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0109] Please refer to Figure 1, the present invention provides a near-space floating airship thermal environment model, which can be specifically divided into two parts: the external thermal environment and the internal thermal environment. The external thermal environment consists of direct solar radiation, atmospheric scattering, earth reflection, atmospheric infrared radiation, earth infrared radiation, and convective heat transfer between the floating airship and the external environment. The internal thermal environment consists of natural convection of internal helium and infrared radiation between the internal helium and the skin.

[0110] Please refer to Figure 2 , the present invention provides a flowchart for calculating the thermal characteristics of a near-space floating airship, including:

[0111] 1. Establish a near-space floating airship thermal environment model.

[0112] The direct solar radiation absorbed by the floating airship skin can be expressed as

[0113] q D =α·I D ·S projected ·(1 + τ / (1 - r))

[0114] where α, τ, and r represent the average visible light absorptivity, transmittance, and reflectivity of the skin respectively, and S projected represents the longitudinal projected area of the airship. I D is the direct radiation from the sun and can be expressed as

[0115] I D =τ atm ·I sun

[0116] where τ atm is the transmittance of direct solar radiation in the earth's atmospheric environment, and I sun represents the intensity of direct solar radiation outside the earth's atmosphere. The intensity of direct solar radiation outside the earth I sun is

[0117]

[0118] where I0 is the solar radiation constant, I0 = 1367 W / m 2 , e earth is the earth's eccentricity, e earth = 0.016708, and ζ is the true anomaly of the earth and can be expressed as

[0119]

[0120] where the solar angle θ day can be expressed as

[0121] θ day = 2π·(N - N0) / 365.2422

[0122] Where N represents the number of days of the current date in a year. For example, N = 1 represents January 1st of each year, and N = 365 represents December 31st of each year. N0 represents the leap year correction term for the number of days.

[0123]

[0124] In the formula, year represents the year corresponding to the calculated date.

[0125] The transmittance τ of direct solar radiation in the earth's atmospheric environment atm is

[0126] τ atm = 0.5·(1 + p h / p0)·(exp(-0.65λ AM ) + exp(-0.095λ AM ))

[0127] In the formula, p h and p0 represent the atmospheric pressure at height h and the atmospheric pressure at sea level respectively, and λ AM represents the air mass ratio when solar radiation passes through the atmosphere. The air mass ratio λ AM is related to the solar altitude angle θ ele . The air mass ratio corresponding to different altitude angles θ ele can be expressed as

[0128]

[0129] where θ DIP represents the airship section angle, defined as the angle between the tangent of the airship and the ground and the horizontal plane at the height where the airship is located. The solar altitude angle can be expressed as

[0130] θ ele = arcsin(sin(θ dec )·sin(Φ) + cos(θ dec )·cos(Φ)·cos(θ hour ))

[0131] where θ dec represents the solar declination angle, and θ hour represents the solar hour angle.

[0132] θ dec = [0.3723 + 23.2567·sin(θ day ) + 0.1149·sin(2θ day )

[0133] - 0.1712·sin(3θ day ) - 0.758·cos(θday ) + 0.3656·cos(2θ day )

[0134] + 0.0201·cos(3θ day )]·π / 180

[0135] θ hour =15(time + e t / 60 - 12.0)·π / 180

[0136] e t =0.0028 - 1.9857·sin(θ day ) + 9.9059·sin(2θ day )

[0137] - 7.0924·cos(θ day ) - 0.6882·cos(2θ day )

[0138] The atmospheric scattering radiation absorbed by the skin can be expressed as

[0139] q S =α·I s ·S surf ·(1 + τ / (1 - r))

[0140] where S surf represents the surface area of the bladder, and I s is the intensity of atmospheric scattering radiation, which can be expressed as

[0141]

[0142] The earth-reflected radiation absorbed by the skin can be expressed as

[0143] q R =α·I R ·S projected ·(1 + τ / (1 - r))

[0144] where I R is the intensity of earth-reflected radiation, which can be expressed as

[0145] I R =r e ·(I D ·sin(θ ele ) + I S )

[0146] where r e represents the earth's surface reflectivity.

[0147] The infrared radiation from the atmosphere absorbed by the skin can be expressed as

[0148] q IR_atm = α IR ·I IR_atm ·S surf ·(1 + τ IR / (1 - r IR ))

[0149] where α IR , τ IR and r IR represent the infrared average absorptivity, transmittance, and reflectivity of the skin, respectively. Generally, assuming the atmosphere is a blackbody, according to the Stefan - Boltzman law, the atmospheric infrared radiation intensity I IR_atm can be expressed as

[0150] I IR_atm = σ·T sky

[0151] where T sky is the sky equivalent temperature, which can be expressed as a function of the sky emissivity ε sky and the atmospheric temperature T atm

[0152]

[0153] The infrared radiation from the earth absorbed by the skin can be expressed as

[0154] q IR_earth = α IR ·I IR_earth_h ·S projected ·(1 + τ IR / (1 - r IR ))

[0155] The direction of the surface radiation is perpendicular to the ground, and there are also losses during the radiation to the high altitude. In the space at height h, the earth infrared radiation intensity I IR_earth_h can be expressed as

[0156] I IR_earth_h = τ IR_gh ·I IR_earth

[0157] where I IR_earth is the ground infrared radiation, and the main energy comes from the long - wave radiation of the ground. The radiation intensity is related to the earth surface emissivity ε g and the earth surface temperature T g and can be expressed as

[0158]

[0159] where ε g ​ε is the emissivity of the Earth's surface, which is related to the surface properties. The emissivity in desert areas is about 0.85, the average emissivity of the Earth's surface is about 0.95, and 0.98 is taken in the case of snow cover. T e0 is the temperature of the Earth's surface (the emissivity is low in hot areas of the surface and high in cold areas). τ IR_gh represents the transmittance of the surface radiation at height h in the atmosphere, and its expression is

[0160] τ IR_gh = 1.716 - 0.5(exp(-0.65p h / p0) + exp(-0.95p h / p0))

[0161] The infrared radiation of the internal helium gas absorbed by the skin can be expressed as

[0162] q IR_He = α IR ·I IR_He ·S surf ·(1 / (1 - r IR ))

[0163] where I IR_He is the infrared radiation between the internal helium and the skin, and can be expressed as

[0164]

[0165] where ε He represents the emissivity of helium, T He and T f represent the temperatures of helium and the skin respectively.

[0166] The convective heat transfer between the skin and the external environment can be expressed as

[0167] q conv_ex = h ex ·S surf ·(T atm - T f )

[0168] where h ex is the convective heat transfer coefficient between the floating balloon and the external environment, and can be expressed as

[0169]

[0170] where h ex_force is the external forced convective heat transfer coefficient, h ex_natural is the external natural convective heat transfer coefficient. The external forced convective heat transfer coefficient h ex_force can be expressed as

[0171]

[0172] where Re atm represents the atmospheric Reynolds number, k atmh represents the atmospheric thermal conductivity at height h, and L0 represents the characteristic length of the aerostat.

[0173]

[0174] where D represents the characteristic diameter of the aerostat, υ atm represents the air velocity, ρ atmh , μ atmh and T atmh represent the atmospheric density, atmospheric viscosity coefficient, and atmospheric temperature at height h, respectively.

[0175] The external natural convection heat transfer coefficient h ex_natural can be expressed as

[0176]

[0177] where Nu atm_natural is the external atmospheric Nusselt number, and L0 is the characteristic length of the aerostat.

[0178]

[0179] In the formula, Gr atmh and Pr atmh represent the atmospheric Grashof number and Prandtl number at height h, respectively.

[0180]

[0181] Pr atmh = 0.804 - 3.25·10 -4 ·T atmh

[0182] The convective heat transfer between the skin and helium can be expressed as

[0183] q conv_in = h in ·S surf ·(T He - T f )

[0184] 2. Establish the differential equation of the thermal equilibrium of the skin and helium temperatures of the near-space aerostat.

[0185] Based on the thermal model in step 1, establish the differential equations of the skin temperature T f and the helium temperature T He , expressed as

[0186]

[0187] where m f , c f and T f represent the mass, specific heat capacity and temperature of the skin respectively; m He , c v_He represent the mass and specific heat capacity at constant volume of helium respectively, γ = c p_He / c v_He , and V represents the volume of the aerostat. Since the external pressure decreases during the ascent of the aerostat, the volume of the aerostat will increase, and helium leakage may also occur. Therefore, the helium mass change term and the aerostat volume change term are added to the helium balance equation to make the calculation more accurate.

[0188] 3. Establish a kinematic model of a near-space aerostat considering the wind field environment and volume change.

[0189] The volume of the aerostat can be expressed as

[0190]

[0191] where P He represents the pressure of helium, R represents the radius of the fully formed aerostat, and ΔP represents the pressure difference between helium and the external atmosphere, which can be expressed as

[0192] ΛP = P He -P atm

[0193] The total buoyancy B and drag D acting on the aerostat can be expressed as

[0194] B = ρ atm ·g·V

[0195]

[0196] where ρ atm is the atmospheric density at the corresponding altitude, C d represents the drag coefficient, S represents the reference area, and v r represents the wind speed relative to the aerostat.

[0197]

[0198] where v rx , v ry and v rh represent the components of the relative wind speed in three directions and can be expressed as

[0199]

[0200] where v wx , vwy and v wh represent the components of the absolute wind speed in three directions, v x , v y and v h represent the absolute velocity of the aerostat in three directions. Therefore, the drag force on the aerostat can be expressed as

[0201]

[0202] Therefore, the differential equations for controlling the horizontal and vertical motions of the aerostat are

[0203]

[0204] where x, y, and h represent the coordinate positions of the aerostat in three directions, m represents the total mass of the aerostat, m add represents the added mass, which can be expressed as

[0205] m add = C V ·ρ atm ·V

[0206] where C V is the drag coefficient, and its value can be C V = 0.5.

[0207] 4. Simultaneously solve the differential equations of the skin temperature T f and the helium temperature T He in step 2 and the differential equations for controlling the horizontal and vertical motions of the aerostat in step 3.

[0208] This method establishes a detailed thermal environment model of the aerostat, and at the same time introduces the influence of the external wind field during the ascent of the aerostat, thereby reflecting the changes in the external convective environment caused by the wind field environment; in addition, the change in the helium temperature caused by the external work done by the volume expansion during the ascent of the balloon and the change in the buoyancy balance caused by the helium leakage are also considered in the thermal equilibrium equation of the helium temperature. This method can simultaneously obtain the changes in the external skin temperature, internal helium temperature, volume, and three-dimensional motion trajectory of the aerostat during the entire process of ascent and level flight, improving the calculation accuracy.

[0209] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating thermal characteristics of a near-space floating balloon, characterized in that: The following steps are involved: Step S1: Establish a thermal environment model of a near-space floating balloon. The thermal environment of a near-space floating balloon is divided into two parts: external thermal environment and internal thermal environment. The external thermal environment is composed of direct solar radiation, atmospheric scattering, earth reflection, atmospheric infrared radiation, earth infrared radiation, and convective heat exchange between the floating balloon and the external environment. The internal thermal environment is composed of internal helium natural convection and infrared radiation between the internal helium and the skin. The direct solar radiation absorbed by the floating balloon skin can be expressed as q D =α·I D ·S projected ·(1+τ / (1-r)) Where α, τ and r represent the average visible light absorptivity, transmittance and reflectivity of the skin, respectively. projected It represents the longitudinal projection area of ​​the airship. D is the direct radiation from the sun, which can be expressed as I D =τ atm ·I sun where τ atm is the transmittance of direct solar radiation in the Earth’s atmosphere, I sun Indicates the direct solar radiation intensity outside the Earth's atmosphere. sun for Where I0 is the solar radiation constant, I0=1367W / m 2 , e earth is the eccentricity of the Earth, e earth =0.016708, is the true anomaly of the Earth, which can be expressed as The sun angle θ day It can be expressed as i day =2π·(N-N0) / 365.2422 Where N represents the number of days in a year for the current date, such as N = 1 for January 1 of each year, and N = 365 for December 31 of each year. N0 represents the leap year correction for the number of days. In the formula, year represents the year corresponding to the calculation date. The transmittance of direct solar radiation in the Earth's atmosphere τ atm for t atm =0.5·(1+p h / p0)·(exp(-0.65λ AM )+exp(-0.095l AM )) Where p h and p0 represent the atmospheric pressure at height h and the atmospheric pressure at sea level, respectively, AM Indicates the air mass ratio when solar radiation passes through the atmosphere. Air mass ratio λ AM The solar altitude angle θ ele For different height angles θ ele The corresponding air mass ratio can be expressed as where θ DIP represents the airship tangent angle, which is defined as the angle between the tangent line between the airship and the ground and the horizontal plane at the height of the airship. The solar altitude angle can be expressed as i ele =arcsin(sin(θ) dec )·sin(Φ)+cos(θ dec )·cos(Φ)·cos(θ hour )) where θ dec represents the solar declination angle, θ hour Represents the solar hour angle. i dec =[0.3723+23.2567·sin(θ day )+0.1149·sin(2θ day )-0.1712·sin(3θ day )-0.758·cos(θ day )+0.3656·cos(2θ day )+0.0201·cos(3θ day )]·π / 180 i hour =15(time+e t / 60-12.0)·π / 180 e t =0.0028-1.9857·sin(θ day )+9.9059·sin(2θ day ) -7.0924·cos(θ day )-0.6882·cos(2θ day ) The atmospheric scattered radiation absorbed by the skin can be expressed as q S =α·I s ·S surf ·(1+τ / (1-r)) Where S surf represents the surface area of ​​the capsule, I s is the atmospheric scattered radiation intensity, which can be expressed as The earth reflected radiation absorbed by the skin can be expressed as q R =α·I R ·S projected ·(1+τ / (1-r)) Among them I R is the radiation intensity reflected by the earth, which can be expressed as IS R =r e ·(IS D ·sin(θ ele )+I S ) where r e Represents the reflectivity of the earth's surface. The infrared radiation absorbed by the skin from the atmosphere can be expressed as q IR_atm =a IR ·I IR_atm ·S surf ·(1+τ IR / (1-r IR )) where α IR , τ IR and r IR They represent the average infrared absorptivity, transmittance and reflectivity of the skin respectively. In general, assuming that the atmosphere is a black body, according to the Stefan-Boltzman law, the atmospheric infrared radiation intensity I IR_atm It can be expressed as I IR_atm =σ·T sky Where T sky is the equivalent sky temperature, which can be expressed as the sky emissivity ε sky and atmospheric temperature T atm Function The earth's infrared radiation absorbed by the skin can be expressed as q IR_earth =a IR ·I IR_earth_h ·S projected ·(1+τ IR / (1-r IR )) The direction of surface radiation is perpendicular to the ground, and there is also loss in the process of radiating to the high altitude. At a height of h in space, the intensity of the earth's infrared radiation is IR_earth_h It can be expressed as I IR_earth_h =τ IR_gh ·I IR_earth Among them I IR_earth It is ground infrared radiation, the main energy comes from the long-wave radiation of the ground, and the radiation intensity is related to the emissivity of the earth's surface ε g and the Earth's surface temperature T g It can be expressed as where ε g is the emissivity of the earth's surface, which is related to the surface properties. The emissivity in desert areas is about 0.85, and the average emissivity of the earth's surface is about 0.

95. In the case of snow, it is 0.

98. e0 is the surface temperature of the Earth (hot areas on the surface have low emissivity, while cold areas have high emissivity). IR_gh It represents the transmittance of surface radiation in the atmosphere at height h, and its expression is t IR_gh =1.716-0.5(exp(-0.65p h / p0)+exp(-0.95p h / p0)) The infrared radiation of the internal helium gas absorbed by the skin can be expressed as q IR_He =α IR ·I IR_He ·S surf ·(1 / (1-r IR )) Among them I IR_He is the infrared radiation between the internal helium and the skin, which can be expressed as where ε He represents the emissivity of helium, T He and T f represent the temperatures of helium and skin respectively. The convective heat transfer between the skin and the external environment can be expressed as q conv_ex =h ex ·S surf ·(T atm -T f ) where h ex is the convective heat transfer coefficient between the floating balloon and the external environment, which can be expressed as where h ex_force is the external forced convection heat transfer coefficient, h ex_natural is the external natural convection heat transfer coefficient. The external forced convection heat transfer coefficient h ex_force It can be expressed as Among them, Re atm represents the atmospheric Reynolds number, k atmh represents the thermal conductivity of the atmosphere at a height of h, and L0 represents the characteristic length of the floating balloon. Where D is the characteristic diameter of the floating balloon, υ atm represents the air velocity, ρ atmh , μ atmh and T atmh They represent the atmospheric density, atmospheric viscosity coefficient and atmospheric temperature at height h respectively. External natural convection heat transfer coefficient h ex_natural It can be expressed as Among them Nu atm_natural is the Nusselt number of the external atmosphere, and L0 is the characteristic length of the floating balloon. In the formula, Gr atmh and Pr atmh They represent the atmospheric Grashof number and Prandtl number at altitude h respectively. Pr atmh =0.804-3.25 10 -4 ·T atmh The convective heat transfer between the skin and helium can be expressed as q conv_in =h in ·S surf ·(T He -T f ) Step S2: Establish the thermal balance differential equation of the near-space floating balloon skin and helium temperature. Based on the thermal model in step S1, establish the skin temperature T f and the helium temperature T He The differential equation is expressed as Where m f , c f and T f Respectively represent the mass, specific heat capacity and temperature of the skin; m He ,c v_He They represent the mass and constant volume specific heat of helium, γ=c p_He / c v_He , V represents the volume of the floating balloon. Step S3: Establish a kinematic model of a near-space floating balloon that takes into account wind environment and volume changes. The volume of a floating balloon can be expressed as Where P He represents the pressure of helium, R represents the radius of the fully formed floating balloon, and ΔP represents the pressure difference between helium and the external atmosphere, which can be expressed as ΛP=P He -P atm The total buoyancy B and drag D on the floating balloon can be expressed as B=ρ atm ·g·V where ρ atm is the atmospheric density at the corresponding height, C d represents the drag coefficient, S represents the reference area, v r Indicates wind speed relative to the floating balloon. where v rx ,v ry and v rh Represents the components of relative wind speed in three directions, which can be expressed as where v wx ,v wy and v wh Represents the components of absolute wind speed in three directions, v x ,v y and v h represents the absolute speed of the floating balloon in three directions. Therefore, the resistance of the floating balloon can be expressed as Therefore, the differential equations controlling the horizontal and vertical motion of the floating balloon are obtained as follows: Where x, y and h represent the coordinates of the balloon in three directions, m represents the total mass of the balloon, add represents the additional mass, which can be expressed as m add =C V ·r atm ·V Among them C V is the drag coefficient, which can be taken as C V =0.

5. Step S4: Combine and solve the skin temperature T in step S2 f and the helium temperature T He The differential equations for controlling the horizontal and vertical motions of the floating balloon in step S3.

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